LMFDB - Embedded newform 315.2.k.b.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	315.16
Dual form			315.2.k.b.256.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.517769 + 0.896802i) q^{2} +(-1.26722 - 1.18074i) q^{3} +(0.463831 - 0.803378i) q^{4} -1.00000 q^{5} +(0.402766 - 1.74780i) q^{6} +(-1.07729 - 2.41649i) q^{7} +3.03170 q^{8} +(0.211690 + 2.99252i) q^{9} +O(q^{10})$	\(q+(0.517769 + 0.896802i) q^{2} +(-1.26722 - 1.18074i) q^{3} +(0.463831 - 0.803378i) q^{4} -1.00000 q^{5} +(0.402766 - 1.74780i) q^{6} +(-1.07729 - 2.41649i) q^{7} +3.03170 q^{8} +(0.211690 + 2.99252i) q^{9} +(-0.517769 - 0.896802i) q^{10} -5.83753 q^{11} +(-1.53636 + 0.470391i) q^{12} +(-1.79251 - 3.10472i) q^{13} +(1.60933 - 2.21730i) q^{14} +(1.26722 + 1.18074i) q^{15} +(0.642061 + 1.11208i) q^{16} +(-1.70903 - 2.96012i) q^{17} +(-2.57409 + 1.73928i) q^{18} +(2.47463 - 4.28619i) q^{19} +(-0.463831 + 0.803378i) q^{20} +(-1.48809 + 4.33423i) q^{21} +(-3.02249 - 5.23511i) q^{22} +6.56558 q^{23} +(-3.84183 - 3.57967i) q^{24} +1.00000 q^{25} +(1.85622 - 3.21506i) q^{26} +(3.26514 - 4.04213i) q^{27} +(-2.44104 - 0.255371i) q^{28} +(-1.65608 + 2.86841i) q^{29} +(-0.402766 + 1.74780i) q^{30} +(-1.07598 + 1.86366i) q^{31} +(2.36683 - 4.09946i) q^{32} +(7.39743 + 6.89262i) q^{33} +(1.76976 - 3.06532i) q^{34} +(1.07729 + 2.41649i) q^{35} +(2.50231 + 1.21796i) q^{36} +(0.0816545 - 0.141430i) q^{37} +5.12516 q^{38} +(-1.39438 + 6.05087i) q^{39} -3.03170 q^{40} +(4.52266 + 7.83348i) q^{41} +(-4.65744 + 0.909606i) q^{42} +(0.873314 - 1.51262i) q^{43} +(-2.70762 + 4.68974i) q^{44} +(-0.211690 - 2.99252i) q^{45} +(3.39945 + 5.88803i) q^{46} +(-3.56373 - 6.17256i) q^{47} +(0.499452 - 2.16736i) q^{48} +(-4.67888 + 5.20654i) q^{49} +(0.517769 + 0.896802i) q^{50} +(-1.32943 + 5.76905i) q^{51} -3.32569 q^{52} +(3.06590 + 5.31029i) q^{53} +(5.31558 + 0.835297i) q^{54} +5.83753 q^{55} +(-3.26603 - 7.32609i) q^{56} +(-8.19680 + 2.50964i) q^{57} -3.42986 q^{58} +(1.59717 - 2.76639i) q^{59} +(1.53636 - 0.470391i) q^{60} +(-2.41883 - 4.18953i) q^{61} -2.22844 q^{62} +(7.00336 - 3.73537i) q^{63} +7.47012 q^{64} +(1.79251 + 3.10472i) q^{65} +(-2.35116 + 10.2028i) q^{66} +(8.13210 - 14.0852i) q^{67} -3.17080 q^{68} +(-8.32003 - 7.75227i) q^{69} +(-1.60933 + 2.21730i) q^{70} +5.78505 q^{71} +(0.641780 + 9.07244i) q^{72} +(5.42624 + 9.39852i) q^{73} +0.169113 q^{74} +(-1.26722 - 1.18074i) q^{75} +(-2.29562 - 3.97613i) q^{76} +(6.28872 + 14.1063i) q^{77} +(-6.14839 + 1.88247i) q^{78} +(3.53361 + 6.12039i) q^{79} +(-0.642061 - 1.11208i) q^{80} +(-8.91038 + 1.26697i) q^{81} +(-4.68339 + 8.11187i) q^{82} +(0.158379 - 0.274321i) q^{83} +(2.79181 + 3.20585i) q^{84} +(1.70903 + 2.96012i) q^{85} +1.80870 q^{86} +(5.48547 - 1.67950i) q^{87} -17.6977 q^{88} +(1.01109 - 1.75127i) q^{89} +(2.57409 - 1.73928i) q^{90} +(-5.57149 + 7.67629i) q^{91} +(3.04532 - 5.27464i) q^{92} +(3.56401 - 1.09120i) q^{93} +(3.69037 - 6.39191i) q^{94} +(-2.47463 + 4.28619i) q^{95} +(-7.83970 + 2.40030i) q^{96} +(-0.865269 + 1.49869i) q^{97} +(-7.09182 - 1.50025i) q^{98} +(-1.23574 - 17.4689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.517769	+	0.896802i	0.366118	+	0.634135i	0.988955	−	0.148217i	$-0.0473533\pi$
$2$	0.517769	+	0.896802i	0.366118	+	0.634135i	−0.622837	+	0.782352i	$0.714020\pi$
$3$	−1.26722	−	1.18074i	−0.731629	−	0.681703i
$3$	−1.26722	−	1.18074i	−0.731629	−	0.681703i
$4$	0.463831	−	0.803378i	0.231915	−	0.401689i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.402766	−	1.74780i	0.164429	−	0.713535i
$7$	−1.07729	−	2.41649i	−0.407178	−	0.913349i
$7$	−1.07729	−	2.41649i	−0.407178	−	0.913349i
$8$	3.03170			1.07187
$9$	0.211690	+	2.99252i	0.0705632	+	0.997507i
$10$	−0.517769	−	0.896802i	−0.163733	−	0.283594i
$11$	−5.83753			−1.76008			−0.880040	−	0.474899i	$-0.842485\pi$
$11$	−5.83753			−1.76008			−0.880040	+	0.474899i	$0.842485\pi$
$12$	−1.53636	+	0.470391i	−0.443509	+	0.135790i
$13$	−1.79251	−	3.10472i	−0.497154	−	0.861096i	0.502841	−	0.864379i	$-0.332288\pi$
$13$	−1.79251	−	3.10472i	−0.497154	−	0.861096i	−0.999995	+	0.00328344i	$0.998955\pi$
$14$	1.60933	−	2.21730i	0.430111	−	0.592599i
$15$	1.26722	+	1.18074i	0.327195	+	0.304867i
$16$	0.642061	+	1.11208i	0.160515	+	0.278021i
$17$	−1.70903	−	2.96012i	−0.414500	−	0.717936i	0.580876	−	0.813992i	$-0.302710\pi$
$17$	−1.70903	−	2.96012i	−0.414500	−	0.717936i	−0.995376	+	0.0960568i	$0.969377\pi$
$18$	−2.57409	+	1.73928i	−0.606720	+	0.409952i
$19$	2.47463	−	4.28619i	0.567720	−	0.983320i	−0.429071	−	0.903271i	$-0.641159\pi$
$19$	2.47463	−	4.28619i	0.567720	−	0.983320i	0.996791	−	0.0800491i	$-0.0255077\pi$
$20$	−0.463831	+	0.803378i	−0.103716	+	0.179641i
$21$	−1.48809	+	4.33423i	−0.324729	+	0.945807i
$22$	−3.02249	−	5.23511i	−0.644397	−	1.11613i
$23$	6.56558			1.36902			0.684509	−	0.729004i	$-0.260017\pi$
$23$	6.56558			1.36902			0.684509	+	0.729004i	$0.260017\pi$
$24$	−3.84183	−	3.57967i	−0.784211	−	0.730696i
$25$	1.00000			0.200000
$26$	1.85622	−	3.21506i	0.364034	−	0.630525i
$27$	3.26514	−	4.04213i	0.628377	−	0.777909i
$28$	−2.44104	−	0.255371i	−0.461313	−	0.0482605i
$29$	−1.65608	+	2.86841i	−0.307526	+	0.532650i	−0.977820	−	0.209445i	$-0.932834\pi$
$29$	−1.65608	+	2.86841i	−0.307526	+	0.532650i	0.670295	+	0.742095i	$0.266168\pi$
$30$	−0.402766	+	1.74780i	−0.0735348	+	0.319103i
$31$	−1.07598	+	1.86366i	−0.193252	+	0.334723i	−0.946326	−	0.323213i	$-0.895237\pi$
$31$	−1.07598	+	1.86366i	−0.193252	+	0.334723i	0.753074	+	0.657936i	$0.228570\pi$
$32$	2.36683	−	4.09946i	0.418400	−	0.724689i
$33$	7.39743	+	6.89262i	1.28773	+	1.19985i
$34$	1.76976	−	3.06532i	0.303512	−	0.525698i
$35$	1.07729	+	2.41649i	0.182096	+	0.408462i
$36$	2.50231	+	1.21796i	0.417052	+	0.202993i
$37$	0.0816545	−	0.141430i	0.0134239	−	0.0232509i	−0.859235	−	0.511580i	$-0.829060\pi$
$37$	0.0816545	−	0.141430i	0.0134239	−	0.0232509i	0.872659	+	0.488329i	$0.162394\pi$
$38$	5.12516			0.831410
$39$	−1.39438	+	6.05087i	−0.223279	+	0.968914i
$40$	−3.03170			−0.479355
$41$	4.52266	+	7.83348i	0.706321	+	1.22338i	0.966213	+	0.257746i	$0.0829799\pi$
$41$	4.52266	+	7.83348i	0.706321	+	1.22338i	−0.259891	+	0.965638i	$0.583687\pi$
$42$	−4.65744	+	0.909606i	−0.718658	+	0.140355i
$43$	0.873314	−	1.51262i	0.133179	−	0.230673i	−0.791721	−	0.610883i	$-0.790815\pi$
$43$	0.873314	−	1.51262i	0.133179	−	0.230673i	0.924900	+	0.380209i	$0.124148\pi$
$44$	−2.70762	+	4.68974i	−0.408190	+	0.707005i
$45$	−0.211690	−	2.99252i	−0.0315568	−	0.446099i
$46$	3.39945	+	5.88803i	0.501222	+	0.868142i
$47$	−3.56373	−	6.17256i	−0.519823	−	0.900360i	−0.999734	−	0.0230428i	$-0.992665\pi$
$47$	−3.56373	−	6.17256i	−0.519823	−	0.900360i	0.479912	−	0.877317i	$-0.340669\pi$
$48$	0.499452	−	2.16736i	0.0720897	−	0.312832i
$49$	−4.67888	+	5.20654i	−0.668412	+	0.743791i
$50$	0.517769	+	0.896802i	0.0732236	+	0.126827i
$51$	−1.32943	+	5.76905i	−0.186158	+	0.807829i
$52$	−3.32569			−0.461190
$53$	3.06590	+	5.31029i	0.421133	+	0.729425i	0.996051	−	0.0887871i	$-0.0282991\pi$
$53$	3.06590	+	5.31029i	0.421133	+	0.729425i	−0.574917	+	0.818212i	$0.694966\pi$
$54$	5.31558	+	0.835297i	0.723359	+	0.113670i
$55$	5.83753			0.787132
$56$	−3.26603	−	7.32609i	−0.436442	−	0.978990i
$57$	−8.19680	+	2.50964i	−1.08569	+	0.332410i
$58$	−3.42986			−0.450363
$59$	1.59717	−	2.76639i	0.207934	−	0.360153i	−0.743129	−	0.669148i	$-0.766659\pi$
$59$	1.59717	−	2.76639i	0.207934	−	0.360153i	0.951064	+	0.308995i	$0.0999926\pi$
$60$	1.53636	−	0.470391i	0.198343	−	0.0607273i
$61$	−2.41883	−	4.18953i	−0.309699	−	0.536415i	0.668597	−	0.743625i	$-0.266895\pi$
$61$	−2.41883	−	4.18953i	−0.309699	−	0.536415i	−0.978297	+	0.207210i	$0.933562\pi$
$62$	−2.22844			−0.283013
$63$	7.00336	−	3.73537i	0.882340	−	0.470612i
$64$	7.47012			0.933765
$65$	1.79251	+	3.10472i	0.222334	+	0.385094i
$66$	−2.35116	+	10.2028i	−0.289408	+	1.25588i
$67$	8.13210	−	14.0852i	0.993495	−	1.72078i	0.398125	−	0.917331i	$-0.369661\pi$
$67$	8.13210	−	14.0852i	0.993495	−	1.72078i	0.595369	−	0.803452i	$-0.297006\pi$
$68$	−3.17080			−0.384516
$69$	−8.32003	−	7.75227i	−1.00161	−	0.933263i
$70$	−1.60933	+	2.21730i	−0.192352	+	0.265018i
$71$	5.78505			0.686559			0.343279	−	0.939233i	$-0.388462\pi$
$71$	5.78505			0.686559			0.343279	+	0.939233i	$0.388462\pi$
$72$	0.641780	+	9.07244i	0.0756345	+	1.06920i
$73$	5.42624	+	9.39852i	0.635093	+	1.10001i	0.986495	+	0.163789i	$0.0523716\pi$
$73$	5.42624	+	9.39852i	0.635093	+	1.10001i	−0.351402	+	0.936225i	$0.614295\pi$
$74$	0.169113			0.0196590
$75$	−1.26722	−	1.18074i	−0.146326	−	0.136341i
$76$	−2.29562	−	3.97613i	−0.263326	−	0.456094i
$77$	6.28872	+	14.1063i	0.716666	+	1.60757i
$78$	−6.14839	+	1.88247i	−0.696168	+	0.213148i
$79$	3.53361	+	6.12039i	0.397562	+	0.688598i	0.993425	−	0.114489i	$-0.0365229\pi$
$79$	3.53361	+	6.12039i	0.397562	+	0.688598i	−0.595862	+	0.803087i	$0.703190\pi$
$80$	−0.642061	−	1.11208i	−0.0717846	−	0.124335i
$81$	−8.91038	+	1.26697i	−0.990042	+	0.140775i
$82$	−4.68339	+	8.11187i	−0.517194	+	0.895806i
$83$	0.158379	−	0.274321i	0.0173844	−	0.0301106i	−0.857202	−	0.514980i	$-0.827799\pi$
$83$	0.158379	−	0.274321i	0.0173844	−	0.0301106i	0.874587	+	0.484869i	$0.161133\pi$
$84$	2.79181	+	3.20585i	0.304611	+	0.349787i
$85$	1.70903	+	2.96012i	0.185370	+	0.321071i
$86$	1.80870			0.195037
$87$	5.48547	−	1.67950i	0.588104	−	0.180061i
$88$	−17.6977			−1.88658
$89$	1.01109	−	1.75127i	0.107176	−	0.185634i	−0.807449	−	0.589937i	$-0.799153\pi$
$89$	1.01109	−	1.75127i	0.107176	−	0.185634i	0.914625	+	0.404303i	$0.132486\pi$
$90$	2.57409	−	1.73928i	0.271333	−	0.183336i
$91$	−5.57149	+	7.67629i	−0.584050	+	0.804694i
$92$	3.04532	−	5.27464i	0.317496	−	0.549920i
$93$	3.56401	−	1.09120i	0.369570	−	0.113152i
$94$	3.69037	−	6.39191i	0.380633	−	0.659276i
$95$	−2.47463	+	4.28619i	−0.253892	+	0.439754i
$96$	−7.83970	+	2.40030i	−0.800136	+	0.244980i
$97$	−0.865269	+	1.49869i	−0.0878547	+	0.152169i	−0.906604	−	0.421982i	$-0.861334\pi$
$97$	−0.865269	+	1.49869i	−0.0878547	+	0.152169i	0.818749	+	0.574151i	$0.194668\pi$
$98$	−7.09182	−	1.50025i	−0.716382	−	0.151548i
$99$	−1.23574	−	17.4689i	−0.124197	−	1.75569i
$100$	0.463831	−	0.803378i	0.0463831	−	0.0803378i
$101$	11.9826			1.19231			0.596155	−	0.802869i	$-0.296694\pi$
$101$	11.9826			1.19231			0.596155	+	0.802869i	$0.296694\pi$
$102$	−5.86204	+	1.79480i	−0.580428	+	0.177711i
$103$	−15.9659			−1.57317			−0.786583	−	0.617485i	$-0.788152\pi$
$103$	−15.9659			−1.57317			−0.786583	+	0.617485i	$0.788152\pi$
$104$	−5.43437	−	9.41261i	−0.532884	−	0.922982i
$105$	1.48809	−	4.33423i	0.145223	−	0.422978i
$106$	−3.17485	+	5.49901i	−0.308369	+	0.534111i
$107$	−3.16539	+	5.48261i	−0.306010	+	0.530024i	−0.977486	−	0.211002i	$-0.932327\pi$
$107$	−3.16539	+	5.48261i	−0.306010	+	0.530024i	0.671476	+	0.741026i	$0.265661\pi$
$108$	−1.73289	−	4.49801i	−0.166747	−	0.432821i
$109$	−6.50604	−	11.2688i	−0.623166	−	1.07935i	−0.988893	−	0.148632i	$-0.952513\pi$
$109$	−6.50604	−	11.2688i	−0.623166	−	1.07935i	0.365727	−	0.930722i	$-0.380820\pi$
$110$	3.02249	+	5.23511i	0.288183	+	0.499148i
$111$	−0.270466	+	0.0828095i	−0.0256715	+	0.00785993i
$112$	1.99565	−	2.74957i	0.188571	−	0.259810i
$113$	−3.99350	−	6.91695i	−0.375677	−	0.650692i	0.614751	−	0.788721i	$-0.289257\pi$
$113$	−3.99350	−	6.91695i	−0.375677	−	0.650692i	−0.990428	+	0.138029i	$0.955923\pi$
$114$	−6.49470	−	6.05149i	−0.608284	−	0.566774i
$115$	−6.56558			−0.612244
$116$	1.53628	+	2.66091i	0.142640	+	0.247059i
$117$	8.91150	−	6.02137i	0.823868	−	0.556676i
$118$	3.30787			0.304514
$119$	−5.31200	+	7.31878i	−0.486950	+	0.670911i
$120$	3.84183	+	3.57967i	0.350710	+	0.326777i
$121$	23.0767			2.09788
$122$	2.50479	−	4.33842i	0.226773	−	0.392782i
$123$	3.51813	−	15.2668i	0.317219	−	1.37656i
$124$	0.998148	+	1.72884i	0.0896363	+	0.155255i
$125$	−1.00000			−0.0894427
$126$	6.97601	+	4.34657i	0.621472	+	0.387223i
$127$	12.4831			1.10770			0.553850	−	0.832617i	$-0.313158\pi$
$127$	12.4831			1.10770			0.553850	+	0.832617i	$0.313158\pi$
$128$	−0.865855	−	1.49970i	−0.0765315	−	0.132556i
$129$	−2.89270	+	0.885667i	−0.254688	+	0.0779786i
$130$	−1.85622	+	3.21506i	−0.162801	+	0.281979i
$131$	−0.747915			−0.0653457			−0.0326728	−	0.999466i	$-0.510402\pi$
$131$	−0.747915			−0.0653457			−0.0326728	+	0.999466i	$0.510402\pi$
$132$	8.96853	−	2.74592i	0.780611	−	0.239002i
$133$	−13.0235	−	1.36246i	−1.12928	−	0.118140i
$134$	16.8422			1.45494
$135$	−3.26514	+	4.04213i	−0.281019	+	0.347891i
$136$	−5.18127	−	8.97422i	−0.444290	−	0.769533i
$137$	0.454324			0.0388155			0.0194078	−	0.999812i	$-0.493822\pi$
$137$	0.454324			0.0388155			0.0194078	+	0.999812i	$0.493822\pi$
$138$	2.64440	−	11.4753i	0.225106	−	0.976843i
$139$	3.73096	+	6.46221i	0.316456	+	0.548117i	0.979746	−	0.200245i	$-0.0641738\pi$
$139$	3.73096	+	6.46221i	0.316456	+	0.548117i	−0.663290	+	0.748362i	$0.730840\pi$
$140$	2.44104	+	0.255371i	0.206305	+	0.0215828i
$141$	−2.77218	+	12.0298i	−0.233460	+	1.01309i
$142$	2.99532	+	5.18804i	0.251361	+	0.435371i
$143$	10.4638	+	18.1239i	0.875031	+	1.51560i
$144$	−3.19201	+	2.15680i	−0.266001	+	0.179733i
$145$	1.65608	−	2.86841i	0.137530	−	0.238208i
$146$	−5.61908	+	9.73252i	−0.465038	+	0.805469i
$147$	12.0768	−	1.07327i	0.996074	−	0.0885216i
$148$	−0.0757477	−	0.131199i	−0.00622642	−	0.0107845i
$149$	−10.9673			−0.898474			−0.449237	−	0.893413i	$-0.648304\pi$
$149$	−10.9673			−0.898474			−0.449237	+	0.893413i	$0.648304\pi$
$150$	0.402766	−	1.74780i	0.0328857	−	0.142707i
$151$	7.66468			0.623743			0.311871	−	0.950124i	$-0.399044\pi$
$151$	7.66468			0.623743			0.311871	+	0.950124i	$0.399044\pi$
$152$	7.50236	−	12.9945i	0.608522	−	1.05399i
$153$	8.49645	−	5.74093i	0.686898	−	0.464127i
$154$	−9.39450	+	12.9436i	−0.757030	+	1.04302i
$155$	1.07598	−	1.86366i	0.0864251	−	0.149693i
$156$	4.21438	+	3.92679i	0.337420	+	0.314395i
$157$	−0.347523	+	0.601927i	−0.0277353	+	0.0480390i	−0.879560	−	0.475788i	$-0.842163\pi$
$157$	−0.347523	+	0.601927i	−0.0277353	+	0.0480390i	0.851825	+	0.523827i	$0.175496\pi$
$158$	−3.65919	+	6.33790i	−0.291109	+	0.504216i
$159$	2.38493	−	10.3493i	0.189137	−	0.820756i
$160$	−2.36683	+	4.09946i	−0.187114	+	0.324091i
$161$	−7.07305	−	15.8657i	−0.557434	−	1.25039i
$162$	−5.74974	−	7.33484i	−0.451742	−	0.576280i
$163$	6.74697	−	11.6861i	0.528464	−	0.915326i	−0.470985	−	0.882141i	$-0.656102\pi$
$163$	6.74697	−	11.6861i	0.528464	−	0.915326i	0.999449	−	0.0331851i	$-0.0105651\pi$
$164$	8.39100			0.655227
$165$	−7.39743	−	6.89262i	−0.575889	−	0.536590i
$166$	0.328015			0.0254589
$167$	−10.1631	−	17.6030i	−0.786446	−	1.36216i	−0.928132	−	0.372252i	$-0.878586\pi$
$167$	−10.1631	−	17.6030i	−0.786446	−	1.36216i	0.141686	−	0.989912i	$-0.454748\pi$
$168$	−4.51146	+	13.1401i	−0.348067	+	1.01378i
$169$	0.0737915	−	0.127811i	0.00567627	−	0.00983158i
$170$	−1.76976	+	3.06532i	−0.135735	+	0.235099i
$171$	13.3504	+	6.49805i	1.02093	+	0.496919i
$172$	−0.810140	−	1.40320i	−0.0617726	−	0.106993i
$173$	−2.40292	−	4.16198i	−0.182691	−	0.316430i	0.760105	−	0.649800i	$-0.225147\pi$
$173$	−2.40292	−	4.16198i	−0.182691	−	0.316430i	−0.942796	+	0.333370i	$0.891814\pi$
$174$	4.34638	+	4.04978i	0.329499	+	0.307013i
$175$	−1.07729	−	2.41649i	−0.0814356	−	0.182670i
$176$	−3.74805	−	6.49181i	−0.282520	−	0.489339i
$177$	−5.29036	+	1.61977i	−0.397648	+	0.121749i
$178$	2.09405			0.156956
$179$	−5.55776	−	9.62632i	−0.415406	−	0.719505i	0.580065	−	0.814570i	$-0.303027\pi$
$179$	−5.55776	−	9.62632i	−0.415406	−	0.719505i	−0.995471	+	0.0950657i	$0.969694\pi$
$180$	−2.50231	−	1.21796i	−0.186512	−	0.0907811i
$181$	13.1850			0.980032			0.490016	−	0.871713i	$-0.336991\pi$
$181$	13.1850			0.980032			0.490016	+	0.871713i	$0.336991\pi$
$182$	−9.76886	−	1.02197i	−0.724116	−	0.0757538i
$183$	−1.88158	+	8.16507i	−0.139090	+	0.603580i
$184$	19.9049			1.46741
$185$	−0.0816545	+	0.141430i	−0.00600336	+	0.0103981i
$186$	2.82393	+	2.63122i	0.207060	+	0.192930i
$187$	9.97650	+	17.2798i	0.729554	+	1.26362i
$188$	−6.61186			−0.482220
$189$	−13.2853	−	3.53564i	−0.966364	−	0.257180i
$190$	−5.12516			−0.371818
$191$	−11.5066	−	19.9300i	−0.832588	−	1.44209i	−0.895979	−	0.444096i	$-0.853525\pi$
$191$	−11.5066	−	19.9300i	−0.832588	−	1.44209i	0.0633907	−	0.997989i	$-0.479809\pi$
$192$	−9.46628	−	8.82030i	−0.683170	−	0.636550i
$193$	1.91993	−	3.32541i	0.138200	−	0.239369i	−0.788616	−	0.614887i	$-0.789202\pi$
$193$	1.91993	−	3.32541i	0.138200	−	0.239369i	0.926815	+	0.375518i	$0.122535\pi$
$194$	−1.79204			−0.128661
$195$	1.39438	−	6.05087i	0.0998533	−	0.433311i
$196$	2.01261	+	6.17386i	0.143758	+	0.440990i
$197$	−24.6818			−1.75851			−0.879254	−	0.476353i	$-0.841958\pi$
$197$	−24.6818			−1.75851			−0.879254	+	0.476353i	$0.841958\pi$
$198$	15.0263	−	10.1531i	1.06788	−	0.721548i
$199$	7.80224	+	13.5139i	0.553086	+	0.957973i	0.998050	+	0.0624244i	$0.0198832\pi$
$199$	7.80224	+	13.5139i	0.553086	+	0.957973i	−0.444964	+	0.895549i	$0.646783\pi$
$200$	3.03170			0.214374
$201$	−26.9362	+	8.24713i	−1.89993	+	0.581708i
$202$	6.20420	+	10.7460i	0.436526	+	0.756086i
$203$	8.71557	+	0.911784i	0.611713	+	0.0639947i
$204$	4.01810	+	3.74390i	0.281323	+	0.262125i
$205$	−4.52266	−	7.83348i	−0.315876	−	0.547114i
$206$	−8.26664	−	14.3182i	−0.575964	−	0.997599i
$207$	1.38987	+	19.6476i	0.0966023	+	1.36561i
$208$	2.30181	−	3.98685i	0.159602	−	0.276438i
$209$	−14.4457	+	25.0208i	−0.999233	+	1.73072i
$210$	4.65744	−	0.909606i	0.321394	−	0.0627688i
$211$	−3.84763	−	6.66429i	−0.264882	−	0.458788i	0.702651	−	0.711535i	$-0.252000\pi$
$211$	−3.84763	−	6.66429i	−0.264882	−	0.458788i	−0.967533	+	0.252746i	$0.918666\pi$
$212$	5.68823			0.390669
$213$	−7.33092	−	6.83065i	−0.502306	−	0.468029i
$214$	−6.55576			−0.448143
$215$	−0.873314	+	1.51262i	−0.0595595	+	0.103160i
$216$	9.89895	−	12.2546i	0.673538	−	0.833817i
$217$	5.66267	+	0.592403i	0.384407	+	0.0402149i
$218$	6.73725	−	11.6693i	0.456304	−	0.790342i
$219$	4.22101	−	18.3170i	0.285229	−	1.23775i
$220$	2.70762	−	4.68974i	0.182548	−	0.316182i
$221$	−6.12691	+	10.6121i	−0.412141	+	0.713849i
$222$	−0.214303	−	0.199679i	−0.0143831	−	0.0134016i
$223$	3.50344	−	6.06814i	0.234608	−	0.406353i	−0.724551	−	0.689221i	$-0.757953\pi$
$223$	3.50344	−	6.06814i	0.234608	−	0.406353i	0.959159	+	0.282869i	$0.0912861\pi$
$224$	−12.4561	−	1.30310i	−0.832257	−	0.0870670i
$225$	0.211690	+	2.99252i	0.0141126	+	0.199501i
$226$	4.13542	−	7.16277i	0.275084	−	0.476460i
$227$	−5.76648			−0.382735			−0.191367	−	0.981518i	$-0.561292\pi$
$227$	−5.76648			−0.382735			−0.191367	+	0.981518i	$0.561292\pi$
$228$	−1.78574	+	7.74917i	−0.118263	+	0.513202i
$229$	−5.90760			−0.390385			−0.195192	−	0.980765i	$-0.562533\pi$
$229$	−5.90760			−0.390385			−0.195192	+	0.980765i	$0.562533\pi$
$230$	−3.39945	−	5.88803i	−0.224153	−	0.388245i
$231$	8.68678	−	25.3012i	0.571548	−	1.66470i
$232$	−5.02073	+	8.69617i	−0.329627	+	0.570931i
$233$	−10.9322	+	18.9351i	−0.716191	+	1.24048i	0.246307	+	0.969192i	$0.420783\pi$
$233$	−10.9322	+	18.9351i	−0.716191	+	1.24048i	−0.962498	+	0.271287i	$0.912551\pi$
$234$	10.0141	+	4.87417i	0.654641	+	0.318635i
$235$	3.56373	+	6.17256i	0.232472	+	0.402653i
$236$	−1.48164	−	2.56627i	−0.0964463	−	0.167050i
$237$	2.74875	−	11.9282i	0.178551	−	0.774818i
$238$	−9.31388	−	0.974376i	−0.603729	−	0.0631594i
$239$	0.485841	+	0.841502i	0.0314265	+	0.0544322i	0.881311	−	0.472537i	$-0.156662\pi$
$239$	0.485841	+	0.841502i	0.0314265	+	0.0544322i	−0.849884	+	0.526969i	$0.823328\pi$
$240$	−0.499452	+	2.16736i	−0.0322395	+	0.139903i
$241$	29.2105			1.88162			0.940808	−	0.338939i	$-0.110068\pi$
$241$	29.2105			1.88162			0.940808	+	0.338939i	$0.110068\pi$
$242$	11.9484	+	20.6952i	0.768073	+	1.33034i
$243$	12.7874	+	8.91534i	0.820310	+	0.571919i
$244$	−4.48771			−0.287296
$245$	4.67888	−	5.20654i	0.298923	−	0.332634i
$246$	15.5129	−	4.74963i	0.989067	−	0.302826i
$247$	−17.7433			−1.12898
$248$	−3.26206	+	5.65006i	−0.207141	+	0.358779i
$249$	−0.524603	+	0.160619i	−0.0332454	+	0.0101788i
$250$	−0.517769	−	0.896802i	−0.0327466	−	0.0567187i
$251$	−14.4782			−0.913855			−0.456928	−	0.889504i	$-0.651050\pi$
$251$	−14.4782			−0.913855			−0.456928	+	0.889504i	$0.651050\pi$
$252$	0.247459	−	7.35892i	0.0155885	−	0.463569i
$253$	−38.3267			−2.40958
$254$	6.46338	+	11.1949i	0.405549	+	0.702431i
$255$	1.32943	−	5.76905i	0.0832524	−	0.361272i
$256$	8.36675	−	14.4916i	0.522922	−	0.905727i
$257$	−8.84909			−0.551991			−0.275995	−	0.961159i	$-0.589007\pi$
$257$	−8.84909			−0.551991			−0.275995	+	0.961159i	$0.589007\pi$
$258$	−2.29202	−	2.13561i	−0.142695	−	0.132957i
$259$	−0.429730	−	0.0449564i	−0.0267021	−	0.00279346i
$260$	3.32569			0.206251
$261$	−8.93435	−	4.34863i	−0.553022	−	0.269174i
$262$	−0.387247	−	0.670732i	−0.0239242	−	0.0414380i
$263$	16.8457			1.03875			0.519375	−	0.854546i	$-0.326165\pi$
$263$	16.8457			1.03875			0.519375	+	0.854546i	$0.326165\pi$
$264$	22.4268	+	20.8964i	1.38027	+	1.28608i
$265$	−3.06590	−	5.31029i	−0.188337	−	0.326209i
$266$	−5.52129	−	12.3849i	−0.338532	−	0.759367i
$267$	−3.34908	+	1.02540i	−0.204960	+	0.0627533i
$268$	−7.54384	−	13.0663i	−0.460813	−	0.798152i
$269$	6.33133	+	10.9662i	0.386028	+	0.668620i	0.991911	−	0.126934i	$-0.0405135\pi$
$269$	6.33133	+	10.9662i	0.386028	+	0.668620i	−0.605883	+	0.795554i	$0.707180\pi$
$270$	−5.31558	−	0.835297i	−0.323496	−	0.0508346i
$271$	−12.0800	+	20.9232i	−0.733809	+	1.27099i	0.221435	+	0.975175i	$0.428926\pi$
$271$	−12.0800	+	20.9232i	−0.733809	+	1.27099i	−0.955244	+	0.295819i	$0.904407\pi$
$272$	2.19460	−	3.80116i	0.133067	−	0.230479i
$273$	16.1240	−	3.14905i	0.975870	−	0.190589i
$274$	0.235235	+	0.407439i	0.0142111	+	0.0246143i
$275$	−5.83753			−0.352016
$276$	−10.0871	+	3.08839i	−0.607171	+	0.185899i
$277$	−10.6266			−0.638490			−0.319245	−	0.947672i	$-0.603429\pi$
$277$	−10.6266			−0.638490			−0.319245	+	0.947672i	$0.603429\pi$
$278$	−3.86355	+	6.69186i	−0.231720	+	0.401351i
$279$	−5.80481	−	2.82539i	−0.347525	−	0.169151i
$280$	3.26603	+	7.32609i	0.195183	+	0.437818i
$281$	−7.18007	+	12.4363i	−0.428327	+	0.741885i	−0.996725	−	0.0808695i	$-0.974230\pi$
$281$	−7.18007	+	12.4363i	−0.428327	+	0.741885i	0.568397	+	0.822754i	$0.307564\pi$
$282$	−12.2237	+	3.74257i	−0.727912	+	0.222867i
$283$	−14.2581	+	24.6957i	−0.847553	+	1.46801i	0.0358320	+	0.999358i	$0.488592\pi$
$283$	−14.2581	+	24.6957i	−0.847553	+	1.46801i	−0.883385	+	0.468647i	$0.844741\pi$
$284$	2.68328	−	4.64758i	0.159223	−	0.275783i
$285$	8.19680	−	2.50964i	0.485536	−	0.148658i
$286$	−10.8357	+	18.7680i	−0.640729	+	1.10977i
$287$	14.0573	−	19.3679i	0.829778	−	1.14325i
$288$	12.7688	+	6.21496i	0.752407	+	0.366220i
$289$	2.65844	−	4.60456i	0.156379	−	0.270856i
$290$	3.42986			0.201408
$291$	2.86605	−	0.877508i	0.168011	−	0.0514404i
$292$	10.0674			0.589151
$293$	9.16903	+	15.8812i	0.535660	+	0.927791i	0.999131	+	0.0416785i	$0.0132705\pi$
$293$	9.16903	+	15.8812i	0.535660	+	0.927791i	−0.463471	+	0.886112i	$0.653396\pi$
$294$	7.21548	+	10.2748i	0.420815	+	0.599236i
$295$	−1.59717	+	2.76639i	−0.0929911	+	0.161065i
$296$	0.247552	−	0.428773i	0.0143887	−	0.0249219i
$297$	−19.0604	+	23.5961i	−1.10599	+	1.36918i
$298$	−5.67851	−	9.83547i	−0.328947	−	0.569754i
$299$	−11.7689	−	20.3843i	−0.680613	−	1.17886i
$300$	−1.53636	+	0.470391i	−0.0887017	+	0.0271581i
$301$	−4.59606	−	0.480819i	−0.264913	−	0.0277140i
$302$	3.96853	+	6.87370i	0.228363	+	0.395537i
$303$	−15.1845	−	14.1483i	−0.872329	−	0.812801i
$304$	6.35547			0.364511
$305$	2.41883	+	4.18953i	0.138502	+	0.239892i
$306$	9.54768	+	4.64716i	0.545805	+	0.265660i
$307$	30.0042			1.71243			0.856214	−	0.516622i	$-0.172811\pi$
$307$	30.0042			1.71243			0.856214	+	0.516622i	$0.172811\pi$
$308$	14.2496	+	1.49073i	0.811948	+	0.0849424i
$309$	20.2323	+	18.8516i	1.15097	+	1.07243i
$310$	2.22844			0.126567
$311$	4.92269	−	8.52635i	0.279140	−	0.483485i	−0.692031	−	0.721868i	$-0.743284\pi$
$311$	4.92269	−	8.52635i	0.279140	−	0.483485i	0.971171	+	0.238383i	$0.0766172\pi$
$312$	−4.22733	+	18.3444i	−0.239326	+	1.03855i
$313$	11.5027	+	19.9233i	0.650172	+	1.12613i	0.983081	+	0.183172i	$0.0586367\pi$
$313$	11.5027	+	19.9233i	0.650172	+	1.12613i	−0.332908	+	0.942959i	$0.608030\pi$
$314$	−0.719746			−0.0406176
$315$	−7.00336	+	3.73537i	−0.394595	+	0.210464i
$316$	6.55599			0.368803
$317$	3.65117	+	6.32402i	0.205070	+	0.355192i	0.950155	−	0.311778i	$-0.100924\pi$
$317$	3.65117	+	6.32402i	0.205070	+	0.355192i	−0.745085	+	0.666970i	$0.767591\pi$
$318$	10.5162	−	3.21976i	0.589717	−	0.180555i
$319$	9.66739	−	16.7444i	0.541270	−	0.937507i
$320$	−7.47012			−0.417592
$321$	10.4848	−	3.21016i	0.585205	−	0.179174i
$322$	10.5662	−	14.5579i	0.588830	−	0.811279i
$323$	−16.9169			−0.941280
$324$	−3.11505	+	7.74606i	−0.173058	+	0.430337i
$325$	−1.79251	−	3.10472i	−0.0994308	−	0.172219i
$326$	13.9735			0.773920
$327$	−5.06097	+	21.9620i	−0.279873	+	1.21450i
$328$	13.7114	+	23.7488i	0.757084	+	1.31131i
$329$	−11.0768	+	15.2614i	−0.610682	+	0.841386i
$330$	2.35116	−	10.2028i	0.129427	−	0.561646i
$331$	15.2792	+	26.4644i	0.839822	+	1.45461i	0.890043	+	0.455877i	$0.150674\pi$
$331$	15.2792	+	26.4644i	0.839822	+	1.45461i	−0.0502207	+	0.998738i	$0.515992\pi$
$332$	−0.146922	−	0.254477i	−0.00806340	−	0.0139662i
$333$	0.440517	+	0.214414i	0.0241402	+	0.0117498i
$334$	10.5243	−	18.2286i	0.575864	−	0.997425i
$335$	−8.13210	+	14.0852i	−0.444304	+	0.769558i
$336$	−5.77547	+	1.12796i	−0.315078	+	0.0615353i
$337$	−4.91898	−	8.51992i	−0.267954	−	0.464110i	0.700380	−	0.713771i	$-0.253014\pi$
$337$	−4.91898	−	8.51992i	−0.267954	−	0.464110i	−0.968333	+	0.249661i	$0.919681\pi$
$338$	0.152828			0.00831273
$339$	−3.10650	+	13.4806i	−0.168722	+	0.732166i
$340$	3.17080			0.171961
$341$	6.28108	−	10.8792i	0.340140	−	0.589139i
$342$	1.08494	+	15.3371i	0.0586669	+	0.829337i
$343$	17.6221	+	5.69752i	0.951504	+	0.307637i
$344$	2.64763	−	4.58583i	0.142751	−	0.247251i
$345$	8.32003	+	7.75227i	0.447935	+	0.417368i
$346$	2.48832	−	4.30989i	0.133773	−	0.231701i
$347$	−5.36161	+	9.28658i	−0.287826	+	0.498530i	−0.973291	−	0.229577i	$-0.926266\pi$
$347$	−5.36161	+	9.28658i	−0.287826	+	0.498530i	0.685464	+	0.728106i	$0.259599\pi$
$348$	1.19505	−	5.18591i	0.0640615	−	0.277994i
$349$	−1.12721	+	1.95238i	−0.0603381	+	0.104509i	−0.894617	−	0.446835i	$-0.852551\pi$
$349$	−1.12721	+	1.95238i	−0.0603381	+	0.104509i	0.834278	+	0.551343i	$0.185885\pi$
$350$	1.60933	−	2.21730i	0.0860222	−	0.118520i
$351$	−18.4025	−	2.89179i	−0.982254	−	0.154353i
$352$	−13.8164	+	23.9307i	−0.736417	+	1.27551i
$353$	−6.57812			−0.350118			−0.175059	−	0.984558i	$-0.556012\pi$
$353$	−6.57812			−0.350118			−0.175059	+	0.984558i	$0.556012\pi$
$354$	−4.19179	−	3.90574i	−0.222791	−	0.207588i
$355$	−5.78505			−0.307038
$356$	−0.937954	−	1.62458i	−0.0497114	−	0.0861027i
$357$	15.3731	−	3.00239i	0.813629	−	0.158903i
$358$	5.75527	−	9.96842i	0.304175	−	0.526847i
$359$	13.3871	−	23.1872i	0.706545	−	1.22377i	−0.259586	−	0.965720i	$-0.583586\pi$
$359$	13.3871	−	23.1872i	0.706545	−	1.22377i	0.966131	−	0.258052i	$-0.0830807\pi$
$360$	−0.641780	−	9.07244i	−0.0338248	−	0.478160i
$361$	−2.74763	−	4.75903i	−0.144612	−	0.250475i
$362$	6.82677	+	11.8243i	0.358807	+	0.621472i
$363$	−29.2433	−	27.2477i	−1.53487	−	1.43013i
$364$	3.58274	+	8.03651i	0.187787	+	0.421228i
$365$	−5.42624	−	9.39852i	−0.284022	−	0.491941i
$366$	−8.29668	+	2.54022i	−0.433674	+	0.132779i
$367$	−21.8757			−1.14190			−0.570952	−	0.820983i	$-0.693426\pi$
$367$	−21.8757			−1.14190			−0.570952	+	0.820983i	$0.693426\pi$
$368$	4.21550	+	7.30147i	0.219748	+	0.380615i
$369$	−22.4845	+	15.1924i	−1.17049	+	0.790886i
$370$	−0.169113			−0.00879175
$371$	9.52942	−	13.1295i	0.494743	−	0.681647i
$372$	0.776448	−	3.36938i	0.0402569	−	0.174694i
$373$	21.2709			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$373$	21.2709			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$374$	−10.3310	+	17.8939i	−0.534206	+	0.925271i
$375$	1.26722	+	1.18074i	0.0654389	+	0.0609733i
$376$	−10.8042	−	18.7134i	−0.557182	−	0.965068i
$377$	11.8742			0.611550
$378$	−3.70795	−	13.7449i	−0.190716	−	0.706963i
$379$	−10.0763			−0.517583			−0.258791	−	0.965933i	$-0.583324\pi$
$379$	−10.0763			−0.517583			−0.258791	+	0.965933i	$0.583324\pi$
$380$	2.29562	+	3.97613i	0.117763	+	0.203971i
$381$	−15.8189	−	14.7394i	−0.810425	−	0.755121i
$382$	11.9155	−	20.6383i	0.609651	−	1.05595i
$383$	30.6928			1.56833			0.784165	−	0.620552i	$-0.213092\pi$
$383$	30.6928			1.56833			0.784165	+	0.620552i	$0.213092\pi$
$384$	−0.673538	+	2.92281i	−0.0343714	+	0.149154i
$385$	−6.28872	−	14.1063i	−0.320503	−	0.718926i
$386$	3.97632			0.202389
$387$	4.71143	+	2.29321i	0.239496	+	0.116570i
$388$	0.802676	+	1.39028i	0.0407497	+	0.0705806i
$389$	30.2258			1.53251			0.766253	−	0.642539i	$-0.222119\pi$
$389$	30.2258			1.53251			0.766253	+	0.642539i	$0.222119\pi$
$390$	6.14839	−	1.88247i	0.311336	−	0.0953226i
$391$	−11.2208	−	19.4349i	−0.567458	−	0.982867i
$392$	−14.1850	+	15.7847i	−0.716450	+	0.797247i
$393$	0.947773	+	0.883096i	0.0478088	+	0.0445463i
$394$	−12.7795	−	22.1347i	−0.643821	−	1.11513i
$395$	−3.53361	−	6.12039i	−0.177795	−	0.307950i
$396$	−14.6073	−	7.10985i	−0.734046	−	0.357284i
$397$	15.4935	−	26.8355i	0.777596	−	1.34684i	−0.155728	−	0.987800i	$-0.549772\pi$
$397$	15.4935	−	26.8355i	0.777596	−	1.34684i	0.933324	−	0.359035i	$-0.116894\pi$
$398$	−8.07951	+	13.9941i	−0.404989	+	0.701462i
$399$	14.8949	+	17.1039i	0.745676	+	0.856266i
$400$	0.642061	+	1.11208i	0.0321031	+	0.0556041i
$401$	0.644091			0.0321644			0.0160822	−	0.999871i	$-0.494881\pi$
$401$	0.644091			0.0321644			0.0160822	+	0.999871i	$0.494881\pi$
$402$	−21.3428	−	19.8863i	−1.06448	−	0.991840i
$403$	7.71486			0.384304
$404$	5.55788	−	9.62653i	0.276515	−	0.478938i
$405$	8.91038	−	1.26697i	0.442760	−	0.0629563i
$406$	3.69496	+	8.28823i	0.183378	+	0.411338i
$407$	−0.476660	+	0.825600i	−0.0236272	+	0.0409235i
$408$	−4.03045	+	17.4901i	−0.199537	+	0.865887i
$409$	−15.9888	+	27.6934i	−0.790595	+	1.36935i	0.135004	+	0.990845i	$0.456895\pi$
$409$	−15.9888	+	27.6934i	−0.790595	+	1.36935i	−0.925599	+	0.378505i	$0.876438\pi$
$410$	4.68339	−	8.11187i	0.231296	−	0.400617i
$411$	−0.575729	−	0.536441i	−0.0283986	−	0.0264607i
$412$	−7.40547	+	12.8266i	−0.364841	+	0.631924i
$413$	−8.40558	−	0.879354i	−0.413611	−	0.0432702i
$414$	−16.9004	+	11.4194i	−0.830610	+	0.561232i
$415$	−0.158379	+	0.274321i	−0.00777452	+	0.0134659i
$416$	−16.9703			−0.832036
$417$	2.90227	−	12.5943i	0.142125	−	0.616747i
$418$	−29.9182			−1.46335
$419$	−9.95547	−	17.2434i	−0.486356	−	0.842394i	0.513521	−	0.858077i	$-0.328341\pi$
$419$	−9.95547	−	17.2434i	−0.486356	−	0.842394i	−0.999877	+	0.0156832i	$0.995008\pi$
$420$	−2.79181	−	3.20585i	−0.136226	−	0.156430i
$421$	12.4166	−	21.5062i	0.605147	−	1.04815i	−0.386881	−	0.922130i	$-0.626447\pi$
$421$	12.4166	−	21.5062i	0.605147	−	1.04815i	0.992028	−	0.126016i	$-0.0402192\pi$
$422$	3.98436	−	6.90112i	0.193956	−	0.335941i
$423$	17.7171	−	11.9712i	0.861435	−	0.582059i
$424$	9.29490	+	16.0992i	0.451400	+	0.781848i
$425$	−1.70903	−	2.96012i	−0.0829001	−	0.143587i
$426$	2.33002	−	10.1111i	0.112890	−	0.489884i
$427$	−7.51820	+	10.3584i	−0.363831	+	0.501280i
$428$	2.93641	+	5.08601i	0.141937	+	0.245842i
$429$	8.13970	−	35.3221i	0.392989	−	1.70537i
$430$	−1.80870			−0.0872233
$431$	−1.73040	−	2.99714i	−0.0833503	−	0.144367i	0.821337	−	0.570444i	$-0.193229\pi$
$431$	−1.73040	−	2.99714i	−0.0833503	−	0.144367i	−0.904687	+	0.426077i	$0.859895\pi$
$432$	6.59161	+	1.03581i	0.317139	+	0.0498356i
$433$	−2.96019			−0.142258			−0.0711289	−	0.997467i	$-0.522660\pi$
$433$	−2.96019			−0.142258			−0.0711289	+	0.997467i	$0.522660\pi$
$434$	2.40068	+	5.38502i	0.115237	+	0.258489i
$435$	−5.48547	+	1.67950i	−0.263008	+	0.0805259i
$436$	−12.0708			−0.578087
$437$	16.2474	−	28.1413i	0.777219	−	1.34618i
$438$	18.6122	−	5.69856i	0.889326	−	0.272288i
$439$	0.763935	+	1.32317i	0.0364606	+	0.0631517i	0.883680	−	0.468092i	$-0.155058\pi$
$439$	0.763935	+	1.32317i	0.0364606	+	0.0631517i	−0.847219	+	0.531243i	$0.821725\pi$
$440$	17.6977			0.843703
$441$	−16.5712	−	12.8995i	−0.789103	−	0.614261i
$442$	−12.6893			−0.603569
$443$	8.09912	+	14.0281i	0.384801	+	0.666494i	0.991742	−	0.128253i	$-0.0409368\pi$
$443$	8.09912	+	14.0281i	0.384801	+	0.666494i	−0.606941	+	0.794747i	$0.707604\pi$
$444$	−0.0589233	+	0.255696i	−0.00279637	+	0.0121348i
$445$	−1.01109	+	1.75127i	−0.0479305	+	0.0830181i
$446$	7.25589			0.343576
$447$	13.8979	+	12.9495i	0.657350	+	0.612492i
$448$	−8.04750	−	18.0515i	−0.380209	−	0.852853i
$449$	26.1011			1.23179			0.615894	−	0.787829i	$-0.288795\pi$
$449$	26.1011			1.23179			0.615894	+	0.787829i	$0.288795\pi$
$450$	−2.57409	+	1.73928i	−0.121344	+	0.0819904i
$451$	−26.4012	−	45.7281i	−1.24318	−	2.15325i
$452$	−7.40924			−0.348501
$453$	−9.71283	−	9.05002i	−0.456349	−	0.425207i
$454$	−2.98571	−	5.17139i	−0.140126	−	0.242706i
$455$	5.57149	−	7.67629i	0.261195	−	0.359870i
$456$	−24.8503	+	7.60848i	−1.16372	+	0.356300i
$457$	2.23807	+	3.87646i	0.104693	+	0.181333i	0.913613	−	0.406586i	$-0.133281\pi$
$457$	2.23807	+	3.87646i	0.104693	+	0.181333i	−0.808920	+	0.587919i	$0.799947\pi$
$458$	−3.05877	−	5.29794i	−0.142927	−	0.247557i
$459$	−17.5454	−	2.75711i	−0.818951	−	0.128691i
$460$	−3.04532	+	5.27464i	−0.141989	+	0.245932i
$461$	1.73535	−	3.00572i	0.0808234	−	0.139990i	−0.822780	−	0.568359i	$-0.807578\pi$
$461$	1.73535	−	3.00572i	0.0808234	−	0.139990i	0.903604	+	0.428369i	$0.140912\pi$
$462$	27.1879	−	5.30985i	1.26490	−	0.247037i
$463$	14.0111	+	24.2680i	0.651152	+	1.12783i	0.982844	+	0.184441i	$0.0590475\pi$
$463$	14.0111	+	24.2680i	0.651152	+	1.12783i	−0.331691	+	0.943388i	$0.607619\pi$
$464$	−4.25321			−0.197450
$465$	−3.56401	+	1.09120i	−0.165277	+	0.0506033i
$466$	−22.6414			−1.04884
$467$	−6.82281	+	11.8175i	−0.315722	+	0.546847i	−0.979591	−	0.201003i	$-0.935580\pi$
$467$	−6.82281	+	11.8175i	−0.315722	+	0.546847i	0.663869	+	0.747849i	$0.268913\pi$
$468$	−0.704014	−	9.95220i	−0.0325431	−	0.460041i
$469$	−42.7975	−	4.47728i	−1.97620	−	0.206742i
$470$	−3.69037	+	6.39191i	−0.170224	+	0.294837i
$471$	1.15111	−	0.352438i	0.0530403	−	0.0162395i
$472$	4.84216	−	8.38686i	0.222878	−	0.386037i
$473$	−5.09799	+	8.82999i	−0.234406	+	0.406003i
$474$	12.1204	−	3.71095i	0.556710	−	0.170449i
$475$	2.47463	−	4.28619i	0.113544	−	0.196664i
$476$	3.41588	+	7.66222i	0.156566	+	0.351197i
$477$	−15.2421	+	10.2989i	−0.697890	+	0.471554i
$478$	−0.503107	+	0.871407i	−0.0230116	+	0.0398572i
$479$	−7.62321			−0.348313			−0.174157	−	0.984718i	$-0.555720\pi$
$479$	−7.62321			−0.348313			−0.174157	+	0.984718i	$0.555720\pi$
$480$	7.83970	−	2.40030i	0.357832	−	0.109558i
$481$	−0.585467			−0.0266950
$482$	15.1243	+	26.1961i	0.688894	+	1.19320i
$483$	−9.77020	+	28.4568i	−0.444559	+	1.29483i
$484$	10.7037	−	18.5393i	0.486531	−	0.842697i
$485$	0.865269	−	1.49869i	0.0392898	−	0.0680520i
$486$	−1.37439	+	16.0838i	−0.0623436	+	0.729577i
$487$	12.6129	+	21.8461i	0.571544	+	0.989943i	0.996408	+	0.0846856i	$0.0269886\pi$
$487$	12.6129	+	21.8461i	0.571544	+	0.989943i	−0.424864	+	0.905257i	$0.639678\pi$
$488$	−7.33317	−	12.7014i	−0.331957	−	0.574967i
$489$	−22.3482	+	6.84241i	−1.01062	+	0.309424i
$490$	7.09182	+	1.50025i	0.320376	+	0.0677743i
$491$	19.8083	+	34.3090i	0.893937	+	1.54834i	0.835114	+	0.550076i	$0.185401\pi$
$491$	19.8083	+	34.3090i	0.893937	+	1.54834i	0.0588227	+	0.998268i	$0.481265\pi$
$492$	−10.6332	−	9.90761i	−0.479383	−	0.446670i
$493$	11.3211			0.509878
$494$	−9.18691	−	15.9122i	−0.413339	−	0.715923i
$495$	1.23574	+	17.4689i	0.0555425	+	0.785170i
$496$	−2.76339			−0.124080
$497$	−6.23218	−	13.9795i	−0.279552	−	0.627067i
$498$	−0.415667	−	0.387302i	−0.0186265	−	0.0173554i
$499$	−44.1524			−1.97653			−0.988266	−	0.152743i	$-0.951189\pi$
$499$	−44.1524			−1.97653			−0.988266	+	0.152743i	$0.951189\pi$
$500$	−0.463831	+	0.803378i	−0.0207431	+	0.0359282i
$501$	−7.90577	+	34.3069i	−0.353204	+	1.53272i
$502$	−7.49636	−	12.9841i	−0.334579	−	0.579508i
$503$	−7.42967			−0.331273			−0.165636	−	0.986187i	$-0.552968\pi$
$503$	−7.42967			−0.331273			−0.165636	+	0.986187i	$0.552968\pi$
$504$	21.2321	−	11.3245i	0.945753	−	0.504435i
$505$	−11.9826			−0.533217
$506$	−19.8444	−	34.3715i	−0.882191	−	1.52800i
$507$	−0.244422	+	0.0748352i	−0.0108551	+	0.00332355i
$508$	5.79006	−	10.0287i	0.256892	−	0.444951i
$509$	12.5038			0.554223			0.277111	−	0.960838i	$-0.410623\pi$
$509$	12.5038			0.554223			0.277111	+	0.960838i	$0.410623\pi$
$510$	5.86204	−	1.79480i	0.259575	−	0.0794749i
$511$	16.8658	−	23.2374i	0.746100	−	1.02796i
$512$	13.8647			0.612741
$513$	−9.24532	−	23.9978i	−0.408191	−	1.05953i
$514$	−4.58178	−	7.93588i	−0.202094	−	0.350037i
$515$	15.9659			0.703541
$516$	−0.630198	+	2.73473i	−0.0277429	+	0.120390i
$517$	20.8033	+	36.0325i	0.914930	+	1.58471i
$518$	−0.182184	−	0.408660i	−0.00800470	−	0.0179555i
$519$	−1.86921	+	8.11138i	−0.0820490	+	0.356050i
$520$	5.43437	+	9.41261i	0.238313	+	0.412770i
$521$	8.18142	+	14.1706i	0.358435	+	0.620827i	0.987699	−	0.156364i	$-0.0499773\pi$
$521$	8.18142	+	14.1706i	0.358435	+	0.620827i	−0.629265	+	0.777191i	$0.716644\pi$
$522$	−0.726066	−	10.2639i	−0.0317790	−	0.449240i
$523$	0.681193	−	1.17986i	0.0297865	−	0.0515917i	−0.850748	−	0.525574i	$-0.823851\pi$
$523$	0.681193	−	1.17986i	0.0297865	−	0.0515917i	0.880534	+	0.473982i	$0.157184\pi$
$524$	−0.346906	+	0.600859i	−0.0151547	+	0.0262486i
$525$	−1.48809	+	4.33423i	−0.0649457	+	0.189161i
$526$	8.72218	+	15.1073i	0.380305	+	0.658707i
$527$	7.35554			0.320413
$528$	−2.91556	+	12.6520i	−0.126884	+	0.550609i
$529$	20.1068			0.874211
$530$	3.17485	−	5.49901i	0.137907	−	0.238862i
$531$	8.61658	+	4.19396i	0.373928	+	0.182002i
$532$	−7.13525	+	9.83081i	−0.309352	+	0.426220i
$533$	16.2139	−	28.0832i	0.702300	−	1.21642i
$534$	−2.65363	−	2.47254i	−0.114834	−	0.106997i
$535$	3.16539	−	5.48261i	0.136852	−	0.237034i
$536$	24.6541	−	42.7022i	1.06490	−	1.84445i
$537$	−4.32331	+	18.7609i	−0.186565	+	0.809594i
$538$	−6.55633	+	11.3559i	−0.282663	+	0.489588i
$539$	27.3131	−	30.3933i	1.17646	−	1.30913i
$540$	1.73289	+	4.49801i	0.0745716	+	0.193564i
$541$	21.7040	−	37.5924i	0.933127	−	1.61622i	0.155187	−	0.987885i	$-0.450402\pi$
$541$	21.7040	−	37.5924i	0.933127	−	1.61622i	0.777940	−	0.628338i	$-0.216265\pi$
$542$	−25.0186			−1.07464
$543$	−16.7083	−	15.5681i	−0.717020	−	0.668090i
$544$	−16.1799			−0.693707
$545$	6.50604	+	11.2688i	0.278688	+	0.482702i
$546$	11.1726	+	12.8296i	0.478143	+	0.549055i
$547$	0.444714	−	0.770267i	0.0190146	−	0.0329343i	−0.856362	−	0.516377i	$-0.827280\pi$
$547$	0.444714	−	0.770267i	0.0190146	−	0.0329343i	0.875376	+	0.483442i	$0.160614\pi$
$548$	0.210730	−	0.364994i	0.00900192	−	0.0155918i
$549$	12.0252	−	8.12528i	0.513224	−	0.346778i
$550$	−3.02249	−	5.23511i	−0.128879	−	0.223226i
$551$	8.19637	+	14.1965i	0.349177	+	0.604792i
$552$	−25.2239	−	23.5026i	−1.07360	−	1.00034i
$553$	10.9832	−	15.1324i	0.467051	−	0.643495i
$554$	−5.50212	−	9.52994i	−0.233763	−	0.404889i
$555$	0.270466	−	0.0828095i	0.0114807	−	0.00351507i
$556$	6.92213			0.293564
$557$	−3.48898	−	6.04310i	−0.147833	−	0.256054i	0.782593	−	0.622533i	$-0.213896\pi$
$557$	−3.48898	−	6.04310i	−0.147833	−	0.256054i	−0.930426	+	0.366479i	$0.880563\pi$
$558$	−0.471738	−	6.66866i	−0.0199703	−	0.282307i
$559$	−6.26171			−0.264842
$560$	−1.99565	+	2.74957i	−0.0843317	+	0.116191i
$561$	7.76060	−	33.6770i	0.327653	−	1.42184i
$562$	−14.8705			−0.627273
$563$	−3.82036	+	6.61705i	−0.161009	+	0.278876i	−0.935231	−	0.354039i	$-0.884808\pi$
$563$	−3.82036	+	6.61705i	−0.161009	+	0.278876i	0.774222	+	0.632914i	$0.218141\pi$
$564$	8.37868	+	7.80691i	0.352806	+	0.328730i
$565$	3.99350	+	6.91695i	0.168008	+	0.290998i
$566$	−29.5295			−1.24122
$567$	12.6607	+	20.1670i	0.531700	+	0.846933i
$568$	17.5385			0.735901
$569$	−5.09242	−	8.82034i	−0.213486	−	0.369768i	0.739317	−	0.673357i	$-0.235148\pi$
$569$	−5.09242	−	8.82034i	−0.213486	−	0.369768i	−0.952803	+	0.303589i	$0.901815\pi$
$570$	6.49470	+	6.05149i	0.272033	+	0.253469i
$571$	−10.7518	+	18.6226i	−0.449947	+	0.779331i	−0.998382	−	0.0568619i	$-0.981891\pi$
$571$	−10.7518	+	18.6226i	−0.449947	+	0.779331i	0.548435	+	0.836193i	$0.315224\pi$
$572$	19.4138			0.811732
$573$	−8.95085	+	38.8420i	−0.373927	+	1.62265i
$574$	24.6477	+	2.57853i	1.02877	+	0.107626i
$575$	6.56558			0.273804
$576$	1.58135	+	22.3545i	0.0658894	+	0.931437i
$577$	−17.3700	−	30.0857i	−0.723121	−	1.25248i	−0.959743	−	0.280881i	$-0.909373\pi$
$577$	−17.3700	−	30.0857i	−0.723121	−	1.25248i	0.236621	−	0.971602i	$-0.423960\pi$
$578$	5.50584			0.229013
$579$	−6.35943	+	1.94709i	−0.264289	+	0.0809181i
$580$	−1.53628	−	2.66091i	−0.0637905	−	0.110488i
$581$	−0.833515	−	0.0871986i	−0.0345800	−	0.00361761i
$582$	2.27090	+	2.11594i	0.0941320	+	0.0877084i
$583$	−17.8973	−	30.9990i	−0.741229	−	1.28385i
$584$	16.4507	+	28.4935i	0.680737	+	1.17907i
$585$	−8.91150	+	6.02137i	−0.368445	+	0.248953i
$586$	−9.49487	+	16.4456i	−0.392230	+	0.679362i
$587$	0.651989	−	1.12928i	0.0269105	−	0.0466103i	−0.852257	−	0.523124i	$-0.824766\pi$
$587$	0.651989	−	1.12928i	0.0269105	−	0.0466103i	0.879167	+	0.476514i	$0.158100\pi$
$588$	4.73933	−	10.2000i	0.195447	−	0.420642i
$589$	5.32533	+	9.22374i	0.219426	+	0.380058i
$590$	−3.30787			−0.136183
$591$	31.2773	+	29.1429i	1.28658	+	1.19878i
$592$	0.209709			0.00861898
$593$	−6.40563	+	11.0949i	−0.263048	+	0.455612i	−0.967050	−	0.254585i	$-0.918061\pi$
$593$	−6.40563	+	11.0949i	−0.263048	+	0.455612i	0.704003	+	0.710197i	$0.251394\pi$
$594$	−31.0299	−	4.87607i	−1.27317	−	0.200067i
$595$	5.31200	−	7.31878i	0.217771	−	0.300041i
$596$	−5.08696	+	8.81087i	−0.208370	+	0.360907i
$597$	6.06927	−	26.3375i	0.248399	−	1.07792i
$598$	12.1871	−	21.1087i	0.498369	−	0.863200i
$599$	−4.91215	+	8.50810i	−0.200705	+	0.347632i	−0.948756	−	0.316010i	$-0.897657\pi$
$599$	−4.91215	+	8.50810i	−0.200705	+	0.347632i	0.748051	+	0.663642i	$0.230990\pi$
$600$	−3.84183	−	3.57967i	−0.156842	−	0.146139i
$601$	−6.13096	+	10.6191i	−0.250087	+	0.433163i	−0.963550	−	0.267530i	$-0.913793\pi$
$601$	−6.13096	+	10.6191i	−0.250087	+	0.433163i	0.713463	+	0.700693i	$0.247126\pi$
$602$	−1.94850	−	4.37071i	−0.0794149	−	0.178137i
$603$	43.8718	+	21.3538i	1.78660	+	0.869594i
$604$	3.55511	−	6.15764i	0.144656	−	0.250551i
$605$	−23.0767			−0.938202
$606$	4.82618	−	20.9431i	0.196050	−	0.850755i
$607$	−28.8254			−1.16999			−0.584993	−	0.811039i	$-0.698903\pi$
$607$	−28.8254			−1.16999			−0.584993	+	0.811039i	$0.698903\pi$
$608$	−11.7141	−	20.2893i	−0.475068	−	0.822841i
$609$	−9.96795	−	11.4463i	−0.403922	−	0.463827i
$610$	−2.50479	+	4.33842i	−0.101416	+	0.175658i
$611$	−12.7761	+	22.1288i	−0.516864	+	0.895234i
$612$	−0.671225	−	9.48869i	−0.0271327	−	0.383557i
$613$	−0.236184	−	0.409083i	−0.00953939	−	0.0165227i	0.861216	−	0.508239i	$-0.169703\pi$
$613$	−0.236184	−	0.409083i	−0.00953939	−	0.0165227i	−0.870756	+	0.491716i	$0.836370\pi$
$614$	15.5352	+	26.9078i	0.626950	+	1.08591i
$615$	−3.51813	+	15.2668i	−0.141865	+	0.615618i
$616$	19.0655	+	42.7663i	0.768173	+	1.72310i
$617$	−4.68688	−	8.11791i	−0.188687	−	0.326815i	0.756126	−	0.654426i	$-0.227090\pi$
$617$	−4.68688	−	8.11791i	−0.188687	−	0.326815i	−0.944813	+	0.327611i	$0.893756\pi$
$618$	−6.43053	+	27.9051i	−0.258674	+	1.12251i
$619$	4.88425			0.196314			0.0981572	−	0.995171i	$-0.468705\pi$
$619$	4.88425			0.196314			0.0981572	+	0.995171i	$0.468705\pi$
$620$	−0.998148	−	1.72884i	−0.0400866	−	0.0694320i
$621$	21.4376	−	26.5389i	0.860260	−	1.06497i
$622$	10.1953			0.408793
$623$	−5.32117	−	0.556677i	−0.213188	−	0.0223028i
$624$	−7.62434	+	2.33436i	−0.305218	+	0.0934494i
$625$	1.00000			0.0400000
$626$	−11.9115	+	20.6313i	−0.476080	+	0.824594i
$627$	47.8490	−	14.6501i	1.91091	−	0.585068i
$628$	0.322383	+	0.558384i	0.0128645	+	0.0222820i
$629$	−0.558200			−0.0222569
$630$	−6.97601	−	4.34657i	−0.277931	−	0.173171i
$631$	8.12284			0.323365			0.161683	−	0.986843i	$-0.448308\pi$
$631$	8.12284			0.323365			0.161683	+	0.986843i	$0.448308\pi$
$632$	10.7129	+	18.5552i	0.426135	+	0.738087i
$633$	−2.99302	+	12.9882i	−0.118962	+	0.516234i
$634$	−3.78093	+	6.54876i	−0.150160	+	0.260084i
$635$	−12.4831			−0.495378
$636$	−7.20823	−	6.71634i	−0.285825	−	0.266320i
$637$	24.5518	+	5.19385i	0.972779	+	0.205788i
$638$	20.0219			0.792675
$639$	1.22463	+	17.3119i	0.0484458	+	0.684847i
$640$	0.865855	+	1.49970i	0.0342259	+	0.0592810i
$641$	43.2132			1.70682			0.853409	−	0.521241i	$-0.174531\pi$
$641$	43.2132			1.70682			0.853409	+	0.521241i	$0.174531\pi$
$642$	8.30759	+	7.74067i	0.327874	+	0.305500i
$643$	−4.16247	−	7.20960i	−0.164152	−	0.284319i	0.772202	−	0.635377i	$-0.219155\pi$
$643$	−4.16247	−	7.20960i	−0.164152	−	0.284319i	−0.936354	+	0.351058i	$0.885822\pi$
$644$	−16.0268	−	1.67666i	−0.631546	−	0.0660695i
$645$	2.89270	−	0.885667i	0.113900	−	0.0348731i
$646$	−8.75904	−	15.1711i	−0.344620	−	0.596899i
$647$	−4.25708	−	7.37348i	−0.167363	−	0.289881i	0.770129	−	0.637888i	$-0.220192\pi$
$647$	−4.25708	−	7.37348i	−0.167363	−	0.289881i	−0.937492	+	0.348007i	$0.886859\pi$
$648$	−27.0136	+	3.84108i	−1.06120	+	0.150892i
$649$	−9.32354	+	16.1489i	−0.365981	+	0.633898i
$650$	1.85622	−	3.21506i	0.0728068	−	0.126105i
$651$	−6.47636	−	7.43686i	−0.253829	−	0.291473i
$652$	−6.25891	−	10.8407i	−0.245118	−	0.424556i
$653$	22.8749			0.895163			0.447581	−	0.894243i	$-0.352285\pi$
$653$	22.8749			0.895163			0.447581	+	0.894243i	$0.352285\pi$
$654$	−22.3160	+	6.83255i	−0.872624	+	0.267174i
$655$	0.747915			0.0292235
$656$	−5.80765	+	10.0591i	−0.226751	+	0.392744i
$657$	−26.9766	+	18.2277i	−1.05246	+	0.711130i
$658$	−19.4216	−	2.03180i	−0.757134	−	0.0792080i
$659$	−7.96931	+	13.8032i	−0.310440	+	0.537698i	−0.978458	−	0.206447i	$-0.933810\pi$
$659$	−7.96931	+	13.8032i	−0.310440	+	0.537698i	0.668018	+	0.744145i	$0.267143\pi$
$660$	−8.96853	+	2.74592i	−0.349100	+	0.106885i
$661$	−4.46078	+	7.72630i	−0.173504	+	0.300518i	−0.939643	−	0.342157i	$-0.888842\pi$
$661$	−4.46078	+	7.72630i	−0.173504	+	0.300518i	0.766138	+	0.642676i	$0.222176\pi$
$662$	−15.8222	+	27.4049i	−0.614948	+	1.06512i
$663$	20.2943	−	6.21358i	0.788167	−	0.241315i
$664$	0.480159	−	0.831659i	0.0186338	−	0.0322746i
$665$	13.0235	+	1.36246i	0.505028	+	0.0528338i
$666$	0.0357994	+	0.506073i	0.00138720	+	0.0196099i
$667$	−10.8731	+	18.8328i	−0.421008	+	0.729208i
$668$	−18.8559			−0.729555
$669$	−11.6045	+	3.55300i	−0.448658	+	0.137367i
$670$	−16.8422			−0.650671
$671$	14.1200	+	24.4565i	0.545096	+	0.944133i
$672$	14.2460	+	16.3588i	0.549550	+	0.631053i
$673$	6.98022	−	12.0901i	0.269068	−	0.466039i	−0.699554	−	0.714580i	$-0.746618\pi$
$673$	6.98022	−	12.0901i	0.269068	−	0.466039i	0.968621	+	0.248541i	$0.0799511\pi$
$674$	5.09379	−	8.82270i	0.196205	−	0.339838i
$675$	3.26514	−	4.04213i	0.125675	−	0.155582i
$676$	−0.0684535	−	0.118565i	−0.00263283	−	0.00456019i
$677$	4.15236	+	7.19209i	0.159588	+	0.276415i	0.934720	−	0.355385i	$-0.115650\pi$
$677$	4.15236	+	7.19209i	0.159588	+	0.276415i	−0.775132	+	0.631799i	$0.782317\pi$
$678$	−13.6979	+	4.19392i	−0.526064	+	0.161066i
$679$	4.55372	+	0.476390i	0.174756	+	0.0182822i
$680$	5.18127	+	8.97422i	0.198693	+	0.344146i
$681$	7.30740	+	6.80874i	0.280020	+	0.260911i
$682$	13.0086			0.498125
$683$	−9.51866	−	16.4868i	−0.364221	−	0.630850i	0.624429	−	0.781081i	$-0.285332\pi$
$683$	−9.51866	−	16.4868i	−0.364221	−	0.630850i	−0.988651	+	0.150231i	$0.951998\pi$
$684$	11.4127	−	7.71141i	0.436376	−	0.294853i
$685$	−0.454324			−0.0173588
$686$	4.01462	+	18.7535i	0.153279	+	0.716013i
$687$	7.48622	+	6.97536i	0.285617	+	0.266126i
$688$	2.24288			0.0855092
$689$	10.9913	−	19.0375i	0.418736	−	0.725272i
$690$	−2.64440	+	11.4753i	−0.100670	+	0.436857i
$691$	13.0517	+	22.6063i	0.496511	+	0.859982i	0.999992	−	0.00402403i	$-0.00128089\pi$
$691$	13.0517	+	22.6063i	0.496511	+	0.859982i	−0.503481	+	0.864006i	$0.667948\pi$
$692$	−4.45820			−0.169475
$693$	−40.8823	+	21.8053i	−1.55299	+	0.828315i
$694$	−11.1043			−0.421513
$695$	−3.73096	−	6.46221i	−0.141523	−	0.245125i
$696$	16.6303	−	5.09175i	0.630370	−	0.193002i
$697$	15.4587	−	26.7753i	0.585541	−	1.01419i
$698$	−2.33454			−0.0883635
$699$	36.2110	−	11.0868i	1.36962	−	0.419342i
$700$	−2.44104	−	0.255371i	−0.0922626	−	0.00965210i
$701$	−16.0576			−0.606489			−0.303244	−	0.952913i	$-0.598070\pi$
$701$	−16.0576			−0.606489			−0.303244	+	0.952913i	$0.598070\pi$
$702$	−6.93489	−	18.0007i	−0.261740	−	0.679393i
$703$	−0.404130	−	0.699974i	−0.0152421	−	0.0264000i
$704$	−43.6070			−1.64350
$705$	2.77218	−	12.0298i	0.104406	−	0.453070i
$706$	−3.40595	−	5.89927i	−0.128184	−	0.222022i
$707$	−12.9087	−	28.9558i	−0.485483	−	1.08900i
$708$	−1.15255	+	5.00146i	−0.0433154	+	0.187966i
$709$	9.33691	+	16.1720i	0.350655	+	0.607352i	0.986364	−	0.164576i	$-0.0526257\pi$
$709$	9.33691	+	16.1720i	0.350655	+	0.607352i	−0.635709	+	0.771928i	$0.719292\pi$
$710$	−2.99532	−	5.18804i	−0.112412	−	0.194704i
$711$	−17.5674	+	11.8700i	−0.658828	+	0.445161i
$712$	3.06534	−	5.30933i	0.114878	−	0.198975i
$713$	−7.06445	+	12.2360i	−0.264566	+	0.458242i
$714$	10.6522	+	12.2321i	0.398650	+	0.457773i
$715$	−10.4638	−	18.1239i	−0.391326	−	0.677796i
$716$	−10.3114			−0.385356
$717$	0.377930	−	1.64002i	0.0141141	−	0.0612477i
$718$	27.7258			1.03472
$719$	13.7114	−	23.7489i	0.511350	−	0.885685i	−0.488563	−	0.872529i	$-0.662479\pi$
$719$	13.7114	−	23.7489i	0.511350	−	0.885685i	0.999913	−	0.0131562i	$-0.00418786\pi$
$720$	3.19201	−	2.15680i	0.118959	−	0.0803791i
$721$	17.1999	+	38.5815i	0.640559	+	1.43685i
$722$	2.84527	−	4.92816i	0.105890	−	0.183407i
$723$	−37.0162	−	34.4902i	−1.37665	−	1.28270i
$724$	6.11560	−	10.5925i	0.227284	−	0.393668i
$725$	−1.65608	+	2.86841i	−0.0615051	+	0.106530i
$726$	9.29453	−	40.3334i	0.344952	−	1.49691i
$727$	23.9907	−	41.5532i	0.889767	−	1.54112i	0.0496172	−	0.998768i	$-0.484200\pi$
$727$	23.9907	−	41.5532i	0.889767	−	1.54112i	0.840150	−	0.542354i	$-0.182467\pi$
$728$	−16.8911	+	23.2722i	−0.626026	+	0.862527i
$729$	−5.67767	−	26.3963i	−0.210284	−	0.977640i
$730$	5.61908	−	9.73252i	0.207971	−	0.360217i
$731$	−5.97008			−0.220811
$732$	5.68691	+	5.29883i	0.210194	+	0.195850i
$733$	30.2164			1.11607			0.558035	−	0.829818i	$-0.311556\pi$
$733$	30.2164			1.11607			0.558035	+	0.829818i	$0.311556\pi$
$734$	−11.3266	−	19.6182i	−0.418071	−	0.724121i
$735$	−12.0768	+	1.07327i	−0.445458	+	0.0395881i
$736$	15.5396	−	26.9153i	0.572797	−	0.992113i
$737$	−47.4714	+	82.2228i	−1.74863	+	3.02872i
$738$	−25.2664	−	12.2979i	−0.930068	−	0.452694i
$739$	−4.22504	−	7.31799i	−0.155421	−	0.269197i	0.777791	−	0.628523i	$-0.216340\pi$
$739$	−4.22504	−	7.31799i	−0.155421	−	0.269197i	−0.933212	+	0.359326i	$0.883007\pi$
$740$	0.0757477	+	0.131199i	0.00278454	+	0.00482297i
$741$	22.4846	+	20.9502i	0.825992	+	0.769626i
$742$	16.7086	+	1.74797i	0.613391	+	0.0641702i
$743$	−7.90830	−	13.6976i	−0.290128	−	0.502516i	0.683712	−	0.729752i	$-0.260364\pi$
$743$	−7.90830	−	13.6976i	−0.290128	−	0.502516i	−0.973840	+	0.227236i	$0.927031\pi$
$744$	10.8050	−	3.30820i	0.396131	−	0.121285i
$745$	10.9673			0.401810
$746$	11.0134	+	19.0758i	0.403230	+	0.698416i
$747$	0.854438	+	0.415882i	0.0312622	+	0.0152163i
$748$	18.5096			0.676779
$749$	16.6588	+	1.74276i	0.608698	+	0.0636792i
$750$	−0.402766	+	1.74780i	−0.0147070	+	0.0638205i
$751$	−5.02365			−0.183316			−0.0916578	−	0.995791i	$-0.529217\pi$
$751$	−5.02365			−0.183316			−0.0916578	+	0.995791i	$0.529217\pi$
$752$	4.57626	−	7.92632i	0.166879	−	0.289043i
$753$	18.3470	+	17.0950i	0.668604	+	0.622978i
$754$	6.14807	+	10.6488i	0.223899	+	0.387805i
$755$	−7.66468			−0.278946
$756$	−9.00259	+	9.03318i	−0.327421	+	0.328534i
$757$	−29.8206			−1.08385			−0.541924	−	0.840428i	$-0.682304\pi$
$757$	−29.8206			−1.08385			−0.541924	+	0.840428i	$0.682304\pi$
$758$	−5.21717	−	9.03641i	−0.189496	−	0.328217i
$759$	48.5684	+	45.2541i	1.76292	+	1.64262i
$760$	−7.50236	+	12.9945i	−0.272139	+	0.471359i
$761$	9.36794			0.339588			0.169794	−	0.985480i	$-0.445690\pi$
$761$	9.36794			0.339588			0.169794	+	0.985480i	$0.445690\pi$
$762$	5.02779	−	21.8180i	0.182138	−	0.790382i
$763$	−20.2221	+	27.8616i	−0.732088	+	1.00866i
$764$	−21.3485			−0.772360
$765$	−8.49645	+	5.74093i	−0.307190	+	0.207564i
$766$	15.8918	+	27.5254i	0.574194	+	0.994533i
$767$	−11.4518			−0.413501
$768$	−27.7134	+	8.48509i	−1.00002	+	0.306179i
$769$	21.8494	+	37.8443i	0.787910	+	1.36470i	0.927245	+	0.374455i	$0.122170\pi$
$769$	21.8494	+	37.8443i	0.787910	+	1.36470i	−0.139335	+	0.990245i	$0.544496\pi$
$770$	9.39450	−	12.9436i	0.338554	−	0.466454i
$771$	11.2137	+	10.4485i	0.403853	+	0.376294i
$772$	−1.78104	−	3.08486i	−0.0641012	−	0.111026i
$773$	−9.05433	−	15.6826i	−0.325662	−	0.564062i	0.655984	−	0.754774i	$-0.272254\pi$
$773$	−9.05433	−	15.6826i	−0.325662	−	0.564062i	−0.981646	+	0.190712i	$0.938920\pi$
$774$	0.382883	+	5.41257i	0.0137624	+	0.194551i
$775$	−1.07598	+	1.86366i	−0.0386505	+	0.0669446i
$776$	−2.62324	+	4.54358i	−0.0941688	+	0.163105i
$777$	0.491480	+	0.564370i	0.0176317	+	0.0202467i
$778$	15.6500	+	27.1065i	0.561078	+	0.971816i
$779$	44.7677			1.60397
$780$	−4.21438	−	3.92679i	−0.150899	−	0.140602i
$781$	−33.7704			−1.20840
$782$	11.6195	−	20.1256i	0.415513	−	0.719690i
$783$	6.18716	+	16.0598i	0.221111	+	0.573932i
$784$	−8.79423	−	1.86039i	−0.314080	−	0.0664424i
$785$	0.347523	−	0.601927i	0.0124036	−	0.0214837i
$786$	−0.301235	+	1.30720i	−0.0107447	+	0.0466264i
$787$	−6.73109	+	11.6586i	−0.239937	+	0.415584i	−0.960696	−	0.277602i	$-0.910460\pi$
$787$	−6.73109	+	11.6586i	−0.239937	+	0.415584i	0.720759	+	0.693186i	$0.243794\pi$
$788$	−11.4482	+	19.8289i	−0.407825	+	0.706374i
$789$	−21.3472	−	19.8904i	−0.759980	−	0.708118i
$790$	3.65919	−	6.33790i	0.130188	−	0.225492i
$791$	−12.4126	+	17.1019i	−0.441341	+	0.608072i
$792$	−3.74641	−	52.9606i	−0.133123	−	1.88187i
$793$	−8.67156	+	15.0196i	−0.307936	+	0.533361i
$794$	32.0882			1.13877
$795$	−2.38493	+	10.3493i	−0.0845846	+	0.367053i
$796$	14.4757			0.513076
$797$	−23.8792	−	41.3600i	−0.845845	−	1.46505i	−0.884885	−	0.465809i	$-0.845763\pi$
$797$	−23.8792	−	41.3600i	−0.845845	−	1.46505i	0.0390399	−	0.999238i	$-0.487570\pi$
$798$	−7.62671	+	22.2136i	−0.269983	+	0.786354i
$799$	−12.1810	+	21.0981i	−0.430934	+	0.746399i
$800$	2.36683	−	4.09946i	0.0836799	−	0.144938i
$801$	5.45475	+	2.65500i	0.192734	+	0.0938098i
$802$	0.333490	+	0.577622i	0.0117759	+	0.0203965i
$803$	−31.6758	−	54.8641i	−1.11781	−	1.93611i
$804$	−5.86826	+	25.4652i	−0.206958	+	0.898089i
$805$	7.07305	+	15.8657i	0.249292	+	0.559192i
$806$	3.99451	+	6.91870i	0.140701	+	0.243701i
$807$	4.92507	−	21.3722i	0.173371	−	0.752338i
$808$	36.3276			1.27800
$809$	17.4794	+	30.2751i	0.614542	+	1.06442i	0.990465	+	0.137766i	$0.0439924\pi$
$809$	17.4794	+	30.2751i	0.614542	+	1.06442i	−0.375923	+	0.926651i	$0.622674\pi$
$810$	5.74974	+	7.33484i	0.202025	+	0.257720i
$811$	−42.8214			−1.50366			−0.751832	−	0.659355i	$-0.770830\pi$
$811$	−42.8214			−1.50366			−0.751832	+	0.659355i	$0.770830\pi$
$812$	4.77505	−	6.57898i	0.167572	−	0.230877i
$813$	40.0130	−	12.2509i	1.40332	−	0.429657i
$814$	−0.987200			−0.0346013
$815$	−6.74697	+	11.6861i	−0.236336	+	0.409346i
$816$	−7.26924	+	2.22564i	−0.254474	+	0.0779131i
$817$	−4.32227	−	7.48639i	−0.151217	−	0.261915i
$818$	−33.1140			−1.15780
$819$	−24.1509	−	15.0478i	−0.843901	−	0.525813i
$820$	−8.39100			−0.293026
$821$	−18.2492	−	31.6085i	−0.636900	−	1.10314i	−0.986109	−	0.166098i	$-0.946883\pi$
$821$	−18.2492	−	31.6085i	−0.636900	−	1.10314i	0.349209	−	0.937045i	$-0.386450\pi$
$822$	0.182987	−	0.794067i	0.00638239	−	0.0276963i
$823$	3.14542	−	5.44803i	0.109642	−	0.189906i	−0.805983	−	0.591939i	$-0.798363\pi$
$823$	3.14542	−	5.44803i	0.109642	−	0.189906i	0.915625	+	0.402032i	$0.131696\pi$
$824$	−48.4039			−1.68623
$825$	7.39743	+	6.89262i	0.257545	+	0.239970i
$826$	−3.56354	−	7.99344i	−0.123991	−	0.278127i
$827$	1.71886			0.0597708			0.0298854	−	0.999553i	$-0.490486\pi$
$827$	1.71886			0.0597708			0.0298854	+	0.999553i	$0.490486\pi$
$828$	16.4291	+	7.99659i	0.570952	+	0.277901i
$829$	−3.54597	−	6.14179i	−0.123157	−	0.213313i	0.797854	−	0.602850i	$-0.205968\pi$
$829$	−3.54597	−	6.14179i	−0.123157	−	0.213313i	−0.921011	+	0.389537i	$0.872635\pi$
$830$	−0.328015			−0.0113856
$831$	13.4662	+	12.5473i	0.467138	+	0.435260i
$832$	−13.3903	−	23.1927i	−0.464225	−	0.804061i
$833$	23.4083	+	4.95195i	0.811051	+	0.171575i
$834$	12.7973	−	3.91820i	0.443135	−	0.135676i
$835$	10.1631	+	17.6030i	0.351709	+	0.609178i
$836$	13.4008	+	23.2108i	0.463475	+	0.802762i
$837$	4.01991	+	10.4344i	0.138948	+	0.360665i
$838$	10.3093	−	17.8562i	0.356128	−	0.616831i
$839$	9.00448	−	15.5962i	0.310869	−	0.538441i	−0.667682	−	0.744447i	$-0.732713\pi$
$839$	9.00448	−	15.5962i	0.310869	−	0.538441i	0.978551	+	0.206006i	$0.0660465\pi$
$840$	4.51146	−	13.1401i	0.155660	−	0.453377i
$841$	9.01482	+	15.6141i	0.310856	+	0.538418i
$842$	25.7157			0.886221
$843$	23.7828	−	7.28164i	0.819122	−	0.250793i
$844$	−7.13859			−0.245720
$845$	−0.0737915	+	0.127811i	−0.00253850	+	0.00439682i
$846$	19.9092	+	9.69042i	0.684491	+	0.333164i
$847$	−24.8604	−	55.7647i	−0.854212	−	1.91610i
$848$	−3.93699	+	6.81906i	−0.135197	+	0.234168i
$849$	47.2273	−	14.4597i	1.62084	−	0.496257i
$850$	1.76976	−	3.06532i	0.0607024	−	0.105140i
$851$	0.536109	−	0.928568i	0.0183776	−	0.0318309i
$852$	−8.88790	+	2.72124i	−0.304495	+	0.0932280i
$853$	−1.41412	+	2.44933i	−0.0484185	+	0.0838634i	−0.889219	−	0.457482i	$-0.848751\pi$
$853$	−1.41412	+	2.44933i	−0.0484185	+	0.0838634i	0.840800	+	0.541345i	$0.182085\pi$
$854$	−13.1822	−	1.37906i	−0.451084	−	0.0471904i
$855$	−13.3504	−	6.49805i	−0.456573	−	0.222229i
$856$	−9.59652	+	16.6217i	−0.328002	+	0.568117i
$857$	38.2236			1.30569			0.652847	−	0.757490i	$-0.273575\pi$
$857$	38.2236			1.30569			0.652847	+	0.757490i	$0.273575\pi$
$858$	35.8914	−	10.9890i	1.22531	−	0.375157i
$859$	9.05085			0.308811			0.154406	−	0.988008i	$-0.450654\pi$
$859$	9.05085			0.308811			0.154406	+	0.988008i	$0.450654\pi$
$860$	0.810140	+	1.40320i	0.0276255	+	0.0478488i
$861$	−40.6823	+	7.94532i	−1.38645	+	0.270776i
$862$	1.79189	−	3.10365i	0.0610321	−	0.105711i
$863$	17.8144	−	30.8555i	0.606410	−	1.05033i	−0.385417	−	0.922742i	$-0.625942\pi$
$863$	17.8144	−	30.8555i	0.606410	−	1.05033i	0.991827	−	0.127590i	$-0.0407242\pi$
$864$	−8.84254	−	22.9524i	−0.300829	−	0.780855i
$865$	2.40292	+	4.16198i	0.0817018	+	0.141512i
$866$	−1.53270	−	2.65471i	−0.0520831	−	0.0902106i
$867$	−8.80563	+	2.69605i	−0.299055	+	0.0915625i
$868$	3.10244	−	4.27449i	0.105304	−	0.145086i
$869$	−20.6275	−	35.7280i	−0.699742	−	1.21199i
$870$	−4.34638	−	4.04978i	−0.147356	−	0.137301i
$871$	−58.3076			−1.97568
$872$	−19.7244	−	34.1637i	−0.667952	−	1.15693i
$873$	−4.66803	−	2.27208i	−0.157989	−	0.0768982i
$874$	33.6496			1.13822
$875$	1.07729	+	2.41649i	0.0364191	+	0.0816924i
$876$	−12.7576	−	11.8870i	−0.431040	−	0.401626i
$877$	3.01293			0.101739			0.0508697	−	0.998705i	$-0.483801\pi$
$877$	3.01293			0.101739			0.0508697	+	0.998705i	$0.483801\pi$
$878$	−0.791084	+	1.37020i	−0.0266978	+	0.0462419i
$879$	7.13248	−	30.9513i	0.240573	−	1.04396i
$880$	3.74805	+	6.49181i	0.126347	+	0.218839i
$881$	41.4228			1.39557			0.697785	−	0.716307i	$-0.254169\pi$
$881$	41.4228			1.39557			0.697785	+	0.716307i	$0.254169\pi$
$882$	2.98826	−	21.5400i	0.100620	−	0.725290i
$883$	−36.5932			−1.23146			−0.615730	−	0.787957i	$-0.711139\pi$
$883$	−36.5932			−1.23146			−0.615730	+	0.787957i	$0.711139\pi$
$884$	5.68370	+	9.84446i	0.191164	+	0.331105i
$885$	5.29036	−	1.61977i	0.177834	−	0.0544478i
$886$	−8.38694	+	14.5266i	−0.281765	+	0.488031i
$887$	−49.0382			−1.64654			−0.823272	−	0.567648i	$-0.807854\pi$
$887$	−49.0382			−1.64654			−0.823272	+	0.567648i	$0.807854\pi$
$888$	−0.819974	+	0.251054i	−0.0275165	+	0.00842482i
$889$	−13.4480	−	30.1654i	−0.451031	−	1.01172i
$890$	−2.09405			−0.0701929
$891$	52.0145	−	7.39598i	1.74255	−	0.247775i
$892$	−3.25001	−	5.62918i	−0.108818	−	0.188479i
$893$	−35.2757			−1.18046
$894$	−4.41725	+	19.1686i	−0.147735	+	0.641093i
$895$	5.55776	+	9.62632i	0.185775	+	0.321772i
$896$	−2.69125	+	3.70795i	−0.0899083	+	0.123874i
$897$	−9.15488	+	39.7274i	−0.305673	+	1.32646i
$898$	13.5143	+	23.4075i	0.450979	+	0.781119i
$899$	−3.56382	−	6.17272i	−0.118860	−	0.205872i
$900$	2.50231	+	1.21796i	0.0834105	+	0.0405985i
$901$	10.4794	−	18.1509i	0.349120	−	0.604693i
$902$	27.3394	−	47.3532i	0.910303	−	1.57669i
$903$	5.25649	+	6.03607i	0.174925	+	0.200868i
$904$	−12.1071	−	20.9702i	−0.402677	−	0.697457i
$905$	−13.1850			−0.438284
$906$	3.08708	−	13.3963i	0.102561	−	0.445063i
$907$	−30.4869			−1.01230			−0.506150	−	0.862445i	$-0.668932\pi$
$907$	−30.4869			−1.01230			−0.506150	+	0.862445i	$0.668932\pi$
$908$	−2.67467	+	4.63267i	−0.0887621	+	0.153740i
$909$	2.53659	+	35.8581i	0.0841332	+	1.18934i
$910$	9.76886	+	1.02197i	0.323834	+	0.0338781i
$911$	−24.2118	+	41.9360i	−0.802172	+	1.38940i	0.116012	+	0.993248i	$0.462989\pi$
$911$	−24.2118	+	41.9360i	−0.802172	+	1.38940i	−0.918184	+	0.396154i	$0.870345\pi$
$912$	−8.05377	−	7.50418i	−0.266687	−	0.248488i
$913$	−0.924542	+	1.60135i	−0.0305979	+	0.0529971i
$914$	−2.31761	+	4.01422i	−0.0766597	+	0.132779i
$915$	1.88158	−	8.16507i	0.0622031	−	0.269929i
$916$	−2.74012	+	4.74603i	−0.0905362	+	0.156813i
$917$	0.805723	+	1.80733i	0.0266073	+	0.0596834i
$918$	−6.61190	−	17.1623i	−0.218225	−	0.566441i
$919$	10.8008	−	18.7076i	0.356287	−	0.617107i	−0.631050	−	0.775742i	$-0.717376\pi$
$919$	10.8008	−	18.7076i	0.356287	−	0.617107i	0.987337	+	0.158635i	$0.0507093\pi$
$920$	−19.9049			−0.656245
$921$	−38.0218	−	35.4272i	−1.25286	−	1.16737i
$922$	3.59404			0.118364
$923$	−10.3698	−	17.9610i	−0.341325	−	0.591193i
$924$	−16.2972	−	18.7142i	−0.536140	−	0.615653i
$925$	0.0816545	−	0.141430i	0.00268478	−	0.00465018i
$926$	−14.5091	+	25.1304i	−0.476797	+	0.825837i
$927$	−3.37981	−	47.7783i	−0.111008	−	1.56924i
$928$	7.83929	+	13.5780i	0.257337	+	0.445721i
$929$	22.0154	+	38.1317i	0.722300	+	1.25106i	0.960076	+	0.279741i	$0.0902484\pi$
$929$	22.0154	+	38.1317i	0.722300	+	1.25106i	−0.237775	+	0.971320i	$0.576418\pi$
$930$	−2.82393	−	2.63122i	−0.0926002	−	0.0862811i
$931$	10.7377	+	32.9389i	0.351914	+	1.07953i
$932$	10.1414	+	17.5654i	0.332191	+	0.575372i
$933$	−16.3056	+	4.99232i	−0.533820	+	0.163441i
$934$	−14.1306			−0.462366
$935$	−9.97650	−	17.2798i	−0.326266	−	0.565110i
$936$	27.0170	−	18.2550i	0.883079	−	0.596684i
$937$	6.39390			0.208880			0.104440	−	0.994531i	$-0.466695\pi$
$937$	6.39390			0.208880			0.104440	+	0.994531i	$0.466695\pi$
$938$	−18.1440	−	40.6991i	−0.592422	−	1.32887i
$939$	8.94783	−	38.8290i	0.292002	−	1.26714i
$940$	6.61186			0.215655
$941$	2.62442	−	4.54564i	0.0855538	−	0.148184i	−0.820073	−	0.572259i	$-0.806067\pi$
$941$	2.62442	−	4.54564i	0.0855538	−	0.148184i	0.905627	+	0.424075i	$0.139401\pi$
$942$	0.912076	+	0.849835i	0.0297170	+	0.0276891i
$943$	29.6939	+	51.4313i	0.966967	+	1.67484i
$944$	4.10193			0.133507
$945$	13.2853	+	3.53564i	0.432171	+	0.115014i
$946$	−10.5583			−0.343281
$947$	7.49809	+	12.9871i	0.243655	+	0.422023i	0.961753	−	0.273919i	$-0.0883202\pi$
$947$	7.49809	+	12.9871i	0.243655	+	0.422023i	−0.718097	+	0.695943i	$0.754987\pi$
$948$	−8.30787	−	7.74094i	−0.269827	−	0.251414i
$949$	19.4532	−	33.6939i	0.631478	−	1.09375i
$950$	5.12516			0.166282
$951$	2.84020	−	12.3250i	0.0920999	−	0.399666i
$952$	−16.1044	+	22.1884i	−0.521947	+	0.719129i
$953$	−26.1263			−0.846315			−0.423158	−	0.906056i	$-0.639078\pi$
$953$	−26.1263			−0.846315			−0.423158	+	0.906056i	$0.639078\pi$
$954$	−17.1280	−	8.33674i	−0.554539	−	0.269912i
$955$	11.5066	+	19.9300i	0.372345	+	0.644920i
$956$	0.901392			0.0291531
$957$	−32.0216	+	9.80413i	−1.03511	+	0.316923i
$958$	−3.94706	−	6.83651i	−0.127524	−	0.220878i
$959$	−0.489440	−	1.09787i	−0.0158048	−	0.0354521i
$960$	9.46628	+	8.82030i	0.305523	+	0.284674i
$961$	13.1845	+	22.8363i	0.425307	+	0.736654i
$962$	−0.303137	−	0.525048i	−0.00977352	−	0.0169282i
$963$	−17.0769	−	8.31188i	−0.550296	−	0.267847i
$964$	13.5487	−	23.4671i	0.436376	−	0.755825i
$965$	−1.91993	+	3.32541i	−0.0618047	+	0.107049i
$966$	−30.5788	+	5.97209i	−0.983856	+	0.192149i
$967$	27.3517	+	47.3745i	0.879572	+	1.52346i	0.851812	+	0.523848i	$0.175504\pi$
$967$	27.3517	+	47.3745i	0.879572	+	1.52346i	0.0277597	+	0.999615i	$0.491163\pi$
$968$	69.9618			2.24866
$969$	21.4374	+	19.9745i	0.688668	+	0.641673i
$970$	1.79204			0.0575389
$971$	−9.25478	+	16.0297i	−0.297000	+	0.514419i	−0.975448	−	0.220229i	$-0.929319\pi$
$971$	−9.25478	+	16.0297i	−0.297000	+	0.514419i	0.678448	+	0.734648i	$0.262653\pi$
$972$	13.0936	−	6.13789i	0.419976	−	0.196873i
$973$	11.5965	−	15.9775i	0.371768	−	0.512216i
$974$	−13.0611	+	22.6225i	−0.418505	+	0.724872i
$975$	−1.39438	+	6.05087i	−0.0446558	+	0.193783i
$976$	3.10607	−	5.37987i	0.0994229	−	0.172206i
$977$	−1.28412	+	2.22416i	−0.0410827	+	0.0711573i	−0.885836	−	0.463999i	$-0.846414\pi$
$977$	−1.28412	+	2.22416i	−0.0410827	+	0.0711573i	0.844753	+	0.535157i	$0.179747\pi$
$978$	−17.7075	−	16.4991i	−0.566223	−	0.527583i
$979$	−5.90229	+	10.2231i	−0.188638	+	0.326731i
$980$	−2.01261	−	6.17386i	−0.0642905	−	0.197217i
$981$	32.3449	−	21.8550i	1.03269	−	0.697775i
$982$	−20.5123	+	35.5283i	−0.654573	+	1.13375i
$983$	1.99771			0.0637170			0.0318585	−	0.999492i	$-0.489857\pi$
$983$	1.99771			0.0637170			0.0318585	+	0.999492i	$0.489857\pi$
$984$	10.6659	−	46.2845i	0.340017	−	1.47550i
$985$	24.6818			0.786429
$986$	5.86173	+	10.1528i	0.186675	+	0.323331i
$987$	32.0565	−	6.26068i	1.02037	−	0.199280i
$988$	−8.22987	+	14.2545i	−0.261827	+	0.453498i
$989$	5.73382	−	9.93126i	0.182325	−	0.315796i
$990$	−15.0263	+	10.1531i	−0.477568	+	0.322686i
$991$	17.7719	+	30.7819i	0.564545	+	0.977820i	0.997092	+	0.0762087i	$0.0242815\pi$
$991$	17.7719	+	30.7819i	0.564545	+	0.977820i	−0.432547	+	0.901611i	$0.642385\pi$
$992$	5.09333	+	8.82190i	0.161713	+	0.280096i
$993$	11.8855	−	51.5770i	0.377176	−	1.63675i
$994$	9.31004	−	12.8272i	0.295296	−	0.406854i
$995$	−7.80224	−	13.5139i	−0.247348	−	0.428419i
$996$	−0.114289	+	0.495955i	−0.00362139	+	0.0157149i
$997$	−12.8569			−0.407181			−0.203590	−	0.979056i	$-0.565261\pi$
$997$	−12.8569			−0.407181			−0.203590	+	0.979056i	$0.565261\pi$
$998$	−22.8607	−	39.5959i	−0.723644	−	1.25339i
$999$	−0.305064	−	0.791847i	−0.00965180	−	0.0250529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.16.9	✓	24
3.2	odd	2		945.2.k.b.856.4		24
7.4	even	3		315.2.l.b.151.4	yes	24
9.4	even	3		315.2.l.b.121.4	yes	24
9.5	odd	6		945.2.l.b.226.9		24
21.11	odd	6		945.2.l.b.46.9		24
63.4	even	3	inner	315.2.k.b.256.9	yes	24
63.32	odd	6		945.2.k.b.361.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.9	✓	24	1.1	even	1	trivial
315.2.k.b.256.9	yes	24	63.4	even	3	inner
315.2.l.b.121.4	yes	24	9.4	even	3
315.2.l.b.151.4	yes	24	7.4	even	3
945.2.k.b.361.4		24	63.32	odd	6
945.2.k.b.856.4		24	3.2	odd	2
945.2.l.b.46.9		24	21.11	odd	6
945.2.l.b.226.9		24	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.517769 + 0.896802i) q^{2} +(-1.26722 - 1.18074i) q^{3} +(0.463831 - 0.803378i) q^{4} -1.00000 q^{5} +(0.402766 - 1.74780i) q^{6} +(-1.07729 - 2.41649i) q^{7} +3.03170 q^{8} +(0.211690 + 2.99252i) q^{9} +O(q^{10})\)	\(q+(0.517769 + 0.896802i) q^{2} +(-1.26722 - 1.18074i) q^{3} +(0.463831 - 0.803378i) q^{4} -1.00000 q^{5} +(0.402766 - 1.74780i) q^{6} +(-1.07729 - 2.41649i) q^{7} +3.03170 q^{8} +(0.211690 + 2.99252i) q^{9} +(-0.517769 - 0.896802i) q^{10} -5.83753 q^{11} +(-1.53636 + 0.470391i) q^{12} +(-1.79251 - 3.10472i) q^{13} +(1.60933 - 2.21730i) q^{14} +(1.26722 + 1.18074i) q^{15} +(0.642061 + 1.11208i) q^{16} +(-1.70903 - 2.96012i) q^{17} +(-2.57409 + 1.73928i) q^{18} +(2.47463 - 4.28619i) q^{19} +(-0.463831 + 0.803378i) q^{20} +(-1.48809 + 4.33423i) q^{21} +(-3.02249 - 5.23511i) q^{22} +6.56558 q^{23} +(-3.84183 - 3.57967i) q^{24} +1.00000 q^{25} +(1.85622 - 3.21506i) q^{26} +(3.26514 - 4.04213i) q^{27} +(-2.44104 - 0.255371i) q^{28} +(-1.65608 + 2.86841i) q^{29} +(-0.402766 + 1.74780i) q^{30} +(-1.07598 + 1.86366i) q^{31} +(2.36683 - 4.09946i) q^{32} +(7.39743 + 6.89262i) q^{33} +(1.76976 - 3.06532i) q^{34} +(1.07729 + 2.41649i) q^{35} +(2.50231 + 1.21796i) q^{36} +(0.0816545 - 0.141430i) q^{37} +5.12516 q^{38} +(-1.39438 + 6.05087i) q^{39} -3.03170 q^{40} +(4.52266 + 7.83348i) q^{41} +(-4.65744 + 0.909606i) q^{42} +(0.873314 - 1.51262i) q^{43} +(-2.70762 + 4.68974i) q^{44} +(-0.211690 - 2.99252i) q^{45} +(3.39945 + 5.88803i) q^{46} +(-3.56373 - 6.17256i) q^{47} +(0.499452 - 2.16736i) q^{48} +(-4.67888 + 5.20654i) q^{49} +(0.517769 + 0.896802i) q^{50} +(-1.32943 + 5.76905i) q^{51} -3.32569 q^{52} +(3.06590 + 5.31029i) q^{53} +(5.31558 + 0.835297i) q^{54} +5.83753 q^{55} +(-3.26603 - 7.32609i) q^{56} +(-8.19680 + 2.50964i) q^{57} -3.42986 q^{58} +(1.59717 - 2.76639i) q^{59} +(1.53636 - 0.470391i) q^{60} +(-2.41883 - 4.18953i) q^{61} -2.22844 q^{62} +(7.00336 - 3.73537i) q^{63} +7.47012 q^{64} +(1.79251 + 3.10472i) q^{65} +(-2.35116 + 10.2028i) q^{66} +(8.13210 - 14.0852i) q^{67} -3.17080 q^{68} +(-8.32003 - 7.75227i) q^{69} +(-1.60933 + 2.21730i) q^{70} +5.78505 q^{71} +(0.641780 + 9.07244i) q^{72} +(5.42624 + 9.39852i) q^{73} +0.169113 q^{74} +(-1.26722 - 1.18074i) q^{75} +(-2.29562 - 3.97613i) q^{76} +(6.28872 + 14.1063i) q^{77} +(-6.14839 + 1.88247i) q^{78} +(3.53361 + 6.12039i) q^{79} +(-0.642061 - 1.11208i) q^{80} +(-8.91038 + 1.26697i) q^{81} +(-4.68339 + 8.11187i) q^{82} +(0.158379 - 0.274321i) q^{83} +(2.79181 + 3.20585i) q^{84} +(1.70903 + 2.96012i) q^{85} +1.80870 q^{86} +(5.48547 - 1.67950i) q^{87} -17.6977 q^{88} +(1.01109 - 1.75127i) q^{89} +(2.57409 - 1.73928i) q^{90} +(-5.57149 + 7.67629i) q^{91} +(3.04532 - 5.27464i) q^{92} +(3.56401 - 1.09120i) q^{93} +(3.69037 - 6.39191i) q^{94} +(-2.47463 + 4.28619i) q^{95} +(-7.83970 + 2.40030i) q^{96} +(-0.865269 + 1.49869i) q^{97} +(-7.09182 - 1.50025i) q^{98} +(-1.23574 - 17.4689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more