LMFDB - Embedded newform 429.2.bq.a.29.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

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

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.16
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.127461 + 1.21271i) q^{2} +(0.478976 - 1.66451i) q^{3} +(0.501877 + 0.106677i) q^{4} +(-1.76681 - 2.43180i) q^{5} +(1.95751 + 0.793018i) q^{6} +(0.706704 - 3.32478i) q^{7} +(-0.946962 + 2.91445i) q^{8} +(-2.54116 - 1.59452i) q^{9} +O(q^{10})$	\(q+(-0.127461 + 1.21271i) q^{2} +(0.478976 - 1.66451i) q^{3} +(0.501877 + 0.106677i) q^{4} +(-1.76681 - 2.43180i) q^{5} +(1.95751 + 0.793018i) q^{6} +(0.706704 - 3.32478i) q^{7} +(-0.946962 + 2.91445i) q^{8} +(-2.54116 - 1.59452i) q^{9} +(3.17427 - 1.83266i) q^{10} +(0.977496 + 3.16931i) q^{11} +(0.417952 - 0.784281i) q^{12} +(-3.56970 - 0.507177i) q^{13} +(3.94192 + 1.28081i) q^{14} +(-4.89401 + 1.77609i) q^{15} +(-2.47622 - 1.10248i) q^{16} +(-0.701640 - 6.67566i) q^{17} +(2.25759 - 2.87846i) q^{18} +(2.21285 - 1.99246i) q^{19} +(-0.627301 - 1.40894i) q^{20} +(-5.19563 - 2.76880i) q^{21} +(-3.96804 + 0.781457i) q^{22} +(-1.33742 + 0.772162i) q^{23} +(4.39755 + 2.97218i) q^{24} +(-1.24696 + 3.83776i) q^{25} +(1.07006 - 4.26437i) q^{26} +(-3.87124 + 3.46605i) q^{27} +(0.709357 - 1.59324i) q^{28} +(4.52019 - 5.02018i) q^{29} +(-1.53008 - 6.16139i) q^{30} +(2.88677 + 2.09736i) q^{31} +(-1.41182 + 2.44534i) q^{32} +(5.74353 - 0.109027i) q^{33} +8.18507 q^{34} +(-9.33381 + 4.15568i) q^{35} +(-1.10525 - 1.07134i) q^{36} +(-1.99150 + 2.21178i) q^{37} +(2.13423 + 2.93751i) q^{38} +(-2.55400 + 5.69887i) q^{39} +(8.76046 - 2.84645i) q^{40} +(9.93295 - 2.11131i) q^{41} +(4.02000 - 5.94787i) q^{42} +(-5.36011 - 3.09466i) q^{43} +(0.152490 + 1.69488i) q^{44} +(0.612196 + 8.99681i) q^{45} +(-0.765939 - 1.72033i) q^{46} +(9.12373 + 2.96448i) q^{47} +(-3.02114 + 3.59362i) q^{48} +(-4.15992 - 1.85212i) q^{49} +(-4.49515 - 2.00137i) q^{50} +(-11.4478 - 2.02960i) q^{51} +(-1.73745 - 0.635346i) q^{52} +(-2.55432 + 3.51572i) q^{53} +(-3.70988 - 5.13648i) q^{54} +(5.98007 - 7.97663i) q^{55} +(9.02069 + 5.20810i) q^{56} +(-2.25656 - 4.63765i) q^{57} +(5.51188 + 6.12156i) q^{58} +(-0.231237 + 1.08788i) q^{59} +(-2.64565 + 0.369298i) q^{60} +(13.9103 - 1.46204i) q^{61} +(-2.91144 + 3.23348i) q^{62} +(-7.09727 + 7.32196i) q^{63} +(-7.17132 - 5.21027i) q^{64} +(5.07362 + 9.57689i) q^{65} +(-0.599857 + 6.97913i) q^{66} +(4.67660 + 8.10010i) q^{67} +(0.360004 - 3.42521i) q^{68} +(0.644675 + 2.59600i) q^{69} +(-3.84994 - 11.8489i) q^{70} +(7.95390 - 0.835989i) q^{71} +(7.05353 - 5.89615i) q^{72} +(-6.98392 + 2.26921i) q^{73} +(-2.42841 - 2.69702i) q^{74} +(5.79071 + 3.91377i) q^{75} +(1.32313 - 0.763909i) q^{76} +(11.2281 - 1.01020i) q^{77} +(-6.58554 - 3.82364i) q^{78} +(8.57951 - 11.8087i) q^{79} +(1.69398 + 7.96955i) q^{80} +(3.91503 + 8.10386i) q^{81} +(1.29435 + 12.3149i) q^{82} +(-6.89311 + 5.00814i) q^{83} +(-2.31219 - 1.94385i) q^{84} +(-14.9942 + 13.5008i) q^{85} +(4.43613 - 6.10581i) q^{86} +(-6.19106 - 9.92844i) q^{87} +(-10.1624 - 0.152349i) q^{88} +(-14.2430 + 8.22321i) q^{89} +(-10.9885 - 0.404325i) q^{90} +(-4.20898 + 11.5101i) q^{91} +(-0.753594 + 0.244858i) q^{92} +(4.87376 - 3.80046i) q^{93} +(-4.75797 + 10.6866i) q^{94} +(-8.75496 - 1.86092i) q^{95} +(3.39406 + 3.52124i) q^{96} +(1.49929 - 0.667525i) q^{97} +(2.77631 - 4.80871i) q^{98} +(2.56954 - 9.61236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.127461	+	1.21271i	−0.0901285	+	0.857515i	0.852288	+	0.523073i	$0.175215\pi$
$2$	−0.127461	+	1.21271i	−0.0901285	+	0.857515i	−0.942416	+	0.334442i	$0.891452\pi$
$3$	0.478976	−	1.66451i	0.276537	−	0.961003i
$3$	0.478976	−	1.66451i	0.276537	−	0.961003i
$4$	0.501877	+	0.106677i	0.250938	+	0.0533386i
$5$	−1.76681	−	2.43180i	−0.790140	−	1.08753i	−0.994091	−	0.108553i	$-0.965378\pi$
$5$	−1.76681	−	2.43180i	−0.790140	−	1.08753i	0.203951	−	0.978981i	$-0.434622\pi$
$6$	1.95751	+	0.793018i	0.799151	+	0.323748i
$7$	0.706704	−	3.32478i	0.267109	−	1.25665i	−0.616099	−	0.787668i	$-0.711288\pi$
$7$	0.706704	−	3.32478i	0.267109	−	1.25665i	0.883208	−	0.468981i	$-0.155379\pi$
$8$	−0.946962	+	2.91445i	−0.334802	+	1.03041i
$9$	−2.54116	−	1.59452i	−0.847055	−	0.531506i
$10$	3.17427	−	1.83266i	1.00379	−	0.579539i
$11$	0.977496	+	3.16931i	0.294726	+	0.955582i
$11$	0.977496	+	3.16931i	0.294726	+	0.955582i
$12$	0.417952	−	0.784281i	0.120652	−	0.226402i
$13$	−3.56970	−	0.507177i	−0.990057	−	0.140666i
$13$	−3.56970	−	0.507177i	−0.990057	−	0.140666i
$14$	3.94192	+	1.28081i	1.05352	+	0.342310i
$15$	−4.89401	+	1.77609i	−1.26363	+	0.458584i
$16$	−2.47622	−	1.10248i	−0.619055	−	0.275621i
$17$	−0.701640	−	6.67566i	−0.170173	−	1.61909i	−0.662766	−	0.748826i	$-0.730618\pi$
$17$	−0.701640	−	6.67566i	−0.170173	−	1.61909i	0.492594	−	0.870259i	$-0.336049\pi$
$18$	2.25759	−	2.87846i	0.532118	−	0.678458i
$19$	2.21285	−	1.99246i	0.507664	−	0.457102i	−0.375056	−	0.927002i	$-0.622377\pi$
$19$	2.21285	−	1.99246i	0.507664	−	0.457102i	0.882720	+	0.469900i	$0.155710\pi$
$20$	−0.627301	−	1.40894i	−0.140269	−	0.315049i
$21$	−5.19563	−	2.76880i	−1.13378	−	0.604203i
$22$	−3.96804	+	0.781457i	−0.845989	+	0.166607i
$23$	−1.33742	+	0.772162i	−0.278872	+	0.161007i	−0.632913	−	0.774223i	$-0.718141\pi$
$23$	−1.33742	+	0.772162i	−0.278872	+	0.161007i	0.354041	+	0.935230i	$0.384807\pi$
$24$	4.39755	+	2.97218i	0.897646	+	0.606693i
$25$	−1.24696	+	3.83776i	−0.249393	+	0.767551i
$26$	1.07006	−	4.26437i	0.209855	−	0.836311i
$27$	−3.87124	+	3.46605i	−0.745021	+	0.667041i
$28$	0.709357	−	1.59324i	0.134056	−	0.301094i
$29$	4.52019	−	5.02018i	0.839379	−	0.932225i	−0.159106	−	0.987262i	$-0.550861\pi$
$29$	4.52019	−	5.02018i	0.839379	−	0.932225i	0.998484	+	0.0550370i	$0.0175277\pi$
$30$	−1.53008	−	6.16139i	−0.279354	−	1.12491i
$31$	2.88677	+	2.09736i	0.518479	+	0.376697i	0.816030	−	0.578009i	$-0.196170\pi$
$31$	2.88677	+	2.09736i	0.518479	+	0.376697i	−0.297552	+	0.954706i	$0.596170\pi$
$32$	−1.41182	+	2.44534i	−0.249577	+	0.432279i
$33$	5.74353	−	0.109027i	0.999820	−	0.0189792i
$34$	8.18507			1.40373
$35$	−9.33381	+	4.15568i	−1.57770	+	0.702438i
$36$	−1.10525	−	1.07134i	−0.184209	−	0.178556i
$37$	−1.99150	+	2.21178i	−0.327400	+	0.363615i	−0.884263	−	0.466990i	$-0.845338\pi$
$37$	−1.99150	+	2.21178i	−0.327400	+	0.363615i	0.556862	+	0.830605i	$0.312005\pi$
$38$	2.13423	+	2.93751i	0.346217	+	0.476527i
$39$	−2.55400	+	5.69887i	−0.408967	+	0.912549i
$40$	8.76046	−	2.84645i	1.38515	−	0.450063i
$41$	9.93295	−	2.11131i	1.55127	−	0.329732i	0.648958	−	0.760824i	$-0.275205\pi$
$41$	9.93295	−	2.11131i	1.55127	−	0.329732i	0.902308	+	0.431092i	$0.141872\pi$
$42$	4.02000	−	5.94787i	0.620299	−	0.917777i
$43$	−5.36011	−	3.09466i	−0.817409	−	0.471931i	0.0321132	−	0.999484i	$-0.489776\pi$
$43$	−5.36011	−	3.09466i	−0.817409	−	0.471931i	−0.849522	+	0.527553i	$0.823110\pi$
$44$	0.152490	+	1.69488i	0.0229887	+	0.255512i
$45$	0.612196	+	8.99681i	0.0912609	+	1.34116i
$46$	−0.765939	−	1.72033i	−0.112932	−	0.253648i
$47$	9.12373	+	2.96448i	1.33083	+	0.432414i	0.886202	−	0.463300i	$-0.153335\pi$
$47$	9.12373	+	2.96448i	1.33083	+	0.432414i	0.444632	+	0.895714i	$0.353335\pi$
$48$	−3.02114	+	3.59362i	−0.436065	+	0.518695i
$49$	−4.15992	−	1.85212i	−0.594275	−	0.264588i
$50$	−4.49515	−	2.00137i	−0.635710	−	0.283036i
$51$	−11.4478	−	2.02960i	−1.60301	−	0.284200i
$52$	−1.73745	−	0.635346i	−0.240940	−	0.0881066i
$53$	−2.55432	+	3.51572i	−0.350863	+	0.482922i	−0.947575	−	0.319534i	$-0.896474\pi$
$53$	−2.55432	+	3.51572i	−0.350863	+	0.482922i	0.596712	+	0.802456i	$0.296474\pi$
$54$	−3.70988	−	5.13648i	−0.504851	−	0.698986i
$55$	5.98007	−	7.97663i	0.806353	−	1.07557i
$56$	9.02069	+	5.20810i	1.20544	+	0.695961i
$57$	−2.25656	−	4.63765i	−0.298889	−	0.614272i
$58$	5.51188	+	6.12156i	0.723745	+	0.803800i
$59$	−0.231237	+	1.08788i	−0.0301045	+	0.141630i	−0.990633	−	0.136551i	$-0.956398\pi$
$59$	−0.231237	+	1.08788i	−0.0301045	+	0.141630i	0.960529	+	0.278181i	$0.0897316\pi$
$60$	−2.64565	+	0.369298i	−0.341553	+	0.0476761i
$61$	13.9103	−	1.46204i	1.78104	−	0.187195i	0.843981	−	0.536373i	$-0.180206\pi$
$61$	13.9103	−	1.46204i	1.78104	−	0.187195i	0.937056	+	0.349178i	$0.113539\pi$
$62$	−2.91144	+	3.23348i	−0.369753	+	0.410652i
$63$	−7.09727	+	7.32196i	−0.894172	+	0.922481i
$64$	−7.17132	−	5.21027i	−0.896415	−	0.651284i
$65$	5.07362	+	9.57689i	0.629305	+	1.18787i
$66$	−0.599857	+	6.97913i	−0.0738373	+	0.859071i
$67$	4.67660	+	8.10010i	0.571337	+	0.989585i	0.996429	+	0.0844349i	$0.0269085\pi$
$67$	4.67660	+	8.10010i	0.571337	+	0.989585i	−0.425092	+	0.905150i	$0.639758\pi$
$68$	0.360004	−	3.42521i	0.0436569	−	0.415367i
$69$	0.644675	+	2.59600i	0.0776097	+	0.312521i
$70$	−3.84994	−	11.8489i	−0.460156	−	1.41621i
$71$	7.95390	−	0.835989i	0.943955	−	0.0992136i	0.379970	−	0.924999i	$-0.375934\pi$
$71$	7.95390	−	0.835989i	0.943955	−	0.0992136i	0.563985	+	0.825785i	$0.309268\pi$
$72$	7.05353	−	5.89615i	0.831266	−	0.694868i
$73$	−6.98392	+	2.26921i	−0.817406	+	0.265591i	−0.687731	−	0.725965i	$-0.741393\pi$
$73$	−6.98392	+	2.26921i	−0.817406	+	0.265591i	−0.129675	+	0.991557i	$0.541393\pi$
$74$	−2.42841	−	2.69702i	−0.282297	−	0.313523i
$75$	5.79071	+	3.91377i	0.668653	+	0.451923i
$76$	1.32313	−	0.763909i	0.151773	−	0.0876264i
$77$	11.2281	−	1.01020i	1.27956	−	0.115123i
$78$	−6.58554	−	3.82364i	−0.745665	−	0.432943i
$79$	8.57951	−	11.8087i	0.965270	−	1.32858i	0.0208698	−	0.999782i	$-0.493356\pi$
$79$	8.57951	−	11.8087i	0.965270	−	1.32858i	0.944400	−	0.328798i	$-0.106644\pi$
$80$	1.69398	+	7.96955i	0.189393	+	0.891023i
$81$	3.91503	+	8.10386i	0.435003	+	0.900429i
$82$	1.29435	+	12.3149i	0.142937	+	1.35995i
$83$	−6.89311	+	5.00814i	−0.756617	+	0.549715i	−0.897871	−	0.440259i	$-0.854887\pi$
$83$	−6.89311	+	5.00814i	−0.756617	+	0.549715i	0.141253	+	0.989973i	$0.454887\pi$
$84$	−2.31219	−	1.94385i	−0.252281	−	0.212092i
$85$	−14.9942	+	13.5008i	−1.62635	+	1.46437i
$86$	4.43613	−	6.10581i	0.478360	−	0.658406i
$87$	−6.19106	−	9.92844i	−0.663752	−	1.06444i
$88$	−10.1624	−	0.152349i	−1.08332	−	0.0162405i
$89$	−14.2430	+	8.22321i	−1.50976	+	0.871658i	−0.509821	+	0.860281i	$0.670288\pi$
$89$	−14.2430	+	8.22321i	−1.50976	+	0.871658i	−0.999935	+	0.0113776i	$0.996378\pi$
$90$	−10.9885	−	0.404325i	−1.15829	−	0.0426196i
$91$	−4.20898	+	11.5101i	−0.441221	+	1.20658i
$92$	−0.753594	+	0.244858i	−0.0785676	+	0.0255282i
$93$	4.87376	−	3.80046i	0.505385	−	0.394089i
$94$	−4.75797	+	10.6866i	−0.490748	+	1.10224i
$95$	−8.75496	−	1.86092i	−0.898239	−	0.190927i
$96$	3.39406	+	3.52124i	0.346405	+	0.359385i
$97$	1.49929	−	0.667525i	0.152229	−	0.0677769i	−0.329208	−	0.944258i	$-0.606782\pi$
$97$	1.49929	−	0.667525i	0.152229	−	0.0677769i	0.481437	+	0.876481i	$0.340115\pi$
$98$	2.77631	−	4.80871i	0.280449	−	0.485753i
$99$	2.56954	−	9.61236i	0.258248	−	0.966079i
$100$	−1.03522	+	1.79306i	−0.103522	+	0.179306i
$101$	0.260931	−	2.48259i	0.0259636	−	0.247027i	−0.973841	−	0.227233i	$-0.927032\pi$
$101$	0.260931	−	2.48259i	0.0259636	−	0.247027i	0.999804	−	0.0197942i	$-0.00630109\pi$
$102$	3.92045	−	13.6241i	0.388183	−	1.34899i
$103$	−2.42886	−	7.47526i	−0.239323	−	0.736559i	−0.996519	−	0.0833715i	$-0.973431\pi$
$103$	−2.42886	−	7.47526i	−0.239323	−	0.736559i	0.757196	−	0.653188i	$-0.226569\pi$
$104$	4.85852	−	9.92344i	0.476417	−	0.973074i
$105$	2.44649	+	17.5267i	0.238753	+	1.71043i
$106$	−3.93797	−	3.54577i	−0.382490	−	0.344395i
$107$	12.7574	−	2.71167i	1.23331	−	0.262148i	0.455263	−	0.890357i	$-0.349545\pi$
$107$	12.7574	−	2.71167i	1.23331	−	0.262148i	0.778044	+	0.628210i	$0.216212\pi$
$108$	−2.31263	+	1.32656i	−0.222533	+	0.127648i
$109$		−	0.235357i		−	0.0225431i	−0.999936	−	0.0112716i	$-0.996412\pi$
$109$		−	0.235357i		−	0.0225431i	0.999936	−	0.0112716i	$-0.00358792\pi$
$110$	8.91111	+	8.26880i	0.849641	+	0.788399i
$111$	2.72765	+	4.37425i	0.258897	+	0.415186i
$112$	−5.41548	+	7.45377i	−0.511715	+	0.704315i
$113$	−0.638846	+	0.575219i	−0.0600976	+	0.0541121i	−0.698632	−	0.715481i	$-0.746208\pi$
$113$	−0.638846	+	0.575219i	−0.0600976	+	0.0541121i	0.638535	+	0.769593i	$0.279541\pi$
$114$	5.91175	−	2.14544i	0.553686	−	0.200939i
$115$	4.24071	+	1.88809i	0.395449	+	0.176065i
$116$	2.80412	−	2.03731i	0.260356	−	0.189160i
$117$	8.26250	+	6.98077i	0.763868	+	0.645373i
$118$	−1.28981	−	0.419086i	−0.118737	−	0.0385800i
$119$	−22.6910	−	2.38492i	−2.08008	−	0.218625i
$120$	−0.541878	−	15.9452i	−0.0494664	−	1.45559i
$121$	−9.08900	+	6.19597i	−0.826273	+	0.563270i
$122$			17.0556i			1.54414i
$123$	1.24335	−	17.5447i	0.112109	−	1.58195i
$124$	1.22506	+	1.36057i	0.110014	+	0.122183i
$125$	−2.75796	+	0.896117i	−0.246680	+	0.0801511i
$126$	−7.97479	−	9.54020i	−0.710451	−	0.849908i
$127$	−4.07365	+	9.14957i	−0.361478	+	0.811893i	0.637657	+	0.770320i	$0.279904\pi$
$127$	−4.07365	+	9.14957i	−0.361478	+	0.811893i	−0.999135	+	0.0415732i	$0.986763\pi$
$128$	3.45384	−	3.83588i	0.305279	−	0.339047i
$129$	−7.71845	+	7.43967i	−0.679571	+	0.655026i
$130$	−12.2607	+	4.93215i	−1.07533	+	0.432578i
$131$	−0.444540			−0.0388396			−0.0194198	−	0.999811i	$-0.506182\pi$
$131$	−0.444540			−0.0388396			−0.0194198	+	0.999811i	$0.506182\pi$
$132$	2.89417	+	0.557985i	0.251905	+	0.0485664i
$133$	−5.06067	−	8.76534i	−0.438816	−	0.760051i
$134$	−10.4192	+	4.63891i	−0.900078	+	0.400741i
$135$	15.2685	+	3.29025i	1.31410	+	0.283180i
$136$	20.1203	+	4.27670i	1.72530	+	0.366724i
$137$	−2.64915	+	0.278437i	−0.226332	+	0.0237884i	−0.217015	−	0.976168i	$-0.569632\pi$
$137$	−2.64915	+	0.278437i	−0.226332	+	0.0237884i	−0.00931639	+	0.999957i	$0.502966\pi$
$138$	−3.23036	+	0.450915i	−0.274987	+	0.0383844i
$139$	−3.11740	+	14.6662i	−0.264414	+	1.24397i	0.622715	+	0.782449i	$0.286030\pi$
$139$	−3.11740	+	14.6662i	−0.264414	+	1.24397i	−0.887129	+	0.461522i	$0.847304\pi$
$140$	−5.12774	+	1.08993i	−0.433373	+	0.0921163i
$141$	9.30445	−	13.7666i	0.783576	−	1.15936i
$142$			9.75233i			0.818397i
$143$	−1.88197	−	11.8092i	−0.157378	−	0.987538i
$144$	4.53455	+	6.74997i	0.377879	+	0.562498i
$145$	−20.1944	−	2.12252i	−1.67705	−	0.176265i
$146$	−1.86172	−	8.75870i	−0.154077	−	0.724875i
$147$	−5.07536	+	6.03710i	−0.418609	+	0.497931i
$148$	−1.23543	+	0.897595i	−0.101552	+	0.0737818i
$149$	−0.464631	−	4.42067i	−0.0380640	−	0.362155i	−0.996930	−	0.0782963i	$-0.975052\pi$
$149$	−0.464631	−	4.42067i	−0.0380640	−	0.362155i	0.958866	−	0.283859i	$-0.0916147\pi$
$150$	−5.48436	+	6.52359i	−0.447796	+	0.532649i
$151$	−0.402002	−	0.130618i	−0.0327145	−	0.0106296i	0.292614	−	0.956231i	$-0.405475\pi$
$151$	−0.402002	−	0.130618i	−0.0327145	−	0.0106296i	−0.325329	+	0.945601i	$0.605475\pi$
$152$	3.71144	+	8.33604i	0.301038	+	0.676142i
$153$	−8.86148	+	18.0827i	−0.716408	+	1.46190i
$154$	−0.206059	+	13.7451i	−0.0166047	+	1.10761i
$155$		−	10.7257i		−	0.861506i
$156$	−1.88973	+	2.58767i	−0.151300	+	0.207180i
$157$	3.65095	−	11.2365i	0.291378	−	0.896768i	−0.693037	−	0.720902i	$-0.743728\pi$
$157$	3.65095	−	11.2365i	0.291378	−	0.896768i	0.984414	−	0.175866i	$-0.0562724\pi$
$158$	13.2269	+	11.9096i	1.05228	+	0.947477i
$159$	4.62848	+	5.93563i	0.367063	+	0.470726i
$160$	8.44099	−	0.887184i	0.667319	−	0.0701381i
$161$	1.62211	+	4.99233i	0.127840	+	0.393451i
$162$	−10.3266	+	3.71487i	−0.811338	+	0.291868i
$163$	−5.62018	+	2.50227i	−0.440207	+	0.195993i	−0.614858	−	0.788638i	$-0.710787\pi$
$163$	−5.62018	+	2.50227i	−0.440207	+	0.195993i	0.174652	+	0.984630i	$0.444120\pi$
$164$	5.21034			0.406859
$165$	−10.4128	−	13.7745i	−0.810638	−	1.07234i
$166$	−5.19482	−	8.99769i	−0.403196	−	0.698356i
$167$	1.20120	−	11.4286i	0.0929514	−	0.884374i	−0.844335	−	0.535815i	$-0.820004\pi$
$167$	1.20120	−	11.4286i	0.0929514	−	0.884374i	0.937287	−	0.348559i	$-0.113329\pi$
$168$	12.9896	−	12.5204i	1.00217	−	0.965973i
$169$	12.4855	+	3.62094i	0.960426	+	0.278534i
$170$	−14.4614	−	19.9045i	−1.10914	−	1.52660i
$171$	−8.80024	+	1.53474i	−0.672971	+	0.117364i
$172$	−2.35998	−	2.12494i	−0.179947	−	0.162025i
$173$	7.26631	+	8.07006i	0.552448	+	0.613555i	0.953093	−	0.302678i	$-0.0978807\pi$
$173$	7.26631	+	8.07006i	0.552448	+	0.613555i	−0.400645	+	0.916233i	$0.631214\pi$
$174$	12.8294	−	6.24247i	0.972597	−	0.473241i
$175$	11.8785	+	6.85804i	0.897928	+	0.518419i
$176$	1.07361	−	8.92558i	0.0809268	−	0.672791i
$177$	1.70003	+	0.905966i	0.127782	+	0.0680966i
$178$	−8.15693	−	18.3208i	−0.611388	−	1.37320i
$179$	1.12346	+	5.28548i	0.0839716	+	0.395055i	0.999981	−	0.00610065i	$-0.00194191\pi$
$179$	1.12346	+	5.28548i	0.0839716	+	0.395055i	−0.916010	+	0.401156i	$0.868609\pi$
$180$	−0.652507	+	4.58059i	−0.0486350	+	0.341417i
$181$	7.61884	−	5.53541i	0.566304	−	0.411444i	−0.267457	−	0.963570i	$-0.586183\pi$
$181$	7.61884	−	5.53541i	0.566304	−	0.411444i	0.833761	+	0.552126i	$0.186183\pi$
$182$	−13.4219	−	6.57135i	−0.994896	−	0.487101i
$183$	4.22915	−	23.8541i	0.312628	−	1.76335i
$184$	−0.983938	−	4.62906i	−0.0725369	−	0.341259i
$185$	8.89720	+	0.935134i	0.654135	+	0.0687524i
$186$	3.98764	+	6.39487i	0.292388	+	0.468894i
$187$	20.4714	−	8.74915i	1.49701	−	0.639801i
$188$	4.26275	+	2.46110i	0.310893	+	0.179494i
$189$	8.78803	+	15.3205i	0.639235	+	1.11440i
$190$	3.37267	−	10.3800i	0.244680	−	0.753046i
$191$	2.38386	−	11.2152i	0.172490	−	0.811502i	−0.803777	−	0.594931i	$-0.797179\pi$
$191$	2.38386	−	11.2152i	0.172490	−	0.811502i	0.976267	−	0.216571i	$-0.0694873\pi$
$192$	−12.1074	+	9.44111i	−0.873778	+	0.681354i
$193$	2.03218	−	4.56435i	0.146280	−	0.328549i	−0.825514	−	0.564381i	$-0.809115\pi$
$193$	2.03218	−	4.56435i	0.146280	−	0.328549i	0.971794	+	0.235832i	$0.0757815\pi$
$194$	0.618414	+	1.90328i	0.0443995	+	0.136648i
$195$	18.3709	−	3.85797i	1.31557	−	0.276275i
$196$	−1.89019	−	1.37330i	−0.135014	−	0.0980931i
$197$	4.98268	+	8.63026i	0.355001	+	0.614880i	0.987118	−	0.159993i	$-0.0511471\pi$
$197$	4.98268	+	8.63026i	0.355001	+	0.614880i	−0.632117	+	0.774873i	$0.717814\pi$
$198$	11.3295	+	4.34130i	0.805152	+	0.308523i
$199$	0.308403	−	0.534169i	0.0218621	−	0.0378662i	−0.854887	−	0.518814i	$-0.826374\pi$
$199$	0.308403	−	0.534169i	0.0218621	−	0.0378662i	0.876749	+	0.480947i	$0.159707\pi$
$200$	−10.0041	−	7.26842i	−0.707399	−	0.513955i
$201$	15.7227	−	3.90447i	1.10899	−	0.275400i
$202$	2.97740	+	0.632866i	0.209489	+	0.0445283i
$203$	−13.4966	−	18.5764i	−0.947274	−	1.30381i
$204$	−5.52885	−	2.23982i	−0.387097	−	0.156819i
$205$	−22.6839	−	20.4247i	−1.58431	−	1.42652i
$206$	9.37491	−	1.99270i	0.653181	−	0.138838i
$207$	4.62984	+	0.170355i	0.321796	+	0.0118405i
$208$	8.28022	+	5.19143i	0.574130	+	0.359961i
$209$	8.47778	+	5.06559i	0.586420	+	0.350394i
$210$	−21.5666	+	0.732912i	−1.48824	+	0.0505758i
$211$	12.8407	+	1.34961i	0.883989	+	0.0929110i	0.535633	−	0.844451i	$-0.320073\pi$
$211$	12.8407	+	1.34961i	0.883989	+	0.0929110i	0.348357	+	0.937362i	$0.386740\pi$
$212$	−1.65700	+	1.49197i	−0.113803	+	0.102469i
$213$	2.41822	−	13.6397i	0.165694	−	0.934580i
$214$	1.66240	+	15.8167i	0.113639	+	1.08121i
$215$	1.94468	+	18.5024i	0.132626	+	1.26185i
$216$	−6.43571	−	14.5648i	−0.437894	−	0.991006i
$217$	9.01335	−	8.11566i	0.611866	−	0.550927i
$218$	0.285420	+	0.0299988i	0.0193311	+	0.00203178i
$219$	0.431990	+	12.7117i	0.0291912	+	0.858975i
$220$	3.85218	−	3.36534i	0.259714	−	0.226891i
$221$	−0.881095	+	24.1860i	−0.0592689	+	1.62692i
$222$	−5.65237	+	2.75030i	−0.379362	+	0.184588i
$223$	16.6386	−	3.53664i	1.11420	−	0.236831i	0.386206	−	0.922413i	$-0.373785\pi$
$223$	16.6386	−	3.53664i	1.11420	−	0.236831i	0.727995	+	0.685582i	$0.240452\pi$
$224$	7.13249	+	6.42212i	0.476559	+	0.429096i
$225$	9.28811	−	7.76407i	0.619207	−	0.517604i
$226$	−0.616146	−	0.848052i	−0.0409854	−	0.0564116i
$227$	2.14991	+	0.456978i	0.142695	+	0.0303307i	0.278705	−	0.960377i	$-0.410095\pi$
$227$	2.14991	+	0.456978i	0.142695	+	0.0303307i	−0.136011	+	0.990707i	$0.543428\pi$
$228$	−0.637785	−	2.56825i	−0.0422383	−	0.170087i
$229$	12.6079	+	9.16021i	0.833156	+	0.605324i	0.920451	−	0.390859i	$-0.127822\pi$
$229$	12.6079	+	9.16021i	0.833156	+	0.605324i	−0.0872941	+	0.996183i	$0.527822\pi$
$230$	−2.83023	+	4.90210i	−0.186620	+	0.323235i
$231$	3.69648	−	19.1730i	0.243211	−	1.26149i
$232$	10.3506	+	17.9278i	0.679552	+	1.17702i
$233$	−12.0602	−	8.76225i	−0.790090	−	0.574034i	0.117900	−	0.993025i	$-0.462384\pi$
$233$	−12.0602	−	8.76225i	−0.790090	−	0.574034i	−0.907990	+	0.418991i	$0.862384\pi$
$234$	−9.51880	+	9.13023i	−0.622263	+	0.596862i
$235$	−8.91085	−	27.4248i	−0.581279	−	1.78899i
$236$	−0.232105	+	0.521316i	−0.0151087	+	0.0339348i
$237$	−15.5462	−	19.9367i	−1.00984	−	1.29503i
$238$	5.78442	−	27.2136i	0.374948	−	1.76399i
$239$	1.07930	−	3.32175i	0.0698143	−	0.214866i	−0.910062	−	0.414472i	$-0.863966\pi$
$239$	1.07930	−	3.32175i	0.0698143	−	0.214866i	0.979876	+	0.199606i	$0.0639662\pi$
$240$	14.0768	+	0.997583i	0.908650	+	0.0643937i
$241$	−2.06940	−	1.19477i	−0.133302	−	0.0769619i	0.431866	−	0.901938i	$-0.357855\pi$
$241$	−2.06940	−	1.19477i	−0.133302	−	0.0769619i	−0.565168	+	0.824976i	$0.691189\pi$
$242$	−6.35542	−	11.8121i	−0.408542	−	0.759308i
$243$	15.3641	−	2.63503i	0.985610	−	0.169038i
$244$	7.13724	+	0.750155i	0.456915	+	0.0480237i
$245$	2.84580	+	13.3884i	0.181811	+	0.855355i
$246$	21.1182	+	3.74409i	1.34645	+	0.238714i
$247$	−8.90976	+	5.99019i	−0.566914	+	0.381147i
$248$	−8.84631	+	6.42722i	−0.561741	+	0.408129i
$249$	5.03445	+	13.8724i	0.319045	+	0.879128i
$250$	−0.735197	−	3.45883i	−0.0464979	−	0.218756i
$251$	−5.40701	−	12.1443i	−0.341287	−	0.766544i	−0.999901	−	0.0140626i	$-0.995524\pi$
$251$	−5.40701	−	12.1443i	−0.341287	−	0.766544i	0.658614	−	0.752481i	$-0.271143\pi$
$252$	−4.34304	+	2.91760i	−0.273586	+	0.183792i
$253$	−3.75455	−	3.48392i	−0.236046	−	0.219032i
$254$	−10.5765	−	6.10637i	−0.663632	−	0.383148i
$255$	15.2904	+	31.4245i	0.957521	+	1.96788i
$256$	−7.65109	−	8.49739i	−0.478193	−	0.531087i
$257$	−4.34111	−	3.90875i	−0.270791	−	0.243821i	0.522536	−	0.852617i	$-0.324986\pi$
$257$	−4.34111	−	3.90875i	−0.270791	−	0.243821i	−0.793327	+	0.608796i	$0.791653\pi$
$258$	−8.03836	−	10.3085i	−0.500446	−	0.641779i
$259$	5.94629	+	8.18437i	0.369485	+	0.508552i
$260$	1.52470	+	5.34765i	0.0945576	+	0.331647i
$261$	−19.4913	+	5.54958i	−1.20648	+	0.343510i
$262$	0.0566614	−	0.539098i	0.00350056	−	0.0333056i
$263$	2.89114	+	5.00760i	0.178275	+	0.308782i	0.941290	−	0.337599i	$-0.109615\pi$
$263$	2.89114	+	5.00760i	0.178275	+	0.308782i	−0.763014	+	0.646381i	$0.776282\pi$
$264$	−5.12115	+	16.8425i	−0.315185	+	1.03658i
$265$	13.0625			0.802425
$266$	11.2748	−	5.01989i	0.691305	−	0.307789i
$267$	6.86552	+	27.6463i	0.420163	+	1.69193i
$268$	1.48298	+	4.56414i	0.0905873	+	0.278799i
$269$	−22.7454	+	2.39063i	−1.38681	+	0.145759i	−0.768336	−	0.640047i	$-0.778915\pi$
$269$	−22.7454	+	2.39063i	−1.38681	+	0.145759i	−0.618473	+	0.785806i	$0.712248\pi$
$270$	−5.93625	+	18.0968i	−0.361269	+	1.10134i
$271$	−4.60803	−	4.14909i	−0.279918	−	0.252039i	0.517198	−	0.855866i	$-0.326975\pi$
$271$	−4.60803	−	4.14909i	−0.279918	−	0.252039i	−0.797116	+	0.603827i	$0.793642\pi$
$272$	−5.62240	+	17.3040i	−0.340908	+	1.04921i
$273$	17.1426	+	12.5189i	1.03752	+	0.757679i
$274$		−	3.24814i		−	0.196227i
$275$	−13.3819	−	0.200614i	−0.806961	−	0.0120975i
$276$	0.0466135	+	1.37164i	0.00280580	+	0.0825632i
$277$	9.32482	+	20.9439i	0.560274	+	1.25840i	0.942463	+	0.334312i	$0.108504\pi$
$277$	9.32482	+	20.9439i	0.560274	+	1.25840i	−0.382189	+	0.924084i	$0.624830\pi$
$278$	−17.3885	−	5.64986i	−1.04289	−	0.338856i
$279$	−3.99147	−	9.93273i	−0.238963	−	0.594657i
$280$	−3.27276	−	31.1382i	−0.195585	−	1.86086i
$281$	−8.96600	+	6.51418i	−0.534866	+	0.388603i	−0.822175	−	0.569235i	$-0.807240\pi$
$281$	−8.96600	+	6.51418i	−0.534866	+	0.388603i	0.287309	+	0.957838i	$0.407240\pi$
$282$	15.5089	+	13.0383i	0.923544	+	0.776419i
$283$	1.24003	+	5.83389i	0.0737122	+	0.346789i	0.999512	−	0.0312245i	$-0.00994069\pi$
$283$	1.24003	+	5.83389i	0.0737122	+	0.346789i	−0.925800	+	0.378013i	$0.876607\pi$
$284$	4.08106	+	0.428937i	0.242166	+	0.0254527i
$285$	−7.29093	+	13.6813i	−0.431878	+	0.810413i
$286$	14.5611	−	0.777068i	0.861014	−	0.0459490i
$287$		−	34.5170i		−	2.03747i
$288$	7.48680	−	3.96284i	0.441164	−	0.233513i
$289$	−27.4436	+	5.83333i	−1.61433	+	0.343137i
$290$	5.14799	−	24.2194i	0.302300	−	1.42221i
$291$	−0.392978	−	2.81530i	−0.0230368	−	0.165036i
$292$	−3.74714	+	0.393840i	−0.219285	+	0.0230477i
$293$	−4.11621	−	0.874927i	−0.240471	−	0.0511138i	0.0860993	−	0.996287i	$-0.472560\pi$
$293$	−4.11621	−	0.874927i	−0.240471	−	0.0511138i	−0.326571	+	0.945173i	$0.605893\pi$
$294$	−6.67434	−	6.92444i	−0.389255	−	0.403841i
$295$	3.05407	−	1.35976i	0.177815	−	0.0791682i
$296$	−4.56026	−	7.89860i	−0.265060	−	0.459097i
$297$	−14.7691	−	8.88110i	−0.856990	−	0.515334i
$298$	5.42021			0.313984
$299$	5.16583	−	2.07808i	0.298748	−	0.120178i
$300$	2.48871	+	2.58197i	0.143686	+	0.149070i
$301$	−14.0771	+	15.6342i	−0.811389	+	0.901139i
$302$	0.209642	−	0.470863i	0.0120635	−	0.0270951i
$303$	−4.00730	−	1.62342i	−0.230214	−	0.0932631i
$304$	−7.67618	+	2.49414i	−0.440259	+	0.143049i
$305$	−28.1323	−	31.2441i	−1.61085	−	1.78903i
$306$	−20.7996	−	13.0512i	−1.18903	−	0.746090i
$307$		−	26.8550i		−	1.53269i	−0.642427	−	0.766347i	$-0.722072\pi$
$307$		−	26.8550i		−	1.53269i	0.642427	−	0.766347i	$-0.277928\pi$
$308$	5.74286	+	0.690781i	0.327230	+	0.0393609i
$309$	−13.6060	+	0.462382i	−0.774017	+	0.0263040i
$310$	13.0071	+	1.36710i	0.738755	+	0.0776463i
$311$	−14.0478	−	4.56440i	−0.796576	−	0.258823i	−0.117674	−	0.993052i	$-0.537544\pi$
$311$	−14.0478	−	4.56440i	−0.796576	−	0.258823i	−0.678902	+	0.734229i	$0.737544\pi$
$312$	−14.1905	−	12.8401i	−0.803380	−	0.726929i
$313$	−0.512923	+	0.372660i	−0.0289921	+	0.0210640i	−0.602187	−	0.798355i	$-0.705704\pi$
$313$	−0.512923	+	0.372660i	−0.0289921	+	0.0210640i	0.573195	+	0.819419i	$0.305704\pi$
$314$	13.1612	+	5.85975i	0.742731	+	0.330685i
$315$	30.3451	+	4.32266i	1.70975	+	0.243554i
$316$	5.56557	−	5.01126i	0.313088	−	0.281906i
$317$	−8.06721	+	11.1036i	−0.453100	+	0.623638i	−0.973060	−	0.230552i	$-0.925947\pi$
$317$	−8.06721	+	11.1036i	−0.453100	+	0.623638i	0.519960	+	0.854190i	$0.325947\pi$
$318$	−7.78815	+	4.85645i	−0.436738	+	0.272336i
$319$	20.3290	+	9.41866i	1.13820	+	0.527344i
$320$			26.6448i			1.48949i
$321$	1.59690	−	22.5336i	0.0891303	−	1.25771i
$322$	−6.26101	+	1.33082i	−0.348912	+	0.0741636i
$323$	−14.8536	−	13.3743i	−0.826478	−	0.744164i
$324$	1.10036	+	4.48478i	0.0611313	+	0.249155i
$325$	6.39771	−	13.0672i	0.354881	−	0.724839i
$326$	−2.31817	−	7.13459i	−0.128391	−	0.395148i
$327$	−0.391753	−	0.112730i	−0.0216640	−	0.00623400i
$328$	−3.25281	+	30.9484i	−0.179606	+	1.70884i
$329$	16.3040	−	28.2394i	0.898870	−	1.55689i
$330$	18.0317	−	10.8720i	0.992611	−	0.598486i
$331$	−9.43824	+	16.3475i	−0.518772	+	0.898540i	0.480990	+	0.876726i	$0.340277\pi$
$331$	−9.43824	+	16.3475i	−0.518772	+	0.898540i	−0.999762	+	0.0218138i	$0.993056\pi$
$332$	−3.99375	+	1.77813i	−0.219185	+	0.0975876i
$333$	8.58745	−	2.44502i	0.470589	−	0.133986i
$334$	13.7065	+	2.91341i	0.749986	+	0.159415i
$335$	11.4352	−	25.6839i	0.624771	−	1.40326i
$336$	9.81296	+	12.5843i	0.535341	+	0.686528i
$337$	−21.2113	+	6.89198i	−1.15546	+	0.375430i	−0.823196	−	0.567758i	$-0.807811\pi$
$337$	−21.2113	+	6.89198i	−1.15546	+	0.375430i	−0.332260	+	0.943188i	$0.607811\pi$
$338$	−5.98257	+	14.6798i	−0.325409	+	0.798476i
$339$	0.651465	+	1.33888i	0.0353827	+	0.0727179i
$340$	−8.96548	+	5.17622i	−0.486221	+	0.280720i
$341$	−3.82537	+	11.1992i	−0.207155	+	0.606471i
$342$	−0.739507	−	10.8678i	−0.0399880	−	0.587661i
$343$	4.88770	−	6.72734i	0.263911	−	0.363242i
$344$	14.0951	−	12.6912i	0.759955	−	0.684266i
$345$	5.17393	−	6.15435i	0.278555	−	0.331339i
$346$	−10.7128	+	7.78331i	−0.575924	+	0.418433i
$347$	1.81248	+	17.2446i	0.0972991	+	0.925740i	0.928891	+	0.370353i	$0.120763\pi$
$347$	1.81248	+	17.2446i	0.0972991	+	0.925740i	−0.831592	+	0.555387i	$0.812570\pi$
$348$	−2.04801	−	5.64330i	−0.109785	−	0.302512i
$349$	−0.749856	−	3.52779i	−0.0401389	−	0.188838i	0.953510	−	0.301360i	$-0.0974406\pi$
$349$	−0.749856	−	3.52779i	−0.0401389	−	0.188838i	−0.993649	+	0.112522i	$0.964107\pi$
$350$	−9.83085	+	13.5310i	−0.525481	+	0.723263i
$351$	15.5771	−	10.4094i	0.831443	−	0.555610i
$352$	−9.13008	−	2.08417i	−0.486635	−	0.111087i
$353$	12.2269	−	7.05921i	0.650773	−	0.375724i	−0.137979	−	0.990435i	$-0.544061\pi$
$353$	12.2269	−	7.05921i	0.650773	−	0.375724i	0.788752	+	0.614711i	$0.210727\pi$
$354$	−1.31536	+	1.94617i	−0.0699107	+	0.103438i
$355$	−16.0860	−	17.8653i	−0.853754	−	0.948190i
$356$	−8.02546	+	2.60763i	−0.425349	+	0.138204i
$357$	−14.8381	+	36.6269i	−0.785318	+	1.93850i
$358$	−6.55295	+	0.688743i	−0.346334	+	0.0364012i
$359$	−6.56844	−	20.2156i	−0.346669	−	1.06694i	−0.960684	−	0.277643i	$-0.910447\pi$
$359$	−6.56844	−	20.2156i	−0.346669	−	1.06694i	0.614015	−	0.789294i	$-0.289553\pi$
$360$	−26.8005	−	6.73542i	−1.41251	−	0.354988i
$361$	−1.05923	+	10.0779i	−0.0557487	+	0.530414i
$362$	5.74174	+	9.94498i	0.301779	+	0.522697i
$363$	5.95982	+	18.0964i	0.312809	+	0.949816i
$364$	−3.34025	+	5.32763i	−0.175076	+	0.279243i
$365$	17.8575	+	12.9742i	0.934704	+	0.679102i
$366$	28.3891	+	8.16921i	1.48392	+	0.427011i
$367$	−7.06399	+	7.84535i	−0.368737	+	0.409524i	−0.898747	−	0.438467i	$-0.855521\pi$
$367$	−7.06399	+	7.84535i	−0.368737	+	0.409524i	0.530010	+	0.847991i	$0.322188\pi$
$368$	4.16306	−	0.437555i	0.217014	−	0.0228091i
$369$	−28.6078	−	10.4731i	−1.48926	−	0.545206i
$370$	−2.26809	+	10.6705i	−0.117912	+	0.554735i
$371$	9.88386	+	10.9771i	0.513144	+	0.569905i
$372$	2.85145	−	1.38744i	0.147841	−	0.0719355i
$373$	−10.3962	−	6.00223i	−0.538293	−	0.310784i	0.206094	−	0.978532i	$-0.433925\pi$
$373$	−10.3962	−	6.00223i	−0.538293	−	0.310784i	−0.744387	+	0.667749i	$0.767258\pi$
$374$	8.00088	+	25.9410i	0.413715	+	1.34138i
$375$	0.170594	+	5.01987i	0.00880941	+	0.259225i
$376$	−17.2797	+	23.7834i	−0.891131	+	1.22654i
$377$	−18.6819	+	15.6280i	−0.962165	+	0.804884i
$378$	−19.6995	+	8.70456i	−1.01323	+	0.447715i
$379$	−30.8795	−	13.7484i	−1.58617	−	0.706210i	−0.591217	−	0.806512i	$-0.701352\pi$
$379$	−30.8795	−	13.7484i	−1.58617	−	0.706210i	−0.994957	+	0.100302i	$0.968019\pi$
$380$	−4.19539	−	1.86791i	−0.215219	−	0.0958216i
$381$	13.2783	+	11.1630i	0.680270	+	0.571900i
$382$	13.2969	+	4.32043i	0.680329	+	0.221052i
$383$	5.18677	+	11.6497i	0.265032	+	0.595271i	0.996216	−	0.0869088i	$-0.0276989\pi$
$383$	5.18677	+	11.6497i	0.265032	+	0.595271i	−0.731185	+	0.682180i	$0.761032\pi$
$384$	−4.73054	−	7.58624i	−0.241404	−	0.387134i
$385$	−22.2944	−	25.5195i	−1.13623	−	1.30060i
$386$	5.27621	+	3.04622i	0.268552	+	0.155049i
$387$	8.68643	+	16.4108i	0.441556	+	0.834209i
$388$	0.823666	−	0.175076i	0.0418153	−	0.00888812i
$389$	3.52382	−	1.14496i	0.178665	−	0.0580517i	−0.218318	−	0.975878i	$-0.570057\pi$
$389$	3.52382	−	1.14496i	0.178665	−	0.0580517i	0.396983	+	0.917826i	$0.370057\pi$
$390$	2.33703	+	22.7703i	0.118340	+	1.15302i
$391$	6.09308	+	8.38641i	0.308140	+	0.424119i
$392$	9.33719	−	10.3700i	0.471599	−	0.523764i
$393$	−0.212924	+	0.739939i	−0.0107406	+	0.0373250i
$394$	−11.1011	+	4.94252i	−0.559265	+	0.249001i
$395$	−43.8747			−2.20757
$396$	2.31501	−	4.55011i	0.116334	−	0.228652i
$397$	−0.157174	+	0.272234i	−0.00788836	+	0.0136630i	−0.869943	−	0.493153i	$-0.835844\pi$
$397$	−0.157174	+	0.272234i	−0.00788836	+	0.0136630i	0.862054	+	0.506816i	$0.169178\pi$
$398$	0.608483	+	0.442089i	0.0305005	+	0.0221599i
$399$	−17.0139	+	4.22513i	−0.851760	+	0.211521i
$400$	7.31883	−	8.12838i	0.365941	−	0.406419i
$401$	11.9292	−	26.7934i	0.595716	−	1.33800i	−0.324239	−	0.945975i	$-0.605108\pi$
$401$	11.9292	−	26.7934i	0.595716	−	1.33800i	0.919955	−	0.392025i	$-0.128225\pi$
$402$	2.73097	+	19.5647i	0.136208	+	0.975798i
$403$	−9.24117	−	8.95105i	−0.460335	−	0.445883i
$404$	0.395790	−	1.21812i	0.0196913	−	0.0606036i
$405$	12.7899	−	23.8385i	0.635534	−	1.18455i
$406$	24.2481	−	13.9997i	1.20341	−	0.694791i
$407$	−8.95650	−	4.14966i	−0.443957	−	0.205691i
$408$	16.7557	−	31.4419i	0.829533	−	1.55661i
$409$	15.4097	+	34.6108i	0.761961	+	1.71139i	0.700901	+	0.713259i	$0.252781\pi$
$409$	15.4097	+	34.6108i	0.761961	+	1.71139i	0.0610601	+	0.998134i	$0.480552\pi$
$410$	27.6605	−	24.9056i	1.36605	−	1.23000i
$411$	−0.805418	+	4.54289i	−0.0397284	+	0.224084i
$412$	−0.421548	−	4.01076i	−0.0207682	−	0.197596i
$413$	3.45356	+	1.53762i	0.169939	+	0.0756615i
$414$	−0.796715	+	5.59294i	−0.0391564	+	0.274878i
$415$	24.3576	+	7.91426i	1.19567	+	0.388496i
$416$	6.27999	−	8.01310i	0.307902	−	0.392875i
$417$	22.9188	+	12.2137i	1.12234	+	0.598107i
$418$	−7.22367	+	9.63542i	−0.353321	+	0.471284i
$419$	−21.4165	+	12.3648i	−1.04626	+	0.604060i	−0.921601	−	0.388139i	$-0.873118\pi$
$419$	−21.4165	+	12.3648i	−1.04626	+	0.604060i	−0.124662	+	0.992199i	$0.539785\pi$
$420$	−0.641861	+	9.05721i	−0.0313196	+	0.441946i
$421$	−2.13334	+	6.56575i	−0.103973	+	0.319995i	−0.989488	−	0.144615i	$-0.953806\pi$
$421$	−2.13334	+	6.56575i	−0.103973	+	0.319995i	0.885515	+	0.464610i	$0.153806\pi$
$422$	−3.27337	+	15.4000i	−0.159345	+	0.749660i
$423$	−18.4580	−	22.0812i	−0.897458	−	1.07362i
$424$	−7.82755	−	10.7737i	−0.380140	−	0.523217i
$425$	26.4945	+	5.63158i	1.28517	+	0.273172i
$426$	16.2328	+	4.67113i	0.786483	+	0.226317i
$427$	4.96955	−	47.2821i	0.240493	−	2.28814i
$428$	6.69193			0.323467
$429$	−20.5580	−	2.52379i	−0.992549	−	0.121850i
$430$	−22.6859			−1.09401
$431$	1.91445	−	18.2148i	0.0922159	−	0.877375i	−0.846432	−	0.532497i	$-0.821254\pi$
$431$	1.91445	−	18.2148i	0.0922159	−	0.877375i	0.938648	−	0.344878i	$-0.112080\pi$
$432$	13.4073	−	4.31472i	0.645060	−	0.207592i
$433$	19.3755	+	4.11838i	0.931125	+	0.197917i	0.648413	−	0.761288i	$-0.275433\pi$
$433$	19.3755	+	4.11838i	0.931125	+	0.197917i	0.282711	+	0.959205i	$0.408766\pi$
$434$	8.69309	+	11.9650i	0.417281	+	0.574339i
$435$	−13.2056	+	32.5971i	−0.633159	+	1.56291i
$436$	0.0251072	−	0.118120i	0.00120242	−	0.00565693i
$437$	−1.42102	+	4.37345i	−0.0679766	+	0.209210i
$438$	−15.4706	−	1.09636i	−0.739216	−	0.0523863i
$439$	6.01207	−	3.47107i	0.286940	−	0.165665i	−0.349621	−	0.936891i	$-0.613690\pi$
$439$	6.01207	−	3.47107i	0.286940	−	0.165665i	0.636561	+	0.771226i	$0.280356\pi$
$440$	17.5846	+	24.9822i	0.838312	+	1.19098i
$441$	7.61781	+	11.3396i	0.362753	+	0.539981i
$442$	−29.2183	−	4.15128i	−1.38977	−	0.197456i
$443$	8.47322	+	2.75312i	0.402575	+	0.130805i	0.503304	−	0.864109i	$-0.332118\pi$
$443$	8.47322	+	2.75312i	0.402575	+	0.130805i	−0.100729	+	0.994914i	$0.532118\pi$
$444$	0.902309	+	2.48631i	0.0428217	+	0.117995i
$445$	45.1618	+	20.1073i	2.14088	+	0.953180i
$446$	2.16815	+	20.6285i	0.102665	+	0.976790i
$447$	−7.58077	−	1.34401i	−0.358558	−	0.0635696i
$448$	−22.3910	+	20.1610i	−1.05788	+	0.952515i
$449$	7.94014	+	17.8339i	0.374718	+	0.841631i	0.998210	+	0.0598016i	$0.0190468\pi$
$449$	7.94014	+	17.8339i	0.374718	+	0.841631i	−0.623492	+	0.781830i	$0.714287\pi$
$450$	8.23169	+	12.2534i	0.388045	+	0.577630i
$451$	16.4008	+	29.4168i	0.772284	+	1.38518i
$452$	−0.381985	+	0.220539i	−0.0179670	+	0.0103733i
$453$	−0.409965	+	0.606572i	−0.0192618	+	0.0284993i
$454$	−0.828211	+	2.54897i	−0.0388699	+	0.119629i
$455$	35.4266	−	10.1006i	1.66082	−	0.473526i
$456$	15.6531	−	2.18496i	0.733023	−	0.102320i
$457$	0.312330	−	0.701505i	0.0146102	−	0.0328150i	−0.906093	−	0.423079i	$-0.860949\pi$
$457$	0.312330	−	0.701505i	0.0146102	−	0.0328150i	0.920703	+	0.390264i	$0.127616\pi$
$458$	−12.7157	+	14.1222i	−0.594165	+	0.659887i
$459$	25.8544	+	23.4112i	1.20678	+	1.09274i
$460$	1.92690	+	1.39997i	0.0898421	+	0.0652741i
$461$	−0.0456422	+	0.0790546i	−0.00212577	+	0.00368194i	−0.867086	−	0.498158i	$-0.834010\pi$
$461$	−0.0456422	+	0.0790546i	−0.00212577	+	0.00368194i	0.864961	+	0.501840i	$0.167343\pi$
$462$	22.7802	+	6.92657i	1.05983	+	0.322253i
$463$	41.3161			1.92012			0.960061	−	0.279792i	$-0.0902654\pi$
$463$	41.3161			1.92012			0.960061	+	0.279792i	$0.0902654\pi$
$464$	−16.7277	+	7.44764i	−0.776563	+	0.345748i
$465$	−17.8529	−	5.13734i	−0.827910	−	0.238238i
$466$	12.1633	−	13.5087i	0.563453	−	0.625778i
$467$	16.6691	+	22.9431i	0.771356	+	1.06168i	0.996184	+	0.0872819i	$0.0278181\pi$
$467$	16.6691	+	22.9431i	0.771356	+	1.06168i	−0.224828	+	0.974399i	$0.572182\pi$
$468$	3.40206	+	4.38491i	0.157260	+	0.202692i
$469$	30.2360	−	9.82429i	1.39617	−	0.453643i
$470$	34.3941	−	7.31068i	1.58648	−	0.337217i
$471$	−16.9545	−	11.4590i	−0.781220	−	0.528004i
$472$	−2.95161	−	1.70411i	−0.135859	−	0.0784382i
$473$	4.56844	−	20.0128i	0.210057	−	0.920192i
$474$	26.1590	−	16.3119i	1.20152	−	0.749232i
$475$	4.88724	+	10.9769i	0.224242	+	0.503656i
$476$	−11.1336	−	3.61754i	−0.510310	−	0.165810i
$477$	12.0968	−	4.86112i	0.553876	−	0.222575i
$478$	3.89075	+	1.73227i	0.177959	+	0.0792324i
$479$	2.89614	+	1.28945i	0.132328	+	0.0589163i	0.471833	−	0.881688i	$-0.343593\pi$
$479$	2.89614	+	1.28945i	0.132328	+	0.0589163i	−0.339504	+	0.940604i	$0.610259\pi$
$480$	2.56631	−	14.4750i	0.117135	−	0.660692i
$481$	8.23082	−	6.88536i	0.375293	−	0.313946i
$482$	1.71268	−	2.35730i	0.0780103	−	0.107372i
$483$	9.08672	−	0.308800i	0.413460	−	0.0140509i
$484$	−5.22253	+	2.14002i	−0.237388	+	0.0972738i
$485$	−4.27224	−	2.46658i	−0.193992	−	0.112001i
$486$	1.23721	+	18.9681i	0.0561208	+	0.860410i
$487$	−19.2913	−	21.4252i	−0.874174	−	0.970868i	0.125601	−	0.992081i	$-0.459914\pi$
$487$	−19.2913	−	21.4252i	−0.874174	−	0.970868i	−0.999775	+	0.0212127i	$0.993247\pi$
$488$	−8.91154	+	41.9255i	−0.403407	+	1.89788i
$489$	1.47311	+	10.5534i	0.0666161	+	0.477239i
$490$	−16.5990	+	1.74463i	−0.749867	+	0.0788142i
$491$	−14.4685	+	16.0689i	−0.652952	+	0.725177i	−0.975162	−	0.221491i	$-0.928908\pi$
$491$	−14.4685	+	16.0689i	−0.652952	+	0.725177i	0.322210	+	0.946668i	$0.395574\pi$
$492$	2.49563	−	8.67265i	0.112512	−	0.390993i
$493$	−36.6846	−	26.6529i	−1.65219	−	1.20039i
$494$	−6.12871	−	11.5685i	−0.275744	−	0.520490i
$495$	−27.9152	+	10.7346i	−1.25470	+	0.482484i
$496$	−4.83597	−	8.37614i	−0.217141	−	0.376100i
$497$	2.84158	−	27.0358i	0.127462	−	1.21272i
$498$	−17.4649	+	4.33713i	−0.782621	+	0.194351i
$499$	−0.815407	−	2.50957i	−0.0365026	−	0.112344i	0.931145	−	0.364649i	$-0.118811\pi$
$499$	−0.815407	−	2.50957i	−0.0365026	−	0.112344i	−0.967648	+	0.252306i	$0.918811\pi$
$500$	−1.47975	+	0.155528i	−0.0661765	+	0.00695543i
$501$	−18.4477	−	7.47344i	−0.824182	−	0.333889i
$502$	15.4167	−	5.00920i	0.688083	−	0.223572i
$503$	−21.9621	−	24.3914i	−0.979242	−	1.08756i	−0.996147	−	0.0877011i	$-0.972048\pi$
$503$	−21.9621	−	24.3914i	−0.979242	−	1.08756i	0.0169050	−	0.999857i	$-0.494619\pi$
$504$	−14.6186	−	27.6183i	−0.651166	−	1.23022i
$505$	−6.49817	+	3.75172i	−0.289165	+	0.166949i
$506$	4.70354	−	4.10911i	0.209098	−	0.182672i
$507$	12.0074	−	19.0479i	0.533265	−	0.845948i
$508$	−3.02052	+	4.15739i	−0.134014	+	0.184454i
$509$	1.95107	+	9.17907i	0.0864797	+	0.406855i	1.00000		6.18774e-5i	$1.96962e-5\pi$
$509$	1.95107	+	9.17907i	0.0864797	+	0.406855i	−0.913520	+	0.406793i	$0.866647\pi$
$510$	−40.0578	+	14.5374i	−1.77379	+	0.643727i
$511$	2.60907	+	24.8237i	0.115419	+	1.09813i
$512$	19.6319	−	14.2634i	0.867614	−	0.630359i
$513$	−1.66052	+	15.3832i	−0.0733138	+	0.679183i
$514$	5.29350	−	4.76629i	0.233486	−	0.210232i
$515$	−13.8870	+	19.1138i	−0.611935	+	0.842256i
$516$	−4.66735	+	2.91041i	−0.205469	+	0.128124i
$517$	−0.476931	+	31.8137i	−0.0209754	+	1.39916i
$518$	−10.6832	+	6.16794i	−0.469392	+	0.271004i
$519$	16.9131	−	8.22946i	0.742401	−	0.361233i
$520$	−32.7159	+	5.71786i	−1.43469	+	0.250745i
$521$	38.4641	−	12.4977i	1.68514	−	0.547536i	0.699244	−	0.714883i	$-0.253520\pi$
$521$	38.4641	−	12.4977i	1.68514	−	0.547536i	0.985898	+	0.167347i	$0.0535199\pi$
$522$	−4.24565	−	24.3447i	−0.185827	−	1.06554i
$523$	11.2099	−	25.1777i	0.490173	−	1.10095i	−0.483985	−	0.875076i	$-0.660811\pi$
$523$	11.2099	−	25.1777i	0.490173	−	1.10095i	0.974158	−	0.225869i	$-0.0725223\pi$
$524$	−0.223104	−	0.0474222i	−0.00974635	−	0.00207165i
$525$	17.1047	−	16.4870i	0.746512	−	0.719550i
$526$	−6.44128	+	2.86784i	−0.280853	+	0.125044i
$527$	11.9758	−	20.7427i	0.521673	−	0.903565i
$528$	−14.3424	−	6.06218i	−0.624175	−	0.263822i
$529$	−10.3075	+	17.8532i	−0.448154	+	0.776225i
$530$	−1.66496	+	15.8411i	−0.0723213	+	0.688091i
$531$	2.32226	−	2.39578i	0.100778	−	0.103968i
$532$	−1.60477	−	4.93898i	−0.0695756	−	0.214132i
$533$	−36.5285	+	2.49900i	−1.58222	+	0.108244i
$534$	−34.4020	+	4.80206i	−1.48872	+	0.207805i
$535$	−29.1342	−	26.2325i	−1.25958	−	1.13413i
$536$	−28.0359	+	5.95922i	−1.21097	+	0.257399i
$537$	9.33583	+	0.661606i	0.402871	+	0.0285504i
$538$		−	27.8882i		−	1.20235i
$539$	1.80362	−	14.9945i	0.0776873	−	0.645859i
$540$	7.31189	+	3.28010i	0.314654	+	0.141153i
$541$	1.19352	−	1.64274i	0.0513134	−	0.0706268i	−0.782589	−	0.622538i	$-0.786101\pi$
$541$	1.19352	−	1.64274i	0.0513134	−	0.0706268i	0.833903	+	0.551912i	$0.186101\pi$
$542$	5.61899	−	5.05936i	0.241356	−	0.217318i
$543$	−5.56448	−	15.3329i	−0.238795	−	0.657999i
$544$	17.3149	+	7.70907i	0.742369	+	0.330524i
$545$	−0.572341	+	0.415830i	−0.0245164	+	0.0178122i
$546$	−17.3668	+	19.1933i	−0.743231	+	0.821397i
$547$	26.9496	+	8.75644i	1.15228	+	0.374399i	0.822002	−	0.569485i	$-0.192857\pi$
$547$	26.9496	+	8.75644i	1.15228	+	0.374399i	0.330278	+	0.943884i	$0.392857\pi$
$548$	−1.35925	−	0.142863i	−0.0580642	−	0.00610279i
$549$	−37.6797	−	18.4650i	−1.60813	−	0.788068i
$550$	1.94896	−	16.2028i	0.0831039	−	0.690891i
$551$		−	20.1152i		−	0.856938i
$552$	−8.17639	−	0.579440i	−0.348010	−	0.0246626i
$553$	−33.1981	−	36.8702i	−1.41173	−	1.56788i
$554$	−26.5874	+	8.63877i	−1.12959	+	0.367026i
$555$	5.81808	−	14.3615i	0.246964	−	0.609614i
$556$	−3.12910	+	7.02807i	−0.132703	+	0.298056i
$557$	−4.65051	+	5.16492i	−0.197048	+	0.218845i	−0.833569	−	0.552415i	$-0.813706\pi$
$557$	−4.65051	+	5.16492i	−0.197048	+	0.218845i	0.636521	+	0.771260i	$0.280373\pi$
$558$	12.5543	−	3.57446i	0.531465	−	0.151319i
$559$	17.5645	+	13.7655i	0.742897	+	0.582220i
$560$	27.6942			1.17029
$561$	−4.75772	−	38.2653i	−0.200871	−	1.61556i
$562$	−6.75699	−	11.7035i	−0.285026	−	0.493680i
$563$	6.53938	−	2.91152i	0.275602	−	0.122706i	−0.264282	−	0.964446i	$-0.585135\pi$
$563$	6.53938	−	2.91152i	0.275602	−	0.122706i	0.539884	+	0.841740i	$0.318468\pi$
$564$	6.13827	−	5.91656i	0.258468	−	0.249132i
$565$	2.52754	+	0.537244i	0.106334	+	0.0226020i
$566$	−7.23287	+	0.760205i	−0.304020	+	0.0319538i
$567$	29.7103	−	7.28958i	1.24772	−	0.306134i
$568$	−5.09560	+	23.9729i	−0.213807	+	1.00588i
$569$	−21.5160	+	4.57337i	−0.901999	+	0.191726i	−0.635492	−	0.772107i	$-0.719203\pi$
$569$	−21.5160	+	4.57337i	−0.901999	+	0.191726i	−0.266507	+	0.963833i	$0.585869\pi$
$570$	−15.6622	−	10.5856i	−0.656017	−	0.443383i
$571$			14.9477i			0.625542i	0.949829	+	0.312771i	$0.101257\pi$
$571$			14.9477i			0.625542i	−0.949829	+	0.312771i	$0.898743\pi$
$572$	0.315259	−	6.12755i	0.0131816	−	0.256206i
$573$	−17.5259	−	9.33975i	−0.732156	−	0.390174i
$574$	41.8590	+	4.39956i	1.74716	+	0.183634i
$575$	−1.29565	−	6.09557i	−0.0540324	−	0.254203i
$576$	9.91563	+	24.6749i	0.413151	+	1.02812i
$577$	−34.6191	+	25.1523i	−1.44121	+	1.04710i	−0.453425	+	0.891294i	$0.649798\pi$
$577$	−34.6191	+	25.1523i	−1.44121	+	1.04710i	−0.987787	+	0.155808i	$0.950202\pi$
$578$	−3.57614	−	34.0247i	−0.148748	−	1.41524i
$579$	−6.62403	−	5.56880i	−0.275285	−	0.231431i
$580$	−9.90867	−	3.21952i	−0.411435	−	0.133683i
$581$	11.7796	+	26.4574i	0.488699	+	1.09764i
$582$	3.46423	−	0.117727i	0.143597	−	0.00487996i
$583$	−13.6392	−	4.65882i	−0.564880	−	0.192949i
$584$		−	22.5031i		−	0.931187i
$585$	2.37761	−	32.4264i	0.0983022	−	1.34067i
$586$	1.58569	−	4.88024i	0.0655041	−	0.201601i
$587$	10.0148	+	9.01739i	0.413356	+	0.372188i	0.849410	−	0.527733i	$-0.176958\pi$
$587$	10.0148	+	9.01739i	0.413356	+	0.372188i	−0.436054	+	0.899920i	$0.643624\pi$
$588$	−3.19123	+	2.48845i	−0.131604	+	0.102622i
$589$	10.5669	−	1.11063i	0.435402	−	0.0457626i
$590$	1.25972	+	3.87701i	0.0518618	+	0.159614i
$591$	16.7517	−	4.16002i	0.689073	−	0.171120i
$592$	7.36985	−	3.28127i	0.302899	−	0.134859i
$593$	−22.6246			−0.929082			−0.464541	−	0.885552i	$-0.653781\pi$
$593$	−22.6246			−0.929082			−0.464541	+	0.885552i	$0.653781\pi$
$594$	12.6527	−	16.7786i	0.519146	−	0.688435i
$595$	34.2909	+	59.3936i	1.40579	+	2.43490i
$596$	0.238397	−	2.26819i	0.00976511	−	0.0929088i
$597$	−0.741410	−	0.769192i	−0.0303439	−	0.0314809i
$598$	1.86166	+	6.52952i	0.0761291	+	0.267012i
$599$	−13.0917	−	18.0192i	−0.534912	−	0.736243i	0.452957	−	0.891532i	$-0.350369\pi$
$599$	−13.0917	−	18.0192i	−0.534912	−	0.736243i	−0.987869	+	0.155289i	$0.950369\pi$
$600$	−16.8901	+	13.1705i	−0.689534	+	0.537685i
$601$	6.98275	+	6.28730i	0.284832	+	0.256464i	0.799145	−	0.601139i	$-0.205286\pi$
$601$	6.98275	+	6.28730i	0.284832	+	0.256464i	−0.514312	+	0.857603i	$0.671953\pi$
$602$	−17.1654	−	19.0642i	−0.699611	−	0.776997i
$603$	1.03176	−	28.0406i	0.0420164	−	1.14190i
$604$	−0.187822	−	0.108439i	−0.00764235	−	0.00441231i
$605$	31.1259	+	11.1556i	1.26545	+	0.453538i
$606$	2.47951	−	4.65277i	0.100723	−	0.189006i
$607$	−12.7249	−	28.5806i	−0.516489	−	1.16005i	−0.964031	−	0.265790i	$-0.914367\pi$
$607$	−12.7249	−	28.5806i	−0.516489	−	1.16005i	0.447542	−	0.894263i	$-0.352299\pi$
$608$	1.74810	+	8.22418i	0.0708950	+	0.333535i
$609$	−37.3851	+	13.5675i	−1.51492	+	0.549781i
$610$	41.4757	−	30.1339i	1.67930	−	1.22009i
$611$	−31.0655	−	15.2097i	−1.25678	−	0.615317i
$612$	−6.37638	+	8.12998i	−0.257750	+	0.328635i
$613$	−1.35701	−	6.38421i	−0.0548089	−	0.257856i	0.942209	−	0.335026i	$-0.108745\pi$
$613$	−1.35701	−	6.38421i	−0.0548089	−	0.257856i	−0.997018	+	0.0771699i	$0.975412\pi$
$614$	32.5673	+	3.42296i	1.31431	+	0.138139i
$615$	−44.8620	+	27.9746i	−1.80901	+	1.12804i
$616$	−7.68836	+	33.6802i	−0.309773	+	1.35701i
$617$	5.86624	+	3.38688i	0.236166	+	0.136350i	0.613413	−	0.789762i	$-0.289796\pi$
$617$	5.86624	+	3.38688i	0.236166	+	0.136350i	−0.377247	+	0.926113i	$0.623129\pi$
$618$	1.17350	−	16.5590i	0.0472050	−	0.666103i
$619$	−10.8002	+	33.2396i	−0.434097	+	1.33601i	0.459912	+	0.887964i	$0.347881\pi$
$619$	−10.8002	+	33.2396i	−0.434097	+	1.33601i	−0.894009	+	0.448049i	$0.852119\pi$
$620$	1.14418	−	5.38296i	0.0459515	−	0.216185i
$621$	2.50114	−	7.62480i	0.100367	−	0.305973i
$622$	7.32583	−	16.4541i	0.293739	−	0.659749i
$623$	17.2748	+	53.1663i	0.692099	+	2.13006i
$624$	12.6072	−	11.2959i	0.504691	−	0.452198i
$625$	23.3749	+	16.9829i	0.934997	+	0.679315i
$626$	−0.386551	−	0.669526i	−0.0154497	−	0.0267596i
$627$	12.4924	−	11.6850i	0.498897	−	0.466655i
$628$	3.03100	−	5.24985i	0.120950	−	0.209492i
$629$	16.1624	+	11.7427i	0.644438	+	0.468212i
$630$	−9.10994	+	36.2488i	−0.362949	+	1.44419i
$631$	22.8874	+	4.86487i	0.911134	+	0.193667i	0.639552	−	0.768748i	$-0.279120\pi$
$631$	22.8874	+	4.86487i	0.911134	+	0.193667i	0.271582	+	0.962415i	$0.412453\pi$
$632$	26.2913	+	36.1869i	1.04581	+	1.43944i
$633$	8.39682	−	20.7270i	0.333744	−	0.823823i
$634$	−12.4371	−	11.1985i	−0.493942	−	0.444747i
$635$	29.4473	−	6.25922i	1.16858	−	0.248389i
$636$	1.68973	+	3.47271i	0.0670022	+	0.137702i
$637$	13.9103	+	8.72132i	0.551147	+	0.345551i
$638$	−14.0133	+	23.4526i	−0.554790	+	0.928498i
$639$	−21.5452	−	10.5583i	−0.852314	−	0.417678i
$640$	−15.4304	−	1.62180i	−0.609939	−	0.0641071i
$641$	−14.1687	+	12.7576i	−0.559630	+	0.503894i	−0.899701	−	0.436506i	$-0.856216\pi$
$641$	−14.1687	+	12.7576i	−0.559630	+	0.503894i	0.340071	+	0.940400i	$0.389549\pi$
$642$	27.1232	+	4.80874i	1.07047	+	0.189786i
$643$	−4.83485	−	46.0005i	−0.190668	−	1.81408i	−0.503194	−	0.864173i	$-0.667842\pi$
$643$	−4.83485	−	46.0005i	−0.190668	−	1.81408i	0.312526	−	0.949909i	$-0.398825\pi$
$644$	0.281530	+	2.67858i	0.0110938	+	0.105551i
$645$	31.7288	+	5.62527i	1.24932	+	0.221495i
$646$	18.1124	−	16.3084i	0.712622	−	0.641647i
$647$	−22.4689	−	2.36157i	−0.883342	−	0.0928430i	−0.348016	−	0.937489i	$-0.613145\pi$
$647$	−22.4689	−	2.36157i	−0.883342	−	0.0928430i	−0.535326	+	0.844646i	$0.679811\pi$
$648$	−27.3257	+	3.73610i	−1.07345	+	0.146768i
$649$	−3.67387	+	0.330542i	−0.144212	+	0.0129749i
$650$	15.0313	+	9.42412i	0.589575	+	0.369644i
$651$	−9.19139	−	18.8900i	−0.360239	−	0.740357i
$652$	−3.08757	+	0.656284i	−0.120919	+	0.0257021i
$653$	20.6872	+	18.6268i	0.809551	+	0.728923i	0.965938	−	0.258773i	$-0.0833180\pi$
$653$	20.6872	+	18.6268i	0.809551	+	0.728923i	−0.156387	+	0.987696i	$0.549985\pi$
$654$	0.186642	−	0.460714i	0.00729829	−	0.0180153i
$655$	0.785415	+	1.08103i	0.0306887	+	0.0422394i
$656$	−26.9239	−	5.72285i	−1.05120	−	0.223440i
$657$	21.3656	+	5.36954i	0.833551	+	0.209486i
$658$	32.1681	+	23.3715i	1.25404	+	0.911115i
$659$	−7.41180	+	12.8376i	−0.288723	+	0.500082i	−0.973505	−	0.228665i	$-0.926564\pi$
$659$	−7.41180	+	12.8376i	−0.288723	+	0.500082i	0.684783	+	0.728747i	$0.259897\pi$
$660$	−3.75653	−	8.02390i	−0.146223	−	0.312330i
$661$	−6.92434	−	11.9933i	−0.269326	−	0.466486i	0.699362	−	0.714768i	$-0.253468\pi$
$661$	−6.92434	−	11.9933i	−0.269326	−	0.466486i	−0.968688	+	0.248282i	$0.920134\pi$
$662$	−18.6218	−	13.5295i	−0.723756	−	0.525839i
$663$	39.8357	+	13.0511i	1.54709	+	0.506862i
$664$	−8.06846	−	24.8322i	−0.313117	−	0.963675i
$665$	−12.3743	+	27.7932i	−0.479856	+	1.07777i
$666$	1.87054	+	10.7257i	0.0724820	+	0.415614i
$667$	−2.16902	+	10.2044i	−0.0839848	+	0.395117i
$668$	1.82203	−	5.60762i	0.0704963	−	0.216965i
$669$	2.08272	−	29.3890i	0.0805226	−	1.13624i
$670$	29.6895	+	17.1413i	1.14701	+	0.662225i
$671$	18.2310	+	42.6570i	0.703798	+	1.64676i
$672$	14.1060	−	8.79603i	0.544149	−	0.339314i
$673$	−34.4339	−	3.61915i	−1.32733	−	0.139508i	−0.585815	−	0.810445i	$-0.699225\pi$
$673$	−34.4339	−	3.61915i	−1.32733	−	0.139508i	−0.741514	+	0.670937i	$0.765892\pi$
$674$	−5.65436	−	26.6017i	−0.217798	−	1.02466i
$675$	−8.47456	−	19.1789i	−0.326186	−	0.738197i
$676$	5.87993	+	3.14919i	0.226151	+	0.121123i
$677$	27.4344	−	19.9323i	1.05439	−	0.766060i	0.0813488	−	0.996686i	$-0.474077\pi$
$677$	27.4344	−	19.9323i	1.05439	−	0.766060i	0.973043	+	0.230626i	$0.0740772\pi$
$678$	−1.70671	+	0.619383i	−0.0655457	+	0.0237872i
$679$	−1.15982	−	5.45654i	−0.0445099	−	0.209403i
$680$	−25.1486	−	56.4847i	−0.964405	−	2.16609i
$681$	1.79040	−	3.35966i	0.0686082	−	0.128742i
$682$	−13.0938	−	6.06652i	−0.501388	−	0.232299i
$683$	11.4377	+	6.60354i	0.437650	+	0.252678i	0.702600	−	0.711585i	$-0.252022\pi$
$683$	11.4377	+	6.60354i	0.437650	+	0.252678i	−0.264950	+	0.964262i	$0.585355\pi$
$684$	−4.58036	−	0.168535i	−0.175134	−	0.00644409i
$685$	5.35763	+	5.95025i	0.204705	+	0.227347i
$686$	7.53532	+	6.78483i	0.287700	+	0.259046i
$687$	21.2861	−	16.5985i	0.812116	−	0.633272i
$688$	9.86100	+	13.5725i	0.375947	+	0.517447i
$689$	10.9013	−	11.2546i	0.415305	−	0.428766i
$690$	6.80396	+	7.05892i	0.259022	+	0.268728i
$691$	−2.09661	+	19.9479i	−0.0797588	+	0.758854i	0.879419	+	0.476049i	$0.157932\pi$
$691$	−2.09661	+	19.9479i	−0.0797588	+	0.758854i	−0.959177	+	0.282805i	$0.908735\pi$
$692$	2.78590	+	4.82532i	0.105904	+	0.183431i
$693$	−30.1431	−	15.3362i	−1.14504	−	0.582576i
$694$	−21.1437			−0.802605
$695$	41.1731	−	18.3314i	1.56178	−	0.695351i
$696$	34.7986	−	8.64169i	1.31904	−	0.327562i
$697$	−21.0638	−	64.8276i	−0.797847	−	2.45552i
$698$	4.37377	−	0.459701i	0.165550	−	0.0174000i
$699$	−20.3614	+	15.8774i	−0.770138	+	0.600538i
$700$	5.22993	+	4.70905i	0.197673	+	0.177985i
$701$	−1.05686	+	3.25268i	−0.0399171	+	0.122852i	−0.969029	−	0.246946i	$-0.920573\pi$
$701$	−1.05686	+	3.25268i	−0.0399171	+	0.122852i	0.929112	+	0.369798i	$0.120573\pi$
$702$	10.6381	+	20.2173i	0.401508	+	0.763051i
$703$			8.86234i			0.334249i
$704$	9.50300	−	27.8211i	0.358158	−	1.04855i
$705$	−49.9168	+	1.69636i	−1.87997	+	0.0638885i
$706$	7.00232	+	15.7275i	0.263536	+	0.591911i
$707$	−8.06966	−	2.62199i	−0.303491	−	0.0986102i
$708$	0.756561	+	0.636038i	0.0284333	+	0.0239038i
$709$	3.10267	+	29.5199i	0.116523	+	1.10864i	0.883974	+	0.467536i	$0.154858\pi$
$709$	3.10267	+	29.5199i	0.116523	+	1.10864i	−0.767451	+	0.641108i	$0.778475\pi$
$710$	23.7157	−	17.2305i	0.890035	−	0.646648i
$711$	−40.6311	+	16.3276i	−1.52378	+	0.612333i
$712$	−10.4785	−	49.2976i	−0.392700	−	1.84751i
$713$	−5.48033	−	0.576006i	−0.205240	−	0.0215716i
$714$	−42.5266	−	22.6629i	−1.59152	−	0.848136i
$715$	−25.3926	+	25.4412i	−0.949631	+	0.951448i
$716$			2.77251i			0.103613i
$717$	−5.01212	−	3.38755i	−0.187181	−	0.126510i
$718$	25.3528	−	5.38891i	0.946160	−	0.201112i
$719$	0.808210	−	3.80233i	0.0301412	−	0.141803i	−0.960504	−	0.278266i	$-0.910240\pi$
$719$	0.808210	−	3.80233i	0.0301412	−	0.141803i	0.990645	+	0.136463i	$0.0435736\pi$
$720$	8.40291	−	22.9530i	0.313158	−	0.855409i
$721$	−26.5701	+	2.79263i	−0.989522	+	0.104003i
$722$	−12.0865	−	2.56907i	−0.449813	−	0.0956107i
$723$	−2.97989	+	2.87227i	−0.110823	+	0.106821i
$724$	4.41422	−	1.96534i	0.164053	−	0.0730411i
$725$	13.6297	+	23.6074i	0.506195	+	0.876756i
$726$	−22.7054	+	4.92094i	−0.842675	+	0.182633i
$727$	16.3416			0.606077			0.303039	−	0.952978i	$-0.401999\pi$
$727$	16.3416			0.606077			0.303039	+	0.952978i	$0.401999\pi$
$728$	−29.5597	−	23.1664i	−1.09556	−	0.858605i
$729$	2.97302	−	26.8358i	0.110112	−	0.993919i
$730$	−18.0101	+	20.0023i	−0.666584	+	0.740317i
$731$	−16.8980	+	37.9536i	−0.624996	+	1.40377i
$732$	4.66721	−	11.5207i	0.172505	−	0.425817i
$733$	15.9585	−	5.18522i	0.589439	−	0.191520i	0.000914401	−	1.00000i	$-0.499709\pi$
$733$	15.9585	−	5.18522i	0.589439	−	0.191520i	0.588525	+	0.808479i	$0.299709\pi$
$734$	−8.61375	−	9.56654i	−0.317939	−	0.353107i
$735$	23.6482	+	1.67589i	0.872277	+	0.0618160i
$736$		−	4.36061i		−	0.160734i
$737$	−21.1004	+	22.7394i	−0.777241	+	0.837616i
$738$	16.3472	−	33.3580i	0.601747	−	1.22793i
$739$	−0.630408	−	0.0662586i	−0.0231899	−	0.00243736i	0.0929264	−	0.995673i	$-0.470378\pi$
$739$	−0.630408	−	0.0662586i	−0.0231899	−	0.00243736i	−0.116116	+	0.993236i	$0.537045\pi$
$740$	4.36554	+	1.41845i	0.160480	+	0.0521433i
$741$	5.70315	+	17.6995i	0.209510	+	0.650208i
$742$	−14.5719	+	10.5871i	−0.534951	+	0.388665i
$743$	1.17224	+	0.521917i	0.0430055	+	0.0191473i	0.428127	−	0.903719i	$-0.359174\pi$
$743$	1.17224	+	0.521917i	0.0430055	+	0.0191473i	−0.385121	+	0.922866i	$0.625840\pi$
$744$	6.46098	+	17.8032i	0.236871	+	0.652698i
$745$	−9.92926	+	8.94035i	−0.363780	+	0.327549i
$746$	8.60407	−	11.8425i	0.315017	−	0.433584i
$747$	25.5021	−	1.73532i	0.933073	−	0.0634919i
$748$	11.2074	−	2.20717i	0.409784	−	0.0807019i
$749$		−	44.3320i		−	1.61986i
$750$	−6.10938	−	0.432956i	−0.223083	−	0.0158093i
$751$	26.2862	−	5.58731i	0.959198	−	0.203884i	0.298394	−	0.954443i	$-0.403549\pi$
$751$	26.2862	−	5.58731i	0.959198	−	0.203884i	0.660804	+	0.750559i	$0.270216\pi$
$752$	−19.3241	−	17.3995i	−0.704677	−	0.634494i
$753$	−22.8042	+	3.18315i	−0.831029	+	0.116000i
$754$	−16.5710	−	24.6476i	−0.603482	−	0.897614i
$755$	0.392622	+	1.20837i	0.0142890	+	0.0439770i
$756$	2.77616	+	8.62648i	0.100968	+	0.313742i
$757$	−3.04375	+	28.9594i	−0.110627	+	1.05255i	0.788553	+	0.614967i	$0.210831\pi$
$757$	−3.04375	+	28.9594i	−0.110627	+	1.05255i	−0.899180	+	0.437579i	$0.855836\pi$
$758$	20.6088	−	35.6955i	0.748546	−	1.29652i
$759$	−7.59735	+	4.58075i	−0.275766	+	0.166271i
$760$	13.7142	−	23.7537i	0.497466	−	0.861636i
$761$	−24.4121	+	10.8690i	−0.884938	+	0.394000i	−0.798314	−	0.602242i	$-0.794274\pi$
$761$	−24.4121	+	10.8690i	−0.884938	+	0.394000i	−0.0866236	+	0.996241i	$0.527608\pi$
$762$	−15.2300	+	14.6799i	−0.551725	+	0.531798i
$763$	−0.782510	−	0.166328i	−0.0283288	−	0.00602147i
$764$	2.39281	−	5.37433i	0.0865687	−	0.194437i
$765$	59.6301	−	10.3993i	2.15593	−	0.375989i
$766$	−14.7888	+	4.80517i	−0.534341	+	0.173618i
$767$	1.37720	−	3.76614i	0.0497277	−	0.135988i
$768$	−17.8087	+	8.66524i	−0.642614	+	0.312680i
$769$	19.8228	−	11.4447i	0.714827	−	0.412706i	−0.0980185	−	0.995185i	$-0.531250\pi$
$769$	19.8228	−	11.4447i	0.714827	−	0.412706i	0.812846	+	0.582479i	$0.197917\pi$
$770$	33.7895	−	23.7839i	1.21769	−	0.857112i
$771$	−8.58543	+	5.35360i	−0.309197	+	0.192805i
$772$	1.50682	−	2.07396i	0.0542315	−	0.0746433i
$773$	−31.2815	+	28.1660i	−1.12512	+	1.01306i	−0.125337	+	0.992114i	$0.540001\pi$
$773$	−31.2815	+	28.1660i	−1.12512	+	1.01306i	−0.999781	+	0.0209459i	$0.993332\pi$
$774$	−21.0088	+	8.44237i	−0.755144	+	0.303455i
$775$	−11.6488	+	8.46338i	−0.418439	+	0.304014i
$776$	0.525702	+	5.00172i	0.0188716	+	0.179551i
$777$	16.4711	−	5.97753i	0.590896	−	0.214443i
$778$	0.939353	+	4.41931i	0.0336774	+	0.158440i
$779$	17.7735	−	24.4631i	0.636800	−	0.876480i
$780$	9.63150	+	0.0235324i	0.344863	+	0.000842596i
$781$	10.4244	+	24.3912i	0.373015	+	0.872785i
$782$	−10.9469	+	6.32020i	−0.391461	+	0.226010i
$783$	−0.0985617	+	35.1015i	−0.00352231	+	1.25443i
$784$	8.25896	+	9.17250i	0.294963	+	0.327589i
$785$	−33.7754	+	10.9743i	−1.20549	+	0.391689i
$786$	−0.870192	−	0.352528i	−0.0310387	−	0.0125743i
$787$	−32.4030	+	3.40570i	−1.15504	+	0.121400i	−0.662620	−	0.748956i	$-0.730556\pi$
$787$	−32.4030	+	3.40570i	−1.15504	+	0.121400i	−0.492424	+	0.870356i	$0.663889\pi$
$788$	1.58004	+	4.86286i	0.0562866	+	0.173232i
$789$	9.71998	−	2.41380i	0.346040	−	0.0859336i
$790$	5.59231	−	53.2072i	0.198965	−	1.89303i
$791$	1.46100	+	2.53053i	0.0519473	+	0.0899754i
$792$	25.5815	+	16.5913i	0.908999	+	0.589547i
$793$	−50.3973	−	1.83597i	−1.78966	−	0.0651973i
$794$	−0.310107	−	0.225306i	−0.0110053	−	0.00799582i
$795$	6.25664	−	21.7427i	0.221900	−	0.771133i
$796$	0.211764	−	0.235187i	0.00750577	−	0.00833600i
$797$	28.4477	−	2.98997i	1.00767	−	0.105910i	0.413712	−	0.910408i	$-0.364232\pi$
$797$	28.4477	−	2.98997i	1.00767	−	0.105910i	0.593956	+	0.804498i	$0.297565\pi$
$798$	−2.95525	−	21.1715i	−0.104615	−	0.749462i
$799$	13.3883	−	62.9870i	0.473644	−	2.22832i
$800$	−7.62414	−	8.46747i	−0.269554	−	0.299370i
$801$	49.3059	+	1.81421i	1.74214	+	0.0641021i
$802$	30.9721	+	17.8818i	1.09366	+	0.631427i
$803$	−14.0186	−	19.9160i	−0.494705	−	0.702821i
$804$	8.30735	−	0.282314i	0.292978	−	0.00995646i
$805$	9.27441	−	12.7651i	0.326880	−	0.449912i
$806$	12.0329	−	10.0659i	0.423841	−	0.354558i
$807$	−6.91526	+	39.0048i	−0.243429	+	1.37304i
$808$	6.98829	+	3.11139i	0.245847	+	0.109458i
$809$	34.2870	+	15.2655i	1.20547	+	0.536708i	0.908381	−	0.418143i	$-0.137319\pi$
$809$	34.2870	+	15.2655i	1.20547	+	0.536708i	0.297085	+	0.954851i	$0.403986\pi$
$810$	27.2790	+	18.5489i	0.958486	+	0.651741i
$811$	−51.9317	−	16.8736i	−1.82357	−	0.592513i	−0.999668	−	0.0257780i	$-0.991794\pi$
$811$	−51.9317	−	16.8736i	−1.82357	−	0.592513i	−0.823900	−	0.566735i	$-0.808206\pi$
$812$	−4.79193	−	10.7629i	−0.168164	−	0.377702i
$813$	−9.11333	+	5.68279i	−0.319618	+	0.199304i
$814$	6.17393	−	10.3327i	0.216396	−	0.362161i
$815$	16.0148	+	9.24614i	0.560973	+	0.323878i
$816$	26.1096	+	17.6467i	0.914018	+	0.617758i
$817$	−18.0271	+	3.83179i	−0.630690	+	0.134057i
$818$	−43.9370	+	14.2760i	−1.53622	+	0.499148i
$819$	29.0487	−	22.5376i	1.01504	−	0.787529i
$820$	−9.20567	−	12.6705i	−0.321476	−	0.442474i
$821$	−29.5801	+	32.8521i	−1.03235	+	1.14655i	−0.0432894	+	0.999063i	$0.513784\pi$
$821$	−29.5801	+	32.8521i	−1.03235	+	1.14655i	−0.989065	+	0.147483i	$0.952883\pi$
$822$	−5.40654	−	1.55578i	−0.188575	−	0.0542640i
$823$	−6.82138	+	3.03707i	−0.237778	+	0.105866i	−0.522167	−	0.852843i	$-0.674876\pi$
$823$	−6.82138	+	3.03707i	−0.237778	+	0.105866i	0.284388	+	0.958709i	$0.408209\pi$
$824$	24.0863			0.839087
$825$	−6.74355	+	22.1782i	−0.234780	+	0.772146i
$826$	−2.30489	+	3.99218i	−0.0801972	+	0.138906i
$827$	33.0380	+	24.0035i	1.14885	+	0.834685i	0.988327	−	0.152348i	$-0.0486834\pi$
$827$	33.0380	+	24.0035i	1.14885	+	0.834685i	0.160518	+	0.987033i	$0.448683\pi$
$828$	2.30544	+	0.579396i	0.0801194	+	0.0201354i
$829$	0.313231	−	0.347878i	0.0108790	−	0.0120823i	−0.737681	−	0.675150i	$-0.764079\pi$
$829$	0.313231	−	0.347878i	0.0108790	−	0.0120823i	0.748560	+	0.663067i	$0.230746\pi$
$830$	−12.7023	+	28.5299i	−0.440905	+	0.990288i
$831$	39.3276	−	5.48960i	1.36426	−	0.190432i
$832$	22.9569	+	22.2362i	0.795889	+	0.770903i
$833$	−9.44533	+	29.0698i	−0.327261	+	1.00721i
$834$	−17.7329	+	26.2371i	−0.614040	+	0.908517i
$835$	−29.9144	+	17.2711i	−1.03523	+	0.597691i
$836$	3.71442	+	3.44669i	0.128466	+	0.119206i
$837$	−18.4449	+	1.88629i	−0.637550	+	0.0651998i
$838$	−12.2651	−	27.5480i	−0.423693	−	0.951629i
$839$	−0.785928	+	0.707653i	−0.0271333	+	0.0244309i	−0.682586	−	0.730806i	$-0.739145\pi$
$839$	−0.785928	+	0.707653i	−0.0271333	+	0.0244309i	0.655452	+	0.755236i	$0.272478\pi$
$840$	−53.3973	−	9.46693i	−1.84238	−	0.326640i
$841$	−1.73877	−	16.5433i	−0.0599575	−	0.570457i
$842$	−7.69043	−	3.42400i	−0.265030	−	0.117999i
$843$	6.54839	+	18.0441i	0.225539	+	0.621472i
$844$	6.30047	+	2.04715i	0.216871	+	0.0704657i
$845$	−13.2541	−	36.7598i	−0.455956	−	1.26458i
$846$	29.1307	−	19.5697i	1.00154	−	0.672820i
$847$	14.1770	+	34.5977i	0.487128	+	1.18879i
$848$	10.2011	−	5.88961i	0.350307	−	0.202250i
$849$	10.3045	+	0.730253i	0.353649	+	0.0250622i
$850$	−10.2065	+	31.4123i	−0.350079	+	1.07743i
$851$	0.955623	−	4.49585i	0.0327583	−	0.154116i
$852$	2.66870	−	6.58750i	0.0914280	−	0.225684i
$853$	24.9121	+	34.2885i	0.852973	+	1.17402i	0.983200	+	0.182533i	$0.0584296\pi$
$853$	24.9121	+	34.2885i	0.852973	+	1.17402i	−0.130226	+	0.991484i	$0.541570\pi$
$854$	56.7060	+	12.0532i	1.94044	+	0.412453i
$855$	19.2805	+	18.6888i	0.659379	+	0.639145i
$856$	−4.17776	+	39.7487i	−0.142793	+	1.35858i
$857$	53.9118			1.84159			0.920796	−	0.390044i	$-0.127540\pi$
$857$	53.9118			1.84159			0.920796	+	0.390044i	$0.127540\pi$
$858$	5.68096	−	24.6092i	0.193945	−	0.840143i
$859$	−30.7883			−1.05048			−0.525241	−	0.850953i	$-0.676025\pi$
$859$	−30.7883			−1.05048			−0.525241	+	0.850953i	$0.676025\pi$
$860$	−0.997793	+	9.49336i	−0.0340245	+	0.323721i
$861$	−57.4537	−	16.5328i	−1.95802	−	0.563436i
$862$	21.8452	+	4.64335i	0.744052	+	0.158153i
$863$	29.3692	+	40.4233i	0.999740	+	1.37602i	0.925485	+	0.378785i	$0.123658\pi$
$863$	29.3692	+	40.4233i	0.999740	+	1.37602i	0.0742551	+	0.997239i	$0.476342\pi$
$864$	−3.01018	−	14.3599i	−0.102408	−	0.488535i
$865$	6.78660	−	31.9285i	0.230751	−	1.08560i
$866$	−7.46401	+	22.9719i	−0.253637	+	0.780616i
$867$	−3.43524	+	48.4741i	−0.116667	+	1.64627i
$868$	5.38934	−	3.11154i	0.182926	−	0.105613i
$869$	45.8118	+	15.6481i	1.55406	+	0.530827i
$870$	−37.8476	−	20.1694i	−1.28315	−	0.683806i
$871$	−12.5859	−	31.2868i	−0.426456	−	1.06011i
$872$	0.685936	+	0.222874i	0.0232287	+	0.00754747i
$873$	−4.87431	−	0.694347i	−0.164970	−	0.0235001i
$874$	−5.12260	−	2.28073i	−0.173275	−	0.0771468i
$875$	1.03033	+	9.80291i	0.0348314	+	0.331399i
$876$	−1.13924	+	6.42578i	−0.0384914	+	0.217107i
$877$	−4.59023	+	4.13306i	−0.155001	+	0.139563i	−0.742982	−	0.669311i	$-0.766589\pi$
$877$	−4.59023	+	4.13306i	−0.155001	+	0.139563i	0.587982	+	0.808874i	$0.299923\pi$
$878$	3.44310	+	7.73332i	0.116199	+	0.260987i
$879$	−3.42789	+	6.43238i	−0.115620	+	0.216959i
$880$	−23.6021	+	13.1590i	−0.795626	+	0.443588i
$881$	36.1024	−	20.8437i	1.21632	−	0.702242i	0.252191	−	0.967678i	$-0.418849\pi$
$881$	36.1024	−	20.8437i	1.21632	−	0.702242i	0.964129	+	0.265435i	$0.0855157\pi$
$882$	−14.7226	+	7.79284i	−0.495736	+	0.262399i
$883$	9.93038	−	30.5626i	0.334184	−	1.02851i	−0.632939	−	0.774202i	$-0.718151\pi$
$883$	9.93038	−	30.5626i	0.334184	−	1.02851i	0.967123	−	0.254311i	$-0.0818485\pi$
$884$	−3.02229	+	12.0444i	−0.101651	+	0.405096i
$885$	−0.800502	−	5.73481i	−0.0269086	−	0.192773i
$886$	−4.41874	+	9.92465i	−0.148450	+	0.333425i
$887$	24.6885	−	27.4194i	0.828960	−	0.920653i	−0.168927	−	0.985629i	$-0.554030\pi$
$887$	24.6885	−	27.4194i	0.828960	−	0.920653i	0.997887	+	0.0649751i	$0.0206968\pi$
$888$	−15.3315	+	3.80734i	−0.514492	+	0.127766i
$889$	27.5415	+	20.0100i	0.923711	+	0.671115i
$890$	−30.1407	+	52.2053i	−1.01032	+	1.74993i
$891$	−21.8567	+	20.3294i	−0.732227	+	0.681061i
$892$	8.72779			0.292228
$893$	26.0961	−	11.6187i	0.873273	−	0.388806i
$894$	2.59615	−	9.02197i	0.0868282	−	0.301740i
$895$	10.8683	−	12.0705i	0.363287	−	0.403471i
$896$	−10.3126	−	14.1941i	−0.344520	−	0.474192i
$897$	−0.984667	−	9.59390i	−0.0328771	−	0.320331i
$898$	−22.6393	+	7.35597i	−0.755485	+	0.245472i
$899$	23.5779	−	5.01163i	0.786366	−	0.167147i
$900$	5.48973	−	2.90577i	0.182991	−	0.0968591i
$901$	25.2620	+	14.5850i	0.841599	+	0.485897i
$902$	−37.7644	+	16.1399i	−1.25742	+	0.537401i
$903$	19.2806	+	30.9198i	0.641619	+	1.02895i
$904$	−1.07149	−	2.40660i	−0.0356371	−	0.0800422i
$905$	−26.9220	−	8.74749i	−0.894918	−	0.290776i
$906$	−0.683342	−	0.574482i	−0.0227025	−	0.0190859i
$907$	7.98625	+	3.55571i	0.265179	+	0.118065i	0.535019	−	0.844840i	$-0.320304\pi$
$907$	7.98625	+	3.55571i	0.265179	+	0.118065i	−0.269840	+	0.962905i	$0.586971\pi$
$908$	1.03024	+	0.458693i	0.0341898	+	0.0152223i
$909$	−4.62160	+	5.89261i	−0.153289	+	0.195445i
$910$	7.73365	+	44.2496i	0.256368	+	1.46686i
$911$	−8.17730	+	11.2551i	−0.270926	+	0.372898i	−0.922702	−	0.385514i	$-0.874024\pi$
$911$	−8.17730	+	11.2551i	−0.270926	+	0.372898i	0.651776	+	0.758412i	$0.274024\pi$
$912$	0.474809	+	13.9717i	0.0157225	+	0.462649i
$913$	−22.6103	−	16.9509i	−0.748292	−	0.560994i
$914$	0.810912	+	0.468180i	0.0268226	+	0.0154860i
$915$	−65.4806	+	31.8612i	−2.16472	+	1.05330i
$916$	5.35045	+	5.94227i	0.176784	+	0.196338i
$917$	−0.314158	+	1.47800i	−0.0103744	+	0.0488078i
$918$	−31.6864	+	28.3699i	−1.04581	+	0.936345i
$919$	39.2676	−	4.12719i	1.29532	−	0.136143i	0.568334	−	0.822798i	$-0.307588\pi$
$919$	39.2676	−	4.12719i	1.29532	−	0.136143i	0.726984	+	0.686655i	$0.240921\pi$
$920$	−9.51853	+	10.5714i	−0.313817	+	0.348529i
$921$	−44.7003	−	12.8629i	−1.47292	−	0.423846i
$922$	−0.0900527	−	0.0654271i	−0.00296573	−	0.00215473i
$923$	−28.8171	−	1.04981i	−0.948525	−	0.0345548i
$924$	3.90050	−	9.22816i	0.128317	−	0.303584i
$925$	−6.00496	−	10.4009i	−0.197442	−	0.341979i
$926$	−5.26619	+	50.1044i	−0.173058	+	1.64653i
$927$	−5.74730	+	22.8687i	−0.188766	+	0.751107i
$928$	5.89437	+	18.1410i	0.193492	+	0.595508i
$929$	12.5328	−	1.31725i	0.411188	−	0.0432175i	0.103323	−	0.994648i	$-0.467052\pi$
$929$	12.5328	−	1.31725i	0.411188	−	0.0432175i	0.307864	+	0.951430i	$0.400386\pi$
$930$	8.50565	−	20.9956i	0.278911	−	0.688474i
$931$	−12.8956	+	4.19003i	−0.422635	+	0.137323i
$932$	−5.11800	−	5.68412i	−0.167646	−	0.186189i
$933$	−14.3260	+	21.1964i	−0.469013	+	0.693938i
$934$	−29.9480	+	17.2905i	−0.979928	+	0.565762i
$935$	−57.4451	−	34.3242i	−1.87866	−	1.12252i
$936$	−28.1694	+	17.4701i	−0.920745	+	0.571028i
$937$	7.43843	−	10.2381i	0.243003	−	0.334465i	−0.670043	−	0.742323i	$-0.733724\pi$
$937$	7.43843	−	10.2381i	0.243003	−	0.334465i	0.913045	+	0.407858i	$0.133724\pi$
$938$	8.06009	+	37.9198i	0.263171	+	1.23812i
$939$	0.374618	+	1.03226i	0.0122252	+	0.0336865i
$940$	−1.54655	−	14.7144i	−0.0504429	−	0.479932i
$941$	−31.4195	+	22.8276i	−1.02425	+	0.744159i	−0.967149	−	0.254210i	$-0.918185\pi$
$941$	−31.4195	+	22.8276i	−1.02425	+	0.744159i	−0.0570975	+	0.998369i	$0.518185\pi$
$942$	16.0575	−	19.1003i	0.523182	−	0.622320i
$943$	−11.6543	+	10.4936i	−0.379516	+	0.341718i
$944$	1.77197	−	2.43891i	0.0576727	−	0.0793797i
$945$	21.7297	−	48.4391i	0.706866	−	1.57572i
$946$	23.6875	+	8.09105i	0.770146	+	0.263063i
$947$	−12.3519	+	7.13138i	−0.401383	+	0.231739i	−0.687081	−	0.726581i	$-0.741108\pi$
$947$	−12.3519	+	7.13138i	−0.401383	+	0.231739i	0.285698	+	0.958320i	$0.407775\pi$
$948$	−5.67550	−	11.6642i	−0.184332	−	0.378836i
$949$	26.0814	−	4.55833i	0.846638	−	0.147970i
$950$	−13.9348	+	4.52768i	−0.452103	+	0.146897i
$951$	14.6180	+	18.7463i	0.474020	+	0.607889i
$952$	28.4382	−	63.8733i	0.921688	−	2.07014i
$953$	8.26214	+	1.75617i	0.267637	+	0.0568880i	0.339775	−	0.940507i	$-0.389649\pi$
$953$	8.26214	+	1.75617i	0.267637	+	0.0568880i	−0.0721383	+	0.997395i	$0.522982\pi$
$954$	4.35325	+	15.2895i	0.140942	+	0.495017i
$955$	−31.4849	+	14.0180i	−1.01883	+	0.453611i
$956$	0.896032	−	1.55197i	0.0289797	−	0.0501944i
$957$	25.4145	−	29.3264i	0.821535	−	0.947987i
$958$	−1.93287	+	3.34783i	−0.0624482	+	0.108163i
$959$	−0.946422	+	9.00461i	−0.0305616	+	0.290774i
$960$	44.3504	+	12.7622i	1.43140	+	0.411898i
$961$	−5.64502	−	17.3736i	−0.182097	−	0.560438i
$962$	7.30084	+	10.8592i	0.235388	+	0.350115i
$963$	−36.7425	−	13.4511i	−1.18401	−	0.433457i
$964$	−0.911129	−	0.820385i	−0.0293455	−	0.0264228i
$965$	−14.6901	+	3.12247i	−0.472890	+	0.100516i
$966$	−0.783717	+	11.0589i	−0.0252157	+	0.355815i
$967$			8.00815i			0.257525i	0.991675	+	0.128762i	$0.0411005\pi$
$967$			8.00815i			0.257525i	−0.991675	+	0.128762i	$0.958900\pi$
$968$	−9.45090	−	32.3568i	−0.303764	−	1.03999i
$969$	−29.3761	+	18.3180i	−0.943696	+	0.588459i
$970$	3.53578	−	4.86659i	0.113527	−	0.156257i
$971$	30.5049	−	27.4667i	0.978949	−	0.881449i	−0.0140111	−	0.999902i	$-0.504460\pi$
$971$	30.5049	−	27.4667i	0.978949	−	0.881449i	0.992960	+	0.118453i	$0.0377933\pi$
$972$	7.99200	+	0.316540i	0.256343	+	0.0101530i
$973$	46.5588	+	20.7293i	1.49261	+	0.664552i
$974$	28.4414	−	20.6639i	0.911322	−	0.662114i
$975$	−18.6861	−	16.9079i	−0.598435	−	0.541486i
$976$	−36.0570	−	11.7156i	−1.15416	−	0.375008i
$977$	33.3687	+	3.50720i	1.06756	+	0.112205i	0.621977	−	0.783035i	$-0.286330\pi$
$977$	33.3687	+	3.50720i	1.06756	+	0.112205i	0.445583	+	0.895240i	$0.352996\pi$
$978$	−12.9859	+	0.441309i	−0.415244	+	0.0141115i
$979$	−39.9843	−	37.1023i	−1.27791	−	1.18579i
$980$			7.02292i			0.224339i
$981$	−0.375281	+	0.598081i	−0.0119818	+	0.0190952i
$982$	−17.6427	−	19.5942i	−0.563001	−	0.625276i
$983$	6.50821	−	2.11465i	0.207580	−	0.0674467i	−0.203382	−	0.979100i	$-0.565193\pi$
$983$	6.50821	−	2.11465i	0.207580	−	0.0674467i	0.410961	+	0.911653i	$0.365193\pi$
$984$	49.9558	+	20.2379i	1.59253	+	0.645160i
$985$	12.1836	−	27.3649i	0.388203	−	0.871917i
$986$	36.9981	−	41.0906i	1.17826	−	1.30859i
$987$	−39.1954	−	40.6642i	−1.24760	−	1.29435i
$988$	−5.11062	+	2.05587i	−0.162590	+	0.0654059i
$989$	9.55832			0.303937
$990$	−9.45983	−	35.2213i	−0.300653	−	1.11941i
$991$	16.5449	+	28.6567i	0.525568	+	0.910310i	0.999557	+	0.0297789i	$0.00948031\pi$
$991$	16.5449	+	28.6567i	0.525568	+	0.910310i	−0.473989	+	0.880531i	$0.657186\pi$
$992$	−9.20435	+	4.09804i	−0.292238	+	0.130113i
$993$	22.6898	+	23.5401i	0.720040	+	0.747021i
$994$	32.4244	+	6.89201i	1.02844	+	0.218601i
$995$	−1.84388	+	0.193800i	−0.0584549	+	0.00614386i
$996$	1.04680	+	7.49930i	0.0331692	+	0.237624i
$997$	−1.55673	+	7.32384i	−0.0493022	+	0.231948i	−0.995899	−	0.0904709i	$-0.971163\pi$
$997$	−1.55673	+	7.32384i	−0.0493022	+	0.231948i	0.946597	+	0.322419i	$0.104496\pi$
$998$	3.14731	−	0.668981i	0.0996263	−	0.0211762i
$999$	0.0434241	−	15.4650i	0.00137388	−	0.489290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.16	✓	416
3.2	odd	2	inner	429.2.bq.a.29.37	yes	416
11.8	odd	10	inner	429.2.bq.a.107.16	yes	416
13.9	even	3	inner	429.2.bq.a.425.37	yes	416
33.8	even	10	inner	429.2.bq.a.107.37	yes	416
39.35	odd	6	inner	429.2.bq.a.425.16	yes	416
143.74	odd	30	inner	429.2.bq.a.74.37	yes	416
429.74	even	30	inner	429.2.bq.a.74.16	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.16	✓	416	1.1	even	1	trivial
429.2.bq.a.29.37	yes	416	3.2	odd	2	inner
429.2.bq.a.74.16	yes	416	429.74	even	30	inner
429.2.bq.a.74.37	yes	416	143.74	odd	30	inner
429.2.bq.a.107.16	yes	416	11.8	odd	10	inner
429.2.bq.a.107.37	yes	416	33.8	even	10	inner
429.2.bq.a.425.16	yes	416	39.35	odd	6	inner
429.2.bq.a.425.37	yes	416	13.9	even	3	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.127461 + 1.21271i) q^{2} +(0.478976 - 1.66451i) q^{3} +(0.501877 + 0.106677i) q^{4} +(-1.76681 - 2.43180i) q^{5} +(1.95751 + 0.793018i) q^{6} +(0.706704 - 3.32478i) q^{7} +(-0.946962 + 2.91445i) q^{8} +(-2.54116 - 1.59452i) q^{9} +O(q^{10})\)	\(q+(-0.127461 + 1.21271i) q^{2} +(0.478976 - 1.66451i) q^{3} +(0.501877 + 0.106677i) q^{4} +(-1.76681 - 2.43180i) q^{5} +(1.95751 + 0.793018i) q^{6} +(0.706704 - 3.32478i) q^{7} +(-0.946962 + 2.91445i) q^{8} +(-2.54116 - 1.59452i) q^{9} +(3.17427 - 1.83266i) q^{10} +(0.977496 + 3.16931i) q^{11} +(0.417952 - 0.784281i) q^{12} +(-3.56970 - 0.507177i) q^{13} +(3.94192 + 1.28081i) q^{14} +(-4.89401 + 1.77609i) q^{15} +(-2.47622 - 1.10248i) q^{16} +(-0.701640 - 6.67566i) q^{17} +(2.25759 - 2.87846i) q^{18} +(2.21285 - 1.99246i) q^{19} +(-0.627301 - 1.40894i) q^{20} +(-5.19563 - 2.76880i) q^{21} +(-3.96804 + 0.781457i) q^{22} +(-1.33742 + 0.772162i) q^{23} +(4.39755 + 2.97218i) q^{24} +(-1.24696 + 3.83776i) q^{25} +(1.07006 - 4.26437i) q^{26} +(-3.87124 + 3.46605i) q^{27} +(0.709357 - 1.59324i) q^{28} +(4.52019 - 5.02018i) q^{29} +(-1.53008 - 6.16139i) q^{30} +(2.88677 + 2.09736i) q^{31} +(-1.41182 + 2.44534i) q^{32} +(5.74353 - 0.109027i) q^{33} +8.18507 q^{34} +(-9.33381 + 4.15568i) q^{35} +(-1.10525 - 1.07134i) q^{36} +(-1.99150 + 2.21178i) q^{37} +(2.13423 + 2.93751i) q^{38} +(-2.55400 + 5.69887i) q^{39} +(8.76046 - 2.84645i) q^{40} +(9.93295 - 2.11131i) q^{41} +(4.02000 - 5.94787i) q^{42} +(-5.36011 - 3.09466i) q^{43} +(0.152490 + 1.69488i) q^{44} +(0.612196 + 8.99681i) q^{45} +(-0.765939 - 1.72033i) q^{46} +(9.12373 + 2.96448i) q^{47} +(-3.02114 + 3.59362i) q^{48} +(-4.15992 - 1.85212i) q^{49} +(-4.49515 - 2.00137i) q^{50} +(-11.4478 - 2.02960i) q^{51} +(-1.73745 - 0.635346i) q^{52} +(-2.55432 + 3.51572i) q^{53} +(-3.70988 - 5.13648i) q^{54} +(5.98007 - 7.97663i) q^{55} +(9.02069 + 5.20810i) q^{56} +(-2.25656 - 4.63765i) q^{57} +(5.51188 + 6.12156i) q^{58} +(-0.231237 + 1.08788i) q^{59} +(-2.64565 + 0.369298i) q^{60} +(13.9103 - 1.46204i) q^{61} +(-2.91144 + 3.23348i) q^{62} +(-7.09727 + 7.32196i) q^{63} +(-7.17132 - 5.21027i) q^{64} +(5.07362 + 9.57689i) q^{65} +(-0.599857 + 6.97913i) q^{66} +(4.67660 + 8.10010i) q^{67} +(0.360004 - 3.42521i) q^{68} +(0.644675 + 2.59600i) q^{69} +(-3.84994 - 11.8489i) q^{70} +(7.95390 - 0.835989i) q^{71} +(7.05353 - 5.89615i) q^{72} +(-6.98392 + 2.26921i) q^{73} +(-2.42841 - 2.69702i) q^{74} +(5.79071 + 3.91377i) q^{75} +(1.32313 - 0.763909i) q^{76} +(11.2281 - 1.01020i) q^{77} +(-6.58554 - 3.82364i) q^{78} +(8.57951 - 11.8087i) q^{79} +(1.69398 + 7.96955i) q^{80} +(3.91503 + 8.10386i) q^{81} +(1.29435 + 12.3149i) q^{82} +(-6.89311 + 5.00814i) q^{83} +(-2.31219 - 1.94385i) q^{84} +(-14.9942 + 13.5008i) q^{85} +(4.43613 - 6.10581i) q^{86} +(-6.19106 - 9.92844i) q^{87} +(-10.1624 - 0.152349i) q^{88} +(-14.2430 + 8.22321i) q^{89} +(-10.9885 - 0.404325i) q^{90} +(-4.20898 + 11.5101i) q^{91} +(-0.753594 + 0.244858i) q^{92} +(4.87376 - 3.80046i) q^{93} +(-4.75797 + 10.6866i) q^{94} +(-8.75496 - 1.86092i) q^{95} +(3.39406 + 3.52124i) q^{96} +(1.49929 - 0.667525i) q^{97} +(2.77631 - 4.80871i) q^{98} +(2.56954 - 9.61236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

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