LMFDB - Embedded newform 945.2.j.h.541.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(541,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("945.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.j (of order $3$, degree $2$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 7x^{8} - 2x^{7} + 42x^{6} - 6x^{5} + 50x^{4} + 21x^{3} + 48x^{2} + 7x + 1 $ x^10 + 7x^8 - 2x^7 + 42x^6 - 6x^5 + 50x^4 + 21x^3 + 48x^2 + 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.4
Root			$0.655317 + 1.13504i$ of defining polynomial
Character	$\chi$	$=$	945.541
Dual form			945.2.j.h.676.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.655317 - 1.13504i) q^{2} +(0.141120 + 0.244426i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.17793 - 1.50220i) q^{7} +2.99118 q^{8} +O(q^{10})$	\(q+(0.655317 - 1.13504i) q^{2} +(0.141120 + 0.244426i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.17793 - 1.50220i) q^{7} +2.99118 q^{8} +(-0.655317 - 1.13504i) q^{10} +(2.51820 + 4.36166i) q^{11} -3.53882 q^{13} +(-0.277829 - 3.45646i) q^{14} +(1.67793 - 2.90626i) q^{16} +(0.755215 + 1.30807i) q^{17} +(2.38149 - 4.12487i) q^{19} +0.282239 q^{20} +6.60089 q^{22} +(-2.22117 + 3.84717i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.31905 + 4.01671i) q^{26} +(0.674527 + 0.320353i) q^{28} +6.72577 q^{29} +(-3.08846 - 5.34937i) q^{31} +(0.792026 + 1.37183i) q^{32} +1.97962 q^{34} +(-0.211981 - 2.63725i) q^{35} +(-4.07564 + 7.05921i) q^{37} +(-3.12127 - 5.40619i) q^{38} +(1.49559 - 2.59044i) q^{40} +4.64966 q^{41} -3.64084 q^{43} +(-0.710736 + 1.23103i) q^{44} +(2.91113 + 5.04223i) q^{46} +(-0.938159 + 1.62494i) q^{47} +(2.48677 - 6.54339i) q^{49} -1.31063 q^{50} +(-0.499397 - 0.864982i) q^{52} +(-4.69477 - 8.13157i) q^{53} +5.03641 q^{55} +(6.51458 - 4.49336i) q^{56} +(4.40751 - 7.63404i) q^{58} +(-3.49899 - 6.06044i) q^{59} +(2.46655 - 4.27220i) q^{61} -8.09569 q^{62} +8.78784 q^{64} +(-1.76941 + 3.06471i) q^{65} +(-3.52358 - 6.10302i) q^{67} +(-0.213151 + 0.369189i) q^{68} +(-3.13230 - 1.48762i) q^{70} -9.98514 q^{71} +(4.07163 + 7.05227i) q^{73} +(5.34167 + 9.25204i) q^{74} +1.34430 q^{76} +(12.0366 + 5.71654i) q^{77} +(7.73055 - 13.3897i) q^{79} +(-1.67793 - 2.90626i) q^{80} +(3.04700 - 5.27756i) q^{82} +8.26057 q^{83} +1.51043 q^{85} +(-2.38590 + 4.13251i) q^{86} +(7.53240 + 13.0465i) q^{88} +(-0.902114 + 1.56251i) q^{89} +(-7.70732 + 5.31603i) q^{91} -1.25380 q^{92} +(1.22958 + 2.12970i) q^{94} +(-2.38149 - 4.12487i) q^{95} -11.5788 q^{97} +(-5.79740 - 7.11058i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{4} + 5 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q - 4 * q^4 + 5 * q^5 - q^7 + 6 * q^8	$ 10 q - 4 q^{4} + 5 q^{5} - q^{7} + 6 q^{8} - 3 q^{11} - 20 q^{13} + 20 q^{14} - 6 q^{16} + q^{17} + 13 q^{19} - 8 q^{20} - 12 q^{22} + 4 q^{23} - 5 q^{25} + 5 q^{26} + 21 q^{28} + 24 q^{29} + 5 q^{31} - 16 q^{32} - 32 q^{34} + q^{35} - 8 q^{37} - 5 q^{38} + 3 q^{40} + 18 q^{41} + 16 q^{43} + 6 q^{44} + 26 q^{46} - 2 q^{47} - 11 q^{49} + 5 q^{52} + 6 q^{53} - 6 q^{55} - 24 q^{56} - 20 q^{58} + 14 q^{59} + 15 q^{61} - 40 q^{62} - 18 q^{64} - 10 q^{65} + 18 q^{67} - 30 q^{68} - 2 q^{70} + 26 q^{71} + 35 q^{73} + 9 q^{74} - 60 q^{76} + 46 q^{77} - q^{79} + 6 q^{80} + 39 q^{82} + 20 q^{83} + 2 q^{85} - 25 q^{86} + 46 q^{88} - 11 q^{89} + 26 q^{91} - 86 q^{92} - 29 q^{94} - 13 q^{95} - 44 q^{97} - 9 q^{98}+O(q^{100}) $ 10 * q - 4 * q^4 + 5 * q^5 - q^7 + 6 * q^8 - 3 * q^11 - 20 * q^13 + 20 * q^14 - 6 * q^16 + q^17 + 13 * q^19 - 8 * q^20 - 12 * q^22 + 4 * q^23 - 5 * q^25 + 5 * q^26 + 21 * q^28 + 24 * q^29 + 5 * q^31 - 16 * q^32 - 32 * q^34 + q^35 - 8 * q^37 - 5 * q^38 + 3 * q^40 + 18 * q^41 + 16 * q^43 + 6 * q^44 + 26 * q^46 - 2 * q^47 - 11 * q^49 + 5 * q^52 + 6 * q^53 - 6 * q^55 - 24 * q^56 - 20 * q^58 + 14 * q^59 + 15 * q^61 - 40 * q^62 - 18 * q^64 - 10 * q^65 + 18 * q^67 - 30 * q^68 - 2 * q^70 + 26 * q^71 + 35 * q^73 + 9 * q^74 - 60 * q^76 + 46 * q^77 - q^79 + 6 * q^80 + 39 * q^82 + 20 * q^83 + 2 * q^85 - 25 * q^86 + 46 * q^88 - 11 * q^89 + 26 * q^91 - 86 * q^92 - 29 * q^94 - 13 * q^95 - 44 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.655317	−	1.13504i	0.463379	−	0.802596i	−0.535748	−	0.844378i	$-0.679970\pi$
$2$	0.655317	−	1.13504i	0.463379	−	0.802596i	0.999127	+	0.0417821i	$0.0133035\pi$
$3$		0			0
$3$		0			0
$4$	0.141120	+	0.244426i	0.0705598	+	0.122213i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.17793	−	1.50220i	0.823181	−	0.567780i
$7$	2.17793	−	1.50220i	0.823181	−	0.567780i
$8$	2.99118			1.05754
$9$		0			0
$10$	−0.655317	−	1.13504i	−0.207229	−	0.358932i
$11$	2.51820	+	4.36166i	0.759267	+	1.31509i	0.943225	+	0.332155i	$0.107776\pi$
$11$	2.51820	+	4.36166i	0.759267	+	1.31509i	−0.183958	+	0.982934i	$0.558891\pi$
$12$		0			0
$13$	−3.53882			−0.981493			−0.490747	−	0.871302i	$-0.663276\pi$
$13$	−3.53882			−0.981493			−0.490747	+	0.871302i	$0.663276\pi$
$14$	−0.277829	−	3.45646i	−0.0742529	−	0.923779i
$15$		0			0
$16$	1.67793	−	2.90626i	0.419483	−	0.726566i
$17$	0.755215	+	1.30807i	0.183166	+	0.317254i	0.942957	−	0.332914i	$-0.108032\pi$
$17$	0.755215	+	1.30807i	0.183166	+	0.317254i	−0.759791	+	0.650168i	$0.774699\pi$
$18$		0			0
$19$	2.38149	−	4.12487i	0.546352	−	0.946310i	−0.452168	−	0.891933i	$-0.649349\pi$
$19$	2.38149	−	4.12487i	0.546352	−	0.946310i	0.998520	−	0.0543773i	$-0.0173174\pi$
$20$	0.282239			0.0631106
$21$		0			0
$22$	6.60089			1.40731
$23$	−2.22117	+	3.84717i	−0.463145	+	0.802191i	−0.999116	−	0.0420460i	$-0.986612\pi$
$23$	−2.22117	+	3.84717i	−0.463145	+	0.802191i	0.535971	+	0.844237i	$0.319946\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.31905	+	4.01671i	−0.454803	+	0.787742i
$27$		0			0
$28$	0.674527	+	0.320353i	0.127474	+	0.0605411i
$29$	6.72577			1.24895			0.624473	−	0.781047i	$-0.285314\pi$
$29$	6.72577			1.24895			0.624473	+	0.781047i	$0.285314\pi$
$30$		0			0
$31$	−3.08846	−	5.34937i	−0.554704	−	0.960776i	−0.997926	−	0.0643642i	$-0.979498\pi$
$31$	−3.08846	−	5.34937i	−0.554704	−	0.960776i	0.443222	−	0.896412i	$-0.353835\pi$
$32$	0.792026	+	1.37183i	0.140012	+	0.242508i
$33$		0			0
$34$	1.97962			0.339502
$35$	−0.211981	−	2.63725i	−0.0358313	−	0.445776i
$36$		0			0
$37$	−4.07564	+	7.05921i	−0.670030	+	1.16053i	0.307865	+	0.951430i	$0.400386\pi$
$37$	−4.07564	+	7.05921i	−0.670030	+	1.16053i	−0.977895	+	0.209096i	$0.932948\pi$
$38$	−3.12127	−	5.40619i	−0.506336	−	0.877000i
$39$		0			0
$40$	1.49559	−	2.59044i	0.236474	−	0.409584i
$41$	4.64966			0.726155			0.363078	−	0.931759i	$-0.381726\pi$
$41$	4.64966			0.726155			0.363078	+	0.931759i	$0.381726\pi$
$42$		0			0
$43$	−3.64084			−0.555223			−0.277612	−	0.960693i	$-0.589543\pi$
$43$	−3.64084			−0.555223			−0.277612	+	0.960693i	$0.589543\pi$
$44$	−0.710736	+	1.23103i	−0.107147	+	0.185585i
$45$		0			0
$46$	2.91113	+	5.04223i	0.429223	+	0.743437i
$47$	−0.938159	+	1.62494i	−0.136845	+	0.237022i	−0.926301	−	0.376785i	$-0.877029\pi$
$47$	−0.938159	+	1.62494i	−0.136845	+	0.237022i	0.789456	+	0.613807i	$0.210363\pi$
$48$		0			0
$49$	2.48677	−	6.54339i	0.355253	−	0.934770i
$50$	−1.31063			−0.185352
$51$		0			0
$52$	−0.499397	−	0.864982i	−0.0692540	−	0.119951i
$53$	−4.69477	−	8.13157i	−0.644876	−	1.11696i	−0.984330	−	0.176335i	$-0.943576\pi$
$53$	−4.69477	−	8.13157i	−0.644876	−	1.11696i	0.339455	−	0.940622i	$-0.389758\pi$
$54$		0			0
$55$	5.03641			0.679109
$56$	6.51458	−	4.49336i	0.870548	−	0.600451i
$57$		0			0
$58$	4.40751	−	7.63404i	0.578735	−	1.00240i
$59$	−3.49899	−	6.06044i	−0.455530	−	0.789002i	0.543188	−	0.839611i	$-0.317217\pi$
$59$	−3.49899	−	6.06044i	−0.455530	−	0.789002i	−0.998719	+	0.0506094i	$0.983884\pi$
$60$		0			0
$61$	2.46655	−	4.27220i	0.315810	−	0.546999i	−0.663800	−	0.747911i	$-0.731057\pi$
$61$	2.46655	−	4.27220i	0.315810	−	0.546999i	0.979609	+	0.200912i	$0.0643905\pi$
$62$	−8.09569			−1.02815
$63$		0			0
$64$	8.78784			1.09848
$65$	−1.76941	+	3.06471i	−0.219469	+	0.380131i
$66$		0			0
$67$	−3.52358	−	6.10302i	−0.430474	−	0.745603i	0.566440	−	0.824103i	$-0.308320\pi$
$67$	−3.52358	−	6.10302i	−0.430474	−	0.745603i	−0.996914	+	0.0785001i	$0.974987\pi$
$68$	−0.213151	+	0.369189i	−0.0258484	+	0.0447707i
$69$		0			0
$70$	−3.13230	−	1.48762i	−0.374381	−	0.177805i
$71$	−9.98514			−1.18502			−0.592509	−	0.805564i	$-0.701863\pi$
$71$	−9.98514			−1.18502			−0.592509	+	0.805564i	$0.701863\pi$
$72$		0			0
$73$	4.07163	+	7.05227i	0.476548	+	0.825405i	0.999639	−	0.0268715i	$-0.00855449\pi$
$73$	4.07163	+	7.05227i	0.476548	+	0.825405i	−0.523091	+	0.852277i	$0.675221\pi$
$74$	5.34167	+	9.25204i	0.620956	+	1.07553i
$75$		0			0
$76$	1.34430			0.154202
$77$	12.0366	+	5.71654i	1.37169	+	0.651460i
$78$		0			0
$79$	7.73055	−	13.3897i	0.869755	−	1.50646i	0.00750748	−	0.999972i	$-0.497610\pi$
$79$	7.73055	−	13.3897i	0.869755	−	1.50646i	0.862247	−	0.506488i	$-0.169056\pi$
$80$	−1.67793	−	2.90626i	−0.187598	−	0.324930i
$81$		0			0
$82$	3.04700	−	5.27756i	0.336485	−	0.582809i
$83$	8.26057			0.906716			0.453358	−	0.891329i	$-0.350226\pi$
$83$	8.26057			0.906716			0.453358	+	0.891329i	$0.350226\pi$
$84$		0			0
$85$	1.51043			0.163829
$86$	−2.38590	+	4.13251i	−0.257279	+	0.445620i
$87$		0			0
$88$	7.53240	+	13.0465i	0.802957	+	1.39076i
$89$	−0.902114	+	1.56251i	−0.0956239	+	0.165625i	−0.909869	−	0.414896i	$-0.863818\pi$
$89$	−0.902114	+	1.56251i	−0.0956239	+	0.165625i	0.814245	+	0.580522i	$0.197151\pi$
$90$		0			0
$91$	−7.70732	+	5.31603i	−0.807946	+	0.557272i
$92$	−1.25380			−0.130718
$93$		0			0
$94$	1.22958	+	2.12970i	0.126822	+	0.219662i
$95$	−2.38149	−	4.12487i	−0.244336	−	0.423203i
$96$		0			0
$97$	−11.5788			−1.17565			−0.587826	−	0.808988i	$-0.700016\pi$
$97$	−11.5788			−1.17565			−0.587826	+	0.808988i	$0.700016\pi$
$98$	−5.79740	−	7.11058i	−0.585626	−	0.718277i
$99$		0			0
$100$	0.141120	−	0.244426i	0.0141120	−	0.0244426i
$101$	3.05866	+	5.29775i	0.304348	+	0.527146i	0.977116	−	0.212707i	$-0.0682281\pi$
$101$	3.05866	+	5.29775i	0.304348	+	0.527146i	−0.672768	+	0.739854i	$0.734895\pi$
$102$		0			0
$103$	−4.05703	+	7.02698i	−0.399751	+	0.692389i	−0.993695	−	0.112118i	$-0.964237\pi$
$103$	−4.05703	+	7.02698i	−0.399751	+	0.692389i	0.593944	+	0.804506i	$0.297570\pi$
$104$	−10.5853			−1.03797
$105$		0			0
$106$	−12.3062			−1.19529
$107$	−6.53516	+	11.3192i	−0.631778	+	1.09427i	0.355410	+	0.934711i	$0.384341\pi$
$107$	−6.53516	+	11.3192i	−0.631778	+	1.09427i	−0.987188	+	0.159561i	$0.948992\pi$
$108$		0			0
$109$	−1.78160	−	3.08582i	−0.170646	−	0.295568i	0.768000	−	0.640450i	$-0.221252\pi$
$109$	−1.78160	−	3.08582i	−0.170646	−	0.295568i	−0.938646	+	0.344882i	$0.887919\pi$
$110$	3.30044	−	5.71654i	0.314685	−	0.545050i
$111$		0			0
$112$	−0.711378	−	8.85023i	−0.0672189	−	0.836268i
$113$	−13.0731			−1.22981			−0.614905	−	0.788601i	$-0.710806\pi$
$113$	−13.0731			−1.22981			−0.614905	+	0.788601i	$0.710806\pi$
$114$		0			0
$115$	2.22117	+	3.84717i	0.207125	+	0.358751i
$116$	0.949139	+	1.64396i	0.0881253	+	0.152638i
$117$		0			0
$118$	−9.17180			−0.844333
$119$	3.60979	+	1.71440i	0.330909	+	0.157159i
$120$		0			0
$121$	−7.18271	+	12.4408i	−0.652973	+	1.13098i
$122$	−3.23275	−	5.59928i	−0.292679	−	0.506935i
$123$		0			0
$124$	0.871685	−	1.50980i	0.0782797	−	0.135584i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.84697			0.518835			0.259417	−	0.965765i	$-0.416470\pi$
$127$	5.84697			0.518835			0.259417	+	0.965765i	$0.416470\pi$
$128$	4.17477	−	7.23091i	0.369001	−	0.639128i
$129$		0			0
$130$	2.31905	+	4.01671i	0.203394	+	0.352289i
$131$	−5.82366	+	10.0869i	−0.508816	+	0.881294i	0.491132	+	0.871085i	$0.336583\pi$
$131$	−5.82366	+	10.0869i	−0.508816	+	0.881294i	−0.999948	+	0.0102094i	$0.996750\pi$
$132$		0			0
$133$	−1.00966	−	12.5612i	−0.0875488	−	1.08919i
$134$	−9.23625			−0.797890
$135$		0			0
$136$	2.25898	+	3.91267i	0.193706	+	0.335509i
$137$	0.351491	+	0.608801i	0.0300299	+	0.0520134i	0.880650	−	0.473768i	$-0.157106\pi$
$137$	0.351491	+	0.608801i	0.0300299	+	0.0520134i	−0.850620	+	0.525781i	$0.823773\pi$
$138$		0			0
$139$	−22.9376			−1.94554			−0.972770	−	0.231773i	$-0.925547\pi$
$139$	−22.9376			−1.94554			−0.972770	+	0.231773i	$0.925547\pi$
$140$	0.614698	−	0.423981i	0.0519514	−	0.0358329i
$141$		0			0
$142$	−6.54343	+	11.3336i	−0.549113	+	0.951091i
$143$	−8.91148	−	15.4351i	−0.745215	−	1.29075i
$144$		0			0
$145$	3.36289	−	5.82469i	0.279273	−	0.483714i
$146$	10.6728			0.883289
$147$		0			0
$148$	−2.30061			−0.189109
$149$	−3.38149	+	5.85692i	−0.277023	+	0.479818i	−0.970643	−	0.240523i	$-0.922681\pi$
$149$	−3.38149	+	5.85692i	−0.277023	+	0.479818i	0.693621	+	0.720340i	$0.256014\pi$
$150$		0			0
$151$	11.7752	+	20.3952i	0.958250	+	1.65974i	0.726749	+	0.686903i	$0.241030\pi$
$151$	11.7752	+	20.3952i	0.958250	+	1.65974i	0.231502	+	0.972835i	$0.425636\pi$
$152$	7.12348	−	12.3382i	0.577790	−	1.00076i
$153$		0			0
$154$	14.3763	−	9.91588i	1.15847	−	0.799044i
$155$	−6.17693			−0.496143
$156$		0			0
$157$	4.11546	+	7.12819i	0.328450	+	0.568892i	0.982204	−	0.187815i	$-0.0601405\pi$
$157$	4.11546	+	7.12819i	0.328450	+	0.568892i	−0.653755	+	0.756707i	$0.726807\pi$
$158$	−10.1319	−	17.5490i	−0.806052	−	1.39612i
$159$		0			0
$160$	1.58405			0.125230
$161$	0.941688	+	11.7155i	0.0742154	+	0.923312i
$162$		0			0
$163$	−10.9463	+	18.9596i	−0.857382	+	1.48503i	0.0170355	+	0.999855i	$0.494577\pi$
$163$	−10.9463	+	18.9596i	−0.857382	+	1.48503i	−0.874417	+	0.485174i	$0.838756\pi$
$164$	0.656158	+	1.13650i	0.0512374	+	0.0887457i
$165$		0			0
$166$	5.41329	−	9.37610i	0.420153	−	0.727726i
$167$	14.9250			1.15493			0.577466	−	0.816415i	$-0.304042\pi$
$167$	14.9250			1.15493			0.577466	+	0.816415i	$0.304042\pi$
$168$		0			0
$169$	−0.476726			−0.0366713
$170$	0.989810	−	1.71440i	0.0759149	−	0.131489i
$171$		0			0
$172$	−0.513794	−	0.889918i	−0.0391764	−	0.0678556i
$173$	7.78359	−	13.4816i	0.591776	−	1.02499i	−0.402218	−	0.915544i	$-0.631761\pi$
$173$	7.78359	−	13.4816i	0.591776	−	1.02499i	0.993993	−	0.109441i	$-0.0349062\pi$
$174$		0			0
$175$	−2.38991	−	1.13504i	−0.180660	−	0.0858011i
$176$	16.9015			1.27400
$177$		0			0
$178$	1.18234	+	2.04788i	0.0886202	+	0.153495i
$179$	3.51824	+	6.09378i	0.262966	+	0.455470i	0.967029	−	0.254667i	$-0.0819660\pi$
$179$	3.51824	+	6.09378i	0.262966	+	0.455470i	−0.704063	+	0.710138i	$0.748633\pi$
$180$		0			0
$181$	−13.1249			−0.975569			−0.487784	−	0.872964i	$-0.662195\pi$
$181$	−13.1249			−0.975569			−0.487784	+	0.872964i	$0.662195\pi$
$182$	0.983188	+	12.2318i	0.0728787	+	0.906682i
$183$		0			0
$184$	−6.64390	+	11.5076i	−0.489795	+	0.848350i
$185$	4.07564	+	7.05921i	0.299647	+	0.519003i
$186$		0			0
$187$	−3.80357	+	6.58798i	−0.278145	+	0.481760i
$188$	−0.529570			−0.0386229
$189$		0			0
$190$	−6.24253			−0.452881
$191$	−9.50099	+	16.4562i	−0.687467	+	1.19073i	0.285187	+	0.958472i	$0.407944\pi$
$191$	−9.50099	+	16.4562i	−0.687467	+	1.19073i	−0.972655	+	0.232257i	$0.925389\pi$
$192$		0			0
$193$	−2.61508	−	4.52946i	−0.188238	−	0.326038i	0.756425	−	0.654081i	$-0.226944\pi$
$193$	−2.61508	−	4.52946i	−0.188238	−	0.326038i	−0.944663	+	0.328043i	$0.893611\pi$
$194$	−7.58780	+	13.1425i	−0.544772	+	0.943573i
$195$		0			0
$196$	1.95031	−	0.315569i	0.139308	−	0.0225406i
$197$	−16.1141			−1.14808			−0.574041	−	0.818827i	$-0.694625\pi$
$197$	−16.1141			−1.14808			−0.574041	+	0.818827i	$0.694625\pi$
$198$		0			0
$199$	−5.70793	−	9.88643i	−0.404625	−	0.700831i	0.589653	−	0.807657i	$-0.299265\pi$
$199$	−5.70793	−	9.88643i	−0.404625	−	0.700831i	−0.994278	+	0.106826i	$0.965931\pi$
$200$	−1.49559	−	2.59044i	−0.105754	−	0.183172i
$201$		0			0
$202$	8.01756			0.564114
$203$	14.6483	−	10.1035i	1.02811	−	0.709125i
$204$		0			0
$205$	2.32483	−	4.02673i	0.162373	−	0.281239i
$206$	5.31728	+	9.20980i	0.370472	+	0.641677i
$207$		0			0
$208$	−5.93790	+	10.2848i	−0.411720	+	0.713119i
$209$	23.9884			1.65931
$210$		0			0
$211$	21.2493			1.46286			0.731431	−	0.681915i	$-0.238853\pi$
$211$	21.2493			1.46286			0.731431	+	0.681915i	$0.238853\pi$
$212$	1.32505	−	2.29505i	0.0910046	−	0.157625i
$213$		0			0
$214$	8.56521	+	14.8354i	0.585505	+	1.01413i
$215$	−1.82042	+	3.15306i	−0.124152	+	0.215037i
$216$		0			0
$217$	−14.7623	−	7.01107i	−1.00213	−	0.475942i
$218$	−4.67004			−0.316295
$219$		0			0
$220$	0.710736	+	1.23103i	0.0479178	+	0.0829961i
$221$	−2.67257	−	4.62903i	−0.179777	−	0.311382i
$222$		0			0
$223$	−19.4592			−1.30308			−0.651541	−	0.758613i	$-0.725877\pi$
$223$	−19.4592			−1.30308			−0.651541	+	0.758613i	$0.725877\pi$
$224$	3.78575	+	1.79797i	0.252946	+	0.120132i
$225$		0			0
$226$	−8.56700	+	14.8385i	−0.569868	+	0.987041i
$227$	−2.06846	−	3.58268i	−0.137289	−	0.237791i	0.789181	−	0.614161i	$-0.210505\pi$
$227$	−2.06846	−	3.58268i	−0.137289	−	0.237791i	−0.926469	+	0.376370i	$0.877172\pi$
$228$		0			0
$229$	−5.07960	+	8.79813i	−0.335670	+	0.581397i	−0.983613	−	0.180291i	$-0.942296\pi$
$229$	−5.07960	+	8.79813i	−0.335670	+	0.581397i	0.647944	+	0.761688i	$0.275629\pi$
$230$	5.82227			0.383909
$231$		0			0
$232$	20.1180			1.32081
$233$	8.98939	−	15.5701i	0.588914	−	1.02003i	−0.405460	−	0.914113i	$-0.632889\pi$
$233$	8.98939	−	15.5701i	0.588914	−	1.02003i	0.994375	−	0.105917i	$-0.0337779\pi$
$234$		0			0
$235$	0.938159	+	1.62494i	0.0611987	+	0.105999i
$236$	0.987553	−	1.71049i	0.0642842	−	0.111344i
$237$		0			0
$238$	4.31148	−	2.97379i	0.279471	−	0.192762i
$239$	2.64692			0.171215			0.0856076	−	0.996329i	$-0.472717\pi$
$239$	2.64692			0.171215			0.0856076	+	0.996329i	$0.472717\pi$
$240$		0			0
$241$	−6.45788	−	11.1854i	−0.415989	−	0.720513i	0.579543	−	0.814942i	$-0.303231\pi$
$241$	−6.45788	−	11.1854i	−0.415989	−	0.720513i	−0.995532	+	0.0944282i	$0.969898\pi$
$242$	9.41390	+	16.3053i	0.605148	+	1.04815i
$243$		0			0
$244$	1.39232			0.0891339
$245$	−4.42336	−	5.42530i	−0.282598	−	0.346610i
$246$		0			0
$247$	−8.42769	+	14.5972i	−0.536241	+	0.928797i
$248$	−9.23815	−	16.0009i	−0.586623	−	1.01606i
$249$		0			0
$250$	−0.655317	+	1.13504i	−0.0414459	+	0.0717864i
$251$	21.8811			1.38112			0.690560	−	0.723275i	$-0.257364\pi$
$251$	21.8811			1.38112			0.690560	+	0.723275i	$0.257364\pi$
$252$		0			0
$253$	−22.3734			−1.40660
$254$	3.83162	−	6.63655i	0.240417	−	0.416414i
$255$		0			0
$256$	3.31625	+	5.74391i	0.207266	+	0.358994i
$257$	−10.8993	+	18.8782i	−0.679881	+	1.17759i	0.295136	+	0.955455i	$0.404635\pi$
$257$	−10.8993	+	18.8782i	−0.679881	+	1.17759i	−0.975016	+	0.222133i	$0.928698\pi$
$258$		0			0
$259$	1.72791	+	21.4969i	0.107367	+	1.33575i
$260$	−0.998795			−0.0619426
$261$		0			0
$262$	7.63269	+	13.2202i	0.471549	+	0.816747i
$263$	8.64851	+	14.9797i	0.533290	+	0.923685i	0.999244	+	0.0388763i	$0.0123778\pi$
$263$	8.64851	+	14.9797i	0.533290	+	0.923685i	−0.465954	+	0.884809i	$0.654289\pi$
$264$		0			0
$265$	−9.38953			−0.576794
$266$	−14.9191	−	7.08554i	−0.914749	−	0.434442i
$267$		0			0
$268$	0.994493	−	1.72251i	0.0607483	−	0.105219i
$269$	−12.0346	−	20.8445i	−0.733760	−	1.27091i	−0.955265	−	0.295751i	$-0.904430\pi$
$269$	−12.0346	−	20.8445i	−0.733760	−	1.27091i	0.221505	−	0.975159i	$-0.428903\pi$
$270$		0			0
$271$	12.3897	−	21.4595i	0.752619	−	1.30357i	−0.193930	−	0.981015i	$-0.562124\pi$
$271$	12.3897	−	21.4595i	0.752619	−	1.30357i	0.946549	−	0.322559i	$-0.104543\pi$
$272$	5.06879			0.307341
$273$		0			0
$274$	0.921353			0.0556610
$275$	2.51820	−	4.36166i	0.151853	−	0.263018i
$276$		0			0
$277$	−7.16734	−	12.4142i	−0.430644	−	0.745897i	0.566285	−	0.824209i	$-0.308380\pi$
$277$	−7.16734	−	12.4142i	−0.430644	−	0.745897i	−0.996929	+	0.0783127i	$0.975047\pi$
$278$	−15.0314	+	26.0351i	−0.901522	+	1.56148i
$279$		0			0
$280$	−0.634072	−	7.88848i	−0.0378931	−	0.471427i
$281$	15.0012			0.894895			0.447447	−	0.894310i	$-0.352333\pi$
$281$	15.0012			0.894895			0.447447	+	0.894310i	$0.352333\pi$
$282$		0			0
$283$	10.6507	+	18.4475i	0.633116	+	1.09659i	0.986911	+	0.161265i	$0.0515575\pi$
$283$	10.6507	+	18.4475i	0.633116	+	1.09659i	−0.353796	+	0.935323i	$0.615109\pi$
$284$	−1.40910	−	2.44063i	−0.0836147	−	0.144825i
$285$		0			0
$286$	−23.3594			−1.38127
$287$	10.1266	−	6.98474i	0.597757	−	0.412296i
$288$		0			0
$289$	7.35930	−	12.7467i	0.432900	−	0.749805i
$290$	−4.40751	−	7.63404i	−0.258818	−	0.448286i
$291$		0			0
$292$	−1.14917	+	1.99043i	−0.0672503	+	0.116481i
$293$	−25.8451			−1.50989			−0.754944	−	0.655790i	$-0.772336\pi$
$293$	−25.8451			−1.50989			−0.754944	+	0.655790i	$0.772336\pi$
$294$		0			0
$295$	−6.99799			−0.407439
$296$	−12.1910	+	21.1154i	−0.708585	+	1.22731i
$297$		0			0
$298$	4.43190	+	7.67628i	0.256733	+	0.444675i
$299$	7.86031	−	13.6145i	0.454574	−	0.787345i
$300$		0			0
$301$	−7.92950	+	5.46928i	−0.457049	+	0.315244i
$302$	30.8659			1.77613
$303$		0			0
$304$	−7.99197	−	13.8425i	−0.458371	−	0.793922i
$305$	−2.46655	−	4.27220i	−0.141234	−	0.244625i
$306$		0			0
$307$	−11.4637			−0.654266			−0.327133	−	0.944978i	$-0.606083\pi$
$307$	−11.4637			−0.654266			−0.327133	+	0.944978i	$0.606083\pi$
$308$	0.301325	+	3.74877i	0.0171696	+	0.213606i
$309$		0			0
$310$	−4.04784	+	7.01107i	−0.229902	+	0.398202i
$311$	8.50781	+	14.7360i	0.482434	+	0.835600i	0.999797	−	0.0201662i	$-0.00641953\pi$
$311$	8.50781	+	14.7360i	0.482434	+	0.835600i	−0.517363	+	0.855766i	$0.673086\pi$
$312$		0			0
$313$	9.10314	−	15.7671i	0.514540	−	0.891209i	−0.485318	−	0.874338i	$-0.661296\pi$
$313$	9.10314	−	15.7671i	0.514540	−	0.891209i	0.999858	−	0.0168712i	$-0.00537053\pi$
$314$	10.7877			0.608787
$315$		0			0
$316$	4.36373			0.245479
$317$	3.80447	−	6.58953i	0.213680	−	0.370105i	−0.739183	−	0.673504i	$-0.764788\pi$
$317$	3.80447	−	6.58953i	0.213680	−	0.370105i	0.952863	+	0.303399i	$0.0981216\pi$
$318$		0			0
$319$	16.9369	+	29.3355i	0.948283	+	1.64247i
$320$	4.39392	−	7.61049i	0.245628	−	0.425439i
$321$		0			0
$322$	13.9147	+	6.60852i	0.775436	+	0.368278i
$323$	7.19416			0.400294
$324$		0			0
$325$	1.76941	+	3.06471i	0.0981493	+	0.170000i
$326$	14.3466	+	24.8491i	0.794586	+	1.37626i
$327$		0			0
$328$	13.9080			0.767939
$329$	0.397743	+	4.94831i	0.0219283	+	0.272809i
$330$		0			0
$331$	4.18750	−	7.25296i	0.230166	−	0.398659i	−0.727691	−	0.685905i	$-0.759407\pi$
$331$	4.18750	−	7.25296i	0.230166	−	0.398659i	0.957857	+	0.287246i	$0.0927399\pi$
$332$	1.16573	+	2.01910i	0.0639777	+	0.110813i
$333$		0			0
$334$	9.78061	−	16.9405i	0.535171	−	0.926944i
$335$	−7.04716			−0.385028
$336$		0			0
$337$	−13.8554			−0.754753			−0.377376	−	0.926060i	$-0.623174\pi$
$337$	−13.8554			−0.754753			−0.377376	+	0.926060i	$0.623174\pi$
$338$	−0.312407	+	0.541104i	−0.0169927	+	0.0294322i
$339$		0			0
$340$	0.213151	+	0.369189i	0.0115597	+	0.0200221i
$341$	15.5548	−	26.9416i	0.842338	−	1.45897i
$342$		0			0
$343$	−4.41349	−	17.9867i	−0.238306	−	0.971190i
$344$	−10.8904			−0.587172
$345$		0			0
$346$	−10.2014	−	17.6694i	−0.548433	−	0.949913i
$347$	9.10061	+	15.7627i	0.488546	+	0.846187i	0.999913	−	0.0131755i	$-0.00419401\pi$
$347$	9.10061	+	15.7627i	0.488546	+	0.846187i	−0.511367	+	0.859362i	$0.670861\pi$
$348$		0			0
$349$	−36.3329			−1.94486			−0.972428	−	0.233203i	$-0.925079\pi$
$349$	−36.3329			−1.94486			−0.972428	+	0.233203i	$0.925079\pi$
$350$	−2.85447	+	1.96884i	−0.152578	+	0.105239i
$351$		0			0
$352$	−3.98897	+	6.90910i	−0.212613	+	0.368256i
$353$	−4.26162	−	7.38134i	−0.226823	−	0.392869i	0.730042	−	0.683403i	$-0.239501\pi$
$353$	−4.26162	−	7.38134i	−0.226823	−	0.392869i	−0.956865	+	0.290533i	$0.906167\pi$
$354$		0			0
$355$	−4.99257	+	8.64739i	−0.264978	+	0.458956i
$356$	−0.509224			−0.0269888
$357$		0			0
$358$	9.22226			0.487411
$359$	0.701466	−	1.21497i	0.0370219	−	0.0641239i	−0.846921	−	0.531719i	$-0.821546\pi$
$359$	0.701466	−	1.21497i	0.0370219	−	0.0641239i	0.883943	+	0.467595i	$0.154880\pi$
$360$		0			0
$361$	−1.84304	−	3.19223i	−0.0970019	−	0.168012i
$362$	−8.60099	+	14.8974i	−0.452058	+	0.782987i
$363$		0			0
$364$	−2.38703	−	1.13367i	−0.125114	−	0.0594207i
$365$	8.14326			0.426238
$366$		0			0
$367$	−1.29853	−	2.24913i	−0.0677829	−	0.117403i	0.830142	−	0.557552i	$-0.188259\pi$
$367$	−1.29853	−	2.24913i	−0.0677829	−	0.117403i	−0.897925	+	0.440148i	$0.854926\pi$
$368$	7.45393	+	12.9106i	0.388563	+	0.673010i
$369$		0			0
$370$	10.6833			0.555400
$371$	−22.4402	−	10.6575i	−1.16503	−	0.553311i
$372$		0			0
$373$	18.9396	−	32.8044i	0.980656	−	1.69855i	0.320815	−	0.947142i	$-0.396043\pi$
$373$	18.9396	−	32.8044i	0.980656	−	1.69855i	0.659842	−	0.751405i	$-0.270623\pi$
$374$	4.98509	+	8.63442i	0.257773	+	0.446475i
$375$		0			0
$376$	−2.80620	+	4.86048i	−0.144719	+	0.250660i
$377$	−23.8013			−1.22583
$378$		0			0
$379$	12.7422			0.654522			0.327261	−	0.944934i	$-0.393874\pi$
$379$	12.7422			0.654522			0.327261	+	0.944934i	$0.393874\pi$
$380$	0.672151	−	1.16420i	0.0344806	−	0.0597222i
$381$		0			0
$382$	12.4523	+	21.5680i	0.637116	+	1.10352i
$383$	14.6880	−	25.4404i	0.750523	−	1.29994i	−0.197046	−	0.980394i	$-0.563135\pi$
$383$	14.6880	−	25.4404i	0.750523	−	1.29994i	0.947569	−	0.319550i	$-0.103532\pi$
$384$		0			0
$385$	10.9690	−	7.56571i	0.559030	−	0.385584i
$386$	−6.85484			−0.348902
$387$		0			0
$388$	−1.63400	−	2.83017i	−0.0829537	−	0.143680i
$389$	−5.19763	−	9.00256i	−0.263530	−	0.456448i	0.703647	−	0.710550i	$-0.251554\pi$
$389$	−5.19763	−	9.00256i	−0.263530	−	0.456448i	−0.967178	+	0.254102i	$0.918220\pi$
$390$		0			0
$391$	−6.70983			−0.339330
$392$	7.43837	−	19.5725i	0.375695	−	0.988559i
$393$		0			0
$394$	−10.5598	+	18.2902i	−0.531997	+	0.921446i
$395$	−7.73055	−	13.3897i	−0.388966	−	0.673709i
$396$		0			0
$397$	13.3645	−	23.1480i	0.670746	−	1.16177i	−0.306947	−	0.951727i	$-0.599307\pi$
$397$	13.3645	−	23.1480i	0.670746	−	1.16177i	0.977693	−	0.210039i	$-0.0673593\pi$
$398$	−14.9620			−0.749978
$399$		0			0
$400$	−3.35586			−0.167793
$401$	−10.7204	+	18.5683i	−0.535352	+	0.927257i	0.463794	+	0.885943i	$0.346488\pi$
$401$	−10.7204	+	18.5683i	−0.535352	+	0.927257i	−0.999146	+	0.0413142i	$0.986846\pi$
$402$		0			0
$403$	10.9295	+	18.9305i	0.544438	+	0.942995i
$404$	−0.863273	+	1.49523i	−0.0429495	+	0.0743906i
$405$		0			0
$406$	−1.86862	−	23.2474i	−0.0927378	−	1.15375i
$407$	−41.0531			−2.03493
$408$		0			0
$409$	9.64493	+	16.7055i	0.476911	+	0.826034i	0.999650	−	0.0264588i	$-0.00842308\pi$
$409$	9.64493	+	16.7055i	0.476911	+	0.826034i	−0.522739	+	0.852493i	$0.675090\pi$
$410$	−3.04700	−	5.27756i	−0.150481	−	0.260640i
$411$		0			0
$412$	−2.29010			−0.112825
$413$	−16.7246	−	7.94301i	−0.822963	−	0.390850i
$414$		0			0
$415$	4.13029	−	7.15387i	0.202748	−	0.351170i
$416$	−2.80284	−	4.85466i	−0.137421	−	0.238019i
$417$		0			0
$418$	15.7200	−	27.2278i	0.768889	−	1.33176i
$419$	−31.2412			−1.52623			−0.763116	−	0.646261i	$-0.776332\pi$
$419$	−31.2412			−1.52623			−0.763116	+	0.646261i	$0.776332\pi$
$420$		0			0
$421$	34.1516			1.66445			0.832223	−	0.554442i	$-0.187068\pi$
$421$	34.1516			1.66445			0.832223	+	0.554442i	$0.187068\pi$
$422$	13.9250	−	24.1188i	0.677860	−	1.17409i
$423$		0			0
$424$	−14.0429	−	24.3230i	−0.681983	−	1.18123i
$425$	0.755215	−	1.30807i	0.0366333	−	0.0634507i
$426$		0			0
$427$	−1.04572	−	13.0098i	−0.0506061	−	0.629589i
$428$	−3.68896			−0.178313
$429$		0			0
$430$	2.38590	+	4.13251i	0.115059	+	0.199287i
$431$	−17.2968	−	29.9589i	−0.833157	−	1.44307i	−0.895522	−	0.445017i	$-0.853198\pi$
$431$	−17.2968	−	29.9589i	−0.833157	−	1.44307i	0.0623656	−	0.998053i	$-0.480136\pi$
$432$		0			0
$433$	32.0346			1.53948			0.769742	−	0.638356i	$-0.220385\pi$
$433$	32.0346			1.53948			0.769742	+	0.638356i	$0.220385\pi$
$434$	−17.6319	+	12.1614i	−0.846356	+	0.583764i
$435$		0			0
$436$	0.502837	−	0.870938i	0.0240815	−	0.0417104i
$437$	10.5794	+	18.3240i	0.506081	+	0.876558i
$438$		0			0
$439$	−2.96480	+	5.13518i	−0.141502	+	0.245089i	−0.928062	−	0.372425i	$-0.878527\pi$
$439$	−2.96480	+	5.13518i	−0.141502	+	0.245089i	0.786560	+	0.617513i	$0.211860\pi$
$440$	15.0648			0.718186
$441$		0			0
$442$	−7.00552			−0.333219
$443$	0.164137	−	0.284294i	0.00779839	−	0.0135072i	−0.862100	−	0.506738i	$-0.830851\pi$
$443$	0.164137	−	0.284294i	0.00779839	−	0.0135072i	0.869898	+	0.493231i	$0.164184\pi$
$444$		0			0
$445$	0.902114	+	1.56251i	0.0427643	+	0.0740700i
$446$	−12.7519	+	22.0870i	−0.603821	+	1.04585i
$447$		0			0
$448$	19.1393	−	13.2011i	0.904247	−	0.623694i
$449$	3.28231			0.154902			0.0774509	−	0.996996i	$-0.475322\pi$
$449$	3.28231			0.154902			0.0774509	+	0.996996i	$0.475322\pi$
$450$		0			0
$451$	11.7088	+	20.2802i	0.551346	+	0.954959i
$452$	−1.84487	−	3.19540i	−0.0867752	−	0.150299i
$453$		0			0
$454$	−5.42199			−0.254467
$455$	0.750162	+	9.33275i	0.0351682	+	0.437526i
$456$		0			0
$457$	10.9021	−	18.8829i	0.509977	−	0.883306i	−0.489956	−	0.871747i	$-0.662987\pi$
$457$	10.9021	−	18.8829i	0.509977	−	0.883306i	0.999933	−	0.0115588i	$-0.00367935\pi$
$458$	6.65750	+	11.5311i	0.311084	+	0.538814i
$459$		0			0
$460$	−0.626900	+	1.08582i	−0.0292294	+	0.0506267i
$461$	−6.55824			−0.305448			−0.152724	−	0.988269i	$-0.548805\pi$
$461$	−6.55824			−0.305448			−0.152724	+	0.988269i	$0.548805\pi$
$462$		0			0
$463$	4.40172			0.204565			0.102283	−	0.994755i	$-0.467385\pi$
$463$	4.40172			0.204565			0.102283	+	0.994755i	$0.467385\pi$
$464$	11.2854	−	19.5469i	0.523911	−	0.907440i
$465$		0			0
$466$	−11.7818	−	20.4067i	−0.545781	−	0.945321i
$467$	−3.83554	+	6.64335i	−0.177488	+	0.307417i	−0.941019	−	0.338353i	$-0.890130\pi$
$467$	−3.83554	+	6.64335i	−0.177488	+	0.307417i	0.763532	+	0.645770i	$0.223464\pi$
$468$		0			0
$469$	−16.8421	−	7.99883i	−0.777696	−	0.369351i
$470$	2.45916			0.113433
$471$		0			0
$472$	−10.4661	−	18.1279i	−0.481742	−	0.834402i
$473$	−9.16838	−	15.8801i	−0.421563	−	0.730168i
$474$		0			0
$475$	−4.76299			−0.218541
$476$	0.0903679	+	1.12426i	0.00414200	+	0.0515306i
$477$		0			0
$478$	1.73457	−	3.00437i	0.0793375	−	0.137417i
$479$	7.34733	+	12.7260i	0.335708	+	0.581464i	0.983621	−	0.180251i	$-0.0576911\pi$
$479$	7.34733	+	12.7260i	0.335708	+	0.581464i	−0.647912	+	0.761715i	$0.724358\pi$
$480$		0			0
$481$	14.4230	−	24.9813i	0.657630	−	1.13905i
$482$	−16.9278			−0.771042
$483$		0			0
$484$	−4.05448			−0.184295
$485$	−5.78941	+	10.0276i	−0.262884	+	0.455328i
$486$		0			0
$487$	3.32591	+	5.76065i	0.150711	+	0.261040i	0.931489	−	0.363769i	$-0.118510\pi$
$487$	3.32591	+	5.76065i	0.150711	+	0.261040i	−0.780778	+	0.624809i	$0.785177\pi$
$488$	7.37790	−	12.7789i	0.333982	−	0.578474i
$489$		0			0
$490$	−9.05665	+	1.46541i	−0.409138	+	0.0662003i
$491$	8.53854			0.385339			0.192669	−	0.981264i	$-0.438285\pi$
$491$	8.53854			0.385339			0.192669	+	0.981264i	$0.438285\pi$
$492$		0			0
$493$	5.07940	+	8.79778i	0.228765	+	0.396232i
$494$	11.0456	+	19.1316i	0.496966	+	0.860770i
$495$		0			0
$496$	−20.7289			−0.930756
$497$	−21.7470	+	14.9997i	−0.975484	+	0.672829i
$498$		0			0
$499$	−8.53764	+	14.7876i	−0.382197	+	0.661985i	−0.991376	−	0.131048i	$-0.958166\pi$
$499$	−8.53764	+	14.7876i	−0.382197	+	0.661985i	0.609179	+	0.793033i	$0.291499\pi$
$500$	−0.141120	−	0.244426i	−0.00631106	−	0.0109311i
$501$		0			0
$502$	14.3390	−	24.8359i	0.639982	−	1.10848i
$503$	−18.4481			−0.822562			−0.411281	−	0.911509i	$-0.634918\pi$
$503$	−18.4481			−0.822562			−0.411281	+	0.911509i	$0.634918\pi$
$504$		0			0
$505$	6.11732			0.272217
$506$	−14.6617	+	25.3947i	−0.651790	+	1.12893i
$507$		0			0
$508$	0.825122	+	1.42915i	0.0366089	+	0.0634084i
$509$	1.30999	−	2.26897i	0.0580644	−	0.100570i	−0.835532	−	0.549442i	$-0.814840\pi$
$509$	1.30999	−	2.26897i	0.0580644	−	0.100570i	0.893596	+	0.448871i	$0.148174\pi$
$510$		0			0
$511$	19.4617	+	9.24294i	0.860933	+	0.408884i
$512$	25.3918			1.12217
$513$		0			0
$514$	14.2850	+	24.7424i	0.630085	+	1.09134i
$515$	4.05703	+	7.02698i	0.178774	+	0.309646i
$516$		0			0
$517$	−9.44990			−0.415606
$518$	25.5322	+	12.1260i	1.12182	+	0.532787i
$519$		0			0
$520$	−5.29263	+	9.16710i	−0.232097	+	0.402004i
$521$	18.5419	+	32.1156i	0.812337	+	1.40701i	0.911224	+	0.411910i	$0.135138\pi$
$521$	18.5419	+	32.1156i	0.812337	+	1.40701i	−0.0988877	+	0.995099i	$0.531528\pi$
$522$		0			0
$523$	−14.5577	+	25.2146i	−0.636562	+	1.10256i	0.349620	+	0.936892i	$0.386311\pi$
$523$	−14.5577	+	25.2146i	−0.636562	+	1.10256i	−0.986182	+	0.165666i	$0.947023\pi$
$524$	−3.28733			−0.143608
$525$		0			0
$526$	22.6701			0.988461
$527$	4.66490	−	8.07985i	0.203206	−	0.351964i
$528$		0			0
$529$	1.63285	+	2.82818i	0.0709935	+	0.122964i
$530$	−6.15312	+	10.6575i	−0.267274	+	0.462933i
$531$		0			0
$532$	2.92780	−	2.01942i	0.126936	−	0.0875528i
$533$	−16.4543			−0.712716
$534$		0			0
$535$	6.53516	+	11.3192i	0.282540	+	0.489373i
$536$	−10.5397	−	18.2552i	−0.455244	−	0.788506i
$537$		0			0
$538$	−31.5458			−1.36004
$539$	34.8022	−	5.63116i	1.49904	−	0.242551i
$540$		0			0
$541$	−11.2639	+	19.5096i	−0.484271	+	0.838783i	−0.999837	−	0.0180676i	$-0.994249\pi$
$541$	−11.2639	+	19.5096i	−0.484271	+	0.838783i	0.515565	+	0.856850i	$0.327582\pi$
$542$	−16.2383	−	28.1256i	−0.697496	−	1.20810i
$543$		0			0
$544$	−1.19630	+	2.07205i	−0.0512909	+	0.0888385i
$545$	−3.56319			−0.152630
$546$		0			0
$547$	18.6039			0.795444			0.397722	−	0.917506i	$-0.369801\pi$
$547$	18.6039			0.795444			0.397722	+	0.917506i	$0.369801\pi$
$548$	−0.0992046	+	0.171827i	−0.00423781	+	0.00734011i
$549$		0			0
$550$	−3.30044	−	5.71654i	−0.140731	−	0.243754i
$551$	16.0174	−	27.7429i	0.682364	−	1.18189i
$552$		0			0
$553$	−3.27745	−	40.7747i	−0.139372	−	1.73392i
$554$	−18.7875			−0.798205
$555$		0			0
$556$	−3.23694	−	5.60655i	−0.137277	−	0.237771i
$557$	6.35773	+	11.0119i	0.269386	+	0.466589i	0.968703	−	0.248221i	$-0.0798461\pi$
$557$	6.35773	+	11.0119i	0.269386	+	0.466589i	−0.699318	+	0.714811i	$0.746513\pi$
$558$		0			0
$559$	12.8843			0.544948
$560$	−8.02022	−	3.80905i	−0.338916	−	0.160962i
$561$		0			0
$562$	9.83052	−	17.0270i	0.414676	−	0.718239i
$563$	16.8193	+	29.1318i	0.708848	+	1.22776i	0.965285	+	0.261200i	$0.0841181\pi$
$563$	16.8193	+	29.1318i	0.708848	+	1.22776i	−0.256437	+	0.966561i	$0.582549\pi$
$564$		0			0
$565$	−6.53653	+	11.3216i	−0.274994	+	0.476304i
$566$	27.9182			1.17349
$567$		0			0
$568$	−29.8674			−1.25321
$569$	12.1346	−	21.0178i	0.508711	−	0.881113i	−0.491238	−	0.871025i	$-0.663456\pi$
$569$	12.1346	−	21.0178i	0.508711	−	0.881113i	0.999949	−	0.0100875i	$-0.00321102\pi$
$570$		0			0
$571$	−10.6506	−	18.4474i	−0.445714	−	0.772000i	0.552387	−	0.833587i	$-0.313717\pi$
$571$	−10.6506	−	18.4474i	−0.445714	−	0.772000i	−0.998102	+	0.0615878i	$0.980384\pi$
$572$	2.51517	−	4.35640i	0.105165	−	0.182150i
$573$		0			0
$574$	−1.29181	−	16.0714i	−0.0539192	−	0.670807i
$575$	4.44233			0.185258
$576$		0			0
$577$	−10.5186	−	18.2187i	−0.437893	−	0.758453i	0.559634	−	0.828740i	$-0.310942\pi$
$577$	−10.5186	−	18.2187i	−0.437893	−	0.758453i	−0.997527	+	0.0702870i	$0.977608\pi$
$578$	−9.64535	−	16.7062i	−0.401194	−	0.694888i
$579$		0			0
$580$	1.89828			0.0788217
$581$	17.9910	−	12.4091i	0.746391	−	0.514815i
$582$		0			0
$583$	23.6448	−	40.9539i	0.979266	−	1.69614i
$584$	12.1790	+	21.0946i	0.503969	+	0.872901i
$585$		0			0
$586$	−16.9367	+	29.3353i	−0.699650	+	1.21183i
$587$	−29.7134			−1.22640			−0.613202	−	0.789926i	$-0.710119\pi$
$587$	−29.7134			−1.22640			−0.613202	+	0.789926i	$0.710119\pi$
$588$		0			0
$589$	−29.4206			−1.21226
$590$	−4.58590	+	7.94301i	−0.188799	+	0.327009i
$591$		0			0
$592$	13.6773	+	23.6897i	0.562132	+	0.973642i
$593$	14.6206	−	25.3237i	0.600397	−	1.03992i	−0.392364	−	0.919810i	$-0.628343\pi$
$593$	14.6206	−	25.3237i	0.600397	−	1.03992i	0.992761	−	0.120108i	$-0.0383241\pi$
$594$		0			0
$595$	3.28961	−	2.26897i	0.134861	−	0.0930188i
$596$	−1.90878			−0.0781867
$597$		0			0
$598$	−10.3020	−	17.8436i	−0.421280	−	0.729678i
$599$	−21.9777	−	38.0664i	−0.897983	−	1.55535i	−0.830069	−	0.557661i	$-0.811699\pi$
$599$	−21.9777	−	38.0664i	−0.897983	−	1.55535i	−0.0679138	−	0.997691i	$-0.521634\pi$
$600$		0			0
$601$	32.1919			1.31313			0.656567	−	0.754267i	$-0.272008\pi$
$601$	32.1919			1.31313			0.656567	+	0.754267i	$0.272008\pi$
$602$	1.01153	+	12.5844i	0.0412270	+	0.512903i
$603$		0			0
$604$	−3.32342	+	5.75633i	−0.135228	+	0.234222i
$605$	7.18271	+	12.4408i	0.292019	+	0.505791i
$606$		0			0
$607$	12.7907	−	22.1541i	0.519159	−	0.899209i	−0.480593	−	0.876944i	$-0.659579\pi$
$607$	12.7907	−	22.1541i	0.519159	−	0.899209i	0.999752	−	0.0222656i	$-0.00708795\pi$
$608$	7.54483			0.305983
$609$		0			0
$610$	−6.46550			−0.261780
$611$	3.31998	−	5.75037i	0.134312	−	0.232635i
$612$		0			0
$613$	−4.80322	−	8.31943i	−0.194000	−	0.336018i	0.752572	−	0.658510i	$-0.228813\pi$
$613$	−4.80322	−	8.31943i	−0.194000	−	0.336018i	−0.946572	+	0.322492i	$0.895480\pi$
$614$	−7.51233	+	13.0117i	−0.303173	+	0.525111i
$615$		0			0
$616$	36.0036	+	17.0992i	1.45062	+	0.688946i
$617$	13.4891			0.543052			0.271526	−	0.962431i	$-0.412472\pi$
$617$	13.4891			0.543052			0.271526	+	0.962431i	$0.412472\pi$
$618$		0			0
$619$	−3.69577	−	6.40126i	−0.148546	−	0.257289i	0.782145	−	0.623097i	$-0.214126\pi$
$619$	−3.69577	−	6.40126i	−0.148546	−	0.257289i	−0.930690	+	0.365808i	$0.880793\pi$
$620$	−0.871685	−	1.50980i	−0.0350077	−	0.0606352i
$621$		0			0
$622$	22.3013			0.894199
$623$	0.382462	+	4.75819i	0.0153230	+	0.190633i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−11.9309	−	20.6649i	−0.476854	−	0.825935i
$627$		0			0
$628$	−1.16155	+	2.01186i	−0.0463507	+	0.0802818i
$629$	−12.3119			−0.490908
$630$		0			0
$631$	41.7055			1.66027			0.830134	−	0.557564i	$-0.188264\pi$
$631$	41.7055			1.66027			0.830134	+	0.557564i	$0.188264\pi$
$632$	23.1235	−	40.0510i	0.919802	−	1.59314i
$633$		0			0
$634$	−4.98626	−	8.63646i	−0.198030	−	0.342998i
$635$	2.92348	−	5.06362i	0.116015	−	0.200944i
$636$		0			0
$637$	−8.80024	+	23.1559i	−0.348678	+	0.917471i
$638$	44.3961			1.75766
$639$		0			0
$640$	−4.17477	−	7.23091i	−0.165022	−	0.285827i
$641$	−5.66474	−	9.81162i	−0.223744	−	0.387536i	0.732198	−	0.681092i	$-0.238495\pi$
$641$	−5.66474	−	9.81162i	−0.223744	−	0.387536i	−0.955942	+	0.293556i	$0.905161\pi$
$642$		0			0
$643$	29.5254			1.16437			0.582184	−	0.813057i	$-0.302198\pi$
$643$	29.5254			1.16437			0.582184	+	0.813057i	$0.302198\pi$
$644$	−2.73069	+	1.88346i	−0.107604	+	0.0742188i
$645$		0			0
$646$	4.71445	−	8.16567i	0.185488	−	0.321274i
$647$	4.02009	+	6.96299i	0.158046	+	0.273744i	0.934164	−	0.356844i	$-0.116147\pi$
$647$	4.02009	+	6.96299i	0.158046	+	0.273744i	−0.776118	+	0.630588i	$0.782814\pi$
$648$		0			0
$649$	17.6224	−	30.5228i	0.691738	−	1.19813i
$650$	4.63810			0.181921
$651$		0			0
$652$	−6.17896			−0.241987
$653$	−13.8396	+	23.9709i	−0.541586	+	0.938054i	0.457227	+	0.889350i	$0.348843\pi$
$653$	−13.8396	+	23.9709i	−0.541586	+	0.938054i	−0.998813	+	0.0487045i	$0.984491\pi$
$654$		0			0
$655$	5.82366	+	10.0869i	0.227549	+	0.394127i
$656$	7.80181	−	13.5131i	0.304610	−	0.527599i
$657$		0			0
$658$	5.87719	+	2.79126i	0.229117	+	0.108814i
$659$	−16.8807			−0.657579			−0.328790	−	0.944403i	$-0.606641\pi$
$659$	−16.8807			−0.657579			−0.328790	+	0.944403i	$0.606641\pi$
$660$		0			0
$661$	−5.42709	−	9.39999i	−0.211089	−	0.365617i	0.740966	−	0.671542i	$-0.234368\pi$
$661$	−5.42709	−	9.39999i	−0.211089	−	0.365617i	−0.952056	+	0.305925i	$0.901034\pi$
$662$	−5.48827	−	9.50597i	−0.213308	−	0.369460i
$663$		0			0
$664$	24.7089			0.958890
$665$	−11.3831	−	5.40619i	−0.441419	−	0.209643i
$666$		0			0
$667$	−14.9391	+	25.8752i	−0.578443	+	1.00189i
$668$	2.10621	+	3.64807i	0.0814918	+	0.141148i
$669$		0			0
$670$	−4.61812	+	7.99883i	−0.178414	+	0.309022i
$671$	24.8451			0.959136
$672$		0			0
$673$	−28.3291			−1.09201			−0.546003	−	0.837783i	$-0.683851\pi$
$673$	−28.3291			−1.09201			−0.546003	+	0.837783i	$0.683851\pi$
$674$	−9.07969	+	15.7265i	−0.349736	+	0.605761i
$675$		0			0
$676$	−0.0672754	−	0.116524i	−0.00258752	−	0.00448171i
$677$	−0.120717	+	0.209087i	−0.00463952	+	0.00803588i	−0.868336	−	0.495977i	$-0.834810\pi$
$677$	−0.120717	+	0.209087i	−0.00463952	+	0.00803588i	0.863696	+	0.504013i	$0.168143\pi$
$678$		0			0
$679$	−25.2179	+	17.3937i	−0.967773	+	0.667511i
$680$	4.51797			0.173256
$681$		0			0
$682$	−20.3866	−	35.3106i	−0.780643	−	1.35211i
$683$	7.74424	+	13.4134i	0.296325	+	0.513250i	0.975292	−	0.220918i	$-0.0709055\pi$
$683$	7.74424	+	13.4134i	0.296325	+	0.513250i	−0.678967	+	0.734169i	$0.737572\pi$
$684$		0			0
$685$	0.702983			0.0268596
$686$	−23.3079	−	6.77748i	−0.889899	−	0.258765i
$687$		0			0
$688$	−6.10908	+	10.5812i	−0.232907	+	0.403406i
$689$	16.6139	+	28.7762i	0.632941	+	1.09629i
$690$		0			0
$691$	−8.59357	+	14.8845i	−0.326915	+	0.566233i	−0.981898	−	0.189410i	$-0.939342\pi$
$691$	−8.59357	+	14.8845i	−0.326915	+	0.566233i	0.654983	+	0.755643i	$0.272676\pi$
$692$	4.39367			0.167022
$693$		0			0
$694$	23.8551			0.905528
$695$	−11.4688	+	19.8645i	−0.435036	+	0.753504i
$696$		0			0
$697$	3.51149	+	6.08208i	0.133007	+	0.230375i
$698$	−23.8096	+	41.2394i	−0.901206	+	1.56093i
$699$		0			0
$700$	−0.0598293	−	0.744334i	−0.00226133	−	0.0281332i
$701$	9.16592			0.346192			0.173096	−	0.984905i	$-0.444623\pi$
$701$	9.16592			0.346192			0.173096	+	0.984905i	$0.444623\pi$
$702$		0			0
$703$	19.4122	+	33.6229i	0.732145	+	1.26811i
$704$	22.1296	+	38.3295i	0.834040	+	1.44460i
$705$		0			0
$706$	−11.1708			−0.420420
$707$	14.6199	+	6.94341i	0.549836	+	0.261134i
$708$		0			0
$709$	−7.84726	+	13.5919i	−0.294710	+	0.510453i	−0.974917	−	0.222567i	$-0.928556\pi$
$709$	−7.84726	+	13.5919i	−0.294710	+	0.510453i	0.680207	+	0.733020i	$0.261890\pi$
$710$	6.54343	+	11.3336i	0.245571	+	0.425341i
$711$		0			0
$712$	−2.69839	+	4.67374i	−0.101126	+	0.175156i
$713$	27.4399			1.02763
$714$		0			0
$715$	−17.8230			−0.666541
$716$	−0.992986	+	1.71990i	−0.0371096	+	0.0642758i
$717$		0			0
$718$	−0.919365	−	1.59239i	−0.0343104	−	0.0594273i
$719$	18.0566	−	31.2750i	0.673399	−	1.16636i	−0.303536	−	0.952820i	$-0.598167\pi$
$719$	18.0566	−	31.2750i	0.673399	−	1.16636i	0.976934	−	0.213541i	$-0.0684996\pi$
$720$		0			0
$721$	1.72002	+	21.3988i	0.0640570	+	0.796931i
$722$	−4.83109			−0.179794
$723$		0			0
$724$	−1.85219	−	3.20808i	−0.0688359	−	0.119227i
$725$	−3.36289	−	5.82469i	−0.124895	−	0.216324i
$726$		0			0
$727$	−26.8410			−0.995476			−0.497738	−	0.867327i	$-0.665836\pi$
$727$	−26.8410			−0.995476			−0.497738	+	0.867327i	$0.665836\pi$
$728$	−23.0540	+	15.9012i	−0.854437	+	0.589338i
$729$		0			0
$730$	5.33641	−	9.24294i	0.197510	−	0.342097i
$731$	−2.74962	−	4.76248i	−0.101698	−	0.176147i
$732$		0			0
$733$	14.7989	−	25.6324i	0.546609	−	0.946754i	−0.451895	−	0.892071i	$-0.649252\pi$
$733$	14.7989	−	25.6324i	0.546609	−	0.946754i	0.998504	−	0.0546830i	$-0.0174148\pi$
$734$	−3.40381			−0.125637
$735$		0			0
$736$	−7.03689			−0.259383
$737$	17.7462	−	30.7373i	0.653689	−	1.13222i
$738$		0			0
$739$	16.4065	+	28.4169i	0.603523	+	1.04533i	0.992283	+	0.123993i	$0.0395700\pi$
$739$	16.4065	+	28.4169i	0.603523	+	1.04533i	−0.388761	+	0.921339i	$0.627097\pi$
$740$	−1.15030	+	1.99239i	−0.0422860	+	0.0732415i
$741$		0			0
$742$	−26.8021	+	18.4865i	−0.983937	+	0.678660i
$743$	16.2198			0.595047			0.297524	−	0.954714i	$-0.403839\pi$
$743$	16.2198			0.595047			0.297524	+	0.954714i	$0.403839\pi$
$744$		0			0
$745$	3.38149	+	5.85692i	0.123888	+	0.214581i
$746$	−24.8229	−	42.9945i	−0.908831	−	1.57414i
$747$		0			0
$748$	−2.14703			−0.0785033
$749$	2.77066	+	34.4697i	0.101238	+	1.25949i
$750$		0			0
$751$	0.0442396	−	0.0766253i	0.00161433	−	0.00279610i	−0.865217	−	0.501397i	$-0.832819\pi$
$751$	0.0442396	−	0.0766253i	0.00161433	−	0.00279610i	0.866831	+	0.498601i	$0.166153\pi$
$752$	3.14833	+	5.45307i	0.114808	+	0.198853i
$753$		0			0
$754$	−15.5974	+	27.0155i	−0.568024	+	0.983847i
$755$	23.5504			0.857085
$756$		0			0
$757$	38.0943			1.38456			0.692280	−	0.721629i	$-0.256606\pi$
$757$	38.0943			1.38456			0.692280	+	0.721629i	$0.256606\pi$
$758$	8.35016	−	14.4629i	0.303292	−	0.525316i
$759$		0			0
$760$	−7.12348	−	12.3382i	−0.258396	−	0.447555i
$761$	−5.61117	+	9.71883i	−0.203405	+	0.352307i	−0.949623	−	0.313394i	$-0.898534\pi$
$761$	−5.61117	+	9.71883i	−0.203405	+	0.352307i	0.746219	+	0.665701i	$0.231867\pi$
$762$		0			0
$763$	−8.51572	−	4.04438i	−0.308290	−	0.146416i
$764$	−5.36310			−0.194030
$765$		0			0
$766$	−19.2506	−	33.3431i	−0.695553	−	1.20473i
$767$	12.3823	+	21.4468i	0.447100	+	0.774400i
$768$		0			0
$769$	10.2232			0.368658			0.184329	−	0.982865i	$-0.440989\pi$
$769$	10.2232			0.368658			0.184329	+	0.982865i	$0.440989\pi$
$770$	−1.39926	−	17.4082i	−0.0504259	−	0.627347i
$771$		0			0
$772$	0.738079	−	1.27839i	0.0265641	−	0.0460103i
$773$	19.4101	+	33.6193i	0.698134	+	1.20920i	0.969113	+	0.246618i	$0.0793192\pi$
$773$	19.4101	+	33.6193i	0.698134	+	1.20920i	−0.270979	+	0.962585i	$0.587347\pi$
$774$		0			0
$775$	−3.08846	+	5.34937i	−0.110941	+	0.192155i
$776$	−34.6343			−1.24330
$777$		0			0
$778$	−13.6244			−0.488458
$779$	11.0731	−	19.1793i	0.396737	−	0.687168i
$780$		0			0
$781$	−25.1446	−	43.5518i	−0.899746	−	1.55841i
$782$	−4.39706	+	7.61593i	−0.157239	+	0.272345i
$783$		0			0
$784$	−14.8442	−	18.2066i	−0.530149	−	0.650235i
$785$	8.23093			0.293774
$786$		0			0
$787$	9.10821	+	15.7759i	0.324672	+	0.562349i	0.981446	−	0.191739i	$-0.0614126\pi$
$787$	9.10821	+	15.7759i	0.324672	+	0.562349i	−0.656774	+	0.754088i	$0.728079\pi$
$788$	−2.27402	−	3.93871i	−0.0810084	−	0.140311i
$789$		0			0
$790$	−20.2638			−0.720955
$791$	−28.4722	+	19.6384i	−1.01236	+	0.698261i
$792$		0			0
$793$	−8.72870	+	15.1185i	−0.309965	+	0.536875i
$794$	−17.5160	−	30.3386i	−0.621619	−	1.07668i
$795$		0			0
$796$	1.61100	−	2.79034i	0.0571005	−	0.0989009i
$797$	−39.3577			−1.39412			−0.697060	−	0.717013i	$-0.745509\pi$
$797$	−39.3577			−1.39412			−0.697060	+	0.717013i	$0.745509\pi$
$798$		0			0
$799$	−2.83404			−0.100261
$800$	0.792026	−	1.37183i	0.0280024	−	0.0485015i
$801$		0			0
$802$	14.0505	+	24.3363i	0.496142	+	0.859343i
$803$	−20.5064	+	35.5181i	−0.723655	+	1.25341i
$804$		0			0
$805$	10.6168	+	5.04223i	0.374192	+	0.177715i
$806$	28.6492			1.00913
$807$		0			0
$808$	9.14900	+	15.8465i	0.321861	+	0.557479i
$809$	13.8959	+	24.0684i	0.488554	+	0.846200i	0.999913	−	0.0131672i	$-0.00419137\pi$
$809$	13.8959	+	24.0684i	0.488554	+	0.846200i	−0.511360	+	0.859367i	$0.670858\pi$
$810$		0			0
$811$	−20.0045			−0.702452			−0.351226	−	0.936291i	$-0.614235\pi$
$811$	−20.0045			−0.702452			−0.351226	+	0.936291i	$0.614235\pi$
$812$	4.53672	+	2.15462i	0.159208	+	0.0756125i
$813$		0			0
$814$	−26.9028	+	46.5970i	−0.942943	+	1.63323i
$815$	10.9463	+	18.9596i	0.383433	+	0.664125i
$816$		0			0
$817$	−8.67065	+	15.0180i	−0.303347	+	0.525413i
$818$	25.2819			0.883962
$819$		0			0
$820$	1.31232			0.0458281
$821$	16.9571	−	29.3705i	0.591805	−	1.02504i	−0.402184	−	0.915559i	$-0.631749\pi$
$821$	16.9571	−	29.3705i	0.591805	−	1.02504i	0.993989	−	0.109478i	$-0.0349179\pi$
$822$		0			0
$823$	0.628826	+	1.08916i	0.0219195	+	0.0379657i	0.876777	−	0.480897i	$-0.159689\pi$
$823$	0.628826	+	1.08916i	0.0219195	+	0.0379657i	−0.854858	+	0.518863i	$0.826356\pi$
$824$	−12.1353	+	21.0190i	−0.422753	+	0.732230i
$825$		0			0
$826$	−19.9756	+	13.7779i	−0.695038	+	0.479395i
$827$	−12.2053			−0.424421			−0.212210	−	0.977224i	$-0.568066\pi$
$827$	−12.2053			−0.424421			−0.212210	+	0.977224i	$0.568066\pi$
$828$		0			0
$829$	−7.14467	−	12.3749i	−0.248145	−	0.429799i	0.714866	−	0.699261i	$-0.246488\pi$
$829$	−7.14467	−	12.3749i	−0.248145	−	0.429799i	−0.963011	+	0.269462i	$0.913154\pi$
$830$	−5.41329	−	9.37610i	−0.187898	−	0.325449i
$831$		0			0
$832$	−31.0986			−1.07815
$833$	10.4373	−	1.68880i	0.361630	−	0.0585133i
$834$		0			0
$835$	7.46251	−	12.9254i	0.258251	−	0.447303i
$836$	3.38523	+	5.86339i	0.117081	+	0.202789i
$837$		0			0
$838$	−20.4729	+	35.4601i	−0.707224	+	1.22495i
$839$	−20.9146			−0.722052			−0.361026	−	0.932556i	$-0.617573\pi$
$839$	−20.9146			−0.722052			−0.361026	+	0.932556i	$0.617573\pi$
$840$		0			0
$841$	16.2360			0.559864
$842$	22.3801	−	38.7635i	0.771269	−	1.33588i
$843$		0			0
$844$	2.99869	+	5.19389i	0.103219	+	0.178781i
$845$	−0.238363	+	0.412857i	−0.00819994	+	0.0142027i
$846$		0			0
$847$	3.04519	+	37.8851i	0.104634	+	1.30175i
$848$	−31.5100			−1.08206
$849$		0			0
$850$	−0.989810	−	1.71440i	−0.0339502	−	0.0588035i
$851$	−18.1053	−	31.3593i	−0.620642	−	1.07498i
$852$		0			0
$853$	14.7825			0.506142			0.253071	−	0.967448i	$-0.418559\pi$
$853$	14.7825			0.506142			0.253071	+	0.967448i	$0.418559\pi$
$854$	−15.4520	−	7.33861i	−0.528755	−	0.251122i
$855$		0			0
$856$	−19.5478	+	33.8579i	−0.668132	+	1.15724i
$857$	−10.5207	−	18.2224i	−0.359381	−	0.622466i	0.628477	−	0.777828i	$-0.283679\pi$
$857$	−10.5207	−	18.2224i	−0.359381	−	0.622466i	−0.987858	+	0.155363i	$0.950345\pi$
$858$		0			0
$859$	−5.98778	+	10.3711i	−0.204300	+	0.353859i	−0.949910	−	0.312525i	$-0.898825\pi$
$859$	−5.98778	+	10.3711i	−0.204300	+	0.353859i	0.745609	+	0.666383i	$0.232159\pi$
$860$	−1.02759			−0.0350405
$861$		0			0
$862$	−45.3395			−1.54427
$863$	27.3751	−	47.4150i	0.931859	−	1.61403i	0.151717	−	0.988424i	$-0.451520\pi$
$863$	27.3751	−	47.4150i	0.931859	−	1.61403i	0.780142	−	0.625603i	$-0.215147\pi$
$864$		0			0
$865$	−7.78359	−	13.4816i	−0.264650	−	0.458387i
$866$	20.9928	−	36.3606i	0.713364	−	1.23558i
$867$		0			0
$868$	−0.369561	−	4.59770i	−0.0125437	−	0.156056i
$869$	77.8684			2.64150
$870$		0			0
$871$	12.4693	+	21.5975i	0.422507	+	0.731804i
$872$	−5.32908	−	9.23023i	−0.180465	−	0.312575i
$873$		0			0
$874$	27.7314			0.938029
$875$	−2.17793	+	1.50220i	−0.0736275	+	0.0507837i
$876$		0			0
$877$	13.4716	−	23.3334i	0.454902	−	0.787913i	−0.543781	−	0.839227i	$-0.683008\pi$
$877$	13.4716	−	23.3334i	0.454902	−	0.787913i	0.998683	+	0.0513141i	$0.0163410\pi$
$878$	3.88576	+	6.73034i	0.131138	+	0.227138i
$879$		0			0
$880$	8.45075	−	14.6371i	0.284875	−	0.493417i
$881$	−5.55657			−0.187206			−0.0936028	−	0.995610i	$-0.529838\pi$
$881$	−5.55657			−0.187206			−0.0936028	+	0.995610i	$0.529838\pi$
$882$		0			0
$883$	0.333833			0.0112344			0.00561719	−	0.999984i	$-0.498212\pi$
$883$	0.333833			0.0112344			0.00561719	+	0.999984i	$0.498212\pi$
$884$	0.754304	−	1.30649i	0.0253700	−	0.0439421i
$885$		0			0
$886$	−0.215124	−	0.372605i	−0.00722722	−	0.0125179i
$887$	−25.3569	+	43.9194i	−0.851400	+	1.47467i	0.0285455	+	0.999592i	$0.490912\pi$
$887$	−25.3569	+	43.9194i	−0.851400	+	1.47467i	−0.879945	+	0.475075i	$0.842421\pi$
$888$		0			0
$889$	12.7343	−	8.78334i	0.427095	−	0.294584i
$890$	2.36468			0.0792644
$891$		0			0
$892$	−2.74607	−	4.75633i	−0.0919452	−	0.159254i
$893$	4.46844	+	7.73957i	0.149531	+	0.258995i
$894$		0			0
$895$	7.03649			0.235204
$896$	−1.76994	−	22.0198i	−0.0591295	−	0.735629i
$897$		0			0
$898$	2.15095	−	3.72556i	0.0717782	−	0.124323i
$899$	−20.7723	−	35.9787i	−0.692795	−	1.19996i
$900$		0			0
$901$	7.09111	−	12.2822i	0.236239	−	0.409178i
$902$	30.6919			1.02193
$903$		0			0
$904$	−39.1039			−1.30058
$905$	−6.56247	+	11.3665i	−0.218144	+	0.377836i
$906$		0			0
$907$	1.81193	+	3.13835i	0.0601640	+	0.104207i	0.894539	−	0.446991i	$-0.147504\pi$
$907$	1.81193	+	3.13835i	0.0601640	+	0.104207i	−0.834375	+	0.551198i	$0.814171\pi$
$908$	0.583801	−	1.01117i	0.0193741	−	0.0335570i
$909$		0			0
$910$	11.0847	+	5.26444i	0.367453	+	0.174515i
$911$	−35.5729			−1.17858			−0.589291	−	0.807921i	$-0.700593\pi$
$911$	−35.5729			−1.17858			−0.589291	+	0.807921i	$0.700593\pi$
$912$		0			0
$913$	20.8018	+	36.0298i	0.688440	+	1.19241i
$914$	−14.2886	−	24.7486i	−0.472625	−	0.818611i
$915$		0			0
$916$	−2.86733			−0.0947391
$917$	2.46901	+	30.7168i	0.0815338	+	1.01436i
$918$		0			0
$919$	14.3043	−	24.7757i	0.471854	−	0.817275i	−0.527628	−	0.849476i	$-0.676918\pi$
$919$	14.3043	−	24.7757i	0.471854	−	0.817275i	0.999481	+	0.0322011i	$0.0102517\pi$
$920$	6.64390	+	11.5076i	0.219043	+	0.379394i
$921$		0			0
$922$	−4.29773	+	7.44388i	−0.141538	+	0.245151i
$923$	35.3357			1.16309
$924$		0			0
$925$	8.15127			0.268012
$926$	2.88452	−	4.99613i	0.0947912	−	0.164183i
$927$		0			0
$928$	5.32699	+	9.22662i	0.174867	+	0.302879i
$929$	11.9165	−	20.6400i	0.390967	−	0.677175i	−0.601610	−	0.798790i	$-0.705474\pi$
$929$	11.9165	−	20.6400i	0.390967	−	0.677175i	0.992577	+	0.121615i	$0.0388073\pi$
$930$		0			0
$931$	−21.0684	−	25.8407i	−0.690489	−	0.846893i
$932$	5.07432			0.166215
$933$		0			0
$934$	5.02699	+	8.70699i	0.164488	+	0.284902i
$935$	3.80357	+	6.58798i	0.124390	+	0.215450i
$936$		0			0
$937$	−47.1193			−1.53932			−0.769661	−	0.638453i	$-0.779575\pi$
$937$	−47.1193			−1.53932			−0.769661	+	0.638453i	$0.779575\pi$
$938$	−20.1159	+	13.8747i	−0.656808	+	0.453026i
$939$		0			0
$940$	−0.264785	+	0.458621i	−0.00863634	+	0.0149586i
$941$	−4.53975	−	7.86308i	−0.147992	−	0.256329i	0.782493	−	0.622659i	$-0.213948\pi$
$941$	−4.53975	−	7.86308i	−0.147992	−	0.256329i	−0.930485	+	0.366330i	$0.880614\pi$
$942$		0			0
$943$	−10.3277	+	17.8880i	−0.336315	+	0.582515i
$944$	−23.4843			−0.764348
$945$		0			0
$946$	−24.0328			−0.781373
$947$	−10.4933	+	18.1749i	−0.340986	+	0.590606i	−0.984616	−	0.174731i	$-0.944094\pi$
$947$	−10.4933	+	18.1749i	−0.340986	+	0.590606i	0.643630	+	0.765337i	$0.277428\pi$
$948$		0			0
$949$	−14.4088	−	24.9567i	−0.467729	−	0.810130i
$950$	−3.12127	+	5.40619i	−0.101267	+	0.175400i
$951$		0			0
$952$	10.7975	+	5.12808i	0.349950	+	0.166202i
$953$	−8.81353			−0.285498			−0.142749	−	0.989759i	$-0.545594\pi$
$953$	−8.81353			−0.285498			−0.142749	+	0.989759i	$0.545594\pi$
$954$		0			0
$955$	9.50099	+	16.4562i	0.307445	+	0.532510i
$956$	0.373533	+	0.646977i	0.0120809	+	0.0209247i
$957$		0			0
$958$	19.2593			0.622240
$959$	1.68007	+	0.797915i	0.0542522	+	0.0257660i
$960$		0			0
$961$	−3.57720	+	6.19590i	−0.115394	+	0.199868i
$962$	−18.9032	−	32.7413i	−0.609464	−	1.05562i
$963$		0			0
$964$	1.82267	−	3.15695i	0.0587042	−	0.101679i
$965$	−5.23017			−0.168365
$966$		0			0
$967$	53.4961			1.72032			0.860159	−	0.510026i	$-0.170364\pi$
$967$	53.4961			1.72032			0.860159	+	0.510026i	$0.170364\pi$
$968$	−21.4848	+	37.2127i	−0.690546	+	1.19606i
$969$		0			0
$970$	7.58780	+	13.1425i	0.243630	+	0.421979i
$971$	−19.5975	+	33.9439i	−0.628915	+	1.08931i	0.358855	+	0.933393i	$0.383167\pi$
$971$	−19.5975	+	33.9439i	−0.628915	+	1.08931i	−0.987770	+	0.155919i	$0.950166\pi$
$972$		0			0
$973$	−49.9565	+	34.4569i	−1.60153	+	1.10464i
$974$	8.71810			0.279346
$975$		0			0
$976$	−8.27741	−	14.3369i	−0.264954	−	0.458913i
$977$	−11.3779	−	19.7071i	−0.364011	−	0.630485i	0.624606	−	0.780940i	$-0.285260\pi$
$977$	−11.3779	−	19.7071i	−0.364011	−	0.630485i	−0.988617	+	0.150455i	$0.951926\pi$
$978$		0			0
$979$	−9.08683			−0.290416
$980$	0.701864	−	1.84680i	0.0224202	−	0.0589939i
$981$		0			0
$982$	5.59545	−	9.69160i	0.178558	−	0.309271i
$983$	22.5811	+	39.1116i	0.720224	+	1.24747i	0.960910	+	0.276862i	$0.0892944\pi$
$983$	22.5811	+	39.1116i	0.720224	+	1.24747i	−0.240685	+	0.970603i	$0.577372\pi$
$984$		0			0
$985$	−8.05705	+	13.9552i	−0.256719	+	0.444650i
$986$	13.3145			0.424019
$987$		0			0
$988$	−4.75725			−0.151348
$989$	8.08691	−	14.0069i	0.257149	−	0.445395i
$990$		0			0
$991$	1.98566	+	3.43926i	0.0630766	+	0.109252i	0.895839	−	0.444378i	$-0.146575\pi$
$991$	1.98566	+	3.43926i	0.0630766	+	0.109252i	−0.832763	+	0.553630i	$0.813242\pi$
$992$	4.89229	−	8.47369i	0.155330	−	0.269040i
$993$		0			0
$994$	2.77416	+	34.5133i	0.0879911	+	1.09469i
$995$	−11.4159			−0.361907
$996$		0			0
$997$	8.66350	+	15.0056i	0.274376	+	0.475233i	0.969977	−	0.243195i	$-0.0781955\pi$
$997$	8.66350	+	15.0056i	0.274376	+	0.475233i	−0.695602	+	0.718428i	$0.744862\pi$
$998$	11.1897	+	19.3812i	0.354204	+	0.613500i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.j.h.541.4	yes	10
3.2	odd	2		945.2.j.f.541.2	✓	10
7.2	even	3		6615.2.a.bm.1.2		5
7.4	even	3	inner	945.2.j.h.676.4	yes	10
7.5	odd	6		6615.2.a.bq.1.2		5
21.2	odd	6		6615.2.a.bp.1.4		5
21.5	even	6		6615.2.a.bl.1.4		5
21.11	odd	6		945.2.j.f.676.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.j.f.541.2	✓	10	3.2	odd	2
945.2.j.f.676.2	yes	10	21.11	odd	6
945.2.j.h.541.4	yes	10	1.1	even	1	trivial
945.2.j.h.676.4	yes	10	7.4	even	3	inner
6615.2.a.bl.1.4		5	21.5	even	6
6615.2.a.bm.1.2		5	7.2	even	3
6615.2.a.bp.1.4		5	21.2	odd	6
6615.2.a.bq.1.2		5	7.5	odd	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.655317 - 1.13504i) q^{2} +(0.141120 + 0.244426i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.17793 - 1.50220i) q^{7} +2.99118 q^{8} +O(q^{10})\)	\(q+(0.655317 - 1.13504i) q^{2} +(0.141120 + 0.244426i) q^{4} +(0.500000 - 0.866025i) q^{5} +(2.17793 - 1.50220i) q^{7} +2.99118 q^{8} +(-0.655317 - 1.13504i) q^{10} +(2.51820 + 4.36166i) q^{11} -3.53882 q^{13} +(-0.277829 - 3.45646i) q^{14} +(1.67793 - 2.90626i) q^{16} +(0.755215 + 1.30807i) q^{17} +(2.38149 - 4.12487i) q^{19} +0.282239 q^{20} +6.60089 q^{22} +(-2.22117 + 3.84717i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.31905 + 4.01671i) q^{26} +(0.674527 + 0.320353i) q^{28} +6.72577 q^{29} +(-3.08846 - 5.34937i) q^{31} +(0.792026 + 1.37183i) q^{32} +1.97962 q^{34} +(-0.211981 - 2.63725i) q^{35} +(-4.07564 + 7.05921i) q^{37} +(-3.12127 - 5.40619i) q^{38} +(1.49559 - 2.59044i) q^{40} +4.64966 q^{41} -3.64084 q^{43} +(-0.710736 + 1.23103i) q^{44} +(2.91113 + 5.04223i) q^{46} +(-0.938159 + 1.62494i) q^{47} +(2.48677 - 6.54339i) q^{49} -1.31063 q^{50} +(-0.499397 - 0.864982i) q^{52} +(-4.69477 - 8.13157i) q^{53} +5.03641 q^{55} +(6.51458 - 4.49336i) q^{56} +(4.40751 - 7.63404i) q^{58} +(-3.49899 - 6.06044i) q^{59} +(2.46655 - 4.27220i) q^{61} -8.09569 q^{62} +8.78784 q^{64} +(-1.76941 + 3.06471i) q^{65} +(-3.52358 - 6.10302i) q^{67} +(-0.213151 + 0.369189i) q^{68} +(-3.13230 - 1.48762i) q^{70} -9.98514 q^{71} +(4.07163 + 7.05227i) q^{73} +(5.34167 + 9.25204i) q^{74} +1.34430 q^{76} +(12.0366 + 5.71654i) q^{77} +(7.73055 - 13.3897i) q^{79} +(-1.67793 - 2.90626i) q^{80} +(3.04700 - 5.27756i) q^{82} +8.26057 q^{83} +1.51043 q^{85} +(-2.38590 + 4.13251i) q^{86} +(7.53240 + 13.0465i) q^{88} +(-0.902114 + 1.56251i) q^{89} +(-7.70732 + 5.31603i) q^{91} -1.25380 q^{92} +(1.22958 + 2.12970i) q^{94} +(-2.38149 - 4.12487i) q^{95} -11.5788 q^{97} +(-5.79740 - 7.11058i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{4} + 5 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q - 4 * q^4 + 5 * q^5 - q^7 + 6 * q^8	\( 10 q - 4 q^{4} + 5 q^{5} - q^{7} + 6 q^{8} - 3 q^{11} - 20 q^{13} + 20 q^{14} - 6 q^{16} + q^{17} + 13 q^{19} - 8 q^{20} - 12 q^{22} + 4 q^{23} - 5 q^{25} + 5 q^{26} + 21 q^{28} + 24 q^{29} + 5 q^{31} - 16 q^{32} - 32 q^{34} + q^{35} - 8 q^{37} - 5 q^{38} + 3 q^{40} + 18 q^{41} + 16 q^{43} + 6 q^{44} + 26 q^{46} - 2 q^{47} - 11 q^{49} + 5 q^{52} + 6 q^{53} - 6 q^{55} - 24 q^{56} - 20 q^{58} + 14 q^{59} + 15 q^{61} - 40 q^{62} - 18 q^{64} - 10 q^{65} + 18 q^{67} - 30 q^{68} - 2 q^{70} + 26 q^{71} + 35 q^{73} + 9 q^{74} - 60 q^{76} + 46 q^{77} - q^{79} + 6 q^{80} + 39 q^{82} + 20 q^{83} + 2 q^{85} - 25 q^{86} + 46 q^{88} - 11 q^{89} + 26 q^{91} - 86 q^{92} - 29 q^{94} - 13 q^{95} - 44 q^{97} - 9 q^{98}+O(q^{100}) \) 10 * q - 4 * q^4 + 5 * q^5 - q^7 + 6 * q^8 - 3 * q^11 - 20 * q^13 + 20 * q^14 - 6 * q^16 + q^17 + 13 * q^19 - 8 * q^20 - 12 * q^22 + 4 * q^23 - 5 * q^25 + 5 * q^26 + 21 * q^28 + 24 * q^29 + 5 * q^31 - 16 * q^32 - 32 * q^34 + q^35 - 8 * q^37 - 5 * q^38 + 3 * q^40 + 18 * q^41 + 16 * q^43 + 6 * q^44 + 26 * q^46 - 2 * q^47 - 11 * q^49 + 5 * q^52 + 6 * q^53 - 6 * q^55 - 24 * q^56 - 20 * q^58 + 14 * q^59 + 15 * q^61 - 40 * q^62 - 18 * q^64 - 10 * q^65 + 18 * q^67 - 30 * q^68 - 2 * q^70 + 26 * q^71 + 35 * q^73 + 9 * q^74 - 60 * q^76 + 46 * q^77 - q^79 + 6 * q^80 + 39 * q^82 + 20 * q^83 + 2 * q^85 - 25 * q^86 + 46 * q^88 - 11 * q^89 + 26 * q^91 - 86 * q^92 - 29 * q^94 - 13 * q^95 - 44 * q^97 - 9 * q^98

Introduction

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