LMFDB - Embedded newform 425.2.m.e.376.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			376.2
Character	$\chi$	$=$	425.376
Dual form			425.2.m.e.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.672981 - 0.672981i) q^{2} +(2.28645 - 0.947078i) q^{3} -1.09419i q^{4} +(-2.17610 - 0.901371i) q^{6} +(0.204115 - 0.492777i) q^{7} +(-2.08233 + 2.08233i) q^{8} +(2.20957 - 2.20957i) q^{9} +(4.31906 + 1.78902i) q^{11} +(-1.03629 - 2.50182i) q^{12} -3.92573i q^{13} +(-0.468995 + 0.194264i) q^{14} +0.614355 q^{16} +(0.867192 - 4.03088i) q^{17} -2.97399 q^{18} +(-0.708548 - 0.708548i) q^{19} -1.32002i q^{21} +(-1.70268 - 4.11062i) q^{22} +(-5.30129 - 2.19587i) q^{23} +(-2.78902 + 6.73328i) q^{24} +(-2.64194 + 2.64194i) q^{26} +(0.118196 - 0.285350i) q^{27} +(-0.539193 - 0.223341i) q^{28} +(3.17120 + 7.65596i) q^{29} +(-2.29036 + 0.948699i) q^{31} +(3.75122 + 3.75122i) q^{32} +11.5697 q^{33} +(-3.29631 + 2.12910i) q^{34} +(-2.41769 - 2.41769i) q^{36} +(-3.78211 + 1.56660i) q^{37} +0.953679i q^{38} +(-3.71797 - 8.97598i) q^{39} +(-0.311708 + 0.752530i) q^{41} +(-0.888349 + 0.888349i) q^{42} +(-4.55216 + 4.55216i) q^{43} +(1.95753 - 4.72589i) q^{44} +(2.08989 + 5.04545i) q^{46} -1.70505i q^{47} +(1.40469 - 0.581842i) q^{48} +(4.74858 + 4.74858i) q^{49} +(-1.83477 - 10.0377i) q^{51} -4.29551 q^{52} +(5.77230 + 5.77230i) q^{53} +(-0.271578 + 0.112491i) q^{54} +(0.601090 + 1.45116i) q^{56} +(-2.29111 - 0.949008i) q^{57} +(3.01816 - 7.28648i) q^{58} +(4.28304 - 4.28304i) q^{59} +(-0.432837 + 1.04496i) q^{61} +(2.17983 + 0.902914i) q^{62} +(-0.637818 - 1.53983i) q^{63} -6.27771i q^{64} +(-7.78616 - 7.78616i) q^{66} +7.68603 q^{67} +(-4.41056 - 0.948875i) q^{68} -14.2008 q^{69} +(6.41424 - 2.65686i) q^{71} +9.20211i q^{72} +(-4.62521 - 11.1662i) q^{73} +(3.59958 + 1.49100i) q^{74} +(-0.775289 + 0.775289i) q^{76} +(1.76317 - 1.76317i) q^{77} +(-3.53854 + 8.54279i) q^{78} +(1.36830 + 0.566769i) q^{79} +8.61002i q^{81} +(0.716212 - 0.296665i) q^{82} +(11.4464 + 11.4464i) q^{83} -1.44436 q^{84} +6.12703 q^{86} +(14.5016 + 14.5016i) q^{87} +(-12.7191 + 5.26841i) q^{88} -12.0717i q^{89} +(-1.93451 - 0.801300i) q^{91} +(-2.40270 + 5.80064i) q^{92} +(-4.33830 + 4.33830i) q^{93} +(-1.14747 + 1.14747i) q^{94} +(12.1297 + 5.02427i) q^{96} +(-0.0872680 - 0.210684i) q^{97} -6.39141i q^{98} +(13.4962 - 5.59031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−0.672981	−	0.672981i	−0.475869	−	0.475869i	0.427938	−	0.903808i	$-0.359240\pi$
$2$	−0.672981	−	0.672981i	−0.475869	−	0.475869i	−0.903808	+	0.427938i	$0.859240\pi$
$3$	2.28645	−	0.947078i	1.32008	−	0.546796i	0.392272	−	0.919849i	$-0.371689\pi$
$3$	2.28645	−	0.947078i	1.32008	−	0.546796i	0.927810	+	0.373054i	$0.121689\pi$
$4$		−	1.09419i		−	0.547097i
$5$		0			0
$5$		0			0
$6$	−2.17610	−	0.901371i	−0.888390	−	0.367983i
$7$	0.204115	−	0.492777i	0.0771481	−	0.186252i	−0.880600	−	0.473860i	$-0.842860\pi$
$7$	0.204115	−	0.492777i	0.0771481	−	0.186252i	0.957748	+	0.287608i	$0.0928601\pi$
$8$	−2.08233	+	2.08233i	−0.736216	+	0.736216i
$9$	2.20957	−	2.20957i	0.736523	−	0.736523i
$10$		0			0
$11$	4.31906	+	1.78902i	1.30225	+	0.539408i	0.922612	−	0.385728i	$-0.126050\pi$
$11$	4.31906	+	1.78902i	1.30225	+	0.539408i	0.379634	+	0.925137i	$0.376050\pi$
$12$	−1.03629	−	2.50182i	−0.299150	−	0.722212i
$13$		−	3.92573i		−	1.08880i	−0.838825	−	0.544401i	$-0.816757\pi$
$13$		−	3.92573i		−	1.08880i	0.838825	−	0.544401i	$-0.183243\pi$
$14$	−0.468995	+	0.194264i	−0.125344	+	0.0519192i
$15$		0			0
$16$	0.614355			0.153589
$17$	0.867192	−	4.03088i	0.210325	−	0.977632i
$17$	0.867192	−	4.03088i	0.210325	−	0.977632i
$18$	−2.97399			−0.700977
$19$	−0.708548	−	0.708548i	−0.162552	−	0.162552i	0.621144	−	0.783696i	$-0.286668\pi$
$19$	−0.708548	−	0.708548i	−0.162552	−	0.162552i	−0.783696	+	0.621144i	$0.786668\pi$
$20$		0			0
$21$		−	1.32002i		−	0.288052i
$22$	−1.70268	−	4.11062i	−0.363012	−	0.876387i
$23$	−5.30129	−	2.19587i	−1.10540	−	0.457870i	−0.246046	−	0.969258i	$-0.579132\pi$
$23$	−5.30129	−	2.19587i	−1.10540	−	0.457870i	−0.859350	+	0.511388i	$0.829132\pi$
$24$	−2.78902	+	6.73328i	−0.569305	+	1.37442i
$25$		0			0
$26$	−2.64194	+	2.64194i	−0.518128	+	0.518128i
$27$	0.118196	−	0.285350i	0.0227468	−	0.0549156i
$28$	−0.539193	−	0.223341i	−0.101898	−	0.0422075i
$29$	3.17120	+	7.65596i	0.588878	+	1.42168i	0.884576	+	0.466395i	$0.154448\pi$
$29$	3.17120	+	7.65596i	0.588878	+	1.42168i	−0.295699	+	0.955281i	$0.595552\pi$
$30$		0			0
$31$	−2.29036	+	0.948699i	−0.411361	+	0.170391i	−0.578760	−	0.815498i	$-0.696463\pi$
$31$	−2.29036	+	0.948699i	−0.411361	+	0.170391i	0.167399	+	0.985889i	$0.446463\pi$
$32$	3.75122	+	3.75122i	0.663128	+	0.663128i
$33$	11.5697			2.01402
$34$	−3.29631	+	2.12910i	−0.565312	+	0.365138i
$35$		0			0
$36$	−2.41769	−	2.41769i	−0.402949	−	0.402949i
$37$	−3.78211	+	1.56660i	−0.621775	+	0.257548i	−0.671254	−	0.741227i	$-0.734244\pi$
$37$	−3.78211	+	1.56660i	−0.621775	+	0.257548i	0.0494786	+	0.998775i	$0.484244\pi$
$38$			0.953679i			0.154707i
$39$	−3.71797	−	8.97598i	−0.595352	−	1.43731i
$40$		0			0
$41$	−0.311708	+	0.752530i	−0.0486806	+	0.117525i	−0.946349	−	0.323146i	$-0.895260\pi$
$41$	−0.311708	+	0.752530i	−0.0486806	+	0.117525i	0.897669	+	0.440671i	$0.145260\pi$
$42$	−0.888349	+	0.888349i	−0.137075	+	0.137075i
$43$	−4.55216	+	4.55216i	−0.694197	+	0.694197i	−0.963153	−	0.268955i	$-0.913322\pi$
$43$	−4.55216	+	4.55216i	−0.694197	+	0.694197i	0.268955	+	0.963153i	$0.413322\pi$
$44$	1.95753	−	4.72589i	0.295108	−	0.712455i
$45$		0			0
$46$	2.08989	+	5.04545i	0.308138	+	0.743911i
$47$		−	1.70505i		−	0.248707i	−0.992238	−	0.124354i	$-0.960314\pi$
$47$		−	1.70505i		−	0.248707i	0.992238	−	0.124354i	$-0.0396857\pi$
$48$	1.40469	−	0.581842i	0.202750	−	0.0839817i
$49$	4.74858	+	4.74858i	0.678369	+	0.678369i
$50$		0			0
$51$	−1.83477	−	10.0377i	−0.256919	−	1.40556i
$52$	−4.29551			−0.595680
$53$	5.77230	+	5.77230i	0.792887	+	0.792887i	0.981962	−	0.189076i	$-0.0605492\pi$
$53$	5.77230	+	5.77230i	0.792887	+	0.792887i	−0.189076	+	0.981962i	$0.560549\pi$
$54$	−0.271578	+	0.112491i	−0.0369571	+	0.0153081i
$55$		0			0
$56$	0.601090	+	1.45116i	0.0803240	+	0.193919i
$57$	−2.29111	−	0.949008i	−0.303465	−	0.125699i
$58$	3.01816	−	7.28648i	0.396304	−	0.956761i
$59$	4.28304	−	4.28304i	0.557605	−	0.557605i	−0.371020	−	0.928625i	$-0.620992\pi$
$59$	4.28304	−	4.28304i	0.557605	−	0.557605i	0.928625	+	0.371020i	$0.120992\pi$
$60$		0			0
$61$	−0.432837	+	1.04496i	−0.0554192	+	0.133794i	−0.949164	−	0.314782i	$-0.898069\pi$
$61$	−0.432837	+	1.04496i	−0.0554192	+	0.133794i	0.893745	+	0.448576i	$0.148069\pi$
$62$	2.17983	+	0.902914i	0.276838	+	0.114670i
$63$	−0.637818	−	1.53983i	−0.0803575	−	0.194000i
$64$		−	6.27771i		−	0.784713i
$65$		0			0
$66$	−7.78616	−	7.78616i	−0.958410	−	0.958410i
$67$	7.68603			0.938998			0.469499	−	0.882933i	$-0.344435\pi$
$67$	7.68603			0.938998			0.469499	+	0.882933i	$0.344435\pi$
$68$	−4.41056	−	0.948875i	−0.534859	−	0.115068i
$69$	−14.2008			−1.70957
$70$		0			0
$71$	6.41424	−	2.65686i	0.761230	−	0.315312i	0.0319156	−	0.999491i	$-0.489839\pi$
$71$	6.41424	−	2.65686i	0.761230	−	0.315312i	0.729314	+	0.684179i	$0.239839\pi$
$72$			9.20211i			1.08448i
$73$	−4.62521	−	11.1662i	−0.541340	−	1.30691i	−0.923778	−	0.382929i	$-0.874915\pi$
$73$	−4.62521	−	11.1662i	−0.541340	−	1.30691i	0.382438	−	0.923981i	$-0.375085\pi$
$74$	3.59958	+	1.49100i	0.418443	+	0.173325i
$75$		0			0
$76$	−0.775289	+	0.775289i	−0.0889317	+	0.0889317i
$77$	1.76317	−	1.76317i	0.200932	−	0.200932i
$78$	−3.53854	+	8.54279i	−0.400661	+	0.967281i
$79$	1.36830	+	0.566769i	0.153946	+	0.0637666i	0.458326	−	0.888784i	$-0.348449\pi$
$79$	1.36830	+	0.566769i	0.153946	+	0.0637666i	−0.304380	+	0.952551i	$0.598449\pi$
$80$		0			0
$81$			8.61002i			0.956669i
$82$	0.716212	−	0.296665i	0.0790924	−	0.0327611i
$83$	11.4464	+	11.4464i	1.25640	+	1.25640i	0.952798	+	0.303606i	$0.0981905\pi$
$83$	11.4464	+	11.4464i	1.25640	+	1.25640i	0.303606	+	0.952798i	$0.401810\pi$
$84$	−1.44436			−0.157592
$85$		0			0
$86$	6.12703			0.660694
$87$	14.5016	+	14.5016i	1.55473	+	1.55473i
$88$	−12.7191	+	5.26841i	−1.35586	+	0.561614i
$89$		−	12.0717i		−	1.27960i	−0.768542	−	0.639800i	$-0.779017\pi$
$89$		−	12.0717i		−	1.27960i	0.768542	−	0.639800i	$-0.220983\pi$
$90$		0			0
$91$	−1.93451	−	0.801300i	−0.202792	−	0.0839991i
$92$	−2.40270	+	5.80064i	−0.250499	+	0.604758i
$93$	−4.33830	+	4.33830i	−0.449861	+	0.449861i
$94$	−1.14747	+	1.14747i	−0.118352	+	0.118352i
$95$		0			0
$96$	12.1297	+	5.02427i	1.23798	+	0.512787i
$97$	−0.0872680	−	0.210684i	−0.00886072	−	0.0213917i	0.919387	−	0.393354i	$-0.128685\pi$
$97$	−0.0872680	−	0.210684i	−0.00886072	−	0.0213917i	−0.928248	+	0.371962i	$0.878685\pi$
$98$		−	6.39141i		−	0.645630i
$99$	13.4962	−	5.59031i	1.35642	−	0.561848i
$100$		0			0
$101$	−6.66539			−0.663231			−0.331616	−	0.943415i	$-0.607594\pi$
$101$	−6.66539			−0.663231			−0.331616	+	0.943415i	$0.607594\pi$
$102$	−5.52041	+	7.98994i	−0.546602	+	0.791122i
$103$	−0.350456			−0.0345315			−0.0172657	−	0.999851i	$-0.505496\pi$
$103$	−0.350456			−0.0345315			−0.0172657	+	0.999851i	$0.505496\pi$
$104$	8.17468	+	8.17468i	0.801594	+	0.801594i
$105$		0			0
$106$		−	7.76930i		−	0.754621i
$107$	2.98446	+	7.20512i	0.288518	+	0.696545i	0.999981	−	0.00617913i	$-0.00196689\pi$
$107$	2.98446	+	7.20512i	0.288518	+	0.696545i	−0.711463	+	0.702724i	$0.751967\pi$
$108$	−0.312228	−	0.129329i	−0.0300441	−	0.0124447i
$109$	−4.66038	+	11.2511i	−0.446383	+	1.07766i	0.527284	+	0.849689i	$0.323210\pi$
$109$	−4.66038	+	11.2511i	−0.446383	+	1.07766i	−0.973667	+	0.227975i	$0.926790\pi$
$110$		0			0
$111$	−7.16391	+	7.16391i	−0.679968	+	0.679968i
$112$	0.125399	−	0.302740i	0.0118491	−	0.0286062i
$113$	16.5171	+	6.84161i	1.55380	+	0.643604i	0.983998	−	0.178179i	$-0.0570205\pi$
$113$	16.5171	+	6.84161i	1.55380	+	0.643604i	0.569800	+	0.821783i	$0.307020\pi$
$114$	0.903208	+	2.18054i	0.0845932	+	0.204226i
$115$		0			0
$116$	8.37710	−	3.46991i	0.777794	−	0.322173i
$117$	−8.67417	−	8.67417i	−0.801927	−	0.801927i
$118$	−5.76481			−0.530694
$119$	−1.80932	−	1.25009i	−0.165860	−	0.114596i
$120$		0			0
$121$	7.67557	+	7.67557i	0.697779	+	0.697779i
$122$	0.994531	−	0.411948i	0.0900406	−	0.0372960i
$123$			2.01583i			0.181762i
$124$	1.03806	+	2.50610i	0.0932205	+	0.225054i
$125$		0			0
$126$	−0.607036	+	1.46551i	−0.0540791	+	0.130558i
$127$	−8.76596	+	8.76596i	−0.777853	+	0.777853i	−0.979465	−	0.201612i	$-0.935382\pi$
$127$	−8.76596	+	8.76596i	−0.777853	+	0.777853i	0.201612	+	0.979465i	$0.435382\pi$
$128$	3.27766	−	3.27766i	0.289707	−	0.289707i
$129$	−6.09702	+	14.7195i	−0.536813	+	1.29598i
$130$		0			0
$131$	−3.83884	−	9.26779i	−0.335401	−	0.809730i	−0.998145	−	0.0608839i	$-0.980608\pi$
$131$	−3.83884	−	9.26779i	−0.335401	−	0.809730i	0.662744	−	0.748846i	$-0.269392\pi$
$132$		−	12.6594i		−	1.10186i
$133$	−0.493781	+	0.204531i	−0.0428163	+	0.0177351i
$134$	−5.17255	−	5.17255i	−0.446841	−	0.446841i
$135$		0			0
$136$	6.58785	+	10.1994i	0.564903	+	0.874593i
$137$	−3.06808			−0.262124			−0.131062	−	0.991374i	$-0.541839\pi$
$137$	−3.06808			−0.262124			−0.131062	+	0.991374i	$0.541839\pi$
$138$	9.55686	+	9.55686i	0.813534	+	0.813534i
$139$	−11.3389	+	4.69672i	−0.961753	+	0.398371i	−0.807636	−	0.589682i	$-0.799253\pi$
$139$	−11.3389	+	4.69672i	−0.961753	+	0.398371i	−0.154117	+	0.988053i	$0.549253\pi$
$140$		0			0
$141$	−1.61482	−	3.89851i	−0.135992	−	0.328314i
$142$	−6.10468	−	2.52864i	−0.512293	−	0.212199i
$143$	7.02320	−	16.9555i	0.587309	−	1.41789i
$144$	1.35746	−	1.35746i	0.113122	−	0.113122i
$145$		0			0
$146$	−4.40199	+	10.6274i	−0.364312	+	0.879526i
$147$	15.3547	+	6.36011i	1.26643	+	0.524573i
$148$	1.71417	+	4.13836i	0.140904	+	0.340171i
$149$			5.46544i			0.447747i	0.974618	+	0.223873i	$0.0718702\pi$
$149$			5.46544i			0.447747i	−0.974618	+	0.223873i	$0.928130\pi$
$150$		0			0
$151$	3.54105	+	3.54105i	0.288167	+	0.288167i	0.836355	−	0.548188i	$-0.184682\pi$
$151$	3.54105	+	3.54105i	0.288167	+	0.288167i	−0.548188	+	0.836355i	$0.684682\pi$
$152$	2.95087			0.239347
$153$	−6.99038	−	10.8226i	−0.565139	−	0.874957i
$154$	−2.37316			−0.191235
$155$		0			0
$156$	−9.82146	+	4.06818i	−0.786346	+	0.325715i
$157$		−	10.9442i		−	0.873443i	−0.899597	−	0.436721i	$-0.856140\pi$
$157$		−	10.9442i		−	0.873443i	0.899597	−	0.436721i	$-0.143860\pi$
$158$	−0.539417	−	1.30227i	−0.0429137	−	0.103603i
$159$	18.6649	+	7.73125i	1.48022	+	0.613128i
$160$		0			0
$161$	−2.16414	+	2.16414i	−0.170558	+	0.170558i
$162$	5.79438	−	5.79438i	0.455250	−	0.455250i
$163$	2.82785	−	6.82704i	0.221495	−	0.534735i	−0.773599	−	0.633676i	$-0.781545\pi$
$163$	2.82785	−	6.82704i	0.221495	−	0.534735i	0.995093	+	0.0989404i	$0.0315453\pi$
$164$	0.823413	+	0.341069i	0.0642978	+	0.0266330i
$165$		0			0
$166$		−	15.4064i		−	1.19577i
$167$	−18.0137	+	7.46152i	−1.39394	+	0.577390i	−0.948172	−	0.317758i	$-0.897070\pi$
$167$	−18.0137	+	7.46152i	−1.39394	+	0.577390i	−0.445770	+	0.895147i	$0.647070\pi$
$168$	2.74872	+	2.74872i	0.212069	+	0.212069i
$169$	−2.41138			−0.185491
$170$		0			0
$171$	−3.13117			−0.239447
$172$	4.98094	+	4.98094i	0.379793	+	0.379793i
$173$	−12.2873	+	5.08958i	−0.934189	+	0.386954i	−0.797266	−	0.603628i	$-0.793721\pi$
$173$	−12.2873	+	5.08958i	−0.934189	+	0.386954i	−0.136923	+	0.990582i	$0.543721\pi$
$174$		−	19.5186i		−	1.47970i
$175$		0			0
$176$	2.65344	+	1.09909i	0.200011	+	0.0828471i
$177$	5.73658	−	13.8493i	0.431188	−	1.04098i
$178$	−8.12404	+	8.12404i	−0.608922	+	0.608922i
$179$	−7.18598	+	7.18598i	−0.537105	+	0.537105i	−0.922678	−	0.385572i	$-0.874004\pi$
$179$	−7.18598	+	7.18598i	−0.537105	+	0.537105i	0.385572	+	0.922678i	$0.374004\pi$
$180$		0			0
$181$	−18.1259	−	7.50798i	−1.34728	−	0.558064i	−0.411750	−	0.911297i	$-0.635082\pi$
$181$	−18.1259	−	7.50798i	−1.34728	−	0.558064i	−0.935535	+	0.353233i	$0.885082\pi$
$182$	0.762628	+	1.84115i	0.0565298	+	0.136475i
$183$			2.79918i			0.206921i
$184$	15.6116	−	6.46653i	1.15090	−	0.476719i
$185$		0			0
$186$	5.83919			0.428150
$187$	10.9568	−	15.8582i	0.801238	−	1.15967i
$188$	−1.86566			−0.136067
$189$	−0.116488	−	0.116488i	−0.00847327	−	0.00847327i
$190$		0			0
$191$		−	8.81287i		−	0.637677i	−0.947809	−	0.318838i	$-0.896707\pi$
$191$		−	8.81287i		−	0.637677i	0.947809	−	0.318838i	$-0.103293\pi$
$192$	−5.94548	−	14.3536i	−0.429078	−	1.03589i
$193$	−14.2854	−	5.91720i	−1.02829	−	0.425930i	−0.196192	−	0.980566i	$-0.562858\pi$
$193$	−14.2854	−	5.91720i	−1.02829	−	0.425930i	−0.832093	+	0.554636i	$0.812858\pi$
$194$	−0.0830564	+	0.200516i	−0.00596310	+	0.0143962i
$195$		0			0
$196$	5.19587	−	5.19587i	0.371133	−	0.371133i
$197$	−0.0880736	+	0.212628i	−0.00627498	+	0.0151491i	−0.926986	−	0.375096i	$-0.877610\pi$
$197$	−0.0880736	+	0.212628i	−0.00627498	+	0.0151491i	0.920711	+	0.390245i	$0.127610\pi$
$198$	−12.8449	−	5.32052i	−0.912845	−	0.378113i
$199$	−8.21298	−	19.8279i	−0.582203	−	1.40556i	−0.890812	−	0.454372i	$-0.849864\pi$
$199$	−8.21298	−	19.8279i	−0.582203	−	1.40556i	0.308609	−	0.951189i	$-0.400136\pi$
$200$		0			0
$201$	17.5737	−	7.27927i	1.23955	−	0.513440i
$202$	4.48568	+	4.48568i	0.315611	+	0.315611i
$203$	4.41997			0.310221
$204$	−10.9832	+	2.00759i	−0.768976	+	0.140559i
$205$		0			0
$206$	0.235850	+	0.235850i	0.0164325	+	0.0164325i
$207$	−16.5655	+	6.86165i	−1.15138	+	0.476918i
$208$		−	2.41179i		−	0.167228i
$209$	−1.79266	−	4.32787i	−0.124001	−	0.299365i
$210$		0			0
$211$	−5.94870	+	14.3614i	−0.409525	+	0.988682i	0.575738	+	0.817635i	$0.304715\pi$
$211$	−5.94870	+	14.3614i	−0.409525	+	0.988682i	−0.985263	+	0.171047i	$0.945285\pi$
$212$	6.31601	−	6.31601i	0.433786	−	0.433786i
$213$	12.1496	−	12.1496i	0.832474	−	0.832474i
$214$	2.84042	−	6.85739i	0.194167	−	0.468761i
$215$		0			0
$216$	0.348070	+	0.840316i	0.0236832	+	0.0571763i
$217$			1.32228i			0.0897622i
$218$	10.7081	−	4.43546i	0.725247	−	0.300407i
$219$	−21.1506	−	21.1506i	−1.42923	−	1.42923i
$220$		0			0
$221$	−15.8242	−	3.40436i	−1.06445	−	0.229002i
$222$	9.64235			0.647152
$223$	−0.756286	−	0.756286i	−0.0506447	−	0.0506447i	0.681331	−	0.731976i	$-0.261401\pi$
$223$	−0.756286	−	0.756286i	−0.0506447	−	0.0506447i	−0.731976	+	0.681331i	$0.761401\pi$
$224$	2.61419	−	1.08283i	0.174668	−	0.0723498i
$225$		0			0
$226$	−6.51143	−	15.7200i	−0.433134	−	1.04568i
$227$	1.91049	+	0.791349i	0.126803	+	0.0525237i	0.445183	−	0.895440i	$-0.353139\pi$
$227$	1.91049	+	0.791349i	0.126803	+	0.0525237i	−0.318380	+	0.947963i	$0.603139\pi$
$228$	−1.03840	+	2.50692i	−0.0687696	+	0.166025i
$229$	9.06042	−	9.06042i	0.598730	−	0.598730i	−0.341245	−	0.939974i	$-0.610849\pi$
$229$	9.06042	−	9.06042i	0.598730	−	0.598730i	0.939974	+	0.341245i	$0.110849\pi$
$230$		0			0
$231$	2.36154	−	5.70125i	0.155378	−	0.375115i
$232$	−22.5458	−	9.33876i	−1.48020	−	0.613120i
$233$	2.48129	+	5.99035i	0.162554	+	0.392441i	0.984079	−	0.177732i	$-0.0568761\pi$
$233$	2.48129	+	5.99035i	0.162554	+	0.392441i	−0.821524	+	0.570173i	$0.806876\pi$
$234$			11.6751i			0.763226i
$235$		0			0
$236$	−4.68648	−	4.68648i	−0.305064	−	0.305064i
$237$	3.66533			0.238089
$238$	0.376346	+	2.05892i	0.0243949	+	0.133460i
$239$	−1.26828			−0.0820381			−0.0410190	−	0.999158i	$-0.513060\pi$
$239$	−1.26828			−0.0820381			−0.0410190	+	0.999158i	$0.513060\pi$
$240$		0			0
$241$	−2.30585	+	0.955116i	−0.148533	+	0.0615244i	−0.455712	−	0.890127i	$-0.650615\pi$
$241$	−2.30585	+	0.955116i	−0.148533	+	0.0615244i	0.307178	+	0.951652i	$0.400615\pi$
$242$		−	10.3310i		−	0.664103i
$243$	8.50895	+	20.5424i	0.545849	+	1.31780i
$244$	1.14339	+	0.473608i	0.0731981	+	0.0303196i
$245$		0			0
$246$	1.35662	−	1.35662i	0.0864947	−	0.0864947i
$247$	−2.78157	+	2.78157i	−0.176987	+	0.176987i
$248$	2.79379	−	6.74480i	0.177406	−	0.428296i
$249$	37.0122	+	15.3309i	2.34555	+	0.971559i
$250$		0			0
$251$			17.3565i			1.09553i	0.836632	+	0.547765i	$0.184521\pi$
$251$			17.3565i			1.09553i	−0.836632	+	0.547765i	$0.815479\pi$
$252$	−1.68487	+	0.697896i	−0.106137	+	0.0439633i
$253$	−18.9682	−	18.9682i	−1.19252	−	1.19252i
$254$	11.7987			0.740313
$255$		0			0
$256$	−16.9670			−1.06044
$257$	−10.9991	−	10.9991i	−0.686105	−	0.686105i	0.275264	−	0.961369i	$-0.411235\pi$
$257$	−10.9991	−	10.9991i	−0.686105	−	0.686105i	−0.961369	+	0.275264i	$0.911235\pi$
$258$	14.0091	−	5.80277i	0.872170	−	0.361265i
$259$			2.18350i			0.135676i
$260$		0			0
$261$	23.9234	+	9.90938i	1.48082	+	0.613375i
$262$	−3.65358	+	8.82051i	−0.225719	+	0.544933i
$263$	−6.39290	+	6.39290i	−0.394203	+	0.394203i	−0.876183	−	0.481979i	$-0.839918\pi$
$263$	−6.39290	+	6.39290i	−0.394203	+	0.394203i	0.481979	+	0.876183i	$0.339918\pi$
$264$	−24.0919	+	24.0919i	−1.48275	+	1.48275i
$265$		0			0
$266$	0.469951	+	0.194660i	0.0288145	+	0.0119354i
$267$	−11.4329	−	27.6014i	−0.699680	−	1.68918i
$268$		−	8.41000i		−	0.513723i
$269$	2.79002	−	1.15566i	0.170110	−	0.0704620i	−0.296003	−	0.955187i	$-0.595654\pi$
$269$	2.79002	−	1.15566i	0.170110	−	0.0704620i	0.466113	+	0.884725i	$0.345654\pi$
$270$		0			0
$271$	13.1638			0.799642			0.399821	−	0.916593i	$-0.369072\pi$
$271$	13.1638			0.799642			0.399821	+	0.916593i	$0.369072\pi$
$272$	0.532764	−	2.47639i	0.0323035	−	0.150153i
$273$	−5.18205			−0.313632
$274$	2.06476	+	2.06476i	0.124737	+	0.124737i
$275$		0			0
$276$			15.5384i			0.935302i
$277$	−1.55039	−	3.74298i	−0.0931540	−	0.224894i	0.870434	−	0.492285i	$-0.163838\pi$
$277$	−1.55039	−	3.74298i	−0.0931540	−	0.224894i	−0.963588	+	0.267392i	$0.913838\pi$
$278$	10.7917	+	4.47006i	0.647241	+	0.268096i
$279$	−2.96450	+	7.15692i	−0.177480	+	0.428474i
$280$		0			0
$281$	10.0869	−	10.0869i	0.601731	−	0.601731i	−0.339041	−	0.940772i	$-0.610102\pi$
$281$	10.0869	−	10.0869i	0.601731	−	0.601731i	0.940772	+	0.339041i	$0.110102\pi$
$282$	−1.53688	+	3.71037i	−0.0915201	+	0.220949i
$283$	−5.14980	−	2.13312i	−0.306124	−	0.126801i	0.224333	−	0.974513i	$-0.427980\pi$
$283$	−5.14980	−	2.13312i	−0.306124	−	0.126801i	−0.530457	+	0.847712i	$0.677980\pi$
$284$	−2.90712	−	7.01841i	−0.172506	−	0.416466i
$285$		0			0
$286$	−16.1372	+	6.68425i	−0.954213	+	0.395248i
$287$	0.307205	+	0.307205i	0.0181337	+	0.0181337i
$288$	16.5771			0.976817
$289$	−15.4960	−	6.99109i	−0.911527	−	0.411241i
$290$		0			0
$291$	−0.399068	−	0.399068i	−0.0233938	−	0.0233938i
$292$	−12.2180	+	5.06088i	−0.715006	+	0.296165i
$293$			1.97120i			0.115159i	0.998341	+	0.0575795i	$0.0183383\pi$
$293$			1.97120i			0.115159i	−0.998341	+	0.0575795i	$0.981662\pi$
$294$	−6.05316	−	14.6136i	−0.353028	−	0.852284i
$295$		0			0
$296$	4.61343	−	11.1378i	0.268150	−	0.647372i
$297$	1.02099	−	1.02099i	0.0592438	−	0.0592438i
$298$	3.67814	−	3.67814i	0.213069	−	0.213069i
$299$	−8.62039	+	20.8115i	−0.498530	+	1.20356i
$300$		0			0
$301$	1.31403	+	3.17236i	0.0757396	+	0.182852i
$302$		−	4.76612i		−	0.274260i
$303$	−15.2401	+	6.31264i	−0.875519	+	0.362652i
$304$	−0.435300	−	0.435300i	−0.0249662	−	0.0249662i
$305$		0			0
$306$	−2.57902	+	11.9878i	−0.147433	+	0.685297i
$307$	−1.69613			−0.0968034			−0.0484017	−	0.998828i	$-0.515413\pi$
$307$	−1.69613			−0.0968034			−0.0484017	+	0.998828i	$0.515413\pi$
$308$	−1.92925	−	1.92925i	−0.109929	−	0.109929i
$309$	−0.801300	+	0.331909i	−0.0455844	+	0.0188817i
$310$		0			0
$311$	4.16844	+	10.0635i	0.236371	+	0.570649i	0.996902	−	0.0786518i	$-0.0250615\pi$
$311$	4.16844	+	10.0635i	0.236371	+	0.570649i	−0.760531	+	0.649301i	$0.775062\pi$
$312$	26.4331	+	10.9489i	1.49648	+	0.619861i
$313$	−10.0614	+	24.2903i	−0.568702	+	1.37297i	0.333947	+	0.942592i	$0.391619\pi$
$313$	−10.0614	+	24.2903i	−0.568702	+	1.37297i	−0.902649	+	0.430377i	$0.858381\pi$
$314$	−7.36524	+	7.36524i	−0.415645	+	0.415645i
$315$		0			0
$316$	0.620155	−	1.49719i	0.0348865	−	0.0842234i
$317$	23.1074	+	9.57139i	1.29784	+	0.537583i	0.921313	−	0.388823i	$-0.127118\pi$
$317$	23.1074	+	9.57139i	1.29784	+	0.537583i	0.376527	+	0.926406i	$0.377118\pi$
$318$	−7.35813	−	17.7641i	−0.412623	−	0.996161i
$319$			38.7399i			2.16902i
$320$		0			0
$321$	13.6476	+	13.6476i	0.761735	+	0.761735i
$322$	2.91286			0.162327
$323$	−3.47052	+	2.24162i	−0.193105	+	0.124727i
$324$	9.42103			0.523390
$325$		0			0
$326$	−6.49756	+	2.69138i	−0.359867	+	0.149062i
$327$			30.1389i			1.66668i
$328$	−0.917938	−	2.21610i	−0.0506847	−	0.122364i
$329$	−0.840209	−	0.348026i	−0.0463222	−	0.0191873i
$330$		0			0
$331$	22.8306	−	22.8306i	1.25488	−	1.25488i	0.301376	−	0.953505i	$-0.402554\pi$
$331$	22.8306	−	22.8306i	1.25488	−	1.25488i	0.953505	−	0.301376i	$-0.0974458\pi$
$332$	12.5245	−	12.5245i	0.687374	−	0.687374i
$333$	−4.89532	+	11.8183i	−0.268262	+	0.647641i
$334$	17.1443	+	7.10142i	0.938097	+	0.388572i
$335$		0			0
$336$		−	0.810961i		−	0.0442416i
$337$	11.8844	−	4.92267i	0.647383	−	0.268155i	−0.0347353	−	0.999397i	$-0.511059\pi$
$337$	11.8844	−	4.92267i	0.647383	−	0.268155i	0.682119	+	0.731242i	$0.261059\pi$
$338$	1.62281	+	1.62281i	0.0882693	+	0.0882693i
$339$	44.2450			2.40306
$340$		0			0
$341$	−11.5895			−0.627604
$342$	2.10722	+	2.10722i	0.113945	+	0.113945i
$343$	6.75868	−	2.79954i	0.364934	−	0.151161i
$344$		−	18.9582i		−	1.02216i
$345$		0			0
$346$	11.6943	+	4.84395i	0.628691	+	0.260412i
$347$	−10.3086	+	24.8871i	−0.553394	+	1.33601i	0.361521	+	0.932364i	$0.382257\pi$
$347$	−10.3086	+	24.8871i	−0.553394	+	1.33601i	−0.914915	+	0.403647i	$0.867743\pi$
$348$	15.8675	−	15.8675i	0.850589	−	0.850589i
$349$	10.1253	−	10.1253i	0.541995	−	0.541995i	−0.382119	−	0.924113i	$-0.624805\pi$
$349$	10.1253	−	10.1253i	0.541995	−	0.541995i	0.924113	+	0.382119i	$0.124805\pi$
$350$		0			0
$351$	−1.12021	−	0.464005i	−0.0597922	−	0.0247667i
$352$	9.49076	+	22.9127i	0.505859	+	1.22125i
$353$		−	1.65351i		−	0.0880076i	−0.999031	−	0.0440038i	$-0.985989\pi$
$353$		−	1.65351i		−	0.0880076i	0.999031	−	0.0440038i	$-0.0140114\pi$
$354$	−13.1809	+	5.45973i	−0.700559	+	0.290181i
$355$		0			0
$356$	−13.2088			−0.700065
$357$	−5.32084	−	1.14471i	−0.281609	−	0.0605845i
$358$	9.67206			0.511184
$359$	−12.2781	−	12.2781i	−0.648012	−	0.648012i	0.304500	−	0.952512i	$-0.401511\pi$
$359$	−12.2781	−	12.2781i	−0.648012	−	0.648012i	−0.952512	+	0.304500i	$0.901511\pi$
$360$		0			0
$361$		−	17.9959i		−	0.947154i
$362$	7.14564	+	17.2511i	0.375566	+	0.906697i
$363$	24.8191	+	10.2804i	1.30267	+	0.539582i
$364$	−0.876777	+	2.11673i	−0.0459556	+	0.110947i
$365$		0			0
$366$	1.88380	−	1.88380i	0.0984676	−	0.0984676i
$367$	3.66265	−	8.84242i	0.191189	−	0.461571i	−0.798996	−	0.601337i	$-0.794635\pi$
$367$	3.66265	−	8.84242i	0.191189	−	0.461571i	0.990185	+	0.139766i	$0.0446350\pi$
$368$	−3.25688	−	1.34904i	−0.169776	−	0.0703237i
$369$	0.974026	+	2.35151i	0.0507058	+	0.122415i
$370$		0			0
$371$	4.02267	−	1.66624i	0.208846	−	0.0865070i
$372$	4.74694	+	4.74694i	0.246117	+	0.246117i
$373$	−14.4236			−0.746828			−0.373414	−	0.927665i	$-0.621813\pi$
$373$	−14.4236			−0.746828			−0.373414	+	0.927665i	$0.621813\pi$
$374$	−18.0460	+	3.29858i	−0.933134	+	0.170565i
$375$		0			0
$376$	3.55049	+	3.55049i	0.183102	+	0.183102i
$377$	30.0553	−	12.4493i	1.54793	−	0.641172i
$378$			0.156789i			0.00806434i
$379$	−3.64196	−	8.79246i	−0.187075	−	0.451638i	0.802319	−	0.596895i	$-0.203599\pi$
$379$	−3.64196	−	8.79246i	−0.187075	−	0.451638i	−0.989394	+	0.145257i	$0.953599\pi$
$380$		0			0
$381$	−11.7409	+	28.3450i	−0.601503	+	1.45216i
$382$	−5.93089	+	5.93089i	−0.303451	+	0.303451i
$383$	−19.6401	+	19.6401i	−1.00356	+	1.00356i	−0.00356842	+	0.999994i	$0.501136\pi$
$383$	−19.6401	+	19.6401i	−1.00356	+	1.00356i	−0.999994	+	0.00356842i	$0.998864\pi$
$384$	4.39000	−	10.5984i	0.224026	−	0.540847i
$385$		0			0
$386$	5.63163	+	13.5960i	0.286643	+	0.692016i
$387$			20.1166i			1.02258i
$388$	−0.230529	+	0.0954881i	−0.0117033	+	0.00484767i
$389$	−14.8835	−	14.8835i	−0.754624	−	0.754624i	0.220715	−	0.975338i	$-0.429161\pi$
$389$	−14.8835	−	14.8835i	−0.754624	−	0.754624i	−0.975338	+	0.220715i	$0.929161\pi$
$390$		0			0
$391$	−13.4485	+	19.4646i	−0.680121	+	0.984369i
$392$	−19.7763			−0.998852
$393$	−17.5546	−	17.5546i	−0.885514	−	0.885514i
$394$	0.202367	−	0.0838230i	0.0101951	−	0.00422294i
$395$		0			0
$396$	−6.11688	−	14.7675i	−0.307385	−	0.742093i
$397$	−27.3935	−	11.3468i	−1.37484	−	0.569478i	−0.431744	−	0.901996i	$-0.642102\pi$
$397$	−27.3935	−	11.3468i	−1.37484	−	0.569478i	−0.943097	+	0.332518i	$0.892102\pi$
$398$	−7.81661	+	18.8710i	−0.391811	+	0.945916i
$399$	−0.935298	+	0.935298i	−0.0468235	+	0.0468235i
$400$		0			0
$401$	6.33937	−	15.3046i	0.316573	−	0.764275i	−0.682858	−	0.730551i	$-0.739263\pi$
$401$	6.33937	−	15.3046i	0.316573	−	0.764275i	0.999431	−	0.0337238i	$-0.0107366\pi$
$402$	−16.7256	−	6.92796i	−0.834196	−	0.345535i
$403$	3.72434	+	8.99135i	0.185523	+	0.447891i
$404$			7.29322i			0.362851i
$405$		0			0
$406$	−2.97455	−	2.97455i	−0.147625	−	0.147625i
$407$	−19.1379			−0.948629
$408$	24.7224	+	17.0812i	1.22394	+	0.845647i
$409$	−19.3593			−0.957257			−0.478629	−	0.878017i	$-0.658866\pi$
$409$	−19.3593			−0.957257			−0.478629	+	0.878017i	$0.658866\pi$
$410$		0			0
$411$	−7.01500	+	2.90571i	−0.346024	+	0.143328i
$412$			0.383467i			0.0188921i
$413$	−1.23635	−	2.98482i	−0.0608369	−	0.146873i
$414$	15.7660	+	6.53050i	0.774857	+	0.320956i
$415$		0			0
$416$	14.7263	−	14.7263i	0.722015	−	0.722015i
$417$	−21.4776	+	21.4776i	−1.05176	+	1.05176i
$418$	−1.70615	+	4.11900i	−0.0834503	+	0.201467i
$419$	13.3054	+	5.51126i	0.650009	+	0.269243i	0.683228	−	0.730205i	$-0.260576\pi$
$419$	13.3054	+	5.51126i	0.650009	+	0.269243i	−0.0332183	+	0.999448i	$0.510576\pi$
$420$		0			0
$421$		−	26.7439i		−	1.30342i	−0.758468	−	0.651710i	$-0.774052\pi$
$421$		−	26.7439i		−	1.30342i	0.758468	−	0.651710i	$-0.225948\pi$
$422$	13.6683	−	5.66161i	0.665364	−	0.275603i
$423$	−3.76743	−	3.76743i	−0.183179	−	0.183179i
$424$	−24.0397			−1.16747
$425$		0			0
$426$	−16.3529			−0.792298
$427$	0.426584	+	0.426584i	0.0206439	+	0.0206439i
$428$	7.88379	−	3.26557i	0.381077	−	0.157847i
$429$		−	45.4194i		−	2.19287i
$430$		0			0
$431$	−26.4399	−	10.9518i	−1.27356	−	0.527527i	−0.359518	−	0.933138i	$-0.617059\pi$
$431$	−26.4399	−	10.9518i	−1.27356	−	0.527527i	−0.914046	+	0.405611i	$0.867059\pi$
$432$	0.0726141	−	0.175306i	0.00349365	−	0.00843442i
$433$	25.5919	−	25.5919i	1.22987	−	1.22987i	0.265855	−	0.964013i	$-0.414346\pi$
$433$	25.5919	−	25.5919i	1.22987	−	1.22987i	0.964013	−	0.265855i	$-0.0856542\pi$
$434$	0.889869	−	0.889869i	0.0427151	−	0.0427151i
$435$		0			0
$436$	12.3109	+	5.09935i	0.589586	+	0.244215i
$437$	2.20034	+	5.31210i	0.105257	+	0.254112i
$438$			28.4679i			1.36025i
$439$	29.9716	−	12.4146i	1.43047	−	0.592519i	0.473000	−	0.881063i	$-0.343171\pi$
$439$	29.9716	−	12.4146i	1.43047	−	0.592519i	0.957467	+	0.288544i	$0.0931711\pi$
$440$		0			0
$441$	20.9846			0.999268
$442$	8.35828	+	12.9404i	0.397563	+	0.615513i
$443$	1.88468			0.0895437			0.0447719	−	0.998997i	$-0.485744\pi$
$443$	1.88468			0.0895437			0.0447719	+	0.998997i	$0.485744\pi$
$444$	7.83870	+	7.83870i	0.372008	+	0.372008i
$445$		0			0
$446$			1.01793i			0.0482005i
$447$	5.17620	+	12.4965i	0.244826	+	0.591062i
$448$	−3.09351	−	1.28137i	−0.146154	−	0.0605391i
$449$	0.766010	−	1.84931i	0.0361503	−	0.0872745i	−0.904773	−	0.425894i	$-0.859960\pi$
$449$	0.766010	−	1.84931i	0.0361503	−	0.0872745i	0.940924	+	0.338619i	$0.109960\pi$
$450$		0			0
$451$	−2.69258	+	2.69258i	−0.126788	+	0.126788i
$452$	7.48604	−	18.0729i	0.352114	−	0.850078i
$453$	11.4501	+	4.74278i	0.537972	+	0.222835i
$454$	−0.753158	−	1.81828i	−0.0353474	−	0.0853363i
$455$		0			0
$456$	6.74700	−	2.79470i	0.315957	−	0.130874i
$457$	−12.4863	−	12.4863i	−0.584086	−	0.584086i	0.351938	−	0.936023i	$-0.385523\pi$
$457$	−12.4863	−	12.4863i	−0.584086	−	0.584086i	−0.936023	+	0.351938i	$0.885523\pi$
$458$	−12.1950			−0.569834
$459$	−1.04771	−	0.723885i	−0.0489030	−	0.0337881i
$460$		0			0
$461$	−22.5151	−	22.5151i	−1.04863	−	1.04863i	−0.998755	−	0.0498792i	$-0.984116\pi$
$461$	−22.5151	−	22.5151i	−1.04863	−	1.04863i	−0.0498792	−	0.998755i	$-0.515884\pi$
$462$	−5.42610	+	2.24757i	−0.252445	+	0.104566i
$463$		−	15.7977i		−	0.734179i	−0.930186	−	0.367090i	$-0.880354\pi$
$463$		−	15.7977i		−	0.734179i	0.930186	−	0.367090i	$-0.119646\pi$
$464$	1.94825	+	4.70348i	0.0904450	+	0.218354i
$465$		0			0
$466$	2.36154	−	5.70125i	0.109396	−	0.264105i
$467$	−6.26872	+	6.26872i	−0.290082	+	0.290082i	−0.837112	−	0.547031i	$-0.815758\pi$
$467$	−6.26872	+	6.26872i	−0.290082	+	0.290082i	0.547031	+	0.837112i	$0.315758\pi$
$468$	−9.49122	+	9.49122i	−0.438732	+	0.438732i
$469$	1.56883	−	3.78750i	0.0724419	−	0.174890i
$470$		0			0
$471$	−10.3650	−	25.0234i	−0.477595	−	1.15302i
$472$			17.8374i			0.821035i
$473$	−27.8049	+	11.5172i	−1.27847	+	0.529560i
$474$	−2.46670	−	2.46670i	−0.113299	−	0.113299i
$475$		0			0
$476$	−1.36784	+	1.97974i	−0.0626950	+	0.0907413i
$477$	25.5086			1.16796
$478$	0.853527	+	0.853527i	0.0390394	+	0.0390394i
$479$	−11.0031	+	4.55765i	−0.502746	+	0.208244i	−0.619619	−	0.784903i	$-0.712713\pi$
$479$	−11.0031	+	4.55765i	−0.502746	+	0.208244i	0.116873	+	0.993147i	$0.462713\pi$
$480$		0			0
$481$	6.15006	+	14.8476i	0.280419	+	0.676991i
$482$	2.19457	+	0.909021i	0.0999600	+	0.0414048i
$483$	−2.89859	+	6.99782i	−0.131890	+	0.318412i
$484$	8.39855	−	8.39855i	0.381752	−	0.381752i
$485$		0			0
$486$	8.09830	−	19.5510i	0.367346	−	0.886852i
$487$	24.7378	+	10.2467i	1.12098	+	0.464324i	0.864704	−	0.502281i	$-0.167506\pi$
$487$	24.7378	+	10.2467i	1.12098	+	0.464324i	0.256272	+	0.966605i	$0.417506\pi$
$488$	−1.27465	−	3.07727i	−0.0577006	−	0.139302i
$489$		−	18.2879i		−	0.827006i
$490$		0			0
$491$	16.3477	+	16.3477i	0.737761	+	0.737761i	0.972144	−	0.234383i	$-0.0753070\pi$
$491$	16.3477	+	16.3477i	0.737761	+	0.737761i	−0.234383	+	0.972144i	$0.575307\pi$
$492$	2.20571			0.0994411
$493$	33.6103	−	6.14355i	1.51373	−	0.276691i
$494$	3.74389			0.168446
$495$		0			0
$496$	−1.40710	+	0.582838i	−0.0631805	+	0.0261702i
$497$		−	3.70309i		−	0.166106i
$498$	−14.5911	−	35.2259i	−0.653841	−	1.57851i
$499$	−4.58831	−	1.90054i	−0.205401	−	0.0850799i	0.277611	−	0.960694i	$-0.410457\pi$
$499$	−4.58831	−	1.90054i	−0.205401	−	0.0850799i	−0.483012	+	0.875614i	$0.660457\pi$
$500$		0			0
$501$	−34.1208	+	34.1208i	−1.52440	+	1.52440i
$502$	11.6806	−	11.6806i	0.521330	−	0.521330i
$503$	8.94738	−	21.6009i	0.398944	−	0.963136i	−0.588973	−	0.808153i	$-0.700468\pi$
$503$	8.94738	−	21.6009i	0.398944	−	0.963136i	0.987917	−	0.154983i	$-0.0495323\pi$
$504$	4.53458	+	1.87829i	0.201986	+	0.0836655i
$505$		0			0
$506$			25.5305i			1.13497i
$507$	−5.51349	+	2.28376i	−0.244863	+	0.101425i
$508$	9.59165	+	9.59165i	0.425561	+	0.425561i
$509$	−23.9562			−1.06184			−0.530921	−	0.847422i	$-0.678154\pi$
$509$	−23.9562			−1.06184			−0.530921	+	0.847422i	$0.678154\pi$
$510$		0			0
$511$	−6.44654			−0.285178
$512$	4.86316	+	4.86316i	0.214924	+	0.214924i
$513$	−0.285931	+	0.118437i	−0.0126242	+	0.00522911i
$514$			14.8044i			0.652993i
$515$		0			0
$516$	16.1060	+	6.67132i	0.709027	+	0.293688i
$517$	3.05036	−	7.36423i	0.134155	−	0.323878i
$518$	1.46946	−	1.46946i	0.0645642	−	0.0645642i
$519$	−23.2741	+	23.2741i	−1.02162	+	1.02162i
$520$		0			0
$521$	7.00747	+	2.90259i	0.307003	+	0.127165i	0.530866	−	0.847456i	$-0.321867\pi$
$521$	7.00747	+	2.90259i	0.307003	+	0.127165i	−0.223863	+	0.974621i	$0.571867\pi$
$522$	−9.43114	−	22.7688i	−0.412790	−	0.996563i
$523$			17.3848i			0.760185i	0.924948	+	0.380093i	$0.124108\pi$
$523$			17.3848i			0.760185i	−0.924948	+	0.380093i	$0.875892\pi$
$524$	−10.1407	+	4.20044i	−0.443001	+	0.183497i
$525$		0			0
$526$	8.60461			0.375179
$527$	1.83791	+	10.0549i	0.0800605	+	0.437997i
$528$	7.10788			0.309331
$529$	7.01842	+	7.01842i	0.305149	+	0.305149i
$530$		0			0
$531$		−	18.9273i		−	0.821377i
$532$	0.223796	+	0.540292i	0.00970280	+	0.0234246i
$533$	2.95423	+	1.22368i	0.127962	+	0.0530036i
$534$	−10.8811	+	26.2693i	−0.470871	+	1.13678i
$535$		0			0
$536$	−16.0049	+	16.0049i	−0.691305	+	0.691305i
$537$	−9.62469	+	23.2361i	−0.415336	+	1.00271i
$538$	−2.65537	−	1.09989i	−0.114481	−	0.0474196i
$539$	12.0141	+	29.0047i	0.517486	+	1.24932i
$540$		0			0
$541$	−20.5428	+	8.50911i	−0.883204	+	0.365835i	−0.777739	−	0.628588i	$-0.783633\pi$
$541$	−20.5428	+	8.50911i	−0.883204	+	0.365835i	−0.105466	+	0.994423i	$0.533633\pi$
$542$	−8.85896	−	8.85896i	−0.380525	−	0.380525i
$543$	−48.5545			−2.08367
$544$	18.3737	−	11.8677i	0.787767	−	0.508822i
$545$		0			0
$546$	3.48742	+	3.48742i	0.149248	+	0.149248i
$547$	37.1299	−	15.3797i	1.58756	−	0.657589i	0.597972	−	0.801517i	$-0.295974\pi$
$547$	37.1299	−	15.3797i	1.58756	−	0.657589i	0.989588	+	0.143929i	$0.0459736\pi$
$548$			3.35707i			0.143407i
$549$	1.35253	+	3.26530i	0.0577246	+	0.139360i
$550$		0			0
$551$	3.17767	−	7.67157i	0.135373	−	0.326820i
$552$	29.5708	−	29.5708i	1.25862	−	1.25862i
$553$	0.558581	−	0.558581i	0.0237533	−	0.0237533i
$554$	−1.47557	+	3.56234i	−0.0626909	+	0.151349i
$555$		0			0
$556$	5.13912	+	12.4069i	0.217947	+	0.526172i
$557$		−	6.44000i		−	0.272872i	−0.990649	−	0.136436i	$-0.956435\pi$
$557$		−	6.44000i		−	0.272872i	0.990649	−	0.136436i	$-0.0435647\pi$
$558$	6.81152	−	2.82143i	0.288355	−	0.119440i
$559$	17.8705	+	17.8705i	0.755844	+	0.755844i
$560$		0			0
$561$	10.0331	−	46.6359i	0.423598	−	1.96897i
$562$	−13.5765			−0.572691
$563$	−14.0594	−	14.0594i	−0.592532	−	0.592532i	0.345782	−	0.938315i	$-0.387614\pi$
$563$	−14.0594	−	14.0594i	−0.592532	−	0.592532i	−0.938315	+	0.345782i	$0.887614\pi$
$564$	−4.26572	+	1.76692i	−0.179619	+	0.0744008i
$565$		0			0
$566$	2.03017	+	4.90127i	0.0853345	+	0.206016i
$567$	4.24282	+	1.75743i	0.178182	+	0.0738052i
$568$	−7.82410	+	18.8891i	−0.328292	+	0.792567i
$569$	−4.57941	+	4.57941i	−0.191979	+	0.191979i	−0.796551	−	0.604572i	$-0.793344\pi$
$569$	−4.57941	+	4.57941i	−0.191979	+	0.191979i	0.604572	+	0.796551i	$0.293344\pi$
$570$		0			0
$571$	−14.0045	+	33.8098i	−0.586069	+	1.41490i	0.301164	+	0.953572i	$0.402625\pi$
$571$	−14.0045	+	33.8098i	−0.586069	+	1.41490i	−0.887232	+	0.461323i	$0.847375\pi$
$572$	−18.5526	−	7.68473i	−0.775723	−	0.321315i
$573$	−8.34647	−	20.1502i	−0.348679	−	0.841785i
$574$		−	0.413486i		−	0.0172586i
$575$		0			0
$576$	−13.8710	−	13.8710i	−0.577959	−	0.577959i
$577$	−19.2887			−0.802999			−0.401500	−	0.915859i	$-0.631511\pi$
$577$	−19.2887			−0.802999			−0.401500	+	0.915859i	$0.631511\pi$
$578$	5.72361	+	15.1334i	0.238071	+	0.629465i
$579$	−38.2669			−1.59032
$580$		0			0
$581$	7.97688	−	3.30413i	0.330937	−	0.137079i
$582$			0.537130i			0.0222647i
$583$	14.6042	+	35.2577i	0.604845	+	1.46022i
$584$	32.8831	+	13.6206i	1.36071	+	0.563625i
$585$		0			0
$586$	1.32658	−	1.32658i	0.0548006	−	0.0548006i
$587$	−12.6487	+	12.6487i	−0.522068	+	0.522068i	−0.918196	−	0.396127i	$-0.870354\pi$
$587$	−12.6487	+	12.6487i	−0.522068	+	0.522068i	0.396127	+	0.918196i	$0.370354\pi$
$588$	6.95919	−	16.8010i	0.286992	−	0.692860i
$589$	2.29503	+	0.950633i	0.0945651	+	0.0391702i
$590$		0			0
$591$			0.569576i			0.0234292i
$592$	−2.32356	+	0.962450i	−0.0954977	+	0.0395565i
$593$	−15.9962	−	15.9962i	−0.656884	−	0.656884i	0.297757	−	0.954642i	$-0.403761\pi$
$593$	−15.9962	−	15.9962i	−0.656884	−	0.656884i	−0.954642	+	0.297757i	$0.903761\pi$
$594$	−1.37421			−0.0563847
$595$		0			0
$596$	5.98025			0.244961
$597$	−37.5571	−	37.5571i	−1.53711	−	1.53711i
$598$	19.8071	−	8.20436i	0.809972	−	0.335501i
$599$		−	17.4019i		−	0.711023i	−0.934672	−	0.355511i	$-0.884307\pi$
$599$		−	17.4019i		−	0.711023i	0.934672	−	0.355511i	$-0.115693\pi$
$600$		0			0
$601$	19.9088	+	8.24649i	0.812096	+	0.336381i	0.749790	−	0.661676i	$-0.230155\pi$
$601$	19.9088	+	8.24649i	0.812096	+	0.336381i	0.0623060	+	0.998057i	$0.480155\pi$
$602$	1.25062	−	3.01926i	0.0509713	−	0.123056i
$603$	16.9828	−	16.9828i	0.691593	−	0.691593i
$604$	3.87460	−	3.87460i	0.157655	−	0.157655i
$605$		0			0
$606$	14.5046	+	6.00799i	0.589208	+	0.244058i
$607$	6.14655	+	14.8391i	0.249481	+	0.602300i	0.998160	−	0.0606323i	$-0.0193117\pi$
$607$	6.14655	+	14.8391i	0.249481	+	0.602300i	−0.748679	+	0.662932i	$0.769312\pi$
$608$		−	5.31584i		−	0.215586i
$609$	10.1060	−	4.18605i	0.409517	−	0.169627i
$610$		0			0
$611$	−6.69358			−0.270793
$612$	−11.8420	+	7.64882i	−0.478686	+	0.309185i
$613$	15.6440			0.631855			0.315928	−	0.948783i	$-0.397684\pi$
$613$	15.6440			0.631855			0.315928	+	0.948783i	$0.397684\pi$
$614$	1.14147	+	1.14147i	0.0460658	+	0.0460658i
$615$		0			0
$616$			7.34301i			0.295858i
$617$	−8.96313	−	21.6389i	−0.360842	−	0.871150i	−0.995177	−	0.0980919i	$-0.968726\pi$
$617$	−8.96313	−	21.6389i	−0.360842	−	0.871150i	0.634335	−	0.773058i	$-0.281274\pi$
$618$	0.762628	+	0.315891i	0.0306774	+	0.0127070i
$619$	−11.0559	+	26.6912i	−0.444372	+	1.07281i	0.530026	+	0.847981i	$0.322182\pi$
$619$	−11.0559	+	26.6912i	−0.444372	+	1.07281i	−0.974398	+	0.224828i	$0.927818\pi$
$620$		0			0
$621$	−1.25318	+	1.25318i	−0.0502884	+	0.0502884i
$622$	3.96727	−	9.57783i	0.159073	−	0.384036i
$623$	−5.94866	−	2.46402i	−0.238328	−	0.0987187i
$624$	−2.28416	−	5.51444i	−0.0914394	−	0.220754i
$625$		0			0
$626$	23.1180	−	9.57580i	0.923982	−	0.382726i
$627$	−8.19766	−	8.19766i	−0.327383	−	0.327383i
$628$	−11.9751			−0.477858
$629$	3.03497	+	16.6038i	0.121012	+	0.662036i
$630$		0			0
$631$	29.7914	+	29.7914i	1.18598	+	1.18598i	0.978169	+	0.207809i	$0.0666332\pi$
$631$	29.7914	+	29.7914i	1.18598	+	1.18598i	0.207809	+	0.978169i	$0.433367\pi$
$632$	−4.02946	+	1.66906i	−0.160284	+	0.0663916i
$633$			38.4705i			1.52907i
$634$	−9.10946	−	21.9922i	−0.361783	−	0.873421i
$635$		0			0
$636$	8.45948	−	20.4230i	0.335440	−	0.809824i
$637$	18.6417	−	18.6417i	0.738610	−	0.738610i
$638$	26.0712	−	26.0712i	1.03217	−	1.03217i
$639$	8.30217	−	20.0432i	0.328429	−	0.792897i
$640$		0			0
$641$	7.27533	+	17.5642i	0.287358	+	0.693744i	0.999969	−	0.00781522i	$-0.00248769\pi$
$641$	7.27533	+	17.5642i	0.287358	+	0.693744i	−0.712611	+	0.701559i	$0.752488\pi$
$642$		−	18.3692i		−	0.724973i
$643$	18.7908	−	7.78340i	0.741036	−	0.306947i	0.0199581	−	0.999801i	$-0.493647\pi$
$643$	18.7908	−	7.78340i	0.741036	−	0.306947i	0.721078	+	0.692853i	$0.243647\pi$
$644$	2.36799	+	2.36799i	0.0933119	+	0.0933119i
$645$		0			0
$646$	3.84416	+	0.827023i	0.151247	+	0.0325388i
$647$	16.7736			0.659440			0.329720	−	0.944079i	$-0.393046\pi$
$647$	16.7736			0.659440			0.329720	+	0.944079i	$0.393046\pi$
$648$	−17.9289	−	17.9289i	−0.704315	−	0.704315i
$649$	26.1612	−	10.8363i	1.02692	−	0.425362i
$650$		0			0
$651$	1.25230	+	3.02332i	0.0490816	+	0.118493i
$652$	−7.47010	−	3.09422i	−0.292552	−	0.121179i
$653$	2.56320	−	6.18810i	0.100306	−	0.242159i	−0.865758	−	0.500462i	$-0.833163\pi$
$653$	2.56320	−	6.18810i	0.100306	−	0.242159i	0.966064	+	0.258303i	$0.0831633\pi$
$654$	20.2829	−	20.2829i	0.793124	−	0.793124i
$655$		0			0
$656$	−0.191500	+	0.462321i	−0.00747680	+	0.0180506i
$657$	−34.8923	−	14.4529i	−1.36128	−	0.563860i
$658$	0.331230	+	0.799660i	0.0129127	+	0.0311740i
$659$		−	36.0525i		−	1.40440i	−0.711978	−	0.702202i	$-0.752200\pi$
$659$		−	36.0525i		−	1.40440i	0.711978	−	0.702202i	$-0.247800\pi$
$660$		0			0
$661$	−31.6304	−	31.6304i	−1.23028	−	1.23028i	−0.963855	−	0.266427i	$-0.914157\pi$
$661$	−31.6304	−	31.6304i	−1.23028	−	1.23028i	−0.266427	−	0.963855i	$-0.585843\pi$
$662$	−30.7291			−1.19432
$663$	−39.4053	+	7.20280i	−1.53037	+	0.279734i
$664$	−47.6704			−1.84997
$665$		0			0
$666$	11.2480	−	4.65907i	0.435850	−	0.180535i
$667$		−	47.5501i		−	1.84115i
$668$	8.16434	+	19.7105i	0.315888	+	0.762621i
$669$	−2.44547	−	1.01295i	−0.0945474	−	0.0391628i
$670$		0			0
$671$	−3.73891	+	3.73891i	−0.144339	+	0.144339i
$672$	4.95168	−	4.95168i	0.191015	−	0.191015i
$673$	−1.88991	+	4.56264i	−0.0728506	+	0.175877i	−0.956110	−	0.293007i	$-0.905344\pi$
$673$	−1.88991	+	4.56264i	−0.0728506	+	0.175877i	0.883260	+	0.468884i	$0.155344\pi$
$674$	−11.3108	−	4.68510i	−0.435677	−	0.180463i
$675$		0			0
$676$			2.63851i			0.101481i
$677$	−26.2906	+	10.8899i	−1.01043	+	0.418534i	−0.825612	−	0.564238i	$-0.809170\pi$
$677$	−26.2906	+	10.8899i	−1.01043	+	0.418534i	−0.184819	+	0.982773i	$0.559170\pi$
$678$	−29.7761	−	29.7761i	−1.14354	−	1.14354i
$679$	−0.121633			−0.00466783
$680$		0			0
$681$	5.11770			0.196111
$682$	7.79949	+	7.79949i	0.298658	+	0.298658i
$683$	30.2745	−	12.5401i	1.15842	−	0.479835i	0.281073	−	0.959686i	$-0.409310\pi$
$683$	30.2745	−	12.5401i	1.15842	−	0.479835i	0.877350	+	0.479852i	$0.159310\pi$
$684$			3.42611i			0.131000i
$685$		0			0
$686$	−6.43250	−	2.66443i	−0.245594	−	0.101728i
$687$	12.1353	−	29.2971i	0.462989	−	1.11775i
$688$	−2.79664	+	2.79664i	−0.106621	+	0.106621i
$689$	22.6605	−	22.6605i	0.863297	−	0.863297i
$690$		0			0
$691$	6.13856	+	2.54268i	0.233522	+	0.0967279i	0.496376	−	0.868108i	$-0.334664\pi$
$691$	6.13856	+	2.54268i	0.233522	+	0.0967279i	−0.262854	+	0.964836i	$0.584664\pi$
$692$	5.56898	+	13.4447i	0.211701	+	0.511091i
$693$		−	7.79168i		−	0.295982i
$694$	23.6860	−	9.81108i	0.899110	−	0.372423i
$695$		0			0
$696$	−60.3943			−2.28924
$697$	2.76305	+	1.90905i	0.104658	+	0.0723103i
$698$	−13.6283			−0.515837
$699$	11.3467	+	11.3467i	0.429170	+	0.429170i
$700$		0			0
$701$		−	24.2220i		−	0.914852i	−0.889248	−	0.457426i	$-0.848772\pi$
$701$		−	24.2220i		−	0.914852i	0.889248	−	0.457426i	$-0.151228\pi$
$702$	0.441611	+	1.06614i	0.0166675	+	0.0402390i
$703$	3.78982	+	1.56980i	0.142936	+	0.0592060i
$704$	11.2309	−	27.1138i	0.423281	−	1.02189i
$705$		0			0
$706$	−1.11278	+	1.11278i	−0.0418801	+	0.0418801i
$707$	−1.36050	+	3.28455i	−0.0511670	+	0.123528i
$708$	−15.1538	−	6.27693i	−0.569516	−	0.235901i
$709$	−0.466820	−	1.12700i	−0.0175318	−	0.0423255i	0.914871	−	0.403746i	$-0.132292\pi$
$709$	−0.466820	−	1.12700i	−0.0175318	−	0.0423255i	−0.932403	+	0.361420i	$0.882292\pi$
$710$		0			0
$711$	4.27567	−	1.77104i	0.160350	−	0.0664192i
$712$	25.1373	+	25.1373i	0.942062	+	0.942062i
$713$	14.2251			0.532734
$714$	2.81046	+	4.35119i	0.105179	+	0.162839i
$715$		0			0
$716$	7.86285	+	7.86285i	0.293849	+	0.293849i
$717$	−2.89985	+	1.20116i	−0.108297	+	0.0448581i
$718$			16.5258i			0.616738i
$719$	6.74904	+	16.2936i	0.251697	+	0.607650i	0.998341	−	0.0575735i	$-0.0183364\pi$
$719$	6.74904	+	16.2936i	0.251697	+	0.607650i	−0.746645	+	0.665223i	$0.768336\pi$
$720$		0			0
$721$	−0.0715333	+	0.172697i	−0.00266404	+	0.00643156i
$722$	−12.1109	+	12.1109i	−0.450721	+	0.450721i
$723$	−4.36765	+	4.36765i	−0.162435	+	0.162435i
$724$	−8.21518	+	19.8332i	−0.305315	+	0.737095i
$725$		0			0
$726$	−9.78428	−	23.6213i	−0.363129	−	0.876670i
$727$			11.3177i			0.419751i	0.977728	+	0.209876i	$0.0673059\pi$
$727$			11.3177i			0.419751i	−0.977728	+	0.209876i	$0.932694\pi$
$728$	5.69687	−	2.35972i	0.211140	−	0.0874570i
$729$	20.6459	+	20.6459i	0.764664	+	0.764664i
$730$		0			0
$731$	14.4016	+	22.2968i	0.532662	+	0.824676i
$732$	3.06285			0.113206
$733$	−1.79642	−	1.79642i	−0.0663522	−	0.0663522i	0.673152	−	0.739504i	$-0.264940\pi$
$733$	−1.79642	−	1.79642i	−0.0663522	−	0.0663522i	−0.739504	+	0.673152i	$0.764940\pi$
$734$	−8.41568	+	3.48589i	−0.310628	+	0.128666i
$735$		0			0
$736$	−11.6491	−	28.1235i	−0.429393	−	1.03665i
$737$	33.1965	+	13.7504i	1.22281	+	0.506503i
$738$	0.927018	−	2.23802i	0.0341240	−	0.0823827i
$739$	−12.6407	+	12.6407i	−0.464997	+	0.464997i	−0.900289	−	0.435292i	$-0.856645\pi$
$739$	−12.6407	+	12.6407i	−0.464997	+	0.464997i	0.435292	+	0.900289i	$0.356645\pi$
$740$		0			0
$741$	−3.72555	+	8.99428i	−0.136862	+	0.330413i
$742$	−3.82853	−	1.58583i	−0.140550	−	0.0582176i
$743$	−4.57351	−	11.0414i	−0.167786	−	0.405071i	0.817513	−	0.575910i	$-0.195352\pi$
$743$	−4.57351	−	11.0414i	−0.167786	−	0.405071i	−0.985299	+	0.170839i	$0.945352\pi$
$744$		−	18.0676i		−	0.662390i
$745$		0			0
$746$	9.70683	+	9.70683i	0.355392	+	0.355392i
$747$	50.5831			1.85074
$748$	−17.3519	−	11.9888i	−0.634450	−	0.438354i
$749$	4.15968			0.151992
$750$		0			0
$751$	24.7061	−	10.2336i	0.901537	−	0.373429i	0.116726	−	0.993164i	$-0.462760\pi$
$751$	24.7061	−	10.2336i	0.901537	−	0.373429i	0.784811	+	0.619735i	$0.212760\pi$
$752$		−	1.04751i		−	0.0381987i
$753$	16.4379	+	39.6847i	0.599031	+	1.44619i
$754$	−28.6048	−	11.8485i	−1.04172	−	0.431496i
$755$		0			0
$756$	−0.127461	+	0.127461i	−0.00463569	+	0.00463569i
$757$	−0.179229	+	0.179229i	−0.00651419	+	0.00651419i	−0.710356	−	0.703842i	$-0.751466\pi$
$757$	−0.179229	+	0.179229i	−0.00651419	+	0.00651419i	0.703842	+	0.710356i	$0.251466\pi$
$758$	−3.46619	+	8.36813i	−0.125898	+	0.303944i
$759$	−61.3341	−	25.4054i	−2.22629	−	0.922159i
$760$		0			0
$761$			32.3234i			1.17172i	0.810412	+	0.585860i	$0.199243\pi$
$761$			32.3234i			1.17172i	−0.810412	+	0.585860i	$0.800757\pi$
$762$	26.9770	−	11.1742i	0.977274	−	0.404800i
$763$	4.59305	+	4.59305i	0.166279	+	0.166279i
$764$	−9.64298			−0.348871
$765$		0			0
$766$	26.4348			0.955129
$767$	−16.8141	−	16.8141i	−0.607121	−	0.607121i
$768$	−38.7942	+	16.0691i	−1.39986	+	0.579843i
$769$		−	7.23844i		−	0.261025i	−0.991447	−	0.130512i	$-0.958338\pi$
$769$		−	7.23844i		−	0.261025i	0.991447	−	0.130512i	$-0.0416622\pi$
$770$		0			0
$771$	−35.5659	−	14.7319i	−1.28087	−	0.530555i
$772$	−6.47456	+	15.6310i	−0.233025	+	0.562571i
$773$	−5.84658	+	5.84658i	−0.210287	+	0.210287i	−0.804389	−	0.594102i	$-0.797507\pi$
$773$	−5.84658	+	5.84658i	−0.210287	+	0.210287i	0.594102	+	0.804389i	$0.297507\pi$
$774$	13.5381	−	13.5381i	0.486616	−	0.486616i
$775$		0			0
$776$	0.620435	+	0.256992i	0.0222723	+	0.00922549i
$777$	2.06795	+	4.99247i	0.0741872	+	0.179104i
$778$			20.0326i			0.718205i
$779$	0.754064	−	0.312344i	0.0270172	−	0.0111909i
$780$		0			0
$781$	32.4567			1.16139
$782$	22.1499	−	4.04873i	0.792080	−	0.144782i
$783$	2.55945			0.0914673
$784$	2.91732	+	2.91732i	0.104190	+	0.104190i
$785$		0			0
$786$			23.6279i			0.842778i
$787$	4.08149	+	9.85358i	0.145489	+	0.351242i	0.979779	−	0.200085i	$-0.0641217\pi$
$787$	4.08149	+	9.85358i	0.145489	+	0.351242i	−0.834289	+	0.551327i	$0.814122\pi$
$788$	0.232657	+	0.0963695i	0.00828805	+	0.00343302i
$789$	−8.56247	+	20.6716i	−0.304832	+	0.735929i
$790$		0			0
$791$	6.74277	−	6.74277i	0.239745	−	0.239745i
$792$	−16.4627	+	39.7445i	−0.584977	+	1.41226i
$793$	4.10224	+	1.69920i	0.145675	+	0.0603405i
$794$	10.7992	+	26.0715i	0.383248	+	0.925242i
$795$		0			0
$796$	−21.6955	+	8.98658i	−0.768978	+	0.318521i
$797$	16.0429	+	16.0429i	0.568269	+	0.568269i	0.931643	−	0.363374i	$-0.118375\pi$
$797$	16.0429	+	16.0429i	0.568269	+	0.568269i	−0.363374	+	0.931643i	$0.618375\pi$
$798$	1.25888			0.0445637
$799$	−6.87286	−	1.47861i	−0.243144	−	0.0523093i
$800$		0			0
$801$	−26.6733	−	26.6733i	−0.942454	−	0.942454i
$802$	−14.5660	+	6.03342i	−0.514342	+	0.213048i
$803$		−	56.5023i		−	1.99392i
$804$	−7.96493	−	19.2290i	−0.280901	−	0.678156i
$805$		0			0
$806$	3.54460	−	8.55742i	0.124853	−	0.301422i
$807$	5.28472	−	5.28472i	0.186031	−	0.186031i
$808$	13.8796	−	13.8796i	0.488281	−	0.488281i
$809$	−7.24370	+	17.4878i	−0.254675	+	0.614840i	−0.998570	−	0.0534567i	$-0.982976\pi$
$809$	−7.24370	+	17.4878i	−0.254675	+	0.614840i	0.743895	+	0.668296i	$0.232976\pi$
$810$		0			0
$811$	−10.8154	−	26.1106i	−0.379779	−	0.916867i	−0.992007	−	0.126186i	$-0.959726\pi$
$811$	−10.8154	−	26.1106i	−0.379779	−	0.916867i	0.612228	−	0.790681i	$-0.290274\pi$
$812$		−	4.83630i		−	0.169721i
$813$	30.0983	−	12.4671i	1.05559	−	0.437241i
$814$	12.8794	+	12.8794i	0.451423	+	0.451423i
$815$		0			0
$816$	−1.12720	−	6.16671i	−0.0394598	−	0.215878i
$817$	6.45084			0.225686
$818$	13.0285	+	13.0285i	0.455530	+	0.455530i
$819$	−6.04495	+	2.50390i	−0.211228	+	0.0874934i
$820$		0			0
$821$	5.59227	+	13.5009i	0.195172	+	0.471186i	0.990922	−	0.134439i	$-0.0429232\pi$
$821$	5.59227	+	13.5009i	0.195172	+	0.471186i	−0.795750	+	0.605625i	$0.792923\pi$
$822$	6.67645	+	2.76548i	0.232868	+	0.0964570i
$823$	−7.45453	+	17.9968i	−0.259848	+	0.627330i	−0.998928	−	0.0462883i	$-0.985261\pi$
$823$	−7.45453	+	17.9968i	−0.259848	+	0.627330i	0.739080	+	0.673618i	$0.235261\pi$
$824$	0.729767	−	0.729767i	0.0254226	−	0.0254226i
$825$		0			0
$826$	−1.17668	+	2.84076i	−0.0409420	+	0.0988428i
$827$	−9.01621	−	3.73464i	−0.313524	−	0.129866i	0.220372	−	0.975416i	$-0.429273\pi$
$827$	−9.01621	−	3.73464i	−0.313524	−	0.129866i	−0.533896	+	0.845550i	$0.679273\pi$
$828$	7.50797	+	18.1258i	0.260920	+	0.629916i
$829$			5.96301i			0.207104i	0.994624	+	0.103552i	$0.0330208\pi$
$829$			5.96301i			0.207104i	−0.994624	+	0.103552i	$0.966979\pi$
$830$		0			0
$831$	−7.08978	−	7.08978i	−0.245942	−	0.245942i
$832$	−24.6446			−0.854398
$833$	23.2589	−	15.0230i	0.805873	−	0.520517i
$834$	28.9081			1.00100
$835$		0			0
$836$	−4.73552	+	1.96152i	−0.163782	+	0.0678405i
$837$			0.765686i			0.0264660i
$838$	−5.24528	−	12.6632i	−0.181195	−	0.437444i
$839$	20.9048	+	8.65906i	0.721715	+	0.298944i	0.713142	−	0.701019i	$-0.247271\pi$
$839$	20.9048	+	8.65906i	0.721715	+	0.298944i	0.00857233	+	0.999963i	$0.497271\pi$
$840$		0			0
$841$	−28.0511	+	28.0511i	−0.967281	+	0.967281i
$842$	−17.9982	+	17.9982i	−0.620258	+	0.620258i
$843$	13.5100	−	32.6161i	0.465310	−	1.12336i
$844$	15.7142	+	6.50903i	0.540904	+	0.224050i
$845$		0			0
$846$			5.07081i			0.174338i
$847$	5.34904	−	2.21564i	0.183795	−	0.0761304i
$848$	3.54624	+	3.54624i	0.121779	+	0.121779i
$849$	−13.7950			−0.473443
$850$		0			0
$851$	23.4901			0.805232
$852$	−13.2940	−	13.2940i	−0.455444	−	0.455444i
$853$	6.10940	−	2.53060i	0.209182	−	0.0866459i	−0.275632	−	0.961263i	$-0.588887\pi$
$853$	6.10940	−	2.53060i	0.209182	−	0.0866459i	0.484814	+	0.874617i	$0.338887\pi$
$854$		−	0.574166i		−	0.0196476i
$855$		0			0
$856$	−21.2181	−	8.78882i	−0.725219	−	0.300396i
$857$	10.4589	−	25.2501i	0.357270	−	0.862526i	−0.638412	−	0.769695i	$-0.720408\pi$
$857$	10.4589	−	25.2501i	0.357270	−	0.862526i	0.995682	−	0.0928314i	$-0.0295918\pi$
$858$	−30.5664	+	30.5664i	−1.04352	+	1.04352i
$859$	10.0721	−	10.0721i	0.343654	−	0.343654i	−0.514085	−	0.857739i	$-0.671868\pi$
$859$	10.0721	−	10.0721i	0.343654	−	0.343654i	0.857739	+	0.514085i	$0.171868\pi$
$860$		0			0
$861$	0.993355	+	0.411461i	0.0338534	+	0.0140226i
$862$	10.4232	+	25.1639i	0.355016	+	0.857084i
$863$			31.4670i			1.07115i	0.844488	+	0.535574i	$0.179905\pi$
$863$			31.4670i			1.07115i	−0.844488	+	0.535574i	$0.820095\pi$
$864$	1.51379	−	0.627031i	0.0515001	−	0.0213320i
$865$		0			0
$866$	−34.4457			−1.17051
$867$	−42.0518	−	1.30888i	−1.42815	−	0.0444521i
$868$	1.44683			0.0491086
$869$	4.89583	+	4.89583i	0.166080	+	0.166080i
$870$		0			0
$871$		−	30.1733i		−	1.02238i
$872$	−13.7242	−	33.1331i	−0.464759	−	1.12203i
$873$	−0.658344	−	0.272695i	−0.0222816	−	0.00922933i
$874$	2.09415	−	5.05573i	0.0708358	−	0.171013i
$875$		0			0
$876$	−23.1429	+	23.1429i	−0.781925	+	0.781925i
$877$	2.13245	−	5.14819i	0.0720078	−	0.173842i	−0.883778	−	0.467907i	$-0.845008\pi$
$877$	2.13245	−	5.14819i	0.0720078	−	0.173842i	0.955785	+	0.294065i	$0.0950082\pi$
$878$	−28.5251	−	11.8155i	−0.962677	−	0.398754i
$879$	1.86688	+	4.50705i	0.0629684	+	0.152019i
$880$		0			0
$881$	29.7926	−	12.3405i	1.00374	−	0.415762i	0.180572	−	0.983562i	$-0.442205\pi$
$881$	29.7926	−	12.3405i	1.00374	−	0.415762i	0.823167	+	0.567800i	$0.192205\pi$
$882$	−14.1223	−	14.1223i	−0.475521	−	0.475521i
$883$	38.2240			1.28634			0.643169	−	0.765724i	$-0.277619\pi$
$883$	38.2240			1.28634			0.643169	+	0.765724i	$0.277619\pi$
$884$	−3.72503	+	17.3147i	−0.125286	+	0.582356i
$885$		0			0
$886$	−1.26835	−	1.26835i	−0.0426111	−	0.0426111i
$887$	−5.72381	+	2.37088i	−0.192187	+	0.0796063i	−0.476701	−	0.879065i	$-0.658168\pi$
$887$	−5.72381	+	2.37088i	−0.192187	+	0.0796063i	0.284515	+	0.958672i	$0.408168\pi$
$888$		−	29.8353i		−	1.00121i
$889$	2.53040	+	6.10892i	0.0848668	+	0.204887i
$890$		0			0
$891$	−15.4035	+	37.1872i	−0.516035	+	1.24582i
$892$	−0.827523	+	0.827523i	−0.0277075	+	0.0277075i
$893$	−1.20811	+	1.20811i	−0.0404279	+	0.0404279i
$894$	4.92639	−	11.8934i	0.164763	−	0.397773i
$895$		0			0
$896$	−0.946134	−	2.28417i	−0.0316081	−	0.0763088i
$897$			55.7485i			1.86139i
$898$	−1.76006	+	0.729042i	−0.0587340	+	0.0243284i
$899$	−14.5264	−	14.5264i	−0.484483	−	0.484483i
$900$		0			0
$901$	28.2731	−	18.2618i	0.941915	−	0.608387i
$902$	3.62410			0.120669
$903$	6.00894	+	6.00894i	0.199965	+	0.199965i
$904$	−48.6406	+	20.1476i	−1.61776	+	0.670099i
$905$		0			0
$906$	−4.51389	−	10.8975i	−0.149964	−	0.362045i
$907$	10.0069	+	4.14501i	0.332275	+	0.137633i	0.542583	−	0.840002i	$-0.317447\pi$
$907$	10.0069	+	4.14501i	0.332275	+	0.137633i	−0.210307	+	0.977635i	$0.567447\pi$
$908$	0.865889	−	2.09044i	0.0287355	−	0.0693737i
$909$	−14.7276	+	14.7276i	−0.488485	+	0.488485i
$910$		0			0
$911$	−15.0373	+	36.3032i	−0.498207	+	1.20278i	0.452241	+	0.891896i	$0.350625\pi$
$911$	−15.0373	+	36.3032i	−0.498207	+	1.20278i	−0.950448	+	0.310882i	$0.899375\pi$
$912$	−1.40755	−	0.583028i	−0.0466088	−	0.0193060i
$913$	28.9599	+	69.9154i	0.958433	+	2.31386i
$914$			16.8061i			0.555897i
$915$		0			0
$916$	−9.91385	−	9.91385i	−0.327563	−	0.327563i
$917$	−5.35051			−0.176689
$918$	0.217929	+	1.19225i	0.00719272	+	0.0393501i
$919$	48.2620			1.59202			0.796008	−	0.605286i	$-0.206941\pi$
$919$	48.2620			1.59202			0.796008	+	0.605286i	$0.206941\pi$
$920$		0			0
$921$	−3.87812	+	1.60637i	−0.127788	+	0.0529317i
$922$			30.3045i			0.998026i
$923$	−10.4301	−	25.1806i	−0.343312	−	0.828829i
$924$	−6.23827	−	2.58398i	−0.205224	−	0.0850066i
$925$		0			0
$926$	−10.6315	+	10.6315i	−0.349374	+	0.349374i
$927$	−0.774357	+	0.774357i	−0.0254332	+	0.0254332i
$928$	−16.8233	+	40.6151i	−0.552252	+	1.33325i
$929$	−21.5317	−	8.91871i	−0.706431	−	0.292613i	0.000395678	−	1.00000i	$-0.499874\pi$
$929$	−21.5317	−	8.91871i	−0.706431	−	0.292613i	−0.706827	+	0.707387i	$0.749874\pi$
$930$		0			0
$931$		−	6.72920i		−	0.220541i
$932$	6.55460	−	2.71501i	0.214703	−	0.0889330i
$933$	19.0619	+	19.0619i	0.624057	+	0.624057i
$934$	8.43745			0.276082
$935$		0			0
$936$	36.1250			1.18078
$937$	6.87594	+	6.87594i	0.224627	+	0.224627i	0.810444	−	0.585816i	$-0.199226\pi$
$937$	6.87594	+	6.87594i	0.224627	+	0.224627i	−0.585816	+	0.810444i	$0.699226\pi$
$938$	−3.60471	+	1.49312i	−0.117698	+	0.0487520i
$939$			65.0674i			2.12339i
$940$		0			0
$941$	13.0919	+	5.42286i	0.426785	+	0.176780i	0.585728	−	0.810508i	$-0.300809\pi$
$941$	13.0919	+	5.42286i	0.426785	+	0.176780i	−0.158943	+	0.987288i	$0.550809\pi$
$942$	−9.86479	+	23.8157i	−0.321412	+	0.775958i
$943$	3.30491	−	3.30491i	0.107623	−	0.107623i
$944$	2.63131	−	2.63131i	0.0856418	−	0.0856418i
$945$		0			0
$946$	26.4630	+	10.9613i	0.860387	+	0.356384i
$947$	14.7284	+	35.5574i	0.478607	+	1.15546i	0.960262	+	0.279099i	$0.0900358\pi$
$947$	14.7284	+	35.5574i	0.478607	+	1.15546i	−0.481655	+	0.876361i	$0.659964\pi$
$948$		−	4.01058i		−	0.130257i
$949$	−43.8357	+	18.1573i	−1.42297	+	0.589412i
$950$		0			0
$951$	61.8987			2.00720
$952$	6.37071	−	1.16449i	0.206476	−	0.0377412i
$953$	−37.7984			−1.22441			−0.612206	−	0.790698i	$-0.709718\pi$
$953$	−37.7984			−1.22441			−0.612206	+	0.790698i	$0.709718\pi$
$954$	−17.1668	−	17.1668i	−0.555795	−	0.555795i
$955$		0			0
$956$			1.38774i			0.0448828i
$957$	36.6897	+	88.5768i	1.18601	+	2.86328i
$958$	10.4721	+	4.33769i	0.338339	+	0.140145i
$959$	−0.626240	+	1.51188i	−0.0202223	+	0.0488210i
$960$		0			0
$961$	−17.5746	+	17.5746i	−0.566922	+	0.566922i
$962$	5.85325	−	14.1310i	0.188716	−	0.455602i
$963$	22.5145	+	9.32583i	0.725521	+	0.300521i
$964$	1.04508	+	2.52305i	0.0336598	+	0.0812620i
$965$		0			0
$966$	6.66009	−	2.75870i	0.214285	−	0.0887598i
$967$	3.39288	+	3.39288i	0.109108	+	0.109108i	0.759553	−	0.650445i	$-0.225418\pi$
$967$	3.39288	+	3.39288i	0.109108	+	0.109108i	−0.650445	+	0.759553i	$0.725418\pi$
$968$	−31.9662			−1.02743
$969$	−5.81217	+	8.41221i	−0.186714	+	0.270239i
$970$		0			0
$971$	−25.8080	−	25.8080i	−0.828217	−	0.828217i	0.159053	−	0.987270i	$-0.449156\pi$
$971$	−25.8080	−	25.8080i	−0.828217	−	0.828217i	−0.987270	+	0.159053i	$0.949156\pi$
$972$	22.4774	−	9.31043i	0.720962	−	0.298632i
$973$			6.54621i			0.209862i
$974$	−9.75221	−	23.5439i	−0.312481	−	0.754396i
$975$		0			0
$976$	−0.265916	+	0.641978i	−0.00851176	+	0.0205492i
$977$	−44.0684	+	44.0684i	−1.40987	+	1.40987i	−0.649569	+	0.760303i	$0.725051\pi$
$977$	−44.0684	+	44.0684i	−1.40987	+	1.40987i	−0.760303	+	0.649569i	$0.774949\pi$
$978$	−12.3074	+	12.3074i	−0.393547	+	0.393547i
$979$	21.5965	−	52.1385i	0.690227	−	1.66635i
$980$		0			0
$981$	14.5627	+	35.1576i	0.464953	+	1.12249i
$982$		−	22.0034i		−	0.702156i
$983$	−37.1141	+	15.3732i	−1.18376	+	0.490328i	−0.885717	−	0.464225i	$-0.846333\pi$
$983$	−37.1141	+	15.3732i	−1.18376	+	0.490328i	−0.298040	+	0.954553i	$0.596333\pi$
$984$	−4.19764	−	4.19764i	−0.133816	−	0.133816i
$985$		0			0
$986$	−26.7536	−	18.4846i	−0.852008	−	0.588670i
$987$	−2.25070			−0.0716407
$988$	3.04358	+	3.04358i	0.0968291	+	0.0968291i
$989$	34.1282	−	14.1364i	1.08521	−	0.449511i
$990$		0			0
$991$	9.59778	+	23.1711i	0.304883	+	0.736054i	0.999855	+	0.0170168i	$0.00541686\pi$
$991$	9.59778	+	23.1711i	0.304883	+	0.736054i	−0.694972	+	0.719037i	$0.744583\pi$
$992$	−12.1504	−	5.03287i	−0.385776	−	0.159794i
$993$	30.5786	−	73.8232i	0.970382	−	2.34271i
$994$	−2.49211	+	2.49211i	−0.0790449	+	0.0790449i
$995$		0			0
$996$	16.7750	−	40.4985i	0.531536	−	1.28324i
$997$	34.5204	+	14.2988i	1.09327	+	0.452848i	0.855146	−	0.518387i	$-0.173467\pi$
$997$	34.5204	+	14.2988i	1.09327	+	0.452848i	0.238125	+	0.971235i	$0.423467\pi$
$998$	1.80882	+	4.36687i	0.0572571	+	0.138231i
$999$			1.26439i			0.0400035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.e.376.2		24
5.2	odd	4		85.2.m.a.19.5	yes	24
5.3	odd	4		85.2.m.a.19.2	yes	24
5.4	even	2	inner	425.2.m.e.376.5		24
15.2	even	4		765.2.bh.b.19.2		24
15.8	even	4		765.2.bh.b.19.5		24
17.3	odd	16		7225.2.a.by.1.8		24
17.9	even	8	inner	425.2.m.e.26.2		24
17.14	odd	16		7225.2.a.by.1.7		24
85.3	even	16		1445.2.b.i.579.18		24
85.9	even	8	inner	425.2.m.e.26.5		24
85.14	odd	16		7225.2.a.by.1.18		24
85.37	even	16		1445.2.b.i.579.7		24
85.43	odd	8		85.2.m.a.9.5	yes	24
85.48	even	16		1445.2.b.i.579.17		24
85.54	odd	16		7225.2.a.by.1.17		24
85.77	odd	8		85.2.m.a.9.2	✓	24
85.82	even	16		1445.2.b.i.579.8		24
255.77	even	8		765.2.bh.b.604.5		24
255.128	even	8		765.2.bh.b.604.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.2	✓	24	85.77	odd	8
85.2.m.a.9.5	yes	24	85.43	odd	8
85.2.m.a.19.2	yes	24	5.3	odd	4
85.2.m.a.19.5	yes	24	5.2	odd	4
425.2.m.e.26.2		24	17.9	even	8	inner
425.2.m.e.26.5		24	85.9	even	8	inner
425.2.m.e.376.2		24	1.1	even	1	trivial
425.2.m.e.376.5		24	5.4	even	2	inner
765.2.bh.b.19.2		24	15.2	even	4
765.2.bh.b.19.5		24	15.8	even	4
765.2.bh.b.604.2		24	255.128	even	8
765.2.bh.b.604.5		24	255.77	even	8
1445.2.b.i.579.7		24	85.37	even	16
1445.2.b.i.579.8		24	85.82	even	16
1445.2.b.i.579.17		24	85.48	even	16
1445.2.b.i.579.18		24	85.3	even	16
7225.2.a.by.1.7		24	17.14	odd	16
7225.2.a.by.1.8		24	17.3	odd	16
7225.2.a.by.1.17		24	85.54	odd	16
7225.2.a.by.1.18		24	85.14	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.672981 - 0.672981i) q^{2} +(2.28645 - 0.947078i) q^{3} -1.09419i q^{4} +(-2.17610 - 0.901371i) q^{6} +(0.204115 - 0.492777i) q^{7} +(-2.08233 + 2.08233i) q^{8} +(2.20957 - 2.20957i) q^{9} +(4.31906 + 1.78902i) q^{11} +(-1.03629 - 2.50182i) q^{12} -3.92573i q^{13} +(-0.468995 + 0.194264i) q^{14} +0.614355 q^{16} +(0.867192 - 4.03088i) q^{17} -2.97399 q^{18} +(-0.708548 - 0.708548i) q^{19} -1.32002i q^{21} +(-1.70268 - 4.11062i) q^{22} +(-5.30129 - 2.19587i) q^{23} +(-2.78902 + 6.73328i) q^{24} +(-2.64194 + 2.64194i) q^{26} +(0.118196 - 0.285350i) q^{27} +(-0.539193 - 0.223341i) q^{28} +(3.17120 + 7.65596i) q^{29} +(-2.29036 + 0.948699i) q^{31} +(3.75122 + 3.75122i) q^{32} +11.5697 q^{33} +(-3.29631 + 2.12910i) q^{34} +(-2.41769 - 2.41769i) q^{36} +(-3.78211 + 1.56660i) q^{37} +0.953679i q^{38} +(-3.71797 - 8.97598i) q^{39} +(-0.311708 + 0.752530i) q^{41} +(-0.888349 + 0.888349i) q^{42} +(-4.55216 + 4.55216i) q^{43} +(1.95753 - 4.72589i) q^{44} +(2.08989 + 5.04545i) q^{46} -1.70505i q^{47} +(1.40469 - 0.581842i) q^{48} +(4.74858 + 4.74858i) q^{49} +(-1.83477 - 10.0377i) q^{51} -4.29551 q^{52} +(5.77230 + 5.77230i) q^{53} +(-0.271578 + 0.112491i) q^{54} +(0.601090 + 1.45116i) q^{56} +(-2.29111 - 0.949008i) q^{57} +(3.01816 - 7.28648i) q^{58} +(4.28304 - 4.28304i) q^{59} +(-0.432837 + 1.04496i) q^{61} +(2.17983 + 0.902914i) q^{62} +(-0.637818 - 1.53983i) q^{63} -6.27771i q^{64} +(-7.78616 - 7.78616i) q^{66} +7.68603 q^{67} +(-4.41056 - 0.948875i) q^{68} -14.2008 q^{69} +(6.41424 - 2.65686i) q^{71} +9.20211i q^{72} +(-4.62521 - 11.1662i) q^{73} +(3.59958 + 1.49100i) q^{74} +(-0.775289 + 0.775289i) q^{76} +(1.76317 - 1.76317i) q^{77} +(-3.53854 + 8.54279i) q^{78} +(1.36830 + 0.566769i) q^{79} +8.61002i q^{81} +(0.716212 - 0.296665i) q^{82} +(11.4464 + 11.4464i) q^{83} -1.44436 q^{84} +6.12703 q^{86} +(14.5016 + 14.5016i) q^{87} +(-12.7191 + 5.26841i) q^{88} -12.0717i q^{89} +(-1.93451 - 0.801300i) q^{91} +(-2.40270 + 5.80064i) q^{92} +(-4.33830 + 4.33830i) q^{93} +(-1.14747 + 1.14747i) q^{94} +(12.1297 + 5.02427i) q^{96} +(-0.0872680 - 0.210684i) q^{97} -6.39141i q^{98} +(13.4962 - 5.59031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Introduction

L-functions

Modular forms

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