LMFDB - Embedded newform 756.2.bs.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(11,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13, 12]))

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

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

chi := DirichletCharacter("756.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bs (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	756.11
Dual form			756.2.bs.a.275.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41111 + 0.0937031i) q^{2} +(1.68184 - 0.414019i) q^{3} +(1.98244 - 0.264450i) q^{4} +(-2.78746 + 0.491505i) q^{5} +(-2.33446 + 0.741819i) q^{6} +(2.41910 + 1.07144i) q^{7} +(-2.77265 + 0.558927i) q^{8} +(2.65718 - 1.39263i) q^{9} +O(q^{10})$	\(q+(-1.41111 + 0.0937031i) q^{2} +(1.68184 - 0.414019i) q^{3} +(1.98244 - 0.264450i) q^{4} +(-2.78746 + 0.491505i) q^{5} +(-2.33446 + 0.741819i) q^{6} +(2.41910 + 1.07144i) q^{7} +(-2.77265 + 0.558927i) q^{8} +(2.65718 - 1.39263i) q^{9} +(3.88735 - 0.954760i) q^{10} +(-0.791789 + 4.49046i) q^{11} +(3.22466 - 1.26553i) q^{12} +(-4.82592 + 4.04942i) q^{13} +(-3.51400 - 1.28523i) q^{14} +(-4.48458 + 1.98070i) q^{15} +(3.86013 - 1.04851i) q^{16} -5.02863i q^{17} +(-3.61906 + 2.21413i) q^{18} +2.82448i q^{19} +(-5.39600 + 1.71152i) q^{20} +(4.51213 + 0.800431i) q^{21} +(0.696528 - 6.41071i) q^{22} +(-2.77708 + 2.33025i) q^{23} +(-4.43175 + 2.08796i) q^{24} +(2.82992 - 1.03001i) q^{25} +(6.43043 - 6.16637i) q^{26} +(3.89237 - 3.44230i) q^{27} +(5.07905 + 1.48433i) q^{28} +(-4.12541 + 4.91647i) q^{29} +(6.14262 - 3.21519i) q^{30} +(0.0834733 - 0.229341i) q^{31} +(-5.34881 + 1.84127i) q^{32} +(0.527473 + 7.88005i) q^{33} +(0.471198 + 7.09592i) q^{34} +(-7.26976 - 1.79759i) q^{35} +(4.89941 - 3.46349i) q^{36} +(-2.71086 + 4.69535i) q^{37} +(-0.264663 - 3.98564i) q^{38} +(-6.43988 + 8.80851i) q^{39} +(7.45395 - 2.92076i) q^{40} +(3.56309 + 4.24633i) q^{41} +(-6.44209 - 0.706693i) q^{42} +(-1.05467 - 2.89769i) q^{43} +(-0.382173 + 9.11145i) q^{44} +(-6.72230 + 5.18792i) q^{45} +(3.70040 - 3.54845i) q^{46} +(6.10689 - 2.22273i) q^{47} +(6.05802 - 3.36160i) q^{48} +(4.70405 + 5.18381i) q^{49} +(-3.89680 + 1.71862i) q^{50} +(-2.08195 - 8.45735i) q^{51} +(-8.49622 + 9.30395i) q^{52} +(3.70048 + 2.13647i) q^{53} +(-5.16999 + 5.22218i) q^{54} -12.9062i q^{55} +(-7.30617 - 1.61862i) q^{56} +(1.16939 + 4.75033i) q^{57} +(5.36070 - 7.32422i) q^{58} +(3.80592 - 3.19355i) q^{59} +(-8.36661 + 5.11256i) q^{60} +(5.81934 - 2.11807i) q^{61} +(-0.0962997 + 0.331446i) q^{62} +(7.92008 - 0.521910i) q^{63} +(7.37520 - 3.09942i) q^{64} +(11.4618 - 13.6596i) q^{65} +(-1.48271 - 11.0702i) q^{66} +(-11.9457 + 2.10634i) q^{67} +(-1.32982 - 9.96895i) q^{68} +(-3.70584 + 5.06887i) q^{69} +(10.4268 + 1.85539i) q^{70} +(3.81597 + 6.60946i) q^{71} +(-6.58905 + 5.34644i) q^{72} +(0.109243 + 0.189215i) q^{73} +(3.38534 - 6.87965i) q^{74} +(4.33303 - 2.90394i) q^{75} +(0.746934 + 5.59936i) q^{76} +(-6.72665 + 10.0145i) q^{77} +(8.26197 - 13.0332i) q^{78} +(-13.6186 - 2.40132i) q^{79} +(-10.2446 + 4.81996i) q^{80} +(5.12117 - 7.40092i) q^{81} +(-5.42579 - 5.65815i) q^{82} +(5.61528 + 4.71178i) q^{83} +(9.15670 + 0.393574i) q^{84} +(2.47160 + 14.0171i) q^{85} +(1.75978 + 3.99012i) q^{86} +(-4.90276 + 9.97671i) q^{87} +(-0.314485 - 12.8930i) q^{88} +13.9080i q^{89} +(8.99975 - 7.95060i) q^{90} +(-16.0130 + 4.62529i) q^{91} +(-4.88916 + 5.35397i) q^{92} +(0.0454372 - 0.420274i) q^{93} +(-8.40920 + 3.70874i) q^{94} +(-1.38825 - 7.87314i) q^{95} +(-8.23352 + 5.31123i) q^{96} +(14.8755 - 5.41422i) q^{97} +(-7.12366 - 6.87412i) q^{98} +(4.14962 + 13.0346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41111	+	0.0937031i	−0.997803	+	0.0662581i
$2$	−1.41111	+	0.0937031i	−0.997803	+	0.0662581i
$3$	1.68184	−	0.414019i	0.971011	−	0.239034i
$3$	1.68184	−	0.414019i	0.971011	−	0.239034i
$4$	1.98244	−	0.264450i	0.991220	−	0.132225i
$5$	−2.78746	+	0.491505i	−1.24659	+	0.219808i	−0.757739	−	0.652558i	$-0.773696\pi$
$5$	−2.78746	+	0.491505i	−1.24659	+	0.219808i	−0.488853	+	0.872366i	$0.662585\pi$
$6$	−2.33446	+	0.741819i	−0.953039	+	0.302846i
$7$	2.41910	+	1.07144i	0.914332	+	0.404964i
$7$	2.41910	+	1.07144i	0.914332	+	0.404964i
$8$	−2.77265	+	0.558927i	−0.980281	+	0.197611i
$9$	2.65718	−	1.39263i	0.885725	−	0.464210i
$10$	3.88735	−	0.954760i	1.22929	−	0.301922i
$11$	−0.791789	+	4.49046i	−0.238733	+	1.35392i	0.595873	+	0.803078i	$0.296806\pi$
$11$	−0.791789	+	4.49046i	−0.238733	+	1.35392i	−0.834607	+	0.550846i	$0.814305\pi$
$12$	3.22466	−	1.26553i	0.930879	−	0.365327i
$13$	−4.82592	+	4.04942i	−1.33847	+	1.12311i	−0.356451	+	0.934314i	$0.616013\pi$
$13$	−4.82592	+	4.04942i	−1.33847	+	1.12311i	−0.982017	+	0.188794i	$0.939542\pi$
$14$	−3.51400	−	1.28523i	−0.939155	−	0.343493i
$15$	−4.48458	+	1.98070i	−1.15791	+	0.511414i
$16$	3.86013	−	1.04851i	0.965033	−	0.262128i
$17$		−	5.02863i		−	1.21962i	−0.792547	−	0.609811i	$-0.791246\pi$
$17$		−	5.02863i		−	1.21962i	0.792547	−	0.609811i	$-0.208754\pi$
$18$	−3.61906	+	2.21413i	−0.853021	+	0.521876i
$19$			2.82448i			0.647980i	0.946060	+	0.323990i	$0.105024\pi$
$19$			2.82448i			0.647980i	−0.946060	+	0.323990i	$0.894976\pi$
$20$	−5.39600	+	1.71152i	−1.20658	+	0.382708i
$21$	4.51213	+	0.800431i	0.984627	+	0.174668i
$22$	0.696528	−	6.41071i	0.148500	−	1.36677i
$23$	−2.77708	+	2.33025i	−0.579061	+	0.485890i	−0.884639	−	0.466277i	$-0.845595\pi$
$23$	−2.77708	+	2.33025i	−0.579061	+	0.485890i	0.305577	+	0.952167i	$0.401151\pi$
$24$	−4.43175	+	2.08796i	−0.904628	+	0.426203i
$25$	2.82992	−	1.03001i	0.565983	−	0.206001i
$26$	6.43043	−	6.16637i	1.26111	−	1.20932i
$27$	3.89237	−	3.44230i	0.749087	−	0.662471i
$28$	5.07905	+	1.48433i	0.959851	+	0.280511i
$29$	−4.12541	+	4.91647i	−0.766069	+	0.912965i	−0.998215	−	0.0597156i	$-0.980981\pi$
$29$	−4.12541	+	4.91647i	−0.766069	+	0.912965i	0.232147	+	0.972681i	$0.425425\pi$
$30$	6.14262	−	3.21519i	1.12148	−	0.587011i
$31$	0.0834733	−	0.229341i	0.0149922	−	0.0411908i	−0.931971	−	0.362533i	$-0.881912\pi$
$31$	0.0834733	−	0.229341i	0.0149922	−	0.0411908i	0.946963	+	0.321343i	$0.104134\pi$
$32$	−5.34881	+	1.84127i	−0.945544	+	0.325493i
$33$	0.527473	+	7.88005i	0.0918213	+	1.37174i
$34$	0.471198	+	7.09592i	0.0808097	+	1.21694i
$35$	−7.26976	−	1.79759i	−1.22881	−	0.303848i
$36$	4.89941	−	3.46349i	0.816568	−	0.577249i
$37$	−2.71086	+	4.69535i	−0.445663	+	0.771910i	−0.998098	−	0.0616453i	$-0.980365\pi$
$37$	−2.71086	+	4.69535i	−0.445663	+	0.771910i	0.552435	+	0.833556i	$0.313699\pi$
$38$	−0.264663	−	3.98564i	−0.0429339	−	0.646556i
$39$	−6.43988	+	8.80851i	−1.03121	+	1.41049i
$40$	7.45395	−	2.92076i	1.17857	−	0.461813i
$41$	3.56309	+	4.24633i	0.556462	+	0.663165i	0.968794	−	0.247869i	$-0.0797301\pi$
$41$	3.56309	+	4.24633i	0.556462	+	0.663165i	−0.412332	+	0.911034i	$0.635286\pi$
$42$	−6.44209	−	0.706693i	−0.994037	−	0.109045i
$43$	−1.05467	−	2.89769i	−0.160836	−	0.441893i	0.832930	−	0.553378i	$-0.186662\pi$
$43$	−1.05467	−	2.89769i	−0.160836	−	0.441893i	−0.993766	+	0.111485i	$0.964439\pi$
$44$	−0.382173	+	9.11145i	−0.0576147	+	1.37360i
$45$	−6.72230	+	5.18792i	−1.00210	+	0.773369i
$46$	3.70040	−	3.54845i	0.545595	−	0.523190i
$47$	6.10689	−	2.22273i	0.890782	−	0.324218i	0.144229	−	0.989544i	$-0.453930\pi$
$47$	6.10689	−	2.22273i	0.890782	−	0.324218i	0.746553	+	0.665326i	$0.231708\pi$
$48$	6.05802	−	3.36160i	0.874400	−	0.485205i
$49$	4.70405	+	5.18381i	0.672008	+	0.740544i
$50$	−3.89680	+	1.71862i	−0.551090	+	0.243049i
$51$	−2.08195	−	8.45735i	−0.291531	−	1.18427i
$52$	−8.49622	+	9.30395i	−1.17821	+	1.29023i
$53$	3.70048	+	2.13647i	0.508300	+	0.293467i	0.732135	−	0.681160i	$-0.238524\pi$
$53$	3.70048	+	2.13647i	0.508300	+	0.293467i	−0.223834	+	0.974627i	$0.571857\pi$
$54$	−5.16999	+	5.22218i	−0.703547	+	0.710649i
$55$		−	12.9062i		−	1.74027i
$56$	−7.30617	−	1.61862i	−0.976328	−	0.216297i
$57$	1.16939	+	4.75033i	0.154889	+	0.629196i
$58$	5.36070	−	7.32422i	0.703894	−	0.961717i
$59$	3.80592	−	3.19355i	0.495489	−	0.415765i	−0.360500	−	0.932759i	$-0.617394\pi$
$59$	3.80592	−	3.19355i	0.495489	−	0.415765i	0.855989	+	0.516995i	$0.172949\pi$
$60$	−8.36661	+	5.11256i	−1.08012	+	0.660028i
$61$	5.81934	−	2.11807i	0.745091	−	0.271191i	0.0585522	−	0.998284i	$-0.481352\pi$
$61$	5.81934	−	2.11807i	0.745091	−	0.271191i	0.686538	+	0.727094i	$0.259129\pi$
$62$	−0.0962997	+	0.331446i	−0.0122301	+	0.0420937i
$63$	7.92008	−	0.521910i	0.997836	−	0.0657545i
$64$	7.37520	−	3.09942i	0.921900	−	0.387428i
$65$	11.4618	−	13.6596i	1.42166	−	1.69426i
$66$	−1.48271	−	11.0702i	−0.182508	−	1.36264i
$67$	−11.9457	+	2.10634i	−1.45940	+	0.257331i	−0.846312	−	0.532688i	$-0.821182\pi$
$67$	−11.9457	+	2.10634i	−1.45940	+	0.257331i	−0.613083	+	0.790018i	$0.710071\pi$
$68$	−1.32982	−	9.96895i	−0.161264	−	1.20891i
$69$	−3.70584	+	5.06887i	−0.446131	+	0.610220i
$70$	10.4268	+	1.85539i	1.24625	+	0.221762i
$71$	3.81597	+	6.60946i	0.452872	+	0.784398i	0.998563	−	0.0535887i	$-0.0170660\pi$
$71$	3.81597	+	6.60946i	0.452872	+	0.784398i	−0.545691	+	0.837987i	$0.683733\pi$
$72$	−6.58905	+	5.34644i	−0.776527	+	0.630084i
$73$	0.109243	+	0.189215i	0.0127860	+	0.0221460i	0.872348	−	0.488886i	$-0.162597\pi$
$73$	0.109243	+	0.189215i	0.0127860	+	0.0221460i	−0.859562	+	0.511032i	$0.829263\pi$
$74$	3.38534	−	6.87965i	0.393538	−	0.799743i
$75$	4.33303	−	2.90394i	0.500335	−	0.335319i
$76$	0.746934	+	5.59936i	0.0856792	+	0.642291i
$77$	−6.72665	+	10.0145i	−0.766573	+	1.14126i
$78$	8.26197	−	13.0332i	0.935484	−	1.47572i
$79$	−13.6186	−	2.40132i	−1.53221	−	0.270170i	−0.656991	−	0.753898i	$-0.728171\pi$
$79$	−13.6186	−	2.40132i	−1.53221	−	0.270170i	−0.875218	+	0.483728i	$0.839282\pi$
$80$	−10.2446	+	4.81996i	−1.14538	+	0.538888i
$81$	5.12117	−	7.40092i	0.569019	−	0.822324i
$82$	−5.42579	−	5.65815i	−0.599179	−	0.624838i
$83$	5.61528	+	4.71178i	0.616357	+	0.517185i	0.896656	−	0.442728i	$-0.145989\pi$
$83$	5.61528	+	4.71178i	0.616357	+	0.517185i	−0.280299	+	0.959913i	$0.590434\pi$
$84$	9.15670	+	0.393574i	0.999078	+	0.0429425i
$85$	2.47160	+	14.0171i	0.268082	+	1.52037i
$86$	1.75978	+	3.99012i	0.189762	+	0.430265i
$87$	−4.90276	+	9.97671i	−0.525631	+	1.06962i
$88$	−0.314485	−	12.8930i	−0.0335242	−	1.37440i
$89$			13.9080i			1.47425i	0.675758	+	0.737123i	$0.263816\pi$
$89$			13.9080i			1.47425i	−0.675758	+	0.737123i	$0.736184\pi$
$90$	8.99975	−	7.95060i	0.948657	−	0.838067i
$91$	−16.0130	+	4.62529i	−1.67862	+	0.484862i
$92$	−4.88916	+	5.35397i	−0.509730	+	0.558190i
$93$	0.0454372	−	0.420274i	0.00471162	−	0.0435804i
$94$	−8.40920	+	3.70874i	−0.867342	+	0.382527i
$95$	−1.38825	−	7.87314i	−0.142431	−	0.807767i
$96$	−8.23352	+	5.31123i	−0.840330	+	0.542075i
$97$	14.8755	−	5.41422i	1.51037	−	0.549731i	0.551651	−	0.834075i	$-0.313998\pi$
$97$	14.8755	−	5.41422i	1.51037	−	0.549731i	0.958722	+	0.284344i	$0.0917757\pi$
$98$	−7.12366	−	6.87412i	−0.719598	−	0.694391i
$99$	4.14962	+	13.0346i	0.417052	+	1.31003i
$100$	5.33775	−	2.79029i	0.533775	−	0.279029i
$101$	1.49178	−	1.77783i	0.148438	−	0.176901i	−0.686702	−	0.726939i	$-0.740942\pi$
$101$	1.49178	−	1.77783i	0.148438	−	0.176901i	0.835140	+	0.550038i	$0.185387\pi$
$102$	3.73033	+	11.7391i	0.369358	+	1.16235i
$103$	10.9914	−	1.93809i	1.08302	−	0.190965i	0.396469	−	0.918048i	$-0.370236\pi$
$103$	10.9914	−	1.93809i	1.08302	−	0.190965i	0.686550	+	0.727083i	$0.259124\pi$
$104$	11.1173	−	13.9250i	1.09014	−	1.36546i
$105$	−12.9708	−	0.0134385i	−1.26582	−	0.00131146i
$106$	−5.42197	−	2.66805i	−0.526628	−	0.259144i
$107$	−4.36358	−	7.55793i	−0.421843	−	0.730653i	0.574277	−	0.818661i	$-0.305283\pi$
$107$	−4.36358	−	7.55793i	−0.421843	−	0.730653i	−0.996120	+	0.0880080i	$0.971950\pi$
$108$	6.80608	−	7.85349i	0.654915	−	0.755703i
$109$	−5.15007	+	8.92019i	−0.493287	+	0.854399i	−0.999970	−	0.00773376i	$-0.997538\pi$
$109$	−5.15007	+	8.92019i	−0.493287	+	0.854399i	0.506683	+	0.862133i	$0.330872\pi$
$110$	1.20935	+	18.2120i	0.115307	+	1.73644i
$111$	−2.61527	+	9.01917i	−0.248231	+	0.856062i
$112$	10.4614	+	1.59943i	0.988514	+	0.151132i
$113$	−5.39433	+	14.8208i	−0.507456	+	1.39422i	0.376397	+	0.926458i	$0.377163\pi$
$113$	−5.39433	+	14.8208i	−0.507456	+	1.39422i	−0.883853	+	0.467765i	$0.845059\pi$
$114$	−2.09525	−	6.59364i	−0.196238	−	0.617551i
$115$	6.59568	−	7.86043i	0.615051	−	0.732989i
$116$	−6.87821	+	10.8376i	−0.638626	+	1.00624i
$117$	−7.18396	+	17.4807i	−0.664158	+	1.61610i
$118$	−5.07131	+	4.86306i	−0.466852	+	0.447681i
$119$	5.38785	−	12.1647i	0.493903	−	1.11514i
$120$	11.3271	−	7.99834i	1.03402	−	0.730145i
$121$	−9.20067	−	3.34877i	−0.836425	−	0.304434i
$122$	−8.01324	+	3.53411i	−0.725485	+	0.319963i
$123$	7.75062	+	5.66646i	0.698849	+	0.510927i
$124$	0.104832	−	0.476729i	0.00941415	−	0.0428115i
$125$	4.87424	−	2.81414i	0.435965	−	0.251705i
$126$	−11.1272	+	1.47861i	−0.991286	+	0.131725i
$127$	4.65184	+	2.68574i	0.412784	+	0.238321i	0.691985	−	0.721912i	$-0.256736\pi$
$127$	4.65184	+	2.68574i	0.412784	+	0.238321i	−0.279201	+	0.960233i	$0.590070\pi$
$128$	−10.1168	+	5.06469i	−0.894204	+	0.447660i
$129$	−2.97349	−	4.43679i	−0.261801	−	0.390638i
$130$	−14.8938	+	20.3491i	−1.30627	+	1.78474i
$131$	−2.23040	+	1.87153i	−0.194871	+	0.163516i	−0.735002	−	0.678064i	$-0.762819\pi$
$131$	−2.23040	+	1.87153i	−0.194871	+	0.163516i	0.540131	+	0.841581i	$0.318375\pi$
$132$	3.12956	+	15.4822i	0.272393	+	1.34756i
$133$	−3.02625	+	6.83269i	−0.262409	+	0.592469i
$134$	16.6592	−	4.09162i	1.43914	−	0.353462i
$135$	−9.15794	+	11.5084i	−0.788190	+	0.990486i
$136$	2.81064	+	13.9426i	0.241010	+	1.19557i
$137$	−7.43578	−	20.4296i	−0.635281	−	1.74542i	−0.666064	−	0.745895i	$-0.732022\pi$
$137$	−7.43578	−	20.4296i	−0.635281	−	1.74542i	0.0307822	−	0.999526i	$-0.490200\pi$
$138$	4.75436	−	7.49996i	0.404718	−	0.638439i
$139$	−13.9079	+	2.45234i	−1.17965	+	0.208005i	−0.728885	−	0.684636i	$-0.759961\pi$
$139$	−13.9079	+	2.45234i	−1.17965	+	0.208005i	−0.450769	+	0.892641i	$0.648850\pi$
$140$	−14.8872	−	1.64112i	−1.25820	−	0.138700i
$141$	9.35057	−	6.26665i	0.787460	−	0.527747i
$142$	−6.00406	−	8.96907i	−0.503850	−	0.752668i
$143$	−14.3627	−	24.8769i	−1.20107	−	2.08031i
$144$	8.79686	−	8.16181i	0.733072	−	0.680151i
$145$	9.08295	−	15.7321i	0.754298	−	1.30648i
$146$	−0.171884	−	0.256766i	−0.0142252	−	0.0212501i
$147$	10.0577	+	6.77077i	0.829542	+	0.558444i
$148$	−4.13243	+	10.0251i	−0.339684	+	0.824060i
$149$	3.79088	−	10.4154i	0.310561	−	0.853259i	−0.681983	−	0.731368i	$-0.738882\pi$
$149$	3.79088	−	10.4154i	0.310561	−	0.853259i	0.992544	−	0.121891i	$-0.0388958\pi$
$150$	−5.84225	+	4.50379i	−0.477018	+	0.367733i
$151$	3.70958	+	0.654099i	0.301881	+	0.0532298i	0.322537	−	0.946557i	$-0.395464\pi$
$151$	3.70958	+	0.654099i	0.301881	+	0.0532298i	−0.0206557	+	0.999787i	$0.506575\pi$
$152$	−1.57868	−	7.83130i	−0.128048	−	0.635203i
$153$	−7.00301	−	13.3619i	−0.566160	−	1.08025i
$154$	8.55363	−	14.7618i	0.689271	−	1.18954i
$155$	−0.119956	+	0.680307i	−0.00963514	+	0.0546436i
$156$	−10.4373	+	19.1654i	−0.835650	+	1.53446i
$157$	1.85193	−	1.55396i	0.147800	−	0.124019i	−0.565889	−	0.824481i	$-0.691467\pi$
$157$	1.85193	−	1.55396i	0.147800	−	0.124019i	0.713690	+	0.700462i	$0.247023\pi$
$158$	19.4423	+	2.11242i	1.54674	+	0.168055i
$159$	7.10816	+	2.06114i	0.563714	+	0.163459i
$160$	14.0046	−	7.76143i	1.10716	−	0.613595i
$161$	−9.21473	+	2.66163i	−0.726223	+	0.209766i
$162$	−6.53303	+	10.9234i	−0.513283	+	0.858219i
$163$	18.5877	−	10.7316i	1.45590	−	0.840565i	0.457096	−	0.889417i	$-0.348890\pi$
$163$	18.5877	−	10.7316i	1.45590	−	0.840565i	0.998806	+	0.0488519i	$0.0155562\pi$
$164$	8.18656	+	7.47583i	0.639263	+	0.583764i
$165$	−5.34340	−	21.7061i	−0.415983	−	1.68982i
$166$	−8.36526	−	6.12265i	−0.649270	−	0.475210i
$167$	−6.96060	−	2.53345i	−0.538627	−	0.196044i	0.0583590	−	0.998296i	$-0.481413\pi$
$167$	−6.96060	−	2.53345i	−0.538627	−	0.196044i	−0.596986	+	0.802251i	$0.703635\pi$
$168$	−12.9579	+	0.302636i	−0.999727	+	0.0233488i
$169$	4.63420	−	26.2819i	0.356477	−	2.02168i
$170$	−4.80113	−	19.5480i	−0.368230	−	1.49927i
$171$	3.93345	+	7.50514i	0.300799	+	0.573933i
$172$	−2.85712	−	5.46558i	−0.217853	−	0.416747i
$173$	2.31862	−	2.76322i	0.176281	−	0.210084i	−0.670668	−	0.741758i	$-0.733992\pi$
$173$	2.31862	−	2.76322i	0.176281	−	0.210084i	0.846949	+	0.531674i	$0.178437\pi$
$174$	5.98347	−	14.5376i	0.453606	−	1.10209i
$175$	7.94942	+	0.540390i	0.600920	+	0.0408497i
$176$	1.65189	+	18.1640i	0.124516	+	1.36916i
$177$	5.07877	−	6.94676i	0.381743	−	0.522151i
$178$	−1.30322	−	19.6257i	−0.0976808	−	1.47101i
$179$	13.1303			0.981406			0.490703	−	0.871327i	$-0.336740\pi$
$179$	13.1303			0.981406			0.490703	+	0.871327i	$0.336740\pi$
$180$	−11.9546	+	12.0624i	−0.891044	+	0.899082i
$181$	1.35921	−	2.35422i	0.101029	−	0.174988i	−0.811080	−	0.584936i	$-0.801120\pi$
$181$	1.35921	−	2.35422i	0.101029	−	0.174988i	0.912109	+	0.409948i	$0.134453\pi$
$182$	22.1627	−	8.02725i	1.64281	−	0.595019i
$183$	8.91029	−	5.97157i	0.658668	−	0.441431i
$184$	6.39744	−	8.01315i	0.471626	−	0.590737i
$185$	5.24864	−	14.4205i	0.385888	−	1.06022i
$186$	−0.0247357	+	0.597309i	−0.00181371	+	0.0437968i
$187$	22.5808	+	3.98161i	1.65127	+	0.291164i
$188$	11.5187	−	6.02139i	0.840091	−	0.439155i
$189$	13.1042	−	4.15683i	0.953192	−	0.302365i
$190$	2.69670	+	10.9797i	0.195639	+	0.796555i
$191$	0.228927	−	1.29831i	0.0165646	−	0.0939425i	−0.975405	−	0.220422i	$-0.929257\pi$
$191$	0.228927	−	1.29831i	0.0165646	−	0.0939425i	0.991969	+	0.126479i	$0.0403677\pi$
$192$	11.1207	−	8.26621i	0.802567	−	0.596562i
$193$	−6.10853	−	2.22332i	−0.439702	−	0.160038i	0.112677	−	0.993632i	$-0.464057\pi$
$193$	−6.10853	−	2.22332i	−0.439702	−	0.160038i	−0.552379	+	0.833593i	$0.686280\pi$
$194$	−20.4835	+	9.03392i	−1.47063	+	0.648598i
$195$	13.6215	−	27.7186i	0.975457	−	1.98497i
$196$	10.6964	+	9.03260i	0.764026	+	0.645186i
$197$	3.27265	+	1.88947i	0.233167	+	0.134619i	0.612032	−	0.790833i	$-0.290352\pi$
$197$	3.27265	+	1.88947i	0.233167	+	0.134619i	−0.378865	+	0.925452i	$0.623686\pi$
$198$	−7.07693	−	18.0044i	−0.502936	−	1.27952i
$199$		−	5.08772i		−	0.360659i	−0.983606	−	0.180329i	$-0.942284\pi$
$199$		−	5.08772i		−	0.360659i	0.983606	−	0.180329i	$-0.0577163\pi$
$200$	−7.27067	+	4.43756i	−0.514114	+	0.313783i
$201$	−19.2186	+	8.48827i	−1.35558	+	0.598716i
$202$	−1.93847	+	2.64849i	−0.136390	+	0.186347i
$203$	−15.2474	+	7.47330i	−1.07016	+	0.524523i
$204$	−6.36388	−	16.2156i	−0.445561	−	1.13532i
$205$	−12.0191	−	10.0852i	−0.839449	−	0.704382i
$206$	−15.3285	+	3.76478i	−1.06799	+	0.262304i
$207$	−4.13402	+	10.0593i	−0.287334	+	0.699171i
$208$	−14.3828	+	20.6913i	−0.997268	+	1.43469i
$209$	−12.6832	−	2.23639i	−0.877316	−	0.154695i
$210$	18.3045	−	1.19644i	1.26313	−	0.0825623i
$211$	4.89377	−	13.4455i	0.336901	−	0.925629i	−0.649367	−	0.760476i	$-0.724966\pi$
$211$	4.89377	−	13.4455i	0.336901	−	0.925629i	0.986268	−	0.165153i	$-0.0528119\pi$
$212$	7.90097	+	3.25684i	0.542641	+	0.223681i
$213$	9.15430	+	9.53617i	0.627242	+	0.653407i
$214$	6.86567	+	10.2562i	0.469327	+	0.701097i
$215$	4.36409	+	7.55882i	0.297628	+	0.515507i
$216$	−8.86820	+	11.7199i	−0.603404	+	0.797435i
$217$	0.447654	−	0.465361i	0.0303887	−	0.0315908i
$218$	6.43145	−	13.0699i	0.435593	−	0.885206i
$219$	0.262069	+	0.273001i	0.0177090	+	0.0184477i
$220$	−3.41303	−	25.5857i	−0.230107	−	1.72499i
$221$	20.3630	+	24.2677i	1.36977	+	1.63242i
$222$	2.84530	−	12.9721i	0.190964	−	0.870628i
$223$	−18.8055	−	3.31591i	−1.25931	−	0.222050i	−0.496135	−	0.868245i	$-0.665248\pi$
$223$	−18.8055	−	3.31591i	−1.25931	−	0.222050i	−0.763172	+	0.646195i	$0.776359\pi$
$224$	−14.9121	−	1.27670i	−0.996355	−	0.0853029i
$225$	6.08517	−	6.67793i	0.405678	−	0.445195i
$226$	6.22322	−	21.4192i	0.413962	−	1.42478i
$227$	2.93535	−	16.6472i	0.194826	−	1.10491i	−0.717841	−	0.696207i	$-0.754869\pi$
$227$	2.93535	−	16.6472i	0.194826	−	1.10491i	0.912667	−	0.408705i	$-0.134020\pi$
$228$	3.57447	+	9.10799i	0.236725	+	0.603191i
$229$	−7.73223	−	2.81430i	−0.510960	−	0.185974i	0.0736568	−	0.997284i	$-0.476533\pi$
$229$	−7.73223	−	2.81430i	−0.510960	−	0.185974i	−0.584617	+	0.811309i	$0.698755\pi$
$230$	−8.57066	+	11.7099i	−0.565133	+	0.772130i
$231$	−7.16696	+	19.6278i	−0.471551	+	1.29141i
$232$	8.69037	−	15.9375i	0.570551	−	1.04635i
$233$	20.0364	+	11.5680i	1.31263	+	0.757845i	0.982530	−	0.186102i	$-0.0595856\pi$
$233$	20.0364	+	11.5680i	1.31263	+	0.757845i	0.330096	+	0.943947i	$0.392919\pi$
$234$	8.49933	−	25.3403i	0.555619	−	1.65655i
$235$	−15.9303	+	9.19734i	−1.03918	+	0.599969i
$236$	6.70048	−	7.33749i	0.436164	−	0.477630i
$237$	−23.8985	+	1.59971i	−1.55237	+	0.103912i
$238$	−6.46295	+	17.6706i	−0.418931	+	1.14541i
$239$	−0.924569	−	5.24349i	−0.0598054	−	0.339173i	0.940194	−	0.340641i	$-0.110644\pi$
$239$	−0.924569	−	5.24349i	−0.0598054	−	0.339173i	−0.999999	+	0.00146754i	$0.999533\pi$
$240$	−15.2343	+	12.3479i	−0.983369	+	0.797053i
$241$	10.2542	−	3.73221i	0.660528	−	0.240413i	0.0100638	−	0.999949i	$-0.496797\pi$
$241$	10.2542	−	3.73221i	0.660528	−	0.240413i	0.650464	+	0.759537i	$0.274574\pi$
$242$	13.2969	+	3.86334i	0.854758	+	0.248345i
$243$	5.54887	−	14.5674i	0.355960	−	0.934501i
$244$	10.9764	−	5.73787i	0.702690	−	0.367329i
$245$	−15.6602	−	12.1376i	−1.00050	−	0.775444i
$246$	−11.4679	−	7.26972i	−0.731167	−	0.463500i
$247$	−11.4375	−	13.6307i	−0.727752	−	0.867301i
$248$	−0.103257	+	0.682538i	−0.00655685	+	0.0433412i
$249$	11.3948	+	5.59962i	0.722114	+	0.354862i
$250$	−6.61437	+	4.42778i	−0.418330	+	0.280038i
$251$	3.87450	−	6.71082i	0.244556	−	0.423583i	−0.717451	−	0.696609i	$-0.754691\pi$
$251$	3.87450	−	6.71082i	0.244556	−	0.423583i	0.962007	+	0.273026i	$0.0880245\pi$
$252$	15.5631	−	3.12912i	0.980380	−	0.197116i
$253$	−8.26502	−	14.3154i	−0.519617	−	0.900003i
$254$	−6.81591	−	3.35398i	−0.427668	−	0.210447i
$255$	9.96019	+	22.5513i	0.623731	+	1.41222i
$256$	13.8012	−	8.09479i	0.862578	−	0.505924i
$257$	−0.0307503	+	0.0844856i	−0.00191815	+	0.00527007i	−0.940648	−	0.339384i	$-0.889781\pi$
$257$	−0.0307503	+	0.0844856i	−0.00191815	+	0.00527007i	0.938730	+	0.344654i	$0.112004\pi$
$258$	4.61165	+	5.98216i	0.287109	+	0.372433i
$259$	−11.5886	+	8.45399i	−0.720080	+	0.525305i
$260$	19.1100	−	30.1104i	1.18515	−	1.86737i
$261$	−4.11512	+	18.8091i	−0.254719	+	1.16425i
$262$	2.97197	−	2.84992i	0.183609	−	0.176069i
$263$	−1.47597	−	1.23849i	−0.0910122	−	0.0763683i	0.596146	−	0.802876i	$-0.296698\pi$
$263$	−1.47597	−	1.23849i	−0.0910122	−	0.0763683i	−0.687159	+	0.726507i	$0.741142\pi$
$264$	−5.86688	−	21.5538i	−0.361081	−	1.32655i
$265$	−11.3651	−	4.13654i	−0.698150	−	0.254106i
$266$	3.63011	−	9.92522i	0.222576	−	0.608554i
$267$	5.75819	+	23.3911i	0.352395	+	1.43151i
$268$	−23.1245	+	7.33473i	−1.41256	+	0.448040i
$269$	−7.40586	−	4.27577i	−0.451543	−	0.260699i	0.256939	−	0.966428i	$-0.417286\pi$
$269$	−7.40586	−	4.27577i	−0.451543	−	0.260699i	−0.708482	+	0.705729i	$0.750620\pi$
$270$	11.8444	−	17.0977i	0.720830	−	1.04053i
$271$	−12.3290	+	7.11816i	−0.748934	+	0.432397i	−0.825309	−	0.564682i	$-0.808999\pi$
$271$	−12.3290	+	7.11816i	−0.748934	+	0.432397i	0.0763747	+	0.997079i	$0.475665\pi$
$272$	−5.27257	−	19.4112i	−0.319697	−	1.17697i
$273$	−25.0164	+	14.4087i	−1.51406	+	0.872055i
$274$	12.4070	+	28.1316i	0.749534	+	1.69949i
$275$	2.38450	+	13.5232i	0.143791	+	0.815478i
$276$	−6.00614	+	11.0287i	−0.361527	+	0.663852i
$277$	4.50362	+	3.77898i	0.270596	+	0.227057i	0.767981	−	0.640473i	$-0.221262\pi$
$277$	4.50362	+	3.77898i	0.270596	+	0.227057i	−0.497384	+	0.867530i	$0.665706\pi$
$278$	19.3958	−	4.76373i	1.16328	−	0.285709i
$279$	−0.0975835	−	0.725646i	−0.00584217	−	0.0434433i
$280$	21.1612	+	0.920821i	1.26463	+	0.0550296i
$281$	−2.18034	−	5.99042i	−0.130068	−	0.357359i	0.857515	−	0.514460i	$-0.172007\pi$
$281$	−2.18034	−	5.99042i	−0.130068	−	0.357359i	−0.987583	+	0.157101i	$0.949785\pi$
$282$	−12.6074	+	9.71908i	−0.750762	+	0.578763i
$283$	−23.6030	+	4.16185i	−1.40306	+	0.247396i	−0.823398	−	0.567464i	$-0.807925\pi$
$283$	−23.6030	+	4.16185i	−1.40306	+	0.247396i	−0.579657	+	0.814861i	$0.696813\pi$
$284$	9.31280	+	12.0937i	0.552613	+	0.717630i
$285$	−5.59444	−	12.6666i	−0.331386	−	0.750305i
$286$	22.5983	+	33.7581i	1.33626	+	1.99616i
$287$	4.06980	+	14.0899i	0.240233	+	0.831700i
$288$	−11.6485	+	12.3415i	−0.686396	+	0.727228i
$289$	−8.28708			−0.487476
$290$	−11.3429	+	23.0508i	−0.666076	+	1.35359i
$291$	22.7766	−	15.2646i	1.33519	−	0.894826i
$292$	0.266606	+	0.346218i	0.0156020	+	0.0202609i
$293$	18.1126	−	3.19374i	1.05815	−	0.186580i	0.382614	−	0.923908i	$-0.375024\pi$
$293$	18.1126	−	3.19374i	1.05815	−	0.186580i	0.675535	+	0.737328i	$0.263913\pi$
$294$	−14.8269	−	8.61185i	−0.864721	−	0.502253i
$295$	−9.03923	+	10.7725i	−0.526284	+	0.627201i
$296$	4.89191	−	14.5337i	0.284337	−	0.844756i
$297$	12.3756	+	20.2041i	0.718104	+	1.17236i
$298$	−4.37338	+	15.0524i	−0.253343	+	0.871961i
$299$	3.96580	−	22.4912i	0.229348	−	1.30070i
$300$	7.82201	−	6.90276i	0.451604	−	0.398531i
$301$	0.553332	−	8.13980i	0.0318935	−	0.469170i
$302$	−5.29590	−	0.575404i	−0.304745	−	0.0331108i
$303$	1.77288	−	3.60766i	0.101849	−	0.207254i
$304$	2.96150	+	10.9029i	0.169854	+	0.625322i
$305$	−15.1802	+	8.76428i	−0.869214	+	0.501841i
$306$	11.1340	+	18.1989i	0.636491	+	1.04036i
$307$	14.2482	−	8.22620i	0.813188	−	0.469494i	−0.0348740	−	0.999392i	$-0.511103\pi$
$307$	14.2482	−	8.22620i	0.813188	−	0.469494i	0.848062	+	0.529898i	$0.177770\pi$
$308$	−10.6868	+	21.6320i	−0.608939	+	1.23260i
$309$	17.6834	−	7.81022i	1.00598	−	0.444308i
$310$	0.105524	−	0.971225i	0.00599339	−	0.0551619i
$311$	3.58674	+	20.3414i	0.203385	+	1.15345i	0.899961	+	0.435971i	$0.143595\pi$
$311$	3.58674	+	20.3414i	0.203385	+	1.15345i	−0.696576	+	0.717483i	$0.745294\pi$
$312$	12.9322	−	28.0224i	0.732144	−	1.58645i
$313$	21.4155	+	17.9697i	1.21048	+	1.01571i	0.999268	+	0.0382679i	$0.0121840\pi$
$313$	21.4155	+	17.9697i	1.21048	+	1.01571i	0.211208	+	0.977441i	$0.432260\pi$
$314$	−2.46766	+	2.36633i	−0.139258	+	0.133540i
$315$	−21.8204	+	5.34756i	−1.22944	+	0.301301i
$316$	−27.6330	−	1.15905i	−1.55448	−	0.0652014i
$317$	−5.73785	−	15.7646i	−0.322270	−	0.885428i	−0.990005	−	0.141030i	$-0.954959\pi$
$317$	−5.73785	−	15.7646i	−0.322270	−	0.885428i	0.667736	−	0.744398i	$-0.267264\pi$
$318$	−10.2235	−	2.24243i	−0.573306	−	0.125749i
$319$	−18.8107	−	22.4178i	−1.05320	−	1.25515i
$320$	−19.0347	+	12.2645i	−1.06407	+	0.685605i
$321$	−10.4680	−	10.9046i	−0.584265	−	0.608637i
$322$	12.7536	−	4.61929i	0.710728	−	0.257423i
$323$	14.2033			0.790290
$324$	8.19524	−	16.0262i	0.455291	−	0.890343i
$325$	−9.48601	+	16.4302i	−0.526189	+	0.911386i
$326$	−25.2236	+	16.8852i	−1.39701	+	0.935184i
$327$	−4.96847	+	17.1346i	−0.274757	+	0.947543i
$328$	−12.2526	−	9.78208i	−0.676537	−	0.540125i
$329$	17.1547	+	1.16615i	0.945768	+	0.0642919i
$330$	9.57403	+	30.1289i	0.527033	+	1.65854i
$331$	9.62889	+	26.4552i	0.529252	+	1.45411i	0.859954	+	0.510372i	$0.170492\pi$
$331$	9.62889	+	26.4552i	0.529252	+	1.45411i	−0.330702	+	0.943735i	$0.607286\pi$
$332$	12.3780	+	7.85585i	0.679330	+	0.431146i
$333$	−0.664358	+	16.2516i	−0.0364066	+	0.890581i
$334$	10.0595	+	2.92274i	0.550433	+	0.159925i
$335$	32.2628	−	11.7427i	1.76271	−	0.641573i
$336$	18.2567	−	1.64125i	0.995983	−	0.0895375i
$337$	−20.2949	+	17.0295i	−1.10553	+	0.927654i	−0.997785	−	0.0665243i	$-0.978809\pi$
$337$	−20.2949	+	17.0295i	−1.10553	+	0.927654i	−0.107750	+	0.994178i	$0.534365\pi$
$338$	−4.07666	+	37.5207i	−0.221741	+	2.04086i
$339$	−2.93631	+	27.1596i	−0.159478	+	1.47511i
$340$	8.60661	+	27.1345i	0.466759	+	1.47157i
$341$	0.963753	+	0.556423i	0.0521901	+	0.0301320i
$342$	−6.25377	−	10.2220i	−0.338165	−	0.552741i
$343$	5.82544	+	17.5802i	0.314544	+	0.949243i
$344$	4.54384	+	7.44479i	0.244987	+	0.401396i
$345$	7.83852	−	15.9507i	0.422012	−	0.858759i
$346$	−3.01289	+	4.11646i	−0.161974	+	0.221302i
$347$	−31.4606	−	11.4507i	−1.68889	−	0.614706i	−0.694406	−	0.719583i	$-0.744333\pi$
$347$	−31.4606	−	11.4507i	−1.68889	−	0.614706i	−0.994485	+	0.104877i	$0.966555\pi$
$348$	−7.08109	+	21.0748i	−0.379586	+	1.12973i
$349$	24.0799	+	20.2054i	1.28897	+	1.08157i	0.991941	+	0.126704i	$0.0404398\pi$
$349$	24.0799	+	20.2054i	1.28897	+	1.08157i	0.297028	+	0.954869i	$0.404005\pi$
$350$	−11.2681	−	0.0176624i	−0.602306	−	0.000944095i
$351$	−4.84492	+	32.3741i	−0.258603	+	1.72800i
$352$	−4.03301	−	25.4765i	−0.214960	−	1.35790i
$353$	−1.37068	−	3.76591i	−0.0729540	−	0.200439i	0.897856	−	0.440289i	$-0.145124\pi$
$353$	−1.37068	−	3.76591i	−0.0729540	−	0.200439i	−0.970810	+	0.239850i	$0.922902\pi$
$354$	−6.51574	+	10.2785i	−0.346308	+	0.546297i
$355$	−13.8855	−	16.5480i	−0.736964	−	0.878279i
$356$	3.67797	+	27.5718i	0.194932	+	1.46130i
$357$	4.02507	−	22.6898i	0.213029	−	1.20087i
$358$	−18.5283	+	1.23035i	−0.979249	+	0.0650261i
$359$	1.98399			0.104711			0.0523556	−	0.998629i	$-0.483327\pi$
$359$	1.98399			0.104711			0.0523556	+	0.998629i	$0.483327\pi$
$360$	15.7389	−	18.1416i	0.829514	−	0.956145i
$361$	11.0223			0.580121
$362$	−1.69739	+	3.44942i	−0.0892130	+	0.181297i
$363$	−16.8605	−	1.82284i	−0.884948	−	0.0956745i
$364$	−30.5217	+	13.4040i	−1.59977	+	0.702561i
$365$	−0.397512	−	0.473737i	−0.0208067	−	0.0247965i
$366$	−12.0138	+	9.26144i	−0.627972	+	0.484103i
$367$	−5.89739	−	1.03987i	−0.307841	−	0.0542808i	0.0175934	−	0.999845i	$-0.494400\pi$
$367$	−5.89739	−	1.03987i	−0.307841	−	0.0542808i	−0.325435	+	0.945564i	$0.605511\pi$
$368$	−8.27661	+	11.9069i	−0.431448	+	0.620688i
$369$	15.3813	+	6.32118i	0.800720	+	0.329067i
$370$	−6.05514	+	20.8407i	−0.314792	+	1.08346i
$371$	6.66273	+	9.13317i	0.345912	+	0.474170i
$372$	−0.0210650	−	0.845184i	−0.00109217	−	0.0438208i
$373$	1.76707	+	10.0215i	0.0914953	+	0.518895i	0.995765	+	0.0919340i	$0.0293049\pi$
$373$	1.76707	+	10.0215i	0.0914953	+	0.518895i	−0.904270	+	0.426961i	$0.859584\pi$
$374$	−32.2370	−	3.50258i	−1.66694	−	0.181114i
$375$	7.03258	−	6.75097i	0.363161	−	0.348618i
$376$	−15.6899	+	9.57616i	−0.809147	+	0.493853i
$377$		−	40.4320i		−	2.08235i
$378$	−18.1019	+	7.09364i	−0.931063	+	0.364857i
$379$		−	5.84001i		−	0.299981i	−0.988687	−	0.149990i	$-0.952076\pi$
$379$		−	5.84001i		−	0.299981i	0.988687	−	0.149990i	$-0.0479243\pi$
$380$	−4.83417	−	15.2409i	−0.247987	−	0.781842i
$381$	8.93561	+	2.59104i	0.457785	+	0.132743i
$382$	−0.201385	+	1.85351i	−0.0103037	+	0.0948336i
$383$	−0.860486	−	4.88006i	−0.0439688	−	0.249359i	0.954899	−	0.296931i	$-0.0959630\pi$
$383$	−0.860486	−	4.88006i	−0.0439688	−	0.249359i	−0.998868	+	0.0475713i	$0.984852\pi$
$384$	−14.9179	+	12.7065i	−0.761276	+	0.648428i
$385$	13.8281	−	31.2212i	0.704746	−	1.59118i
$386$	8.82812	+	2.56496i	0.449339	+	0.130553i
$387$	−6.83785	−	6.23090i	−0.347588	−	0.316734i
$388$	28.0579	−	14.6672i	1.42442	−	0.744613i
$389$	9.62113	+	1.69646i	0.487811	+	0.0860142i	0.412143	−	0.911119i	$-0.364780\pi$
$389$	9.62113	+	1.69646i	0.487811	+	0.0860142i	0.0756671	+	0.997133i	$0.475891\pi$
$390$	−16.6241	+	40.3903i	−0.841793	+	2.04524i
$391$	11.7179	+	13.9649i	0.592602	+	0.706235i
$392$	−15.9401	−	11.7437i	−0.805095	−	0.593145i
$393$	−2.97633	+	4.07104i	−0.150136	+	0.205357i
$394$	−4.79510	−	2.35958i	−0.241574	−	0.118874i
$395$	39.1416			1.96943
$396$	11.6734	+	24.7430i	0.586609	+	1.24338i
$397$	−6.58162			−0.330322			−0.165161	−	0.986267i	$-0.552814\pi$
$397$	−6.58162			−0.330322			−0.165161	+	0.986267i	$0.552814\pi$
$398$	0.476735	+	7.17931i	0.0238965	+	0.359866i
$399$	−2.26080	+	12.7444i	−0.113182	+	0.638019i
$400$	9.84388	−	6.94316i	0.492194	−	0.347158i
$401$	19.2827	+	22.9802i	0.962930	+	1.14758i	0.989000	+	0.147916i	$0.0472564\pi$
$401$	19.2827	+	22.9802i	0.962930	+	1.14758i	−0.0260696	+	0.999660i	$0.508299\pi$
$402$	26.3242	−	13.7787i	1.31293	−	0.687219i
$403$	0.525864	+	1.44480i	0.0261951	+	0.0719705i
$404$	2.48721	−	3.91895i	0.123743	−	0.194975i
$405$	−10.6375	+	23.1469i	−0.528581	+	1.15018i
$406$	20.8155	−	11.9744i	1.03305	−	0.594277i
$407$	−18.9378	−	15.8907i	−0.938714	−	0.787674i
$408$	10.4996	+	22.2856i	0.519806	+	1.10330i
$409$	−21.5852	−	7.85635i	−1.06732	−	0.388472i	−0.252144	−	0.967690i	$-0.581136\pi$
$409$	−21.5852	−	7.85635i	−1.06732	−	0.388472i	−0.815173	+	0.579218i	$0.803358\pi$
$410$	17.9052	+	13.1051i	0.884276	+	0.647213i
$411$	−20.9641	−	31.2808i	−1.03408	−	1.54297i
$412$	21.2773	−	6.74882i	1.04826	−	0.332491i
$413$	12.6286	−	3.64770i	0.621411	−	0.179492i
$414$	4.89096	−	14.5821i	0.240377	−	0.716673i
$415$	−17.9682	−	10.3740i	−0.882026	−	0.509238i
$416$	18.3568	−	30.5454i	0.900017	−	1.49761i
$417$	−22.3756	+	9.88259i	−1.09574	+	0.483953i
$418$	18.1069	+	1.96733i	0.885638	+	0.0962253i
$419$	13.8598	−	11.6297i	0.677094	−	0.568149i	−0.238062	−	0.971250i	$-0.576512\pi$
$419$	13.8598	−	11.6297i	0.677094	−	0.568149i	0.915156	+	0.403101i	$0.132068\pi$
$420$	−25.7174	+	3.40349i	−1.25488	+	0.166073i
$421$	−8.42461	+	3.06631i	−0.410590	+	0.149443i	−0.539053	−	0.842272i	$-0.681218\pi$
$421$	−8.42461	+	3.06631i	−0.410590	+	0.149443i	0.128463	+	0.991714i	$0.458996\pi$
$422$	−5.64575	+	19.4316i	−0.274831	+	0.945917i
$423$	13.1317	−	14.4108i	0.638483	−	0.700678i
$424$	−11.4543	−	3.85540i	−0.556269	−	0.187235i
$425$	−5.17951	−	14.2306i	−0.251243	−	0.690285i
$426$	−13.8112	−	12.5988i	−0.669157	−	0.610412i
$427$	16.3469	+	1.11124i	0.791083	+	0.0537767i
$428$	−10.6492	−	13.8292i	−0.514749	−	0.668460i
$429$	−34.4552	−	35.8925i	−1.66351	−	1.73291i
$430$	−6.86648	−	10.2574i	−0.331131	−	0.494654i
$431$	−9.40772	+	16.2947i	−0.453154	+	0.784886i	−0.998580	−	0.0532733i	$-0.983035\pi$
$431$	−9.40772	+	16.2947i	−0.453154	+	0.784886i	0.545426	+	0.838159i	$0.316368\pi$
$432$	11.4158	−	17.3689i	0.549242	−	0.835663i
$433$	16.3860			0.787460			0.393730	−	0.919226i	$-0.371184\pi$
$433$	16.3860			0.787460			0.393730	+	0.919226i	$0.371184\pi$
$434$	−0.588081	+	0.698621i	−0.0282288	+	0.0335349i
$435$	8.76267	−	30.2195i	0.420138	−	1.44891i
$436$	−7.85076	+	19.0457i	−0.375983	+	0.912122i
$437$	−6.58174	−	7.84381i	−0.314847	−	0.375220i
$438$	−0.395388	−	0.360676i	−0.0188923	−	0.0172338i
$439$	8.00568	+	21.9954i	0.382090	+	1.04978i	0.970475	+	0.241203i	$0.0775420\pi$
$439$	8.00568	+	21.9954i	0.382090	+	1.04978i	−0.588384	+	0.808581i	$0.700236\pi$
$440$	7.21361	+	35.7843i	0.343895	+	1.70595i
$441$	19.7186	+	7.22330i	0.938982	+	0.343967i
$442$	−31.0084	−	32.3363i	−1.47492	−	1.53808i
$443$	−0.562285	−	0.471813i	−0.0267150	−	0.0224165i	0.629332	−	0.777136i	$-0.283328\pi$
$443$	−0.562285	−	0.471813i	−0.0267150	−	0.0224165i	−0.656047	+	0.754720i	$0.727773\pi$
$444$	−2.79950	+	18.5716i	−0.132858	+	0.881368i
$445$	−6.83586	−	38.7681i	−0.324051	−	1.83778i
$446$	26.8472	+	2.91697i	1.27125	+	0.138123i
$447$	2.06350	−	19.0865i	0.0976001	−	0.902759i
$448$	21.1621	+	0.404248i	0.999818	+	0.0190989i
$449$	−23.8680	+	13.7802i	−1.12640	+	0.650328i	−0.943027	−	0.332715i	$-0.892035\pi$
$449$	−23.8680	+	13.7802i	−1.12640	+	0.650328i	−0.183374	+	0.983043i	$0.558702\pi$
$450$	−7.96108	+	9.99346i	−0.375289	+	0.471096i
$451$	−21.8892	+	12.6377i	−1.03072	+	0.595087i
$452$	−6.77457	+	30.8079i	−0.318649	+	1.44908i
$453$	6.50973	−	0.435747i	0.305854	−	0.0204732i
$454$	−2.58219	+	23.7660i	−0.121188	+	1.11539i
$455$	42.3624	−	20.7633i	1.98598	−	0.973400i
$456$	−5.89740	−	12.5174i	−0.276171	−	0.586181i
$457$	4.12790	−	23.4105i	0.193095	−	1.09510i	−0.722010	−	0.691883i	$-0.756782\pi$
$457$	4.12790	−	23.4105i	0.193095	−	1.09510i	0.915105	−	0.403215i	$-0.132107\pi$
$458$	11.1747	+	3.24674i	0.522160	+	0.151710i
$459$	−17.3100	−	19.5733i	−0.807964	−	0.913603i
$460$	10.9969	−	17.3271i	0.512731	−	0.807878i
$461$	−18.1204	+	21.5951i	−0.843952	+	1.00578i	0.155886	+	0.987775i	$0.450177\pi$
$461$	−18.1204	+	21.5951i	−0.843952	+	1.00578i	−0.999838	+	0.0180078i	$0.994268\pi$
$462$	8.27416	−	28.3684i	0.384949	−	1.31982i
$463$	−22.0592	+	3.88963i	−1.02518	+	0.180766i	−0.660860	−	0.750509i	$-0.729808\pi$
$463$	−22.0592	+	3.88963i	−1.02518	+	0.180766i	−0.364317	+	0.931275i	$0.618697\pi$
$464$	−10.7696	+	23.3038i	−0.499968	+	1.08185i
$465$	0.0799125	+	1.19383i	0.00370585	+	0.0553626i
$466$	−29.3574	−	14.4462i	−1.35996	−	0.669208i
$467$	28.6084			1.32384			0.661920	−	0.749574i	$-0.269742\pi$
$467$	28.6084			1.32384			0.661920	+	0.749574i	$0.269742\pi$
$468$	−9.61899	+	36.5543i	−0.444638	+	1.68972i
$469$	−31.1545	−	7.70356i	−1.43858	−	0.355717i
$470$	21.6175	−	14.4711i	0.997140	−	0.667504i
$471$	2.47129	−	3.38024i	0.113871	−	0.155753i
$472$	−8.76754	+	10.9818i	−0.403559	+	0.505480i
$473$	13.8470	−	2.44160i	0.636687	−	0.112265i
$474$	33.5734	−	4.49672i	1.54208	−	0.206541i
$475$	2.90923	+	7.99304i	0.133485	+	0.366746i
$476$	7.46412	−	25.5407i	0.342117	−	1.17065i
$477$	12.8082	+	0.523592i	0.586445	+	0.0239736i
$478$	1.79600	+	7.31249i	0.0821469	+	0.334465i
$479$	16.4194	+	13.7775i	0.750220	+	0.629510i	0.935561	−	0.353165i	$-0.114894\pi$
$479$	16.4194	+	13.7775i	0.750220	+	0.629510i	−0.185341	+	0.982674i	$0.559339\pi$
$480$	20.3401	−	18.8517i	0.928397	−	0.860457i
$481$	−5.93107	−	33.6368i	−0.270434	−	1.53370i
$482$	−14.1200	+	6.22738i	−0.643147	+	0.283650i
$483$	−14.3957	+	8.29152i	−0.655029	+	0.377277i
$484$	−19.1254	−	4.20562i	−0.869335	−	0.191165i
$485$	−38.8037	+	22.4033i	−1.76198	+	1.01728i
$486$	−6.46503	+	21.0761i	−0.293260	+	0.956033i
$487$	−6.10707	−	3.52592i	−0.276738	−	0.159775i	0.355208	−	0.934787i	$-0.384410\pi$
$487$	−6.10707	−	3.52592i	−0.276738	−	0.159775i	−0.631946	+	0.775013i	$0.717743\pi$
$488$	−14.9512	+	9.12526i	−0.676808	+	0.413081i
$489$	26.8185	−	25.7445i	1.21277	−	1.16421i
$490$	23.2356	+	15.6601i	1.04968	+	0.707449i
$491$	24.3676	+	8.86908i	1.09969	+	0.400256i	0.827203	−	0.561903i	$-0.189930\pi$
$491$	24.3676	+	8.86908i	1.09969	+	0.400256i	0.272491	+	0.962158i	$0.412153\pi$
$492$	16.8636	+	9.18376i	0.760271	+	0.414036i
$493$	24.7231	+	20.7451i	1.11347	+	0.934314i
$494$	17.4168	+	18.1626i	0.783618	+	0.817176i
$495$	−17.9735	−	34.2939i	−0.807848	−	1.54140i
$496$	0.0817512	−	0.972809i	0.00367074	−	0.0436804i
$497$	2.14960	+	20.0775i	0.0964226	+	0.900598i
$498$	−16.6039	−	6.83394i	−0.744040	−	0.306236i
$499$	0.335112	−	0.920712i	0.0150017	−	0.0412167i	−0.931966	−	0.362546i	$-0.881907\pi$
$499$	0.335112	−	0.920712i	0.0150017	−	0.0412167i	0.946967	+	0.321330i	$0.104130\pi$
$500$	8.91868	−	6.86786i	0.398856	−	0.307140i
$501$	−12.7555	−	1.37904i	−0.569875	−	0.0616109i
$502$	−4.83850	+	9.83274i	−0.215953	+	0.438856i
$503$	−17.7169	−	30.6865i	−0.789957	−	1.36825i	−0.925993	−	0.377541i	$-0.876770\pi$
$503$	−17.7169	−	30.6865i	−0.789957	−	1.36825i	0.136036	−	0.990704i	$-0.456564\pi$
$504$	−21.6679	+	5.87382i	−0.965165	+	0.261641i
$505$	−3.28447	+	5.68886i	−0.146157	+	0.253151i
$506$	13.0042	+	19.4261i	0.578108	+	0.863597i
$507$	−3.08721	−	46.1205i	−0.137108	−	2.04829i
$508$	9.93224	+	4.09414i	0.440672	+	0.181648i
$509$	25.4025	+	30.2736i	1.12595	+	1.34185i	0.932679	+	0.360707i	$0.117464\pi$
$509$	25.4025	+	30.2736i	1.12595	+	1.34185i	0.193269	+	0.981146i	$0.438091\pi$
$510$	−16.1680	−	30.8889i	−0.715931	−	1.36778i
$511$	0.0615385	+	0.574777i	0.00272230	+	0.0254266i
$512$	−18.7165	+	12.7158i	−0.827161	+	0.561965i
$513$	9.72271	+	10.9939i	0.429268	+	0.485394i
$514$	0.0354753	−	0.122100i	0.00156475	−	0.00538558i
$515$	−29.6856	+	10.8047i	−1.30811	+	0.476112i
$516$	−7.06807	−	8.00934i	−0.311154	−	0.352591i
$517$	5.14570	+	29.1827i	0.226307	+	1.28345i
$518$	15.5606	−	13.0154i	0.683692	−	0.571862i
$519$	2.75552	−	5.60725i	0.120954	−	0.246131i
$520$	−24.1447	+	44.2796i	−1.05882	+	1.94179i
$521$	−7.19873	+	4.15619i	−0.315382	+	0.182086i	−0.649332	−	0.760505i	$-0.724952\pi$
$521$	−7.19873	+	4.15619i	−0.315382	+	0.182086i	0.333950	+	0.942591i	$0.391618\pi$
$522$	4.04440	−	26.9272i	0.177019	−	1.17857i
$523$	13.7470	+	7.93681i	0.601112	+	0.347052i	0.769479	−	0.638672i	$-0.220516\pi$
$523$	13.7470	+	7.93681i	0.601112	+	0.347052i	−0.168367	+	0.985724i	$0.553849\pi$
$524$	−3.92671	+	4.30002i	−0.171539	+	0.187847i
$525$	13.5934	−	2.38236i	0.593264	−	0.103975i
$526$	2.19880	+	1.60933i	0.0958722	+	0.0701702i
$527$	−1.15327	−	0.419756i	−0.0502372	−	0.0182848i
$528$	10.2984	+	29.8650i	0.448182	+	1.29971i
$529$	−1.71178	+	9.70801i	−0.0744254	+	0.422087i
$530$	16.4249	+	4.77216i	0.713452	+	0.207289i
$531$	5.66558	−	13.7861i	0.245865	−	0.598264i
$532$	−4.19245	+	14.3457i	−0.181766	+	0.621964i
$533$	−34.3904	−	6.06395i	−1.48961	−	0.262659i
$534$	−10.3172	−	32.4677i	−0.446470	−	1.40502i
$535$	15.8781	+	18.9228i	0.686469	+	0.818102i
$536$	31.9439	−	12.5169i	1.37977	−	0.540648i
$537$	22.0831	−	5.43620i	0.952956	−	0.234590i
$538$	10.8511	+	5.33962i	0.467824	+	0.230207i
$539$	−27.0023	+	17.0189i	−1.16307	+	0.733055i
$540$	−15.1117	+	25.2365i	−0.650302	+	1.08601i
$541$	21.5849	+	37.3861i	0.928007	+	1.60735i	0.786653	+	0.617396i	$0.211812\pi$
$541$	21.5849	+	37.3861i	0.928007	+	1.60735i	0.141354	+	0.989959i	$0.454854\pi$
$542$	16.7305	−	11.1997i	0.718638	−	0.481070i
$543$	1.31128	−	4.52217i	0.0562726	−	0.194065i
$544$	9.25905	+	26.8972i	0.396978	+	1.15321i
$545$	9.97132	−	27.3960i	0.427125	−	1.17352i
$546$	33.9507	−	22.6763i	1.45296	−	0.970457i
$547$	−0.547685	−	0.0965717i	−0.0234173	−	0.00412911i	0.161927	−	0.986803i	$-0.448229\pi$
$547$	−0.547685	−	0.0965717i	−0.0234173	−	0.00412911i	−0.185345	+	0.982674i	$0.559340\pi$
$548$	−20.1436	−	38.5341i	−0.860492	−	1.64610i
$549$	12.5133	−	13.7323i	0.534056	−	0.586079i
$550$	−4.63194	−	18.8592i	−0.197507	−	0.804159i
$551$	−13.8865	−	11.6521i	−0.591583	−	0.496397i
$552$	7.44188	−	16.1255i	0.316747	−	0.686347i
$553$	−30.3718	−	20.4005i	−1.29154	−	0.867516i
$554$	−6.70918	−	4.91054i	−0.285046	−	0.208629i
$555$	2.85700	−	26.4260i	0.121273	−	1.12172i
$556$	−26.9231	+	8.53956i	−1.14179	+	0.362158i
$557$			5.23813i			0.221947i	0.993823	+	0.110973i	$0.0353968\pi$
$557$			5.23813i			0.221947i	−0.993823	+	0.110973i	$0.964603\pi$
$558$	0.205696	+	1.01482i	0.00870781	+	0.0429608i
$559$	16.8237	+	9.71318i	0.711568	+	0.410824i
$560$	−29.9470	+	0.683496i	−1.26549	+	0.0288830i
$561$	39.6258	−	2.65247i	1.67300	−	0.111987i
$562$	3.63801	+	8.24882i	0.153460	+	0.347955i
$563$	26.6188	+	9.68845i	1.12185	+	0.408320i	0.835327	−	0.549754i	$-0.185279\pi$
$563$	26.6188	+	9.68845i	1.12185	+	0.408320i	0.286522	+	0.958074i	$0.407501\pi$
$564$	16.8797	−	14.8960i	0.710765	−	0.627235i
$565$	7.75200	−	43.9638i	0.326129	−	1.84957i
$566$	32.9164	−	8.08449i	1.38358	−	0.339817i
$567$	20.3182	−	12.4165i	0.853285	−	0.521445i
$568$	−14.2746	−	16.1929i	−0.598947	−	0.679438i
$569$	34.7811	+	6.13284i	1.45810	+	0.257102i	0.845790	−	0.533516i	$-0.179130\pi$
$569$	34.7811	+	6.13284i	1.45810	+	0.257102i	0.612309	+	0.790619i	$0.290241\pi$
$570$	9.08125	+	17.3497i	0.380372	+	0.726699i
$571$	−6.38511	+	17.5430i	−0.267209	+	0.734150i	0.731426	+	0.681920i	$0.238855\pi$
$571$	−6.38511	+	17.5430i	−0.267209	+	0.734150i	−0.998635	+	0.0522295i	$0.983367\pi$
$572$	−35.0518	−	45.5187i	−1.46559	−	1.90323i
$573$	−0.152507	−	2.27833i	−0.00637105	−	0.0951787i
$574$	−7.06318	−	19.5010i	−0.294812	−	0.813955i
$575$	−5.45874	+	9.45481i	−0.227645	+	0.394293i
$576$	15.2809	−	18.5066i	0.636703	−	0.771109i
$577$	−20.0864			−0.836209			−0.418104	−	0.908399i	$-0.637305\pi$
$577$	−20.0864			−0.836209			−0.418104	+	0.908399i	$0.637305\pi$
$578$	11.6940	−	0.776525i	0.486404	−	0.0322992i
$579$	−11.1941	−	1.21023i	−0.465210	−	0.0502953i
$580$	13.8460	−	33.5900i	0.574926	−	1.39475i
$581$	8.53553	+	17.4146i	0.354113	+	0.722481i
$582$	−30.7098	+	23.6742i	−1.27296	+	0.981326i
$583$	−12.5238	+	14.9252i	−0.518681	+	0.618140i
$584$	−0.408651	−	0.463568i	−0.0169101	−	0.0191826i
$585$	11.4332	−	52.2579i	0.472703	−	2.16060i
$586$	−25.2595	+	6.20391i	−1.04346	+	0.256281i
$587$	−5.34262	+	30.2995i	−0.220514	+	1.25060i	0.650565	+	0.759451i	$0.274532\pi$
$587$	−5.34262	+	30.2995i	−0.220514	+	1.25060i	−0.871078	+	0.491144i	$0.836579\pi$
$588$	21.7292	+	10.7629i	0.896099	+	0.443855i
$589$	0.647769	+	0.235769i	0.0266909	+	0.00971468i
$590$	11.7459	−	16.0482i	0.483571	−	0.660693i
$591$	6.28635	+	1.82284i	0.258586	+	0.0749816i
$592$	−5.54115	+	20.9670i	−0.227740	+	0.861740i
$593$	−8.69615	+	5.02073i	−0.357108	+	0.206177i	−0.667812	−	0.744330i	$-0.732769\pi$
$593$	−8.69615	+	5.02073i	−0.357108	+	0.206177i	0.310703	+	0.950507i	$0.399435\pi$
$594$	−19.3564	−	27.3505i	−0.794204	−	1.12221i
$595$	−9.03940	+	36.5569i	−0.370579	+	1.49869i
$596$	4.76085	−	21.6503i	0.195012	−	0.886831i
$597$	−2.10641	−	8.55673i	−0.0862097	−	0.350204i
$598$	−3.48867	+	32.1090i	−0.142662	+	1.31303i
$599$	10.2686	−	8.61637i	0.419563	−	0.352055i	−0.408434	−	0.912788i	$-0.633925\pi$
$599$	10.2686	−	8.61637i	0.419563	−	0.352055i	0.827997	+	0.560733i	$0.189480\pi$
$600$	−10.3909	+	10.4735i	−0.424206	+	0.427578i
$601$	−4.54529	+	25.7776i	−0.185406	+	1.05149i	0.740026	+	0.672578i	$0.234813\pi$
$601$	−4.54529	+	25.7776i	−0.185406	+	1.05149i	−0.925432	+	0.378913i	$0.876298\pi$
$602$	−0.0180854	+	11.5380i	−0.000737105	+	0.470252i
$603$	−28.8084	+	22.2328i	−1.17317	+	0.905390i
$604$	7.52700	+	0.315714i	0.306269	+	0.0128462i
$605$	27.2925	+	4.81240i	1.10960	+	0.195652i
$606$	−2.16367	+	5.25691i	−0.0878930	+	0.213547i
$607$	14.3605	−	39.4551i	0.582874	−	1.60143i	−0.200371	−	0.979720i	$-0.564215\pi$
$607$	14.3605	−	39.4551i	0.582874	−	1.60143i	0.783245	−	0.621713i	$-0.213563\pi$
$608$	−5.20062	−	15.1076i	−0.210913	−	0.612694i
$609$	−22.5497	+	18.8816i	−0.913758	+	0.765122i
$610$	20.5996	−	13.7898i	0.834053	−	0.558331i
$611$	−20.4706	+	35.4561i	−0.828151	+	1.43440i
$612$	−17.4166	−	24.6373i	−0.704025	−	0.995904i
$613$	−10.6360	−	18.4221i	−0.429585	−	0.744064i	0.567251	−	0.823545i	$-0.308007\pi$
$613$	−10.6360	−	18.4221i	−0.429585	−	0.744064i	−0.996836	+	0.0794814i	$0.974674\pi$
$614$	−19.3349	+	12.9431i	−0.780293	+	0.522343i
$615$	−24.3897	−	11.9856i	−0.983486	−	0.483305i
$616$	13.0533	−	31.5264i	0.525932	−	1.27024i
$617$	−34.0304	+	6.00048i	−1.37001	+	0.241570i	−0.809765	−	0.586754i	$-0.800405\pi$
$617$	−34.0304	+	6.00048i	−1.37001	+	0.241570i	−0.560248	+	0.828325i	$0.689294\pi$
$618$	−24.2214	+	12.6780i	−0.974326	+	0.509985i
$619$	−4.74370	−	13.0332i	−0.190665	−	0.523849i	0.807118	−	0.590390i	$-0.201026\pi$
$619$	−4.74370	−	13.0332i	−0.190665	−	0.523849i	−0.997784	+	0.0665409i	$0.978804\pi$
$620$	−0.0578994	+	1.38039i	−0.00232529	+	0.0554378i
$621$	−2.78802	+	18.6297i	−0.111879	+	0.747586i
$622$	−6.96732	−	28.3678i	−0.279364	−	1.13744i
$623$	−14.9015	+	33.6448i	−0.597018	+	1.34795i
$624$	−15.6230	+	40.7543i	−0.625419	+	1.63148i
$625$	−23.7384	+	19.9189i	−0.949538	+	0.796757i
$626$	−31.9033	−	23.3505i	−1.27511	−	0.933273i
$627$	−22.2571	+	1.48984i	−0.888861	+	0.0594984i
$628$	3.26040	−	3.57037i	0.130104	−	0.142473i
$629$	23.6111	+	13.6319i	0.941438	+	0.543540i
$630$	30.2898	−	9.59062i	1.20678	−	0.382099i
$631$	23.3571	−	13.4852i	0.929831	−	0.536838i	0.0430731	−	0.999072i	$-0.486285\pi$
$631$	23.3571	−	13.4852i	0.929831	−	0.536838i	0.886758	+	0.462234i	$0.152952\pi$
$632$	39.1017	−	0.953764i	1.55538	−	0.0379387i
$633$	2.66384	−	24.6394i	0.105878	−	0.979327i
$634$	9.57390	+	21.7079i	0.380228	+	0.862130i
$635$	−14.2869	−	5.20001i	−0.566958	−	0.206356i
$636$	14.6366	+	2.20633i	0.580378	+	0.0874867i
$637$	−43.6928	−	5.96792i	−1.73117	−	0.236458i
$638$	28.6446	+	29.8712i	1.13405	+	1.18261i
$639$	19.3442	+	12.2483i	0.765246	+	0.484534i
$640$	25.7108	−	19.0901i	1.01631	−	0.754602i
$641$	−18.9900	+	22.6313i	−0.750058	+	0.893884i	−0.997176	−	0.0751010i	$-0.976072\pi$
$641$	−18.9900	+	22.6313i	−0.750058	+	0.893884i	0.247118	+	0.968985i	$0.420517\pi$
$642$	15.7932	+	14.4067i	0.623308	+	0.568588i
$643$	7.40305	−	20.3397i	0.291948	−	0.802120i	−0.703834	−	0.710365i	$-0.748530\pi$
$643$	7.40305	−	20.3397i	0.291948	−	0.802120i	0.995782	−	0.0917555i	$-0.0292478\pi$
$644$	−17.5638	+	7.71336i	−0.692110	+	0.303949i
$645$	10.4692	+	10.9059i	0.412224	+	0.429420i
$646$	−20.0423	+	1.33089i	−0.788554	+	0.0523631i
$647$	11.1004	−	19.2265i	0.436402	−	0.755871i	−0.561007	−	0.827811i	$-0.689586\pi$
$647$	11.1004	−	19.2265i	0.436402	−	0.755871i	0.997409	+	0.0719405i	$0.0229192\pi$
$648$	−10.0626	+	23.3825i	−0.395298	+	0.918553i
$649$	11.3270	+	19.6190i	0.444624	+	0.770111i
$650$	11.8462	−	24.0737i	0.464646	−	0.944248i
$651$	0.560214	−	0.968001i	0.0219565	−	0.0379390i
$652$	34.0110	−	26.1903i	1.33198	−	1.02569i
$653$	6.92100	−	1.22036i	0.270840	−	0.0477564i	−0.0365787	−	0.999331i	$-0.511646\pi$
$653$	6.92100	−	1.22036i	0.270840	−	0.0477564i	0.307419	+	0.951574i	$0.400535\pi$
$654$	5.40548	−	24.6442i	0.211371	−	0.963666i
$655$	5.29730	−	6.31308i	0.206983	−	0.246672i
$656$	18.2063	+	12.6554i	0.710838	+	0.494112i
$657$	0.553785	+	0.350642i	0.0216052	+	0.0136799i
$658$	−24.3163	−	0.0381150i	−0.947949	−	0.00148588i
$659$	−14.6447	+	5.33025i	−0.570478	+	0.207637i	−0.611122	−	0.791537i	$-0.709281\pi$
$659$	−14.6447	+	5.33025i	−0.570478	+	0.207637i	0.0406434	+	0.999174i	$0.487059\pi$
$660$	−16.3331	−	41.6180i	−0.635767	−	1.61998i
$661$	2.14391	+	12.1587i	0.0833883	+	0.472919i	0.997693	+	0.0678909i	$0.0216270\pi$
$661$	2.14391	+	12.1587i	0.0833883	+	0.472919i	−0.914304	+	0.405028i	$0.867262\pi$
$662$	−16.0663	−	36.4288i	−0.624435	−	1.41584i
$663$	44.2947	+	32.3838i	1.72026	+	1.25768i
$664$	−18.2027	−	9.92558i	−0.706404	−	0.385187i
$665$	5.07726	−	20.5333i	0.196888	−	0.796247i
$666$	−0.585344	−	22.9950i	−0.0226816	−	0.891037i
$667$		−	23.2666i		−	0.900888i
$668$	−14.4689	−	3.18168i	−0.559820	−	0.123103i
$669$	−33.0007	+	2.20899i	−1.27588	+	0.0854045i
$670$	−44.4259	+	19.5933i	−1.71632	+	0.756957i
$671$	4.90340	+	27.8086i	0.189294	+	1.07354i
$672$	−25.6083	+	4.02668i	−0.987862	+	0.155333i
$673$	18.2036	+	15.2747i	0.701698	+	0.588795i	0.922256	−	0.386579i	$-0.126343\pi$
$673$	18.2036	+	15.2747i	0.701698	+	0.588795i	−0.220558	+	0.975374i	$0.570788\pi$
$674$	27.0426	−	25.9321i	1.04164	−	0.998866i
$675$	7.46950	−	13.7506i	0.287501	−	0.529260i
$676$	2.23679	−	53.3277i	0.0860303	−	2.05107i
$677$	−29.0460	−	5.12160i	−1.11633	−	0.196839i	−0.415101	−	0.909775i	$-0.636254\pi$
$677$	−29.0460	−	5.12160i	−1.11633	−	0.196839i	−0.701229	+	0.712937i	$0.747365\pi$
$678$	1.59851	−	38.6002i	0.0613902	−	1.48243i
$679$	41.7861	+	2.84056i	1.60361	+	0.109011i
$680$	−14.6874	−	37.4831i	−0.563237	−	1.43741i
$681$	−1.95547	−	29.2132i	−0.0749336	−	1.11945i
$682$	−1.41210	−	0.694865i	−0.0540719	−	0.0266078i
$683$	−10.9618	−	18.9864i	−0.419441	−	0.726493i	0.576442	−	0.817138i	$-0.304441\pi$
$683$	−10.9618	−	18.9864i	−0.419441	−	0.726493i	−0.995883	+	0.0906447i	$0.971107\pi$
$684$	9.78257	+	13.8383i	0.374046	+	0.529120i
$685$	30.7682	+	53.2921i	1.17559	+	2.03619i
$686$	−9.86763	−	24.2617i	−0.376748	−	0.926316i
$687$	−14.1696	−	1.53192i	−0.540602	−	0.0584462i
$688$	−7.10943	−	10.0796i	−0.271045	−	0.384282i
$689$	−26.5097	+	4.67438i	−1.00994	+	0.178080i
$690$	−9.56635	+	23.2427i	−0.364185	+	0.884833i
$691$	9.74840	−	11.6177i	0.370847	−	0.441958i	−0.548056	−	0.836441i	$-0.684632\pi$
$691$	9.74840	−	11.6177i	0.370847	−	0.441958i	0.918903	+	0.394484i	$0.129076\pi$
$692$	3.86578	−	6.09107i	0.146955	−	0.231548i
$693$	−3.92741	+	35.9780i	−0.149190	+	1.36669i
$694$	45.4671	+	13.2102i	1.72591	+	0.501453i
$695$	37.5625	−	13.6716i	1.42483	−	0.518594i
$696$	8.01740	−	30.4022i	0.303899	−	1.15239i
$697$	21.3532	−	17.9175i	0.808810	−	0.678672i
$698$	−35.8726	−	26.2557i	−1.35780	−	0.993792i
$699$	38.4874	+	11.1601i	1.45573	+	0.422114i
$700$	15.9022	−	1.03093i	0.601045	−	0.0389656i
$701$		−	3.12245i		−	0.117933i	−0.998260	−	0.0589666i	$-0.981219\pi$
$701$		−	3.12245i		−	0.117933i	0.998260	−	0.0589666i	$-0.0187805\pi$
$702$	3.80314	−	46.1373i	0.143540	−	1.74134i
$703$	−13.2619	−	7.65677i	−0.500183	−	0.288781i
$704$	8.07823	+	35.5721i	0.304460	+	1.34067i
$705$	−22.9843	+	22.0639i	−0.865639	+	0.830975i
$706$	2.28705	+	5.18567i	0.0860744	+	0.195165i
$707$	5.51359	−	2.70240i	0.207360	−	0.101634i
$708$	8.23127	−	15.1146i	0.309350	−	0.568042i
$709$	−21.9577	+	7.99195i	−0.824638	+	0.300144i	−0.719656	−	0.694330i	$-0.755701\pi$
$709$	−21.9577	+	7.99195i	−0.824638	+	0.300144i	−0.104982	+	0.994474i	$0.533478\pi$
$710$	21.1445	+	22.0499i	0.793537	+	0.827519i
$711$	−39.5311	+	12.5849i	−1.48253	+	0.471970i
$712$	−7.77357	−	38.5621i	−0.291327	−	1.44518i
$713$	0.302609	+	0.831411i	0.0113328	+	0.0311366i
$714$	−3.55369	+	32.3949i	−0.132994	+	1.21235i
$715$	52.2625	+	62.2840i	1.95451	+	2.32929i
$716$	26.0301	−	3.47231i	0.972789	−	0.129766i
$717$	−3.72588	−	8.43593i	−0.139146	−	0.315045i
$718$	−2.79963	+	0.185906i	−0.104481	+	0.00693796i
$719$	19.2281	−	33.3040i	0.717086	−	1.24203i	−0.245064	−	0.969507i	$-0.578809\pi$
$719$	19.2281	−	33.3040i	0.717086	−	1.24203i	0.962149	−	0.272522i	$-0.0878578\pi$
$720$	−20.5094	+	27.0745i	−0.764339	+	1.00901i
$721$	28.6659	+	7.08819i	1.06757	+	0.263978i
$722$	−15.5536	+	1.03282i	−0.578847	+	0.0384377i
$723$	15.7006	−	10.5224i	0.583913	−	0.391332i
$724$	2.07198	−	5.02655i	0.0770045	−	0.186810i
$725$	−6.61057	+	18.1624i	−0.245510	+	0.674534i
$726$	23.9628	+	0.992344i	0.889343	+	0.0368293i
$727$	7.43471	−	8.86034i	0.275738	−	0.328612i	−0.610347	−	0.792134i	$-0.708970\pi$
$727$	7.43471	−	8.86034i	0.275738	−	0.328612i	0.886085	+	0.463522i	$0.153415\pi$
$728$	41.8134	−	21.7745i	1.54971	−	0.807015i
$729$	3.30112	−	26.7974i	0.122264	−	0.992498i
$730$	0.605322	+	0.631244i	0.0224040	+	0.0233634i
$731$	−14.5714	+	5.30355i	−0.538942	+	0.196159i
$732$	16.0849	−	14.1946i	0.594516	−	0.524648i
$733$	38.8004	−	32.5574i	1.43312	−	1.20253i	0.489286	−	0.872123i	$-0.337257\pi$
$733$	38.8004	−	32.5574i	1.43312	−	1.20253i	0.943837	−	0.330410i	$-0.107187\pi$
$734$	8.41929	+	0.914762i	0.310762	+	0.0337645i
$735$	−31.3632	−	13.9299i	−1.15685	−	0.513812i
$736$	10.5635	−	17.5774i	0.389374	−	0.647911i
$737$		−	55.3093i		−	2.03734i
$738$	−22.2970	−	7.47857i	−0.820763	−	0.275290i
$739$		−	24.9204i		−	0.916712i	−0.888769	−	0.458356i	$-0.848439\pi$
$739$		−	24.9204i		−	0.916712i	0.888769	−	0.458356i	$-0.151561\pi$
$740$	6.59160	−	29.9758i	0.242312	−	1.10193i
$741$	−24.8795	−	18.1893i	−0.913970	−	0.668201i
$742$	−10.2576	−	12.2635i	−0.376569	−	0.450209i
$743$	−8.51987	+	7.14902i	−0.312564	+	0.262272i	−0.785551	−	0.618797i	$-0.787620\pi$
$743$	−8.51987	+	7.14902i	−0.312564	+	0.262272i	0.472987	+	0.881069i	$0.343176\pi$
$744$	0.108921	+	1.19067i	0.00399325	+	0.0436521i
$745$	−5.44774	+	30.8957i	−0.199590	+	1.13193i
$746$	−3.43257	−	13.9759i	−0.125675	−	0.511693i
$747$	21.4825	+	4.70003i	0.786005	+	0.171965i
$748$	45.8181	+	1.92180i	1.67528	+	0.0702681i
$749$	−2.45807	−	22.9587i	−0.0898160	−	0.838891i
$750$	−9.29113	+	10.1853i	−0.339264	+	0.371915i
$751$	15.5489	−	2.74169i	0.567387	−	0.100046i	0.117406	−	0.993084i	$-0.462542\pi$
$751$	15.5489	−	2.74169i	0.567387	−	0.100046i	0.449980	+	0.893038i	$0.351431\pi$
$752$	21.2429	−	14.9832i	0.774648	−	0.546380i
$753$	3.73788	−	12.8907i	0.136216	−	0.469762i
$754$	3.78860	+	57.0538i	0.137973	+	2.07778i
$755$	−10.6618			−0.388023
$756$	24.8791	−	11.7061i	0.904843	−	0.425746i
$757$	13.3092			0.483731			0.241866	−	0.970310i	$-0.422241\pi$
$757$	13.3092			0.483731			0.241866	+	0.970310i	$0.422241\pi$
$758$	0.547227	+	8.24087i	0.0198762	+	0.299322i
$759$	−19.8273	−	20.6544i	−0.719686	−	0.749707i
$760$	8.24964	+	21.0535i	0.299246	+	0.763692i
$761$	−18.1450	+	3.19945i	−0.657755	+	0.115980i	−0.492556	−	0.870281i	$-0.663937\pi$
$761$	−18.1450	+	3.19945i	−0.657755	+	0.115980i	−0.165198	+	0.986260i	$0.552826\pi$
$762$	−12.8519	−	2.81894i	−0.465574	−	0.102119i
$763$	−22.0159	+	16.0608i	−0.797030	+	0.581441i
$764$	0.110496	−	2.63436i	0.00399761	−	0.0953079i
$765$	26.0881	+	33.8039i	0.943217	+	1.22218i
$766$	1.67151	+	6.80565i	0.0603942	+	0.245898i
$767$	−5.43503	+	30.8236i	−0.196248	+	1.11298i
$768$	19.8601	−	19.3281i	0.716640	−	0.697444i
$769$	0.901218	−	0.756211i	0.0324987	−	0.0272697i	−0.626394	−	0.779507i	$-0.715470\pi$
$769$	0.901218	−	0.756211i	0.0324987	−	0.0272697i	0.658892	+	0.752237i	$0.271025\pi$
$770$	−16.5874	+	45.3522i	−0.597769	+	1.63438i
$771$	−0.0167384	+	0.154823i	−0.000602817	+	0.00557580i
$772$	−12.6977	−	2.79220i	−0.457002	−	0.100494i
$773$		−	17.8380i		−	0.641589i	−0.947149	−	0.320795i	$-0.896050\pi$
$773$		−	17.8380i		−	0.641589i	0.947149	−	0.320795i	$-0.103950\pi$
$774$	10.2328	+	8.15173i	0.367810	+	0.293008i
$775$		−	0.734993i		−	0.0264017i
$776$	−38.2183	+	23.3261i	−1.37196	+	0.837357i
$777$	−15.9901	+	19.0162i	−0.573640	+	0.682201i
$778$	−13.7354	−	1.49236i	−0.492438	−	0.0535038i
$779$	−11.9937	+	10.0639i	−0.429718	+	0.360576i
$780$	19.6736	−	58.5527i	0.704429	−	2.09652i
$781$	−32.7009	+	11.9022i	−1.17013	+	0.425893i
$782$	−17.8438	−	18.6079i	−0.638093	−	0.665419i
$783$	0.866348	+	33.3376i	0.0309607	+	1.19139i
$784$	23.5936	+	15.0779i	0.842627	+	0.538498i
$785$	−4.39842	+	5.24183i	−0.156986	+	0.187089i
$786$	3.81845	−	6.02356i	0.136200	−	0.214853i
$787$	−10.0504	+	27.6134i	−0.358260	+	0.984310i	0.621374	+	0.783514i	$0.286575\pi$
$787$	−10.0504	+	27.6134i	−0.358260	+	0.984310i	−0.979633	+	0.200796i	$0.935647\pi$
$788$	6.98750	+	2.88030i	0.248919	+	0.102606i
$789$	−2.99510	−	1.47186i	−0.106629	−	0.0523995i
$790$	−55.2329	+	3.66768i	−1.96510	+	0.130490i
$791$	−28.9289	+	30.0733i	−1.02859	+	1.06928i
$792$	−18.7909	−	33.8211i	−0.667704	−	1.20178i
$793$	−19.5067	+	33.7866i	−0.692704	+	1.19980i
$794$	9.28736	−	0.616718i	0.329596	−	0.0218865i
$795$	−20.8268	−	2.25165i	−0.738651	−	0.0798579i
$796$	−1.34545	−	10.0861i	−0.0476881	−	0.357492i
$797$	−2.66284	−	3.17345i	−0.0943226	−	0.112409i	0.716819	−	0.697260i	$-0.245598\pi$
$797$	−2.66284	−	3.17345i	−0.0943226	−	0.112409i	−0.811141	+	0.584851i	$0.801153\pi$
$798$	1.99604	−	18.1956i	0.0706591	−	0.644116i
$799$	−11.1773	−	30.7093i	−0.395423	−	1.08642i
$800$	−13.2402	+	10.7199i	−0.468110	+	0.379007i
$801$	19.3687	+	36.9561i	0.684359	+	1.30578i
$802$	−29.3632	−	30.6206i	−1.03685	−	1.08125i
$803$	−0.936160	+	0.340734i	−0.0330364	+	0.0120243i
$804$	−35.8551	+	21.9098i	−1.26451	+	0.772701i
$805$	24.3775	−	11.9483i	0.859195	−	0.421122i
$806$	−0.877431	−	1.98949i	−0.0309062	−	0.0700767i
$807$	−14.2257	−	4.12500i	−0.500769	−	0.145207i
$808$	−3.14250	+	5.76311i	−0.110553	+	0.202745i
$809$	8.65519	+	4.99708i	0.304300	+	0.175688i	0.644373	−	0.764711i	$-0.277118\pi$
$809$	8.65519	+	4.99708i	0.304300	+	0.175688i	−0.340073	+	0.940399i	$0.610452\pi$
$810$	12.8417	−	33.6595i	0.451211	−	1.18267i
$811$			56.2187i			1.97410i	0.160399	+	0.987052i	$0.448722\pi$
$811$			56.2187i			1.97410i	−0.160399	+	0.987052i	$0.551278\pi$
$812$	−28.2508	+	18.8476i	−0.991409	+	0.661419i
$813$	−17.7884	+	17.0760i	−0.623865	+	0.598883i
$814$	28.2123	+	20.6490i	0.988841	+	0.723746i
$815$	−46.5379	+	39.0500i	−1.63015	+	1.36786i
$816$	−16.9042	−	30.4635i	−0.591766	−	1.06644i
$817$	8.18446	−	2.97890i	0.286338	−	0.104219i
$818$	31.1951	+	9.06355i	1.09071	+	0.316900i
$819$	−36.1082	+	34.5904i	−1.26172	+	1.20869i
$820$	−26.4941	−	16.8149i	−0.925216	−	0.587201i
$821$	−22.9117	+	27.3051i	−0.799625	+	0.952956i	−0.999640	−	0.0268367i	$-0.991457\pi$
$821$	−22.9117	+	27.3051i	−0.799625	+	0.952956i	0.200015	+	0.979793i	$0.435901\pi$
$822$	32.5136	+	42.1762i	1.13404	+	1.47106i
$823$	38.2648	−	6.74712i	1.33383	−	0.235190i	0.539144	−	0.842213i	$-0.318748\pi$
$823$	38.2648	−	6.74712i	1.33383	−	0.235190i	0.794684	+	0.607023i	$0.207637\pi$
$824$	−29.3922	+	11.5171i	−1.02392	+	0.401216i
$825$	9.60920	+	21.7566i	0.334549	+	0.757467i
$826$	−17.4785	+	6.33063i	−0.608153	+	0.220271i
$827$	20.8340	+	36.0855i	0.724469	+	1.25482i	0.959192	+	0.282754i	$0.0912481\pi$
$827$	20.8340	+	36.0855i	0.724469	+	1.25482i	−0.234724	+	0.972062i	$0.575419\pi$
$828$	−5.53527	+	21.0352i	−0.192364	+	0.731025i
$829$	−21.3768	−	37.0256i	−0.742445	−	1.28595i	−0.951379	−	0.308023i	$-0.900333\pi$
$829$	−21.3768	−	37.0256i	−0.742445	−	1.28595i	0.208934	−	0.977930i	$-0.433001\pi$
$830$	26.3272	+	12.9551i	0.913829	+	0.449678i
$831$	9.13894	+	4.49106i	0.317026	+	0.155793i
$832$	−23.0412	+	44.8229i	−0.798810	+	1.55395i
$833$	26.0674	−	23.6549i	0.903183	−	0.819595i
$834$	30.6483	−	16.0420i	1.06126	−	0.555491i
$835$	20.6476	+	3.64073i	0.714541	+	0.125993i
$836$	−25.7351	−	1.07944i	−0.890068	−	0.0373332i
$837$	−0.464551	−	1.18002i	−0.0160572	−	0.0407875i
$838$	−18.4679	+	17.7095i	−0.637961	+	0.611764i
$839$	−15.8607	−	13.3087i	−0.547573	−	0.459468i	0.326545	−	0.945182i	$-0.394116\pi$
$839$	−15.8607	−	13.3087i	−0.547573	−	0.459468i	−0.874118	+	0.485713i	$0.838560\pi$
$840$	35.9711	−	7.21248i	1.24112	−	0.248854i
$841$	−2.11688	−	12.0054i	−0.0729959	−	0.413980i
$842$	11.6007	−	5.11630i	0.399786	−	0.176319i
$843$	−6.14713	−	9.17224i	−0.211718	−	0.315909i
$844$	6.14594	−	27.9491i	0.211552	−	0.962048i
$845$			75.5375i			2.59857i
$846$	−17.1798	+	21.5657i	−0.590655	+	0.741443i
$847$	−18.6693	−	17.9589i	−0.641486	−	0.617076i
$848$	16.5245	+	4.36708i	0.567453	+	0.149966i
$849$	−37.9735	+	16.7717i	−1.30325	+	0.575603i
$850$	8.64229	+	19.5955i	0.296428	+	0.672121i
$851$	−3.41304	−	19.3563i	−0.116998	−	0.663527i
$852$	20.6697	+	16.4840i	0.708131	+	0.564733i
$853$	27.6536	−	10.0651i	0.946841	−	0.344622i	0.177977	−	0.984035i	$-0.443045\pi$
$853$	27.6536	−	10.0651i	0.946841	−	0.344622i	0.768864	+	0.639413i	$0.220822\pi$
$854$	−23.1714	−	0.0363204i	−0.792908	−	0.00124286i
$855$	−14.6532	−	18.9870i	−0.501128	−	0.649342i
$856$	16.3230	+	18.5166i	0.557909	+	0.632884i
$857$	26.6130	−	31.7162i	0.909084	−	1.08340i	−0.0871067	−	0.996199i	$-0.527762\pi$
$857$	26.6130	−	31.7162i	0.909084	−	1.08340i	0.996190	−	0.0872048i	$-0.0277934\pi$
$858$	51.9832	+	47.4196i	1.77468	+	1.61888i
$859$	−15.7766	+	2.78185i	−0.538292	+	0.0949154i	−0.436183	−	0.899858i	$-0.643670\pi$
$859$	−15.7766	+	2.78185i	−0.538292	+	0.0949154i	−0.102109	+	0.994773i	$0.532559\pi$
$860$	10.6505	+	13.8308i	0.363178	+	0.471627i
$861$	12.6782	+	22.0120i	0.432073	+	0.750167i
$862$	11.7484	−	23.8750i	0.400153	−	0.813186i
$863$	17.0054	+	29.4542i	0.578871	+	1.00263i	0.995609	+	0.0936076i	$0.0298399\pi$
$863$	17.0054	+	29.4542i	0.578871	+	1.00263i	−0.416738	+	0.909027i	$0.636827\pi$
$864$	−14.4813	+	25.5791i	−0.492666	+	0.870219i
$865$	−5.10492	+	8.84199i	−0.173573	+	0.300637i
$866$	−23.1224	+	1.53542i	−0.785730	+	0.0521756i
$867$	−13.9376	+	3.43101i	−0.473344	+	0.116523i
$868$	0.764382	−	1.04093i	0.0259448	−	0.0353316i
$869$	21.5661	−	59.2523i	0.731579	−	2.01000i
$870$	−9.53340	+	43.4640i	−0.323213	+	1.47357i
$871$	49.1193	−	58.5381i	1.66434	−	1.98349i
$872$	9.29362	−	27.6111i	0.314722	−	0.935029i
$873$	31.9867	−	35.1025i	1.08259	−	1.18804i
$874$	10.0225	+	10.4517i	0.339017	+	0.353535i
$875$	14.8064	−	1.58525i	0.500548	−	0.0535913i
$876$	0.591730	+	0.471903i	0.0199927	+	0.0159441i
$877$	14.8655	+	5.41060i	0.501973	+	0.182703i	0.580581	−	0.814203i	$-0.302825\pi$
$877$	14.8655	+	5.41060i	0.501973	+	0.182703i	−0.0786085	+	0.996906i	$0.525048\pi$
$878$	−13.3579	−	30.2877i	−0.450807	−	1.02216i
$879$	29.1402	−	12.8703i	0.982876	−	0.434105i
$880$	−13.5323	−	49.8195i	−0.456172	−	1.67941i
$881$	−8.29314	+	4.78805i	−0.279403	+	0.161313i	−0.633153	−	0.774027i	$-0.718240\pi$
$881$	−8.29314	+	4.78805i	−0.279403	+	0.161313i	0.353750	+	0.935340i	$0.384906\pi$
$882$	−28.5019	−	8.34514i	−0.959709	−	0.280996i
$883$	−28.8205	−	16.6395i	−0.969887	−	0.559965i	−0.0706854	−	0.997499i	$-0.522519\pi$
$883$	−28.8205	−	16.6395i	−0.969887	−	0.559965i	−0.899202	+	0.437534i	$0.855852\pi$
$884$	46.7861	+	42.7243i	1.57359	+	1.43697i
$885$	−10.7425	+	21.8601i	−0.361105	+	0.734819i
$886$	0.837654	+	0.613090i	0.0281415	+	0.0205972i
$887$	−24.0794	+	20.2051i	−0.808509	+	0.678419i	−0.950251	−	0.311484i	$-0.899174\pi$
$887$	−24.0794	+	20.2051i	−0.808509	+	0.678419i	0.141743	+	0.989904i	$0.454729\pi$
$888$	2.21017	−	26.4688i	0.0741685	−	0.888234i
$889$	8.37566	+	11.4812i	0.280910	+	0.385068i
$890$	13.2788	+	54.0653i	0.445107	+	1.81227i
$891$	29.1786	+	28.8564i	0.977521	+	0.966725i
$892$	−38.1576	−	1.60049i	−1.27761	−	0.0535884i
$893$	6.27805	+	17.2488i	0.210087	+	0.577209i
$894$	−1.12335	+	27.1264i	−0.0375706	+	0.907242i
$895$	−36.6003	+	6.45362i	−1.22341	+	0.215721i
$896$	−29.8999	+	1.41252i	−0.998886	+	0.0471890i
$897$	−2.64193	−	39.4685i	−0.0882115	−	1.31781i
$898$	32.3891	−	21.6818i	1.08084	−	0.723532i
$899$	0.783186	+	1.35652i	0.0261207	+	0.0452424i
$900$	10.2975	−	14.8478i	0.343250	−	0.494927i
$901$	10.7435	−	18.6083i	0.357919	−	0.619934i
$902$	29.7038	−	19.8843i	0.989027	−	0.662073i
$903$	−2.43942	−	13.9189i	−0.0811787	−	0.463193i
$904$	6.67285	−	44.1080i	0.221936	−	1.46701i
$905$	−2.63164	+	7.23037i	−0.0874787	+	0.240346i
$906$	−9.14509	+	1.22487i	−0.303825	+	0.0406935i
$907$	24.6822	+	4.35214i	0.819559	+	0.144510i	0.567681	−	0.823248i	$-0.307841\pi$
$907$	24.6822	+	4.35214i	0.819559	+	0.144510i	0.251878	+	0.967759i	$0.418952\pi$
$908$	1.41680	−	33.7783i	0.0470183	−	1.12097i
$909$	1.48806	−	6.80151i	0.0493558	−	0.225592i
$910$	−57.8323	+	33.2687i	−1.91712	+	1.10285i
$911$	8.22479	−	46.6451i	0.272499	−	1.54542i	−0.474296	−	0.880366i	$-0.657297\pi$
$911$	8.22479	−	46.6451i	0.272499	−	1.54542i	0.746795	−	0.665055i	$-0.231592\pi$
$912$	9.49477	+	17.1108i	0.314403	+	0.566594i
$913$	−25.6042	+	21.4844i	−0.847374	+	0.711031i
$914$	−3.63127	+	33.4215i	−0.120112	+	1.10549i
$915$	−21.9021	+	21.0250i	−0.724060	+	0.695065i
$916$	−16.0729	−	3.53440i	−0.531064	−	0.116780i
$917$	−7.40078	+	2.13768i	−0.244395	+	0.0705924i
$918$	26.2604	+	25.9980i	0.866722	+	0.858061i
$919$	34.1929	−	19.7413i	1.12792	−	0.651205i	0.184509	−	0.982831i	$-0.440930\pi$
$919$	34.1929	−	19.7413i	1.12792	−	0.651205i	0.943411	+	0.331625i	$0.107597\pi$
$920$	−13.8941	+	25.4807i	−0.458076	+	0.840075i
$921$	20.5574	−	19.7342i	0.677389	−	0.650264i
$922$	23.5463	−	32.1709i	0.775456	−	1.05949i
$923$	−45.1800	−	16.4442i	−1.48712	−	0.541267i
$924$	−9.01750	+	40.8061i	−0.296654	+	1.34242i
$925$	−2.83527	+	16.0796i	−0.0932232	+	0.528695i
$926$	30.7634	−	7.55569i	1.01095	−	0.248295i
$927$	26.5071	−	20.4568i	0.870609	−	0.671890i
$928$	13.0135	−	33.8932i	0.427188	−	1.11260i
$929$	−10.8255	+	12.9014i	−0.355174	+	0.423280i	−0.913816	−	0.406129i	$-0.866878\pi$
$929$	−10.8255	+	12.9014i	−0.355174	+	0.423280i	0.558641	+	0.829409i	$0.311323\pi$
$930$	−0.224631	−	1.67714i	−0.00736593	−	0.0549954i
$931$	−14.6416	+	13.2865i	−0.479858	+	0.435448i
$932$	42.7800	+	17.6343i	1.40131	+	0.577629i
$933$	14.4540	+	32.7260i	0.473204	+	1.07140i
$934$	−40.3695	+	2.68070i	−1.32093	+	0.0877151i
$935$	−64.9003			−2.12247
$936$	10.1482	−	52.4833i	0.331703	−	1.71547i
$937$	2.11580	−	3.66467i	0.0691201	−	0.119719i	−0.829394	−	0.558664i	$-0.811314\pi$
$937$	2.11580	−	3.66467i	0.0691201	−	0.119719i	0.898514	+	0.438944i	$0.144648\pi$
$938$	44.6842	+	7.95126i	1.45899	+	0.259618i
$939$	43.4573	+	21.3558i	1.41817	+	0.696920i
$940$	−29.1486	+	22.4459i	−0.950721	+	0.732106i
$941$	5.41494	−	14.8774i	0.176522	−	0.484990i	−0.819604	−	0.572931i	$-0.805806\pi$
$941$	5.41494	−	14.8774i	0.176522	−	0.484990i	0.996126	+	0.0879406i	$0.0280286\pi$
$942$	−3.17051	+	5.00144i	−0.103301	+	0.162956i
$943$	−19.7900	−	3.48951i	−0.644451	−	0.113634i
$944$	11.3429	−	16.3181i	0.369180	−	0.531108i
$945$	−34.4845	+	18.0278i	−1.12178	+	0.586445i
$946$	−19.3108	+	4.74287i	−0.627849	+	0.154204i
$947$	1.51763	−	8.60693i	0.0493165	−	0.279688i	−0.950170	−	0.311732i	$-0.899091\pi$
$947$	1.51763	−	8.60693i	0.0493165	−	0.279688i	0.999486	+	0.0320448i	$0.0102019\pi$
$948$	−46.9542	+	9.49128i	−1.52500	+	0.308262i
$949$	−1.29341	−	0.470763i	−0.0419859	−	0.0152816i
$950$	−4.85420	−	11.0064i	−0.157491	−	0.357096i
$951$	−16.1770	−	24.1380i	−0.524575	−	0.782727i
$952$	−8.13943	+	36.7400i	−0.263800	+	1.19075i
$953$	7.97967	+	4.60707i	0.258487	+	0.149238i	0.623644	−	0.781708i	$-0.285651\pi$
$953$	7.97967	+	4.60707i	0.258487	+	0.149238i	−0.365157	+	0.930946i	$0.618985\pi$
$954$	−18.1227	+	0.461320i	−0.586745	+	0.0149358i
$955$			3.73152i			0.120749i
$956$	−3.21954	−	10.1504i	−0.104127	−	0.328287i
$957$	−40.9181	−	29.9151i	−1.32269	−	0.967018i
$958$	−24.4605	−	17.9030i	−0.790282	−	0.578418i
$959$	3.90117	−	57.3882i	0.125975	−	1.85316i
$960$	−26.9356	+	28.5076i	−0.869344	+	0.920080i
$961$	23.7017	+	19.8881i	0.764573	+	0.641553i
$962$	11.5212	+	46.9093i	0.371460	+	1.51242i
$963$	−22.1202	−	14.0059i	−0.712813	−	0.451335i
$964$	19.3413	−	10.1106i	0.622940	−	0.325640i
$965$	18.1201	+	3.19506i	0.583306	+	0.102853i
$966$	19.5370	−	13.0491i	0.628592	−	0.419849i
$967$	−8.43131	+	23.1648i	−0.271133	+	0.744931i	0.727157	+	0.686471i	$0.240841\pi$
$967$	−8.43131	+	23.1648i	−0.271133	+	0.744931i	−0.998290	+	0.0584598i	$0.981381\pi$
$968$	27.3820	+	4.14247i	0.880091	+	0.133144i
$969$	23.8876	−	5.88042i	0.767381	−	0.188906i
$970$	52.6568	−	35.2495i	1.69071	−	1.13179i
$971$	−23.2814	−	40.3245i	−0.747134	−	1.29407i	−0.949191	−	0.314700i	$-0.898096\pi$
$971$	−23.2814	−	40.3245i	−0.747134	−	1.29407i	0.202057	−	0.979374i	$-0.435237\pi$
$972$	7.14795	−	30.3464i	0.229270	−	0.973363i
$973$	−36.2721	−	8.96898i	−1.16283	−	0.287532i
$974$	8.94811	+	4.40319i	0.286716	+	0.141087i
$975$	−9.15152	+	31.5604i	−0.293083	+	1.01074i
$976$	20.2426	−	14.2777i	0.647950	−	0.457017i
$977$	14.8971	+	17.7537i	0.476601	+	0.567991i	0.949757	−	0.312988i	$-0.101330\pi$
$977$	14.8971	+	17.7537i	0.476601	+	0.567991i	−0.473156	+	0.880979i	$0.656885\pi$
$978$	−35.4314	+	38.8413i	−1.13297	+	1.24201i
$979$	−62.4534	−	11.0122i	−1.99602	−	0.351952i
$980$	−34.2553	−	19.9207i	−1.09424	−	0.636345i
$981$	−1.26214	+	30.8746i	−0.0402971	+	0.985752i
$982$	−35.2163	−	10.2319i	−1.12380	−	0.326513i
$983$	4.45945	−	25.2908i	0.142234	−	0.806651i	−0.827312	−	0.561743i	$-0.810131\pi$
$983$	4.45945	−	25.2908i	0.142234	−	0.806651i	0.969546	−	0.244908i	$-0.0787578\pi$
$984$	−24.6569	−	11.3791i	−0.786033	−	0.362752i
$985$	−10.0511	−	3.65829i	−0.320254	−	0.116563i
$986$	−36.8308	−	26.9569i	−1.17293	−	0.858484i
$987$	29.3342	−	5.14109i	0.933719	−	0.163643i
$988$	−26.2788	−	23.9974i	−0.836041	−	0.763459i
$989$	9.68124	+	5.58947i	0.307845	+	0.177735i
$990$	28.5759	+	46.7082i	0.908203	+	1.48448i
$991$	37.7382	−	21.7882i	1.19879	−	0.692124i	0.238508	−	0.971141i	$-0.423342\pi$
$991$	37.7382	−	21.7882i	1.19879	−	0.692124i	0.960286	+	0.279017i	$0.0900085\pi$
$992$	−0.0242044	+	1.38040i	−0.000768492	+	0.0438276i
$993$	27.1472	+	40.5068i	0.861490	+	1.28544i
$994$	−4.91463	−	28.1300i	−0.155883	−	0.892230i
$995$	2.50064	+	14.1818i	0.0792756	+	0.449594i
$996$	24.0703	+	8.08757i	0.762695	+	0.256265i
$997$	−1.63082	+	0.593569i	−0.0516485	+	0.0187985i	−0.367715	−	0.929938i	$-0.619860\pi$
$997$	−1.63082	+	0.593569i	−0.0516485	+	0.0187985i	0.316067	+	0.948737i	$0.397638\pi$
$998$	−0.386605	+	1.33062i	−0.0122378	+	0.0421201i
$999$	5.61112	+	27.6076i	0.177528	+	0.873467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bs.a.11.5	✓	840
4.3	odd	2	inner	756.2.bs.a.11.21	yes	840
7.2	even	3		756.2.ci.a.443.97	yes	840
27.5	odd	18		756.2.ci.a.599.75	yes	840
28.23	odd	6		756.2.ci.a.443.75	yes	840
108.59	even	18		756.2.ci.a.599.97	yes	840
189.86	odd	18	inner	756.2.bs.a.275.21	yes	840
756.275	even	18	inner	756.2.bs.a.275.5	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.11.5	✓	840	1.1	even	1	trivial
756.2.bs.a.11.21	yes	840	4.3	odd	2	inner
756.2.bs.a.275.5	yes	840	756.275	even	18	inner
756.2.bs.a.275.21	yes	840	189.86	odd	18	inner
756.2.ci.a.443.75	yes	840	28.23	odd	6
756.2.ci.a.443.97	yes	840	7.2	even	3
756.2.ci.a.599.75	yes	840	27.5	odd	18
756.2.ci.a.599.97	yes	840	108.59	even	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41111 + 0.0937031i) q^{2} +(1.68184 - 0.414019i) q^{3} +(1.98244 - 0.264450i) q^{4} +(-2.78746 + 0.491505i) q^{5} +(-2.33446 + 0.741819i) q^{6} +(2.41910 + 1.07144i) q^{7} +(-2.77265 + 0.558927i) q^{8} +(2.65718 - 1.39263i) q^{9} +O(q^{10})\)	\(q+(-1.41111 + 0.0937031i) q^{2} +(1.68184 - 0.414019i) q^{3} +(1.98244 - 0.264450i) q^{4} +(-2.78746 + 0.491505i) q^{5} +(-2.33446 + 0.741819i) q^{6} +(2.41910 + 1.07144i) q^{7} +(-2.77265 + 0.558927i) q^{8} +(2.65718 - 1.39263i) q^{9} +(3.88735 - 0.954760i) q^{10} +(-0.791789 + 4.49046i) q^{11} +(3.22466 - 1.26553i) q^{12} +(-4.82592 + 4.04942i) q^{13} +(-3.51400 - 1.28523i) q^{14} +(-4.48458 + 1.98070i) q^{15} +(3.86013 - 1.04851i) q^{16} -5.02863i q^{17} +(-3.61906 + 2.21413i) q^{18} +2.82448i q^{19} +(-5.39600 + 1.71152i) q^{20} +(4.51213 + 0.800431i) q^{21} +(0.696528 - 6.41071i) q^{22} +(-2.77708 + 2.33025i) q^{23} +(-4.43175 + 2.08796i) q^{24} +(2.82992 - 1.03001i) q^{25} +(6.43043 - 6.16637i) q^{26} +(3.89237 - 3.44230i) q^{27} +(5.07905 + 1.48433i) q^{28} +(-4.12541 + 4.91647i) q^{29} +(6.14262 - 3.21519i) q^{30} +(0.0834733 - 0.229341i) q^{31} +(-5.34881 + 1.84127i) q^{32} +(0.527473 + 7.88005i) q^{33} +(0.471198 + 7.09592i) q^{34} +(-7.26976 - 1.79759i) q^{35} +(4.89941 - 3.46349i) q^{36} +(-2.71086 + 4.69535i) q^{37} +(-0.264663 - 3.98564i) q^{38} +(-6.43988 + 8.80851i) q^{39} +(7.45395 - 2.92076i) q^{40} +(3.56309 + 4.24633i) q^{41} +(-6.44209 - 0.706693i) q^{42} +(-1.05467 - 2.89769i) q^{43} +(-0.382173 + 9.11145i) q^{44} +(-6.72230 + 5.18792i) q^{45} +(3.70040 - 3.54845i) q^{46} +(6.10689 - 2.22273i) q^{47} +(6.05802 - 3.36160i) q^{48} +(4.70405 + 5.18381i) q^{49} +(-3.89680 + 1.71862i) q^{50} +(-2.08195 - 8.45735i) q^{51} +(-8.49622 + 9.30395i) q^{52} +(3.70048 + 2.13647i) q^{53} +(-5.16999 + 5.22218i) q^{54} -12.9062i q^{55} +(-7.30617 - 1.61862i) q^{56} +(1.16939 + 4.75033i) q^{57} +(5.36070 - 7.32422i) q^{58} +(3.80592 - 3.19355i) q^{59} +(-8.36661 + 5.11256i) q^{60} +(5.81934 - 2.11807i) q^{61} +(-0.0962997 + 0.331446i) q^{62} +(7.92008 - 0.521910i) q^{63} +(7.37520 - 3.09942i) q^{64} +(11.4618 - 13.6596i) q^{65} +(-1.48271 - 11.0702i) q^{66} +(-11.9457 + 2.10634i) q^{67} +(-1.32982 - 9.96895i) q^{68} +(-3.70584 + 5.06887i) q^{69} +(10.4268 + 1.85539i) q^{70} +(3.81597 + 6.60946i) q^{71} +(-6.58905 + 5.34644i) q^{72} +(0.109243 + 0.189215i) q^{73} +(3.38534 - 6.87965i) q^{74} +(4.33303 - 2.90394i) q^{75} +(0.746934 + 5.59936i) q^{76} +(-6.72665 + 10.0145i) q^{77} +(8.26197 - 13.0332i) q^{78} +(-13.6186 - 2.40132i) q^{79} +(-10.2446 + 4.81996i) q^{80} +(5.12117 - 7.40092i) q^{81} +(-5.42579 - 5.65815i) q^{82} +(5.61528 + 4.71178i) q^{83} +(9.15670 + 0.393574i) q^{84} +(2.47160 + 14.0171i) q^{85} +(1.75978 + 3.99012i) q^{86} +(-4.90276 + 9.97671i) q^{87} +(-0.314485 - 12.8930i) q^{88} +13.9080i q^{89} +(8.99975 - 7.95060i) q^{90} +(-16.0130 + 4.62529i) q^{91} +(-4.88916 + 5.35397i) q^{92} +(0.0454372 - 0.420274i) q^{93} +(-8.40920 + 3.70874i) q^{94} +(-1.38825 - 7.87314i) q^{95} +(-8.23352 + 5.31123i) q^{96} +(14.8755 - 5.41422i) q^{97} +(-7.12366 - 6.87412i) q^{98} +(4.14962 + 13.0346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} - 6 q^{10} - 3 q^{12} - 24 q^{13} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} - 15 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} + 33 q^{30} + 27 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} + 6 q^{37} - 9 q^{38} + 12 q^{40} - 24 q^{41} - 21 q^{42} - 9 q^{44} - 30 q^{45} + 3 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} + 27 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} + 18 q^{65} - 3 q^{66} + 60 q^{68} - 48 q^{69} + 24 q^{70} - 63 q^{72} + 6 q^{73} - 75 q^{74} + 12 q^{77} + 6 q^{78} + 18 q^{81} - 6 q^{82} + 132 q^{84} + 6 q^{85} - 81 q^{86} + 45 q^{88} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} - 111 q^{96} - 24 q^{97} - 9 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 - 6 * q^10 - 3 * q^12 - 24 * q^13 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 - 15 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 + 33 * q^30 + 27 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 + 6 * q^37 - 9 * q^38 + 12 * q^40 - 24 * q^41 - 21 * q^42 - 9 * q^44 - 30 * q^45 + 3 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 + 27 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 + 18 * q^65 - 3 * q^66 + 60 * q^68 - 48 * q^69 + 24 * q^70 - 63 * q^72 + 6 * q^73 - 75 * q^74 + 12 * q^77 + 6 * q^78 + 18 * q^81 - 6 * q^82 + 132 * q^84 + 6 * q^85 - 81 * q^86 + 45 * q^88 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 - 111 * q^96 - 24 * q^97 - 9 * q^98

Introduction

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