LMFDB - Embedded newform 300.2.w.a.103.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.16
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.170201 + 1.40393i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.94206 + 0.477901i) q^{4} +(0.0997280 + 2.23384i) q^{5} +(-0.387729 - 1.36002i) q^{6} +(2.03014 + 2.03014i) q^{7} +(-1.00148 - 2.64519i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(0.170201 + 1.40393i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.94206 + 0.477901i) q^{4} +(0.0997280 + 2.23384i) q^{5} +(-0.387729 - 1.36002i) q^{6} +(2.03014 + 2.03014i) q^{7} +(-1.00148 - 2.64519i) q^{8} +(0.951057 - 0.309017i) q^{9} +(-3.11920 + 0.520213i) q^{10} +(-3.90886 - 1.27006i) q^{11} +(1.84339 - 0.775823i) q^{12} +(-2.28342 + 4.48146i) q^{13} +(-2.50466 + 3.19572i) q^{14} +(-0.447950 - 2.19074i) q^{15} +(3.54322 - 1.85623i) q^{16} +(1.11123 - 7.01601i) q^{17} +(0.595710 + 1.28263i) q^{18} +(-5.34832 + 3.88579i) q^{19} +(-1.26123 - 4.29060i) q^{20} +(-2.32273 - 1.68756i) q^{21} +(1.11780 - 5.70394i) q^{22} +(0.683618 + 1.34168i) q^{23} +(1.40295 + 2.45596i) q^{24} +(-4.98011 + 0.445553i) q^{25} +(-6.68031 - 2.44302i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(-4.91288 - 2.97246i) q^{28} +(0.370327 - 0.509711i) q^{29} +(2.99941 - 1.00176i) q^{30} +(3.16553 + 4.35697i) q^{31} +(3.20908 + 4.65852i) q^{32} +(4.05941 + 0.642948i) q^{33} +(10.0392 + 0.365961i) q^{34} +(-4.33256 + 4.73748i) q^{35} +(-1.69933 + 1.05464i) q^{36} +(8.74359 + 4.45508i) q^{37} +(-6.36568 - 6.84733i) q^{38} +(1.55425 - 4.78349i) q^{39} +(5.80906 - 2.50095i) q^{40} +(1.20194 + 3.69918i) q^{41} +(1.97390 - 3.54819i) q^{42} +(4.26195 - 4.26195i) q^{43} +(8.19821 + 0.598500i) q^{44} +(0.785142 + 2.09369i) q^{45} +(-1.76727 + 1.18811i) q^{46} +(1.30515 + 8.24040i) q^{47} +(-3.20922 + 2.38766i) q^{48} +1.24297i q^{49} +(-1.47315 - 6.91591i) q^{50} +7.10347i q^{51} +(2.29285 - 9.79453i) q^{52} +(-0.811396 - 5.12295i) q^{53} +(-0.789023 - 1.17365i) q^{54} +(2.44730 - 8.85843i) q^{55} +(3.33696 - 7.40327i) q^{56} +(4.67461 - 4.67461i) q^{57} +(0.778630 + 0.433161i) q^{58} +(1.42595 + 4.38863i) q^{59} +(1.91690 + 4.04048i) q^{60} +(-2.83426 + 8.72296i) q^{61} +(-5.57813 + 5.18575i) q^{62} +(2.55813 + 1.30343i) q^{63} +(-5.99407 + 5.29822i) q^{64} +(-10.2386 - 4.65387i) q^{65} +(-0.211742 + 5.80858i) q^{66} +(11.3977 + 1.80522i) q^{67} +(1.19489 + 14.1566i) q^{68} +(-0.885086 - 1.21822i) q^{69} +(-7.38852 - 5.27631i) q^{70} +(-3.24029 + 4.45988i) q^{71} +(-1.76987 - 2.20625i) q^{72} +(2.13466 - 1.08767i) q^{73} +(-4.76648 + 13.0337i) q^{74} +(4.84910 - 1.21913i) q^{75} +(8.52976 - 10.1024i) q^{76} +(-5.35713 - 10.5140i) q^{77} +(6.98024 + 1.36791i) q^{78} +(-3.03872 - 2.20776i) q^{79} +(4.49988 + 7.72988i) q^{80} +(0.809017 - 0.587785i) q^{81} +(-4.98884 + 2.31704i) q^{82} +(1.25058 - 7.89584i) q^{83} +(5.31739 + 2.16732i) q^{84} +(15.7835 + 1.78261i) q^{85} +(6.70888 + 5.25811i) q^{86} +(-0.286031 + 0.561367i) q^{87} +(0.555087 + 11.6116i) q^{88} +(6.30465 + 2.04851i) q^{89} +(-2.80578 + 1.45864i) q^{90} +(-13.7337 + 4.46234i) q^{91} +(-1.96882 - 2.27892i) q^{92} +(-3.80814 - 3.80814i) q^{93} +(-11.3468 + 3.23487i) q^{94} +(-9.21361 - 11.5598i) q^{95} +(-3.89832 - 4.09915i) q^{96} +(-4.60222 + 0.728920i) q^{97} +(-1.74504 + 0.211554i) q^{98} -4.11001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.170201	+	1.40393i	0.120350	+	0.992732i
$2$	0.170201	+	1.40393i	0.120350	+	0.992732i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$4$	−1.94206	+	0.477901i	−0.971032	+	0.238950i
$5$	0.0997280	+	2.23384i	0.0445997	+	0.999005i
$5$	0.0997280	+	2.23384i	0.0445997	+	0.999005i
$6$	−0.387729	−	1.36002i	−0.158290	−	0.555228i
$7$	2.03014	+	2.03014i	0.767322	+	0.767322i	0.977634	−	0.210312i	$-0.0674480\pi$
$7$	2.03014	+	2.03014i	0.767322	+	0.767322i	−0.210312	+	0.977634i	$0.567448\pi$
$8$	−1.00148	−	2.64519i	−0.354077	−	0.935216i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	−3.11920	+	0.520213i	−0.986376	+	0.164506i
$11$	−3.90886	−	1.27006i	−1.17856	−	0.382939i	−0.346731	−	0.937964i	$-0.612708\pi$
$11$	−3.90886	−	1.27006i	−1.17856	−	0.382939i	−0.831833	+	0.555026i	$0.812708\pi$
$12$	1.84339	−	0.775823i	0.532142	−	0.223961i
$13$	−2.28342	+	4.48146i	−0.633306	+	1.24293i	0.321839	+	0.946794i	$0.395699\pi$
$13$	−2.28342	+	4.48146i	−0.633306	+	1.24293i	−0.955145	+	0.296139i	$0.904301\pi$
$14$	−2.50466	+	3.19572i	−0.669398	+	0.854092i
$15$	−0.447950	−	2.19074i	−0.115660	−	0.565647i
$16$	3.54322	−	1.85623i	0.885805	−	0.464057i
$17$	1.11123	−	7.01601i	0.269512	−	1.70163i	−0.366880	−	0.930268i	$-0.619574\pi$
$17$	1.11123	−	7.01601i	0.269512	−	1.70163i	0.636393	−	0.771365i	$-0.280426\pi$
$18$	0.595710	+	1.28263i	0.140410	+	0.302318i
$19$	−5.34832	+	3.88579i	−1.22699	+	0.891460i	−0.996661	−	0.0816526i	$-0.973980\pi$
$19$	−5.34832	+	3.88579i	−1.22699	+	0.891460i	−0.230329	+	0.973113i	$0.573980\pi$
$20$	−1.26123	−	4.29060i	−0.282020	−	0.959408i
$21$	−2.32273	−	1.68756i	−0.506862	−	0.368257i
$22$	1.11780	−	5.70394i	0.238315	−	1.21608i
$23$	0.683618	+	1.34168i	0.142544	+	0.279759i	0.951230	−	0.308482i	$-0.0998209\pi$
$23$	0.683618	+	1.34168i	0.142544	+	0.279759i	−0.808686	+	0.588240i	$0.799821\pi$
$24$	1.40295	+	2.45596i	0.286376	+	0.501320i
$25$	−4.98011	+	0.445553i	−0.996022	+	0.0891107i
$26$	−6.68031	−	2.44302i	−1.31012	−	0.479116i
$27$	−0.891007	+	0.453990i	−0.171474	+	0.0873705i
$28$	−4.91288	−	2.97246i	−0.928446	−	0.561742i
$29$	0.370327	−	0.509711i	0.0687679	−	0.0946509i	−0.773248	−	0.634104i	$-0.781369\pi$
$29$	0.370327	−	0.509711i	0.0687679	−	0.0946509i	0.842016	+	0.539453i	$0.181369\pi$
$30$	2.99941	−	1.00176i	0.547615	−	0.182895i
$31$	3.16553	+	4.35697i	0.568546	+	0.782536i	0.992381	−	0.123203i	$-0.0393167\pi$
$31$	3.16553	+	4.35697i	0.568546	+	0.782536i	−0.423836	+	0.905739i	$0.639317\pi$
$32$	3.20908	+	4.65852i	0.567291	+	0.823518i
$33$	4.05941	+	0.642948i	0.706653	+	0.111923i
$34$	10.0392	+	0.365961i	1.72170	+	0.0627617i
$35$	−4.33256	+	4.73748i	−0.732336	+	0.800781i
$36$	−1.69933	+	1.05464i	−0.283222	+	0.175774i
$37$	8.74359	+	4.45508i	1.43744	+	0.732411i	0.987049	−	0.160422i	$-0.0512854\pi$
$37$	8.74359	+	4.45508i	1.43744	+	0.732411i	0.450389	+	0.892833i	$0.351285\pi$
$38$	−6.36568	−	6.84733i	−1.03265	−	1.11078i
$39$	1.55425	−	4.78349i	0.248879	−	0.765971i
$40$	5.80906	−	2.50095i	0.918494	−	0.395435i
$41$	1.20194	+	3.69918i	0.187711	+	0.577715i	0.999985	−	0.00556161i	$-0.00177033\pi$
$41$	1.20194	+	3.69918i	0.187711	+	0.577715i	−0.812274	+	0.583277i	$0.801770\pi$
$42$	1.97390	−	3.54819i	0.304579	−	0.547498i
$43$	4.26195	−	4.26195i	0.649941	−	0.649941i	−0.303038	−	0.952979i	$-0.598001\pi$
$43$	4.26195	−	4.26195i	0.649941	−	0.649941i	0.952979	+	0.303038i	$0.0980009\pi$
$44$	8.19821	+	0.598500i	1.23593	+	0.0902272i
$45$	0.785142	+	2.09369i	0.117042	+	0.312109i
$46$	−1.76727	+	1.18811i	−0.260570	+	0.175177i
$47$	1.30515	+	8.24040i	0.190376	+	1.20199i	0.878984	+	0.476852i	$0.158222\pi$
$47$	1.30515	+	8.24040i	0.190376	+	1.20199i	−0.688608	+	0.725134i	$0.741778\pi$
$48$	−3.20922	+	2.38766i	−0.463211	+	0.344629i
$49$			1.24297i			0.177567i
$50$	−1.47315	−	6.91591i	−0.208334	−	0.978058i
$51$			7.10347i			0.994685i
$52$	2.29285	−	9.79453i	0.317961	−	1.35826i
$53$	−0.811396	−	5.12295i	−0.111454	−	0.703691i	−0.978621	−	0.205674i	$-0.934061\pi$
$53$	−0.811396	−	5.12295i	−0.111454	−	0.703691i	0.867167	−	0.498018i	$-0.165939\pi$
$54$	−0.789023	−	1.17365i	−0.107372	−	0.159713i
$55$	2.44730	−	8.85843i	0.329994	−	1.19447i
$56$	3.33696	−	7.40327i	0.445921	−	0.989304i
$57$	4.67461	−	4.67461i	0.619167	−	0.619167i
$58$	0.778630	+	0.433161i	0.102239	+	0.0568768i
$59$	1.42595	+	4.38863i	0.185643	+	0.571351i	0.999959	−	0.00907149i	$-0.00288758\pi$
$59$	1.42595	+	4.38863i	0.185643	+	0.571351i	−0.814316	+	0.580422i	$0.802888\pi$
$60$	1.91690	+	4.04048i	0.247471	+	0.521624i
$61$	−2.83426	+	8.72296i	−0.362890	+	1.11686i	0.588402	+	0.808569i	$0.299757\pi$
$61$	−2.83426	+	8.72296i	−0.362890	+	1.11686i	−0.951292	+	0.308292i	$0.900243\pi$
$62$	−5.57813	+	5.18575i	−0.708423	+	0.658591i
$63$	2.55813	+	1.30343i	0.322294	+	0.164217i
$64$	−5.99407	+	5.29822i	−0.749258	+	0.662278i
$65$	−10.2386	−	4.65387i	−1.26994	−	0.577241i
$66$	−0.211742	+	5.80858i	−0.0260636	+	0.714987i
$67$	11.3977	+	1.80522i	1.39245	+	0.220543i	0.807185	−	0.590299i	$-0.200990\pi$
$67$	11.3977	+	1.80522i	1.39245	+	0.220543i	0.585266	+	0.810841i	$0.300990\pi$
$68$	1.19489	+	14.1566i	0.144901	+	1.71674i
$69$	−0.885086	−	1.21822i	−0.106552	−	0.146656i
$70$	−7.38852	−	5.27631i	−0.883097	−	0.630639i
$71$	−3.24029	+	4.45988i	−0.384552	+	0.529290i	−0.956783	−	0.290802i	$-0.906078\pi$
$71$	−3.24029	+	4.45988i	−0.384552	+	0.529290i	0.572232	+	0.820092i	$0.306078\pi$
$72$	−1.76987	−	2.20625i	−0.208582	−	0.260009i
$73$	2.13466	−	1.08767i	0.249844	−	0.127302i	−0.324585	−	0.945857i	$-0.605224\pi$
$73$	2.13466	−	1.08767i	0.249844	−	0.127302i	0.574428	+	0.818555i	$0.305224\pi$
$74$	−4.76648	+	13.0337i	−0.554092	+	1.51513i
$75$	4.84910	−	1.21913i	0.559925	−	0.140773i
$76$	8.52976	−	10.1024i	0.978431	−	1.15883i
$77$	−5.35713	−	10.5140i	−0.610501	−	1.19818i
$78$	6.98024	+	1.36791i	0.790357	+	0.154886i
$79$	−3.03872	−	2.20776i	−0.341883	−	0.248392i	0.403573	−	0.914947i	$-0.367768\pi$
$79$	−3.03872	−	2.20776i	−0.341883	−	0.248392i	−0.745456	+	0.666555i	$0.767768\pi$
$80$	4.49988	+	7.72988i	0.503102	+	0.864227i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	−4.98884	+	2.31704i	−0.550925	+	0.255875i
$83$	1.25058	−	7.89584i	0.137269	−	0.866681i	−0.818915	−	0.573915i	$-0.805424\pi$
$83$	1.25058	−	7.89584i	0.137269	−	0.866681i	0.956184	−	0.292767i	$-0.0945759\pi$
$84$	5.31739	+	2.16732i	0.580174	+	0.236474i
$85$	15.7835	+	1.78261i	1.71196	+	0.193352i
$86$	6.70888	+	5.25811i	0.723437	+	0.566996i
$87$	−0.286031	+	0.561367i	−0.0306657	+	0.0601849i
$88$	0.555087	+	11.6116i	0.0591724	+	1.23780i
$89$	6.30465	+	2.04851i	0.668292	+	0.217141i	0.623462	−	0.781853i	$-0.285725\pi$
$89$	6.30465	+	2.04851i	0.668292	+	0.217141i	0.0448297	+	0.998995i	$0.485725\pi$
$90$	−2.80578	+	1.45864i	−0.295755	+	0.153754i
$91$	−13.7337	+	4.46234i	−1.43968	+	0.467780i
$92$	−1.96882	−	2.27892i	−0.205263	−	0.237594i
$93$	−3.80814	−	3.80814i	−0.394885	−	0.394885i
$94$	−11.3468	+	3.23487i	−1.17034	+	0.333651i
$95$	−9.21361	−	11.5598i	−0.945297	−	1.18601i
$96$	−3.89832	−	4.09915i	−0.397871	−	0.418368i
$97$	−4.60222	+	0.728920i	−0.467285	+	0.0740106i	−0.385637	−	0.922651i	$-0.626018\pi$
$97$	−4.60222	+	0.728920i	−0.467285	+	0.0740106i	−0.0816477	+	0.996661i	$0.526018\pi$
$98$	−1.74504	+	0.211554i	−0.176276	+	0.0213702i
$99$	−4.11001			−0.413072
$100$	9.45876	−	3.24529i	0.945876	−	0.324529i
$101$	4.01036			0.399045			0.199523	−	0.979893i	$-0.436061\pi$
$101$	4.01036			0.399045			0.199523	+	0.979893i	$0.436061\pi$
$102$	−9.97281	+	1.20901i	−0.987455	+	0.119710i
$103$	−0.702077	+	0.111198i	−0.0691777	+	0.0109567i	−0.190927	−	0.981604i	$-0.561149\pi$
$103$	−0.702077	+	0.111198i	−0.0691777	+	0.0109567i	0.121750	+	0.992561i	$0.461149\pi$
$104$	14.1411	+	1.55197i	1.38665	+	0.152184i
$105$	3.53811	−	5.35692i	0.345285	−	0.522782i
$106$	7.05419	−	2.01108i	0.685163	−	0.195333i
$107$	3.54316	+	3.54316i	0.342530	+	0.342530i	0.857318	−	0.514787i	$-0.172129\pi$
$107$	3.54316	+	3.54316i	0.342530	+	0.342530i	−0.514787	+	0.857318i	$0.672129\pi$
$108$	1.51343	−	1.30749i	0.145630	−	0.125813i
$109$	−10.7742	+	3.50074i	−1.03198	+	0.335310i	−0.775572	−	0.631259i	$-0.782538\pi$
$109$	−10.7742	+	3.50074i	−1.03198	+	0.335310i	−0.256406	+	0.966569i	$0.582538\pi$
$110$	12.8532	+	1.92814i	1.22550	+	0.183841i
$111$	−9.33287	−	3.03243i	−0.885837	−	0.287826i
$112$	10.9617	+	3.42484i	1.03578	+	0.323617i
$113$	−4.83668	+	9.49253i	−0.454997	+	0.892982i	0.543565	+	0.839367i	$0.317074\pi$
$113$	−4.83668	+	9.49253i	−0.454997	+	0.892982i	−0.998562	+	0.0536145i	$0.982926\pi$
$114$	7.35846	+	5.76722i	0.689183	+	0.540150i
$115$	−2.92892	+	1.66090i	−0.273123	+	0.154880i
$116$	−0.475606	+	1.16687i	−0.0441589	+	0.108341i
$117$	−0.786812	+	4.96774i	−0.0727408	+	0.459267i
$118$	−5.91865	+	2.74889i	−0.544856	+	0.253056i
$119$	16.4995	−	11.9876i	1.51250	−	1.09890i
$120$	−5.34631	+	3.37890i	−0.488049	+	0.308450i
$121$	4.76691	+	3.46336i	0.433355	+	0.314851i
$122$	−12.7289	−	2.49446i	−1.15242	−	0.225838i
$123$	−1.76582	−	3.46561i	−0.159219	−	0.312484i
$124$	−8.22986	−	6.94871i	−0.739063	−	0.624013i
$125$	−1.49195	−	11.0803i	−0.133444	−	0.991056i
$126$	−1.39454	+	3.81329i	−0.124235	+	0.339715i
$127$	13.1537	−	6.70216i	1.16720	−	0.594721i	0.240551	−	0.970636i	$-0.422672\pi$
$127$	13.1537	−	6.70216i	1.16720	−	0.594721i	0.926654	+	0.375916i	$0.122672\pi$
$128$	−8.45855	−	7.51352i	−0.747637	−	0.664107i
$129$	−3.54276	+	4.87619i	−0.311923	+	0.429325i
$130$	4.79111	−	15.1664i	0.420208	−	1.33018i
$131$	−0.479143	−	0.659484i	−0.0418630	−	0.0576194i	0.787572	−	0.616222i	$-0.211338\pi$
$131$	−0.479143	−	0.659484i	−0.0418630	−	0.0576194i	−0.829435	+	0.558603i	$0.811338\pi$
$132$	−8.19090	+	0.691352i	−0.712927	+	0.0601745i
$133$	−18.7466	−	2.96916i	−1.62553	−	0.257459i
$134$	−0.594513	+	16.3089i	−0.0513581	+	1.40887i
$135$	−1.10300	−	1.94509i	−0.0949313	−	0.167407i
$136$	−19.6716	+	4.08700i	−1.68682	+	0.350458i
$137$	8.38549	+	4.27262i	0.716421	+	0.365035i	0.773896	−	0.633312i	$-0.218305\pi$
$137$	8.38549	+	4.27262i	0.716421	+	0.365035i	−0.0574756	+	0.998347i	$0.518305\pi$
$138$	1.55965	−	1.44994i	0.132767	−	0.123427i
$139$	5.80871	−	17.8774i	0.492688	−	1.51634i	−0.327841	−	0.944733i	$-0.606321\pi$
$139$	5.80871	−	17.8774i	0.492688	−	1.51634i	0.820529	−	0.571605i	$-0.193679\pi$
$140$	6.15006	−	11.2710i	0.519775	−	0.952576i
$141$	−2.57816	−	7.93477i	−0.217121	−	0.668228i
$142$	−6.81287	−	3.79008i	−0.571723	−	0.318056i
$143$	14.6173	−	14.6173i	1.22236	−	1.22236i
$144$	2.79620	−	2.86029i	0.233016	−	0.238358i
$145$	1.17555	+	0.776419i	0.0976238	+	0.0644781i
$146$	1.89033	+	2.81181i	0.156445	+	0.232707i
$147$	−0.194443	−	1.22766i	−0.0160374	−	0.101256i
$148$	−19.1097	−	4.47348i	−1.57081	−	0.367718i
$149$		−	1.77846i		−	0.145697i	−0.997343	−	0.0728486i	$-0.976791\pi$
$149$		−	1.77846i		−	0.145697i	0.997343	−	0.0728486i	$-0.0232090\pi$
$150$	2.53690	+	6.60032i	0.207137	+	0.538913i
$151$		−	8.52233i		−	0.693537i	−0.937951	−	0.346769i	$-0.887279\pi$
$151$		−	8.52233i		−	0.693537i	0.937951	−	0.346769i	$-0.112721\pi$
$152$	15.6349	+	10.2558i	1.26816	+	0.831855i
$153$	−1.11123	−	7.01601i	−0.0898374	−	0.567211i
$154$	13.8491	−	9.31054i	1.11599	−	0.750264i
$155$	−9.41711	+	7.50580i	−0.756400	+	0.602881i
$156$	−0.732418	+	10.0326i	−0.0586404	+	0.803252i
$157$	−3.84462	+	3.84462i	−0.306834	+	0.306834i	−0.843680	−	0.536846i	$-0.819616\pi$
$157$	−3.84462	+	3.84462i	−0.306834	+	0.306834i	0.536846	+	0.843680i	$0.319616\pi$
$158$	2.58236	−	4.64192i	0.205441	−	0.369292i
$159$	1.60281	+	4.93295i	0.127111	+	0.391208i
$160$	−10.0864	+	7.63317i	−0.797397	+	0.603455i
$161$	−1.33595	+	4.11164i	−0.105288	+	0.324042i
$162$	0.962907	+	1.03577i	0.0756531	+	0.0813774i
$163$	9.00299	+	4.58725i	0.705169	+	0.359301i	0.769517	−	0.638626i	$-0.220497\pi$
$163$	9.00299	+	4.58725i	0.705169	+	0.359301i	−0.0643486	+	0.997927i	$0.520497\pi$
$164$	−4.10208	−	6.60964i	−0.320319	−	0.516126i
$165$	−1.03141	+	9.13221i	−0.0802950	+	0.710942i
$166$	11.2981	+	0.411853i	0.876902	+	0.0319660i
$167$	−2.64020	−	0.418167i	−0.204305	−	0.0323588i	0.0534430	−	0.998571i	$-0.482980\pi$
$167$	−2.64020	−	0.418167i	−0.204305	−	0.0323588i	−0.257748	+	0.966212i	$0.582980\pi$
$168$	−2.13775	+	7.83414i	−0.164931	+	0.604417i
$169$	−7.22827	−	9.94886i	−0.556021	−	0.765297i
$170$	0.183686	+	22.4624i	0.0140881	+	1.72279i
$171$	−3.88579	+	5.34832i	−0.297153	+	0.408997i
$172$	−6.24018	+	10.3138i	−0.475809	+	0.786417i
$173$	5.11453	−	2.60598i	0.388850	−	0.198129i	−0.248625	−	0.968600i	$-0.579979\pi$
$173$	5.11453	−	2.60598i	0.388850	−	0.198129i	0.637475	+	0.770471i	$0.279979\pi$
$174$	−0.836805	−	0.306024i	−0.0634381	−	0.0231996i
$175$	−11.0149	−	9.20580i	−0.832646	−	0.695893i
$176$	−16.2075	+	2.75561i	−1.22168	+	0.207712i
$177$	−2.09493	−	4.11153i	−0.157464	−	0.309041i
$178$	−1.80291	+	9.19998i	−0.135134	+	0.689568i
$179$	−15.5749	−	11.3158i	−1.16412	−	0.845785i	−0.173830	−	0.984776i	$-0.555614\pi$
$179$	−15.5749	−	11.3158i	−1.16412	−	0.845785i	−0.990294	+	0.138990i	$0.955614\pi$
$180$	−2.52537	−	3.69086i	−0.188230	−	0.275101i
$181$	7.64374	−	5.55350i	0.568155	−	0.412788i	−0.266280	−	0.963896i	$-0.585795\pi$
$181$	7.64374	−	5.55350i	0.568155	−	0.412788i	0.834434	+	0.551107i	$0.185795\pi$
$182$	−8.60231	−	18.5217i	−0.637646	−	1.37292i
$183$	1.43479	−	9.05894i	0.106063	−	0.669656i
$184$	2.86436	−	3.15196i	0.211163	−	0.232366i
$185$	−9.07997	+	19.9761i	−0.667573	+	1.46867i
$186$	4.69823	−	5.99452i	0.344491	−	0.439540i
$187$	−13.2544	+	26.0133i	−0.969259	+	1.90228i
$188$	−6.47278	−	15.3796i	−0.472076	−	1.12168i
$189$	−2.73054	−	0.887205i	−0.198617	−	0.0645347i
$190$	14.6610	−	14.9028i	1.06362	−	1.08116i
$191$	3.67019	−	1.19252i	0.265565	−	0.0862874i	−0.173208	−	0.984885i	$-0.555413\pi$
$191$	3.67019	−	1.19252i	0.265565	−	0.0862874i	0.438773	+	0.898598i	$0.355413\pi$
$192$	5.09145	−	6.17067i	0.367443	−	0.445330i
$193$	0.281618	+	0.281618i	0.0202713	+	0.0202713i	0.717170	−	0.696898i	$-0.245437\pi$
$193$	0.281618	+	0.281618i	0.0202713	+	0.0202713i	−0.696898	+	0.717170i	$0.745437\pi$
$194$	−1.80666	−	6.33715i	−0.129710	−	0.454981i
$195$	10.8406	+	2.99490i	0.776309	+	0.214469i
$196$	−0.594015	−	2.41392i	−0.0424297	−	0.172423i
$197$	−16.4751	+	2.60941i	−1.17381	+	0.185912i	−0.712723	−	0.701445i	$-0.752538\pi$
$197$	−16.4751	+	2.60941i	−1.17381	+	0.185912i	−0.461082	+	0.887358i	$0.652538\pi$
$198$	−0.699527	−	5.77019i	−0.0497132	−	0.410070i
$199$	−3.04098			−0.215569			−0.107785	−	0.994174i	$-0.534376\pi$
$199$	−3.04098			−0.215569			−0.107785	+	0.994174i	$0.534376\pi$
$200$	6.16606	+	12.7271i	0.436006	+	0.899944i
$201$	−11.5398			−0.813953
$202$	0.682565	+	5.63028i	0.0480251	+	0.396145i
$203$	1.78660	−	0.282970i	0.125395	−	0.0198606i
$204$	−3.39476	−	13.7954i	−0.237680	−	0.965870i
$205$	−8.14352	+	3.05385i	−0.568768	+	0.213290i
$206$	−0.275609	−	0.966743i	−0.0192026	−	0.0673562i
$207$	1.06476	+	1.06476i	0.0740059	+	0.0740059i
$208$	0.227957	+	20.1173i	0.0158060	+	1.39489i
$209$	25.8410	−	8.39626i	1.78746	−	0.580781i
$210$	8.12295	+	4.05553i	0.560537	+	0.279858i
$211$	11.6358	+	3.78070i	0.801041	+	0.260274i	0.680799	−	0.732471i	$-0.261633\pi$
$211$	11.6358	+	3.78070i	0.801041	+	0.260274i	0.120242	+	0.992745i	$0.461633\pi$
$212$	4.02405	+	9.56133i	0.276373	+	0.656675i
$213$	2.50272	−	4.91186i	0.171483	−	0.336555i
$214$	−4.37132	+	5.57742i	−0.298817	+	0.381264i
$215$	9.94555	+	9.09548i	0.678281	+	0.620307i
$216$	2.09322	+	1.90222i	0.142425	+	0.129430i
$217$	−2.41881	+	15.2718i	−0.164199	+	1.03671i
$218$	−6.74857	−	14.5304i	−0.457071	−	0.984122i
$219$	−1.93823	+	1.40821i	−0.130974	+	0.0951580i
$220$	−0.519363	+	18.3732i	−0.0350154	+	1.23872i
$221$	28.9046	+	21.0004i	1.94433	+	1.41264i
$222$	2.66888	−	13.6189i	0.179123	−	0.914038i
$223$	10.1792	+	19.9779i	0.681652	+	1.33782i	0.929430	+	0.369000i	$0.120300\pi$
$223$	10.1792	+	19.9779i	0.681652	+	1.33782i	−0.247778	+	0.968817i	$0.579700\pi$
$224$	−2.94257	+	15.9724i	−0.196609	+	1.06720i
$225$	−4.59868	+	1.96268i	−0.306579	+	0.130846i
$226$	−14.1501	−	5.17475i	−0.941250	−	0.344219i
$227$	−3.52190	+	1.79450i	−0.233757	+	0.119105i	−0.566946	−	0.823755i	$-0.691875\pi$
$227$	−3.52190	+	1.79450i	−0.233757	+	0.119105i	0.333189	+	0.942860i	$0.391875\pi$
$228$	−6.84438	+	11.3124i	−0.453280	+	0.749181i
$229$	4.49293	−	6.18399i	0.296901	−	0.408650i	−0.634339	−	0.773055i	$-0.718728\pi$
$229$	4.49293	−	6.18399i	0.296901	−	0.408650i	0.931241	+	0.364405i	$0.118728\pi$
$230$	−2.83029	−	3.82932i	−0.186624	−	0.252498i
$231$	6.93592	+	9.54647i	0.456350	+	0.628112i
$232$	−1.71916	−	0.469118i	−0.112868	−	0.0307991i
$233$	2.66746	+	0.422484i	0.174751	+	0.0276778i	0.243197	−	0.969977i	$-0.421804\pi$
$233$	2.66746	+	0.422484i	0.174751	+	0.0276778i	−0.0684457	+	0.997655i	$0.521804\pi$
$234$	−7.10829	−	0.259121i	−0.464684	−	0.0169393i
$235$	−18.2776	+	3.73730i	−1.19230	+	0.243795i
$236$	−4.86662	−	7.84153i	−0.316790	−	0.510440i
$237$	3.34668	+	1.70522i	0.217390	+	0.110766i
$238$	19.6380	+	21.1239i	1.27294	+	1.36926i
$239$	5.46607	−	16.8228i	0.353570	−	1.08818i	−0.603263	−	0.797542i	$-0.706133\pi$
$239$	5.46607	−	16.8228i	0.353570	−	1.08818i	0.956834	−	0.290636i	$-0.0938668\pi$
$240$	−5.65370	−	6.93078i	−0.364945	−	0.447380i
$241$	−3.20904	−	9.87639i	−0.206712	−	0.636195i	−0.999639	−	0.0268774i	$-0.991444\pi$
$241$	−3.20904	−	9.87639i	−0.206712	−	0.636195i	0.792927	−	0.609317i	$-0.208556\pi$
$242$	−4.05100	+	7.28189i	−0.260408	+	0.468098i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	1.33560	−	18.2950i	0.0855033	−	1.17122i
$245$	−2.77659	+	0.123959i	−0.177390	+	0.00791942i
$246$	4.56495	−	3.06894i	0.291051	−	0.195669i
$247$	−5.20153	−	32.8412i	−0.330965	−	2.08963i
$248$	8.35481	−	12.7369i	0.530531	−	0.808791i
$249$			7.99426i			0.506616i
$250$	15.3021	−	3.98048i	0.967793	−	0.251748i
$251$			5.42401i			0.342360i	0.985240	+	0.171180i	$0.0547580\pi$
$251$			5.42401i			0.342360i	−0.985240	+	0.171180i	$0.945242\pi$
$252$	−5.59096	−	1.30882i	−0.352198	−	0.0824476i
$253$	−0.968150	−	6.11266i	−0.0608670	−	0.384299i
$254$	11.6482	+	17.3263i	0.730871	+	1.08715i
$255$	−15.8680	+	0.708415i	−0.993695	+	0.0443626i
$256$	9.10883	−	13.1541i	0.569302	−	0.822128i
$257$	10.7061	−	10.7061i	0.667828	−	0.667828i	−0.289385	−	0.957213i	$-0.593451\pi$
$257$	10.7061	−	10.7061i	0.667828	−	0.667828i	0.957213	+	0.289385i	$0.0934508\pi$
$258$	−7.44883	−	4.14387i	−0.463744	−	0.257986i
$259$	8.70629	+	26.7952i	0.540982	+	1.66497i
$260$	22.1081	+	4.14507i	1.37109	+	0.257067i
$261$	0.194692	−	0.599201i	0.0120511	−	0.0370896i
$262$	0.844322	−	0.784931i	0.0521624	−	0.0484932i
$263$	−25.7719	−	13.1314i	−1.58916	−	0.809718i	−0.999999	−	0.00170375i	$-0.999458\pi$
$263$	−25.7719	−	13.1314i	−1.58916	−	0.809718i	−0.589163	−	0.808014i	$-0.700542\pi$
$264$	−2.36471	−	11.3818i	−0.145538	−	0.700503i
$265$	11.3629	−	2.32343i	0.698020	−	0.142727i
$266$	0.977835	−	26.8243i	0.0599549	−	1.64470i
$267$	−6.54749	−	1.03702i	−0.400700	−	0.0634646i
$268$	−22.9978	+	1.94112i	−1.40481	+	0.118573i
$269$	−0.237117	−	0.326364i	−0.0144573	−	0.0198988i	0.801727	−	0.597690i	$-0.203915\pi$
$269$	−0.237117	−	0.326364i	−0.0144573	−	0.0198988i	−0.816184	+	0.577791i	$0.803915\pi$
$270$	2.54305	−	1.87960i	0.154765	−	0.114389i
$271$	−7.48792	+	10.3062i	−0.454859	+	0.626060i	−0.973433	−	0.228973i	$-0.926463\pi$
$271$	−7.48792	+	10.3062i	−0.454859	+	0.626060i	0.518574	+	0.855033i	$0.326463\pi$
$272$	−9.08600	−	26.9220i	−0.550920	−	1.63239i
$273$	12.8665	−	6.55582i	0.778717	−	0.396776i
$274$	−4.57126	+	12.4999i	−0.276160	+	0.755145i
$275$	20.0324	+	4.58346i	1.20800	+	0.276393i
$276$	2.30108	+	1.94287i	0.138509	+	0.116947i
$277$	7.48434	+	14.6888i	0.449690	+	0.882567i	0.998900	+	0.0468828i	$0.0149287\pi$
$277$	7.48434	+	14.6888i	0.449690	+	0.882567i	−0.549210	+	0.835684i	$0.685071\pi$
$278$	26.0873	+	5.11230i	1.56461	+	0.306616i
$279$	4.35697	+	3.16553i	0.260845	+	0.189515i
$280$	16.8705	+	6.71594i	1.00821	+	0.401354i
$281$	−2.60100	+	1.88974i	−0.155163	+	0.112732i	−0.662658	−	0.748922i	$-0.730572\pi$
$281$	−2.60100	+	1.88974i	−0.155163	+	0.112732i	0.507495	+	0.861655i	$0.330572\pi$
$282$	10.7011	−	4.97008i	0.637241	−	0.295964i
$283$	−1.48904	+	9.40142i	−0.0885141	+	0.558856i	0.903080	+	0.429472i	$0.141300\pi$
$283$	−1.48904	+	9.40142i	−0.0885141	+	0.558856i	−0.991594	+	0.129385i	$0.958700\pi$
$284$	4.16147	−	10.2099i	0.246938	−	0.605846i
$285$	10.9085	+	9.97615i	0.646165	+	0.590936i
$286$	23.0096	+	18.0338i	1.36059	+	1.06636i
$287$	−5.06977	+	9.94998i	−0.299259	+	0.587328i
$288$	4.49158	+	3.43885i	0.264669	+	0.202636i
$289$	−31.8217	−	10.3395i	−1.87186	−	0.608205i
$290$	−0.889963	+	1.78254i	−0.0522604	+	0.104674i
$291$	4.43153	−	1.43989i	0.259781	−	0.0844079i
$292$	−3.62586	+	3.13247i	−0.212187	+	0.183314i
$293$	2.20299	+	2.20299i	0.128700	+	0.128700i	0.768523	−	0.639822i	$-0.220992\pi$
$293$	2.20299	+	2.20299i	0.128700	+	0.128700i	−0.639822	+	0.768523i	$0.720992\pi$
$294$	1.69047	−	0.481934i	0.0985900	−	0.0281070i
$295$	−9.66130	+	3.62302i	−0.562502	+	0.210940i
$296$	3.02799	−	27.5901i	0.175998	−	1.60364i
$297$	4.05941	−	0.642948i	0.235551	−	0.0373076i
$298$	2.49684	−	0.302695i	0.144638	−	0.0175347i
$299$	−7.57365			−0.437995
$300$	−8.83463	+	4.68501i	−0.510068	+	0.270489i
$301$	17.3047			0.997428
$302$	11.9648	−	1.45051i	0.688496	−	0.0834672i
$303$	−3.96098	+	0.627358i	−0.227553	+	0.0360408i
$304$	−11.7374	+	23.6959i	−0.673186	+	1.35905i
$305$	−19.7684	−	5.46137i	−1.13193	−	0.312717i
$306$	9.66089	−	2.75422i	0.552276	−	0.157448i
$307$	18.9331	+	18.9331i	1.08057	+	1.08057i	0.996456	+	0.0841129i	$0.0268056\pi$
$307$	18.9331	+	18.9331i	1.08057	+	1.08057i	0.0841129	+	0.996456i	$0.473194\pi$
$308$	15.4285	+	17.8586i	0.879121	+	1.01759i
$309$	0.676038	−	0.219658i	0.0384584	−	0.0124959i
$310$	−12.1405	−	11.9435i	−0.689531	−	0.678346i
$311$	16.3213	+	5.30312i	0.925497	+	0.300712i	0.732720	−	0.680530i	$-0.238251\pi$
$311$	16.3213	+	5.30312i	0.925497	+	0.300712i	0.192777	+	0.981243i	$0.438251\pi$
$312$	−14.2098	+	0.679291i	−0.804471	+	0.0384573i
$313$	10.9460	−	21.4827i	0.618703	−	1.21427i	−0.342782	−	0.939415i	$-0.611369\pi$
$313$	10.9460	−	21.4827i	0.618703	−	1.21427i	0.961485	−	0.274858i	$-0.0886307\pi$
$314$	−6.05195	−	4.74324i	−0.341531	−	0.267676i
$315$	−2.65655	+	5.84445i	−0.149679	+	0.329297i
$316$	6.95647	+	2.83540i	0.391332	+	0.159504i
$317$	4.50589	−	28.4490i	0.253076	−	1.59786i	−0.454187	−	0.890907i	$-0.650070\pi$
$317$	4.50589	−	28.4490i	0.253076	−	1.59786i	0.707262	−	0.706951i	$-0.249930\pi$
$318$	−6.65274	+	3.08983i	−0.373067	+	0.173269i
$319$	−2.09492	+	1.52205i	−0.117293	+	0.0852183i
$320$	−12.4332	−	12.8614i	−0.695035	−	0.718976i
$321$	−4.05381	−	2.94527i	−0.226262	−	0.164389i
$322$	−5.99985	−	1.17579i	−0.334358	−	0.0655240i
$323$	21.3195	+	41.8419i	1.18625	+	2.32815i
$324$	−1.29026	+	1.52815i	−0.0716811	+	0.0848970i
$325$	9.37494	−	23.3355i	0.520028	−	1.29442i
$326$	−4.90789	+	13.4204i	−0.271823	+	0.743285i
$327$	10.0939	−	5.14309i	0.558193	−	0.284413i
$328$	8.58132	−	6.88402i	0.473824	−	0.380106i
$329$	−14.0795	+	19.3788i	−0.776230	+	1.06839i
$330$	−12.9966	+	0.106279i	−0.715438	+	0.00585049i
$331$	−12.3027	−	16.9332i	−0.676217	−	0.930732i	0.323664	−	0.946172i	$-0.395085\pi$
$331$	−12.3027	−	16.9332i	−0.676217	−	0.930732i	−0.999881	+	0.0154398i	$0.995085\pi$
$332$	1.34473	+	15.9319i	0.0738015	+	0.874375i
$333$	9.69234	+	1.53512i	0.531137	+	0.0841239i
$334$	0.137715	−	3.77785i	0.00753543	−	0.206715i
$335$	−2.89590	+	25.6407i	−0.158220	+	1.40090i
$336$	−11.3625	−	1.66789i	−0.619873	−	0.0909910i
$337$	−0.00646570	−	0.00329444i	−0.000352209	−	0.000179460i	0.453814	−	0.891096i	$-0.350063\pi$
$337$	−0.00646570	−	0.00329444i	−0.000352209	−	0.000179460i	−0.454167	+	0.890917i	$0.650063\pi$
$338$	12.7373	−	11.8413i	0.692818	−	0.644083i
$339$	3.29218	−	10.1323i	0.178807	−	0.550310i
$340$	−31.5045	+	4.08100i	−1.70857	+	0.221323i
$341$	−6.83995	−	21.0512i	−0.370404	−	1.13999i
$342$	−8.17006	−	4.54510i	−0.441786	−	0.245771i
$343$	11.6876	−	11.6876i	0.631071	−	0.631071i
$344$	−15.5419	−	7.00540i	−0.837964	−	0.377706i
$345$	2.63304	−	2.09863i	0.141758	−	0.112987i
$346$	4.52912	+	6.73692i	0.243487	+	0.362179i
$347$	1.87241	+	11.8219i	0.100516	+	0.634634i	0.985586	+	0.169176i	$0.0541106\pi$
$347$	1.87241	+	11.8219i	0.100516	+	0.634634i	−0.885070	+	0.465459i	$0.845889\pi$
$348$	0.287212	−	1.22691i	0.0153962	−	0.0657690i
$349$			17.1160i			0.916197i	0.888902	+	0.458098i	$0.151469\pi$
$349$			17.1160i			0.916197i	−0.888902	+	0.458098i	$0.848531\pi$
$350$	11.0496	−	17.0310i	0.590626	−	0.910345i
$351$		−	5.02966i		−	0.268463i
$352$	−6.62722	−	22.2852i	−0.353232	−	1.18781i
$353$	4.28029	+	27.0247i	0.227817	+	1.43838i	0.790883	+	0.611967i	$0.209621\pi$
$353$	4.28029	+	27.0247i	0.227817	+	1.43838i	−0.563067	+	0.826411i	$0.690379\pi$
$354$	5.41576	−	3.64093i	0.287844	−	0.193513i
$355$	−10.2858	−	6.79352i	−0.545914	−	0.360563i
$356$	−13.2230	−	0.965329i	−0.700819	−	0.0511623i
$357$	−14.4211	+	14.4211i	−0.763244	+	0.763244i
$358$	13.2358	−	23.7921i	0.699535	−	1.25745i
$359$	−4.36824	−	13.4441i	−0.230547	−	0.709550i	−0.997681	−	0.0680635i	$-0.978318\pi$
$359$	−4.36824	−	13.4441i	−0.230547	−	0.709550i	0.767134	−	0.641487i	$-0.221682\pi$
$360$	4.75191	−	4.17365i	0.250448	−	0.219971i
$361$	7.63392	−	23.4948i	0.401785	−	1.23657i
$362$	9.09772	+	9.78610i	0.478166	+	0.514346i
$363$	−5.25001	−	2.67501i	−0.275554	−	0.140402i
$364$	24.5391	−	15.2295i	1.28620	−	0.798242i
$365$	2.64256	+	4.66003i	0.138318	+	0.243917i
$366$	12.9624	+	0.472521i	0.677553	+	0.0246991i
$367$	0.863623	+	0.136785i	0.0450808	+	0.00714009i	0.178934	−	0.983861i	$-0.442735\pi$
$367$	0.863623	+	0.136785i	0.0450808	+	0.00714009i	−0.133853	+	0.991001i	$0.542735\pi$
$368$	4.91267	+	3.48490i	0.256090	+	0.181663i
$369$	2.28622	+	3.14671i	0.119016	+	0.163811i
$370$	−29.5906	−	9.34774i	−1.53834	−	0.485966i
$371$	8.75308	−	12.0476i	0.454437	−	0.625479i
$372$	9.21555	+	5.57573i	0.477804	+	0.289088i
$373$	13.4164	−	6.83598i	0.694673	−	0.353953i	−0.0707386	−	0.997495i	$-0.522536\pi$
$373$	13.4164	−	6.83598i	0.694673	−	0.353953i	0.765411	+	0.643542i	$0.222536\pi$
$374$	−38.7768	−	14.1809i	−2.00510	−	0.733275i
$375$	3.20693	+	10.7105i	0.165605	+	0.553090i
$376$	20.4903	−	11.7050i	1.05671	−	0.603638i
$377$	1.43864	+	2.82349i	0.0740936	+	0.145417i
$378$	0.780839	−	3.98450i	0.0401620	−	0.204940i
$379$	−12.6266	−	9.17375i	−0.648584	−	0.471224i	0.214205	−	0.976789i	$-0.431284\pi$
$379$	−12.6266	−	9.17375i	−0.648584	−	0.471224i	−0.862789	+	0.505565i	$0.831284\pi$
$380$	23.4179	+	18.0467i	1.20131	+	0.925774i
$381$	−11.9433	+	8.67734i	−0.611876	+	0.444554i
$382$	2.29888	+	4.94973i	0.117621	+	0.253250i
$383$	−4.33189	+	27.3505i	−0.221349	+	1.39754i	0.587356	+	0.809329i	$0.300169\pi$
$383$	−4.33189	+	27.3505i	−0.221349	+	1.39754i	−0.808705	+	0.588214i	$0.799831\pi$
$384$	9.52978	+	6.09780i	0.486315	+	0.311177i
$385$	22.9523	−	13.0155i	1.16976	−	0.663332i
$386$	−0.347442	+	0.443305i	−0.0176843	+	0.0225636i
$387$	2.73634	−	5.37037i	0.139096	−	0.272991i
$388$	8.58945	−	3.61501i	0.436063	−	0.183525i
$389$	−11.9584	−	3.88552i	−0.606315	−	0.197004i	−0.0102599	−	0.999947i	$-0.503266\pi$
$389$	−11.9584	−	3.88552i	−0.606315	−	0.197004i	−0.596055	+	0.802944i	$0.703266\pi$
$390$	−2.35958	+	15.7292i	−0.119482	+	0.796478i
$391$	10.1729	−	3.30537i	0.514464	−	0.167160i
$392$	3.28789	−	1.24481i	0.166063	−	0.0628724i
$393$	0.576410	+	0.576410i	0.0290761	+	0.0290761i
$394$	−6.46751	−	22.6859i	−0.325829	−	1.14290i
$395$	4.62874	−	7.00820i	0.232897	−	0.352621i
$396$	7.98191	−	1.96418i	0.401106	−	0.0987038i
$397$	6.69199	−	1.05991i	0.335861	−	0.0531952i	0.0137739	−	0.999905i	$-0.495616\pi$
$397$	6.69199	−	1.05991i	0.335861	−	0.0531952i	0.322087	+	0.946710i	$0.395616\pi$
$398$	−0.517577	−	4.26934i	−0.0259438	−	0.214002i
$399$	18.9802			0.950201
$400$	−16.8186	+	10.8229i	−0.840929	+	0.541146i
$401$	−13.9504			−0.696648			−0.348324	−	0.937374i	$-0.613249\pi$
$401$	−13.9504			−0.696648			−0.348324	+	0.937374i	$0.613249\pi$
$402$	−1.96408	−	16.2011i	−0.0979592	−	0.808037i
$403$	−26.7538	+	4.23739i	−1.33270	+	0.211079i
$404$	−7.78837	+	1.91655i	−0.387486	+	0.0953521i
$405$	1.39370	+	1.74860i	0.0692536	+	0.0868885i
$406$	0.701352	+	2.46011i	0.0348075	+	0.122093i
$407$	−28.5192	−	28.5192i	−1.41364	−	1.41364i
$408$	18.7900	−	7.11400i	0.930245	−	0.352195i
$409$	13.9221	−	4.52356i	0.688402	−	0.223675i	0.0561321	−	0.998423i	$-0.482123\pi$
$409$	13.9221	−	4.52356i	0.688402	−	0.223675i	0.632270	+	0.774748i	$0.282123\pi$
$410$	−5.67344	−	10.9132i	−0.280191	−	0.538965i
$411$	−8.95063	−	2.90824i	−0.441502	−	0.143453i
$412$	1.31034	−	0.551477i	0.0645556	−	0.0271693i
$413$	−6.01466	+	11.8044i	−0.295962	+	0.580858i
$414$	−1.31363	+	1.67608i	−0.0645614	+	0.0823746i
$415$	17.7628	+	2.00616i	0.871941	+	0.0984785i
$416$	−28.2046	+	3.74402i	−1.38285	+	0.183566i
$417$	−2.94056	+	18.5659i	−0.144000	+	0.909178i
$418$	16.1860	+	34.8501i	0.791681	+	1.70457i
$419$	−22.6725	+	16.4725i	−1.10762	+	0.804735i	−0.982288	−	0.187379i	$-0.940001\pi$
$419$	−22.6725	+	16.4725i	−1.10762	+	0.804735i	−0.125335	+	0.992114i	$0.540001\pi$
$420$	−4.31116	+	12.0943i	−0.210363	+	0.590144i
$421$	−27.0733	−	19.6699i	−1.31947	−	0.958653i	−0.999939	−	0.0110788i	$-0.996473\pi$
$421$	−27.0733	−	19.6699i	−1.31947	−	0.958653i	−0.319535	−	0.947575i	$-0.603527\pi$
$422$	−3.32743	+	16.9794i	−0.161977	+	0.826542i
$423$	3.78769	+	7.43377i	0.184164	+	0.361442i
$424$	−12.7386	+	7.27684i	−0.618640	+	0.353395i
$425$	−2.40803	+	35.4356i	−0.116806	+	1.71888i
$426$	7.32189	+	2.67765i	0.354747	+	0.129733i
$427$	−23.4628	+	11.9549i	−1.13545	+	0.578538i
$428$	−8.57433	−	5.18777i	−0.414456	−	0.250760i
$429$	−12.1507	+	16.7240i	−0.586640	+	0.807441i
$430$	−11.0767	+	15.5110i	−0.534167	+	0.748005i
$431$	9.84116	+	13.5452i	0.474032	+	0.652449i	0.977344	−	0.211655i	$-0.0678854\pi$
$431$	9.84116	+	13.5452i	0.474032	+	0.652449i	−0.503312	+	0.864105i	$0.667885\pi$
$432$	−2.31432	+	3.26250i	−0.111348	+	0.156967i
$433$	15.3537	+	2.43179i	0.737852	+	0.116864i	0.514038	−	0.857767i	$-0.328149\pi$
$433$	15.3537	+	2.43179i	0.737852	+	0.116864i	0.223814	+	0.974632i	$0.428149\pi$
$434$	−21.8522	−	0.796587i	−1.04894	−	0.0382374i
$435$	−1.28253	−	0.582964i	−0.0614927	−	0.0279510i
$436$	19.2511	−	11.9476i	0.921960	−	0.572188i
$437$	−8.86967	−	4.51932i	−0.424294	−	0.216189i
$438$	−2.30692	−	2.48148i	−0.110229	−	0.118570i
$439$	−0.0471984	+	0.145262i	−0.00225266	+	0.00693296i	−0.952177	−	0.305548i	$-0.901160\pi$
$439$	−0.0471984	+	0.145262i	−0.00225266	+	0.00693296i	0.949924	+	0.312481i	$0.101160\pi$
$440$	−25.8832	+	2.39798i	−1.23393	+	0.114319i
$441$	0.384098	+	1.18213i	0.0182904	+	0.0562920i
$442$	−24.5636	+	44.1544i	−1.16837	+	2.10021i
$443$	14.5387	−	14.5387i	0.690756	−	0.690756i	−0.271642	−	0.962398i	$-0.587567\pi$
$443$	14.5387	−	14.5387i	0.690756	−	0.690756i	0.962398	+	0.271642i	$0.0875666\pi$
$444$	19.5742	+	1.42899i	0.928952	+	0.0678169i
$445$	−3.94729	+	14.2879i	−0.187120	+	0.677312i
$446$	−26.3151	+	17.6912i	−1.24606	+	0.837703i
$447$	0.278213	+	1.75657i	0.0131590	+	0.0830827i
$448$	−22.9250	−	1.41267i	−1.08310	−	0.0667423i
$449$		−	0.847419i		−	0.0399922i	−0.999800	−	0.0199961i	$-0.993635\pi$
$449$		−	0.847419i		−	0.0399922i	0.999800	−	0.0199961i	$-0.00636537\pi$
$450$	−3.53818	−	6.12220i	−0.166791	−	0.288603i
$451$		−	15.9861i		−	0.752756i
$452$	4.85666	−	20.7465i	0.228438	−	0.975835i
$453$	1.33319	+	8.41740i	0.0626385	+	0.395484i
$454$	−3.11879	−	4.63910i	−0.146372	−	0.217724i
$455$	−11.3378	−	30.2338i	−0.531524	−	1.41738i
$456$	−17.0468	−	7.68369i	−0.798288	−	0.359822i
$457$	−13.6982	+	13.6982i	−0.640775	+	0.640775i	−0.950746	−	0.309971i	$-0.899681\pi$
$457$	−13.6982	+	13.6982i	−0.640775	+	0.640775i	0.309971	+	0.950746i	$0.399681\pi$
$458$	9.44662	+	5.25527i	0.441412	+	0.245562i
$459$	2.19509	+	6.75580i	0.102458	+	0.315334i
$460$	4.89440	−	4.62530i	0.228202	−	0.215656i
$461$	−2.77560	+	8.54241i	−0.129272	+	0.397860i	−0.994655	−	0.103252i	$-0.967075\pi$
$461$	−2.77560	+	8.54241i	−0.129272	+	0.397860i	0.865383	+	0.501111i	$0.167075\pi$
$462$	−12.2221	+	11.3624i	−0.568625	+	0.528626i
$463$	−10.9751	−	5.59208i	−0.510055	−	0.259886i	0.179969	−	0.983672i	$-0.442400\pi$
$463$	−10.9751	−	5.59208i	−0.510055	−	0.259886i	−0.690024	+	0.723786i	$0.742400\pi$
$464$	0.366010	−	2.49343i	0.0169916	−	0.115755i
$465$	8.12700	−	8.88655i	0.376881	−	0.412104i
$466$	−0.139137	+	3.81684i	−0.00644538	+	0.176812i
$467$	−39.5800	−	6.26886i	−1.83154	−	0.290088i	−0.857172	−	0.515031i	$-0.827781\pi$
$467$	−39.5800	−	6.26886i	−1.83154	−	0.290088i	−0.974372	+	0.224942i	$0.927781\pi$
$468$	−0.846047	−	10.0237i	−0.0391085	−	0.463345i
$469$	19.4741	+	26.8038i	0.899231	+	1.23769i
$470$	−8.35778	−	25.0244i	−0.385516	−	1.15429i
$471$	3.19586	−	4.39872i	0.147257	−	0.202682i
$472$	10.1807	−	8.16704i	0.468604	−	0.375919i
$473$	−22.0723	+	11.2464i	−1.01488	+	0.517110i
$474$	−1.82441	+	4.98874i	−0.0837978	+	0.229141i
$475$	24.9039	−	21.7346i	1.14267	−	0.997252i
$476$	−26.3141	+	31.1657i	−1.20611	+	1.42848i
$477$	−2.35476	−	4.62148i	−0.107817	−	0.211603i
$478$	24.5485	+	4.81074i	1.12282	+	0.220038i
$479$	15.7328	+	11.4306i	0.718852	+	0.522277i	0.886017	−	0.463652i	$-0.153461\pi$
$479$	15.7328	+	11.4306i	0.718852	+	0.522277i	−0.167165	+	0.985929i	$0.553461\pi$
$480$	8.76809	−	9.11705i	0.400207	−	0.416134i
$481$	−39.9305	+	29.0112i	−1.82068	+	1.32280i
$482$	13.3196	−	6.18624i	0.606693	−	0.281776i
$483$	0.676302	−	4.27001i	0.0307728	−	0.194292i
$484$	−10.9128	−	4.44796i	−0.496036	−	0.202180i
$485$	−2.08726	−	10.2079i	−0.0947777	−	0.463519i
$486$	−1.11308	−	0.872382i	−0.0504904	−	0.0395720i
$487$	11.8969	−	23.3489i	0.539099	−	1.05804i	−0.447409	−	0.894329i	$-0.647653\pi$
$487$	11.8969	−	23.3489i	0.539099	−	1.05804i	0.986508	−	0.163712i	$-0.0523468\pi$
$488$	25.9123	−	1.23872i	1.17300	−	0.0560744i
$489$	−9.60975	−	3.12240i	−0.434568	−	0.141200i
$490$	−0.646608	−	3.87706i	−0.0292108	−	0.175148i
$491$	5.45014	−	1.77086i	0.245961	−	0.0799177i	−0.183442	−	0.983031i	$-0.558724\pi$
$491$	5.45014	−	1.77086i	0.245961	−	0.0799177i	0.429403	+	0.903113i	$0.358724\pi$
$492$	5.08555	+	5.88656i	0.229274	+	0.265386i
$493$	−3.16462	−	3.16462i	−0.142527	−	0.142527i
$494$	45.2215	−	12.8922i	2.03461	−	0.580047i
$495$	−0.409883	−	9.18113i	−0.0184229	−	0.412661i
$496$	19.3037	+	9.56179i	0.866762	+	0.429337i
$497$	−15.6324	+	2.47594i	−0.701211	+	0.111061i
$498$	−11.2234	+	1.36063i	−0.502934	+	0.0609712i
$499$	−12.2234			−0.547193			−0.273596	−	0.961845i	$-0.588213\pi$
$499$	−12.2234			−0.547193			−0.273596	+	0.961845i	$0.588213\pi$
$500$	8.19277	+	20.8057i	0.366392	+	0.930461i
$501$	2.67311			0.119426
$502$	−7.61495	+	0.923169i	−0.339872	+	0.0412031i
$503$	−14.7797	+	2.34087i	−0.658992	+	0.104374i	−0.476969	−	0.878920i	$-0.658265\pi$
$503$	−14.7797	+	2.34087i	−0.658992	+	0.104374i	−0.182023	+	0.983294i	$0.558265\pi$
$504$	0.885906	−	8.07211i	0.0394614	−	0.359560i
$505$	0.399945	+	8.95851i	0.0177973	+	0.398648i
$506$	8.41699	−	2.39960i	0.374181	−	0.106675i
$507$	8.69563	+	8.69563i	0.386186	+	0.386186i
$508$	−22.3424	+	19.3022i	−0.991284	+	0.856397i
$509$	39.6985	−	12.8988i	1.75960	−	0.571730i	0.762444	−	0.647054i	$-0.223999\pi$
$509$	39.6985	−	12.8988i	1.75960	−	0.571730i	0.997159	+	0.0753238i	$0.0239990\pi$
$510$	−3.69532	−	22.1571i	−0.163631	−	0.981133i
$511$	6.54179	+	2.12556i	0.289392	+	0.0940291i
$512$	20.0178	+	10.5494i	0.884668	+	0.466221i
$513$	3.00128	−	5.89035i	0.132510	−	0.260065i
$514$	16.8528	+	13.2085i	0.743347	+	0.582601i
$515$	−0.318416	−	1.55724i	−0.0140311	−	0.0686202i
$516$	4.54993	−	11.1630i	0.200299	−	0.491422i
$517$	5.36419	−	33.8681i	0.235917	−	1.48952i
$518$	−36.1369	+	16.7836i	−1.58776	+	0.737430i
$519$	−4.64389	+	3.37398i	−0.203844	+	0.148101i
$520$	−2.05660	+	31.7438i	−0.0901879	+	1.39206i
$521$	0.348795	+	0.253415i	0.0152810	+	0.0111023i	0.595400	−	0.803430i	$-0.296994\pi$
$521$	0.348795	+	0.253415i	0.0152810	+	0.0111023i	−0.580119	+	0.814532i	$0.696994\pi$
$522$	0.874376	+	0.171351i	0.0382704	+	0.00749982i
$523$	−20.4568	−	40.1487i	−0.894513	−	1.75558i	−0.600151	−	0.799887i	$-0.704893\pi$
$523$	−20.4568	−	40.1487i	−0.894513	−	1.75558i	−0.294363	−	0.955694i	$-0.595107\pi$
$524$	1.24570	+	1.05178i	0.0544184	+	0.0459471i
$525$	12.3194	+	7.36935i	0.537661	+	0.321625i
$526$	14.0493	−	38.4170i	0.612577	−	1.67506i
$527$	34.0862	−	17.3678i	1.48482	−	0.756553i
$528$	15.5769	−	5.25709i	0.677896	−	0.228786i
$529$	12.1863	−	16.7730i	0.529839	−	0.729261i
$530$	5.19593	+	15.5574i	0.225697	+	0.675770i
$531$	2.71232	+	3.73319i	0.117705	+	0.162007i
$532$	37.8260	−	3.19270i	1.63996	−	0.138421i
$533$	−19.3223	−	3.06034i	−0.836940	−	0.132558i
$534$	0.341522	−	9.36875i	0.0147791	−	0.405425i
$535$	−7.56152	+	8.26822i	−0.326913	+	0.357466i
$536$	−6.63944	−	31.9570i	−0.286780	−	1.38033i
$537$	17.1533	+	8.74007i	0.740222	+	0.377162i
$538$	0.417836	−	0.388444i	0.0180142	−	0.0167470i
$539$	1.57865	−	4.85858i	0.0679972	−	0.209274i
$540$	3.07166	+	3.25037i	0.132183	+	0.139874i
$541$	−4.70865	−	14.4917i	−0.202441	−	0.623049i	−0.999809	−	0.0195552i	$-0.993775\pi$
$541$	−4.70865	−	14.4917i	−0.202441	−	0.623049i	0.797368	−	0.603493i	$-0.206225\pi$
$542$	−15.7437	−	8.75843i	−0.676252	−	0.376207i
$543$	−6.68087	+	6.68087i	−0.286704	+	0.286704i
$544$	36.2503	−	17.3383i	1.55422	−	0.743373i
$545$	−8.89458	−	23.7187i	−0.381002	−	1.01600i
$546$	11.3938	+	16.9480i	0.487611	+	0.725305i
$547$	−2.61858	−	16.5331i	−0.111962	−	0.706903i	−0.978261	−	0.207377i	$-0.933507\pi$
$547$	−2.61858	−	16.5331i	−0.111962	−	0.706903i	0.866299	−	0.499526i	$-0.166493\pi$
$548$	−18.3270	−	4.29027i	−0.782892	−	0.183271i
$549$			9.17186i			0.391445i
$550$	−3.02534	+	28.9043i	−0.129001	+	1.23248i
$551$			4.16511i			0.177440i
$552$	−2.33602	+	3.56124i	−0.0994275	+	0.151577i
$553$	−1.68697	−	10.6511i	−0.0717372	−	0.452931i
$554$	−19.3483	+	13.0076i	−0.822032	+	0.552639i
$555$	5.84323	−	21.1506i	0.248031	−	0.897792i
$556$	−2.73727	+	37.4949i	−0.116086	+	1.59014i
$557$	27.3212	−	27.3212i	1.15764	−	1.15764i	0.172654	−	0.984983i	$-0.444766\pi$
$557$	27.3212	−	27.3212i	1.15764	−	1.15764i	0.984983	−	0.172654i	$-0.0552343\pi$
$558$	−3.70263	+	6.65568i	−0.156745	+	0.281757i
$559$	9.36794	+	28.8315i	0.396221	+	1.21944i
$560$	−6.55737	+	24.8282i	−0.277099	+	1.04918i
$561$	9.02186	−	27.7664i	0.380903	−	1.17230i
$562$	−3.09576	−	3.33000i	−0.130587	−	0.140467i
$563$	16.9090	+	8.61555i	0.712628	+	0.363102i	0.772423	−	0.635109i	$-0.219045\pi$
$563$	16.9090	+	8.61555i	0.712628	+	0.363102i	−0.0597950	+	0.998211i	$0.519045\pi$
$564$	8.79899	+	14.1777i	0.370504	+	0.596990i
$565$	−21.6872	−	9.85772i	−0.912386	−	0.414717i
$566$	−13.4524	−	0.490385i	−0.565447	−	0.0206124i
$567$	2.83571	+	0.449132i	0.119089	+	0.0188618i
$568$	15.0423	+	4.10470i	0.631161	+	0.172229i
$569$	−14.3767	−	19.7878i	−0.602701	−	0.829547i	0.393251	−	0.919431i	$-0.371350\pi$
$569$	−14.3767	−	19.7878i	−0.602701	−	0.829547i	−0.995952	+	0.0898841i	$0.971350\pi$
$570$	−12.1492	+	17.0128i	−0.508875	+	0.712588i
$571$	16.9704	−	23.3577i	0.710188	−	0.977490i	−0.289605	−	0.957146i	$-0.593524\pi$
$571$	16.9704	−	23.3577i	0.710188	−	0.977490i	0.999793	−	0.0203441i	$-0.00647618\pi$
$572$	−21.4021	+	35.3733i	−0.894866	+	1.47903i
$573$	−3.43845	+	1.75198i	−0.143643	+	0.0731899i
$574$	−14.8320	−	5.42413i	−0.619075	−	0.226399i
$575$	−4.00228	−	6.37710i	−0.166907	−	0.265944i
$576$	−4.06346	+	6.89118i	−0.169311	+	0.287132i
$577$	−3.26771	−	6.41324i	−0.136036	−	0.266986i	0.812931	−	0.582359i	$-0.197870\pi$
$577$	−3.26771	−	6.41324i	−0.136036	−	0.266986i	−0.948968	+	0.315373i	$0.897870\pi$
$578$	9.09989	−	46.4353i	0.378506	−	1.93145i
$579$	−0.322206	−	0.234096i	−0.0133904	−	0.00972871i
$580$	−2.65404	−	0.946060i	−0.110203	−	0.0392830i
$581$	18.5685	−	13.4908i	0.770353	−	0.559694i
$582$	2.77576	+	5.97651i	0.115059	+	0.247734i
$583$	−3.33485	+	21.0554i	−0.138115	+	0.872026i
$584$	−5.01491	−	4.55732i	−0.207519	−	0.188583i
$585$	−11.1756	−	1.26219i	−0.462055	−	0.0521852i
$586$	−2.71791	+	3.46781i	−0.112276	+	0.143254i
$587$	8.38878	−	16.4639i	0.346242	−	0.679538i	−0.650560	−	0.759455i	$-0.725466\pi$
$587$	8.38878	−	16.4639i	0.346242	−	0.679538i	0.996802	+	0.0799173i	$0.0254656\pi$
$588$	0.964322	+	2.29128i	0.0397680	+	0.0944907i
$589$	−33.8605	−	11.0020i	−1.39520	−	0.453328i
$590$	−6.73084	−	12.9472i	−0.277104	−	0.533027i
$591$	15.8641	−	5.15456i	0.652562	−	0.212030i
$592$	39.2501	−	0.444757i	1.61317	−	0.0182794i
$593$	0.577494	+	0.577494i	0.0237148	+	0.0237148i	0.718865	−	0.695150i	$-0.244662\pi$
$593$	0.577494	+	0.577494i	0.0237148	+	0.0237148i	−0.695150	+	0.718865i	$0.744662\pi$
$594$	1.59357	+	5.58972i	0.0653850	+	0.229349i
$595$	28.4238	+	35.6617i	1.16526	+	1.46199i
$596$	0.849928	+	3.45388i	0.0348144	+	0.141477i
$597$	3.00354	−	0.475714i	0.122927	−	0.0194697i
$598$	−1.28904	−	10.6329i	−0.0527128	−	0.434812i
$599$	0.789836			0.0322718			0.0161359	−	0.999870i	$-0.494864\pi$
$599$	0.789836			0.0322718			0.0161359	+	0.999870i	$0.494864\pi$
$600$	−8.08111	−	11.6058i	−0.329910	−	0.473807i
$601$	23.6331			0.964016			0.482008	−	0.876167i	$-0.339908\pi$
$601$	23.6331			0.964016			0.482008	+	0.876167i	$0.339908\pi$
$602$	2.94527	+	24.2947i	0.120040	+	0.990178i
$603$	11.3977	−	1.80522i	0.464150	−	0.0735142i
$604$	4.07283	+	16.5509i	0.165721	+	0.673447i
$605$	−7.26121	+	10.9939i	−0.295210	+	0.446966i
$606$	−1.55493	−	5.45418i	−0.0631648	−	0.221561i
$607$	−2.37288	−	2.37288i	−0.0963122	−	0.0963122i	0.657309	−	0.753621i	$-0.271695\pi$
$607$	−2.37288	−	2.37288i	−0.0963122	−	0.0963122i	−0.753621	+	0.657309i	$0.771695\pi$
$608$	−35.2652	−	12.4455i	−1.43019	−	0.504731i
$609$	−1.72034	+	0.558972i	−0.0697117	+	0.0226507i
$610$	4.30282	−	28.6830i	0.174216	−	1.16134i
$611$	−39.9092	−	12.9673i	−1.61455	−	0.524600i
$612$	5.51103	+	13.0945i	0.222770	+	0.529313i
$613$	−19.9127	+	39.0809i	−0.804267	+	1.57846i	0.0113957	+	0.999935i	$0.496373\pi$
$613$	−19.9127	+	39.0809i	−0.804267	+	1.57846i	−0.815663	+	0.578528i	$0.803627\pi$
$614$	−23.3584	+	29.8033i	−0.942669	+	1.20276i
$615$	7.56554	−	4.29018i	0.305072	−	0.172997i
$616$	−22.4463	+	24.7002i	−0.904389	+	0.995198i
$617$	−6.74622	+	42.5940i	−0.271593	+	1.71477i	0.354530	+	0.935045i	$0.384641\pi$
$617$	−6.74622	+	42.5940i	−0.271593	+	1.71477i	−0.626123	+	0.779725i	$0.715359\pi$
$618$	0.423447	+	0.911727i	0.0170335	+	0.0366750i
$619$	17.0937	−	12.4193i	0.687054	−	0.499174i	−0.188636	−	0.982047i	$-0.560407\pi$
$619$	17.0937	−	12.4193i	0.687054	−	0.499174i	0.875690	+	0.482873i	$0.160407\pi$
$620$	14.7016	−	19.0772i	0.590430	−	0.766158i
$621$	−1.21822	−	0.885086i	−0.0488853	−	0.0355173i
$622$	−4.66733	+	23.8166i	−0.187143	+	0.954961i
$623$	8.64059	+	16.9581i	0.346178	+	0.679413i
$624$	−3.37220	−	19.8340i	−0.134996	−	0.793996i
$625$	24.6030	−	4.43781i	0.984119	−	0.177512i
$626$	32.0233	+	11.7111i	1.27991	+	0.468068i
$627$	−24.2094	+	12.3353i	−0.966831	+	0.492625i
$628$	5.62915	−	9.30385i	0.224628	−	0.371264i
$629$	40.9730	−	56.3945i	1.63370	−	2.24860i
$630$	−8.65737	−	2.73489i	−0.344918	−	0.108961i
$631$	8.57072	+	11.7966i	0.341195	+	0.469615i	0.944790	−	0.327677i	$-0.106266\pi$
$631$	8.57072	+	11.7966i	0.341195	+	0.469615i	−0.603595	+	0.797291i	$0.706266\pi$
$632$	−2.79672	+	10.2490i	−0.111248	+	0.407684i
$633$	−12.0840	−	1.91391i	−0.480294	−	0.0760712i
$634$	40.7075	+	1.48392i	1.61670	+	0.0589341i
$635$	16.2834	+	28.7150i	0.646186	+	1.13952i
$636$	−5.47022	−	8.81411i	−0.216908	−	0.349502i
$637$	−5.57031	−	2.83821i	−0.220704	−	0.112454i
$638$	−2.49341	−	2.68208i	−0.0987151	−	0.106184i
$639$	−1.70352	+	5.24290i	−0.0673902	+	0.207406i
$640$	15.9405	−	19.6444i	0.630102	−	0.776512i
$641$	11.6983	+	36.0038i	0.462057	+	1.42206i	0.862646	+	0.505807i	$0.168805\pi$
$641$	11.6983	+	36.0038i	0.462057	+	1.42206i	−0.400590	+	0.916258i	$0.631195\pi$
$642$	3.44500	−	6.19257i	0.135963	−	0.244401i
$643$	23.2894	−	23.2894i	0.918443	−	0.918443i	−0.0784732	−	0.996916i	$-0.525004\pi$
$643$	23.2894	−	23.2894i	0.918443	−	0.918443i	0.996916	+	0.0784732i	$0.0250045\pi$
$644$	0.629548	−	8.62351i	0.0248077	−	0.339814i
$645$	−11.2460	−	7.42768i	−0.442809	−	0.292464i
$646$	−55.1147	+	37.0527i	−2.16846	+	1.45782i
$647$	−3.38894	−	21.3969i	−0.133233	−	0.841200i	−0.960274	−	0.279058i	$-0.909978\pi$
$647$	−3.38894	−	21.3969i	−0.133233	−	0.841200i	0.827041	−	0.562141i	$-0.190022\pi$
$648$	−2.36502	−	1.55135i	−0.0929068	−	0.0609427i
$649$		−	18.9656i		−	0.744463i
$650$	34.3572	+	9.19008i	1.34760	+	0.360464i
$651$		−	15.4621i		−	0.606008i
$652$	−19.6766	−	4.60620i	−0.770596	−	0.180393i
$653$	6.17299	+	38.9747i	0.241568	+	1.52520i	0.748454	+	0.663187i	$0.230796\pi$
$653$	6.17299	+	38.9747i	0.241568	+	1.52520i	−0.506886	+	0.862013i	$0.669204\pi$
$654$	8.93854	+	13.2958i	0.349525	+	0.519906i
$655$	1.42540	−	1.13610i	0.0556950	−	0.0443911i
$656$	11.1253	+	10.8760i	0.434368	+	0.424635i
$657$	1.69408	−	1.69408i	0.0660923	−	0.0660923i
$658$	−29.6030	−	16.4685i	−1.15404	−	0.642008i
$659$	14.9986	+	46.1611i	0.584264	+	1.79818i	0.602204	+	0.798342i	$0.294289\pi$
$659$	14.9986	+	46.1611i	0.584264	+	1.79818i	−0.0179400	+	0.999839i	$0.505711\pi$
$660$	−2.36123	−	18.2282i	−0.0919109	−	0.709534i
$661$	−5.19782	+	15.9972i	−0.202172	+	0.622221i	0.797646	+	0.603126i	$0.206078\pi$
$661$	−5.19782	+	15.9972i	−0.202172	+	0.622221i	−0.999818	+	0.0190946i	$0.993922\pi$
$662$	21.6792	−	20.1542i	0.842585	−	0.783315i
$663$	−31.8339	−	16.2202i	−1.23633	−	0.629940i
$664$	−22.1384	+	4.59952i	−0.859138	+	0.178496i
$665$	4.76309	−	42.1730i	0.184705	−	1.63540i
$666$	−0.505560	+	13.8687i	−0.0195901	+	0.537401i
$667$	0.937028	+	0.148411i	0.0362819	+	0.00574649i
$668$	5.32729	−	0.449649i	0.206119	−	0.0173974i
$669$	−13.1791	−	18.1395i	−0.509535	−	0.701314i
$670$	−36.4907	+	0.298403i	−1.40976	+	0.0115283i
$671$	22.1574	−	30.4971i	0.855378	−	1.17733i
$672$	0.407713	−	16.2360i	0.0157279	−	0.626319i
$673$	16.7415	−	8.53020i	0.645336	−	0.328815i	−0.100508	−	0.994936i	$-0.532047\pi$
$673$	16.7415	−	8.53020i	0.645336	−	0.328815i	0.745843	+	0.666121i	$0.232047\pi$
$674$	0.00352471	−	0.00963814i	0.000135767	−	0.000371247i
$675$	4.23503	−	2.65791i	0.163006	−	0.102303i
$676$	18.7923	+	15.8669i	0.722782	+	0.610266i
$677$	−1.37849	−	2.70543i	−0.0529796	−	0.103978i	0.862999	−	0.505206i	$-0.168584\pi$
$677$	−1.37849	−	2.70543i	−0.0529796	−	0.103978i	−0.915978	+	0.401228i	$0.868584\pi$
$678$	14.7854	+	2.89748i	0.567829	+	0.111277i
$679$	−10.8230	−	7.86335i	−0.415348	−	0.301768i
$680$	−11.0915	−	43.5356i	−0.425341	−	1.66951i
$681$	3.19782	−	2.32335i	0.122541	−	0.0890311i
$682$	28.3904	−	13.1858i	1.08712	−	0.504909i
$683$	5.65364	−	35.6957i	0.216331	−	1.36586i	−0.605373	−	0.795942i	$-0.706976\pi$
$683$	5.65364	−	35.6957i	0.216331	−	1.36586i	0.821703	−	0.569916i	$-0.193024\pi$
$684$	4.99047	−	12.2438i	0.190815	−	0.468154i
$685$	−8.70809	+	19.1580i	−0.332719	+	0.731988i
$686$	18.3979	+	14.4194i	0.702434	+	0.550535i
$687$	−3.47023	+	6.81071i	−0.132398	+	0.259845i
$688$	7.18987	−	23.0122i	0.274111	−	0.877330i
$689$	24.8111	+	8.06160i	0.945226	+	0.307122i
$690$	3.39449	+	3.33942i	0.129226	+	0.127130i
$691$	−2.18584	+	0.710223i	−0.0831533	+	0.0270182i	−0.350298	−	0.936638i	$-0.613920\pi$
$691$	−2.18584	+	0.710223i	−0.0831533	+	0.0270182i	0.267145	+	0.963656i	$0.413920\pi$
$692$	−8.68733	+	7.50522i	−0.330243	+	0.285306i
$693$	−8.34392	−	8.34392i	−0.316959	−	0.316959i
$694$	−16.2785	+	4.64084i	−0.617924	+	0.176164i
$695$	40.5145	+	11.1929i	1.53680	+	0.424569i
$696$	1.77138	+	0.194407i	0.0671439	+	0.00736898i
$697$	27.2891	−	4.32217i	1.03365	−	0.163714i
$698$	−24.0297	+	2.91315i	−0.909537	+	0.110264i
$699$	−2.70071			−0.102150
$700$	25.7910	+	12.6142i	0.974810	+	0.476773i
$701$	−23.4413			−0.885365			−0.442683	−	0.896678i	$-0.645973\pi$
$701$	−23.4413			−0.885365			−0.442683	+	0.896678i	$0.645973\pi$
$702$	7.06131	−	0.856051i	0.266512	−	0.0323096i
$703$	−64.0750	+	10.1485i	−2.41664	+	0.382758i
$704$	30.1590	−	13.0971i	1.13666	−	0.493617i
$705$	17.4679	−	6.55053i	0.657880	−	0.246707i
$706$	−37.2124	+	10.6089i	−1.40051	+	0.399270i
$707$	8.14160	+	8.14160i	0.306196	+	0.306196i
$708$	6.03339	+	6.98368i	0.226749	+	0.262463i
$709$	−13.5161	+	4.39166i	−0.507609	+	0.164932i	−0.551615	−	0.834099i	$-0.685988\pi$
$709$	−13.5161	+	4.39166i	−0.507609	+	0.164932i	0.0440055	+	0.999031i	$0.485988\pi$
$710$	7.78701	−	15.5969i	0.292241	−	0.585340i
$711$	−3.57223	−	1.16069i	−0.133969	−	0.0435292i
$712$	−0.895308	−	18.7286i	−0.0335531	−	0.701882i
$713$	−3.68164	+	7.22562i	−0.137878	+	0.270602i
$714$	−22.7007	−	17.7918i	−0.849552	−	0.665840i
$715$	34.1105	+	31.1950i	1.27566	+	1.16663i
$716$	35.6553	+	14.5328i	1.33250	+	0.543116i
$717$	−2.76710	+	17.4708i	−0.103339	+	0.652458i
$718$	18.1311	−	8.42091i	0.676647	−	0.314265i
$719$	−21.6382	+	15.7211i	−0.806968	+	0.586296i	−0.912950	−	0.408072i	$-0.866201\pi$
$719$	−21.6382	+	15.7211i	−0.806968	+	0.586296i	0.105982	+	0.994368i	$0.466201\pi$
$720$	6.66831	+	5.96102i	0.248513	+	0.222154i
$721$	−1.65106	−	1.19957i	−0.0614888	−	0.0446743i
$722$	34.2845	+	6.71870i	1.27594	+	0.250044i
$723$	4.71454	+	9.25280i	0.175335	+	0.344115i
$724$	−12.1906	+	14.4382i	−0.453060	+	0.536592i
$725$	−1.61716	+	2.70342i	−0.0600599	+	0.100402i
$726$	2.86199	−	7.82596i	0.106218	−	0.290448i
$727$	−6.67481	+	3.40098i	−0.247555	+	0.126136i	−0.573366	−	0.819299i	$-0.694363\pi$
$727$	−6.67481	+	3.40098i	−0.247555	+	0.126136i	0.325811	+	0.945435i	$0.394363\pi$
$728$	25.5578	+	31.8592i	0.947234	+	1.18078i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	−6.09262	+	4.50312i	−0.225498	+	0.166668i
$731$	−25.1659	−	34.6379i	−0.930794	−	1.28113i
$732$	1.54281	+	18.2787i	0.0570240	+	0.675601i
$733$	21.4291	+	3.39404i	0.791502	+	0.125362i	0.539079	−	0.842255i	$-0.318773\pi$
$733$	21.4291	+	3.39404i	0.791502	+	0.125362i	0.252423	+	0.967617i	$0.418773\pi$
$734$	−0.0450472	+	1.23575i	−0.00166272	+	0.0456124i
$735$	2.72302	−	0.556787i	0.100440	−	0.0205374i
$736$	−4.05644	+	7.49019i	−0.149522	+	0.276092i
$737$	−42.2592	−	21.5322i	−1.55664	−	0.793147i
$738$	−4.02866	+	3.74528i	−0.148297	+	0.137865i
$739$	−10.3439	+	31.8353i	−0.380507	+	1.17108i	0.559181	+	0.829046i	$0.311116\pi$
$739$	−10.3439	+	31.8353i	−0.380507	+	1.17108i	−0.939688	+	0.342034i	$0.888884\pi$
$740$	8.08728	−	43.1342i	0.297294	−	1.58564i
$741$	10.2750	+	31.6231i	0.377461	+	1.16171i
$742$	18.4038	+	10.2382i	0.675624	+	0.375858i
$743$	−5.37518	+	5.37518i	−0.197196	+	0.197196i	−0.798797	−	0.601601i	$-0.794530\pi$
$743$	−5.37518	+	5.37518i	−0.197196	+	0.197196i	0.601601	+	0.798797i	$0.294530\pi$
$744$	−6.25947	+	13.8870i	−0.229483	+	0.509123i
$745$	3.97280	−	0.177362i	0.145552	−	0.00649805i
$746$	11.8807	+	17.6722i	0.434985	+	0.647025i
$747$	−1.25058	−	7.89584i	−0.0457563	−	0.288894i
$748$	13.3092	−	56.8537i	0.486631	−	2.07878i
$749$			14.3863i			0.525662i
$750$	−14.4911	+	6.32526i	−0.529139	+	0.230966i
$751$			18.5583i			0.677204i	0.940930	+	0.338602i	$0.109954\pi$
$751$			18.5583i			0.677204i	−0.940930	+	0.338602i	$0.890046\pi$
$752$	19.9205	+	26.7749i	0.726426	+	0.976380i
$753$	−0.848502	−	5.35723i	−0.0309211	−	0.195228i
$754$	−3.71913	+	2.50031i	−0.135443	+	0.0910560i
$755$	19.0375	−	0.849914i	0.692847	−	0.0309316i
$756$	5.72687	+	0.418083i	0.208284	+	0.0152055i
$757$	−21.2384	+	21.2384i	−0.771923	+	0.771923i	−0.978442	−	0.206520i	$-0.933786\pi$
$757$	−21.2384	+	21.2384i	−0.771923	+	0.771923i	0.206520	+	0.978442i	$0.433786\pi$
$758$	10.7303	−	19.2883i	0.389742	−	0.700582i
$759$	1.91246	+	5.88595i	0.0694179	+	0.213646i
$760$	−21.3506	+	35.9487i	−0.774468	+	1.30400i
$761$	−12.4376	+	38.2789i	−0.450861	+	1.38761i	0.425065	+	0.905163i	$0.360251\pi$
$761$	−12.4376	+	38.2789i	−0.450861	+	1.38761i	−0.875926	+	0.482445i	$0.839749\pi$
$762$	−14.2152	−	15.2908i	−0.514962	−	0.553926i
$763$	−28.9801	−	14.7661i	−1.04915	−	0.534569i
$764$	−6.55783	+	4.06993i	−0.237254	+	0.147245i
$765$	15.5619	−	3.18200i	0.562640	−	0.115045i
$766$	−39.1355	−	1.42662i	−1.41402	−	0.0515459i
$767$	−22.9235	−	3.63073i	−0.827719	−	0.131098i
$768$	−6.93894	+	14.4170i	−0.250388	+	0.520230i
$769$	24.2332	+	33.3541i	0.873871	+	1.20278i	0.978081	+	0.208225i	$0.0667687\pi$
$769$	24.2332	+	33.3541i	0.873871	+	1.20278i	−0.104210	+	0.994555i	$0.533231\pi$
$770$	22.1794	+	30.0082i	0.799291	+	1.08142i
$771$	−8.89948	+	12.2491i	−0.320507	+	0.441140i
$772$	−0.681506	−	0.412335i	−0.0245280	−	0.0148403i
$773$	7.46191	−	3.80203i	0.268386	−	0.136750i	−0.314619	−	0.949218i	$-0.601877\pi$
$773$	7.46191	−	3.80203i	0.268386	−	0.136750i	0.583005	+	0.812468i	$0.301877\pi$
$774$	8.00537	+	2.92760i	0.287747	+	0.105230i
$775$	−17.7059	−	20.2878i	−0.636016	−	0.728759i
$776$	6.53717	+	11.4437i	0.234671	+	0.410807i
$777$	−12.7908	−	25.1033i	−0.458867	−	0.900577i
$778$	3.41969	−	17.4501i	0.122602	−	0.625617i
$779$	−20.8026	−	15.1140i	−0.745330	−	0.541514i
$780$	−22.4843	−	0.635574i	−0.805068	−	0.0227572i
$781$	18.3302	−	13.3176i	0.655904	−	0.476543i
$782$	6.37195	+	13.7195i	0.227860	+	0.490607i
$783$	−0.0985595	+	0.622280i	−0.00352223	+	0.0222385i
$784$	2.30723	+	4.40411i	0.0824011	+	0.157290i
$785$	−8.97170	−	8.20486i	−0.320214	−	0.292844i
$786$	−0.711137	+	0.907348i	−0.0253654	+	0.0323640i
$787$	1.22057	−	2.39551i	0.0435087	−	0.0853906i	−0.868229	−	0.496164i	$-0.834741\pi$
$787$	1.22057	−	2.39551i	0.0435087	−	0.0853906i	0.911737	+	0.410774i	$0.134741\pi$
$788$	30.7487	−	12.9411i	1.09538	−	0.461008i
$789$	27.5088	+	8.93814i	0.979338	+	0.318206i
$790$	10.6269	+	5.30565i	0.378087	+	0.188767i
$791$	−29.0904	+	9.45203i	−1.03433	+	0.336075i
$792$	4.11611	+	10.8718i	0.146259	+	0.386312i
$793$	−32.6198	−	32.6198i	−1.15836	−	1.15836i
$794$	2.62702	+	9.21472i	0.0932295	+	0.327018i
$795$	−10.8596	+	4.07238i	−0.385150	+	0.144433i
$796$	5.90578	−	1.45329i	0.209325	−	0.0515104i
$797$	−12.0646	+	1.91085i	−0.427351	+	0.0676858i	−0.366406	−	0.930455i	$-0.619412\pi$
$797$	−12.0646	+	1.91085i	−0.427351	+	0.0676858i	−0.0609459	+	0.998141i	$0.519412\pi$
$798$	3.23045	+	26.6470i	0.114357	+	0.943294i
$799$	59.2651			2.09665
$800$	−18.0572	−	21.7701i	−0.638418	−	0.769690i
$801$	6.62911			0.234228
$802$	−2.37436	−	19.5854i	−0.0838416	−	0.691585i
$803$	−9.72550	+	1.54037i	−0.343206	+	0.0543584i
$804$	22.4110	−	5.51487i	0.790374	−	0.194494i
$805$	−9.31798	−	2.57426i	−0.328416	−	0.0907308i
$806$	−10.5025	−	36.8394i	−0.369936	−	1.29761i
$807$	0.285252	+	0.285252i	0.0100414	+	0.0100414i
$808$	−4.01630	−	10.6082i	−0.141293	−	0.373194i
$809$	0.215955	−	0.0701681i	0.00759258	−	0.00246698i	−0.305218	−	0.952282i	$-0.598729\pi$
$809$	0.215955	−	0.0701681i	0.00759258	−	0.00246698i	0.312811	+	0.949815i	$0.398729\pi$
$810$	−2.21771	+	2.25428i	−0.0779223	+	0.0792073i
$811$	23.7919	+	7.73047i	0.835448	+	0.271453i	0.695338	−	0.718683i	$-0.255255\pi$
$811$	23.7919	+	7.73047i	0.835448	+	0.271453i	0.140110	+	0.990136i	$0.455255\pi$
$812$	−3.33446	+	1.40336i	−0.117017	+	0.0492484i
$813$	5.78348	−	11.3507i	0.202836	−	0.398087i
$814$	35.1851	−	44.8931i	1.23324	−	1.57350i
$815$	−9.34935	+	20.5687i	−0.327494	+	0.720492i
$816$	13.1857	+	25.1692i	0.461590	+	0.881097i
$817$	−6.23326	+	39.3553i	−0.218074	+	1.37687i
$818$	8.72032	+	18.7758i	0.304899	+	0.656479i
$819$	−11.6826	+	8.48788i	−0.408222	+	0.296590i
$820$	14.3558	−	9.82257i	0.501326	−	0.343019i
$821$	10.8910	+	7.91278i	0.380099	+	0.276158i	0.761386	−	0.648299i	$-0.224519\pi$
$821$	10.8910	+	7.91278i	0.380099	+	0.276158i	−0.381287	+	0.924457i	$0.624519\pi$
$822$	2.55957	−	13.0611i	0.0892753	−	0.455558i
$823$	22.7225	+	44.5954i	0.792056	+	1.55450i	0.831662	+	0.555282i	$0.187390\pi$
$823$	22.7225	+	44.5954i	0.792056	+	1.55450i	−0.0396057	+	0.999215i	$0.512610\pi$
$824$	0.997257	+	1.74576i	0.0347411	+	0.0608166i
$825$	−20.5028	−	1.39327i	−0.713815	−	0.0485073i
$826$	−17.5963	−	6.43506i	−0.612255	−	0.223904i
$827$	21.4490	−	10.9288i	0.745853	−	0.380031i	−0.0393857	−	0.999224i	$-0.512540\pi$
$827$	21.4490	−	10.9288i	0.745853	−	0.380031i	0.785239	+	0.619193i	$0.212540\pi$
$828$	−2.57668	−	1.55898i	−0.0895459	−	0.0541784i
$829$	−21.0048	+	28.9106i	−0.729526	+	1.00411i	0.269627	+	0.962965i	$0.413100\pi$
$829$	−21.0048	+	28.9106i	−0.729526	+	1.00411i	−0.999153	+	0.0411418i	$0.986900\pi$
$830$	0.206721	+	25.2792i	0.00717539	+	0.877455i
$831$	−9.69004	−	13.3372i	−0.336144	−	0.462662i
$832$	−10.0568	−	38.9602i	−0.348657	−	1.35070i
$833$	8.72068	+	1.38122i	0.302153	+	0.0478564i
$834$	−26.5658	−	0.968413i	−0.919900	−	0.0335334i
$835$	0.670818	−	5.93950i	0.0232146	−	0.205545i
$836$	−46.1723	+	28.6555i	−1.59690	+	0.991072i
$837$	−4.79853	−	2.44497i	−0.165861	−	0.0845107i
$838$	−26.9852	−	29.0270i	−0.932188	−	1.00272i
$839$	−1.08261	+	3.33194i	−0.0373759	+	0.115031i	−0.968004	−	0.250936i	$-0.919262\pi$
$839$	−1.08261	+	3.33194i	−0.0373759	+	0.115031i	0.930628	+	0.365967i	$0.119262\pi$
$840$	−17.7134	−	3.99413i	−0.611171	−	0.137810i
$841$	8.83883	+	27.2031i	0.304787	+	0.938039i
$842$	23.0074	−	41.3570i	0.792887	−	1.42526i
$843$	2.27336	−	2.27336i	0.0782985	−	0.0782985i
$844$	−24.4042	−	1.78160i	−0.840029	−	0.0613252i
$845$	21.5033	−	17.1390i	0.739737	−	0.589600i
$846$	−9.79186	+	6.58291i	−0.336651	+	0.226325i
$847$	2.64639	+	16.7086i	0.0909309	+	0.574115i
$848$	−12.3843	−	16.6456i	−0.425279	−	0.571613i
$849$		−	9.51861i		−	0.326678i
$850$	−50.1591	+	2.65046i	−1.72044	+	0.0909099i
$851$			14.7766i			0.506537i
$852$	−2.51305	+	10.7352i	−0.0860958	+	0.367782i
$853$	4.11245	+	25.9650i	0.140807	+	0.889024i	0.952411	+	0.304815i	$0.0985948\pi$
$853$	4.11245	+	25.9650i	0.140807	+	0.889024i	−0.811604	+	0.584208i	$0.801405\pi$
$854$	−20.7773	−	30.9055i	−0.710984	−	1.05757i
$855$	−12.3348	−	8.14686i	−0.421843	−	0.278617i
$856$	5.82393	−	12.9208i	0.199058	−	0.441622i
$857$	32.6711	−	32.6711i	1.11602	−	1.11602i	0.123705	−	0.992319i	$-0.460522\pi$
$857$	32.6711	−	32.6711i	1.11602	−	1.11602i	0.992319	−	0.123705i	$-0.0394775\pi$
$858$	−25.5474	−	14.2123i	−0.872175	−	0.485201i
$859$	11.2793	+	34.7140i	0.384843	+	1.18443i	0.936594	+	0.350417i	$0.113960\pi$
$859$	11.2793	+	34.7140i	0.384843	+	1.18443i	−0.551751	+	0.834009i	$0.686040\pi$
$860$	−23.6616	−	12.9110i	−0.806855	−	0.440262i
$861$	3.45083	−	10.6206i	0.117604	−	0.361948i
$862$	−17.3416	+	16.1217i	−0.590657	+	0.549109i
$863$	−28.0303	−	14.2822i	−0.954164	−	0.486171i	−0.0936541	−	0.995605i	$-0.529855\pi$
$863$	−28.0303	−	14.2822i	−0.954164	−	0.486171i	−0.860510	+	0.509434i	$0.829855\pi$
$864$	−4.97424	−	2.69388i	−0.169227	−	0.0916476i
$865$	6.33141	+	11.1652i	0.215274	+	0.379627i
$866$	−0.800861	+	21.9695i	−0.0272144	+	0.746554i
$867$	33.0473	+	5.23419i	1.12235	+	0.177762i
$868$	−2.60091	−	30.8147i	−0.0882806	−	1.04592i
$869$	9.07392	+	12.4892i	0.307812	+	0.423666i
$870$	0.600156	−	1.89981i	0.0203472	−	0.0644096i
$871$	−34.1157	+	46.9563i	−1.15597	+	1.59105i
$872$	20.0502	+	24.9938i	0.678987	+	0.846396i
$873$	−4.15172	+	2.11541i	−0.140514	+	0.0715957i
$874$	4.83521	−	13.2216i	0.163553	−	0.447228i
$875$	19.4658	−	25.5236i	0.658065	−	0.862854i
$876$	3.09119	−	3.66112i	0.104442	−	0.123698i
$877$	−0.515662	−	1.01204i	−0.0174127	−	0.0341743i	0.882136	−	0.470994i	$-0.156105\pi$
$877$	−0.515662	−	1.01204i	−0.0174127	−	0.0341743i	−0.899549	+	0.436820i	$0.856105\pi$
$878$	−0.211971	−	0.0415398i	−0.00715368	−	0.00140190i
$879$	−2.52050	−	1.83125i	−0.0850142	−	0.0617665i
$880$	−7.77194	−	35.9301i	−0.261992	−	1.21120i
$881$	28.2714	−	20.5404i	0.952488	−	0.692023i	0.00109374	−	0.999999i	$-0.499652\pi$
$881$	28.2714	−	20.5404i	0.952488	−	0.692023i	0.951394	+	0.307977i	$0.0996519\pi$
$882$	−1.59426	+	0.740448i	−0.0536816	+	0.0249322i
$883$	4.94864	−	31.2445i	0.166535	−	1.05146i	−0.752876	−	0.658162i	$-0.771334\pi$
$883$	4.94864	−	31.2445i	0.166535	−	1.05146i	0.919411	−	0.393298i	$-0.128666\pi$
$884$	−66.1707	−	26.9706i	−2.22556	−	0.907120i
$885$	8.97558	−	5.08977i	0.301711	−	0.171091i
$886$	22.8859	+	17.9369i	0.768868	+	0.602603i
$887$	−6.18807	+	12.1448i	−0.207775	+	0.407782i	−0.971252	−	0.238054i	$-0.923491\pi$
$887$	−6.18807	+	12.1448i	−0.207775	+	0.407782i	0.763477	+	0.645835i	$0.223491\pi$
$888$	1.32534	+	27.7241i	0.0444754	+	0.930361i
$889$	40.3103	+	13.0976i	1.35196	+	0.439280i
$890$	−20.7311	−	3.10993i	−0.694908	−	0.104245i
$891$	−3.90886	+	1.27006i	−0.130952	+	0.0425488i
$892$	−29.3161	−	33.9336i	−0.981577	−	1.13618i
$893$	−39.0008	−	39.0008i	−1.30511	−	1.30511i
$894$	−2.41875	+	0.689561i	−0.0808951	+	0.0230624i
$895$	23.7245	−	35.9204i	0.793024	−	1.20069i
$896$	−1.91855	−	32.4256i	−0.0640943	−	1.08326i
$897$	7.48041	−	1.18478i	0.249763	−	0.0395586i
$898$	1.18972	−	0.144231i	0.0397015	−	0.00481306i
$899$	3.39308			0.113165
$900$	7.99296	−	6.00937i	0.266432	−	0.200312i
$901$	−36.8443			−1.22746
$902$	22.4434	−	2.72085i	0.747285	−	0.0905942i
$903$	−17.0917	+	2.70706i	−0.568775	+	0.0900852i
$904$	29.9534	+	3.28736i	0.996235	+	0.109336i
$905$	13.1679	+	16.5211i	0.437717	+	0.549179i
$906$	−11.5906	+	3.30435i	−0.385071	+	0.109780i
$907$	−26.5016	−	26.5016i	−0.879970	−	0.879970i	0.113561	−	0.993531i	$-0.463774\pi$
$907$	−26.5016	−	26.5016i	−0.879970	−	0.879970i	−0.993531	+	0.113561i	$0.963774\pi$
$908$	5.98217	−	5.16815i	0.198525	−	0.171511i
$909$	3.81408	−	1.23927i	0.126505	−	0.0411039i
$910$	40.5166	−	21.0633i	1.34311	−	0.698243i
$911$	44.1948	+	14.3598i	1.46424	+	0.475760i	0.929362	−	0.369170i	$-0.120358\pi$
$911$	44.1948	+	14.3598i	1.46424	+	0.475760i	0.534877	+	0.844930i	$0.320358\pi$
$912$	7.88603	−	25.2403i	0.261133	−	0.835790i
$913$	−14.9166	+	29.2754i	−0.493666	+	0.968874i
$914$	−21.5628	−	16.8999i	−0.713235	−	0.559000i
$915$	20.3793	+	2.30168i	0.673720	+	0.0760911i
$916$	−5.77023	+	14.1569i	−0.190654	+	0.467757i
$917$	0.366118	−	2.31158i	0.0120903	−	0.0763350i
$918$	−9.11110	+	4.23161i	−0.300711	+	0.139664i
$919$	−0.442425	+	0.321441i	−0.0145943	+	0.0106034i	−0.595058	−	0.803682i	$-0.702871\pi$
$919$	−0.442425	+	0.321441i	−0.0145943	+	0.0106034i	0.580464	+	0.814286i	$0.302871\pi$
$920$	7.32665	+	6.08418i	0.241552	+	0.200590i
$921$	−21.6618	−	15.7382i	−0.713780	−	0.518592i
$922$	−12.4654	−	2.44283i	−0.410526	−	0.0804504i
$923$	−12.5878	−	24.7050i	−0.414333	−	0.813174i
$924$	−18.0323	−	15.2252i	−0.593218	−	0.500871i
$925$	−45.5290	−	18.2911i	−1.49698	−	0.601406i
$926$	5.98295	−	16.3601i	0.196612	−	0.537625i
$927$	−0.633352	+	0.322709i	−0.0208020	+	0.0105992i
$928$	3.56291	+	0.0894703i	0.116958	+	0.00293700i
$929$	−35.2392	+	48.5026i	−1.15616	+	1.59132i	−0.431673	+	0.902030i	$0.642076\pi$
$929$	−35.2392	+	48.5026i	−1.15616	+	1.59132i	−0.724488	+	0.689288i	$0.757924\pi$
$930$	13.8594	+	9.89728i	0.454466	+	0.324544i
$931$	−4.82990	−	6.64779i	−0.158294	−	0.217873i
$932$	−5.38228	+	0.454290i	−0.176302	+	0.0148808i
$933$	−16.9500	−	2.68461i	−0.554917	−	0.0878902i
$934$	2.06452	−	56.6347i	0.0675532	−	1.85314i
$935$	−59.4314	−	27.0140i	−1.94361	−	0.883454i
$936$	13.9286	−	2.89383i	0.455270	−	0.0945878i
$937$	−44.4095	−	22.6278i	−1.45080	−	0.739217i	−0.461776	−	0.886997i	$-0.652787\pi$
$937$	−44.4095	−	22.6278i	−1.45080	−	0.739217i	−0.989020	+	0.147779i	$0.952787\pi$
$938$	−34.3163	+	31.9024i	−1.12047	+	1.04165i
$939$	−7.45058	+	22.9305i	−0.243140	+	0.748309i
$940$	33.7102	−	15.9930i	1.09950	−	0.521633i
$941$	−1.28266	−	3.94763i	−0.0418136	−	0.128689i	0.927971	−	0.372653i	$-0.121552\pi$
$941$	−1.28266	−	3.94763i	−0.0418136	−	0.128689i	−0.969784	+	0.243964i	$0.921552\pi$
$942$	6.71945	+	3.73811i	0.218931	+	0.121794i
$943$	−4.14144	+	4.14144i	−0.134864	+	0.134864i
$944$	13.1988	+	12.9030i	0.429583	+	0.419956i
$945$	1.70957	−	6.18807i	0.0556122	−	0.201298i
$946$	−19.5459	−	29.0739i	−0.635492	−	0.945274i
$947$	6.99032	+	44.1352i	0.227155	+	1.43420i	0.792765	+	0.609527i	$0.208641\pi$
$947$	6.99032	+	44.1352i	0.227155	+	1.43420i	−0.565610	+	0.824673i	$0.691359\pi$
$948$	−7.31438	−	1.71226i	−0.237560	−	0.0556116i
$949$			12.0500i			0.391160i
$950$	34.7526	+	31.2642i	1.12752	+	1.01435i
$951$			28.8037i			0.934023i
$952$	−48.2333	−	31.6389i	−1.56325	−	1.02542i
$953$	−0.490009	−	3.09379i	−0.0158729	−	0.100218i	0.978480	−	0.206342i	$-0.0661559\pi$
$953$	−0.490009	−	3.09379i	−0.0158729	−	0.100218i	−0.994353	+	0.106124i	$0.966156\pi$
$954$	6.08747	−	4.09251i	0.197089	−	0.132500i
$955$	3.02991	+	8.07969i	0.0980457	+	0.261453i
$956$	−2.57580	+	35.2832i	−0.0833075	+	1.14114i
$957$	1.83103	−	1.83103i	0.0591887	−	0.0591887i
$958$	−13.3700	+	24.0334i	−0.431967	+	0.776483i
$959$	8.34971	+	25.6978i	0.269626	+	0.829825i
$960$	14.2921	+	10.7581i	0.461275	+	0.347216i
$961$	0.616861	−	1.89850i	0.0198988	−	0.0612421i
$962$	−47.5261	−	51.1221i	−1.53230	−	1.64824i
$963$	4.46465	+	2.27485i	0.143871	+	0.0733060i
$964$	10.9521	+	17.6470i	0.352743	+	0.568371i
$965$	−0.601006	+	0.657176i	−0.0193471	+	0.0211553i
$966$	6.10991	+	0.222727i	0.196583	+	0.00716611i
$967$	−46.4059	−	7.34998i	−1.49231	−	0.236359i	−0.643662	−	0.765310i	$-0.722586\pi$
$967$	−46.4059	−	7.34998i	−1.49231	−	0.236359i	−0.848653	+	0.528951i	$0.822586\pi$
$968$	4.38728	−	16.0779i	0.141012	−	0.516762i
$969$	−27.6026	−	37.9917i	−0.886722	−	1.22047i
$970$	13.9760	−	4.66778i	0.448743	−	0.149873i
$971$	24.4089	−	33.5959i	0.783318	−	1.07815i	−0.211590	−	0.977359i	$-0.567864\pi$
$971$	24.4089	−	33.5959i	0.783318	−	1.07815i	0.994908	−	0.100787i	$-0.0321360\pi$
$972$	1.03532	−	1.71117i	0.0332079	−	0.0548859i
$973$	48.0861	−	24.5011i	1.54157	−	0.785469i
$974$	34.8052	+	12.7284i	1.11523	+	0.407845i
$975$	−5.60904	+	24.5148i	−0.179633	+	0.785102i
$976$	6.14938	+	36.1684i	0.196837	+	1.15772i
$977$	18.5873	+	36.4797i	0.594662	+	1.16709i	0.970657	+	0.240468i	$0.0773007\pi$
$977$	18.5873	+	36.4797i	0.594662	+	1.16709i	−0.375996	+	0.926621i	$0.622699\pi$
$978$	2.74806	−	14.0229i	0.0878731	−	0.448403i
$979$	−22.0423	−	16.0146i	−0.704474	−	0.511830i
$980$	5.33308	−	1.56767i	0.170359	−	0.0500775i
$981$	−9.16505	+	6.65880i	−0.292618	+	0.212599i
$982$	3.41378	+	7.35023i	0.108938	+	0.234555i
$983$	−6.79981	+	42.9323i	−0.216880	+	1.36933i	0.603433	+	0.797414i	$0.293799\pi$
$983$	−6.79981	+	42.9323i	−0.216880	+	1.36933i	−0.820313	+	0.571915i	$0.806201\pi$
$984$	−7.39877	+	8.14168i	−0.235864	+	0.259547i
$985$	−7.47203	−	36.5426i	−0.238079	−	1.16435i
$986$	3.90430	−	4.98154i	0.124338	−	0.158645i
$987$	10.8747	−	21.3428i	0.346145	−	0.679348i
$988$	25.7965	+	61.2938i	0.820697	+	1.95002i
$989$	8.63169	+	2.80461i	0.274472	+	0.0891813i
$990$	12.8199	−	2.13808i	0.407444	−	0.0679527i
$991$	−22.4669	+	7.29994i	−0.713684	+	0.231890i	−0.643283	−	0.765629i	$-0.722428\pi$
$991$	−22.4669	+	7.29994i	−0.713684	+	0.231890i	−0.0704015	+	0.997519i	$0.522428\pi$
$992$	−10.1386	+	28.7286i	−0.321901	+	0.912133i
$993$	14.8001	+	14.8001i	0.469669	+	0.469669i
$994$	−6.13670	−	21.5255i	−0.194644	−	0.682748i
$995$	−0.303271	−	6.79307i	−0.00961433	−	0.215355i
$996$	−3.82047	−	15.5254i	−0.121056	−	0.491940i
$997$	45.3934	−	7.18961i	1.43762	−	0.227697i	0.611526	−	0.791225i	$-0.290556\pi$
$997$	45.3934	−	7.18961i	1.43762	−	0.227697i	0.826097	+	0.563528i	$0.190556\pi$
$998$	−2.08042	−	17.1608i	−0.0658547	−	0.543216i
$999$	−9.81316			−0.310475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.16	yes	240
3.2	odd	2		900.2.bj.f.703.15		240
4.3	odd	2	inner	300.2.w.a.103.22	yes	240
12.11	even	2		900.2.bj.f.703.9		240
25.17	odd	20	inner	300.2.w.a.67.22	yes	240
75.17	even	20		900.2.bj.f.667.9		240
100.67	even	20	inner	300.2.w.a.67.16	✓	240
300.167	odd	20		900.2.bj.f.667.15		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.16	✓	240	100.67	even	20	inner
300.2.w.a.67.22	yes	240	25.17	odd	20	inner
300.2.w.a.103.16	yes	240	1.1	even	1	trivial
300.2.w.a.103.22	yes	240	4.3	odd	2	inner
900.2.bj.f.667.9		240	75.17	even	20
900.2.bj.f.667.15		240	300.167	odd	20
900.2.bj.f.703.9		240	12.11	even	2
900.2.bj.f.703.15		240	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.170201 + 1.40393i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.94206 + 0.477901i) q^{4} +(0.0997280 + 2.23384i) q^{5} +(-0.387729 - 1.36002i) q^{6} +(2.03014 + 2.03014i) q^{7} +(-1.00148 - 2.64519i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(0.170201 + 1.40393i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.94206 + 0.477901i) q^{4} +(0.0997280 + 2.23384i) q^{5} +(-0.387729 - 1.36002i) q^{6} +(2.03014 + 2.03014i) q^{7} +(-1.00148 - 2.64519i) q^{8} +(0.951057 - 0.309017i) q^{9} +(-3.11920 + 0.520213i) q^{10} +(-3.90886 - 1.27006i) q^{11} +(1.84339 - 0.775823i) q^{12} +(-2.28342 + 4.48146i) q^{13} +(-2.50466 + 3.19572i) q^{14} +(-0.447950 - 2.19074i) q^{15} +(3.54322 - 1.85623i) q^{16} +(1.11123 - 7.01601i) q^{17} +(0.595710 + 1.28263i) q^{18} +(-5.34832 + 3.88579i) q^{19} +(-1.26123 - 4.29060i) q^{20} +(-2.32273 - 1.68756i) q^{21} +(1.11780 - 5.70394i) q^{22} +(0.683618 + 1.34168i) q^{23} +(1.40295 + 2.45596i) q^{24} +(-4.98011 + 0.445553i) q^{25} +(-6.68031 - 2.44302i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(-4.91288 - 2.97246i) q^{28} +(0.370327 - 0.509711i) q^{29} +(2.99941 - 1.00176i) q^{30} +(3.16553 + 4.35697i) q^{31} +(3.20908 + 4.65852i) q^{32} +(4.05941 + 0.642948i) q^{33} +(10.0392 + 0.365961i) q^{34} +(-4.33256 + 4.73748i) q^{35} +(-1.69933 + 1.05464i) q^{36} +(8.74359 + 4.45508i) q^{37} +(-6.36568 - 6.84733i) q^{38} +(1.55425 - 4.78349i) q^{39} +(5.80906 - 2.50095i) q^{40} +(1.20194 + 3.69918i) q^{41} +(1.97390 - 3.54819i) q^{42} +(4.26195 - 4.26195i) q^{43} +(8.19821 + 0.598500i) q^{44} +(0.785142 + 2.09369i) q^{45} +(-1.76727 + 1.18811i) q^{46} +(1.30515 + 8.24040i) q^{47} +(-3.20922 + 2.38766i) q^{48} +1.24297i q^{49} +(-1.47315 - 6.91591i) q^{50} +7.10347i q^{51} +(2.29285 - 9.79453i) q^{52} +(-0.811396 - 5.12295i) q^{53} +(-0.789023 - 1.17365i) q^{54} +(2.44730 - 8.85843i) q^{55} +(3.33696 - 7.40327i) q^{56} +(4.67461 - 4.67461i) q^{57} +(0.778630 + 0.433161i) q^{58} +(1.42595 + 4.38863i) q^{59} +(1.91690 + 4.04048i) q^{60} +(-2.83426 + 8.72296i) q^{61} +(-5.57813 + 5.18575i) q^{62} +(2.55813 + 1.30343i) q^{63} +(-5.99407 + 5.29822i) q^{64} +(-10.2386 - 4.65387i) q^{65} +(-0.211742 + 5.80858i) q^{66} +(11.3977 + 1.80522i) q^{67} +(1.19489 + 14.1566i) q^{68} +(-0.885086 - 1.21822i) q^{69} +(-7.38852 - 5.27631i) q^{70} +(-3.24029 + 4.45988i) q^{71} +(-1.76987 - 2.20625i) q^{72} +(2.13466 - 1.08767i) q^{73} +(-4.76648 + 13.0337i) q^{74} +(4.84910 - 1.21913i) q^{75} +(8.52976 - 10.1024i) q^{76} +(-5.35713 - 10.5140i) q^{77} +(6.98024 + 1.36791i) q^{78} +(-3.03872 - 2.20776i) q^{79} +(4.49988 + 7.72988i) q^{80} +(0.809017 - 0.587785i) q^{81} +(-4.98884 + 2.31704i) q^{82} +(1.25058 - 7.89584i) q^{83} +(5.31739 + 2.16732i) q^{84} +(15.7835 + 1.78261i) q^{85} +(6.70888 + 5.25811i) q^{86} +(-0.286031 + 0.561367i) q^{87} +(0.555087 + 11.6116i) q^{88} +(6.30465 + 2.04851i) q^{89} +(-2.80578 + 1.45864i) q^{90} +(-13.7337 + 4.46234i) q^{91} +(-1.96882 - 2.27892i) q^{92} +(-3.80814 - 3.80814i) q^{93} +(-11.3468 + 3.23487i) q^{94} +(-9.21361 - 11.5598i) q^{95} +(-3.89832 - 4.09915i) q^{96} +(-4.60222 + 0.728920i) q^{97} +(-1.74504 + 0.211554i) q^{98} -4.11001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

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