LMFDB - Embedded newform 731.2.f.d.259.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.10
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19080i q^{2} +(-1.82510 + 1.82510i) q^{3} +0.581989 q^{4} +(0.840782 - 0.840782i) q^{5} +(2.17334 + 2.17334i) q^{6} +(1.07906 + 1.07906i) q^{7} -3.07464i q^{8} -3.66201i q^{9} +O(q^{10})$	\(q-1.19080i q^{2} +(-1.82510 + 1.82510i) q^{3} +0.581989 q^{4} +(0.840782 - 0.840782i) q^{5} +(2.17334 + 2.17334i) q^{6} +(1.07906 + 1.07906i) q^{7} -3.07464i q^{8} -3.66201i q^{9} +(-1.00121 - 1.00121i) q^{10} +(-4.50629 - 4.50629i) q^{11} +(-1.06219 + 1.06219i) q^{12} +1.16831 q^{13} +(1.28495 - 1.28495i) q^{14} +3.06903i q^{15} -2.49731 q^{16} +(2.44625 - 3.31902i) q^{17} -4.36074 q^{18} +3.75790i q^{19} +(0.489326 - 0.489326i) q^{20} -3.93879 q^{21} +(-5.36611 + 5.36611i) q^{22} +(-1.87179 - 1.87179i) q^{23} +(5.61154 + 5.61154i) q^{24} +3.58617i q^{25} -1.39122i q^{26} +(1.20824 + 1.20824i) q^{27} +(0.627999 + 0.627999i) q^{28} +(5.67662 - 5.67662i) q^{29} +3.65461 q^{30} +(6.00800 - 6.00800i) q^{31} -3.17547i q^{32} +16.4489 q^{33} +(-3.95229 - 2.91300i) q^{34} +1.81451 q^{35} -2.13125i q^{36} +(0.212896 - 0.212896i) q^{37} +4.47492 q^{38} +(-2.13228 + 2.13228i) q^{39} +(-2.58510 - 2.58510i) q^{40} +(-4.39509 - 4.39509i) q^{41} +4.69032i q^{42} -1.00000i q^{43} +(-2.62261 - 2.62261i) q^{44} +(-3.07896 - 3.07896i) q^{45} +(-2.22893 + 2.22893i) q^{46} +2.89343 q^{47} +(4.55786 - 4.55786i) q^{48} -4.67127i q^{49} +4.27042 q^{50} +(1.59289 + 10.5222i) q^{51} +0.679941 q^{52} +5.93254i q^{53} +(1.43878 - 1.43878i) q^{54} -7.57762 q^{55} +(3.31771 - 3.31771i) q^{56} +(-6.85856 - 6.85856i) q^{57} +(-6.75974 - 6.75974i) q^{58} +3.71006i q^{59} +1.78614i q^{60} +(2.83517 + 2.83517i) q^{61} +(-7.15434 - 7.15434i) q^{62} +(3.95153 - 3.95153i) q^{63} -8.77599 q^{64} +(0.982291 - 0.982291i) q^{65} -19.5874i q^{66} +3.91792 q^{67} +(1.42369 - 1.93163i) q^{68} +6.83241 q^{69} -2.16072i q^{70} +(-2.80402 + 2.80402i) q^{71} -11.2594 q^{72} +(10.8010 - 10.8010i) q^{73} +(-0.253517 - 0.253517i) q^{74} +(-6.54514 - 6.54514i) q^{75} +2.18705i q^{76} -9.72510i q^{77} +(2.53913 + 2.53913i) q^{78} +(-9.97384 - 9.97384i) q^{79} +(-2.09970 + 2.09970i) q^{80} +6.57570 q^{81} +(-5.23369 + 5.23369i) q^{82} +3.72105i q^{83} -2.29233 q^{84} +(-0.733806 - 4.84733i) q^{85} -1.19080 q^{86} +20.7209i q^{87} +(-13.8552 + 13.8552i) q^{88} -5.25752 q^{89} +(-3.66643 + 3.66643i) q^{90} +(1.26067 + 1.26067i) q^{91} +(-1.08936 - 1.08936i) q^{92} +21.9304i q^{93} -3.44550i q^{94} +(3.15957 + 3.15957i) q^{95} +(5.79557 + 5.79557i) q^{96} +(6.95095 - 6.95095i) q^{97} -5.56256 q^{98} +(-16.5021 + 16.5021i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	1.19080i		−	0.842025i	−0.907055	−	0.421012i	$-0.861675\pi$
$2$		−	1.19080i		−	0.842025i	0.907055	−	0.421012i	$-0.138325\pi$
$3$	−1.82510	+	1.82510i	−1.05372	+	1.05372i	−0.0552522	+	0.998472i	$0.517596\pi$
$3$	−1.82510	+	1.82510i	−1.05372	+	1.05372i	−0.998472	+	0.0552522i	$0.982404\pi$
$4$	0.581989			0.290994
$5$	0.840782	−	0.840782i	0.376009	−	0.376009i	−0.493651	−	0.869660i	$-0.664338\pi$
$5$	0.840782	−	0.840782i	0.376009	−	0.376009i	0.869660	+	0.493651i	$0.164338\pi$
$6$	2.17334	+	2.17334i	0.887262	+	0.887262i
$7$	1.07906	+	1.07906i	0.407846	+	0.407846i	0.880987	−	0.473141i	$-0.156880\pi$
$7$	1.07906	+	1.07906i	0.407846	+	0.407846i	−0.473141	+	0.880987i	$0.656880\pi$
$8$		−	3.07464i		−	1.08705i
$9$		−	3.66201i		−	1.22067i
$10$	−1.00121	−	1.00121i	−0.316609	−	0.316609i
$11$	−4.50629	−	4.50629i	−1.35870	−	1.35870i	−0.875524	−	0.483174i	$-0.839484\pi$
$11$	−4.50629	−	4.50629i	−1.35870	−	1.35870i	−0.483174	−	0.875524i	$-0.660516\pi$
$12$	−1.06219	+	1.06219i	−0.306628	+	0.306628i
$13$	1.16831			0.324030			0.162015	−	0.986788i	$-0.448201\pi$
$13$	1.16831			0.324030			0.162015	+	0.986788i	$0.448201\pi$
$14$	1.28495	−	1.28495i	0.343416	−	0.343416i
$15$			3.06903i			0.792420i
$16$	−2.49731			−0.624328
$17$	2.44625	−	3.31902i	0.593303	−	0.804979i
$17$	2.44625	−	3.31902i	0.593303	−	0.804979i
$18$	−4.36074			−1.02784
$19$			3.75790i			0.862121i	0.902323	+	0.431060i	$0.141860\pi$
$19$			3.75790i			0.862121i	−0.902323	+	0.431060i	$0.858140\pi$
$20$	0.489326	−	0.489326i	0.109417	−	0.109417i
$21$	−3.93879			−0.859514
$22$	−5.36611	+	5.36611i	−1.14406	+	1.14406i
$23$	−1.87179	−	1.87179i	−0.390294	−	0.390294i	0.484498	−	0.874792i	$-0.339002\pi$
$23$	−1.87179	−	1.87179i	−0.390294	−	0.390294i	−0.874792	+	0.484498i	$0.839002\pi$
$24$	5.61154	+	5.61154i	1.14545	+	1.14545i
$25$			3.58617i			0.717234i
$26$		−	1.39122i		−	0.272841i
$27$	1.20824	+	1.20824i	0.232526	+	0.232526i
$28$	0.627999	+	0.627999i	0.118681	+	0.118681i
$29$	5.67662	−	5.67662i	1.05412	−	1.05412i	0.0556731	−	0.998449i	$-0.482270\pi$
$29$	5.67662	−	5.67662i	1.05412	−	1.05412i	0.998449	−	0.0556731i	$-0.0177305\pi$
$30$	3.65461			0.667238
$31$	6.00800	−	6.00800i	1.07907	−	1.07907i	0.0824752	−	0.996593i	$-0.473717\pi$
$31$	6.00800	−	6.00800i	1.07907	−	1.07907i	0.996593	−	0.0824752i	$-0.0262825\pi$
$32$		−	3.17547i		−	0.561349i
$33$	16.4489			2.86339
$34$	−3.95229	−	2.91300i	−0.677813	−	0.499576i
$35$	1.81451			0.306707
$36$		−	2.13125i		−	0.355208i
$37$	0.212896	−	0.212896i	0.0349999	−	0.0349999i	−0.689390	−	0.724390i	$-0.742121\pi$
$37$	0.212896	−	0.212896i	0.0349999	−	0.0349999i	0.724390	+	0.689390i	$0.242121\pi$
$38$	4.47492			0.725927
$39$	−2.13228	+	2.13228i	−0.341438	+	0.341438i
$40$	−2.58510	−	2.58510i	−0.408740	−	0.408740i
$41$	−4.39509	−	4.39509i	−0.686398	−	0.686398i	0.275036	−	0.961434i	$-0.411310\pi$
$41$	−4.39509	−	4.39509i	−0.686398	−	0.686398i	−0.961434	+	0.275036i	$0.911310\pi$
$42$			4.69032i			0.723732i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−2.62261	−	2.62261i	−0.395373	−	0.395373i
$45$	−3.07896	−	3.07896i	−0.458984	−	0.458984i
$46$	−2.22893	+	2.22893i	−0.328637	+	0.328637i
$47$	2.89343			0.422050			0.211025	−	0.977481i	$-0.432320\pi$
$47$	2.89343			0.422050			0.211025	+	0.977481i	$0.432320\pi$
$48$	4.55786	−	4.55786i	0.657870	−	0.657870i
$49$		−	4.67127i		−	0.667324i
$50$	4.27042			0.603929
$51$	1.59289	+	10.5222i	0.223049	+	1.47340i
$52$	0.679941			0.0942909
$53$			5.93254i			0.814897i	0.913228	+	0.407448i	$0.133581\pi$
$53$			5.93254i			0.814897i	−0.913228	+	0.407448i	$0.866419\pi$
$54$	1.43878	−	1.43878i	0.195793	−	0.195793i
$55$	−7.57762			−1.02177
$56$	3.31771	−	3.31771i	0.443348	−	0.443348i
$57$	−6.85856	−	6.85856i	−0.908438	−	0.908438i
$58$	−6.75974	−	6.75974i	−0.887597	−	0.887597i
$59$			3.71006i			0.483008i	0.970400	+	0.241504i	$0.0776407\pi$
$59$			3.71006i			0.483008i	−0.970400	+	0.241504i	$0.922359\pi$
$60$			1.78614i			0.230590i
$61$	2.83517	+	2.83517i	0.363007	+	0.363007i	0.864919	−	0.501912i	$-0.167370\pi$
$61$	2.83517	+	2.83517i	0.363007	+	0.363007i	−0.501912	+	0.864919i	$0.667370\pi$
$62$	−7.15434	−	7.15434i	−0.908602	−	0.908602i
$63$	3.95153	−	3.95153i	0.497845	−	0.497845i
$64$	−8.77599			−1.09700
$65$	0.982291	−	0.982291i	0.121838	−	0.121838i
$66$		−	19.5874i		−	2.41104i
$67$	3.91792			0.478650			0.239325	−	0.970940i	$-0.423074\pi$
$67$	3.91792			0.478650			0.239325	+	0.970940i	$0.423074\pi$
$68$	1.42369	−	1.93163i	0.172648	−	0.234244i
$69$	6.83241			0.822525
$70$		−	2.16072i		−	0.258255i
$71$	−2.80402	+	2.80402i	−0.332776	+	0.332776i	−0.853640	−	0.520864i	$-0.825610\pi$
$71$	−2.80402	+	2.80402i	−0.332776	+	0.332776i	0.520864	+	0.853640i	$0.325610\pi$
$72$	−11.2594			−1.32693
$73$	10.8010	−	10.8010i	1.26416	−	1.26416i	0.315107	−	0.949056i	$-0.397960\pi$
$73$	10.8010	−	10.8010i	1.26416	−	1.26416i	0.949056	−	0.315107i	$-0.102040\pi$
$74$	−0.253517	−	0.253517i	−0.0294708	−	0.0294708i
$75$	−6.54514	−	6.54514i	−0.755767	−	0.755767i
$76$			2.18705i			0.250872i
$77$		−	9.72510i		−	1.10828i
$78$	2.53913	+	2.53913i	0.287500	+	0.287500i
$79$	−9.97384	−	9.97384i	−1.12215	−	1.12215i	−0.991418	−	0.130727i	$-0.958269\pi$
$79$	−9.97384	−	9.97384i	−1.12215	−	1.12215i	−0.130727	−	0.991418i	$-0.541731\pi$
$80$	−2.09970	+	2.09970i	−0.234753	+	0.234753i
$81$	6.57570			0.730633
$82$	−5.23369	+	5.23369i	−0.577964	+	0.577964i
$83$			3.72105i			0.408438i	0.978925	+	0.204219i	$0.0654655\pi$
$83$			3.72105i			0.408438i	−0.978925	+	0.204219i	$0.934535\pi$
$84$	−2.29233			−0.250114
$85$	−0.733806	−	4.84733i	−0.0795924	−	0.525767i
$86$	−1.19080			−0.128408
$87$			20.7209i			2.22151i
$88$	−13.8552	+	13.8552i	−1.47697	+	1.47697i
$89$	−5.25752			−0.557296			−0.278648	−	0.960393i	$-0.589886\pi$
$89$	−5.25752			−0.557296			−0.278648	+	0.960393i	$0.589886\pi$
$90$	−3.66643	+	3.66643i	−0.386476	+	0.386476i
$91$	1.26067	+	1.26067i	0.132154	+	0.132154i
$92$	−1.08936	−	1.08936i	−0.113573	−	0.113573i
$93$			21.9304i			2.27408i
$94$		−	3.44550i		−	0.355377i
$95$	3.15957	+	3.15957i	0.324165	+	0.324165i
$96$	5.79557	+	5.79557i	0.591508	+	0.591508i
$97$	6.95095	−	6.95095i	0.705762	−	0.705762i	−0.259879	−	0.965641i	$-0.583683\pi$
$97$	6.95095	−	6.95095i	0.705762	−	0.705762i	0.965641	+	0.259879i	$0.0836826\pi$
$98$	−5.56256			−0.561903
$99$	−16.5021	+	16.5021i	−1.65852	+	1.65852i
$100$			2.08711i			0.208711i
$101$	4.21250			0.419159			0.209580	−	0.977792i	$-0.432790\pi$
$101$	4.21250			0.419159			0.209580	+	0.977792i	$0.432790\pi$
$102$	12.5299	−	1.89682i	1.24064	−	0.187813i
$103$	0.476574			0.0469582			0.0234791	−	0.999724i	$-0.492526\pi$
$103$	0.476574			0.0469582			0.0234791	+	0.999724i	$0.492526\pi$
$104$		−	3.59212i		−	0.352237i
$105$	−3.31166	+	3.31166i	−0.323185	+	0.323185i
$106$	7.06448			0.686163
$107$	2.82517	−	2.82517i	0.273120	−	0.273120i	−0.557235	−	0.830355i	$-0.688138\pi$
$107$	2.82517	−	2.82517i	0.273120	−	0.273120i	0.830355	+	0.557235i	$0.188138\pi$
$108$	0.703184	+	0.703184i	0.0676639	+	0.0676639i
$109$	−3.33197	−	3.33197i	−0.319145	−	0.319145i	0.529294	−	0.848439i	$-0.322457\pi$
$109$	−3.33197	−	3.33197i	−0.319145	−	0.319145i	−0.848439	+	0.529294i	$0.822457\pi$
$110$			9.02345i			0.860352i
$111$			0.777115i			0.0737605i
$112$	−2.69475	−	2.69475i	−0.254629	−	0.254629i
$113$	7.96540	+	7.96540i	0.749322	+	0.749322i	0.974352	−	0.225030i	$-0.0722479\pi$
$113$	7.96540	+	7.96540i	0.749322	+	0.749322i	−0.225030	+	0.974352i	$0.572248\pi$
$114$	−8.16719	+	8.16719i	−0.764927	+	0.764927i
$115$	−3.14753			−0.293508
$116$	3.30373	−	3.30373i	0.306743	−	0.306743i
$117$		−	4.27835i		−	0.395534i
$118$	4.41795			0.406705
$119$	6.22106	−	0.941765i	0.570283	−	0.0863314i
$120$	9.43616			0.861400
$121$			29.6134i			2.69212i
$122$	3.37613	−	3.37613i	0.305661	−	0.305661i
$123$	16.0430			1.44655
$124$	3.49659	−	3.49659i	0.314003	−	0.314003i
$125$	7.21910	+	7.21910i	0.645696	+	0.645696i
$126$	−4.70549	−	4.70549i	−0.419198	−	0.419198i
$127$			6.07443i			0.539019i	0.962998	+	0.269509i	$0.0868615\pi$
$127$			6.07443i			0.539019i	−0.962998	+	0.269509i	$0.913139\pi$
$128$			4.09953i			0.362350i
$129$	1.82510	+	1.82510i	0.160691	+	0.160691i
$130$	−1.16972	−	1.16972i	−0.102591	−	0.102591i
$131$	−11.7967	+	11.7967i	−1.03068	+	1.03068i	−0.0311673	+	0.999514i	$0.509922\pi$
$131$	−11.7967	+	11.7967i	−1.03068	+	1.03068i	−0.999514	+	0.0311673i	$0.990078\pi$
$132$	9.57308			0.833229
$133$	−4.05499	+	4.05499i	−0.351612	+	0.351612i
$134$		−	4.66547i		−	0.403035i
$135$	2.03174			0.174864
$136$	−10.2048	−	7.52134i	−0.875052	−	0.644949i
$137$	−3.08757			−0.263789			−0.131895	−	0.991264i	$-0.542106\pi$
$137$	−3.08757			−0.263789			−0.131895	+	0.991264i	$0.542106\pi$
$138$		−	8.13605i		−	0.692587i
$139$	−15.7991	+	15.7991i	−1.34006	+	1.34006i	−0.444064	+	0.895995i	$0.646464\pi$
$139$	−15.7991	+	15.7991i	−1.34006	+	1.34006i	−0.895995	+	0.444064i	$0.853536\pi$
$140$	1.05602			0.0892501
$141$	−5.28081	+	5.28081i	−0.444725	+	0.444725i
$142$	3.33904	+	3.33904i	0.280206	+	0.280206i
$143$	−5.26473	−	5.26473i	−0.440259	−	0.440259i
$144$			9.14519i			0.762099i
$145$		−	9.54560i		−	0.792719i
$146$	−12.8619	−	12.8619i	−1.06446	−	1.06446i
$147$	8.52555	+	8.52555i	0.703176	+	0.703176i
$148$	0.123903	−	0.123903i	0.0101848	−	0.0101848i
$149$	−8.34464			−0.683620			−0.341810	−	0.939769i	$-0.611040\pi$
$149$	−8.34464			−0.683620			−0.341810	+	0.939769i	$0.611040\pi$
$150$	−7.79397	+	7.79397i	−0.636375	+	0.636375i
$151$			4.73991i			0.385728i	0.981225	+	0.192864i	$0.0617777\pi$
$151$			4.73991i			0.385728i	−0.981225	+	0.192864i	$0.938222\pi$
$152$	11.5542			0.937168
$153$	−12.1543	−	8.95820i	−0.982615	−	0.724227i
$154$	−11.5807			−0.933198
$155$		−	10.1028i		−	0.811479i
$156$	−1.24096	+	1.24096i	−0.0993566	+	0.0993566i
$157$	17.8350			1.42339			0.711695	−	0.702489i	$-0.247928\pi$
$157$	17.8350			1.42339			0.711695	+	0.702489i	$0.247928\pi$
$158$	−11.8769	+	11.8769i	−0.944874	+	0.944874i
$159$	−10.8275	−	10.8275i	−0.858677	−	0.858677i
$160$	−2.66988	−	2.66988i	−0.211073	−	0.211073i
$161$		−	4.03953i		−	0.318360i
$162$		−	7.83036i		−	0.615211i
$163$	6.30668	+	6.30668i	0.493977	+	0.493977i	0.909557	−	0.415579i	$-0.136421\pi$
$163$	6.30668	+	6.30668i	0.493977	+	0.493977i	−0.415579	+	0.909557i	$0.636421\pi$
$164$	−2.55789	−	2.55789i	−0.199738	−	0.199738i
$165$	13.8300	−	13.8300i	1.07666	−	1.07666i
$166$	4.43103			0.343915
$167$	−0.671694	+	0.671694i	−0.0519773	+	0.0519773i	−0.732618	−	0.680640i	$-0.761702\pi$
$167$	−0.671694	+	0.671694i	−0.0519773	+	0.0519773i	0.680640	+	0.732618i	$0.261702\pi$
$168$			12.1104i			0.934334i
$169$	−11.6351			−0.895005
$170$	−5.77222	+	0.873818i	−0.442709	+	0.0670188i
$171$	13.7615			1.05237
$172$		−	0.581989i		−	0.0443762i
$173$	−11.6121	+	11.6121i	−0.882848	+	0.882848i	−0.993823	−	0.110975i	$-0.964603\pi$
$173$	−11.6121	+	11.6121i	−0.882848	+	0.882848i	0.110975	+	0.993823i	$0.464603\pi$
$174$	24.6745			1.87057
$175$	−3.86969	+	3.86969i	−0.292521	+	0.292521i
$176$	11.2536	+	11.2536i	0.848274	+	0.848274i
$177$	−6.77124	−	6.77124i	−0.508958	−	0.508958i
$178$			6.26067i			0.469257i
$179$			14.8758i			1.11187i	0.831227	+	0.555934i	$0.187639\pi$
$179$			14.8758i			1.11187i	−0.831227	+	0.555934i	$0.812361\pi$
$180$	−1.79192	−	1.79192i	−0.133562	−	0.133562i
$181$	1.00505	+	1.00505i	0.0747051	+	0.0747051i	0.743472	−	0.668767i	$-0.233178\pi$
$181$	1.00505	+	1.00505i	0.0747051	+	0.0747051i	−0.668767	+	0.743472i	$0.733178\pi$
$182$	1.50121	−	1.50121i	0.111277	−	0.111277i
$183$	−10.3490			−0.765018
$184$	−5.75507	+	5.75507i	−0.424269	+	0.424269i
$185$		−	0.357998i		−	0.0263206i
$186$	26.1148			1.91483
$187$	−25.9800	+	3.93294i	−1.89984	+	0.287605i
$188$	1.68394			0.122814
$189$			2.60753i			0.189670i
$190$	3.76243	−	3.76243i	0.272955	−	0.272955i
$191$	−11.4600			−0.829217			−0.414609	−	0.910000i	$-0.636082\pi$
$191$	−11.4600			−0.829217			−0.414609	+	0.910000i	$0.636082\pi$
$192$	16.0171	−	16.0171i	1.15593	−	1.15593i
$193$	4.20194	+	4.20194i	0.302462	+	0.302462i	0.841976	−	0.539514i	$-0.181392\pi$
$193$	4.20194	+	4.20194i	0.302462	+	0.302462i	−0.539514	+	0.841976i	$0.681392\pi$
$194$	−8.27722	−	8.27722i	−0.594269	−	0.594269i
$195$			3.58557i			0.256768i
$196$		−	2.71862i		−	0.194187i
$197$	−11.2946	−	11.2946i	−0.804706	−	0.804706i	0.179121	−	0.983827i	$-0.442675\pi$
$197$	−11.2946	−	11.2946i	−0.804706	−	0.804706i	−0.983827	+	0.179121i	$0.942675\pi$
$198$	19.6508	+	19.6508i	1.39652	+	1.39652i
$199$	13.4199	−	13.4199i	0.951313	−	0.951313i	−0.0475555	−	0.998869i	$-0.515143\pi$
$199$	13.4199	−	13.4199i	0.951313	−	0.951313i	0.998869	+	0.0475555i	$0.0151431\pi$
$200$	11.0262			0.779669
$201$	−7.15061	+	7.15061i	−0.504365	+	0.504365i
$202$		−	5.01625i		−	0.352942i
$203$	12.2508			0.859838
$204$	0.927043	+	6.12381i	0.0649060	+	0.428752i
$205$	−7.39063			−0.516184
$206$		−	0.567505i		−	0.0395400i
$207$	−6.85450	+	6.85450i	−0.476421	+	0.476421i
$208$	−2.91763			−0.202301
$209$	16.9342	−	16.9342i	1.17136	−	1.17136i
$210$	3.94354	+	3.94354i	0.272130	+	0.272130i
$211$	12.5981	+	12.5981i	0.867287	+	0.867287i	0.992171	−	0.124884i	$-0.0398559\pi$
$211$	12.5981	+	12.5981i	0.867287	+	0.867287i	−0.124884	+	0.992171i	$0.539856\pi$
$212$			3.45267i			0.237130i
$213$		−	10.2353i		−	0.701309i
$214$	−3.36422	−	3.36422i	−0.229974	−	0.229974i
$215$	−0.840782	−	0.840782i	−0.0573409	−	0.0573409i
$216$	3.71491	−	3.71491i	0.252768	−	0.252768i
$217$	12.9660			0.880187
$218$	−3.96772	+	3.96772i	−0.268728	+	0.268728i
$219$			39.4260i			2.66416i
$220$	−4.41009			−0.297328
$221$	2.85797	−	3.87763i	0.192248	−	0.260837i
$222$	0.925391			0.0621081
$223$		−	28.3218i		−	1.89657i	−0.317424	−	0.948284i	$-0.602818\pi$
$223$		−	28.3218i		−	1.89657i	0.317424	−	0.948284i	$-0.397182\pi$
$224$	3.42652	−	3.42652i	0.228944	−	0.228944i
$225$	13.1326			0.875507
$226$	9.48523	−	9.48523i	0.630948	−	0.630948i
$227$	−3.77194	−	3.77194i	−0.250352	−	0.250352i	0.570763	−	0.821115i	$-0.306648\pi$
$227$	−3.77194	−	3.77194i	−0.250352	−	0.250352i	−0.821115	+	0.570763i	$0.806648\pi$
$228$	−3.99160	−	3.99160i	−0.264350	−	0.264350i
$229$			8.44163i			0.557839i	0.960315	+	0.278919i	$0.0899762\pi$
$229$			8.44163i			0.557839i	−0.960315	+	0.278919i	$0.910024\pi$
$230$			3.74809i			0.247141i
$231$	17.7493	+	17.7493i	1.16782	+	1.16782i
$232$	−17.4536	−	17.4536i	−1.14588	−	1.14588i
$233$	3.96499	−	3.96499i	0.259755	−	0.259755i	−0.565199	−	0.824954i	$-0.691201\pi$
$233$	3.96499	−	3.96499i	0.259755	−	0.259755i	0.824954	+	0.565199i	$0.191201\pi$
$234$	−5.09468			−0.333049
$235$	2.43274	−	2.43274i	0.158695	−	0.158695i
$236$			2.15921i			0.140553i
$237$	36.4066			2.36486
$238$	−1.12146	−	7.40805i	−0.0726932	−	0.480193i
$239$	−4.12291			−0.266689			−0.133344	−	0.991070i	$-0.542572\pi$
$239$	−4.12291			−0.266689			−0.133344	+	0.991070i	$0.542572\pi$
$240$		−	7.66433i		−	0.494730i
$241$	−9.88967	+	9.88967i	−0.637049	+	0.637049i	−0.949827	−	0.312777i	$-0.898741\pi$
$241$	−9.88967	+	9.88967i	−0.637049	+	0.637049i	0.312777	+	0.949827i	$0.398741\pi$
$242$	35.2637			2.26683
$243$	−15.6261	+	15.6261i	−1.00241	+	1.00241i
$244$	1.65004	+	1.65004i	0.105633	+	0.105633i
$245$	−3.92752	−	3.92752i	−0.250920	−	0.250920i
$246$		−	19.1041i		−	1.21803i
$247$			4.39038i			0.279353i
$248$	−18.4724	−	18.4724i	−1.17300	−	1.17300i
$249$	−6.79130	−	6.79130i	−0.430381	−	0.430381i
$250$	8.59652	−	8.59652i	0.543692	−	0.543692i
$251$	26.1906			1.65314			0.826569	−	0.562835i	$-0.190289\pi$
$251$	26.1906			1.65314			0.826569	+	0.562835i	$0.190289\pi$
$252$	2.29974	−	2.29974i	0.144870	−	0.144870i
$253$			16.8696i			1.06058i
$254$	7.23345			0.453867
$255$	10.1862	+	7.50762i	0.637882	+	0.470145i
$256$	−12.6702			−0.791890
$257$		−	3.72021i		−	0.232060i	−0.993246	−	0.116030i	$-0.962983\pi$
$257$		−	3.72021i		−	0.232060i	0.993246	−	0.116030i	$-0.0370169\pi$
$258$	2.17334	−	2.17334i	0.135306	−	0.135306i
$259$	0.459454			0.0285491
$260$	0.571682	−	0.571682i	0.0354542	−	0.0354542i
$261$	−20.7879	−	20.7879i	−1.28674	−	1.28674i
$262$	14.0475	+	14.0475i	0.867859	+	0.867859i
$263$			22.9552i			1.41548i	0.706475	+	0.707738i	$0.250284\pi$
$263$			22.9552i			1.41548i	−0.706475	+	0.707738i	$0.749716\pi$
$264$		−	50.5745i		−	3.11264i
$265$	4.98797	+	4.98797i	0.306409	+	0.306409i
$266$	4.82869	+	4.82869i	0.296066	+	0.296066i
$267$	9.59552	−	9.59552i	0.587236	−	0.587236i
$268$	2.28018			0.139284
$269$	−12.7749	+	12.7749i	−0.778901	+	0.778901i	−0.979644	−	0.200743i	$-0.935664\pi$
$269$	−12.7749	+	12.7749i	−0.778901	+	0.778901i	0.200743	+	0.979644i	$0.435664\pi$
$270$		−	2.41940i		−	0.147240i
$271$	−28.7724			−1.74780			−0.873899	−	0.486107i	$-0.838417\pi$
$271$	−28.7724			−1.74780			−0.873899	+	0.486107i	$0.838417\pi$
$272$	−6.10905	+	8.28862i	−0.370416	+	0.502571i
$273$	−4.60171			−0.278508
$274$			3.67669i			0.222117i
$275$	16.1603	−	16.1603i	0.974505	−	0.974505i
$276$	3.97638			0.239350
$277$	11.5392	−	11.5392i	0.693322	−	0.693322i	−0.269639	−	0.962961i	$-0.586904\pi$
$277$	11.5392	−	11.5392i	0.693322	−	0.693322i	0.962961	+	0.269639i	$0.0869044\pi$
$278$	18.8136	+	18.8136i	1.12836	+	1.12836i
$279$	−22.0014	−	22.0014i	−1.31719	−	1.31719i
$280$		−	5.57895i		−	0.333406i
$281$			21.3860i			1.27578i	0.770127	+	0.637891i	$0.220193\pi$
$281$			21.3860i			1.27578i	−0.770127	+	0.637891i	$0.779807\pi$
$282$	6.28841	+	6.28841i	0.374469	+	0.374469i
$283$	0.190296	+	0.190296i	0.0113120	+	0.0113120i	0.712740	−	0.701428i	$-0.247454\pi$
$283$	0.190296	+	0.190296i	0.0113120	+	0.0113120i	−0.701428	+	0.712740i	$0.747454\pi$
$284$	−1.63191	+	1.63191i	−0.0968360	+	0.0968360i
$285$	−11.5331			−0.683162
$286$	−6.26926	+	6.26926i	−0.370709	+	0.370709i
$287$		−	9.48512i		−	0.559889i
$288$	−11.6286			−0.685223
$289$	−5.03172	−	16.2383i	−0.295984	−	0.955193i
$290$	−11.3669			−0.667489
$291$			25.3724i			1.48736i
$292$	6.28607	−	6.28607i	0.367864	−	0.367864i
$293$	−8.46838			−0.494728			−0.247364	−	0.968923i	$-0.579564\pi$
$293$	−8.46838			−0.494728			−0.247364	+	0.968923i	$0.579564\pi$
$294$	10.1522	−	10.1522i	0.592091	−	0.592091i
$295$	3.11935	+	3.11935i	0.181616	+	0.181616i
$296$	−0.654578	−	0.654578i	−0.0380466	−	0.0380466i
$297$		−	10.8894i		−	0.631867i
$298$			9.93682i			0.575625i
$299$	−2.18682	−	2.18682i	−0.126467	−	0.126467i
$300$	−3.80919	−	3.80919i	−0.219924	−	0.219924i
$301$	1.07906	−	1.07906i	0.0621959	−	0.0621959i
$302$	5.64430			0.324793
$303$	−7.68825	+	7.68825i	−0.441678	+	0.441678i
$304$		−	9.38464i		−	0.538246i
$305$	4.76752			0.272988
$306$	−10.6674	+	14.4733i	−0.609817	+	0.827386i
$307$	−12.1776			−0.695012			−0.347506	−	0.937678i	$-0.612971\pi$
$307$	−12.1776			−0.695012			−0.347506	+	0.937678i	$0.612971\pi$
$308$		−	5.65990i		−	0.322503i
$309$	−0.869797	+	0.869797i	−0.0494810	+	0.0494810i
$310$	−12.0305			−0.683286
$311$	16.0356	−	16.0356i	0.909297	−	0.909297i	−0.0869185	−	0.996215i	$-0.527702\pi$
$311$	16.0356	−	16.0356i	0.909297	−	0.909297i	0.996215	+	0.0869185i	$0.0277020\pi$
$312$	6.55600	+	6.55600i	0.371160	+	0.371160i
$313$	−10.8477	−	10.8477i	−0.613146	−	0.613146i	0.330618	−	0.943765i	$-0.392743\pi$
$313$	−10.8477	−	10.8477i	−0.613146	−	0.613146i	−0.943765	+	0.330618i	$0.892743\pi$
$314$		−	21.2380i		−	1.19853i
$315$		−	6.64474i		−	0.374389i
$316$	−5.80466	−	5.80466i	−0.326538	−	0.326538i
$317$	4.88895	+	4.88895i	0.274591	+	0.274591i	0.830945	−	0.556354i	$-0.187800\pi$
$317$	4.88895	+	4.88895i	0.274591	+	0.274591i	−0.556354	+	0.830945i	$0.687800\pi$
$318$	−12.8934	+	12.8934i	−0.723027	+	0.723027i
$319$	−51.1610			−2.86447
$320$	−7.37869	+	7.37869i	−0.412481	+	0.412481i
$321$			10.3125i			0.575586i
$322$	−4.81029			−0.268067
$323$	12.4725	+	9.19276i	0.693990	+	0.511499i
$324$	3.82698			0.212610
$325$			4.18975i			0.232405i
$326$	7.51001	−	7.51001i	0.415941	−	0.415941i
$327$	12.1624			0.672581
$328$	−13.5133	+	13.5133i	−0.746149	+	0.746149i
$329$	3.12218	+	3.12218i	0.172131	+	0.172131i
$330$	−16.4687	−	16.4687i	−0.906575	−	0.906575i
$331$		−	4.39818i		−	0.241746i	−0.992668	−	0.120873i	$-0.961431\pi$
$331$		−	4.39818i		−	0.241746i	0.992668	−	0.120873i	$-0.0385693\pi$
$332$			2.16561i			0.118853i
$333$	−0.779628	−	0.779628i	−0.0427233	−	0.0427233i
$334$	0.799855	+	0.799855i	0.0437661	+	0.0437661i
$335$	3.29412	−	3.29412i	0.179977	−	0.179977i
$336$	9.83638			0.536619
$337$	−7.74230	+	7.74230i	−0.421750	+	0.421750i	−0.885806	−	0.464056i	$-0.846394\pi$
$337$	−7.74230	+	7.74230i	−0.421750	+	0.421750i	0.464056	+	0.885806i	$0.346394\pi$
$338$			13.8551i			0.753616i
$339$	−29.0754			−1.57916
$340$	−0.427066	−	2.82109i	−0.0231609	−	0.152995i
$341$	−54.1476			−2.93226
$342$		−	16.3872i		−	0.886118i
$343$	12.5940	−	12.5940i	0.680011	−	0.680011i
$344$	−3.07464			−0.165773
$345$	5.74457	−	5.74457i	0.309277	−	0.309277i
$346$	13.8277	+	13.8277i	0.743380	+	0.743380i
$347$	13.8279	+	13.8279i	0.742322	+	0.742322i	0.973024	−	0.230703i	$-0.0741025\pi$
$347$	13.8279	+	13.8279i	0.742322	+	0.742322i	−0.230703	+	0.973024i	$0.574102\pi$
$348$			12.0593i			0.646446i
$349$		−	17.4958i		−	0.936528i	−0.883588	−	0.468264i	$-0.844880\pi$
$349$		−	17.4958i		−	0.936528i	0.883588	−	0.468264i	$-0.155120\pi$
$350$	4.60803	+	4.60803i	0.246310	+	0.246310i
$351$	1.41160	+	1.41160i	0.0753455	+	0.0753455i
$352$	−14.3096	+	14.3096i	−0.762705	+	0.762705i
$353$	22.8666			1.21707			0.608533	−	0.793529i	$-0.291758\pi$
$353$	22.8666			1.21707			0.608533	+	0.793529i	$0.291758\pi$
$354$	−8.06321	+	8.06321i	−0.428555	+	0.428555i
$355$			4.71514i			0.250254i
$356$	−3.05981			−0.162170
$357$	−9.63526	+	13.0729i	−0.509952	+	0.691891i
$358$	17.7141			0.936220
$359$		−	32.0826i		−	1.69326i	−0.532184	−	0.846629i	$-0.678629\pi$
$359$		−	32.0826i		−	1.69326i	0.532184	−	0.846629i	$-0.321371\pi$
$360$	−9.46668	+	9.46668i	−0.498938	+	0.498938i
$361$	4.87821			0.256748
$362$	1.19682	−	1.19682i	0.0629035	−	0.0629035i
$363$	−54.0475	−	54.0475i	−2.83676	−	2.83676i
$364$	0.733696	+	0.733696i	0.0384561	+	0.0384561i
$365$		−	18.1626i		−	0.950674i
$366$			12.3236i			0.644164i
$367$	17.4377	+	17.4377i	0.910241	+	0.910241i	0.996291	−	0.0860501i	$-0.0274245\pi$
$367$	17.4377	+	17.4377i	0.910241	+	0.910241i	−0.0860501	+	0.996291i	$0.527425\pi$
$368$	4.67443	+	4.67443i	0.243672	+	0.243672i
$369$	−16.0949	+	16.0949i	−0.837867	+	0.837867i
$370$	−0.426305			−0.0221626
$371$	−6.40155	+	6.40155i	−0.332352	+	0.332352i
$372$			12.7633i			0.661745i
$373$	28.3141			1.46605			0.733024	−	0.680203i	$-0.238108\pi$
$373$	28.3141			1.46605			0.733024	+	0.680203i	$0.238108\pi$
$374$	4.68335	+	30.9370i	0.242170	+	1.59972i
$375$	−26.3512			−1.36077
$376$		−	8.89625i		−	0.458789i
$377$	6.63203	−	6.63203i	0.341567	−	0.341567i
$378$	3.10505			0.159707
$379$	−22.7433	+	22.7433i	−1.16824	+	1.16824i	−0.185623	+	0.982621i	$0.559430\pi$
$379$	−22.7433	+	22.7433i	−1.16824	+	1.16824i	−0.982621	+	0.185623i	$0.940570\pi$
$380$	1.83884	+	1.83884i	0.0943303	+	0.0943303i
$381$	−11.0865	−	11.0865i	−0.567977	−	0.567977i
$382$			13.6466i			0.698221i
$383$		−	15.0324i		−	0.768118i	−0.923309	−	0.384059i	$-0.874526\pi$
$383$		−	15.0324i		−	0.768118i	0.923309	−	0.384059i	$-0.125474\pi$
$384$	−7.48206	−	7.48206i	−0.381817	−	0.381817i
$385$	−8.17669	−	8.17669i	−0.416723	−	0.416723i
$386$	5.00368	−	5.00368i	0.254681	−	0.254681i
$387$	−3.66201			−0.186151
$388$	4.04537	−	4.04537i	0.205373	−	0.205373i
$389$		−	26.5581i		−	1.34655i	−0.739392	−	0.673275i	$-0.764887\pi$
$389$		−	26.5581i		−	1.34655i	0.739392	−	0.673275i	$-0.235113\pi$
$390$	4.26971			0.216205
$391$	−10.7913	+	1.63363i	−0.545742	+	0.0826162i
$392$	−14.3625			−0.725414
$393$		−	43.0604i		−	2.17211i
$394$	−13.4496	+	13.4496i	−0.677582	+	0.677582i
$395$	−16.7717			−0.843874
$396$	−9.60403	+	9.60403i	−0.482621	+	0.482621i
$397$	−18.4231	−	18.4231i	−0.924629	−	0.924629i	0.0727235	−	0.997352i	$-0.476831\pi$
$397$	−18.4231	−	18.4231i	−0.924629	−	0.924629i	−0.997352	+	0.0727235i	$0.976831\pi$
$398$	−15.9805	−	15.9805i	−0.801029	−	0.801029i
$399$		−	14.8016i		−	0.741005i
$400$		−	8.95579i		−	0.447789i
$401$	23.3831	+	23.3831i	1.16769	+	1.16769i	0.982749	+	0.184946i	$0.0592110\pi$
$401$	23.3831	+	23.3831i	1.16769	+	1.16769i	0.184946	+	0.982749i	$0.440789\pi$
$402$	8.51497	+	8.51497i	0.424688	+	0.424688i
$403$	7.01918	−	7.01918i	0.349650	−	0.349650i
$404$	2.45162			0.121973
$405$	5.52873	−	5.52873i	0.274725	−	0.274725i
$406$		−	14.5883i		−	0.724005i
$407$	−1.91874			−0.0951086
$408$	32.3520	−	4.89756i	1.60166	−	0.242465i
$409$	34.6507			1.71336			0.856682	−	0.515844i	$-0.172522\pi$
$409$	34.6507			1.71336			0.856682	+	0.515844i	$0.172522\pi$
$410$			8.80079i			0.434640i
$411$	5.63514	−	5.63514i	0.277961	−	0.277961i
$412$	0.277360			0.0136646
$413$	−4.00337	+	4.00337i	−0.196993	+	0.196993i
$414$	8.16236	+	8.16236i	0.401158	+	0.401158i
$415$	3.12859	+	3.12859i	0.153576	+	0.153576i
$416$		−	3.70993i		−	0.181894i
$417$		−	57.6699i		−	2.82411i
$418$	−20.1653	−	20.1653i	−0.986316	−	0.986316i
$419$	−3.09043	−	3.09043i	−0.150977	−	0.150977i	0.627577	−	0.778554i	$-0.284047\pi$
$419$	−3.09043	−	3.09043i	−0.150977	−	0.150977i	−0.778554	+	0.627577i	$0.784047\pi$
$420$	−1.92735	+	1.92735i	−0.0940450	+	0.0940450i
$421$	−18.7654			−0.914569			−0.457284	−	0.889321i	$-0.651178\pi$
$421$	−18.7654			−0.914569			−0.457284	+	0.889321i	$0.651178\pi$
$422$	15.0018	−	15.0018i	0.730277	−	0.730277i
$423$		−	10.5958i		−	0.515184i
$424$	18.2404			0.885833
$425$	11.9026	+	8.77267i	0.577359	+	0.425537i
$426$	−12.1882			−0.590520
$427$			6.11863i			0.296101i
$428$	1.64422	−	1.64422i	0.0794763	−	0.0794763i
$429$	19.2174			0.927823
$430$	−1.00121	+	1.00121i	−0.0482824	+	0.0482824i
$431$	28.9483	+	28.9483i	1.39439	+	1.39439i	0.815177	+	0.579212i	$0.196640\pi$
$431$	28.9483	+	28.9483i	1.39439	+	1.39439i	0.579212	+	0.815177i	$0.303360\pi$
$432$	−3.01736	−	3.01736i	−0.145173	−	0.145173i
$433$			35.1428i			1.68886i	0.535668	+	0.844428i	$0.320060\pi$
$433$			35.1428i			1.68886i	−0.535668	+	0.844428i	$0.679940\pi$
$434$		−	15.4399i		−	0.741139i
$435$	17.4217	+	17.4217i	0.835308	+	0.835308i
$436$	−1.93917	−	1.93917i	−0.0928692	−	0.0928692i
$437$	7.03398	−	7.03398i	0.336481	−	0.336481i
$438$	46.9485			2.24329
$439$	−9.14591	+	9.14591i	−0.436510	+	0.436510i	−0.890836	−	0.454325i	$-0.849880\pi$
$439$	−9.14591	+	9.14591i	−0.436510	+	0.436510i	0.454325	+	0.890836i	$0.349880\pi$
$440$			23.2985i			1.11071i
$441$	−17.1062			−0.814583
$442$	−4.61749	−	3.40328i	−0.219632	−	0.161877i
$443$	37.7729			1.79464			0.897322	−	0.441377i	$-0.145510\pi$
$443$	37.7729			1.79464			0.897322	+	0.441377i	$0.145510\pi$
$444$			0.452272i			0.0214639i
$445$	−4.42043	+	4.42043i	−0.209548	+	0.209548i
$446$	−33.7257			−1.59696
$447$	15.2298	−	15.2298i	0.720347	−	0.720347i
$448$	−9.46980	−	9.46980i	−0.447406	−	0.447406i
$449$	−11.6812	−	11.6812i	−0.551268	−	0.551268i	0.375539	−	0.926807i	$-0.377458\pi$
$449$	−11.6812	−	11.6812i	−0.551268	−	0.551268i	−0.926807	+	0.375539i	$0.877458\pi$
$450$		−	15.6383i		−	0.737199i
$451$			39.6112i			1.86522i
$452$	4.63577	+	4.63577i	0.218048	+	0.218048i
$453$	−8.65083	−	8.65083i	−0.406451	−	0.406451i
$454$	−4.49163	+	4.49163i	−0.210803	+	0.210803i
$455$	2.11990			0.0993824
$456$	−21.0876	+	21.0876i	−0.987517	+	0.987517i
$457$			0.512113i			0.0239557i	0.999928	+	0.0119778i	$0.00381275\pi$
$457$			0.512113i			0.0239557i	−0.999928	+	0.0119778i	$0.996187\pi$
$458$	10.0523			0.469714
$459$	6.96584	−	1.05451i	0.325138	−	0.0492204i
$460$	−1.83183			−0.0854093
$461$		−	1.98716i		−	0.0925511i	−0.998929	−	0.0462755i	$-0.985265\pi$
$461$		−	1.98716i		−	0.0925511i	0.998929	−	0.0462755i	$-0.0147352\pi$
$462$	21.1360	−	21.1360i	0.983334	−	0.983334i
$463$	35.5866			1.65385			0.826925	−	0.562312i	$-0.190088\pi$
$463$	35.5866			1.65385			0.826925	+	0.562312i	$0.190088\pi$
$464$	−14.1763	+	14.1763i	−0.658118	+	0.658118i
$465$	18.4387	+	18.4387i	0.855076	+	0.855076i
$466$	−4.72152	−	4.72152i	−0.218720	−	0.218720i
$467$		−	27.5687i		−	1.27573i	−0.770150	−	0.637863i	$-0.779819\pi$
$467$		−	27.5687i		−	1.27573i	0.770150	−	0.637863i	$-0.220181\pi$
$468$		−	2.48995i		−	0.115098i
$469$	4.22766	+	4.22766i	0.195215	+	0.195215i
$470$	−2.89692	−	2.89692i	−0.133625	−	0.133625i
$471$	−32.5508	+	32.5508i	−1.49986	+	1.49986i
$472$	11.4071			0.525054
$473$	−4.50629	+	4.50629i	−0.207200	+	0.207200i
$474$		−	43.3531i		−	1.99127i
$475$	−13.4765			−0.618342
$476$	3.62058	−	0.548096i	0.165949	−	0.0251219i
$477$	21.7250			0.994721
$478$			4.90957i			0.224559i
$479$	−3.33162	+	3.33162i	−0.152226	+	0.152226i	−0.779111	−	0.626886i	$-0.784329\pi$
$479$	−3.33162	+	3.33162i	−0.152226	+	0.152226i	0.626886	+	0.779111i	$0.284329\pi$
$480$	9.74562			0.444825
$481$	0.248728	−	0.248728i	0.0113410	−	0.0113410i
$482$	11.7766	+	11.7766i	0.536411	+	0.536411i
$483$	7.37257	+	7.37257i	0.335463	+	0.335463i
$484$			17.2346i			0.783392i
$485$		−	11.6885i		−	0.530746i
$486$	18.6076	+	18.6076i	0.844056	+	0.844056i
$487$	28.9794	+	28.9794i	1.31318	+	1.31318i	0.919057	+	0.394126i	$0.128952\pi$
$487$	28.9794	+	28.9794i	1.31318	+	1.31318i	0.394126	+	0.919057i	$0.371048\pi$
$488$	8.71713	−	8.71713i	0.394606	−	0.394606i
$489$	−23.0207			−1.04103
$490$	−4.67690	+	4.67690i	−0.211281	+	0.211281i
$491$		−	11.8609i		−	0.535273i	−0.963520	−	0.267637i	$-0.913757\pi$
$491$		−	11.8609i		−	0.535273i	0.963520	−	0.267637i	$-0.0862426\pi$
$492$	9.33685			0.420938
$493$	−4.95436	−	32.7272i	−0.223133	−	1.47396i
$494$	5.22807			0.235222
$495$			27.7493i			1.24724i
$496$	−15.0038	+	15.0038i	−0.673693	+	0.673693i
$497$	−6.05141			−0.271443
$498$	−8.08710	+	8.08710i	−0.362392	+	0.362392i
$499$	−1.27642	−	1.27642i	−0.0571405	−	0.0571405i	0.677959	−	0.735100i	$-0.262865\pi$
$499$	−1.27642	−	1.27642i	−0.0571405	−	0.0571405i	−0.735100	+	0.677959i	$0.762865\pi$
$500$	4.20143	+	4.20143i	0.187894	+	0.187894i
$501$		−	2.45182i		−	0.109539i
$502$		−	31.1879i		−	1.39198i
$503$	18.8231	+	18.8231i	0.839282	+	0.839282i	0.988764	−	0.149483i	$-0.0477609\pi$
$503$	18.8231	+	18.8231i	0.839282	+	0.839282i	−0.149483	+	0.988764i	$0.547761\pi$
$504$	−12.1495	−	12.1495i	−0.541182	−	0.541182i
$505$	3.54179	−	3.54179i	0.157608	−	0.157608i
$506$	20.0884			0.893038
$507$	21.2352	−	21.2352i	0.943088	−	0.943088i
$508$			3.53525i			0.156851i
$509$	−2.72749			−0.120894			−0.0604469	−	0.998171i	$-0.519253\pi$
$509$	−2.72749			−0.120894			−0.0604469	+	0.998171i	$0.519253\pi$
$510$	8.94009	−	12.1297i	0.395874	−	0.537112i
$511$	23.3098			1.03117
$512$			23.2868i			1.02914i
$513$	−4.54045	+	4.54045i	−0.200466	+	0.200466i
$514$	−4.43004			−0.195401
$515$	0.400695	−	0.400695i	0.0176567	−	0.0176567i
$516$	1.06219	+	1.06219i	0.0467603	+	0.0467603i
$517$	−13.0386	−	13.0386i	−0.573439	−	0.573439i
$518$		−	0.547119i		−	0.0240391i
$519$		−	42.3864i		−	1.86056i
$520$	−3.02019	−	3.02019i	−0.132444	−	0.132444i
$521$	13.7370	+	13.7370i	0.601831	+	0.601831i	0.940798	−	0.338967i	$-0.110078\pi$
$521$	13.7370	+	13.7370i	0.601831	+	0.601831i	−0.338967	+	0.940798i	$0.610078\pi$
$522$	−24.7542	+	24.7542i	−1.08346	+	1.08346i
$523$	37.3618			1.63372			0.816858	−	0.576839i	$-0.195714\pi$
$523$	37.3618			1.63372			0.816858	+	0.576839i	$0.195714\pi$
$524$	−6.86554	+	6.86554i	−0.299922	+	0.299922i
$525$		−	14.1252i		−	0.616473i
$526$	27.3351			1.19187
$527$	−5.24357	−	34.6377i	−0.228414	−	1.50884i
$528$	−41.0781			−1.78769
$529$		−	15.9928i		−	0.695341i
$530$	5.93969	−	5.93969i	0.258004	−	0.258004i
$531$	13.5863			0.589594
$532$	−2.35996	+	2.35996i	−0.102317	+	0.102317i
$533$	−5.13482	−	5.13482i	−0.222414	−	0.222414i
$534$	−11.4264	−	11.4264i	−0.494467	−	0.494467i
$535$		−	4.75071i		−	0.205391i
$536$		−	12.0462i		−	0.520316i
$537$	−27.1498	−	27.1498i	−1.17160	−	1.17160i
$538$	15.2124	+	15.2124i	0.655854	+	0.655854i
$539$	−21.0501	+	21.0501i	−0.906692	+	0.906692i
$540$	1.18245			0.0508845
$541$	8.23465	−	8.23465i	0.354035	−	0.354035i	−0.507573	−	0.861609i	$-0.669457\pi$
$541$	8.23465	−	8.23465i	0.354035	−	0.354035i	0.861609	+	0.507573i	$0.169457\pi$
$542$			34.2623i			1.47169i
$543$	−3.66866			−0.157437
$544$	−10.5394	−	7.76800i	−0.451875	−	0.333050i
$545$	−5.60292			−0.240003
$546$			5.47973i			0.234511i
$547$	−24.5263	+	24.5263i	−1.04867	+	1.04867i	−0.0499172	+	0.998753i	$0.515896\pi$
$547$	−24.5263	+	24.5263i	−1.04867	+	1.04867i	−0.998753	+	0.0499172i	$0.984104\pi$
$548$	−1.79693			−0.0767611
$549$	10.3824	−	10.3824i	0.443112	−	0.443112i
$550$	−19.2438	−	19.2438i	−0.820557	−	0.820557i
$551$	21.3322	+	21.3322i	0.908781	+	0.908781i
$552$		−	21.0072i		−	0.894126i
$553$		−	21.5247i		−	0.915324i
$554$	−13.7409	−	13.7409i	−0.583794	−	0.583794i
$555$	0.653384	+	0.653384i	0.0277346	+	0.0277346i
$556$	−9.19487	+	9.19487i	−0.389950	+	0.389950i
$557$	−18.6574			−0.790541			−0.395271	−	0.918565i	$-0.629349\pi$
$557$	−18.6574			−0.790541			−0.395271	+	0.918565i	$0.629349\pi$
$558$	−26.1993	+	26.1993i	−1.10910	+	1.10910i
$559$		−	1.16831i		−	0.0494141i
$560$	−4.53139			−0.191486
$561$	40.2381	−	54.5942i	1.69886	−	2.30497i
$562$	25.4665			1.07424
$563$			7.90207i			0.333032i	0.986039	+	0.166516i	$0.0532518\pi$
$563$			7.90207i			0.333032i	−0.986039	+	0.166516i	$0.946748\pi$
$564$	−3.07337	+	3.07337i	−0.129412	+	0.129412i
$565$	13.3943			0.563504
$566$	0.226606	−	0.226606i	0.00952494	−	0.00952494i
$567$	7.09556	+	7.09556i	0.297986	+	0.297986i
$568$	8.62136	+	8.62136i	0.361744	+	0.361744i
$569$		−	8.50382i		−	0.356499i	−0.983985	−	0.178249i	$-0.942957\pi$
$569$		−	8.50382i		−	0.356499i	0.983985	−	0.178249i	$-0.0570434\pi$
$570$			13.7337i			0.575239i
$571$	20.7419	+	20.7419i	0.868022	+	0.868022i	0.992253	−	0.124232i	$-0.0396466\pi$
$571$	20.7419	+	20.7419i	0.868022	+	0.868022i	−0.124232	+	0.992253i	$0.539647\pi$
$572$	−3.06401	−	3.06401i	−0.128113	−	0.128113i
$573$	20.9157	−	20.9157i	0.873767	−	0.873767i
$574$	−11.2949			−0.471441
$575$	6.71254	−	6.71254i	0.279932	−	0.279932i
$576$			32.1378i			1.33907i
$577$	3.41842			0.142311			0.0711553	−	0.997465i	$-0.477331\pi$
$577$	3.41842			0.142311			0.0711553	+	0.997465i	$0.477331\pi$
$578$	−19.3366	+	5.99179i	−0.804296	+	0.249226i
$579$	−15.3380			−0.637424
$580$		−	5.55543i		−	0.230677i
$581$	−4.01523	+	4.01523i	−0.166580	+	0.166580i
$582$	30.2136			1.25239
$583$	26.7338	−	26.7338i	1.10720	−	1.10720i
$584$	−33.2092	−	33.2092i	−1.37421	−	1.37421i
$585$	−3.59716	−	3.59716i	−0.148724	−	0.148724i
$586$			10.0842i			0.416574i
$587$		−	19.1272i		−	0.789464i	−0.918796	−	0.394732i	$-0.870837\pi$
$587$		−	19.1272i		−	0.789464i	0.918796	−	0.394732i	$-0.129163\pi$
$588$	4.96177	+	4.96177i	0.204620	+	0.204620i
$589$	22.5774	+	22.5774i	0.930287	+	0.930287i
$590$	3.71453	−	3.71453i	0.152925	−	0.152925i
$591$	41.2276			1.69588
$592$	−0.531668	+	0.531668i	−0.0218514	+	0.0218514i
$593$			6.76412i			0.277769i	0.990309	+	0.138885i	$0.0443517\pi$
$593$			6.76412i			0.277769i	−0.990309	+	0.138885i	$0.955648\pi$
$594$	−12.9671			−0.532047
$595$	4.43873	−	6.02237i	0.181970	−	0.246893i
$596$	−4.85649			−0.198929
$597$			48.9855i			2.00484i
$598$	−2.60407	+	2.60407i	−0.106488	+	0.106488i
$599$	0.283853			0.0115979			0.00579896	−	0.999983i	$-0.498154\pi$
$599$	0.283853			0.0115979			0.00579896	+	0.999983i	$0.498154\pi$
$600$	−20.1239	+	20.1239i	−0.821556	+	0.821556i
$601$	7.02948	+	7.02948i	0.286739	+	0.286739i	0.835789	−	0.549051i	$-0.185011\pi$
$601$	7.02948	+	7.02948i	0.286739	+	0.286739i	−0.549051	+	0.835789i	$0.685011\pi$
$602$	−1.28495	−	1.28495i	−0.0523705	−	0.0523705i
$603$		−	14.3475i		−	0.584274i
$604$			2.75857i			0.112245i
$605$	24.8984	+	24.8984i	1.01226	+	1.01226i
$606$	9.15519	+	9.15519i	0.371904	+	0.371904i
$607$	17.7251	−	17.7251i	0.719438	−	0.719438i	−0.249052	−	0.968490i	$-0.580119\pi$
$607$	17.7251	−	17.7251i	0.719438	−	0.719438i	0.968490	+	0.249052i	$0.0801191\pi$
$608$	11.9331			0.483951
$609$	−22.3590	+	22.3590i	−0.906033	+	0.906033i
$610$		−	5.67718i		−	0.229862i
$611$	3.38041			0.136757
$612$	−7.07365	−	5.21357i	−0.285935	−	0.210746i
$613$	−13.0952			−0.528911			−0.264455	−	0.964398i	$-0.585192\pi$
$613$	−13.0952			−0.528911			−0.264455	+	0.964398i	$0.585192\pi$
$614$			14.5011i			0.585217i
$615$	13.4887	−	13.4887i	0.543916	−	0.543916i
$616$	−29.9012			−1.20475
$617$	−0.980064	+	0.980064i	−0.0394559	+	0.0394559i	−0.726559	−	0.687104i	$-0.758882\pi$
$617$	−0.980064	+	0.980064i	−0.0394559	+	0.0394559i	0.687104	+	0.726559i	$0.258882\pi$
$618$	1.03576	+	1.03576i	0.0416642	+	0.0416642i
$619$	−7.09516	−	7.09516i	−0.285179	−	0.285179i	0.549992	−	0.835170i	$-0.314631\pi$
$619$	−7.09516	−	7.09516i	−0.285179	−	0.285179i	−0.835170	+	0.549992i	$0.814631\pi$
$620$		−	5.87973i		−	0.236136i
$621$		−	4.52314i		−	0.181508i
$622$	−19.0953	−	19.0953i	−0.765651	−	0.765651i
$623$	−5.67317	−	5.67317i	−0.227291	−	0.227291i
$624$	5.32497	−	5.32497i	0.213170	−	0.213170i
$625$	−5.79147			−0.231659
$626$	−12.9174	+	12.9174i	−0.516284	+	0.516284i
$627$			61.8133i			2.46859i
$628$	10.3798			0.414198
$629$	−0.185808	−	1.22740i	−0.00740866	−	0.0489397i
$630$	−7.91258			−0.315245
$631$		−	48.4254i		−	1.92778i	−0.266295	−	0.963891i	$-0.585800\pi$
$631$		−	48.4254i		−	1.92778i	0.266295	−	0.963891i	$-0.414200\pi$
$632$	−30.6660	+	30.6660i	−1.21983	+	1.21983i
$633$	−45.9856			−1.82776
$634$	5.82178	−	5.82178i	0.231212	−	0.231212i
$635$	5.10727	+	5.10727i	0.202676	+	0.202676i
$636$	−6.30148	−	6.30148i	−0.249870	−	0.249870i
$637$		−	5.45747i		−	0.216233i
$638$			60.9227i			2.41195i
$639$	10.2684	+	10.2684i	0.406210	+	0.406210i
$640$	3.44681	+	3.44681i	0.136247	+	0.136247i
$641$	−1.39866	+	1.39866i	−0.0552439	+	0.0552439i	−0.734189	−	0.678945i	$-0.762437\pi$
$641$	−1.39866	+	1.39866i	−0.0552439	+	0.0552439i	0.678945	+	0.734189i	$0.262437\pi$
$642$	12.2801			0.484658
$643$	−1.68999	+	1.68999i	−0.0666468	+	0.0666468i	−0.739645	−	0.672998i	$-0.765006\pi$
$643$	−1.68999	+	1.68999i	−0.0666468	+	0.0666468i	0.672998	+	0.739645i	$0.265006\pi$
$644$		−	2.35096i		−	0.0926408i
$645$	3.06903			0.120843
$646$	10.9468	−	14.8523i	0.430695	−	0.584356i
$647$	1.50144			0.0590278			0.0295139	−	0.999564i	$-0.490604\pi$
$647$	1.50144			0.0590278			0.0295139	+	0.999564i	$0.490604\pi$
$648$		−	20.2179i		−	0.794234i
$649$	16.7186	−	16.7186i	0.656263	−	0.656263i
$650$	4.98916			0.195691
$651$	−23.6642	+	23.6642i	−0.927474	+	0.927474i
$652$	3.67042	+	3.67042i	0.143745	+	0.143745i
$653$	12.6304	+	12.6304i	0.494264	+	0.494264i	0.909647	−	0.415382i	$-0.136352\pi$
$653$	12.6304	+	12.6304i	0.494264	+	0.494264i	−0.415382	+	0.909647i	$0.636352\pi$
$654$		−	14.4830i		−	0.566330i
$655$			19.8369i			0.775091i
$656$	10.9759	+	10.9759i	0.428538	+	0.428538i
$657$	−39.5535	−	39.5535i	−1.54313	−	1.54313i
$658$	3.71790	−	3.71790i	0.144939	−	0.144939i
$659$	21.5512			0.839514			0.419757	−	0.907637i	$-0.362115\pi$
$659$	21.5512			0.839514			0.419757	+	0.907637i	$0.362115\pi$
$660$	8.04887	−	8.04887i	0.313302	−	0.313302i
$661$			4.44063i			0.172720i	0.996264	+	0.0863602i	$0.0275236\pi$
$661$			4.44063i			0.172720i	−0.996264	+	0.0863602i	$0.972476\pi$
$662$	−5.23736			−0.203556
$663$	1.86098	+	12.2932i	0.0722745	+	0.477427i
$664$	11.4409			0.443992
$665$			6.81873i			0.264419i
$666$	−0.928383	+	0.928383i	−0.0359741	+	0.0359741i
$667$	−21.2508			−0.822836
$668$	−0.390918	+	0.390918i	−0.0151251	+	0.0151251i
$669$	51.6902	+	51.6902i	1.99846	+	1.99846i
$670$	−3.92264	−	3.92264i	−0.151545	−	0.151545i
$671$		−	25.5522i		−	0.986433i
$672$			12.5075i			0.482488i
$673$	−5.09114	−	5.09114i	−0.196249	−	0.196249i	0.602141	−	0.798390i	$-0.294315\pi$
$673$	−5.09114	−	5.09114i	−0.196249	−	0.196249i	−0.798390	+	0.602141i	$0.794315\pi$
$674$	9.21956	+	9.21956i	0.355124	+	0.355124i
$675$	−4.33297	+	4.33297i	−0.166776	+	0.166776i
$676$	−6.77147			−0.260441
$677$	14.3955	−	14.3955i	0.553265	−	0.553265i	−0.374116	−	0.927382i	$-0.622054\pi$
$677$	14.3955	−	14.3955i	0.553265	−	0.553265i	0.927382	+	0.374116i	$0.122054\pi$
$678$			34.6231i			1.32969i
$679$	15.0010			0.575684
$680$	−14.9038	+	2.25619i	−0.571535	+	0.0865208i
$681$	13.7684			0.527605
$682$			64.4791i			2.46903i
$683$	−21.1733	+	21.1733i	−0.810173	+	0.810173i	−0.984660	−	0.174486i	$-0.944173\pi$
$683$	−21.1733	+	21.1733i	−0.810173	+	0.810173i	0.174486	+	0.984660i	$0.444173\pi$
$684$	8.00902			0.306232
$685$	−2.59598	+	2.59598i	−0.0991872	+	0.0991872i
$686$	−14.9969	−	14.9969i	−0.572586	−	0.572586i
$687$	−15.4069	−	15.4069i	−0.587808	−	0.587808i
$688$			2.49731i			0.0952091i
$689$			6.93103i			0.264051i
$690$	−6.84065	−	6.84065i	−0.260419	−	0.260419i
$691$	−13.9026	−	13.9026i	−0.528880	−	0.528880i	0.391358	−	0.920238i	$-0.372005\pi$
$691$	−13.9026	−	13.9026i	−0.528880	−	0.528880i	−0.920238	+	0.391358i	$0.872005\pi$
$692$	−6.75808	+	6.75808i	−0.256904	+	0.256904i
$693$	−35.6135			−1.35284
$694$	16.4663	−	16.4663i	0.625053	−	0.625053i
$695$			26.5671i			1.00775i
$696$	63.7092			2.41489
$697$	−25.3389	+	3.83589i	−0.959778	+	0.145295i
$698$	−20.8340			−0.788580
$699$			14.4730i			0.547421i
$700$	−2.25211	+	2.25211i	−0.0851219	+	0.0851219i
$701$	−14.9254			−0.563726			−0.281863	−	0.959455i	$-0.590952\pi$
$701$	−14.9254			−0.563726			−0.281863	+	0.959455i	$0.590952\pi$
$702$	1.68094	−	1.68094i	0.0634428	−	0.0634428i
$703$	0.800041	+	0.800041i	0.0301741	+	0.0301741i
$704$	39.5472	+	39.5472i	1.49049	+	1.49049i
$705$			8.88002i			0.334441i
$706$		−	27.2296i		−	1.02480i
$707$	4.54553	+	4.54553i	0.170952	+	0.170952i
$708$	−3.94078	−	3.94078i	−0.148104	−	0.148104i
$709$	−31.6053	+	31.6053i	−1.18696	+	1.18696i	−0.209060	+	0.977903i	$0.567040\pi$
$709$	−31.6053	+	31.6053i	−1.18696	+	1.18696i	−0.977903	+	0.209060i	$0.932960\pi$
$710$	5.61481			0.210720
$711$	−36.5243	+	36.5243i	−1.36977	+	1.36977i
$712$			16.1650i			0.605808i
$713$	−22.4914			−0.842308
$714$	15.5672	+	11.4737i	0.582589	+	0.429392i
$715$	−8.85299			−0.331083
$716$			8.65753i			0.323547i
$717$	7.52474	−	7.52474i	0.281017	−	0.281017i
$718$	−38.2041			−1.42576
$719$	19.6058	−	19.6058i	0.731172	−	0.731172i	−0.239680	−	0.970852i	$-0.577043\pi$
$719$	19.6058	−	19.6058i	0.731172	−	0.731172i	0.970852	+	0.239680i	$0.0770425\pi$
$720$	7.68911	+	7.68911i	0.286556	+	0.286556i
$721$	0.514251	+	0.514251i	0.0191517	+	0.0191517i
$722$		−	5.80898i		−	0.216188i
$723$		−	36.0994i		−	1.34255i
$724$	0.584930	+	0.584930i	0.0217387	+	0.0217387i
$725$	20.3573	+	20.3573i	0.756052	+	0.756052i
$726$	−64.3599	+	64.3599i	−2.38862	+	2.38862i
$727$	13.7943			0.511602			0.255801	−	0.966730i	$-0.417661\pi$
$727$	13.7943			0.511602			0.255801	+	0.966730i	$0.417661\pi$
$728$	3.87611	−	3.87611i	0.143658	−	0.143658i
$729$		−	37.3113i		−	1.38190i
$730$	−21.6281			−0.800491
$731$	−3.31902	−	2.44625i	−0.122758	−	0.0904778i
$732$	−6.02298			−0.222616
$733$			30.3622i			1.12145i	0.828001	+	0.560726i	$0.189478\pi$
$733$			30.3622i			1.12145i	−0.828001	+	0.560726i	$0.810522\pi$
$734$	20.7649	−	20.7649i	0.766445	−	0.766445i
$735$	14.3363			0.528801
$736$	−5.94380	+	5.94380i	−0.219091	+	0.219091i
$737$	−17.6553	−	17.6553i	−0.650341	−	0.650341i
$738$	19.1658	+	19.1658i	0.705504	+	0.705504i
$739$		−	33.0383i		−	1.21533i	−0.794192	−	0.607667i	$-0.792106\pi$
$739$		−	33.0383i		−	1.21533i	0.794192	−	0.607667i	$-0.207894\pi$
$740$		−	0.208351i		−	0.00765913i
$741$	−8.01290	−	8.01290i	−0.294361	−	0.294361i
$742$	7.62299	+	7.62299i	0.279849	+	0.279849i
$743$	7.96776	−	7.96776i	0.292309	−	0.292309i	−0.545683	−	0.837992i	$-0.683730\pi$
$743$	7.96776	−	7.96776i	0.292309	−	0.292309i	0.837992	+	0.545683i	$0.183730\pi$
$744$	67.4282			2.47204
$745$	−7.01603	+	7.01603i	−0.257047	+	0.257047i
$746$		−	33.7165i		−	1.23445i
$747$	13.6265			0.498568
$748$	−15.1200	+	2.28892i	−0.552844	+	0.0836913i
$749$	6.09705			0.222781
$750$			31.3791i			1.14580i
$751$	−11.2439	+	11.2439i	−0.410294	+	0.410294i	−0.881841	−	0.471547i	$-0.843696\pi$
$751$	−11.2439	+	11.2439i	−0.410294	+	0.410294i	0.471547	+	0.881841i	$0.343696\pi$
$752$	−7.22580			−0.263498
$753$	−47.8007	+	47.8007i	−1.74195	+	1.74195i
$754$	−7.89745	−	7.89745i	−0.287608	−	0.287608i
$755$	3.98523	+	3.98523i	0.145037	+	0.145037i
$756$			1.51755i			0.0551928i
$757$			31.0798i			1.12961i	0.825223	+	0.564807i	$0.191049\pi$
$757$			31.0798i			1.12961i	−0.825223	+	0.564807i	$0.808951\pi$
$758$	27.0828	+	27.0828i	0.983691	+	0.983691i
$759$	−30.7888	−	30.7888i	−1.11756	−	1.11756i
$760$	9.71455	−	9.71455i	0.352384	−	0.352384i
$761$	7.90165			0.286434			0.143217	−	0.989691i	$-0.454255\pi$
$761$	7.90165			0.286434			0.143217	+	0.989691i	$0.454255\pi$
$762$	−13.2018	+	13.2018i	−0.478251	+	0.478251i
$763$		−	7.19077i		−	0.260323i
$764$	−6.66959			−0.241297
$765$	−17.7510	+	2.68721i	−0.641788	+	0.0971561i
$766$	−17.9006			−0.646775
$767$			4.33448i			0.156509i
$768$	23.1245	−	23.1245i	0.834434	−	0.834434i
$769$	24.7856			0.893791			0.446896	−	0.894586i	$-0.352530\pi$
$769$	24.7856			0.893791			0.446896	+	0.894586i	$0.352530\pi$
$770$	−9.73683	+	9.73683i	−0.350891	+	0.350891i
$771$	6.78977	+	6.78977i	0.244528	+	0.244528i
$772$	2.44548	+	2.44548i	0.0880147	+	0.0880147i
$773$			19.6312i			0.706087i	0.935607	+	0.353043i	$0.114853\pi$
$773$			19.6312i			0.706087i	−0.935607	+	0.353043i	$0.885147\pi$
$774$			4.36074i			0.156743i
$775$	21.5457	+	21.5457i	0.773945	+	0.773945i
$776$	−21.3717	−	21.3717i	−0.767198	−	0.767198i
$777$	−0.838552	+	0.838552i	−0.0300829	+	0.0300829i
$778$	−31.6255			−1.13383
$779$	16.5163	−	16.5163i	0.591758	−	0.591758i
$780$			2.08676i			0.0747180i
$781$	25.2715			0.904285
$782$	1.94533	+	12.8504i	0.0695649	+	0.459528i
$783$	13.7175			0.490223
$784$			11.6656i			0.416629i
$785$	14.9954	−	14.9954i	0.535208	−	0.535208i
$786$	−51.2764			−1.82897
$787$	25.3511	−	25.3511i	0.903670	−	0.903670i	−0.0920819	−	0.995751i	$-0.529352\pi$
$787$	25.3511	−	25.3511i	0.903670	−	0.903670i	0.995751	+	0.0920819i	$0.0293522\pi$
$788$	−6.57332	−	6.57332i	−0.234165	−	0.234165i
$789$	−41.8956	−	41.8956i	−1.49152	−	1.49152i
$790$			19.9717i			0.710563i
$791$			17.1903i			0.611216i
$792$	50.7380	+	50.7380i	1.80290	+	1.80290i
$793$	3.31235	+	3.31235i	0.117625	+	0.117625i
$794$	−21.9383	+	21.9383i	−0.778560	+	0.778560i
$795$	−18.2071			−0.645741
$796$	7.81024	−	7.81024i	0.276827	−	0.276827i
$797$			26.3868i			0.934668i	0.884081	+	0.467334i	$0.154785\pi$
$797$			26.3868i			0.934668i	−0.884081	+	0.467334i	$0.845215\pi$
$798$	−17.6257			−0.623944
$799$	7.07805	−	9.60334i	0.250403	−	0.339742i
$800$	11.3878			0.402619
$801$			19.2531i			0.680275i
$802$	27.8446	−	27.8446i	0.983228	−	0.983228i
$803$	−97.3451			−3.43523
$804$	−4.16157	+	4.16157i	−0.146767	+	0.146767i
$805$	−3.39637	−	3.39637i	−0.119706	−	0.119706i
$806$	−8.35846	−	8.35846i	−0.294414	−	0.294414i
$807$		−	46.6311i		−	1.64149i
$808$		−	12.9519i		−	0.455647i
$809$	−9.81577	−	9.81577i	−0.345104	−	0.345104i	0.513178	−	0.858282i	$-0.328468\pi$
$809$	−9.81577	−	9.81577i	−0.345104	−	0.345104i	−0.858282	+	0.513178i	$0.828468\pi$
$810$	−6.58363	−	6.58363i	−0.231325	−	0.231325i
$811$	−12.7728	+	12.7728i	−0.448512	+	0.448512i	−0.894860	−	0.446347i	$-0.852725\pi$
$811$	−12.7728	+	12.7728i	−0.448512	+	0.448512i	0.446347	+	0.894860i	$0.352725\pi$
$812$	7.12983			0.250208
$813$	52.5126	−	52.5126i	1.84170	−	1.84170i
$814$			2.28485i			0.0800838i
$815$	10.6051			0.371480
$816$	−3.97794	−	26.2772i	−0.139256	−	0.919888i
$817$	3.75790			0.131472
$818$		−	41.2621i		−	1.44270i
$819$	4.61659	−	4.61659i	0.161317	−	0.161317i
$820$	−4.30126			−0.150207
$821$	10.5065	−	10.5065i	0.366680	−	0.366680i	−0.499585	−	0.866265i	$-0.666514\pi$
$821$	10.5065	−	10.5065i	0.366680	−	0.366680i	0.866265	+	0.499585i	$0.166514\pi$
$822$	−6.71035	−	6.71035i	−0.234050	−	0.234050i
$823$	−27.7079	−	27.7079i	−0.965836	−	0.965836i	0.0335990	−	0.999435i	$-0.489303\pi$
$823$	−27.7079	−	27.7079i	−0.965836	−	0.965836i	−0.999435	+	0.0335990i	$0.989303\pi$
$824$		−	1.46529i		−	0.0510459i
$825$			58.9886i			2.05372i
$826$	4.76722	+	4.76722i	0.165873	+	0.165873i
$827$	−15.9040	−	15.9040i	−0.553037	−	0.553037i	0.374279	−	0.927316i	$-0.377890\pi$
$827$	−15.9040	−	15.9040i	−0.553037	−	0.553037i	−0.927316	+	0.374279i	$0.877890\pi$
$828$	−3.98924	+	3.98924i	−0.138636	+	0.138636i
$829$	−7.96433			−0.276613			−0.138306	−	0.990389i	$-0.544166\pi$
$829$	−7.96433			−0.276613			−0.138306	+	0.990389i	$0.544166\pi$
$830$	3.72553	−	3.72553i	0.129315	−	0.129315i
$831$			42.1204i			1.46114i
$832$	−10.2530			−0.355460
$833$	−15.5040	−	11.4271i	−0.537182	−	0.395925i
$834$	−68.6735			−2.37797
$835$			1.12950i			0.0390879i
$836$	9.85550	−	9.85550i	0.340860	−	0.340860i
$837$	14.5182			0.501824
$838$	−3.68010	+	3.68010i	−0.127127	+	0.127127i
$839$	−4.30403	−	4.30403i	−0.148592	−	0.148592i	0.628897	−	0.777489i	$-0.283507\pi$
$839$	−4.30403	−	4.30403i	−0.148592	−	0.148592i	−0.777489	+	0.628897i	$0.783507\pi$
$840$	10.1822	+	10.1822i	0.351318	+	0.351318i
$841$		−	35.4481i		−	1.22235i
$842$			22.3459i			0.770090i
$843$	−39.0317	−	39.0317i	−1.34432	−	1.34432i
$844$	7.33194	+	7.33194i	0.252376	+	0.252376i
$845$	−9.78255	+	9.78255i	−0.336530	+	0.336530i
$846$	−12.6175			−0.433798
$847$	−31.9545	+	31.9545i	−1.09797	+	1.09797i
$848$		−	14.8154i		−	0.508763i
$849$	−0.694622			−0.0238394
$850$	10.4465	−	14.1736i	0.358313	−	0.486150i
$851$	−0.796991			−0.0273205
$852$		−	5.95681i		−	0.204077i
$853$	−23.5985	+	23.5985i	−0.807998	+	0.807998i	−0.984331	−	0.176332i	$-0.943577\pi$
$853$	−23.5985	+	23.5985i	−0.807998	+	0.807998i	0.176332	+	0.984331i	$0.443577\pi$
$854$	7.28608			0.249325
$855$	11.5704	−	11.5704i	0.395699	−	0.395699i
$856$	−8.68639	−	8.68639i	−0.296895	−	0.296895i
$857$	−30.6026	−	30.6026i	−1.04536	−	1.04536i	−0.998921	−	0.0464429i	$-0.985211\pi$
$857$	−30.6026	−	30.6026i	−1.04536	−	1.04536i	−0.0464429	−	0.998921i	$-0.514789\pi$
$858$		−	22.8841i		−	0.781250i
$859$			20.3558i			0.694531i	0.937767	+	0.347266i	$0.112890\pi$
$859$			20.3558i			0.694531i	−0.937767	+	0.347266i	$0.887110\pi$
$860$	−0.489326	−	0.489326i	−0.0166859	−	0.0166859i
$861$	17.3113	+	17.3113i	0.589969	+	0.589969i
$862$	34.4717	−	34.4717i	1.17411	−	1.17411i
$863$	4.47117			0.152201			0.0761003	−	0.997100i	$-0.475753\pi$
$863$	4.47117			0.152201			0.0761003	+	0.997100i	$0.475753\pi$
$864$	3.83674	−	3.83674i	0.130529	−	0.130529i
$865$			19.5264i			0.663918i
$866$	41.8482			1.42206
$867$	38.8200	+	20.4531i	1.31840	+	0.694625i
$868$	7.54604			0.256129
$869$			89.8901i			3.04931i
$870$	20.7458	−	20.7458i	0.703350	−	0.703350i
$871$	4.57733			0.155097
$872$	−10.2446	+	10.2446i	−0.346926	+	0.346926i
$873$	−25.4545	−	25.4545i	−0.861504	−	0.861504i
$874$	−8.37608	−	8.37608i	−0.283325	−	0.283325i
$875$			15.5797i			0.526688i
$876$			22.9455i			0.775255i
$877$	−32.4241	−	32.4241i	−1.09488	−	1.09488i	−0.994999	−	0.0998860i	$-0.968152\pi$
$877$	−32.4241	−	32.4241i	−1.09488	−	1.09488i	−0.0998860	−	0.994999i	$-0.531848\pi$
$878$	10.8910	+	10.8910i	0.367553	+	0.367553i
$879$	15.4557	−	15.4557i	0.521307	−	0.521307i
$880$	18.9237			0.637917
$881$	7.14860	−	7.14860i	0.240842	−	0.240842i	−0.576356	−	0.817199i	$-0.695526\pi$
$881$	7.14860	−	7.14860i	0.240842	−	0.240842i	0.817199	+	0.576356i	$0.195526\pi$
$882$			20.3702i			0.685899i
$883$	−0.0806660			−0.00271463			−0.00135731	−	0.999999i	$-0.500432\pi$
$883$	−0.0806660			−0.00271463			−0.00135731	+	0.999999i	$0.500432\pi$
$884$	1.66331	−	2.25673i	0.0559430	−	0.0759022i
$885$	−11.3863			−0.382746
$886$		−	44.9800i		−	1.51113i
$887$	−29.8295	+	29.8295i	−1.00158	+	1.00158i	−0.00157776	+	0.999999i	$0.500502\pi$
$887$	−29.8295	+	29.8295i	−1.00158	+	1.00158i	−0.999999	+	0.00157776i	$0.999498\pi$
$888$	2.38935			0.0801813
$889$	−6.55466	+	6.55466i	−0.219836	+	0.219836i
$890$	5.26386	+	5.26386i	0.176445	+	0.176445i
$891$	−29.6320	−	29.6320i	−0.992710	−	0.992710i
$892$		−	16.4830i		−	0.551890i
$893$			10.8732i			0.363858i
$894$	−18.1357	−	18.1357i	−0.606550	−	0.606550i
$895$	12.5073	+	12.5073i	0.418072	+	0.418072i
$896$	−4.42363	+	4.42363i	−0.147783	+	0.147783i
$897$	7.98235			0.266523
$898$	−13.9100	+	13.9100i	−0.464181	+	0.464181i
$899$		−	68.2103i		−	2.27494i
$900$	7.64302			0.254767
$901$	19.6902	+	14.5125i	0.655975	+	0.483481i
$902$	47.1691			1.57056
$903$			3.93879i			0.131075i
$904$	24.4907	−	24.4907i	0.814550	−	0.814550i
$905$	1.69006			0.0561796
$906$	−10.3014	+	10.3014i	−0.342242	+	0.342242i
$907$	1.47989	+	1.47989i	0.0491390	+	0.0491390i	0.731249	−	0.682110i	$-0.238938\pi$
$907$	1.47989	+	1.47989i	0.0491390	+	0.0491390i	−0.682110	+	0.731249i	$0.738938\pi$
$908$	−2.19522	−	2.19522i	−0.0728511	−	0.0728511i
$909$		−	15.4262i		−	0.511655i
$910$		−	2.52438i		−	0.0836824i
$911$	−8.54172	−	8.54172i	−0.283000	−	0.283000i	0.551304	−	0.834304i	$-0.314130\pi$
$911$	−8.54172	−	8.54172i	−0.283000	−	0.283000i	−0.834304	+	0.551304i	$0.814130\pi$
$912$	17.1280	+	17.1280i	0.567163	+	0.567163i
$913$	16.7681	−	16.7681i	0.554944	−	0.554944i
$914$	0.609826			0.0201713
$915$	−8.70123	+	8.70123i	−0.287654	+	0.287654i
$916$			4.91293i			0.162328i
$917$	−25.4586			−0.840718
$918$	−1.25572	−	8.29494i	−0.0414448	−	0.273774i
$919$	47.5044			1.56703			0.783513	−	0.621375i	$-0.213426\pi$
$919$	47.5044			1.56703			0.783513	+	0.621375i	$0.213426\pi$
$920$			9.67751i			0.319058i
$921$	22.2254	−	22.2254i	0.732351	−	0.732351i
$922$	−2.36631			−0.0779303
$923$	−3.27596	+	3.27596i	−0.107829	+	0.107829i
$924$	10.3299	+	10.3299i	0.339829	+	0.339829i
$925$	0.763481	+	0.763481i	0.0251031	+	0.0251031i
$926$		−	42.3766i		−	1.39258i
$927$		−	1.74522i		−	0.0573205i
$928$	−18.0260	−	18.0260i	−0.591731	−	0.591731i
$929$	31.7928	+	31.7928i	1.04309	+	1.04309i	0.999029	+	0.0440603i	$0.0140294\pi$
$929$	31.7928	+	31.7928i	1.04309	+	1.04309i	0.0440603	+	0.999029i	$0.485971\pi$
$930$	21.9569	−	21.9569i	0.719995	−	0.719995i
$931$	17.5541			0.575314
$932$	2.30758	−	2.30758i	0.0755873	−	0.0755873i
$933$			58.5334i			1.91630i
$934$	−32.8288			−1.07419
$935$	−18.5368	+	25.1502i	−0.606217	+	0.822501i
$936$	−13.1544			−0.429965
$937$			31.4220i			1.02651i	0.858235	+	0.513256i	$0.171561\pi$
$937$			31.4220i			1.02651i	−0.858235	+	0.513256i	$0.828439\pi$
$938$	5.03431	−	5.03431i	0.164376	−	0.164376i
$939$	39.5962			1.29217
$940$	1.41583	−	1.41583i	0.0461793	−	0.0461793i
$941$	16.3841	+	16.3841i	0.534108	+	0.534108i	0.921792	−	0.387684i	$-0.126725\pi$
$941$	16.3841	+	16.3841i	0.534108	+	0.534108i	−0.387684	+	0.921792i	$0.626725\pi$
$942$	38.7616	+	38.7616i	1.26292	+	1.26292i
$943$			16.4533i			0.535795i
$944$		−	9.26517i		−	0.301556i
$945$	2.19236	+	2.19236i	0.0713176	+	0.0713176i
$946$	5.36611	+	5.36611i	0.174467	+	0.174467i
$947$	−32.3078	+	32.3078i	−1.04986	+	1.04986i	−0.0511739	+	0.998690i	$0.516296\pi$
$947$	−32.3078	+	32.3078i	−1.04986	+	1.04986i	−0.998690	+	0.0511739i	$0.983704\pi$
$948$	21.1882			0.688162
$949$	12.6189	−	12.6189i	0.409627	−	0.409627i
$950$			16.0478i			0.520660i
$951$	−17.8457			−0.578686
$952$	−2.89559	−	19.1275i	−0.0938465	−	0.619926i
$953$	4.14928			0.134408			0.0672042	−	0.997739i	$-0.478592\pi$
$953$	4.14928			0.134408			0.0672042	+	0.997739i	$0.478592\pi$
$954$		−	25.8702i		−	0.837580i
$955$	−9.63537	+	9.63537i	−0.311793	+	0.311793i
$956$	−2.39949			−0.0776049
$957$	93.3742	−	93.3742i	3.01836	−	3.01836i
$958$	3.96731	+	3.96731i	0.128178	+	0.128178i
$959$	−3.33167	−	3.33167i	−0.107585	−	0.107585i
$960$		−	26.9338i		−	0.869284i
$961$		−	41.1921i		−	1.32878i
$962$	−0.296186	−	0.296186i	−0.00954941	−	0.00954941i
$963$	−10.3458	−	10.3458i	−0.333389	−	0.333389i
$964$	−5.75567	+	5.75567i	−0.185378	+	0.185378i
$965$	7.06583			0.227457
$966$	8.77927	−	8.77927i	0.282469	−	0.282469i
$967$		−	48.2217i		−	1.55070i	−0.631529	−	0.775352i	$-0.717573\pi$
$967$		−	48.2217i		−	1.55070i	0.631529	−	0.775352i	$-0.282427\pi$
$968$	91.0504			2.92647
$969$	−39.5414	+	5.98591i	−1.27025	+	0.192295i
$970$	−13.9187			−0.446902
$971$		−	30.0452i		−	0.964196i	−0.876117	−	0.482098i	$-0.839875\pi$
$971$		−	30.0452i		−	0.964196i	0.876117	−	0.482098i	$-0.160125\pi$
$972$	−9.09419	+	9.09419i	−0.291696	+	0.291696i
$973$	−34.0962			−1.09307
$974$	34.5088	−	34.5088i	1.10573	−	1.10573i
$975$	−7.64673	−	7.64673i	−0.244891	−	0.244891i
$976$	−7.08031	−	7.08031i	−0.226635	−	0.226635i
$977$			41.2539i			1.31983i	0.751341	+	0.659914i	$0.229407\pi$
$977$			41.2539i			1.31983i	−0.751341	+	0.659914i	$0.770593\pi$
$978$			27.4131i			0.876575i
$979$	23.6919	+	23.6919i	0.757197	+	0.757197i
$980$	−2.28577	−	2.28577i	−0.0730163	−	0.0730163i
$981$	−12.2017	+	12.2017i	−0.389570	+	0.389570i
$982$	−14.1239			−0.450713
$983$	23.7687	−	23.7687i	0.758104	−	0.758104i	−0.217873	−	0.975977i	$-0.569912\pi$
$983$	23.7687	−	23.7687i	0.758104	−	0.758104i	0.975977	+	0.217873i	$0.0699119\pi$
$984$		−	49.3265i		−	1.57247i
$985$	−18.9926			−0.605154
$986$	−38.9717	+	5.89966i	−1.24111	+	0.187884i
$987$	−11.3966			−0.362758
$988$			2.55515i			0.0812901i
$989$	−1.87179	+	1.87179i	−0.0595193	+	0.0595193i
$990$	33.0440			1.05021
$991$	18.1061	−	18.1061i	0.575160	−	0.575160i	−0.358406	−	0.933566i	$-0.616680\pi$
$991$	18.1061	−	18.1061i	0.575160	−	0.575160i	0.933566	+	0.358406i	$0.116680\pi$
$992$	−19.0782	−	19.0782i	−0.605734	−	0.605734i
$993$	8.02714	+	8.02714i	0.254733	+	0.254733i
$994$			7.20603i			0.228561i
$995$		−	22.5665i		−	0.715405i
$996$	−3.95246	−	3.95246i	−0.125238	−	0.125238i
$997$	36.0475	+	36.0475i	1.14164	+	1.14164i	0.988151	+	0.153484i	$0.0490495\pi$
$997$	36.0475	+	36.0475i	1.14164	+	1.14164i	0.153484	+	0.988151i	$0.450951\pi$
$998$	−1.51997	+	1.51997i	−0.0481137	+	0.0481137i
$999$	0.514460			0.0162768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.10	✓	68
17.13	even	4	inner	731.2.f.d.302.25	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.10	✓	68	1.1	even	1	trivial
731.2.f.d.302.25	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.19080i q^{2} +(-1.82510 + 1.82510i) q^{3} +0.581989 q^{4} +(0.840782 - 0.840782i) q^{5} +(2.17334 + 2.17334i) q^{6} +(1.07906 + 1.07906i) q^{7} -3.07464i q^{8} -3.66201i q^{9} +O(q^{10})\)	\(q-1.19080i q^{2} +(-1.82510 + 1.82510i) q^{3} +0.581989 q^{4} +(0.840782 - 0.840782i) q^{5} +(2.17334 + 2.17334i) q^{6} +(1.07906 + 1.07906i) q^{7} -3.07464i q^{8} -3.66201i q^{9} +(-1.00121 - 1.00121i) q^{10} +(-4.50629 - 4.50629i) q^{11} +(-1.06219 + 1.06219i) q^{12} +1.16831 q^{13} +(1.28495 - 1.28495i) q^{14} +3.06903i q^{15} -2.49731 q^{16} +(2.44625 - 3.31902i) q^{17} -4.36074 q^{18} +3.75790i q^{19} +(0.489326 - 0.489326i) q^{20} -3.93879 q^{21} +(-5.36611 + 5.36611i) q^{22} +(-1.87179 - 1.87179i) q^{23} +(5.61154 + 5.61154i) q^{24} +3.58617i q^{25} -1.39122i q^{26} +(1.20824 + 1.20824i) q^{27} +(0.627999 + 0.627999i) q^{28} +(5.67662 - 5.67662i) q^{29} +3.65461 q^{30} +(6.00800 - 6.00800i) q^{31} -3.17547i q^{32} +16.4489 q^{33} +(-3.95229 - 2.91300i) q^{34} +1.81451 q^{35} -2.13125i q^{36} +(0.212896 - 0.212896i) q^{37} +4.47492 q^{38} +(-2.13228 + 2.13228i) q^{39} +(-2.58510 - 2.58510i) q^{40} +(-4.39509 - 4.39509i) q^{41} +4.69032i q^{42} -1.00000i q^{43} +(-2.62261 - 2.62261i) q^{44} +(-3.07896 - 3.07896i) q^{45} +(-2.22893 + 2.22893i) q^{46} +2.89343 q^{47} +(4.55786 - 4.55786i) q^{48} -4.67127i q^{49} +4.27042 q^{50} +(1.59289 + 10.5222i) q^{51} +0.679941 q^{52} +5.93254i q^{53} +(1.43878 - 1.43878i) q^{54} -7.57762 q^{55} +(3.31771 - 3.31771i) q^{56} +(-6.85856 - 6.85856i) q^{57} +(-6.75974 - 6.75974i) q^{58} +3.71006i q^{59} +1.78614i q^{60} +(2.83517 + 2.83517i) q^{61} +(-7.15434 - 7.15434i) q^{62} +(3.95153 - 3.95153i) q^{63} -8.77599 q^{64} +(0.982291 - 0.982291i) q^{65} -19.5874i q^{66} +3.91792 q^{67} +(1.42369 - 1.93163i) q^{68} +6.83241 q^{69} -2.16072i q^{70} +(-2.80402 + 2.80402i) q^{71} -11.2594 q^{72} +(10.8010 - 10.8010i) q^{73} +(-0.253517 - 0.253517i) q^{74} +(-6.54514 - 6.54514i) q^{75} +2.18705i q^{76} -9.72510i q^{77} +(2.53913 + 2.53913i) q^{78} +(-9.97384 - 9.97384i) q^{79} +(-2.09970 + 2.09970i) q^{80} +6.57570 q^{81} +(-5.23369 + 5.23369i) q^{82} +3.72105i q^{83} -2.29233 q^{84} +(-0.733806 - 4.84733i) q^{85} -1.19080 q^{86} +20.7209i q^{87} +(-13.8552 + 13.8552i) q^{88} -5.25752 q^{89} +(-3.66643 + 3.66643i) q^{90} +(1.26067 + 1.26067i) q^{91} +(-1.08936 - 1.08936i) q^{92} +21.9304i q^{93} -3.44550i q^{94} +(3.15957 + 3.15957i) q^{95} +(5.79557 + 5.79557i) q^{96} +(6.95095 - 6.95095i) q^{97} -5.56256 q^{98} +(-16.5021 + 16.5021i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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