LMFDB - Embedded newform 231.2.ba.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(19,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.ba (of order $30$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	231.19
Dual form			231.2.ba.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64148 + 0.277631i) q^{2} +(0.743145 + 0.669131i) q^{3} +(4.94404 - 1.05089i) q^{4} +(1.44910 + 3.25473i) q^{5} +(-2.14877 - 1.56118i) q^{6} +(1.42250 + 2.23081i) q^{7} +(-7.71576 + 2.50700i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-2.64148 + 0.277631i) q^{2} +(0.743145 + 0.669131i) q^{3} +(4.94404 - 1.05089i) q^{4} +(1.44910 + 3.25473i) q^{5} +(-2.14877 - 1.56118i) q^{6} +(1.42250 + 2.23081i) q^{7} +(-7.71576 + 2.50700i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-4.73138 - 8.19500i) q^{10} +(1.12772 - 3.11901i) q^{11} +(4.37732 + 2.52725i) q^{12} +(1.80443 - 1.31100i) q^{13} +(-4.37685 - 5.49770i) q^{14} +(-1.10095 + 3.38837i) q^{15} +(10.4500 - 4.65264i) q^{16} +(0.0154591 - 0.147084i) q^{17} +(-0.552220 - 2.59799i) q^{18} +(-4.87719 - 1.03668i) q^{19} +(10.5848 + 14.5687i) q^{20} +(-0.435577 + 2.60965i) q^{21} +(-2.11291 + 8.55191i) q^{22} +(-1.68815 + 2.92395i) q^{23} +(-7.41144 - 3.29979i) q^{24} +(-5.14774 + 5.71714i) q^{25} +(-4.40240 + 3.96394i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(9.37723 + 9.53431i) q^{28} +(3.76257 + 1.22253i) q^{29} +(1.96742 - 9.25598i) q^{30} +(1.44578 - 3.24727i) q^{31} +(-12.2599 + 7.07825i) q^{32} +(2.92509 - 1.56329i) q^{33} +0.392810i q^{34} +(-5.19933 + 7.86252i) q^{35} +(1.56193 + 4.80711i) q^{36} +(-0.0321926 - 0.0357535i) q^{37} +(13.1708 + 1.38431i) q^{38} +(2.21818 + 0.233141i) q^{39} +(-19.3405 - 21.4799i) q^{40} +(-1.87245 - 5.76281i) q^{41} +(0.426048 - 7.01427i) q^{42} +11.1948i q^{43} +(2.29775 - 16.6057i) q^{44} +(-3.08543 + 1.78137i) q^{45} +(3.64742 - 8.19225i) q^{46} +(1.86853 - 8.79073i) q^{47} +(10.8791 + 3.53483i) q^{48} +(-2.95299 + 6.34664i) q^{49} +(12.0104 - 16.5309i) q^{50} +(0.109906 - 0.0989602i) q^{51} +(7.54349 - 8.37789i) q^{52} +(4.53960 + 2.02116i) q^{53} +(1.32802 - 2.30019i) q^{54} +(11.7857 - 0.849347i) q^{55} +(-16.5683 - 13.6462i) q^{56} +(-2.93079 - 4.03388i) q^{57} +(-10.2782 - 2.18469i) q^{58} +(-1.52064 - 7.15405i) q^{59} +(-1.88234 + 17.9092i) q^{60} +(-2.07208 + 0.922549i) q^{61} +(-2.91745 + 8.97899i) q^{62} +(-2.06989 + 1.64789i) q^{63} +(11.9105 - 8.65351i) q^{64} +(6.88175 + 3.97318i) q^{65} +(-7.29254 + 4.94149i) q^{66} +(-3.70969 - 6.42537i) q^{67} +(-0.0781380 - 0.743433i) q^{68} +(-3.21104 + 1.04333i) q^{69} +(11.5511 - 22.2122i) q^{70} +(-10.8246 - 7.86454i) q^{71} +(-3.29979 - 7.41144i) q^{72} +(-0.101975 + 0.0216755i) q^{73} +(0.0949623 + 0.0855044i) q^{74} +(-7.65103 + 0.804156i) q^{75} -25.2025 q^{76} +(8.56209 - 1.92108i) q^{77} -5.92402 q^{78} +(6.38894 - 0.671505i) q^{79} +(30.2862 + 27.2698i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(6.54597 + 14.7025i) q^{82} +(1.32010 + 0.959106i) q^{83} +(0.588942 + 13.3600i) q^{84} +(0.501119 - 0.162824i) q^{85} +(-3.10803 - 29.5709i) q^{86} +(1.97810 + 3.42617i) q^{87} +(-0.881819 + 26.8928i) q^{88} +(13.3021 + 7.67995i) q^{89} +(7.65554 - 5.56207i) q^{90} +(5.49139 + 2.16045i) q^{91} +(-5.27352 + 16.2302i) q^{92} +(3.24727 - 1.44578i) q^{93} +(-2.49510 + 23.7393i) q^{94} +(-3.69343 - 17.3762i) q^{95} +(-13.8472 - 2.94330i) q^{96} +(-2.98618 - 4.11013i) q^{97} +(6.03823 - 17.5844i) q^{98} +(3.21981 + 0.795514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−2.64148	+	0.277631i	−1.86781	+	0.196315i	−0.969840	−	0.243744i	$-0.921624\pi$
$2$	−2.64148	+	0.277631i	−1.86781	+	0.196315i	−0.897969	+	0.440059i	$0.854958\pi$
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	4.94404	−	1.05089i	2.47202	−	0.525444i
$5$	1.44910	+	3.25473i	0.648057	+	1.45556i	0.876207	+	0.481935i	$0.160066\pi$
$5$	1.44910	+	3.25473i	0.648057	+	1.45556i	−0.228150	+	0.973626i	$0.573268\pi$
$6$	−2.14877	−	1.56118i	−0.877233	−	0.637347i
$7$	1.42250	+	2.23081i	0.537655	+	0.843165i
$7$	1.42250	+	2.23081i	0.537655	+	0.843165i
$8$	−7.71576	+	2.50700i	−2.72793	+	0.886360i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	−4.73138	−	8.19500i	−1.49619	−	2.59149i
$11$	1.12772	−	3.11901i	0.340020	−	0.940418i
$11$	1.12772	−	3.11901i	0.340020	−	0.940418i
$12$	4.37732	+	2.52725i	1.26362	+	0.729554i
$13$	1.80443	−	1.31100i	0.500460	−	0.363605i	−0.308733	−	0.951149i	$-0.599905\pi$
$13$	1.80443	−	1.31100i	0.500460	−	0.363605i	0.809193	+	0.587543i	$0.199905\pi$
$14$	−4.37685	−	5.49770i	−1.16976	−	1.46932i
$15$	−1.10095	+	3.38837i	−0.284264	+	0.874875i
$16$	10.4500	−	4.65264i	2.61250	−	1.16316i
$17$	0.0154591	−	0.147084i	0.00374938	−	0.0356730i	−0.992487	−	0.122348i	$-0.960958\pi$
$17$	0.0154591	−	0.147084i	0.00374938	−	0.0356730i	0.996237	+	0.0866751i	$0.0276242\pi$
$18$	−0.552220	−	2.59799i	−0.130159	−	0.612352i
$19$	−4.87719	−	1.03668i	−1.11890	−	0.237830i	−0.388905	−	0.921278i	$-0.627146\pi$
$19$	−4.87719	−	1.03668i	−1.11890	−	0.237830i	−0.730000	+	0.683448i	$0.760480\pi$
$20$	10.5848	+	14.5687i	2.36683	+	3.25766i
$21$	−0.435577	+	2.60965i	−0.0950506	+	0.569472i
$22$	−2.11291	+	8.55191i	−0.450474	+	1.82327i
$23$	−1.68815	+	2.92395i	−0.352003	+	0.609687i	−0.986600	−	0.163156i	$-0.947833\pi$
$23$	−1.68815	+	2.92395i	−0.352003	+	0.609687i	0.634598	+	0.772843i	$0.281166\pi$
$24$	−7.41144	−	3.29979i	−1.51285	−	0.673566i
$25$	−5.14774	+	5.71714i	−1.02955	+	1.14343i
$26$	−4.40240	+	3.96394i	−0.863382	+	0.777393i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	9.37723	+	9.53431i	1.77213	+	1.80182i
$29$	3.76257	+	1.22253i	0.698691	+	0.227019i	0.636760	−	0.771062i	$-0.280274\pi$
$29$	3.76257	+	1.22253i	0.698691	+	0.227019i	0.0619311	+	0.998080i	$0.480274\pi$
$30$	1.96742	−	9.25598i	0.359200	−	1.68990i
$31$	1.44578	−	3.24727i	0.259669	−	0.583226i	−0.735918	−	0.677071i	$-0.763249\pi$
$31$	1.44578	−	3.24727i	0.259669	−	0.583226i	0.995587	+	0.0938445i	$0.0299157\pi$
$32$	−12.2599	+	7.07825i	−2.16726	+	1.25127i
$33$	2.92509	−	1.56329i	0.509192	−	0.272134i
$34$			0.392810i			0.0673664i
$35$	−5.19933	+	7.86252i	−0.878847	+	1.32901i
$36$	1.56193	+	4.80711i	0.260321	+	0.801185i
$37$	−0.0321926	−	0.0357535i	−0.00529242	−	0.00587783i	0.740493	−	0.672064i	$-0.234592\pi$
$37$	−0.0321926	−	0.0357535i	−0.00529242	−	0.00587783i	−0.745785	+	0.666186i	$0.767925\pi$
$38$	13.1708	+	1.38431i	2.13659	+	0.224564i
$39$	2.21818	+	0.233141i	0.355194	+	0.0373324i
$40$	−19.3405	−	21.4799i	−3.05801	−	3.39626i
$41$	−1.87245	−	5.76281i	−0.292428	−	0.900000i	−0.984073	−	0.177763i	$-0.943114\pi$
$41$	−1.87245	−	5.76281i	−0.292428	−	0.900000i	0.691646	−	0.722237i	$-0.256886\pi$
$42$	0.426048	−	7.01427i	0.0657406	−	1.08233i
$43$			11.1948i			1.70719i	0.520934	+	0.853597i	$0.325584\pi$
$43$			11.1948i			1.70719i	−0.520934	+	0.853597i	$0.674416\pi$
$44$	2.29775	−	16.6057i	0.346398	−	2.50340i
$45$	−3.08543	+	1.78137i	−0.459949	+	0.265552i
$46$	3.64742	−	8.19225i	0.537783	−	1.20788i
$47$	1.86853	−	8.79073i	0.272553	−	1.28226i	−0.602456	−	0.798152i	$-0.705811\pi$
$47$	1.86853	−	8.79073i	0.272553	−	1.28226i	0.875008	−	0.484108i	$-0.160856\pi$
$48$	10.8791	+	3.53483i	1.57026	+	0.510208i
$49$	−2.95299	+	6.34664i	−0.421855	+	0.906663i
$50$	12.0104	−	16.5309i	1.69853	−	2.33782i
$51$	0.109906	−	0.0989602i	0.0153900	−	0.0138572i
$52$	7.54349	−	8.37789i	1.04609	−	1.16180i
$53$	4.53960	+	2.02116i	0.623562	+	0.277628i	0.694097	−	0.719881i	$-0.255804\pi$
$53$	4.53960	+	2.02116i	0.623562	+	0.277628i	−0.0705346	+	0.997509i	$0.522471\pi$
$54$	1.32802	−	2.30019i	0.180720	−	0.313016i
$55$	11.7857	−	0.849347i	1.58919	−	0.114526i
$56$	−16.5683	−	13.6462i	−2.21403	−	1.82354i
$57$	−2.93079	−	4.03388i	−0.388192	−	0.534300i
$58$	−10.2782	−	2.18469i	−1.34959	−	0.286864i
$59$	−1.52064	−	7.15405i	−0.197971	−	0.931378i	−0.959163	−	0.282852i	$-0.908719\pi$
$59$	−1.52064	−	7.15405i	−0.197971	−	0.931378i	0.761193	−	0.648526i	$-0.224614\pi$
$60$	−1.88234	+	17.9092i	−0.243009	+	2.31207i
$61$	−2.07208	+	0.922549i	−0.265302	+	0.118120i	−0.535077	−	0.844803i	$-0.679717\pi$
$61$	−2.07208	+	0.922549i	−0.265302	+	0.118120i	0.269775	+	0.962923i	$0.413051\pi$
$62$	−2.91745	+	8.97899i	−0.370516	+	1.14033i
$63$	−2.06989	+	1.64789i	−0.260782	+	0.207615i
$64$	11.9105	−	8.65351i	1.48882	−	1.08169i
$65$	6.88175	+	3.97318i	0.853577	+	0.492813i
$66$	−7.29254	+	4.94149i	−0.897649	+	0.608256i
$67$	−3.70969	−	6.42537i	−0.453210	−	0.784983i	0.545373	−	0.838194i	$-0.316388\pi$
$67$	−3.70969	−	6.42537i	−0.453210	−	0.784983i	−0.998583	+	0.0532101i	$0.983055\pi$
$68$	−0.0781380	−	0.743433i	−0.00947562	−	0.0901545i
$69$	−3.21104	+	1.04333i	−0.386564	+	0.125602i
$70$	11.5511	−	22.2122i	1.38061	−	2.65486i
$71$	−10.8246	−	7.86454i	−1.28465	−	0.933350i	−0.284963	−	0.958539i	$-0.591981\pi$
$71$	−10.8246	−	7.86454i	−1.28465	−	0.933350i	−0.999683	+	0.0251890i	$0.991981\pi$
$72$	−3.29979	−	7.41144i	−0.388884	−	0.873447i
$73$	−0.101975	+	0.0216755i	−0.0119353	+	0.00253693i	−0.213875	−	0.976861i	$-0.568609\pi$
$73$	−0.101975	+	0.0216755i	−0.0119353	+	0.00253693i	0.201940	+	0.979398i	$0.435275\pi$
$74$	0.0949623	+	0.0855044i	0.0110391	+	0.00993969i
$75$	−7.65103	+	0.804156i	−0.883465	+	0.0928559i
$76$	−25.2025			−2.89092
$77$	8.56209	−	1.92108i	0.975741	−	0.218928i
$78$	−5.92402			−0.670763
$79$	6.38894	−	0.671505i	0.718812	−	0.0755502i	0.261942	−	0.965084i	$-0.415637\pi$
$79$	6.38894	−	0.671505i	0.718812	−	0.0755502i	0.456870	+	0.889533i	$0.348970\pi$
$80$	30.2862	+	27.2698i	3.38610	+	3.04886i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	6.54597	+	14.7025i	0.722882	+	1.62362i
$83$	1.32010	+	0.959106i	0.144899	+	0.105276i	0.657873	−	0.753129i	$-0.271456\pi$
$83$	1.32010	+	0.959106i	0.144899	+	0.105276i	−0.512974	+	0.858404i	$0.671456\pi$
$84$	0.588942	+	13.3600i	0.0642589	+	1.45769i
$85$	0.501119	−	0.162824i	0.0543540	−	0.0176607i
$86$	−3.10803	−	29.5709i	−0.335147	−	3.18871i
$87$	1.97810	+	3.42617i	0.212075	+	0.367324i
$88$	−0.881819	+	26.8928i	−0.0940022	+	2.86678i
$89$	13.3021	+	7.67995i	1.41002	+	0.814073i	0.995389	−	0.0959192i	$-0.0305791\pi$
$89$	13.3021	+	7.67995i	1.41002	+	0.814073i	0.414626	+	0.909992i	$0.363912\pi$
$90$	7.65554	−	5.56207i	0.806965	−	0.586294i
$91$	5.49139	+	2.16045i	0.575654	+	0.226476i
$92$	−5.27352	+	16.2302i	−0.549802	+	1.69212i
$93$	3.24727	−	1.44578i	0.336726	−	0.149920i
$94$	−2.49510	+	23.7393i	−0.257350	+	2.44852i
$95$	−3.69343	−	17.3762i	−0.378937	−	1.78276i
$96$	−13.8472	−	2.94330i	−1.41327	−	0.300400i
$97$	−2.98618	−	4.11013i	−0.303201	−	0.417321i	0.630045	−	0.776559i	$-0.283037\pi$
$97$	−2.98618	−	4.11013i	−0.303201	−	0.417321i	−0.933246	+	0.359238i	$0.883037\pi$
$98$	6.03823	−	17.5844i	0.609954	−	1.77629i
$99$	3.21981	+	0.795514i	0.323603	+	0.0799521i
$100$	−19.4426	+	33.6755i	−1.94426	+	3.36755i
$101$	−5.45282	−	2.42775i	−0.542575	−	0.241570i	0.117101	−	0.993120i	$-0.462640\pi$
$101$	−5.45282	−	2.42775i	−0.542575	−	0.241570i	−0.659676	+	0.751550i	$0.729307\pi$
$102$	−0.262841	+	0.291915i	−0.0260252	+	0.0289039i
$103$	3.54126	−	3.18857i	0.348931	−	0.314179i	−0.475964	−	0.879465i	$-0.657901\pi$
$103$	3.54126	−	3.18857i	0.348931	−	0.314179i	0.824895	+	0.565286i	$0.191234\pi$
$104$	−10.6359	+	14.6391i	−1.04294	+	1.43548i
$105$	−9.12491	+	2.36396i	−0.890500	+	0.230699i
$106$	−12.5524	−	4.07852i	−1.21920	−	0.396141i
$107$	−2.45232	+	11.5373i	−0.237075	+	1.11535i	0.685062	+	0.728485i	$0.259775\pi$
$107$	−2.45232	+	11.5373i	−0.237075	+	1.11535i	−0.922137	+	0.386864i	$0.873558\pi$
$108$	−2.05585	+	4.61751i	−0.197824	+	0.444320i
$109$	6.67938	−	3.85634i	0.639768	−	0.369370i	−0.144757	−	0.989467i	$-0.546240\pi$
$109$	6.67938	−	3.85634i	0.639768	−	0.369370i	0.784525	+	0.620097i	$0.212907\pi$
$110$	−30.8960	+	5.51562i	−2.94582	+	0.525893i
$111$		−	0.0481110i		−	0.00456650i
$112$	25.2442	+	16.6935i	2.38536	+	1.57739i
$113$	2.34203	+	7.20803i	0.220320	+	0.678074i	0.998733	+	0.0503222i	$0.0160248\pi$
$113$	2.34203	+	7.20803i	0.220320	+	0.678074i	−0.778413	+	0.627752i	$0.783975\pi$
$114$	8.86154	+	9.84174i	0.829959	+	0.921763i
$115$	−11.9630	−	1.25736i	−1.11555	−	0.117249i
$116$	19.8870	+	2.09021i	1.84647	+	0.194071i
$117$	1.49243	+	1.65751i	0.137975	+	0.153237i
$118$	6.00293	+	18.4751i	0.552614	+	1.70077i
$119$	0.350105	−	0.174740i	0.0320941	−	0.0160184i
$120$		−	28.9040i		−	2.63856i
$121$	−8.45651	−	7.03473i	−0.768773	−	0.639521i
$122$	5.21723	−	3.01217i	0.472345	−	0.272709i
$123$	2.46457	−	5.53552i	0.222223	−	0.499121i
$124$	3.73547	−	17.5740i	0.335455	−	1.57819i
$125$	−9.12549	−	2.96505i	−0.816208	−	0.265202i
$126$	5.01008	−	4.92754i	0.446333	−	0.438980i
$127$	11.8105	−	16.2558i	1.04801	−	1.44247i	0.157494	−	0.987520i	$-0.449659\pi$
$127$	11.8105	−	16.2558i	1.04801	−	1.44247i	0.890519	−	0.454946i	$-0.150341\pi$
$128$	−8.01828	+	7.21969i	−0.708722	+	0.638137i
$129$	−7.49079	+	8.31937i	−0.659528	+	0.732480i
$130$	−19.2811	−	8.58450i	−1.69106	−	0.752910i
$131$	3.70839	−	6.42312i	0.324004	−	0.561191i	−0.657307	−	0.753623i	$-0.728304\pi$
$131$	3.70839	−	6.42312i	0.324004	−	0.561191i	0.981310	+	0.192432i	$0.0616376\pi$
$132$	12.8189	−	10.8029i	1.11574	−	0.940273i
$133$	−4.62518	−	12.3547i	−0.401054	−	1.07129i
$134$	11.5829	+	15.9426i	1.00061	+	1.37723i
$135$	−3.48489	−	0.740737i	−0.299932	−	0.0637525i
$136$	0.249460	+	1.17362i	0.0213910	+	0.100637i
$137$	−0.252318	+	2.40065i	−0.0215570	+	0.205101i	−0.999999	−	0.00142059i	$-0.999548\pi$
$137$	−0.252318	+	2.40065i	−0.0215570	+	0.205101i	0.978442	+	0.206522i	$0.0662145\pi$
$138$	8.19225	−	3.64742i	0.697370	−	0.310489i
$139$	6.59180	−	20.2875i	0.559109	−	1.72076i	−0.125728	−	0.992065i	$-0.540127\pi$
$139$	6.59180	−	20.2875i	0.559109	−	1.72076i	0.684837	−	0.728696i	$-0.259873\pi$
$140$	−17.4431	+	44.3366i	−1.47421	+	3.74712i
$141$	7.27074	−	5.28250i	0.612306	−	0.444867i
$142$	30.7764	+	17.7688i	2.58270	+	1.49112i
$143$	−2.05413	−	7.10649i	−0.171775	−	0.594275i
$144$	5.71947	+	9.90641i	0.476623	+	0.825535i
$145$	1.47332	+	14.0177i	0.122353	+	1.16411i
$146$	0.263348	−	0.0855671i	0.0217949	−	0.00708158i
$147$	−6.44123	+	2.74054i	−0.531264	+	0.226036i
$148$	−0.196734	−	0.142936i	−0.0161715	−	0.0117493i
$149$	6.18530	+	13.8924i	0.506719	+	1.13811i	0.968021	+	0.250867i	$0.0807158\pi$
$149$	6.18530	+	13.8924i	0.506719	+	1.13811i	−0.461302	+	0.887243i	$0.652618\pi$
$150$	19.9868	−	4.24832i	1.63191	−	0.346874i
$151$	3.90566	+	3.51667i	0.317838	+	0.286183i	0.812571	−	0.582863i	$-0.198067\pi$
$151$	3.90566	+	3.51667i	0.317838	+	0.286183i	−0.494733	+	0.869045i	$0.664734\pi$
$152$	40.2302	−	4.22837i	3.26310	−	0.342966i
$153$	0.147894			0.0119565
$154$	−22.0832	+	7.45160i	−1.77952	+	0.600467i
$155$	12.6641			1.01720
$156$	11.2118	−	1.17841i	0.897663	−	0.0943482i
$157$	−9.54070	−	8.59048i	−0.761431	−	0.685595i	0.193937	−	0.981014i	$-0.437874\pi$
$157$	−9.54070	−	8.59048i	−0.761431	−	0.685595i	−0.955368	+	0.295419i	$0.904541\pi$
$158$	−16.6898	+	3.54753i	−1.32777	+	0.282227i
$159$	2.02116	+	4.53960i	0.160289	+	0.360014i
$160$	−40.8036	−	29.6456i	−3.22581	−	2.34369i
$161$	−8.92416	+	0.393400i	−0.703322	+	0.0310043i
$162$	2.52603	−	0.820758i	0.198464	−	0.0644849i
$163$	−1.37574	−	13.0893i	−0.107757	−	1.02523i	−0.906109	−	0.423044i	$-0.860961\pi$
$163$	−1.37574	−	13.0893i	−0.107757	−	1.02523i	0.798352	−	0.602191i	$-0.205705\pi$
$164$	−15.3135	−	26.5238i	−1.19579	−	2.07116i
$165$	9.32683	+	7.25501i	0.726093	+	0.564802i
$166$	−3.75328	−	2.16696i	−0.291311	−	0.168189i
$167$	−11.5996	+	8.42762i	−0.897606	+	0.652149i	−0.937850	−	0.347041i	$-0.887186\pi$
$167$	−11.5996	+	8.42762i	−0.897606	+	0.652149i	0.0402442	+	0.999190i	$0.487186\pi$
$168$	−3.18160	−	21.2274i	−0.245465	−	1.63773i
$169$	−2.47995	+	7.63252i	−0.190766	+	0.587117i
$170$	−1.27849	+	0.569221i	−0.0980559	+	0.0436573i
$171$	0.521195	−	4.95883i	0.0398567	−	0.379212i
$172$	11.7645	+	55.3477i	0.897035	+	4.22022i
$173$	0.747942	+	0.158980i	0.0568650	+	0.0120870i	0.236256	−	0.971691i	$-0.424079\pi$
$173$	0.747942	+	0.158980i	0.0568650	+	0.0120870i	−0.179391	+	0.983778i	$0.557413\pi$
$174$	−6.17632	−	8.50098i	−0.468226	−	0.644457i
$175$	−20.0765	−	3.35097i	−1.51764	−	0.253309i
$176$	−2.72701	−	37.8405i	−0.205556	−	2.85234i
$177$	3.65694	−	6.33400i	0.274872	−	0.476093i
$178$	−37.2693	−	16.5934i	−2.79345	−	1.24373i
$179$	12.3691	−	13.7373i	0.924508	−	1.02677i	−0.0750539	−	0.997179i	$-0.523913\pi$
$179$	12.3691	−	13.7373i	0.924508	−	1.02677i	0.999562	−	0.0295909i	$-0.00942044\pi$
$180$	−13.3825	+	12.0496i	−0.997471	+	0.898127i
$181$	−3.33835	+	4.59484i	−0.248137	+	0.341532i	−0.914858	−	0.403776i	$-0.867697\pi$
$181$	−3.33835	+	4.59484i	−0.248137	+	0.341532i	0.666720	+	0.745308i	$0.267697\pi$
$182$	−15.1052	−	4.18220i	−1.11967	−	0.310005i
$183$	−2.15716	−	0.700904i	−0.159462	−	0.0518123i
$184$	5.69497	−	26.7927i	0.419839	−	1.97519i
$185$	0.0697177	−	0.156589i	0.00512575	−	0.0115126i
$186$	−8.17620	+	4.72053i	−0.599508	+	0.346126i
$187$	−0.441322	−	0.214086i	−0.0322727	−	0.0156555i
$188$		−	45.4254i		−	3.31299i
$189$	−2.64088	−	0.160408i	−0.192096	−	0.0116679i
$190$	14.5803	+	44.8735i	1.05776	+	3.25546i
$191$	12.3119	+	13.6738i	0.890859	+	0.989399i	0.999989	−	0.00462875i	$-0.00147338\pi$
$191$	12.3119	+	13.6738i	0.890859	+	0.989399i	−0.109131	+	0.994027i	$0.534807\pi$
$192$	14.6416	+	1.53889i	1.05666	+	0.111060i
$193$	9.87696	+	1.03811i	0.710959	+	0.0747248i	0.453103	−	0.891458i	$-0.350317\pi$
$193$	9.87696	+	1.03811i	0.710959	+	0.0747248i	0.257856	+	0.966183i	$0.416984\pi$
$194$	9.02905	+	10.0278i	0.648248	+	0.719952i
$195$	2.45556	+	7.55744i	0.175846	+	0.541200i
$196$	−7.93008	+	34.4813i	−0.566434	+	2.46295i
$197$			1.19303i			0.0849997i	0.999096	+	0.0424998i	$0.0135322\pi$
$197$			1.19303i			0.0849997i	−0.999096	+	0.0424998i	$0.986468\pi$
$198$	−8.72592	−	1.20742i	−0.620124	−	0.0858073i
$199$	−10.4282	+	6.02070i	−0.739233	+	0.426796i	−0.821790	−	0.569790i	$-0.807025\pi$
$199$	−10.4282	+	6.02070i	−0.739233	+	0.426796i	0.0825574	+	0.996586i	$0.473691\pi$
$200$	25.3858	−	57.0175i	1.79505	−	4.03175i
$201$	1.54257	−	7.25724i	0.108805	−	0.511886i
$202$	15.0775	+	4.89898i	1.06085	+	0.344691i
$203$	2.62502	+	10.1326i	0.184240	+	0.711170i
$204$	0.439386	−	0.604763i	0.0307632	−	0.0423419i
$205$	16.0430	−	14.4452i	1.12049	−	1.00890i
$206$	−8.46893	+	9.40570i	−0.590058	+	0.655326i
$207$	−3.08440	−	1.37326i	−0.214380	−	0.0954483i
$208$	12.7567	−	22.0953i	0.884520	−	1.53203i
$209$	−8.73351	+	14.0429i	−0.604109	+	0.971371i
$210$	23.4470	−	8.77771i	1.61799	−	0.605719i
$211$	−0.314910	−	0.433436i	−0.0216793	−	0.0298390i	0.798040	−	0.602605i	$-0.205870\pi$
$211$	−0.314910	−	0.433436i	−0.0216793	−	0.0298390i	−0.819719	+	0.572766i	$0.805870\pi$
$212$	24.5680	+	5.22209i	1.68734	+	0.358655i
$213$	−2.78185	−	13.0876i	−0.190609	−	0.896746i
$214$	3.27466	−	31.1563i	0.223851	−	2.12980i
$215$	−36.4361	+	16.2224i	−2.48492	+	1.10636i
$216$	2.50700	−	7.71576i	0.170580	−	0.524991i
$217$	9.30064	−	1.39399i	0.631369	−	0.0946303i
$218$	−16.5728	+	12.0408i	−1.12245	+	0.815509i
$219$	−0.0902863	−	0.0521268i	−0.00610098	−	0.00352240i
$220$	57.3766	−	16.5847i	3.86833	−	1.11814i
$221$	−0.164931	−	0.285669i	−0.0110945	−	0.0192162i
$222$	0.0133571	+	0.127084i	0.000896470	+	0.00852934i
$223$	−11.1267	+	3.61528i	−0.745098	+	0.242097i	−0.656871	−	0.754003i	$-0.728120\pi$
$223$	−11.1267	+	3.61528i	−0.745098	+	0.242097i	−0.0882277	+	0.996100i	$0.528120\pi$
$224$	−33.2299	−	17.2806i	−2.22027	−	1.15461i
$225$	−6.22391	−	4.52194i	−0.414927	−	0.301462i
$226$	−8.18760	−	18.3896i	−0.544631	−	1.22326i
$227$	3.36018	−	0.714228i	0.223023	−	0.0474050i	−0.0950448	−	0.995473i	$-0.530299\pi$
$227$	3.36018	−	0.714228i	0.223023	−	0.0474050i	0.318068	+	0.948068i	$0.396966\pi$
$228$	−18.7291	−	16.8637i	−1.24036	−	1.11683i
$229$	12.6888	−	1.33364i	0.838498	−	0.0881296i	0.324462	−	0.945899i	$-0.394817\pi$
$229$	12.6888	−	1.33364i	0.838498	−	0.0881296i	0.514035	+	0.857769i	$0.328150\pi$
$230$	31.9491			2.10666
$231$	7.64833	+	4.30152i	0.503223	+	0.283019i
$232$	−32.0960			−2.10720
$233$	−15.3525	+	1.61362i	−1.00578	+	0.105712i	−0.593069	−	0.805151i	$-0.702084\pi$
$233$	−15.3525	+	1.61362i	−1.00578	+	0.105712i	−0.412709	+	0.910863i	$0.635417\pi$
$234$	−4.40240	−	3.96394i	−0.287794	−	0.259131i
$235$	31.3192	−	6.65709i	2.04304	−	0.434261i
$236$	−15.0362	−	33.7719i	−0.978775	−	2.19836i
$237$	5.19723	+	3.77601i	0.337597	+	0.245278i
$238$	−0.876283	+	0.558773i	−0.0568010	+	0.0362199i
$239$	10.4809	−	3.40546i	0.677955	−	0.220281i	0.0502553	−	0.998736i	$-0.483996\pi$
$239$	10.4809	−	3.40546i	0.677955	−	0.220281i	0.627700	+	0.778455i	$0.283996\pi$
$240$	4.25996	+	40.5308i	0.274979	+	2.61625i
$241$	12.4498	+	21.5636i	0.801960	+	1.38904i	0.918324	+	0.395829i	$0.129543\pi$
$241$	12.4498	+	21.5636i	0.801960	+	1.38904i	−0.116364	+	0.993207i	$0.537124\pi$
$242$	24.2908	+	16.2343i	1.56147	+	1.04358i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−9.27495	+	6.73864i	−0.593768	+	0.431397i
$245$	−24.9358	−	0.414260i	−1.59309	−	0.0264661i
$246$	−4.97328	+	15.3062i	−0.317085	+	0.975887i
$247$	−10.1597	+	4.52337i	−0.646443	+	0.287815i
$248$	−3.01436	+	28.6797i	−0.191412	+	1.82116i
$249$	0.339255	+	1.59607i	0.0214994	+	0.101147i
$250$	24.9280	+	5.29861i	1.57658	+	0.335113i
$251$	−15.9067	−	21.8938i	−1.00403	−	1.38192i	−0.922823	−	0.385224i	$-0.874124\pi$
$251$	−15.9067	−	21.8938i	−1.00403	−	1.38192i	−0.0812021	−	0.996698i	$-0.525876\pi$
$252$	−8.50189	+	10.3225i	−0.535569	+	0.650254i
$253$	7.21611	+	8.56275i	0.453673	+	0.538335i
$254$	−26.6841	+	46.2182i	−1.67431	+	2.89999i
$255$	0.481355	+	0.214313i	0.0301436	+	0.0134208i
$256$	−0.526464	+	0.584697i	−0.0329040	+	0.0365436i
$257$	0.752289	−	0.677364i	0.0469265	−	0.0422528i	−0.645334	−	0.763901i	$-0.723282\pi$
$257$	0.752289	−	0.677364i	0.0469265	−	0.0422528i	0.692260	+	0.721648i	$0.256615\pi$
$258$	17.4771	−	24.0551i	1.08807	−	1.49761i
$259$	0.0339651	−	0.122675i	0.00211049	−	0.00762263i
$260$	38.1991	+	12.4116i	2.36901	+	0.769737i
$261$	−0.822540	+	3.86975i	−0.0509139	+	0.239531i
$262$	−8.01239	+	17.9961i	−0.495007	+	1.11180i
$263$	−12.6157	+	7.28366i	−0.777916	+	0.449130i	−0.835691	−	0.549200i	$-0.814933\pi$
$263$	−12.6157	+	7.28366i	−0.777916	+	0.449130i	0.0577754	+	0.998330i	$0.481599\pi$
$264$	−18.6501	+	19.3952i	−1.14783	+	1.19369i
$265$			17.7041i			1.08755i
$266$	15.6474	+	31.3507i	0.959401	+	1.92224i
$267$	4.74647	+	14.6081i	0.290479	+	0.894003i
$268$	−25.0932	−	27.8688i	−1.53281	−	1.70236i
$269$	7.42512	+	0.780412i	0.452718	+	0.0475825i	0.328144	−	0.944628i	$-0.393577\pi$
$269$	7.42512	+	0.780412i	0.452718	+	0.0475825i	0.124574	+	0.992210i	$0.460244\pi$
$270$	9.41093	+	0.989129i	0.572731	+	0.0601964i
$271$	−7.33290	−	8.14401i	−0.445442	−	0.494713i	0.478049	−	0.878333i	$-0.341344\pi$
$271$	−7.33290	−	8.14401i	−0.445442	−	0.494713i	−0.923491	+	0.383620i	$0.874677\pi$
$272$	−0.522779	−	1.60895i	−0.0316981	−	0.0975568i
$273$	2.63528	+	5.27998i	0.159494	+	0.319559i
$274$		−	6.41132i		−	0.387322i
$275$	12.0267	+	22.5032i	0.725235	+	1.35699i
$276$	−14.7791	+	8.53273i	−0.889598	+	0.513610i
$277$	−2.46632	+	5.53945i	−0.148187	+	0.332833i	−0.972353	−	0.233514i	$-0.924977\pi$
$277$	−2.46632	+	5.53945i	−0.148187	+	0.332833i	0.824166	+	0.566348i	$0.191644\pi$
$278$	−11.7797	+	55.4190i	−0.706498	+	3.32381i
$279$	3.38060	+	1.09842i	0.202391	+	0.0657610i
$280$	20.4054	−	73.7001i	1.21946	−	4.40442i
$281$	4.30956	−	5.93160i	0.257087	−	0.353850i	−0.660891	−	0.750482i	$-0.729821\pi$
$281$	4.30956	−	5.93160i	0.257087	−	0.353850i	0.917978	+	0.396632i	$0.129821\pi$
$282$	−17.7389	+	15.9722i	−1.05634	+	0.951130i
$283$	8.28364	−	9.19992i	0.492412	−	0.546878i	−0.444805	−	0.895628i	$-0.646727\pi$
$283$	8.28364	−	9.19992i	0.492412	−	0.546878i	0.937216	+	0.348749i	$0.113394\pi$
$284$	−61.7821	−	27.5072i	−3.66609	−	1.63225i
$285$	8.88220	−	15.3844i	0.526136	−	0.911294i
$286$	7.39893	+	18.2014i	0.437508	+	1.07627i
$287$	10.1921	−	12.3747i	0.601623	−	0.730454i
$288$	−8.32099	−	11.4529i	−0.490319	−	0.674866i
$289$	16.6071	+	3.52995i	0.976889	+	0.207644i
$290$	−7.78350	−	36.6185i	−0.457063	−	2.15031i
$291$	0.531046	−	5.05257i	0.0311305	−	0.296187i
$292$	−0.481392	+	0.214330i	−0.0281714	+	0.0125427i
$293$	2.62831	−	8.08910i	0.153547	−	0.472570i	−0.844463	−	0.535613i	$-0.820081\pi$
$293$	2.62831	−	8.08910i	0.153547	−	0.472570i	0.998011	+	0.0630429i	$0.0200805\pi$
$294$	16.2535	−	9.02737i	0.947925	−	0.526487i
$295$	21.0810	−	15.3162i	1.22738	−	0.891744i
$296$	0.338024	+	0.195158i	0.0196473	+	0.0113434i
$297$	1.86048	+	2.74565i	0.107956	+	0.159319i
$298$	−20.1953	−	34.9793i	−1.16988	−	2.02630i
$299$	0.787151	+	7.48924i	0.0455221	+	0.433114i
$300$	−36.9820	+	12.0162i	−2.13515	+	0.693754i
$301$	−24.9735	+	15.9246i	−1.43945	+	0.917880i
$302$	−11.2931	−	8.20488i	−0.649842	−	0.472138i
$303$	−2.42775	−	5.45282i	−0.139471	−	0.313256i
$304$	−55.7899	+	11.8585i	−3.19977	+	0.680132i
$305$	−6.00530	−	5.40719i	−0.343862	−	0.309615i
$306$	−0.390658	+	0.0410599i	−0.0223325	+	0.00234724i
$307$	−19.1751			−1.09438			−0.547189	−	0.837009i	$-0.684302\pi$
$307$	−19.1751			−1.09438			−0.547189	+	0.837009i	$0.684302\pi$
$308$	40.3125	−	18.4957i	2.29702	−	1.05389i
$309$	4.76524			0.271085
$310$	−33.4519	+	3.51593i	−1.89994	+	0.199692i
$311$	−4.83692	−	4.35518i	−0.274277	−	0.246960i	0.520500	−	0.853862i	$-0.325745\pi$
$311$	−4.83692	−	4.35518i	−0.274277	−	0.246960i	−0.794777	+	0.606902i	$0.792412\pi$
$312$	−17.6995	+	3.76214i	−1.00204	+	0.212989i
$313$	9.20554	+	20.6760i	0.520328	+	1.16868i	0.962385	+	0.271689i	$0.0875821\pi$
$313$	9.20554	+	20.6760i	0.520328	+	1.16868i	−0.442057	+	0.896987i	$0.645751\pi$
$314$	27.5866	+	20.0428i	1.55680	+	1.13108i
$315$	−8.36292	−	4.34899i	−0.471197	−	0.245038i
$316$	30.8815	−	10.0340i	1.73722	−	0.564457i
$317$	−0.328491	−	3.12538i	−0.0184499	−	0.175539i	0.981416	−	0.191890i	$-0.0614617\pi$
$317$	−0.328491	−	3.12538i	−0.0184499	−	0.175539i	−0.999866	+	0.0163511i	$0.994795\pi$
$318$	−6.59919	−	11.4301i	−0.370064	−	0.640970i
$319$	8.05621	−	10.3568i	0.451061	−	0.579872i
$320$	45.4244	+	26.2258i	2.53930	+	1.46607i
$321$	−9.54237	+	6.93294i	−0.532603	+	0.386959i
$322$	23.4638	−	3.51678i	1.30759	−	0.195983i
$323$	−0.227875	+	0.701328i	−0.0126793	+	0.0390230i
$324$	−4.61751	+	2.05585i	−0.256528	+	0.114214i
$325$	−1.79359	+	17.0649i	−0.0994906	+	0.946589i
$326$	7.26800	+	34.1932i	0.402537	+	1.89379i
$327$	7.54414	+	1.60356i	0.417192	+	0.0886769i
$328$	28.8948	+	39.7702i	1.59545	+	2.19594i
$329$	22.2684	−	8.33650i	1.22770	−	0.459606i
$330$	−26.6509	−	16.5745i	−1.46708	−	0.912399i
$331$	0.0775113	−	0.134253i	0.00426041	−	0.00737924i	−0.863887	−	0.503685i	$-0.831977\pi$
$331$	0.0775113	−	0.134253i	0.00426041	−	0.00737924i	0.868148	+	0.496306i	$0.165311\pi$
$332$	7.53453	+	3.35459i	0.413511	+	0.184107i
$333$	0.0321926	−	0.0357535i	0.00176414	−	0.00195928i
$334$	28.3004	−	25.4818i	1.54853	−	1.39430i
$335$	15.5371	−	21.3850i	0.848885	−	1.16839i
$336$	7.58998	+	29.2974i	0.414067	+	1.59830i
$337$	−25.1318	−	8.16582i	−1.36902	−	0.444821i	−0.469974	−	0.882680i	$-0.655737\pi$
$337$	−25.1318	−	8.16582i	−1.36902	−	0.444821i	−0.899043	+	0.437860i	$0.855737\pi$
$338$	4.43173	−	20.8497i	0.241054	−	1.13407i
$339$	−3.08264	+	6.92373i	−0.167426	+	0.376046i
$340$	2.30645	−	1.33163i	0.125085	−	0.0722177i
$341$	−8.49785	−	8.17140i	−0.460184	−	0.442506i
$342$			13.2434i			0.716119i
$343$	−18.3587	+	2.44056i	−0.991279	+	0.131778i
$344$	−28.0654	−	86.3766i	−1.51319	−	4.65711i
$345$	−8.04889	−	8.93920i	−0.433338	−	0.481270i
$346$	−2.01981	−	0.212291i	−0.108586	−	0.0114128i
$347$	−28.1701	−	2.96080i	−1.51225	−	0.158944i	−0.688226	−	0.725496i	$-0.741610\pi$
$347$	−28.1701	−	2.96080i	−1.51225	−	0.158944i	−0.824026	+	0.566552i	$0.808277\pi$
$348$	13.3803	+	14.8604i	0.717261	+	0.796599i
$349$	−2.75050	−	8.46518i	−0.147231	−	0.453131i	0.850060	−	0.526686i	$-0.176566\pi$
$349$	−2.75050	−	8.46518i	−0.147231	−	0.453131i	−0.997291	+	0.0735550i	$0.976566\pi$
$350$	53.9620	+	3.27766i	2.88439	+	0.175198i
$351$			2.23040i			0.119050i
$352$	8.25148	+	46.2211i	0.439805	+	2.46359i
$353$	10.0267	−	5.78892i	0.533668	−	0.308113i	−0.208841	−	0.977950i	$-0.566969\pi$
$353$	10.0267	−	5.78892i	0.533668	−	0.308113i	0.742509	+	0.669836i	$0.233636\pi$
$354$	−7.90122	+	17.7464i	−0.419945	+	0.943212i
$355$	9.91103	−	46.6277i	0.526023	−	2.47474i
$356$	73.8367	+	23.9910i	3.91334	+	1.27152i
$357$	0.377103	+	0.104409i	0.0199584	+	0.00552591i
$358$	−28.8588	+	39.7207i	−1.52523	+	2.09930i
$359$	−6.64622	+	5.98429i	−0.350774	+	0.315839i	−0.825616	−	0.564233i	$-0.809172\pi$
$359$	−6.64622	+	5.98429i	−0.350774	+	0.315839i	0.474841	+	0.880071i	$0.342505\pi$
$360$	19.3405	−	21.4799i	1.01934	−	1.13209i
$361$	5.35492	+	2.38416i	0.281838	+	0.125482i
$362$	7.54251	−	13.0640i	0.396425	−	0.686629i
$363$	−1.57725	−	10.8863i	−0.0827844	−	0.571384i
$364$	29.4201	+	4.91050i	1.54203	+	0.257380i
$365$	−0.218321	−	0.300493i	−0.0114274	−	0.0157285i
$366$	5.89269	+	1.25253i	0.308016	+	0.0654708i
$367$	2.66660	+	12.5454i	0.139196	+	0.654864i	0.991314	+	0.131515i	$0.0419842\pi$
$367$	2.66660	+	12.5454i	0.139196	+	0.654864i	−0.852119	+	0.523349i	$0.824682\pi$
$368$	−4.03702	+	38.4096i	−0.210444	+	2.00224i
$369$	5.53552	−	2.46457i	0.288167	−	0.128300i
$370$	−0.140684	+	0.432981i	−0.00731382	+	0.0225096i
$371$	1.94877	+	13.0021i	0.101175	+	0.675034i
$372$	14.5353	−	10.5605i	0.753619	−	0.547536i
$373$	−12.3446	−	7.12718i	−0.639181	−	0.369031i	0.145118	−	0.989414i	$-0.453644\pi$
$373$	−12.3446	−	7.12718i	−0.639181	−	0.369031i	−0.784299	+	0.620383i	$0.786977\pi$
$374$	1.22518	+	0.442979i	0.0633526	+	0.0229059i
$375$	−4.79755	−	8.30961i	−0.247745	−	0.429106i
$376$	7.62128	+	72.5116i	0.393038	+	3.73950i
$377$	8.39204	−	2.72674i	0.432212	−	0.140434i
$378$	7.02038	−	0.309477i	0.361089	−	0.0159178i
$379$	−11.8614	−	8.61780i	−0.609279	−	0.442667i	0.239882	−	0.970802i	$-0.422891\pi$
$379$	−11.8614	−	8.61780i	−0.609279	−	0.442667i	−0.849160	+	0.528135i	$0.822891\pi$
$380$	−36.5209	−	82.0273i	−1.87348	−	4.20791i
$381$	19.6541	−	4.17762i	1.00691	−	0.214026i
$382$	−36.3179	−	32.7008i	−1.85819	−	1.67312i
$383$	−38.3268	+	4.02831i	−1.95841	+	0.205837i	−0.997480	−	0.0709522i	$-0.977396\pi$
$383$	−38.3268	+	4.02831i	−1.95841	+	0.205837i	−0.960931	+	0.276789i	$0.910730\pi$
$384$	−10.7897			−0.550607
$385$	18.6599	+	25.0835i	0.950998	+	1.27837i
$386$	−26.3780			−1.34260
$387$	−11.1335	+	1.17018i	−0.565947	+	0.0594834i
$388$	−19.0831	−	17.1825i	−0.968799	−	0.872310i
$389$	−13.3330	+	2.83402i	−0.676012	+	0.143691i	−0.533110	−	0.846046i	$-0.678977\pi$
$389$	−13.3330	+	2.83402i	−0.676012	+	0.143691i	−0.142902	+	0.989737i	$0.545643\pi$
$390$	−8.58450	−	19.2811i	−0.434693	−	0.976336i
$391$	0.403968	+	0.293500i	0.0204296	+	0.0148429i
$392$	6.87349	−	56.3723i	0.347164	−	2.84723i
$393$	7.05378	−	2.29191i	0.355816	−	0.115612i
$394$	−0.331221	−	3.15136i	−0.0166867	−	0.158763i
$395$	11.4438	+	19.8212i	0.575799	+	0.997314i
$396$	16.7549	+	0.549395i	0.841964	+	0.0276081i
$397$	−6.75860	−	3.90208i	−0.339204	−	0.195840i	0.320716	−	0.947175i	$-0.396077\pi$
$397$	−6.75860	−	3.90208i	−0.339204	−	0.195840i	−0.659920	+	0.751336i	$0.729410\pi$
$398$	25.8743	−	18.7987i	1.29696	−	0.942296i
$399$	4.82976	−	12.2762i	0.241790	−	0.614579i
$400$	−27.1940	+	83.6947i	−1.35970	+	4.18473i
$401$	−11.6768	+	5.19885i	−0.583112	+	0.259618i	−0.677022	−	0.735962i	$-0.736730\pi$
$401$	−11.6768	+	5.19885i	−0.583112	+	0.259618i	0.0939102	+	0.995581i	$0.470063\pi$
$402$	−2.05985	+	19.5981i	−0.102736	+	0.977466i
$403$	−1.64835	−	7.75489i	−0.0821103	−	0.386299i
$404$	−29.5103	−	6.27260i	−1.46819	−	0.312073i
$405$	−2.09413	−	2.88232i	−0.104058	−	0.143224i
$406$	−9.74707	−	26.0363i	−0.483739	−	1.29216i
$407$	−0.147820	+	0.0600893i	−0.00732715	+	0.00297852i
$408$	−0.599919	+	1.03909i	−0.0297004	+	0.0514426i
$409$	−4.81079	−	2.14190i	−0.237878	−	0.105910i	0.284336	−	0.958725i	$-0.408227\pi$
$409$	−4.81079	−	2.14190i	−0.237878	−	0.105910i	−0.522214	+	0.852815i	$0.674894\pi$
$410$	−38.3669	+	42.6108i	−1.89481	+	2.10440i
$411$	−1.79386	+	1.61520i	−0.0884845	+	0.0796718i
$412$	14.1573	−	19.4859i	0.697481	−	0.960001i
$413$	13.7962	−	13.5689i	0.678866	−	0.667681i
$414$	8.52863	+	2.77112i	0.419159	+	0.136193i
$415$	−1.20868	+	5.68640i	−0.0593318	+	0.279134i
$416$	−12.8426	+	28.8449i	−0.629660	+	1.41424i
$417$	18.4736	−	10.6658i	0.904658	−	0.522304i
$418$	19.1706	−	39.5189i	0.937666	−	1.93293i
$419$			35.5826i			1.73833i	0.494526	+	0.869163i	$0.335342\pi$
$419$			35.5826i			1.73833i	−0.494526	+	0.869163i	$0.664658\pi$
$420$	−42.6297	+	21.2768i	−2.08012	+	1.03820i
$421$	−7.53198	−	23.1810i	−0.367086	−	1.12977i	−0.948664	−	0.316284i	$-0.897565\pi$
$421$	−7.53198	−	23.1810i	−0.367086	−	1.12977i	0.581578	−	0.813490i	$-0.302435\pi$
$422$	0.952163	+	1.05748i	0.0463506	+	0.0514775i
$423$	8.93789	+	0.939410i	0.434575	+	0.0456757i
$424$	−40.0936	−	4.21400i	−1.94712	−	0.204650i
$425$	0.761318	+	0.845530i	0.0369294	+	0.0410142i
$426$	10.9817	+	33.7982i	0.532066	+	1.63753i
$427$	−5.00556	−	3.31008i	−0.242236	−	0.160186i
$428$			59.6179i			2.88174i
$429$	3.22865	−	6.65563i	0.155881	−	0.321337i
$430$	91.7415	−	52.9670i	4.42417	−	2.55429i
$431$	3.82580	−	8.59290i	0.184282	−	0.413905i	−0.797654	−	0.603115i	$-0.793926\pi$
$431$	3.82580	−	8.59290i	0.184282	−	0.413905i	0.981937	+	0.189210i	$0.0605926\pi$
$432$	−2.37829	+	11.1890i	−0.114426	+	0.538330i
$433$	−12.8293	−	4.16849i	−0.616536	−	0.200325i	−0.0159343	−	0.999873i	$-0.505072\pi$
$433$	−12.8293	−	4.16849i	−0.616536	−	0.200325i	−0.600602	+	0.799548i	$0.705072\pi$
$434$	−24.1804	+	6.26435i	−1.16070	+	0.300698i
$435$	−8.28480	+	11.4030i	−0.397226	+	0.546734i
$436$	28.9705	−	26.0852i	1.38744	−	1.24925i
$437$	11.2646	−	12.5106i	0.538859	−	0.598464i
$438$	0.252961	+	0.112626i	0.0120870	+	0.00538146i
$439$	0.891836	−	1.54470i	0.0425650	−	0.0737247i	−0.843958	−	0.536409i	$-0.819780\pi$
$439$	0.891836	−	1.54470i	0.0425650	−	0.0737247i	0.886523	+	0.462684i	$0.153114\pi$
$440$	−88.8066	+	36.1002i	−4.23369	+	1.72101i
$441$	−6.62055	−	2.27341i	−0.315264	−	0.108257i
$442$	0.514973	+	0.708800i	0.0244948	+	0.0337142i
$443$	26.8170	+	5.70012i	1.27411	+	0.270821i	0.794826	−	0.606838i	$-0.207562\pi$
$443$	26.8170	+	5.70012i	1.27411	+	0.270821i	0.479286	+	0.877659i	$0.340896\pi$
$444$	−0.0505593	−	0.237863i	−0.00239944	−	0.0112885i
$445$	−5.72016	+	54.4236i	−0.271161	+	2.57993i
$446$	28.3872	−	12.6388i	1.34417	−	0.598465i
$447$	−4.69926	+	14.4628i	−0.222268	+	0.684069i
$448$	36.2470	+	14.2605i	1.71251	+	0.673743i
$449$	−11.3278	+	8.23015i	−0.534594	+	0.388405i	−0.822073	−	0.569382i	$-0.807183\pi$
$449$	−11.3278	+	8.23015i	−0.534594	+	0.388405i	0.287480	+	0.957787i	$0.407183\pi$
$450$	17.6958	+	10.2167i	0.834186	+	0.481618i
$451$	−20.0859	−	0.658620i	−0.945807	−	0.0310132i
$452$	19.1539	+	33.1756i	0.900925	+	1.56045i
$453$	0.549358	+	5.22679i	0.0258111	+	0.245576i
$454$	−8.67755	+	2.81951i	−0.407258	+	0.132326i
$455$	0.925899	+	21.0037i	0.0434068	+	0.984669i
$456$	32.7262	+	23.7770i	1.53254	+	1.11346i
$457$	14.8504	+	33.3546i	0.694673	+	1.56026i	0.822691	+	0.568489i	$0.192472\pi$
$457$	14.8504	+	33.3546i	0.694673	+	1.56026i	−0.128017	+	0.991772i	$0.540861\pi$
$458$	−33.1469	+	7.04559i	−1.54885	+	0.329219i
$459$	0.109906	+	0.0989602i	0.00512999	+	0.00461907i
$460$	−60.4668	+	6.35532i	−2.81928	+	0.296318i
$461$	−13.0560			−0.608079			−0.304040	−	0.952659i	$-0.598336\pi$
$461$	−13.0560			−0.608079			−0.304040	+	0.952659i	$0.598336\pi$
$462$	−21.3971	−	9.23896i	−0.995485	−	0.429835i
$463$	23.2078			1.07856			0.539278	−	0.842128i	$-0.318697\pi$
$463$	23.2078			1.07856			0.539278	+	0.842128i	$0.318697\pi$
$464$	45.0068	−	4.73041i	2.08939	−	0.219604i
$465$	9.41123	+	8.47391i	0.436435	+	0.392968i
$466$	40.1054	−	8.52467i	1.85785	−	0.394898i
$467$	6.07426	+	13.6430i	0.281083	+	0.631323i	0.997818	−	0.0660224i	$-0.0210309\pi$
$467$	6.07426	+	13.6430i	0.281083	+	0.631323i	−0.716735	+	0.697346i	$0.754364\pi$
$468$	9.12051	+	6.62644i	0.421596	+	0.306307i
$469$	9.05671	−	17.4157i	0.418200	−	0.804181i
$470$	−80.8808	+	26.2797i	−3.73075	+	1.21219i
$471$	−1.34197	−	12.7679i	−0.0618345	−	0.588316i
$472$	29.6681	+	51.3867i	1.36559	+	2.36527i
$473$	34.9168	+	12.6246i	1.60548	+	0.580479i
$474$	−14.7767	−	8.53134i	−0.678717	−	0.391858i
$475$	31.0333	−	22.5470i	1.42391	−	1.03453i
$476$	1.54730	−	1.23184i	0.0709206	−	0.0564615i
$477$	−1.53557	+	4.72600i	−0.0703090	+	0.216389i
$478$	−26.7397	+	11.9053i	−1.22305	+	0.544535i
$479$	−1.36706	+	13.0067i	−0.0624624	+	0.594290i	0.917862	+	0.396899i	$0.129914\pi$
$479$	−1.36706	+	13.0067i	−0.0624624	+	0.594290i	−0.980325	+	0.197391i	$0.936753\pi$
$480$	−10.4862	−	49.3339i	−0.478630	−	2.25178i
$481$	−0.104962	−	0.0223104i	−0.00478586	−	0.00101727i
$482$	−38.8726	−	53.5035i	−1.77060	−	2.43702i
$483$	−6.89518	−	5.67908i	−0.313742	−	0.258407i
$484$	−49.2021	−	25.8932i	−2.23646	−	1.17696i
$485$	9.05009	−	15.6752i	0.410944	−	0.711775i
$486$	2.42640	+	1.08030i	0.110064	+	0.0490036i
$487$	−14.4028	+	15.9959i	−0.652653	+	0.724845i	−0.975106	−	0.221741i	$-0.928826\pi$
$487$	−14.4028	+	15.9959i	−0.652653	+	0.724845i	0.322453	+	0.946586i	$0.395493\pi$
$488$	13.6748	−	12.3129i	0.619031	−	0.557378i
$489$	7.73609	−	10.6478i	0.349838	−	0.481511i
$490$	65.9824	−	5.82868i	2.98078	−	0.263313i
$491$	31.0512	+	10.0892i	1.40132	+	0.455317i	0.909618	−	0.415445i	$-0.136374\pi$
$491$	31.0512	+	10.0892i	1.40132	+	0.455317i	0.491704	+	0.870763i	$0.336374\pi$
$492$	6.36773	−	29.9578i	0.287079	−	1.35060i
$493$	0.237980	−	0.534513i	0.0107181	−	0.0240732i
$494$	25.5807	−	14.7690i	1.15093	−	0.664490i
$495$	2.07664	+	11.6324i	0.0933380	+	0.522837i
$496$		−	40.6606i		−	1.82571i
$497$	2.14625	−	35.3349i	0.0962725	−	1.58499i
$498$	−1.33925	−	4.12180i	−0.0600134	−	0.184702i
$499$	−1.83260	−	2.03531i	−0.0820386	−	0.0911131i	0.700728	−	0.713429i	$-0.252859\pi$
$499$	−1.83260	−	2.03531i	−0.0820386	−	0.0911131i	−0.782766	+	0.622316i	$0.786192\pi$
$500$	−48.2328	−	5.06947i	−2.15703	−	0.226713i
$501$	−14.2594	−	1.49872i	−0.637062	−	0.0669579i
$502$	48.0957	+	53.4157i	2.14662	+	2.38406i
$503$	−5.05569	−	15.5598i	−0.225422	−	0.693778i	−0.998248	−	0.0591604i	$-0.981158\pi$
$503$	−5.05569	−	15.5598i	−0.225422	−	0.693778i	0.772826	−	0.634617i	$-0.218842\pi$
$504$	11.8395	−	17.9040i	0.527375	−	0.797506i
$505$		−	21.2655i		−	0.946303i
$506$	−21.4385	−	20.6149i	−0.953057	−	0.916445i
$507$	−6.95012	+	4.01265i	−0.308665	+	0.178208i
$508$	41.3086	−	92.7807i	1.83277	−	4.11648i
$509$	−0.559875	+	2.63401i	−0.0248160	+	0.116750i	−0.988812	−	0.149166i	$-0.952341\pi$
$509$	−0.559875	+	2.63401i	−0.0248160	+	0.116750i	0.963996	+	0.265916i	$0.0856745\pi$
$510$	−1.33099	−	0.432464i	−0.0589372	−	0.0191498i
$511$	−0.193414	−	0.196654i	−0.00855613	−	0.00869946i
$512$	13.9123	−	19.1487i	0.614843	−	0.846259i
$513$	3.70543	−	3.33639i	0.163599	−	0.147305i
$514$	−1.79910	+	1.99810i	−0.0793548	+	0.0881325i
$515$	15.5096	+	6.90531i	0.683434	+	0.304284i
$516$	−28.2921	+	49.0033i	−1.24549	+	2.15725i
$517$	−25.3113	−	15.7414i	−1.11319	−	0.692307i
$518$	−0.0556599	+	0.333472i	−0.00244555	+	0.0146519i
$519$	0.449451	+	0.618616i	0.0197287	+	0.0271542i
$520$	−63.0588	−	13.4036i	−2.76531	−	0.587785i
$521$	1.75088	+	8.23725i	0.0767075	+	0.360881i	0.999714	−	0.0239032i	$-0.00760934\pi$
$521$	1.75088	+	8.23725i	0.0767075	+	0.360881i	−0.923007	+	0.384784i	$0.874276\pi$
$522$	1.09836	−	10.4502i	0.0480740	−	0.457394i
$523$	12.1129	−	5.39301i	0.529660	−	0.235820i	−0.124441	−	0.992227i	$-0.539714\pi$
$523$	12.1129	−	5.39301i	0.529660	−	0.235820i	0.654101	+	0.756407i	$0.273047\pi$
$524$	11.5845	−	35.6533i	0.506070	−	1.55752i
$525$	−12.6775	−	15.9241i	−0.553292	−	0.694983i
$526$	31.3019	−	22.7421i	1.36483	−	0.991605i
$527$	−0.455269	−	0.262850i	−0.0198318	−	0.0114499i
$528$	23.2937	−	29.9457i	1.01373	−	1.30322i
$529$	5.80033	+	10.0465i	0.252188	+	0.436803i
$530$	−4.91519	−	46.7649i	−0.213502	−	2.03134i
$531$	6.95591	−	2.26011i	0.301861	−	0.0980805i
$532$	−35.8505	−	56.2218i	−1.55432	−	2.43753i
$533$	−10.9337	−	7.94383i	−0.473593	−	0.344085i
$534$	−16.5934	−	37.2693i	−0.718065	−	1.61280i
$535$	−41.1044	+	8.73700i	−1.77710	+	0.377734i
$536$	44.7315	+	40.2764i	1.93211	+	1.73968i
$537$	18.3840	−	1.93224i	0.793329	−	0.0833823i
$538$	−19.8300			−0.854931
$539$	16.4651	+	16.3676i	0.709204	+	0.705004i
$540$	−18.0079			−0.774937
$541$	31.7828	−	3.34050i	1.36645	−	0.143619i	0.607266	−	0.794499i	$-0.292266\pi$
$541$	31.7828	−	3.34050i	1.36645	−	0.143619i	0.759181	+	0.650879i	$0.225600\pi$
$542$	21.6307	+	19.4764i	0.929120	+	0.836583i
$543$	−5.55542	+	1.18084i	−0.238406	+	0.0506748i
$544$	0.851568	+	1.91265i	0.0365107	+	0.0820043i
$545$	22.2304	+	16.1514i	0.952247	+	0.691848i
$546$	−8.42692	−	13.2153i	−0.360639	−	0.565564i
$547$	−31.6659	+	10.2889i	−1.35394	+	0.439921i	−0.894015	−	0.448038i	$-0.852123\pi$
$547$	−31.6659	+	10.2889i	−1.35394	+	0.439921i	−0.459923	+	0.887959i	$0.652123\pi$
$548$	1.27534	+	12.1341i	0.0544799	+	0.518342i
$549$	−1.13409	−	1.96429i	−0.0484016	−	0.0838340i
$550$	−38.0158	−	56.1028i	−1.62100	−	2.39223i
$551$	−17.0834	−	9.86310i	−0.727777	−	0.420182i
$552$	22.1600	−	16.1002i	0.943193	−	0.685270i
$553$	10.5863	+	13.2973i	0.450174	+	0.565457i
$554$	4.97682	−	15.3171i	0.211445	−	0.650760i
$555$	0.156589	−	0.0697177i	0.00664681	−	0.00295935i
$556$	11.2703	−	107.229i	0.477966	−	4.54754i
$557$	−5.69607	−	26.7979i	−0.241350	−	1.13546i	−0.917201	−	0.398424i	$-0.869557\pi$
$557$	−5.69607	−	26.7979i	−0.241350	−	1.13546i	0.675851	−	0.737038i	$-0.263776\pi$
$558$	−9.23475	−	1.96291i	−0.390938	−	0.0830965i
$559$	14.6764	+	20.2003i	0.620745	+	0.854382i
$560$	−17.7515	+	106.354i	−0.750139	+	4.49427i
$561$	−0.184715	−	0.454399i	−0.00779867	−	0.0191847i
$562$	−9.73683	+	16.8647i	−0.410723	+	0.711394i
$563$	−37.0768	−	16.5077i	−1.56260	−	0.695715i	−0.570516	−	0.821286i	$-0.693257\pi$
$563$	−37.0768	−	16.5077i	−1.56260	−	0.695715i	−0.992085	+	0.125572i	$0.959923\pi$
$564$	30.3955	−	33.7576i	1.27988	−	1.42145i
$565$	−20.0664	+	18.0678i	−0.844198	+	0.760120i
$566$	−19.3269	+	26.6012i	−0.812370	+	1.11813i
$567$	−1.85523	−	1.88630i	−0.0779122	−	0.0792173i
$568$	103.237	+	33.5436i	4.33171	+	1.40746i
$569$	−4.53502	+	21.3356i	−0.190118	+	0.894434i	0.774866	+	0.632125i	$0.217817\pi$
$569$	−4.53502	+	21.3356i	−0.190118	+	0.894434i	−0.964984	+	0.262309i	$0.915516\pi$
$570$	−19.1910	+	43.1036i	−0.803821	+	1.80541i
$571$	−8.31911	+	4.80304i	−0.348144	+	0.201001i	−0.663868	−	0.747850i	$-0.731086\pi$
$571$	−8.31911	+	4.80304i	−0.348144	+	0.201001i	0.315724	+	0.948851i	$0.397753\pi$
$572$	−17.6238	−	32.9761i	−0.736890	−	1.37880i
$573$			18.3999i			0.768665i
$574$	−23.4868	+	35.5171i	−0.980319	+	1.48245i
$575$	−8.02653	−	24.7031i	−0.334730	−	1.03019i
$576$	9.85109	+	10.9407i	0.410462	+	0.455864i
$577$	25.6930	+	2.70044i	1.06961	+	0.112421i	0.622935	−	0.782274i	$-0.285940\pi$
$577$	25.6930	+	2.70044i	1.06961	+	0.112421i	0.446679	+	0.894695i	$0.352607\pi$
$578$	−44.8474	−	4.71365i	−1.86541	−	0.196062i
$579$	6.64538	+	7.38044i	0.276173	+	0.306721i
$580$	22.0152	+	67.7560i	0.914133	+	2.81341i
$581$	−0.261742	+	4.30921i	−0.0108589	+	0.178776i
$582$			13.4937i			0.559332i
$583$	11.4234	−	11.8798i	0.473110	−	0.492011i
$584$	0.732478	−	0.422896i	0.0303101	−	0.0174996i
$585$	−3.23208	+	7.25937i	−0.133630	+	0.300138i
$586$	−4.69684	+	22.0969i	−0.194025	+	0.912814i
$587$	−34.4634	−	11.1978i	−1.42246	−	0.462184i	−0.506074	−	0.862490i	$-0.668904\pi$
$587$	−34.4634	−	11.1978i	−1.42246	−	0.462184i	−0.916381	+	0.400306i	$0.868904\pi$
$588$	−28.9657	+	20.3184i	−1.19453	+	0.837915i
$589$	−10.4177	+	14.3387i	−0.429254	+	0.590817i
$590$	−51.4327	+	46.3102i	−2.11745	+	1.90656i
$591$	−0.798291	+	0.886592i	−0.0328373	+	0.0364695i
$592$	−0.502760	−	0.223843i	−0.0206633	−	0.00919990i
$593$	−2.51950	+	4.36391i	−0.103464	+	0.179204i	−0.913109	−	0.407714i	$-0.866326\pi$
$593$	−2.51950	+	4.36391i	−0.103464	+	0.179204i	0.809646	+	0.586919i	$0.199659\pi$
$594$	−5.67670	−	6.73606i	−0.232918	−	0.276384i
$595$	1.07607	+	0.886283i	0.0441146	+	0.0363341i
$596$	45.1798	+	62.1846i	1.85064	+	2.54718i
$597$	−11.7783	−	2.50355i	−0.482053	−	0.102463i
$598$	−4.15849	−	19.5641i	−0.170053	−	0.800037i
$599$	−1.56482	+	14.8883i	−0.0639368	+	0.608318i	0.914901	+	0.403679i	$0.132269\pi$
$599$	−1.56482	+	14.8883i	−0.0639368	+	0.608318i	−0.978837	+	0.204639i	$0.934398\pi$
$600$	57.0175	−	25.3858i	2.32773	−	1.03637i
$601$	7.28316	−	22.4153i	0.297086	−	0.914338i	−0.685426	−	0.728142i	$-0.740384\pi$
$601$	7.28316	−	22.4153i	0.297086	−	0.914338i	0.982513	−	0.186196i	$-0.0596159\pi$
$602$	61.5457	−	48.9980i	2.50842	−	1.99701i
$603$	6.00240	−	4.36100i	0.244437	−	0.177594i
$604$	23.0054	+	13.2822i	0.936075	+	0.540443i
$605$	10.6419	−	37.7177i	0.432653	−	1.53344i
$606$	7.92672	+	13.7295i	0.322001	+	0.557722i
$607$	2.64058	+	25.1235i	0.107178	+	1.01973i	0.907469	+	0.420119i	$0.138012\pi$
$607$	2.64058	+	25.1235i	0.107178	+	1.01973i	−0.800291	+	0.599612i	$0.795322\pi$
$608$	67.1317	−	21.8124i	2.72255	−	0.884610i
$609$	−4.82927	+	9.28648i	−0.195692	+	0.376307i
$610$	17.3641	+	12.6157i	0.703051	+	0.510796i
$611$	−8.15300	−	18.3119i	−0.329835	−	0.740822i
$612$	0.731193	−	0.155420i	0.0295567	−	0.00628248i
$613$	−22.9345	−	20.6504i	−0.926318	−	0.834060i	0.0601209	−	0.998191i	$-0.480851\pi$
$613$	−22.9345	−	20.6504i	−0.926318	−	0.834060i	−0.986439	+	0.164131i	$0.947518\pi$
$614$	50.6506	−	5.32359i	2.04409	−	0.214843i
$615$	21.5880			0.870513
$616$	−61.2469	+	36.2878i	−2.46771	+	1.46208i
$617$	−42.6656			−1.71765			−0.858826	−	0.512267i	$-0.828806\pi$
$617$	−42.6656			−1.71765			−0.858826	+	0.512267i	$0.828806\pi$
$618$	−12.5873	+	1.32298i	−0.506335	+	0.0532179i
$619$	34.0462	+	30.6553i	1.36843	+	1.23214i	0.945353	+	0.326049i	$0.105717\pi$
$619$	34.0462	+	30.6553i	1.36843	+	1.23214i	0.423079	+	0.906093i	$0.360949\pi$
$620$	62.6117	−	13.3085i	2.51455	−	0.534483i
$621$	−1.37326	−	3.08440i	−0.0551071	−	0.123773i
$622$	13.9858	+	10.1613i	0.560778	+	0.407429i
$623$	1.78971	+	40.5990i	0.0717033	+	1.62657i
$624$	24.2647	−	7.88409i	0.971367	−	0.315616i
$625$	0.447479	+	4.25748i	0.0178992	+	0.170299i
$626$	−30.0565	−	52.0595i	−1.20130	−	2.08071i
$627$	−15.8868	+	4.59209i	−0.634459	+	0.183390i
$628$	−56.1973	−	32.4455i	−2.24252	−	1.29472i
$629$	−0.00575642	+	0.00418228i	−0.000229523	+	0.000166758i
$630$	23.2979	+	9.16597i	0.928211	+	0.365181i
$631$	−5.00329	+	15.3985i	−0.199178	+	0.613006i	0.800725	+	0.599033i	$0.204448\pi$
$631$	−5.00329	+	15.3985i	−0.199178	+	0.613006i	−0.999902	+	0.0139735i	$0.995552\pi$
$632$	−47.6121	+	21.1983i	−1.89391	+	0.843222i
$633$	0.0560018	−	0.532822i	0.00222587	−	0.0211778i
$634$	1.73540	+	8.16443i	0.0689217	+	0.324251i
$635$	70.0228	+	14.8838i	2.77877	+	0.590646i
$636$	14.7633	+	20.3200i	0.585404	+	0.805740i
$637$	2.99197	+	15.3235i	0.118546	+	0.607137i
$638$	−18.4049	+	29.5940i	−0.728659	+	1.17164i
$639$	6.68998	−	11.5874i	0.264652	−	0.458390i
$640$	−35.1175	−	15.6353i	−1.38814	−	0.618039i
$641$	−15.7130	+	17.4510i	−0.620625	+	0.689274i	−0.968712	−	0.248189i	$-0.920165\pi$
$641$	−15.7130	+	17.4510i	−0.620625	+	0.689274i	0.348087	+	0.937462i	$0.386831\pi$
$642$	23.2812	−	20.9625i	0.918835	−	0.827323i
$643$	−15.2881	+	21.0423i	−0.602906	+	0.829828i	−0.995970	−	0.0896823i	$-0.971415\pi$
$643$	−15.2881	+	21.0423i	−0.602906	+	0.829828i	0.393065	+	0.919511i	$0.371415\pi$
$644$	−43.7080	+	11.3233i	−1.72234	+	0.446200i
$645$	−37.9322	−	12.3249i	−1.49358	−	0.485294i
$646$	0.407218	−	1.91581i	0.0160218	−	0.0753765i
$647$	13.4659	−	30.2449i	0.529398	−	1.18905i	−0.428919	−	0.903343i	$-0.641105\pi$
$647$	13.4659	−	30.2449i	0.529398	−	1.18905i	0.958318	−	0.285705i	$-0.0922278\pi$
$648$	7.02592	−	4.05642i	0.276004	−	0.159351i
$649$	−24.0284	−	3.32485i	−0.943199	−	0.130512i
$650$		−	45.5745i		−	1.78758i
$651$	7.84449	+	5.18741i	0.307450	+	0.203310i
$652$	−20.5572	−	63.2684i	−0.805081	−	2.47778i
$653$	−29.3972	−	32.6489i	−1.15040	−	1.27765i	−0.954894	−	0.296947i	$-0.904032\pi$
$653$	−29.3972	−	32.6489i	−1.15040	−	1.27765i	−0.195506	−	0.980702i	$-0.562635\pi$
$654$	−20.3729	−	2.14128i	−0.796643	−	0.0837305i
$655$	26.2794	+	2.76207i	1.02682	+	0.107923i
$656$	−46.3794	−	51.5095i	−1.81081	−	2.01111i
$657$	−0.0322161	−	0.0991511i	−0.00125687	−	0.00386825i
$658$	−56.5071	+	28.2031i	−2.20287	+	1.09947i
$659$			9.73189i			0.379101i	0.981871	+	0.189550i	$0.0607030\pi$
$659$			9.73189i			0.379101i	−0.981871	+	0.189550i	$0.939297\pi$
$660$	53.7365	+	26.0676i	2.09169	+	1.01468i
$661$	−7.09537	+	4.09651i	−0.275978	+	0.159336i	−0.631601	−	0.775293i	$-0.717602\pi$
$661$	−7.09537	+	4.09651i	−0.275978	+	0.159336i	0.355623	+	0.934629i	$0.384269\pi$
$662$	−0.167472	+	0.376147i	−0.00650897	+	0.0146194i
$663$	0.0685823	−	0.322654i	0.00266352	−	0.0125309i
$664$	−12.5900	−	4.09075i	−0.488588	−	0.158752i
$665$	33.5090	−	32.9570i	1.29942	−	1.27802i
$666$	−0.0751098	+	0.103380i	−0.00291044	+	0.00400588i
$667$	−9.92639	+	8.93777i	−0.384351	+	0.346072i
$668$	−48.4926	+	53.8564i	−1.87623	+	2.08377i
$669$	−10.6878	−	4.75853i	−0.413216	−	0.183976i
$670$	−35.1039	+	60.8017i	−1.35618	+	2.34898i
$671$	0.540724	+	7.50322i	0.0208744	+	0.289658i
$672$	−13.1316	−	35.0772i	−0.506564	−	1.35313i
$673$	−13.2390	−	18.2219i	−0.510325	−	0.702402i	0.473649	−	0.880714i	$-0.342936\pi$
$673$	−13.2390	−	18.2219i	−0.510325	−	0.702402i	−0.983974	+	0.178312i	$0.942936\pi$
$674$	68.6523	+	14.5925i	2.64439	+	0.562082i
$675$	−1.59950	−	7.52506i	−0.0615648	−	0.289640i
$676$	−4.24008	+	40.3416i	−0.163080	+	1.55160i
$677$	3.93244	−	1.75084i	0.151136	−	0.0672901i	−0.329775	−	0.944060i	$-0.606973\pi$
$677$	3.93244	−	1.75084i	0.151136	−	0.0672901i	0.480911	+	0.876770i	$0.340306\pi$
$678$	6.22050	−	19.1447i	0.238897	−	0.735249i
$679$	4.92105	−	12.5083i	0.188853	−	0.480023i
$680$	−3.45832	+	2.51262i	−0.132621	+	0.0963545i
$681$	2.97501	+	1.71762i	0.114003	+	0.0658194i
$682$	24.7155	+	19.2253i	0.946407	+	0.736176i
$683$	18.0976	+	31.3460i	0.692486	+	1.19942i	0.971021	+	0.238995i	$0.0768180\pi$
$683$	18.0976	+	31.3460i	0.692486	+	1.19942i	−0.278535	+	0.960426i	$0.589849\pi$
$684$	−2.63438	−	25.0644i	−0.100728	−	0.958362i
$685$	−8.17911	+	2.65755i	−0.312508	+	0.101540i
$686$	47.8167	−	11.5436i	1.82565	−	0.440738i
$687$	10.3220	+	7.49935i	0.393808	+	0.286118i
$688$	52.0854	+	116.986i	1.98574	+	4.46004i
$689$	10.8412	−	2.30436i	0.413015	−	0.0877891i
$690$	23.7428	+	21.3781i	0.903872	+	0.813850i
$691$	33.0080	−	3.46928i	1.25569	−	0.131978i	0.546777	−	0.837278i	$-0.315855\pi$
$691$	33.0080	−	3.46928i	1.25569	−	0.131978i	0.708908	+	0.705301i	$0.249188\pi$
$692$	3.86493			0.146923
$693$	2.80554	+	8.31438i	0.106574	+	0.315837i
$694$	75.2329			2.85580
$695$	75.5825	−	7.94404i	2.86701	−	0.301335i
$696$	−23.8520	−	21.4764i	−0.904107	−	0.814061i
$697$	−0.876561	+	0.186319i	−0.0332021	+	0.00705733i
$698$	9.61560	+	21.5970i	0.363956	+	0.817458i
$699$	−12.4889	−	9.07370i	−0.472373	−	0.343199i
$700$	−102.781	+	4.53084i	−3.88474	+	0.171250i
$701$	23.7912	−	7.73024i	0.898583	−	0.291967i	0.176931	−	0.984223i	$-0.443383\pi$
$701$	23.7912	−	7.73024i	0.898583	−	0.291967i	0.721652	+	0.692256i	$0.243383\pi$
$702$	−0.619229	−	5.89157i	−0.0233713	−	0.222363i
$703$	0.119944	+	0.207750i	0.00452379	+	0.00783543i
$704$	−13.5587	−	46.9078i	−0.511013	−	1.76791i
$705$	27.7291	+	16.0094i	1.04434	+	0.602950i
$706$	−24.8782	+	18.0751i	−0.936302	+	0.680264i
$707$	−2.34079	−	15.6176i	−0.0880346	−	0.587362i
$708$	11.4237	−	35.1586i	0.429330	−	1.32134i
$709$	−22.2907	+	9.92445i	−0.837144	+	0.372720i	−0.780103	−	0.625651i	$-0.784833\pi$
$709$	−22.2907	+	9.92445i	−0.837144	+	0.372720i	−0.0570409	+	0.998372i	$0.518167\pi$
$710$	−13.2345	+	125.918i	−0.496682	+	4.72561i
$711$	1.33565	+	6.28375i	0.0500909	+	0.235659i
$712$	−121.889	−	25.9083i	−4.56799	−	0.970956i
$713$	7.05418	+	9.70925i	0.264181	+	0.363614i
$714$	−1.02510	−	0.171099i	−0.0383633	−	0.00640322i
$715$	20.1531	−	16.9837i	0.753683	−	0.635153i
$716$	46.7169	−	80.9161i	1.74589	−	3.02398i
$717$	10.0676	+	4.48236i	0.375980	+	0.167397i
$718$	15.8944	−	17.6526i	0.593175	−	0.658788i
$719$	−8.01222	+	7.21423i	−0.298805	+	0.269046i	−0.804871	−	0.593449i	$-0.797766\pi$
$719$	−8.01222	+	7.21423i	−0.298805	+	0.269046i	0.506066	+	0.862495i	$0.331099\pi$
$720$	−23.9546	+	32.9707i	−0.892737	+	1.22875i
$721$	12.1505	+	3.36413i	0.452509	+	0.125287i
$722$	−14.8068	−	4.81103i	−0.551053	−	0.179048i
$723$	−5.17691	+	24.3554i	−0.192531	+	0.905788i
$724$	−11.6763	+	26.2253i	−0.433945	+	0.974657i
$725$	−26.3581	+	15.2179i	−0.978916	+	0.565177i
$726$	7.18867	+	28.3181i	0.266796	+	1.05098i
$727$			31.7183i			1.17637i	0.808727	+	0.588184i	$0.200157\pi$
$727$			31.7183i			1.17637i	−0.808727	+	0.588184i	$0.799843\pi$
$728$	−47.7865	−	2.90256i	−1.77109	−	0.107576i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	0.660116	+	0.733133i	0.0244320	+	0.0271345i
$731$	1.64657	+	0.173062i	0.0609007	+	0.00640092i
$732$	−11.4017	−	1.19836i	−0.421418	−	0.0442928i
$733$	−17.6767	−	19.6320i	−0.652905	−	0.725124i	0.322249	−	0.946655i	$-0.395561\pi$
$733$	−17.6767	−	19.6320i	−0.652905	−	0.725124i	−0.975153	+	0.221531i	$0.928895\pi$
$734$	−10.5268	−	32.3981i	−0.388550	−	1.19583i
$735$	−18.2537	−	16.9932i	−0.673298	−	0.626802i
$736$		−	47.7965i		−	1.76180i
$737$	−24.2243	+	4.32457i	−0.892313	+	0.159298i
$738$	−13.9377	+	8.04694i	−0.513054	+	0.296212i
$739$	−11.6535	+	26.1741i	−0.428679	+	0.962829i	0.562066	+	0.827093i	$0.310007\pi$
$739$	−11.6535	+	26.1741i	−0.428679	+	0.962829i	−0.990745	+	0.135737i	$0.956660\pi$
$740$	0.180130	−	0.847446i	0.00662172	−	0.0311527i
$741$	−10.5768	−	3.43662i	−0.388549	−	0.126247i
$742$	−8.75741	−	33.8037i	−0.321495	−	1.24097i
$743$	28.1360	−	38.7259i	1.03221	−	1.42072i	0.128936	−	0.991653i	$-0.458844\pi$
$743$	28.1360	−	38.7259i	1.03221	−	1.42072i	0.903275	−	0.429063i	$-0.141156\pi$
$744$	−21.4306	+	19.2962i	−0.785683	+	0.707432i
$745$	−36.2530	+	40.2630i	−1.32821	+	1.47512i
$746$	34.5868	+	15.3991i	1.26631	+	0.563800i
$747$	−0.815864	+	1.41312i	−0.0298509	+	0.0517033i
$748$	−2.40690	−	0.594669i	−0.0880049	−	0.0217433i
$749$	−29.2258	+	10.9411i	−1.06789	+	0.399779i
$750$	14.9796	+	20.6177i	0.546979	+	0.752852i
$751$	−19.4820	−	4.14102i	−0.710907	−	0.151108i	−0.161756	−	0.986831i	$-0.551716\pi$
$751$	−19.4820	−	4.14102i	−0.710907	−	0.151108i	−0.549151	+	0.835723i	$0.685049\pi$
$752$	−21.3740	−	100.557i	−0.779429	−	3.66693i
$753$	2.82877	−	26.9139i	0.103086	−	0.980798i
$754$	−21.4104	+	9.53252i	−0.779721	+	0.347154i
$755$	−5.78613	+	17.8079i	−0.210579	+	0.648095i
$756$	−13.2252	+	1.98221i	−0.480997	+	0.0720924i
$757$	−31.0126	+	22.5320i	−1.12717	+	0.818938i	−0.985281	−	0.170944i	$-0.945318\pi$
$757$	−31.0126	+	22.5320i	−1.12717	+	0.818938i	−0.141891	+	0.989882i	$0.545318\pi$
$758$	33.7242	+	19.4707i	1.22492	+	0.707207i
$759$	−0.366984	+	11.1919i	−0.0133207	+	0.406239i
$760$	72.0598	+	124.811i	2.61388	+	4.52738i
$761$	−3.02585	−	28.7890i	−0.109687	−	1.04360i	−0.901483	−	0.432815i	$-0.857520\pi$
$761$	−3.02585	−	28.7890i	−0.109687	−	1.04360i	0.791796	−	0.610786i	$-0.209146\pi$
$762$	−50.7562	+	16.4917i	−1.83870	+	0.597431i
$763$	18.1042	+	9.41474i	0.655414	+	0.340837i
$764$	75.2402	+	54.6652i	2.72210	+	1.97772i
$765$	0.214313	+	0.481355i	0.00774850	+	0.0174034i
$766$	100.121	−	21.2814i	3.61753	−	0.768929i
$767$	−12.1228	−	10.9155i	−0.437730	−	0.394134i
$768$	−0.782477	+	0.0822417i	−0.0282352	+	0.00296764i
$769$	−9.07322			−0.327189			−0.163594	−	0.986528i	$-0.552309\pi$
$769$	−9.07322			−0.327189			−0.163594	+	0.986528i	$0.552309\pi$
$770$	−56.2538	−	61.0770i	−2.02725	−	2.20106i
$771$	1.01230			0.0364572
$772$	49.9231	−	5.24712i	1.79677	−	0.188848i
$773$	−8.32023	−	7.49157i	−0.299258	−	0.269453i	0.505798	−	0.862652i	$-0.331198\pi$
$773$	−8.32023	−	7.49157i	−0.299258	−	0.269453i	−0.805056	+	0.593199i	$0.797865\pi$
$774$	29.0840	−	6.18200i	1.04540	−	0.222207i
$775$	11.1226	+	24.9818i	0.399536	+	0.897373i
$776$	33.3448	+	24.2264i	1.19701	+	0.869678i
$777$	0.107326	−	0.0684379i	0.00385031	−	0.00245520i
$778$	34.4321	−	11.1877i	1.23445	−	0.401098i
$779$	3.15811	+	30.0474i	0.113151	+	1.07656i
$780$	20.0824	+	34.7838i	0.719067	+	1.24546i
$781$	−36.7367	+	24.8932i	−1.31454	+	0.890747i
$782$	−1.14856	−	0.663121i	−0.0410724	−	0.0237132i
$783$	−3.20063	+	2.32540i	−0.114381	+	0.0831028i
$784$	−1.33007	+	80.0615i	−0.0475024	+	2.85934i
$785$	14.1343	−	43.5009i	0.504475	−	1.55261i
$786$	−17.9961	+	8.01239i	−0.641900	+	0.285792i
$787$	4.22293	−	40.1785i	0.150531	−	1.43221i	−0.614856	−	0.788639i	$-0.710786\pi$
$787$	4.22293	−	40.1785i	0.150531	−	1.43221i	0.765387	−	0.643570i	$-0.222547\pi$
$788$	1.25374	+	5.89838i	0.0446626	+	0.210121i
$789$	−14.2490	−	3.02872i	−0.507278	−	0.107825i
$790$	−35.7315	−	49.1802i	−1.27127	−	1.74975i
$791$	−12.7482	+	15.4780i	−0.453273	+	0.550336i
$792$	−26.8376	+	1.93407i	−0.953634	+	0.0687243i
$793$	−2.52947	+	4.38117i	−0.0898241	+	0.155580i
$794$	18.9360	+	8.43087i	0.672015	+	0.299200i
$795$	−11.8463	+	13.1567i	−0.420146	+	0.466619i
$796$	−45.2302	+	40.7255i	−1.60314	+	1.44348i
$797$	29.8838	−	41.1315i	1.05854	−	1.45695i	0.177374	−	0.984144i	$-0.443240\pi$
$797$	29.8838	−	41.1315i	1.05854	−	1.45695i	0.881165	−	0.472809i	$-0.156760\pi$
$798$	−9.34946	+	33.7682i	−0.330967	+	1.19538i
$799$	−1.26409	−	0.410727i	−0.0447202	−	0.0145305i
$800$	22.6433	−	106.529i	0.800563	−	3.76635i
$801$	−6.24743	+	14.0320i	−0.220742	+	0.495795i
$802$	29.4007	−	16.9745i	1.03818	−	0.599391i
$803$	−0.0473931	+	0.342507i	−0.00167247	+	0.0120868i
$804$		−	37.5012i		−	1.32257i
$805$	−14.2124	−	28.4757i	−0.500922	−	1.00364i
$806$	6.50709	+	20.0268i	0.229202	+	0.705412i
$807$	4.99574	+	5.54833i	0.175858	+	0.195311i
$808$	48.1590	+	5.06172i	1.69423	+	0.178071i
$809$	−3.63519	−	0.382074i	−0.127807	−	0.0134330i	0.0404092	−	0.999183i	$-0.487134\pi$
$809$	−3.63519	−	0.382074i	−0.127807	−	0.0134330i	−0.168216	+	0.985750i	$0.553801\pi$
$810$	6.33183	+	7.03221i	0.222478	+	0.247087i
$811$	−12.2446	−	37.6851i	−0.429967	−	1.32330i	−0.898158	−	0.439674i	$-0.855094\pi$
$811$	−12.2446	−	37.6851i	−0.429967	−	1.32330i	0.468191	−	0.883627i	$-0.344906\pi$
$812$	23.6265	+	47.3375i	0.829127	+	1.66122i
$813$		−	10.9588i		−	0.384343i
$814$	0.373780	−	0.199764i	0.0131010	−	0.00700172i
$815$	40.6087	−	23.4454i	1.42246	−	0.821257i
$816$	0.688096	−	1.54549i	0.0240882	−	0.0541029i
$817$	11.6054	−	54.5993i	0.406023	−	1.91019i
$818$	13.3023	+	4.32217i	0.465103	+	0.151121i
$819$	−1.57460	+	5.68714i	−0.0550211	+	0.198725i
$820$	64.1371	−	88.2772i	2.23977	−	3.08277i
$821$	−3.54356	+	3.19064i	−0.123671	+	0.111354i	−0.728646	−	0.684891i	$-0.759850\pi$
$821$	−3.54356	+	3.19064i	−0.123671	+	0.111354i	0.604975	+	0.796245i	$0.293183\pi$
$822$	4.29001	−	4.76454i	0.149631	−	0.166182i
$823$	36.9215	+	16.4385i	1.28700	+	0.573010i	0.932204	−	0.361933i	$-0.117883\pi$
$823$	36.9215	+	16.4385i	1.28700	+	0.573010i	0.354798	+	0.934943i	$0.384550\pi$
$824$	−19.3298	+	33.4802i	−0.673385	+	1.16634i
$825$	−6.12003	+	24.7705i	−0.213072	+	0.862400i
$826$	−32.6752	+	39.6722i	−1.13692	+	1.38037i
$827$	5.99772	+	8.25515i	0.208561	+	0.287060i	0.900464	−	0.434931i	$-0.143227\pi$
$827$	5.99772	+	8.25515i	0.208561	+	0.287060i	−0.691903	+	0.721991i	$0.743227\pi$
$828$	−16.6925	−	3.54811i	−0.580106	−	0.123305i
$829$	−1.43145	−	6.73444i	−0.0497163	−	0.233897i	0.946273	−	0.323369i	$-0.104815\pi$
$829$	−1.43145	−	6.73444i	−0.0497163	−	0.233897i	−0.995989	+	0.0894718i	$0.971482\pi$
$830$	1.61399	−	15.3561i	0.0560224	−	0.533017i
$831$	−5.53945	+	2.46632i	−0.192161	+	0.0855558i
$832$	10.1470	−	31.2294i	0.351785	−	1.08268i
$833$	0.887836	+	0.532449i	0.0307617	+	0.0184483i
$834$	−45.8366	+	33.3022i	−1.58719	+	1.15316i
$835$	−44.2387	−	25.5412i	−1.53094	−	0.883890i
$836$	−28.4213	+	78.6069i	−0.982970	+	2.71868i
$837$	1.77729	+	3.07835i	0.0614321	+	0.106403i
$838$	−9.87884	−	93.9908i	−0.341259	−	3.24686i
$839$	5.84847	−	1.90028i	0.201911	−	0.0656050i	−0.206315	−	0.978486i	$-0.566147\pi$
$839$	5.84847	−	1.90028i	0.201911	−	0.0656050i	0.408227	+	0.912881i	$0.366147\pi$
$840$	64.4792	−	41.1159i	2.22474	−	1.41863i
$841$	−10.7992	−	7.84605i	−0.372385	−	0.270553i
$842$	26.3313	+	59.1411i	0.907438	+	2.03814i
$843$	7.17165	−	1.52438i	0.247005	−	0.0525025i
$844$	−2.01242	−	1.81199i	−0.0692704	−	0.0623714i
$845$	−28.4355	+	2.98869i	−0.978211	+	0.102814i
$846$	−23.8701			−0.820670
$847$	3.66374	−	28.8717i	0.125888	−	0.992045i
$848$	56.8426			1.95198
$849$	12.3119	−	1.29403i	0.422543	−	0.0444111i
$850$	−2.24575	−	2.02208i	−0.0770287	−	0.0693569i
$851$	0.158887	−	0.0337725i	0.00544658	−	0.00115771i
$852$	−27.5072	−	61.7821i	−0.942380	−	2.11662i
$853$	−22.2526	−	16.1675i	−0.761915	−	0.553564i	0.137582	−	0.990490i	$-0.456067\pi$
$853$	−22.2526	−	16.1675i	−0.761915	−	0.553564i	−0.899497	+	0.436927i	$0.856067\pi$
$854$	14.1411	+	7.35381i	0.483897	+	0.251642i
$855$	16.8949	−	5.48950i	0.577795	−	0.187737i
$856$	−10.0024	−	95.1668i	−0.341876	−	3.25273i
$857$	23.8057	+	41.2327i	0.813187	+	1.40848i	0.910622	+	0.413240i	$0.135603\pi$
$857$	23.8057	+	41.2327i	0.813187	+	1.40848i	−0.0974349	+	0.995242i	$0.531064\pi$
$858$	−6.68062	+	18.4771i	−0.228073	+	0.630798i
$859$	−5.66248	−	3.26924i	−0.193201	−	0.111545i	0.400279	−	0.916393i	$-0.368913\pi$
$859$	−5.66248	−	3.26924i	−0.193201	−	0.111545i	−0.593480	+	0.804848i	$0.702247\pi$
$860$	−163.094	+	118.495i	−5.56146	+	4.04063i
$861$	15.8545	−	2.37629i	0.540320	−	0.0809839i
$862$	−7.72013	+	23.7601i	−0.262949	+	0.809273i
$863$	−21.6348	+	9.63243i	−0.736457	+	0.327892i	−0.740460	−	0.672100i	$-0.765392\pi$
$863$	−21.6348	+	9.63243i	−0.736457	+	0.327892i	0.00400344	+	0.999992i	$0.498726\pi$
$864$	1.47976	−	14.0790i	0.0503424	−	0.478976i
$865$	0.566406	+	2.66473i	0.0192584	+	0.0906035i
$866$	35.0456	+	7.44917i	1.19090	+	0.253133i
$867$	9.97949	+	13.7356i	0.338921	+	0.466485i
$868$	44.5178	−	16.6659i	1.51103	−	0.565677i
$869$	5.11049	−	20.6845i	0.173361	−	0.701672i
$870$	18.7183	−	32.4210i	0.634610	−	1.09918i
$871$	−15.1175	−	6.73076i	−0.512238	−	0.228063i
$872$	−41.8686	+	46.4998i	−1.41785	+	1.57468i
$873$	3.77547	−	3.39945i	0.127780	−	0.115054i
$874$	−26.2819	+	36.1739i	−0.888999	+	1.22360i
$875$	−6.36656	−	24.5750i	−0.215229	−	0.830786i
$876$	−0.501159	−	0.162836i	−0.0169326	−	0.00550173i
$877$	−2.50407	+	11.7807i	−0.0845566	+	0.397807i	−0.999989	−	0.00466407i	$-0.998515\pi$
$877$	−2.50407	+	11.7807i	−0.0845566	+	0.397807i	0.915433	+	0.402471i	$0.131849\pi$
$878$	−1.92691	+	4.32791i	−0.0650300	+	0.146060i
$879$	7.36588	−	4.25269i	0.248445	−	0.143440i
$880$	119.209	−	63.7104i	4.01854	−	2.14768i
$881$		−	30.6641i		−	1.03310i	−0.856257	−	0.516549i	$-0.827216\pi$
$881$		−	30.6641i		−	1.03310i	0.856257	−	0.516549i	$-0.172784\pi$
$882$	18.1192	+	4.16709i	0.610105	+	0.140313i
$883$	10.9764	+	33.7819i	0.369385	+	1.13685i	0.947189	+	0.320675i	$0.103910\pi$
$883$	10.9764	+	33.7819i	0.369385	+	1.13685i	−0.577804	+	0.816176i	$0.696090\pi$
$884$	−1.11563	−	1.23904i	−0.0375229	−	0.0416733i
$885$	25.9148	+	2.72375i	0.871115	+	0.0915579i
$886$	−72.4190	−	7.61154i	−2.43296	−	0.255715i
$887$	−26.4807	−	29.4097i	−0.889133	−	0.987482i	0.110847	−	0.993838i	$-0.464644\pi$
$887$	−26.4807	−	29.4097i	−0.889133	−	0.987482i	−0.999980	+	0.00635504i	$0.997977\pi$
$888$	0.120615	+	0.371213i	0.00404756	+	0.0124571i
$889$	53.0639	+	3.22311i	1.77971	+	0.108100i
$890$		−	145.347i		−	4.87205i
$891$	−0.454594	+	3.28532i	−0.0152295	+	0.110062i
$892$	−51.2116	+	29.5670i	−1.71469	+	0.989977i
$893$	−18.2263	+	40.9370i	−0.609921	+	1.36990i
$894$	8.39768	−	39.5080i	0.280860	−	1.32134i
$895$	62.6351	+	20.3514i	2.09366	+	0.680272i
$896$	−27.5117	−	7.61721i	−0.919102	−	0.254473i
$897$	−4.42631	+	6.09230i	−0.147790	+	0.203416i
$898$	27.6373	−	24.8847i	0.922269	−	0.830415i
$899$	9.40972	−	10.4506i	0.313832	−	0.348546i
$900$	−35.5233	−	15.8160i	−1.18411	−	0.527200i
$901$	0.367458	−	0.636456i	0.0122418	−	0.0212034i
$902$	53.2393	−	3.83673i	1.77268	−	0.127749i
$903$	−29.2146	−	4.87620i	−0.972199	−	0.162270i
$904$	−36.1411	−	49.7440i	−1.20204	−	1.65446i
$905$	−19.7926	−	4.20704i	−0.657928	−	0.139847i
$906$	−2.90224	−	13.6539i	−0.0964203	−	0.453622i
$907$	1.13230	−	10.7731i	0.0375975	−	0.357716i	−0.959508	−	0.281682i	$-0.909108\pi$
$907$	1.13230	−	10.7731i	0.0375975	−	0.357716i	0.997105	−	0.0760338i	$-0.0242257\pi$
$908$	15.8623	−	7.06235i	0.526409	−	0.234372i
$909$	1.84448	−	5.67671i	0.0611774	−	0.188285i
$910$	−8.27702	−	55.2238i	−0.274380	−	1.83065i
$911$	15.0515	−	10.9356i	0.498679	−	0.362312i	−0.309833	−	0.950791i	$-0.600273\pi$
$911$	15.0515	−	10.9356i	0.498679	−	0.362312i	0.808512	+	0.588479i	$0.200273\pi$
$912$	−49.3949	−	28.5181i	−1.63563	−	0.944330i
$913$	4.48016	−	3.03580i	0.148272	−	0.100470i
$914$	−48.4873	−	83.9825i	−1.60382	−	2.77790i
$915$	−0.844687	−	8.03666i	−0.0279245	−	0.265684i
$916$	61.3323	−	19.9281i	2.02648	−	0.658442i
$917$	19.6039	−	0.864193i	0.647379	−	0.0285382i
$918$	−0.317790	−	0.230888i	−0.0104886	−	0.00762044i
$919$	−1.11494	−	2.50420i	−0.0367785	−	0.0826058i	0.894222	−	0.447624i	$-0.147730\pi$
$919$	−1.11494	−	2.50420i	−0.0367785	−	0.0826058i	−0.931001	+	0.365018i	$0.881063\pi$
$920$	95.4558	−	20.2897i	3.14708	−	0.668933i
$921$	−14.2498	−	12.8306i	−0.469549	−	0.422783i
$922$	34.4872	−	3.62475i	1.13578	−	0.119375i
$923$	−29.8427			−0.982285
$924$	42.3341	+	13.2293i	1.39269	+	0.435213i
$925$	0.370127			0.0121697
$926$	−61.3029	+	6.44319i	−2.01454	+	0.211736i
$927$	3.54126	+	3.18857i	0.116310	+	0.104726i
$928$	−54.7821	+	11.6443i	−1.79831	+	0.382243i
$929$	−19.7657	−	44.3945i	−0.648491	−	1.45654i	−0.875781	−	0.482708i	$-0.839653\pi$
$929$	−19.7657	−	44.3945i	−0.648491	−	1.45654i	0.227290	−	0.973827i	$-0.427013\pi$
$930$	−27.2122	−	19.7708i	−0.892323	−	0.648311i
$931$	20.9817	−	27.8925i	0.687648	−	0.914139i
$932$	−74.2079	+	24.1116i	−2.43076	+	0.789802i
$933$	−0.680346	−	6.47306i	−0.0222735	−	0.211919i
$934$	−19.8328	−	34.3513i	−0.648948	−	1.12401i
$935$	0.0572719	−	1.74662i	0.00187299	−	0.0571205i
$936$	−15.6706	−	9.04745i	−0.512211	−	0.295725i
$937$	20.8446	−	15.1445i	0.680963	−	0.494748i	−0.192714	−	0.981255i	$-0.561729\pi$
$937$	20.8446	−	15.1445i	0.680963	−	0.494748i	0.873677	+	0.486506i	$0.161729\pi$
$938$	−19.0880	+	48.5176i	−0.623245	+	1.58416i
$939$	−6.99388	+	21.5250i	−0.228237	+	0.702440i
$940$	147.847	−	65.8259i	4.82225	−	2.14701i
$941$	2.94304	−	28.0011i	0.0959402	−	0.912810i	−0.835641	−	0.549276i	$-0.814903\pi$
$941$	2.94304	−	28.0011i	0.0959402	−	0.912810i	0.931581	−	0.363534i	$-0.118430\pi$
$942$	7.08955	+	33.3537i	0.230990	+	1.08672i
$943$	20.0112	+	4.25350i	0.651653	+	0.138513i
$944$	−49.1759	−	67.6848i	−1.60054	−	2.20295i
$945$	−3.30482	−	8.82782i	−0.107506	−	0.287169i
$946$	−95.7370	−	23.6536i	−3.11268	−	0.769046i
$947$	7.02810	−	12.1730i	0.228383	−	0.395570i	−0.728946	−	0.684571i	$-0.759990\pi$
$947$	7.02810	−	12.1730i	0.228383	−	0.395570i	0.957329	+	0.289001i	$0.0933230\pi$
$948$	29.6635	+	13.2070i	0.963426	+	0.428945i
$949$	−0.155591	+	0.172802i	−0.00505071	+	0.00560938i
$950$	−75.7142	+	68.1734i	−2.45649	+	2.21184i
$951$	1.84717	−	2.54241i	0.0598987	−	0.0824434i
$952$	−2.26326	+	2.22597i	−0.0733526	+	0.0721441i
$953$	7.61736	+	2.47503i	0.246750	+	0.0801741i	0.429781	−	0.902933i	$-0.358591\pi$
$953$	7.61736	+	2.47503i	0.246750	+	0.0801741i	−0.183031	+	0.983107i	$0.558591\pi$
$954$	2.74410	−	12.9100i	0.0888435	−	0.417976i
$955$	−26.6632	+	59.8866i	−0.862802	+	1.93789i
$956$	48.2394	−	27.8510i	1.56017	−	0.900767i
$957$	12.9170	−	2.30597i	0.417548	−	0.0745415i
$958$		−	34.7364i		−	1.12228i
$959$	−5.71431	+	2.85205i	−0.184525	+	0.0920975i
$960$	16.2084	+	49.8844i	0.523125	+	1.61001i
$961$	12.2886	+	13.6478i	0.396406	+	0.440253i
$962$	0.283449	+	0.0297917i	0.00913877	+	0.000960524i
$963$	−11.7304	−	1.23291i	−0.378007	−	0.0397301i
$964$	84.2132	+	93.5282i	2.71232	+	3.01234i
$965$	10.9339	+	33.6512i	0.351976	+	1.08327i
$966$	19.7902	+	13.0869i	0.636738	+	0.421063i
$967$			33.1473i			1.06594i	0.846133	+	0.532972i	$0.178925\pi$
$967$			33.1473i			1.06594i	−0.846133	+	0.532972i	$0.821075\pi$
$968$	82.8845	+	33.0779i	2.66401	+	1.06316i
$969$	−0.638625	+	0.368710i	−0.0205156	+	0.0118447i
$970$	−19.5537	+	43.9184i	−0.627832	+	1.41013i
$971$	−3.16542	+	14.8921i	−0.101583	+	0.477912i	0.897719	+	0.440568i	$0.145223\pi$
$971$	−3.16542	+	14.8921i	−0.101583	+	0.477912i	−0.999302	+	0.0373437i	$0.988110\pi$
$972$	−4.80711	−	1.56193i	−0.154188	−	0.0500988i
$973$	54.6342	−	14.1539i	1.75149	−	0.453754i
$974$	33.6037	−	46.2516i	1.07673	−	1.48200i
$975$	−12.7515	+	11.4815i	−0.408376	+	0.367703i
$976$	−17.3609	+	19.2813i	−0.555709	+	0.617178i
$977$	25.9958	+	11.5741i	0.831681	+	0.370288i	0.777995	−	0.628270i	$-0.216237\pi$
$977$	25.9958	+	11.5741i	0.831681	+	0.370288i	0.0536851	+	0.998558i	$0.482903\pi$
$978$	−17.4786	+	30.2738i	−0.558903	+	0.968048i
$979$	38.9548	−	32.8285i	1.24500	−	1.04920i
$980$	−123.719	+	24.1566i	−3.95206	+	0.771655i
$981$	4.53340	+	6.23969i	0.144740	+	0.199218i
$982$	−84.8222	−	18.0295i	−2.70679	−	0.575345i
$983$	4.73274	+	22.2658i	0.150951	+	0.710168i	0.986896	+	0.161356i	$0.0515866\pi$
$983$	4.73274	+	22.2658i	0.150951	+	0.710168i	−0.835945	+	0.548813i	$0.815080\pi$
$984$	−5.13849	+	48.8894i	−0.163809	+	1.55854i
$985$	−3.88298	+	1.72882i	−0.123722	+	0.0550847i
$986$	−0.480223	+	1.47798i	−0.0152934	+	0.0470683i
$987$	22.1268	+	8.70524i	0.704305	+	0.277091i
$988$	−45.4762	+	33.0404i	−1.44679	+	1.05116i
$989$	−32.7331	−	18.8985i	−1.04085	−	0.600937i
$990$	−8.71491	−	30.1502i	−0.276978	−	0.958236i
$991$	−7.62760	−	13.2114i	−0.242299	−	0.419674i	0.719070	−	0.694938i	$-0.244568\pi$
$991$	−7.62760	−	13.2114i	−0.242299	−	0.419674i	−0.961369	+	0.275264i	$0.911235\pi$
$992$	5.25991	+	50.0447i	0.167002	+	1.58892i
$993$	0.147435	−	0.0479046i	0.00467872	−	0.00152021i
$994$	4.14079	+	93.9324i	0.131338	+	2.97935i
$995$	−34.7072	−	25.2163i	−1.10029	−	0.799410i
$996$	3.35459	+	7.53453i	0.106294	+	0.238741i
$997$	57.6653	−	12.2571i	1.82628	−	0.388188i	0.838609	−	0.544734i	$-0.183370\pi$
$997$	57.6653	−	12.2571i	1.82628	−	0.388188i	0.987671	+	0.156547i	$0.0500362\pi$
$998$	5.40585	+	4.86745i	0.171119	+	0.154077i
$999$	0.0478475	−	0.00502897i	0.00151383	−	0.000159110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.19.1	✓	128
3.2	odd	2		693.2.cg.c.19.16		128
7.3	odd	6	inner	231.2.ba.a.52.16	yes	128
11.7	odd	10	inner	231.2.ba.a.40.16	yes	128
21.17	even	6		693.2.cg.c.514.1		128
33.29	even	10		693.2.cg.c.271.1		128
77.73	even	30	inner	231.2.ba.a.73.1	yes	128
231.227	odd	30		693.2.cg.c.73.16		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.1	✓	128	1.1	even	1	trivial
231.2.ba.a.40.16	yes	128	11.7	odd	10	inner
231.2.ba.a.52.16	yes	128	7.3	odd	6	inner
231.2.ba.a.73.1	yes	128	77.73	even	30	inner
693.2.cg.c.19.16		128	3.2	odd	2
693.2.cg.c.73.16		128	231.227	odd	30
693.2.cg.c.271.1		128	33.29	even	10
693.2.cg.c.514.1		128	21.17	even	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.64148 + 0.277631i) q^{2} +(0.743145 + 0.669131i) q^{3} +(4.94404 - 1.05089i) q^{4} +(1.44910 + 3.25473i) q^{5} +(-2.14877 - 1.56118i) q^{6} +(1.42250 + 2.23081i) q^{7} +(-7.71576 + 2.50700i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-2.64148 + 0.277631i) q^{2} +(0.743145 + 0.669131i) q^{3} +(4.94404 - 1.05089i) q^{4} +(1.44910 + 3.25473i) q^{5} +(-2.14877 - 1.56118i) q^{6} +(1.42250 + 2.23081i) q^{7} +(-7.71576 + 2.50700i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-4.73138 - 8.19500i) q^{10} +(1.12772 - 3.11901i) q^{11} +(4.37732 + 2.52725i) q^{12} +(1.80443 - 1.31100i) q^{13} +(-4.37685 - 5.49770i) q^{14} +(-1.10095 + 3.38837i) q^{15} +(10.4500 - 4.65264i) q^{16} +(0.0154591 - 0.147084i) q^{17} +(-0.552220 - 2.59799i) q^{18} +(-4.87719 - 1.03668i) q^{19} +(10.5848 + 14.5687i) q^{20} +(-0.435577 + 2.60965i) q^{21} +(-2.11291 + 8.55191i) q^{22} +(-1.68815 + 2.92395i) q^{23} +(-7.41144 - 3.29979i) q^{24} +(-5.14774 + 5.71714i) q^{25} +(-4.40240 + 3.96394i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(9.37723 + 9.53431i) q^{28} +(3.76257 + 1.22253i) q^{29} +(1.96742 - 9.25598i) q^{30} +(1.44578 - 3.24727i) q^{31} +(-12.2599 + 7.07825i) q^{32} +(2.92509 - 1.56329i) q^{33} +0.392810i q^{34} +(-5.19933 + 7.86252i) q^{35} +(1.56193 + 4.80711i) q^{36} +(-0.0321926 - 0.0357535i) q^{37} +(13.1708 + 1.38431i) q^{38} +(2.21818 + 0.233141i) q^{39} +(-19.3405 - 21.4799i) q^{40} +(-1.87245 - 5.76281i) q^{41} +(0.426048 - 7.01427i) q^{42} +11.1948i q^{43} +(2.29775 - 16.6057i) q^{44} +(-3.08543 + 1.78137i) q^{45} +(3.64742 - 8.19225i) q^{46} +(1.86853 - 8.79073i) q^{47} +(10.8791 + 3.53483i) q^{48} +(-2.95299 + 6.34664i) q^{49} +(12.0104 - 16.5309i) q^{50} +(0.109906 - 0.0989602i) q^{51} +(7.54349 - 8.37789i) q^{52} +(4.53960 + 2.02116i) q^{53} +(1.32802 - 2.30019i) q^{54} +(11.7857 - 0.849347i) q^{55} +(-16.5683 - 13.6462i) q^{56} +(-2.93079 - 4.03388i) q^{57} +(-10.2782 - 2.18469i) q^{58} +(-1.52064 - 7.15405i) q^{59} +(-1.88234 + 17.9092i) q^{60} +(-2.07208 + 0.922549i) q^{61} +(-2.91745 + 8.97899i) q^{62} +(-2.06989 + 1.64789i) q^{63} +(11.9105 - 8.65351i) q^{64} +(6.88175 + 3.97318i) q^{65} +(-7.29254 + 4.94149i) q^{66} +(-3.70969 - 6.42537i) q^{67} +(-0.0781380 - 0.743433i) q^{68} +(-3.21104 + 1.04333i) q^{69} +(11.5511 - 22.2122i) q^{70} +(-10.8246 - 7.86454i) q^{71} +(-3.29979 - 7.41144i) q^{72} +(-0.101975 + 0.0216755i) q^{73} +(0.0949623 + 0.0855044i) q^{74} +(-7.65103 + 0.804156i) q^{75} -25.2025 q^{76} +(8.56209 - 1.92108i) q^{77} -5.92402 q^{78} +(6.38894 - 0.671505i) q^{79} +(30.2862 + 27.2698i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(6.54597 + 14.7025i) q^{82} +(1.32010 + 0.959106i) q^{83} +(0.588942 + 13.3600i) q^{84} +(0.501119 - 0.162824i) q^{85} +(-3.10803 - 29.5709i) q^{86} +(1.97810 + 3.42617i) q^{87} +(-0.881819 + 26.8928i) q^{88} +(13.3021 + 7.67995i) q^{89} +(7.65554 - 5.56207i) q^{90} +(5.49139 + 2.16045i) q^{91} +(-5.27352 + 16.2302i) q^{92} +(3.24727 - 1.44578i) q^{93} +(-2.49510 + 23.7393i) q^{94} +(-3.69343 - 17.3762i) q^{95} +(-13.8472 - 2.94330i) q^{96} +(-2.98618 - 4.11013i) q^{97} +(6.03823 - 17.5844i) q^{98} +(3.21981 + 0.795514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

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