LMFDB - Embedded newform 592.2.ca.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(19,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 35]))

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

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

chi := DirichletCharacter("592.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.ca (of order $36$, degree $12$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$888$
Relative dimension:	$74$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	592.19
Dual form			592.2.ca.a.187.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39566 - 0.228297i) q^{2} +(-3.32903 - 0.291252i) q^{3} +(1.89576 + 0.637253i) q^{4} +(-2.93393 - 1.06786i) q^{5} +(4.57972 + 1.16650i) q^{6} +(0.0360796 + 0.0131319i) q^{7} +(-2.50036 - 1.32219i) q^{8} +(8.04320 + 1.41823i) q^{9} +O(q^{10})$	\(q+(-1.39566 - 0.228297i) q^{2} +(-3.32903 - 0.291252i) q^{3} +(1.89576 + 0.637253i) q^{4} +(-2.93393 - 1.06786i) q^{5} +(4.57972 + 1.16650i) q^{6} +(0.0360796 + 0.0131319i) q^{7} +(-2.50036 - 1.32219i) q^{8} +(8.04320 + 1.41823i) q^{9} +(3.85099 + 2.16019i) q^{10} +(0.601420 + 2.24453i) q^{11} +(-6.12545 - 2.67358i) q^{12} +(1.48282 - 0.261460i) q^{13} +(-0.0473570 - 0.0265646i) q^{14} +(9.45612 + 4.40946i) q^{15} +(3.18782 + 2.41616i) q^{16} +(3.57469 - 2.50302i) q^{17} +(-10.9018 - 3.81562i) q^{18} +(-0.413071 + 0.346608i) q^{19} +(-4.88153 - 3.89407i) q^{20} +(-0.116285 - 0.0542247i) q^{21} +(-0.326961 - 3.26992i) q^{22} +(-0.182396 + 0.680712i) q^{23} +(7.93870 + 5.12984i) q^{24} +(3.63738 + 3.05213i) q^{25} +(-2.12921 + 0.0263884i) q^{26} +(-16.6794 - 4.46922i) q^{27} +(0.0600299 + 0.0478867i) q^{28} +(-2.81258 + 4.87153i) q^{29} +(-12.1909 - 8.31294i) q^{30} +(2.84603 + 2.84603i) q^{31} +(-3.89752 - 4.09992i) q^{32} +(-1.34842 - 7.64728i) q^{33} +(-5.56050 + 2.67729i) q^{34} +(-0.0918318 - 0.0770560i) q^{35} +(14.3442 + 7.81418i) q^{36} +(5.42909 - 2.74316i) q^{37} +(0.655638 - 0.389445i) q^{38} +(-5.01249 + 0.438536i) q^{39} +(5.92397 + 6.54925i) q^{40} +(-1.84995 - 10.4916i) q^{41} +(0.149916 + 0.102227i) q^{42} -4.20916i q^{43} +(-0.290185 + 4.63835i) q^{44} +(-22.0837 - 12.7500i) q^{45} +(0.409968 - 0.908405i) q^{46} +(-10.1387 + 5.85359i) q^{47} +(-9.90863 - 8.97192i) q^{48} +(-5.36118 - 4.49857i) q^{49} +(-4.37978 - 5.09015i) q^{50} +(-12.6293 + 7.29150i) q^{51} +(2.97768 + 0.449262i) q^{52} +(3.17173 - 6.80181i) q^{53} +(22.2585 + 10.0454i) q^{54} +(0.632327 - 7.22753i) q^{55} +(-0.0728492 - 0.0805385i) q^{56} +(1.47608 - 1.03356i) q^{57} +(5.03758 - 6.15692i) q^{58} +(-3.42095 - 9.39899i) q^{59} +(15.1166 + 14.3852i) q^{60} +(2.05594 + 11.6598i) q^{61} +(-3.32237 - 4.62185i) q^{62} +(0.271571 + 0.156792i) q^{63} +(4.50364 + 6.61190i) q^{64} +(-4.62968 - 0.816338i) q^{65} +(0.136092 + 10.9809i) q^{66} +(3.20279 + 6.86840i) q^{67} +(8.37181 - 2.46715i) q^{68} +(0.805461 - 2.21299i) q^{69} +(0.110575 + 0.128509i) q^{70} +(-8.34927 + 7.00587i) q^{71} +(-18.2357 - 14.1807i) q^{72} -13.4393 q^{73} +(-8.20345 + 2.58909i) q^{74} +(-11.2200 - 11.2200i) q^{75} +(-1.00396 + 0.393855i) q^{76} +(-0.00777595 + 0.0888795i) q^{77} +(7.09588 + 0.532288i) q^{78} +(5.62287 - 2.62199i) q^{79} +(-6.77270 - 10.4930i) q^{80} +(31.2002 + 11.3560i) q^{81} +(0.186710 + 15.0651i) q^{82} +(-4.03651 - 5.76473i) q^{83} +(-0.185894 - 0.176900i) q^{84} +(-13.1608 + 3.52641i) q^{85} +(-0.960939 + 5.87457i) q^{86} +(10.7820 - 15.3983i) q^{87} +(1.46392 - 6.40733i) q^{88} +(8.87990 + 4.14077i) q^{89} +(27.9106 + 22.8364i) q^{90} +(0.0569328 + 0.0100388i) q^{91} +(-0.779565 + 1.17423i) q^{92} +(-8.64562 - 10.3035i) q^{93} +(15.4866 - 5.85500i) q^{94} +(1.58205 - 0.575819i) q^{95} +(11.7809 + 14.7839i) q^{96} +(0.168124 - 0.627446i) q^{97} +(6.45540 + 7.50243i) q^{98} +(1.65407 + 18.9062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 888 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 24 q^{8}+O(q^{10}) $ 888 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 24 * q^7 - 24 * q^8	\( 888 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 24 q^{8} - 6 q^{10} - 18 q^{11} + 18 q^{12} - 12 q^{13} - 12 q^{14} + 18 q^{16} - 24 q^{17} - 120 q^{18} - 12 q^{19} - 12 q^{20} - 12 q^{21} - 42 q^{22} - 24 q^{23} - 24 q^{24} - 6 q^{26} - 18 q^{27} - 42 q^{28} - 6 q^{29} - 78 q^{30} + 24 q^{32} - 24 q^{33} - 12 q^{34} - 12 q^{35} + 36 q^{37} - 108 q^{38} - 24 q^{39} + 18 q^{40} - 30 q^{42} - 96 q^{44} - 18 q^{45} + 48 q^{46} - 18 q^{48} - 24 q^{49} + 30 q^{50} - 198 q^{51} - 12 q^{52} - 36 q^{53} + 18 q^{54} - 24 q^{55} + 156 q^{56} - 84 q^{58} - 12 q^{59} + 144 q^{60} - 12 q^{61} - 12 q^{62} - 144 q^{64} + 24 q^{66} - 12 q^{67} + 138 q^{68} + 6 q^{69} + 60 q^{70} - 24 q^{71} - 180 q^{72} + 48 q^{73} - 54 q^{74} - 24 q^{75} + 96 q^{76} - 30 q^{77} + 60 q^{78} - 144 q^{80} - 24 q^{81} - 36 q^{82} + 48 q^{83} - 12 q^{84} - 18 q^{85} + 12 q^{86} - 192 q^{87} - 120 q^{88} - 48 q^{89} - 78 q^{90} - 12 q^{91} + 336 q^{92} + 24 q^{93} - 60 q^{94} - 126 q^{96} - 24 q^{97} + 42 q^{98} - 210 q^{99}+O(q^{100}) \) 888 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 24 * q^7 - 24 * q^8 - 6 * q^10 - 18 * q^11 + 18 * q^12 - 12 * q^13 - 12 * q^14 + 18 * q^16 - 24 * q^17 - 120 * q^18 - 12 * q^19 - 12 * q^20 - 12 * q^21 - 42 * q^22 - 24 * q^23 - 24 * q^24 - 6 * q^26 - 18 * q^27 - 42 * q^28 - 6 * q^29 - 78 * q^30 + 24 * q^32 - 24 * q^33 - 12 * q^34 - 12 * q^35 + 36 * q^37 - 108 * q^38 - 24 * q^39 + 18 * q^40 - 30 * q^42 - 96 * q^44 - 18 * q^45 + 48 * q^46 - 18 * q^48 - 24 * q^49 + 30 * q^50 - 198 * q^51 - 12 * q^52 - 36 * q^53 + 18 * q^54 - 24 * q^55 + 156 * q^56 - 84 * q^58 - 12 * q^59 + 144 * q^60 - 12 * q^61 - 12 * q^62 - 144 * q^64 + 24 * q^66 - 12 * q^67 + 138 * q^68 + 6 * q^69 + 60 * q^70 - 24 * q^71 - 180 * q^72 + 48 * q^73 - 54 * q^74 - 24 * q^75 + 96 * q^76 - 30 * q^77 + 60 * q^78 - 144 * q^80 - 24 * q^81 - 36 * q^82 + 48 * q^83 - 12 * q^84 - 18 * q^85 + 12 * q^86 - 192 * q^87 - 120 * q^88 - 48 * q^89 - 78 * q^90 - 12 * q^91 + 336 * q^92 + 24 * q^93 - 60 * q^94 - 126 * q^96 - 24 * q^97 + 42 * q^98 - 210 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.39566	−	0.228297i	−0.986884	−	0.161431i
$2$	−1.39566	−	0.228297i	−0.986884	−	0.161431i
$3$	−3.32903	−	0.291252i	−1.92202	−	0.168155i	−0.938049	−	0.346501i	$-0.887370\pi$
$3$	−3.32903	−	0.291252i	−1.92202	−	0.168155i	−0.983968	+	0.178347i	$0.942925\pi$
$4$	1.89576	+	0.637253i	0.947880	+	0.318626i
$5$	−2.93393	−	1.06786i	−1.31209	−	0.477563i	−0.411176	−	0.911556i	$-0.634882\pi$
$5$	−2.93393	−	1.06786i	−1.31209	−	0.477563i	−0.900916	+	0.433993i	$0.857104\pi$
$6$	4.57972	+	1.16650i	1.86966	+	0.476221i
$7$	0.0360796	+	0.0131319i	0.0136368	+	0.00496339i	0.348830	−	0.937186i	$-0.386579\pi$
$7$	0.0360796	+	0.0131319i	0.0136368	+	0.00496339i	−0.335193	+	0.942150i	$0.608801\pi$
$8$	−2.50036	−	1.32219i	−0.884012	−	0.467464i
$9$	8.04320	+	1.41823i	2.68107	+	0.472744i
$10$	3.85099	+	2.16019i	1.21779	+	0.683111i
$11$	0.601420	+	2.24453i	0.181335	+	0.676752i	0.995385	+	0.0959573i	$0.0305912\pi$
$11$	0.601420	+	2.24453i	0.181335	+	0.676752i	−0.814050	+	0.580794i	$0.802742\pi$
$12$	−6.12545	−	2.67358i	−1.76826	−	0.771796i
$13$	1.48282	−	0.261460i	0.411259	−	0.0725161i	0.0358090	−	0.999359i	$-0.488599\pi$
$13$	1.48282	−	0.261460i	0.411259	−	0.0725161i	0.375450	+	0.926843i	$0.377488\pi$
$14$	−0.0473570	−	0.0265646i	−0.0126567	−	0.00709968i
$15$	9.45612	+	4.40946i	2.44156	+	1.13852i
$16$	3.18782	+	2.41616i	0.796954	+	0.604039i
$17$	3.57469	−	2.50302i	0.866989	−	0.607072i	−0.0531840	−	0.998585i	$-0.516937\pi$
$17$	3.57469	−	2.50302i	0.866989	−	0.607072i	0.920173	+	0.391513i	$0.128048\pi$
$18$	−10.9018	−	3.81562i	−2.56959	−	0.899350i
$19$	−0.413071	+	0.346608i	−0.0947650	+	0.0795172i	−0.688939	−	0.724819i	$-0.741923\pi$
$19$	−0.413071	+	0.346608i	−0.0947650	+	0.0795172i	0.594174	+	0.804336i	$0.297479\pi$
$20$	−4.88153	−	3.89407i	−1.09154	−	0.870740i
$21$	−0.116285	−	0.0542247i	−0.0253755	−	0.0118328i
$22$	−0.326961	−	3.26992i	−0.0697083	−	0.697148i
$23$	−0.182396	+	0.680712i	−0.0380322	+	0.141938i	−0.982331	−	0.187150i	$-0.940075\pi$
$23$	−0.182396	+	0.680712i	−0.0380322	+	0.141938i	0.944299	+	0.329089i	$0.106741\pi$
$24$	7.93870	+	5.12984i	1.62048	+	1.04712i
$25$	3.63738	+	3.05213i	0.727477	+	0.610425i
$26$	−2.12921	+	0.0263884i	−0.417571	+	0.00517519i
$27$	−16.6794	−	4.46922i	−3.20994	−	0.860102i
$28$	0.0600299	+	0.0478867i	0.0113446	+	0.00904974i
$29$	−2.81258	+	4.87153i	−0.522283	+	0.904620i	0.477381	+	0.878696i	$0.341586\pi$
$29$	−2.81258	+	4.87153i	−0.522283	+	0.904620i	−0.999664	+	0.0259241i	$0.991747\pi$
$30$	−12.1909	−	8.31294i	−2.22575	−	1.51773i
$31$	2.84603	+	2.84603i	0.511163	+	0.511163i	0.914883	−	0.403720i	$-0.132283\pi$
$31$	2.84603	+	2.84603i	0.511163	+	0.511163i	−0.403720	+	0.914883i	$0.632283\pi$
$32$	−3.89752	−	4.09992i	−0.688991	−	0.724770i
$33$	−1.34842	−	7.64728i	−0.234730	−	1.33122i
$34$	−5.56050	+	2.67729i	−0.953617	+	0.459151i
$35$	−0.0918318	−	0.0770560i	−0.0155224	−	0.0130248i
$36$	14.3442	+	7.81418i	2.39070	+	1.30236i
$37$	5.42909	−	2.74316i	0.892537	−	0.450973i
$37$	5.42909	−	2.74316i	0.892537	−	0.450973i
$38$	0.655638	−	0.389445i	0.106359	−	0.0631763i
$39$	−5.01249	+	0.438536i	−0.802641	+	0.0702220i
$40$	5.92397	+	6.54925i	0.936662	+	1.03553i
$41$	−1.84995	−	10.4916i	−0.288914	−	1.63851i	−0.690959	−	0.722894i	$-0.742812\pi$
$41$	−1.84995	−	10.4916i	−0.288914	−	1.63851i	0.402045	−	0.915620i	$-0.368300\pi$
$42$	0.149916	+	0.102227i	0.0231325	+	0.0157740i
$43$		−	4.20916i		−	0.641890i	−0.947098	−	0.320945i	$-0.895999\pi$
$43$		−	4.20916i		−	0.641890i	0.947098	−	0.320945i	$-0.104001\pi$
$44$	−0.290185	+	4.63835i	−0.0437470	+	0.699258i
$45$	−22.0837	−	12.7500i	−3.29204	−	1.90066i
$46$	0.409968	−	0.908405i	0.0604466	−	0.133937i
$47$	−10.1387	+	5.85359i	−1.47888	+	0.853833i	−0.999715	−	0.0238900i	$-0.992395\pi$
$47$	−10.1387	+	5.85359i	−1.47888	+	0.853833i	−0.479168	+	0.877723i	$0.659062\pi$
$48$	−9.90863	−	8.97192i	−1.43019	−	1.29499i
$49$	−5.36118	−	4.49857i	−0.765883	−	0.642652i
$50$	−4.37978	−	5.09015i	−0.619394	−	0.719856i
$51$	−12.6293	+	7.29150i	−1.76845	+	1.02101i
$52$	2.97768	+	0.449262i	0.412930	+	0.0623015i
$53$	3.17173	−	6.80181i	0.435671	−	0.934300i	−0.558801	−	0.829302i	$-0.688739\pi$
$53$	3.17173	−	6.80181i	0.435671	−	0.934300i	0.994472	−	0.104998i	$-0.0334837\pi$
$54$	22.2585	+	10.0454i	3.02900	+	1.36700i
$55$	0.632327	−	7.22753i	0.0852629	−	0.974560i
$56$	−0.0728492	−	0.0805385i	−0.00973488	−	0.0107624i
$57$	1.47608	−	1.03356i	0.195511	−	0.136898i
$58$	5.03758	−	6.15692i	0.661466	−	0.808443i
$59$	−3.42095	−	9.39899i	−0.445370	−	1.22364i	−0.935914	−	0.352228i	$-0.885424\pi$
$59$	−3.42095	−	9.39899i	−0.445370	−	1.22364i	0.490544	−	0.871416i	$-0.336798\pi$
$60$	15.1166	+	14.3852i	1.95155	+	1.85712i
$61$	2.05594	+	11.6598i	0.263236	+	1.49289i	0.774010	+	0.633173i	$0.218248\pi$
$61$	2.05594	+	11.6598i	0.263236	+	1.49289i	−0.510774	+	0.859715i	$0.670641\pi$
$62$	−3.32237	−	4.62185i	−0.421941	−	0.586976i
$63$	0.271571	+	0.156792i	0.0342147	+	0.0197539i
$64$	4.50364	+	6.61190i	0.562955	+	0.826488i
$65$	−4.62968	−	0.816338i	−0.574241	−	0.101254i
$66$	0.136092	+	10.9809i	0.0167518	+	1.35165i
$67$	3.20279	+	6.86840i	0.391283	+	0.839109i	0.998989	+	0.0449470i	$0.0143119\pi$
$67$	3.20279	+	6.86840i	0.391283	+	0.839109i	−0.607707	+	0.794162i	$0.707910\pi$
$68$	8.37181	−	2.46715i	1.01523	−	0.299186i
$69$	0.805461	−	2.21299i	0.0969662	−	0.266412i
$70$	0.110575	+	0.128509i	0.0132162	+	0.0153598i
$71$	−8.34927	+	7.00587i	−0.990876	+	0.831444i	−0.985694	−	0.168543i	$-0.946094\pi$
$71$	−8.34927	+	7.00587i	−0.990876	+	0.831444i	−0.00518198	+	0.999987i	$0.501649\pi$
$72$	−18.2357	−	14.1807i	−2.14910	−	1.67121i
$73$	−13.4393			−1.57295			−0.786476	−	0.617620i	$-0.788097\pi$
$73$	−13.4393			−1.57295			−0.786476	+	0.617620i	$0.788097\pi$
$74$	−8.20345	+	2.58909i	−0.953632	+	0.300976i
$75$	−11.2200	−	11.2200i	−1.29558	−	1.29558i
$76$	−1.00396	+	0.393855i	−0.115162	+	0.0451782i
$77$	−0.00777595	+	0.0888795i	−0.000886151	+	0.0101288i
$78$	7.09588	+	0.532288i	0.803450	+	0.0602698i
$79$	5.62287	−	2.62199i	0.632622	−	0.294997i	−0.0797323	−	0.996816i	$-0.525407\pi$
$79$	5.62287	−	2.62199i	0.632622	−	0.294997i	0.712355	+	0.701820i	$0.247629\pi$
$80$	−6.77270	−	10.4930i	−0.757211	−	1.17315i
$81$	31.2002	+	11.3560i	3.46669	+	1.26177i
$82$	0.186710	+	15.0651i	0.0206187	+	1.66366i
$83$	−4.03651	−	5.76473i	−0.443064	−	0.632761i	0.534056	−	0.845449i	$-0.320667\pi$
$83$	−4.03651	−	5.76473i	−0.443064	−	0.632761i	−0.977120	+	0.212688i	$0.931778\pi$
$84$	−0.185894	−	0.176900i	−0.0202827	−	0.0193014i
$85$	−13.1608	+	3.52641i	−1.42748	+	0.382493i
$86$	−0.960939	+	5.87457i	−0.103621	+	0.633472i
$87$	10.7820	−	15.3983i	1.15595	−	1.65087i
$88$	1.46392	−	6.40733i	0.156055	−	0.683024i
$89$	8.87990	+	4.14077i	0.941267	+	0.438920i	0.831803	−	0.555071i	$-0.187309\pi$
$89$	8.87990	+	4.14077i	0.941267	+	0.438920i	0.109464	+	0.993991i	$0.465087\pi$
$90$	27.9106	+	22.8364i	2.94204	+	2.40717i
$91$	0.0569328	+	0.0100388i	0.00596818	+	0.00105235i
$92$	−0.779565	+	1.17423i	−0.0812753	+	0.122422i
$93$	−8.64562	−	10.3035i	−0.896509	−	1.06842i
$94$	15.4866	−	5.85500i	1.59732	−	0.603898i
$95$	1.58205	−	0.575819i	0.162315	−	0.0590778i
$96$	11.7809	+	14.7839i	1.20238	+	1.50888i
$97$	0.168124	−	0.627446i	0.0170704	−	0.0637075i	−0.956865	−	0.290532i	$-0.906168\pi$
$97$	0.168124	−	0.627446i	0.0170704	−	0.0637075i	0.973936	+	0.226825i	$0.0728344\pi$
$98$	6.45540	+	7.50243i	0.652094	+	0.757860i
$99$	1.65407	+	18.9062i	0.166241	+	1.90014i
$100$	4.95063	+	8.10404i	0.495063	+	0.810404i
$101$	2.65262	−	9.89972i	0.263946	−	0.985059i	−0.698947	−	0.715174i	$-0.746348\pi$
$101$	2.65262	−	9.89972i	0.263946	−	0.985059i	0.962893	−	0.269885i	$-0.0869857\pi$
$102$	19.2908	−	7.29327i	1.91008	−	0.722141i
$103$	−2.82957	−	10.5601i	−0.278805	−	1.04052i	−0.953248	−	0.302189i	$-0.902283\pi$
$103$	−2.82957	−	10.5601i	−0.278805	−	1.04052i	0.674443	−	0.738327i	$-0.264384\pi$
$104$	−4.05328	−	1.30682i	−0.397457	−	0.128144i
$105$	0.283268	+	0.283268i	0.0276441	+	0.0276441i
$106$	−5.97951	+	8.76894i	−0.580781	+	0.851715i
$107$	−2.13051	+	3.04269i	−0.205964	+	0.294148i	−0.908823	−	0.417182i	$-0.863018\pi$
$107$	−2.13051	+	3.04269i	−0.205964	+	0.294148i	0.702859	+	0.711330i	$0.251907\pi$
$108$	−28.7720	−	19.1015i	−2.76859	−	1.83805i
$109$	8.99496	−	10.7198i	0.861561	−	1.02677i	−0.137780	−	0.990463i	$-0.543997\pi$
$109$	8.99496	−	10.7198i	0.861561	−	1.02677i	0.999341	−	0.0363055i	$-0.0115589\pi$
$110$	−2.53254	+	9.94285i	−0.241468	+	0.948013i
$111$	−18.8726	+	7.55084i	−1.79131	+	0.716694i
$112$	0.0832864	+	0.129036i	0.00786982	+	0.0121928i
$113$	−1.09383	+	0.0956975i	−0.102899	+	0.00900246i	−0.138489	−	0.990364i	$-0.544224\pi$
$113$	−1.09383	+	0.0956975i	−0.102899	+	0.00900246i	0.0355901	+	0.999366i	$0.488669\pi$
$114$	−2.29607	+	1.10552i	−0.215046	+	0.103541i
$115$	1.26204	−	1.80239i	0.117686	−	0.168073i
$116$	−8.43637	+	7.44293i	−0.783298	+	0.691059i
$117$	12.2974			1.13689
$118$	2.62874	+	13.8988i	0.241995	+	1.27949i
$119$	0.161843	−	0.0433656i	0.0148361	−	0.00397532i
$120$	−17.8136	−	23.5280i	−1.62615	−	2.14781i
$121$	4.85007	−	2.80019i	0.440915	−	0.254562i
$122$	−0.207500	−	16.7426i	−0.0187862	−	1.51580i
$123$	3.10285	+	35.4657i	0.279774	+	3.19783i
$124$	3.58176	+	7.20904i	0.321651	+	0.647391i
$125$	0.392983	+	0.680667i	0.0351495	+	0.0608807i
$126$	−0.343227	−	0.280827i	−0.0305771	−	0.0250181i
$127$	1.51186	+	4.15379i	0.134156	+	0.368590i	0.988521	−	0.151083i	$-0.0482761\pi$
$127$	1.51186	+	4.15379i	0.134156	+	0.368590i	−0.854365	+	0.519673i	$0.826054\pi$
$128$	−4.77609	−	10.2562i	−0.422151	−	0.906526i
$129$	−1.22593	+	14.0124i	−0.107937	+	1.23372i
$130$	6.27511	+	2.19628i	0.550364	+	0.192626i
$131$	8.05724	+	1.42071i	0.703964	+	0.124128i	0.514160	−	0.857694i	$-0.328104\pi$
$131$	8.05724	+	1.42071i	0.703964	+	0.124128i	0.189804	+	0.981822i	$0.439215\pi$
$132$	2.31697	−	15.3567i	0.201666	−	1.33663i
$133$	−0.0194550	+	0.00708105i	−0.00168697	+	0.000614005i
$134$	−2.90198	−	10.3172i	−0.250693	−	0.891268i
$135$	44.1635	+	30.9236i	3.80099	+	2.66148i
$136$	−12.2475	+	1.53206i	−1.05021	+	0.131373i
$137$	−2.70410	−	1.56121i	−0.231026	−	0.133383i	0.380019	−	0.924979i	$-0.375917\pi$
$137$	−2.70410	−	1.56121i	−0.231026	−	0.133383i	−0.611045	+	0.791595i	$0.709251\pi$
$138$	−1.62937	+	2.90470i	−0.138701	+	0.247265i
$139$	−10.5986	−	15.1363i	−0.898958	−	1.28385i	−0.958346	−	0.285610i	$-0.907804\pi$
$139$	−10.5986	−	15.1363i	−0.898958	−	1.28385i	0.0593875	−	0.998235i	$-0.481085\pi$
$140$	−0.124987	−	0.204600i	−0.0105633	−	0.0172918i
$141$	35.4569	−	16.5338i	2.98601	−	1.39240i
$142$	13.2522	−	7.87173i	1.11210	−	0.660581i
$143$	1.47865	+	3.17098i	0.123651	+	0.265171i
$144$	22.2136	+	23.9547i	1.85113	+	1.99623i
$145$	13.4540	−	11.2893i	1.11730	−	0.937523i
$146$	18.7568	+	3.06816i	1.55232	+	0.253923i
$147$	16.5373	+	16.5373i	1.36398	+	1.36398i
$148$	12.0404	−	1.74068i	0.989711	−	0.143083i
$149$	−6.76581	+	6.76581i	−0.554277	+	0.554277i	−0.927672	−	0.373395i	$-0.878194\pi$
$149$	−6.76581	+	6.76581i	−0.554277	+	0.554277i	0.373395	+	0.927672i	$0.378194\pi$
$150$	13.0979	+	18.2209i	1.06944	+	1.48773i
$151$	−11.4675	−	13.6665i	−0.933216	−	1.11216i	−0.993483	−	0.113981i	$-0.963640\pi$
$151$	−11.4675	−	13.6665i	−0.933216	−	1.11216i	0.0602671	−	0.998182i	$-0.480805\pi$
$152$	1.49111	−	0.320488i	0.120945	−	0.0259950i
$153$	32.3018	−	15.0626i	2.61144	−	1.21774i
$154$	0.0311436	−	0.122271i	0.00250962	−	0.00985286i
$155$	−5.31089	−	11.3892i	−0.426581	−	0.914805i
$156$	−9.78194	−	2.36287i	−0.783182	−	0.189181i
$157$	−14.4752	+	10.1357i	−1.15525	+	0.808915i	−0.984324	−	0.176369i	$-0.943565\pi$
$157$	−14.4752	+	10.1357i	−1.15525	+	0.808915i	−0.170926	+	0.985284i	$0.554676\pi$
$158$	−8.44623	+	2.37573i	−0.671946	+	0.189003i
$159$	−12.5398	+	21.7196i	−0.994474	+	1.72248i
$160$	7.05691	+	16.1909i	0.557897	+	1.28000i
$161$	−0.0155198	+	0.0221646i	−0.00122313	+	0.00174681i
$162$	−40.9525	−	22.9720i	−3.21753	−	1.80485i
$163$	−0.463312	−	1.27294i	−0.0362894	−	0.0997043i	0.920225	−	0.391391i	$-0.128006\pi$
$163$	−0.463312	−	1.27294i	−0.0362894	−	0.0997043i	−0.956514	+	0.291686i	$0.905784\pi$
$164$	3.17874	−	21.0685i	0.248218	−	1.64517i
$165$	−4.21007	+	23.8765i	−0.327754	+	1.85878i
$166$	4.31754	+	8.96715i	0.335106	+	0.695986i
$167$	13.5111	+	1.18206i	1.04552	+	0.0914709i	0.596950	−	0.802278i	$-0.296379\pi$
$167$	13.5111	+	1.18206i	1.04552	+	0.0914709i	0.448567	+	0.893749i	$0.351935\pi$
$168$	0.219060	+	0.289333i	0.0169009	+	0.0223225i
$169$	−10.0856	+	3.67087i	−0.775817	+	0.282374i
$170$	19.1731	−	1.91713i	1.47051	−	0.147037i
$171$	−3.81398	+	2.20200i	−0.291662	+	0.168391i
$172$	2.68230	−	7.97956i	0.204523	−	0.608435i
$173$	5.50576	−	0.481691i	0.418595	−	0.0366223i	0.124087	−	0.992271i	$-0.460400\pi$
$173$	5.50576	−	0.481691i	0.418595	−	0.0366223i	0.294508	+	0.955649i	$0.404844\pi$
$174$	−18.5635	+	19.0294i	−1.40729	+	1.44261i
$175$	0.0911550	+	0.157885i	0.00689067	+	0.0119350i
$176$	−3.50592	+	8.60828i	−0.264269	+	0.648874i
$177$	8.65098	+	32.2859i	0.650247	+	2.42676i
$178$	−11.4480	−	7.80638i	−0.858067	−	0.585113i
$179$		−	16.8461i		−	1.25914i	−0.776945	−	0.629568i	$-0.783232\pi$
$179$		−	16.8461i		−	1.25914i	0.776945	−	0.629568i	$-0.216768\pi$
$180$	−33.7404	−	38.2439i	−2.51486	−	2.85053i
$181$	−15.6980	−	10.9919i	−1.16682	−	0.817018i	−0.180782	−	0.983523i	$-0.557863\pi$
$181$	−15.6980	−	10.9919i	−1.16682	−	0.817018i	−0.986041	+	0.166505i	$0.946752\pi$
$182$	−0.0771673	−	0.0270084i	−0.00572002	−	0.00200200i
$183$	−3.44834	−	39.4147i	−0.254909	−	2.91362i
$184$	1.35609	−	1.46086i	0.0999720	−	0.107696i
$185$	−18.8579	+	2.25072i	−1.38646	+	0.165476i
$186$	9.71414	+	16.3539i	0.712276	+	1.19913i
$187$	7.76800	+	6.51813i	0.568052	+	0.476653i
$188$	−22.9508	+	4.63608i	−1.67386	+	0.338121i
$189$	−0.543095	−	0.380279i	−0.0395043	−	0.0276612i
$190$	−2.33947	+	0.442473i	−0.169723	+	0.0321004i
$191$	−5.18711	+	5.18711i	−0.375326	+	0.375326i	−0.869413	−	0.494086i	$-0.835503\pi$
$191$	−5.18711	+	5.18711i	−0.375326	+	0.375326i	0.494086	+	0.869413i	$0.335503\pi$
$192$	−13.0670	−	23.3229i	−0.943030	−	1.68319i
$193$	−23.8474	+	6.38990i	−1.71658	+	0.459955i	−0.977021	−	0.213142i	$-0.931630\pi$
$193$	−23.8474	+	6.38990i	−1.71658	+	0.459955i	−0.739554	+	0.673097i	$0.764964\pi$
$194$	−0.377889	+	0.837322i	−0.0271308	+	0.0601162i
$195$	15.1746	+	4.06602i	1.08667	+	0.291174i
$196$	−7.29679	−	11.9446i	−0.521200	−	0.853188i
$197$	−17.7110	+	1.54951i	−1.26186	+	0.110398i	−0.698376	−	0.715731i	$-0.746094\pi$
$197$	−17.7110	+	1.54951i	−1.26186	+	0.110398i	−0.563481	+	0.826129i	$0.690538\pi$
$198$	2.00769	−	26.7643i	0.142680	−	1.90205i
$199$	−5.17852	−	1.38758i	−0.367096	−	0.0983630i	0.0705555	−	0.997508i	$-0.477523\pi$
$199$	−5.17852	−	1.38758i	−0.367096	−	0.0983630i	−0.437651	+	0.899145i	$0.644189\pi$
$200$	−5.05929	−	12.4407i	−0.357746	−	0.879693i
$201$	−8.66174	−	23.7979i	−0.610952	−	1.67858i
$202$	−5.96225	+	13.2111i	−0.419502	+	0.929530i
$203$	−0.165449	+	0.138828i	−0.0116122	+	0.00974383i
$204$	−28.5886	+	5.77492i	−2.00160	+	0.404325i
$205$	−5.77596	+	32.7571i	−0.403411	+	2.28786i
$206$	1.53829	+	15.3843i	0.107178	+	1.07188i
$207$	−2.43246	+	5.21642i	−0.169067	+	0.362566i
$208$	5.35868	+	2.74923i	0.371557	+	0.190625i
$209$	−1.02640	−	0.718694i	−0.0709976	−	0.0497131i
$210$	−0.330678	−	0.460017i	−0.0228190	−	0.0317442i
$211$	−7.37186	−	27.5121i	−0.507500	−	1.89401i	−0.443988	−	0.896033i	$-0.646437\pi$
$211$	−7.37186	−	27.5121i	−0.507500	−	1.89401i	−0.0635118	−	0.997981i	$-0.520230\pi$
$212$	10.3473	−	10.8734i	0.710657	−	0.746788i
$213$	29.8355	−	20.8910i	2.04429	−	1.43143i
$214$	3.66812	−	3.76018i	0.250747	−	0.257041i
$215$	−4.49480	+	12.3494i	−0.306543	+	0.842220i
$216$	35.7953	+	33.2279i	2.43556	+	2.26087i
$217$	0.0653099	+	0.140057i	0.00443352	+	0.00950772i
$218$	−15.0012	+	12.9077i	−1.01601	+	0.874219i
$219$	44.7399	+	3.91423i	3.02324	+	0.264499i
$220$	5.80450	−	13.2987i	0.391339	−	0.896599i
$221$	4.64616	−	4.64616i	0.312535	−	0.312535i
$222$	28.0636	−	6.22989i	1.88351	−	0.418123i
$223$		−	10.9749i		−	0.734936i	−0.930036	−	0.367468i	$-0.880225\pi$
$223$		−	10.9749i		−	0.734936i	0.930036	−	0.367468i	$-0.119775\pi$
$224$	−0.0867813	−	0.199105i	−0.00579832	−	0.0133033i
$225$	24.9276	+	29.7075i	1.66184	+	1.98050i
$226$	1.54846	+	0.116156i	0.103002	+	0.00772659i
$227$	−2.95562	−	1.07576i	−0.196172	−	0.0714006i	0.242066	−	0.970260i	$-0.422175\pi$
$227$	−2.95562	−	1.07576i	−0.196172	−	0.0714006i	−0.438238	+	0.898859i	$0.644397\pi$
$228$	3.45693	−	1.01875i	0.228941	−	0.0674682i
$229$	−3.07867	+	1.43561i	−0.203444	+	0.0948675i	−0.521670	−	0.853147i	$-0.674691\pi$
$229$	−3.07867	+	1.43561i	−0.203444	+	0.0948675i	0.318226	+	0.948015i	$0.396913\pi$
$230$	−2.17287	+	2.22740i	−0.143275	+	0.146871i
$231$	0.0517727	−	0.293618i	0.00340640	−	0.0193186i
$232$	13.4736	−	8.46184i	0.884582	−	0.555547i
$233$	−3.92084	+	6.79110i	−0.256863	+	0.444900i	−0.965400	−	0.260774i	$-0.916022\pi$
$233$	−3.92084	+	6.79110i	−0.256863	+	0.444900i	0.708537	+	0.705674i	$0.249356\pi$
$234$	−17.1630	−	2.80746i	−1.12198	−	0.183529i
$235$	35.9971	−	6.34725i	2.34819	−	0.414049i
$236$	−0.495775	−	19.9982i	−0.0322722	−	1.30177i
$237$	−19.4824	+	7.09100i	−1.26552	+	0.460610i
$238$	−0.235778	+	0.0235756i	−0.0152832	+	0.00152818i
$239$	0.175672	+	0.250886i	0.0113633	+	0.0162285i	0.824794	−	0.565434i	$-0.191291\pi$
$239$	0.175672	+	0.250886i	0.0113633	+	0.0162285i	−0.813430	+	0.581663i	$0.802402\pi$
$240$	19.4904	+	36.9040i	1.25810	+	2.38215i
$241$	−20.8021	−	1.81995i	−1.33998	−	0.117233i	−0.605490	−	0.795853i	$-0.707023\pi$
$241$	−20.8021	−	1.81995i	−1.33998	−	0.117233i	−0.734489	+	0.678620i	$0.762578\pi$
$242$	−7.40834	+	2.80087i	−0.476226	+	0.180047i
$243$	−53.6094	−	24.9985i	−3.43905	−	1.60365i
$244$	−3.53268	+	23.4144i	−0.226157	+	1.49895i
$245$	10.9255	+	18.9235i	0.698003	+	1.20898i
$246$	3.76619	−	50.2066i	0.240123	−	3.20106i
$247$	−0.521884	+	0.621957i	−0.0332067	+	0.0395742i
$248$	−3.35313	−	10.8791i	−0.212924	−	0.690824i
$249$	11.7587	+	20.3666i	0.745175	+	1.29068i
$250$	−0.393079	−	1.03970i	−0.0248605	−	0.0657564i
$251$	8.42867	−	14.5989i	0.532013	−	0.921474i	−0.467288	−	0.884105i	$-0.654769\pi$
$251$	8.42867	−	14.5989i	0.532013	−	0.921474i	0.999302	−	0.0373688i	$-0.0118976\pi$
$252$	0.414918	+	0.470299i	0.0261374	+	0.0296260i
$253$	−1.63758			−0.102953
$254$	−1.16175	−	6.14246i	−0.0728945	−	0.385412i
$255$	44.8397	−	7.90644i	2.80797	−	0.495120i
$256$	4.32436	+	15.4045i	0.270273	+	0.962784i
$257$	−0.990079	−	11.3167i	−0.0617594	−	0.705914i	−0.962451	−	0.271455i	$-0.912495\pi$
$257$	−0.990079	−	11.3167i	−0.0617594	−	0.705914i	0.900692	−	0.434459i	$-0.143060\pi$
$258$	4.90998	−	19.2768i	0.305682	−	1.20012i
$259$	0.231902	−	0.0276779i	0.0144097	−	0.00171982i
$260$	−8.25655	−	4.49786i	−0.512050	−	0.278945i
$261$	−29.5311	+	35.1938i	−1.82793	+	2.17844i
$262$	−10.9209	−	3.82228i	−0.674693	−	0.236141i
$263$	7.81742	−	1.37842i	0.482043	−	0.0849971i	0.0726540	−	0.997357i	$-0.476853\pi$
$263$	7.81742	−	1.37842i	0.482043	−	0.0849971i	0.409389	+	0.912360i	$0.365742\pi$
$264$	−6.73960	+	20.9038i	−0.414794	+	1.28654i
$265$	−16.5690	+	16.5690i	−1.01783	+	1.01783i
$266$	0.0287693	−	0.00544125i	0.00176396	−	0.000333624i
$267$	−28.3555	−	16.3710i	−1.73533	−	1.00189i
$268$	1.69481	+	15.0618i	0.103527	+	0.920048i
$269$	−0.270377	+	1.00906i	−0.0164852	+	0.0615236i	−0.973678	−	0.227926i	$-0.926806\pi$
$269$	−0.270377	+	1.00906i	−0.0164852	+	0.0615236i	0.957193	+	0.289450i	$0.0934722\pi$
$270$	−54.5777	−	53.2414i	−3.32149	−	3.24017i
$271$	1.34336	−	1.60095i	0.0816033	−	0.0972510i	−0.723698	−	0.690117i	$-0.757559\pi$
$271$	1.34336	−	1.60095i	0.0816033	−	0.0972510i	0.805301	+	0.592866i	$0.202004\pi$
$272$	17.4431	+	0.657827i	1.05765	+	0.0398866i
$273$	−0.186607	−	0.0500013i	−0.0112940	−	0.00302622i
$274$	3.41759	+	2.79626i	0.206464	+	0.168928i
$275$	−4.66300	+	9.99983i	−0.281189	+	0.603012i
$276$	2.93719	−	3.68201i	0.176798	−	0.221631i
$277$	−3.15777	−	3.76328i	−0.189732	−	0.226114i	0.662790	−	0.748805i	$-0.269372\pi$
$277$	−3.15777	−	3.76328i	−0.189732	−	0.226114i	−0.852522	+	0.522692i	$0.824928\pi$
$278$	11.3365	+	23.5448i	0.679916	+	1.41213i
$279$	18.8549	+	26.9276i	1.12881	+	1.61211i
$280$	0.127730	+	0.314087i	0.00763335	+	0.0187703i
$281$	13.5109	−	28.9742i	0.805993	−	1.72846i	0.130046	−	0.991508i	$-0.458487\pi$
$281$	13.5109	−	28.9742i	0.805993	−	1.72846i	0.675947	−	0.736950i	$-0.263735\pi$
$282$	−53.2606	+	14.9810i	−3.17163	+	0.892105i
$283$	−0.924036	−	5.24047i	−0.0549282	−	0.311513i	0.944948	−	0.327219i	$-0.106112\pi$
$283$	−0.924036	−	5.24047i	−0.0549282	−	0.311513i	−0.999877	+	0.0157058i	$0.995000\pi$
$284$	−20.2927	+	7.96086i	−1.20415	+	0.472390i
$285$	−5.43440	+	1.45614i	−0.321906	+	0.0862545i
$286$	−1.33978	−	4.76320i	−0.0792227	−	0.281654i
$287$	0.0710291	−	0.402826i	0.00419271	−	0.0237781i
$288$	−25.5339	−	38.5040i	−1.50460	−	2.26887i
$289$	0.698919	−	1.92026i	0.0411129	−	0.112957i
$290$	−21.3546	+	12.6845i	−1.25399	+	0.744861i
$291$	−0.742434	+	2.03982i	−0.0435223	+	0.119576i
$292$	−25.4777	−	8.56424i	−1.49097	−	0.501184i
$293$	−0.376676	+	4.30543i	−0.0220057	+	0.251526i	0.977222	+	0.212221i	$0.0680698\pi$
$293$	−0.376676	+	4.30543i	−0.0220057	+	0.251526i	−0.999227	+	0.0393045i	$0.987486\pi$
$294$	−19.3051	−	26.8560i	−1.12590	−	1.56627i
$295$			31.2291i			1.81823i
$296$	−17.2017	−	0.319374i	−0.999828	−	0.0185632i
$297$		−	40.1252i		−	2.32830i
$298$	10.9874	−	7.89819i	0.636484	−	0.457530i
$299$	−0.0924807	+	1.05706i	−0.00534830	+	0.0611313i
$300$	−14.1205	−	28.4205i	−0.815247	−	1.64086i
$301$	0.0552742	−	0.151865i	0.00318595	−	0.00875333i
$302$	12.8848	+	21.6919i	0.741439	+	1.24823i
$303$	−11.7140	+	32.1839i	−0.672950	+	1.84892i
$304$	−2.15425	+	0.106877i	−0.123555	+	0.00612984i
$305$	6.41911	−	36.4046i	0.367557	−	2.08452i
$306$	−48.5212	+	13.6479i	−2.77377	+	0.780198i
$307$	17.1522	−	4.59593i	0.978929	−	0.262303i	0.266336	−	0.963880i	$-0.414187\pi$
$307$	17.1522	−	4.59593i	0.978929	−	0.262303i	0.712594	+	0.701577i	$0.247520\pi$
$308$	−0.0713800	+	0.163539i	−0.00406726	+	0.00931850i
$309$	6.34406	+	35.9790i	0.360901	+	2.04677i
$310$	4.81209	+	17.1080i	0.273308	+	0.971670i
$311$	0.169345	−	0.363162i	0.00960269	−	0.0205930i	−0.901448	−	0.432888i	$-0.857495\pi$
$311$	0.169345	−	0.363162i	0.00960269	−	0.0205930i	0.911051	+	0.412294i	$0.135273\pi$
$312$	13.1129	+	5.53096i	0.742371	+	0.313129i
$313$	−2.56531	−	3.66365i	−0.145000	−	0.207082i	0.740082	−	0.672517i	$-0.234787\pi$
$313$	−2.56531	−	3.66365i	−0.145000	−	0.207082i	−0.885082	+	0.465435i	$0.845898\pi$
$314$	22.5165	−	10.8413i	1.27068	−	0.611812i
$315$	−0.629338	−	0.750016i	−0.0354592	−	0.0422586i
$316$	12.3305	−	1.38747i	0.693644	−	0.0780513i
$317$	−8.27904	+	17.7545i	−0.464997	+	0.997190i	0.524335	+	0.851512i	$0.324314\pi$
$317$	−8.27904	+	17.7545i	−0.464997	+	0.997190i	−0.989332	+	0.145678i	$0.953464\pi$
$318$	22.4600	−	27.4505i	1.25949	−	1.53935i
$319$	−12.6258	−	3.38308i	−0.706911	−	0.189416i
$320$	−6.15274	−	24.2081i	−0.343949	−	1.35327i
$321$	7.97873	−	9.50868i	0.445329	−	0.530723i
$322$	0.0267206	−	0.0273912i	0.00148908	−	0.00152645i
$323$	−0.609032	+	2.27294i	−0.0338875	+	0.126470i
$324$	51.9116	+	41.4106i	2.88398	+	2.30059i
$325$	6.19158	+	3.57471i	0.343447	+	0.198289i
$326$	0.356020	+	1.88237i	0.0197181	+	0.104255i
$327$	−33.0667	+	33.0667i	−1.82859	+	1.82859i
$328$	−9.24632	+	28.6788i	−0.510543	+	1.58352i
$329$	−0.442669	+	0.0780545i	−0.0244051	+	0.00430328i
$330$	11.3268	−	32.3624i	0.623519	−	1.78149i
$331$	19.6523	−	23.4206i	1.08019	−	1.28732i	0.124727	−	0.992191i	$-0.460195\pi$
$331$	19.6523	−	23.4206i	1.08019	−	1.28732i	0.955459	−	0.295124i	$-0.0953610\pi$
$332$	−3.97866	−	13.5008i	−0.218357	−	0.740954i
$333$	47.5577	−	14.3641i	2.60615	−	0.787148i
$334$	−18.5870	−	4.73430i	−1.01704	−	0.259050i
$335$	−2.06224	−	23.5715i	−0.112672	−	1.28785i
$336$	−0.239681	−	0.453822i	−0.0130757	−	0.0247580i
$337$	8.82506	−	1.55610i	0.480732	−	0.0847660i	0.0719694	−	0.997407i	$-0.477072\pi$
$337$	8.82506	−	1.55610i	0.480732	−	0.0847660i	0.408762	+	0.912641i	$0.365961\pi$
$338$	14.9142	−	2.82078i	0.811225	−	0.153430i
$339$	3.66926			0.199287
$340$	−27.1969	−	1.70149i	−1.47496	−	0.0922764i
$341$	−4.67635	+	8.09968i	−0.253239	+	0.438622i
$342$	5.82575	−	2.20254i	0.315021	−	0.119100i
$343$	−0.268737	−	0.465466i	−0.0145104	−	0.0251328i
$344$	−5.56530	+	10.5244i	−0.300061	+	0.567439i
$345$	−4.72633	+	5.63262i	−0.254457	+	0.303250i
$346$	−7.79416	−	0.584669i	−0.419017	−	0.0314320i
$347$	−3.95038	−	6.84225i	−0.212067	−	0.367311i	0.740294	−	0.672283i	$-0.234686\pi$
$347$	−3.95038	−	6.84225i	−0.212067	−	0.367311i	−0.952361	+	0.304972i	$0.901353\pi$
$348$	30.2527	−	22.3206i	1.62172	−	1.19651i
$349$	5.15600	+	2.40428i	0.275994	+	0.128698i	0.555688	−	0.831391i	$-0.312455\pi$
$349$	5.15600	+	2.40428i	0.275994	+	0.128698i	−0.279693	+	0.960089i	$0.590233\pi$
$350$	−0.0911771	−	0.241165i	−0.00487362	−	0.0128908i
$351$	−25.9009	−	2.26604i	−1.38249	−	0.120952i
$352$	6.85834	−	11.2139i	0.365551	−	0.597702i
$353$	3.61449	+	5.16203i	0.192380	+	0.274747i	0.903741	−	0.428080i	$-0.140810\pi$
$353$	3.61449	+	5.16203i	0.192380	+	0.274747i	−0.711361	+	0.702827i	$0.751921\pi$
$354$	−4.70309	−	47.0353i	−0.249966	−	2.49990i
$355$	31.9775	−	11.6388i	1.69719	−	0.617726i
$356$	14.1955	+	13.5086i	0.752357	+	0.715957i
$357$	−0.551409	+	0.0972283i	−0.0291837	+	0.00514587i
$358$	−3.84592	+	23.5115i	−0.203263	+	1.24262i
$359$	−0.251563	+	0.435719i	−0.0132770	+	0.0229964i	−0.872588	−	0.488458i	$-0.837560\pi$
$359$	−0.251563	+	0.435719i	−0.0132770	+	0.0229964i	0.859311	+	0.511454i	$0.170893\pi$
$360$	38.3593	+	61.0785i	2.02171	+	3.21912i
$361$	−3.24882	+	18.4250i	−0.170991	+	0.969737i
$362$	19.3997	+	18.9247i	1.01963	+	0.994663i
$363$	−16.9616	+	7.90932i	−0.890252	+	0.415131i
$364$	0.101534	+	0.0553118i	0.00532182	+	0.00289912i
$365$	39.4300	+	14.3513i	2.06386	+	0.751184i
$366$	−4.18554	+	55.7970i	−0.218782	+	2.91656i
$367$	9.10670	+	10.8529i	0.475366	+	0.566519i	0.949433	−	0.313970i	$-0.101659\pi$
$367$	9.10670	+	10.8529i	0.475366	+	0.566519i	−0.474067	+	0.880489i	$0.657215\pi$
$368$	−2.22615	+	1.72929i	−0.116046	+	0.0901453i
$369$		−	87.0097i		−	4.52955i
$370$	26.8331	+	1.16395i	1.39499	+	0.0605108i
$371$	0.203755	−	0.203755i	0.0105785	−	0.0105785i
$372$	−9.82413	−	25.0423i	−0.509357	−	1.29838i
$373$	11.6945	+	1.02313i	0.605516	+	0.0529758i	0.385791	−	0.922586i	$-0.373929\pi$
$373$	11.6945	+	1.02313i	0.605516	+	0.0529758i	0.219725	+	0.975562i	$0.429484\pi$
$374$	−9.35345	−	10.8705i	−0.483656	−	0.562102i
$375$	−1.11001	−	2.38042i	−0.0573206	−	0.122924i
$376$	33.0900	−	1.23081i	1.70649	−	0.0634743i
$377$	−2.89683	+	7.95896i	−0.149194	+	0.409907i
$378$	0.671161	+	0.654729i	0.0345208	+	0.0336756i
$379$	−21.9289	+	15.3548i	−1.12641	+	0.788721i	−0.979702	−	0.200459i	$-0.935757\pi$
$379$	−21.9289	+	15.3548i	−1.12641	+	0.788721i	−0.146708	+	0.989180i	$0.546868\pi$
$380$	3.36613	−	0.0834494i	0.172679	−	0.00428087i
$381$	−3.82322	−	14.2684i	−0.195869	−	0.730994i
$382$	8.42368	−	6.05527i	0.430993	−	0.309814i
$383$	−18.1390	−	12.7011i	−0.926862	−	0.648996i	0.00952901	−	0.999955i	$-0.496967\pi$
$383$	−18.1390	−	12.7011i	−0.926862	−	0.648996i	−0.936391	+	0.350959i	$0.885856\pi$
$384$	12.9126	+	35.5342i	0.658944	+	1.81334i
$385$	0.117725	−	0.252462i	0.00599983	−	0.0128667i
$386$	34.7418	−	3.47386i	1.76831	−	0.176815i
$387$	5.96957	−	33.8551i	0.303450	−	1.72095i
$388$	0.718564	−	1.08235i	0.0364796	−	0.0549480i
$389$	−2.33233	+	1.95705i	−0.118254	+	0.0992266i	−0.699997	−	0.714146i	$-0.746815\pi$
$389$	−2.33233	+	1.95705i	−0.118254	+	0.0992266i	0.581743	+	0.813372i	$0.302371\pi$
$390$	−20.2504	−	9.13912i	−1.02542	−	0.462777i
$391$	1.05183	+	2.88987i	0.0531932	+	0.146147i
$392$	7.45695	+	18.3365i	0.376633	+	0.926135i
$393$	−26.4090	−	7.07628i	−1.33216	−	0.356951i
$394$	25.0724	+	1.88077i	1.26313	+	0.0947520i
$395$	−19.2970	+	1.68827i	−0.970939	+	0.0849461i
$396$	−8.91227	+	36.8956i	−0.447859	+	1.85407i
$397$	−15.6138	−	4.18369i	−0.783632	−	0.209974i	−0.155246	−	0.987876i	$-0.549617\pi$
$397$	−15.6138	−	4.18369i	−0.783632	−	0.209974i	−0.628385	+	0.777902i	$0.716284\pi$
$398$	6.91070	+	3.11884i	0.346402	+	0.156333i
$399$	0.0668288	−	0.0179067i	0.00334562	−	0.000896457i
$400$	4.22089	+	18.5181i	0.211045	+	0.925906i
$401$	−10.4396	+	10.4396i	−0.521331	+	0.521331i	−0.917973	−	0.396642i	$-0.870175\pi$
$401$	−10.4396	+	10.4396i	−0.521331	+	0.521331i	0.396642	+	0.917973i	$0.370175\pi$
$402$	6.65588	+	35.1914i	0.331965	+	1.75519i
$403$	4.96427	+	3.47602i	0.247288	+	0.173153i
$404$	11.3374	−	17.0771i	0.564055	−	0.849618i
$405$	−79.4126	−	66.6351i	−3.94605	−	3.31113i
$406$	0.262605	−	0.155986i	0.0130329	−	0.00774146i
$407$	9.42228	+	10.5360i	0.467045	+	0.522249i
$408$	41.2185	−	1.53316i	2.04062	−	0.0759026i
$409$	−1.58039	−	18.0639i	−0.0781450	−	0.893202i	−0.929551	−	0.368694i	$-0.879805\pi$
$409$	−1.58039	−	18.0639i	−0.0781450	−	0.893202i	0.851406	−	0.524508i	$-0.175751\pi$
$410$	15.5397	−	44.3993i	0.767450	−	2.19273i
$411$	8.54731	+	5.98489i	0.421608	+	0.295213i
$412$	1.36526	−	21.8225i	0.0672617	−	1.07512i
$413$		−	0.384035i		−	0.0188971i
$414$	4.58579	−	6.72505i	0.225379	−	0.330518i
$415$	5.68688	+	21.2237i	0.279158	+	1.04183i
$416$	−6.85128	−	5.06037i	−0.335911	−	0.248105i
$417$	30.8745	+	53.4761i	1.51193	+	2.61874i
$418$	1.26844	+	1.23738i	0.0620412	+	0.0605222i
$419$	19.1562	−	1.67595i	0.935841	−	0.0818755i	0.390978	−	0.920400i	$-0.372137\pi$
$419$	19.1562	−	1.67595i	0.935841	−	0.0818755i	0.544864	+	0.838525i	$0.316581\pi$
$420$	0.356495	+	0.717522i	0.0173952	+	0.0350115i
$421$	20.5413	−	11.8595i	1.00112	−	0.577999i	0.0925425	−	0.995709i	$-0.470501\pi$
$421$	20.5413	−	11.8595i	1.00112	−	0.577999i	0.908580	+	0.417710i	$0.137167\pi$
$422$	4.00770	+	40.0807i	0.195092	+	1.95110i
$423$	−89.8494	+	32.7025i	−4.36863	+	1.59005i
$424$	−16.9238	+	12.8134i	−0.821890	+	0.622272i
$425$	20.6420	+	1.80595i	1.00129	+	0.0876012i
$426$	−46.4097	+	22.3455i	−2.24856	+	1.08264i
$427$	−0.0789381	+	0.447680i	−0.00382008	+	0.0216648i
$428$	−5.97790	+	4.41053i	−0.288953	+	0.213191i
$429$	−3.99892	−	10.9869i	−0.193070	−	0.530455i
$430$	9.09256	−	16.2094i	0.438482	−	0.781688i
$431$	−16.9337	+	24.1839i	−0.815669	+	1.16490i	0.168155	+	0.985761i	$0.446219\pi$
$431$	−16.9337	+	24.1839i	−0.815669	+	1.16490i	−0.983824	+	0.179136i	$0.942670\pi$
$432$	−42.3724	−	54.5470i	−2.03864	−	2.62439i
$433$	12.8427	−	22.2441i	0.617179	−	1.06899i	−0.372819	−	0.927904i	$-0.621609\pi$
$433$	12.8427	−	22.2441i	0.617179	−	1.06899i	0.989998	−	0.141081i	$-0.0450579\pi$
$434$	−0.0591760	−	0.210383i	−0.00284054	−	0.0100987i
$435$	−48.0769	+	33.6638i	−2.30511	+	1.61406i
$436$	23.8835	−	14.5901i	1.14381	−	0.698738i
$437$	−0.160597	−	0.344402i	−0.00768241	−	0.0164750i
$438$	−61.5483	−	15.6770i	−2.94089	−	0.749074i
$439$	2.51659	−	1.17350i	0.120110	−	0.0560083i	−0.361634	−	0.932320i	$-0.617781\pi$
$439$	2.51659	−	1.17350i	0.120110	−	0.0560083i	0.481745	+	0.876312i	$0.340003\pi$
$440$	−11.1372	+	17.2354i	−0.530945	+	0.821665i
$441$	−36.7410	−	43.7863i	−1.74957	−	2.08506i
$442$	−7.54519	+	5.42378i	−0.358888	+	0.257983i
$443$	−2.62147	+	2.62147i	−0.124550	+	0.124550i	−0.766634	−	0.642084i	$-0.778070\pi$
$443$	−2.62147	+	2.62147i	−0.124550	+	0.124550i	0.642084	+	0.766634i	$0.278070\pi$
$444$	−40.5897	+	2.28799i	−1.92630	+	0.108583i
$445$	−21.6312	−	21.6312i	−1.02542	−	1.02542i
$446$	−2.50555	+	15.3173i	−0.118641	+	0.725296i
$447$	24.4942	−	20.5530i	1.15853	−	0.972126i
$448$	0.0756625	+	0.297696i	0.00357472	+	0.0140648i
$449$	−2.22416	−	4.76972i	−0.104964	−	0.225097i	0.846810	−	0.531895i	$-0.178520\pi$
$449$	−2.22416	−	4.76972i	−0.104964	−	0.225097i	−0.951775	+	0.306798i	$0.900742\pi$
$450$	−28.0084	−	47.1526i	−1.32033	−	2.22280i
$451$	22.4361	−	10.4621i	1.05648	−	0.492643i
$452$	−2.13462	−	0.515625i	−0.100404	−	0.0242530i
$453$	34.1954	+	48.8361i	1.60664	+	2.29452i
$454$	3.87947	+	2.17616i	0.182072	+	0.102132i
$455$	−0.156317	−	0.0902495i	−0.00732824	−	0.00423096i
$456$	−5.05729	+	0.632624i	−0.236829	+	0.0296254i
$457$	−5.24522	−	3.67274i	−0.245361	−	0.171804i	0.444427	−	0.895815i	$-0.353407\pi$
$457$	−5.24522	−	3.67274i	−0.245361	−	0.171804i	−0.689788	+	0.724011i	$0.742296\pi$
$458$	4.62453	−	1.30077i	0.216090	−	0.0607812i
$459$	−70.8100	+	25.7727i	−3.30513	+	1.20297i
$460$	3.54111	−	2.61265i	0.165105	−	0.121815i
$461$	−10.8395	−	1.91130i	−0.504847	−	0.0890181i	−0.0845762	−	0.996417i	$-0.526954\pi$
$461$	−10.8395	−	1.91130i	−0.504847	−	0.0890181i	−0.420270	+	0.907399i	$0.638065\pi$
$462$	−0.139290	+	0.397972i	−0.00648034	+	0.0185154i
$463$	3.04276	−	34.7789i	0.141409	−	1.61631i	−0.511781	−	0.859116i	$-0.671014\pi$
$463$	3.04276	−	34.7789i	0.141409	−	1.61631i	0.653190	−	0.757194i	$-0.273430\pi$
$464$	−20.7364	+	8.73392i	−0.962662	+	0.405462i
$465$	14.3630	+	39.4619i	0.666067	+	1.83000i
$466$	7.02257	−	8.58298i	0.325314	−	0.397599i
$467$	18.2057	+	31.5332i	0.842460	+	1.45918i	0.887809	+	0.460212i	$0.152226\pi$
$467$	18.2057	+	31.5332i	0.842460	+	1.45918i	−0.0453498	+	0.998971i	$0.514440\pi$
$468$	23.3129	+	7.83655i	1.07764	+	0.362245i
$469$	0.0253601	+	0.289868i	0.00117102	+	0.0133848i
$470$	−51.6889	+	0.640609i	−2.38423	+	0.0295491i
$471$	51.1406	−	29.5260i	2.35643	−	1.36049i
$472$	−3.87361	+	28.0240i	−0.178297	+	1.28991i
$473$	9.44758	−	2.53147i	0.434400	−	0.116397i
$474$	28.8097	−	5.44889i	1.32327	−	0.250276i
$475$	−2.56039			−0.117479
$476$	0.334450	+	0.0209239i	0.0153295	+	0.000959043i
$477$	35.1574	−	50.2100i	1.60975	−	2.29896i
$478$	−0.187903	−	0.390258i	−0.00859448	−	0.0178500i
$479$	−6.00318	+	0.525210i	−0.274292	+	0.0239975i	−0.223472	−	0.974710i	$-0.571739\pi$
$479$	−6.00318	+	0.525210i	−0.274292	+	0.0239975i	−0.0508203	+	0.998708i	$0.516184\pi$
$480$	−18.7770	−	55.9553i	−0.857050	−	2.55400i
$481$	7.33312	−	5.48710i	0.334361	−	0.250190i
$482$	28.6172	+	7.28909i	1.30348	+	0.332009i
$483$	0.0581214	−	0.0692664i	0.00264462	−	0.00315173i
$484$	10.9790	−	2.21777i	0.499045	−	0.100808i
$485$	−1.16329	+	1.66135i	−0.0528222	+	0.0754380i
$486$	69.1137	+	47.1284i	3.13506	+	2.13779i
$487$	−6.08938	−	6.08938i	−0.275936	−	0.275936i	0.555548	−	0.831484i	$-0.312508\pi$
$487$	−6.08938	−	6.08938i	−0.275936	−	0.275936i	−0.831484	+	0.555548i	$0.812508\pi$
$488$	10.2759	−	31.8722i	0.465168	−	1.44278i
$489$	1.17163	+	4.37259i	0.0529831	+	0.197736i
$490$	−10.9281	−	28.9051i	−0.493682	−	1.30580i
$491$	2.78647	−	10.3993i	0.125752	−	0.469312i	−0.874114	−	0.485722i	$-0.838557\pi$
$491$	2.78647	−	10.3993i	0.125752	−	0.469312i	0.999865	+	0.0164095i	$0.00522353\pi$
$492$	−16.7184	+	69.2118i	−0.753722	+	3.12031i
$493$	2.13946	+	24.4541i	0.0963564	+	1.10136i
$494$	0.870366	−	0.748899i	0.0391596	−	0.0336946i
$495$	15.3362	−	57.2356i	0.689313	−	2.57255i
$496$	2.19617	+	15.9491i	0.0986110	+	0.716136i
$497$	−0.393238	+	0.143127i	−0.0176392	+	0.00642013i
$498$	−11.7615	−	31.1094i	−0.527046	−	1.39405i
$499$	11.5076	+	13.7143i	0.515152	+	0.613935i	0.959427	−	0.281956i	$-0.0909832\pi$
$499$	11.5076	+	13.7143i	0.515152	+	0.613935i	−0.444275	+	0.895890i	$0.646539\pi$
$500$	0.311245	+	1.54081i	0.0139193	+	0.0689072i
$501$	−44.6345	−	7.87026i	−1.99412	−	0.351617i
$502$	−15.0965	+	18.4509i	−0.673789	+	0.823505i
$503$	−1.20861	−	0.563584i	−0.0538893	−	0.0251290i	0.395487	−	0.918472i	$-0.370576\pi$
$503$	−1.20861	−	0.563584i	−0.0538893	−	0.0251290i	−0.449376	+	0.893343i	$0.648354\pi$
$504$	−0.471718	−	0.751104i	−0.0210120	−	0.0334568i
$505$	−18.3541	+	26.2124i	−0.816748	+	1.16644i
$506$	2.28551	+	0.373854i	0.101603	+	0.0166198i
$507$	34.6445	−	9.28297i	1.53862	−	0.412271i
$508$	0.219103	+	8.83803i	0.00972112	+	0.392124i
$509$	10.3742	+	14.8160i	0.459830	+	0.656706i	0.980378	−	0.197127i	$-0.0631611\pi$
$509$	10.3742	+	14.8160i	0.459830	+	0.656706i	−0.520548	+	0.853833i	$0.674272\pi$
$510$	−64.3861	+	0.797973i	−2.85107	+	0.0353348i
$511$	−0.484885	−	0.176484i	−0.0214500	−	0.00780717i
$512$	−2.51855	−	22.4868i	−0.111305	−	0.993786i
$513$	8.43882	−	3.93509i	0.372583	−	0.173738i
$514$	−1.20174	+	16.0203i	−0.0530066	+	0.706625i
$515$	−2.97497	+	34.0041i	−0.131093	+	1.49840i
$516$	−11.2535	+	25.7830i	−0.495408	+	1.13503i
$517$	−19.2362	−	19.2362i	−0.846006	−	0.846006i
$518$	−0.329977	−	0.0143135i	−0.0144983	−	0.000628899i
$519$	−18.4691			−0.810705
$520$	10.4965	+	8.16245i	0.460303	+	0.357947i
$521$	20.5345	−	17.2305i	0.899634	−	0.754882i	−0.0704850	−	0.997513i	$-0.522455\pi$
$521$	20.5345	−	17.2305i	0.899634	−	0.754882i	0.970119	+	0.242630i	$0.0780102\pi$
$522$	49.2502	−	42.3769i	2.15562	−	1.85479i
$523$	−7.78314	+	21.3840i	−0.340333	+	0.935058i	0.644965	+	0.764212i	$0.276872\pi$
$523$	−7.78314	+	21.3840i	−0.340333	+	0.935058i	−0.985298	+	0.170845i	$0.945350\pi$
$524$	14.3693	+	7.82782i	0.627724	+	0.341960i
$525$	−0.257473	−	0.552154i	−0.0112371	−	0.0240980i
$526$	−11.2252	+	0.139120i	−0.489441	+	0.00606592i
$527$	17.2974	+	3.04999i	0.753485	+	0.132860i
$528$	14.1785	−	27.6361i	0.617040	−	1.20271i
$529$	19.4885	+	11.2517i	0.847325	+	0.489204i
$530$	26.9075	−	19.3422i	1.16879	−	0.840170i
$531$	−14.1854	−	80.4496i	−0.615596	−	3.49122i
$532$	−0.0413945	+	0.00102621i	−0.00179468	+	4.44917e-5i
$533$	−5.48628	−	15.0734i	−0.237637	−	0.652903i
$534$	35.8373	+	29.3219i	1.55083	+	1.26888i
$535$	9.49994	−	6.65193i	0.410718	−	0.287588i
$536$	1.07318	−	21.4082i	0.0463545	−	0.924693i
$537$	−4.90647	+	56.0812i	−0.211730	+	2.42008i
$538$	0.607722	−	1.34659i	0.0262008	−	0.0580554i
$539$	6.87285	−	14.7389i	0.296034	−	0.634848i
$540$	64.0173	+	86.7671i	2.75487	+	3.73386i
$541$	−39.2571	+	22.6651i	−1.68779	+	0.974448i	−0.731591	+	0.681744i	$0.761222\pi$
$541$	−39.2571	+	22.6651i	−1.68779	+	0.974448i	−0.956203	+	0.292704i	$0.905445\pi$
$542$	−2.24037	+	1.92771i	−0.0962322	+	0.0828022i
$543$	49.0577	+	41.1643i	2.10527	+	1.76653i
$544$	−24.1946	−	4.90033i	−1.03734	−	0.210100i
$545$	−37.8378	+	21.8457i	−1.62079	+	0.935766i
$546$	0.249026	+	0.112387i	0.0106573	+	0.00480972i
$547$	2.86848	+	1.65612i	0.122647	+	0.0708104i	0.560068	−	0.828446i	$-0.310775\pi$
$547$	2.86848	+	1.65612i	0.122647	+	0.0708104i	−0.437421	+	0.899257i	$0.644108\pi$
$548$	−4.13143	−	4.68287i	−0.176486	−	0.200042i
$549$			96.6981i			4.12698i
$550$	8.79092	−	12.8919i	0.374846	−	0.549711i
$551$	−0.526715	−	2.98715i	−0.0224388	−	0.127257i
$552$	−4.93993	+	4.46830i	−0.210257	+	0.190184i
$553$	0.237302	−	0.0207613i	0.0100911	−	0.000882859i
$554$	3.54804	+	5.97319i	0.150742	+	0.253776i
$555$	63.4340	−	2.00032i	2.69263	−	0.0849088i
$556$	−10.4467	−	35.4488i	−0.443038	−	1.50336i
$557$	21.3047	+	17.8768i	0.902710	+	0.757464i	0.970718	−	0.240221i	$-0.0772199\pi$
$557$	21.3047	+	17.8768i	0.902710	+	0.757464i	−0.0680080	+	0.997685i	$0.521664\pi$
$558$	−20.1676	−	41.8864i	−0.853763	−	1.77319i
$559$	−1.10053	−	6.24141i	−0.0465474	−	0.263983i
$560$	−0.106564	−	0.467521i	−0.00450313	−	0.0197564i
$561$	−23.9615	−	23.9615i	−1.01166	−	1.01166i
$562$	−25.4714	+	37.3538i	−1.07445	+	1.57568i
$563$	−3.93154	+	6.80963i	−0.165695	+	0.286992i	−0.936902	−	0.349593i	$-0.886320\pi$
$563$	−3.93154	+	6.80963i	−0.165695	+	0.286992i	0.771207	+	0.636584i	$0.219653\pi$
$564$	77.7541	−	8.74918i	3.27404	−	0.368407i
$565$	3.31140	+	0.887288i	0.139312	+	0.0373285i
$566$	0.0932601	+	7.52489i	0.00392002	+	0.316295i
$567$	0.976566	+	0.819436i	0.0410119	+	0.0344131i
$568$	30.1393	−	6.47792i	1.26462	−	0.271807i
$569$	−7.98742	+	29.8095i	−0.334850	+	1.24968i	0.569182	+	0.822212i	$0.307260\pi$
$569$	−7.98742	+	29.8095i	−0.334850	+	1.24968i	−0.904032	+	0.427465i	$0.859407\pi$
$570$	7.91704	−	0.791630i	0.331608	−	0.0331577i
$571$	−35.5860	−	16.5940i	−1.48923	−	0.694438i	−0.503688	−	0.863886i	$-0.668024\pi$
$571$	−35.5860	−	16.5940i	−1.48923	−	0.694438i	−0.985539	+	0.169448i	$0.945802\pi$
$572$	0.782455	+	6.95369i	0.0327161	+	0.290748i
$573$	18.7788	−	15.7573i	0.784497	−	0.658271i
$574$	−0.191097	+	0.545994i	−0.00797623	+	0.0227894i
$575$	−2.74106	+	1.91931i	−0.114310	+	0.0800409i
$576$	26.8464	+	59.5681i	1.11860	+	2.48200i
$577$	7.84649	+	3.65888i	0.326654	+	0.152321i	0.579026	−	0.815309i	$-0.303433\pi$
$577$	7.84649	+	3.65888i	0.326654	+	0.152321i	−0.252372	+	0.967630i	$0.581211\pi$
$578$	−1.41385	+	2.52048i	−0.0588083	+	0.104838i
$579$	81.2499	−	14.3266i	3.37663	−	0.595391i
$580$	32.6997	−	12.8281i	1.35778	−	0.532660i
$581$	−0.0699336	−	0.260996i	−0.00290134	−	0.0108279i
$582$	1.50187	−	2.67741i	0.0622547	−	0.110982i
$583$	17.1744	+	3.02831i	0.711291	+	0.125420i
$584$	33.6032	+	17.7693i	1.39051	+	0.735299i
$585$	−36.0797	−	13.1319i	−1.49171	−	0.542938i
$586$	1.50863	−	5.92294i	0.0623210	−	0.244675i
$587$	−11.9821	−	4.36114i	−0.494555	−	0.180003i	0.0826882	−	0.996575i	$-0.473649\pi$
$587$	−11.9821	−	4.36114i	−0.494555	−	0.180003i	−0.577244	+	0.816572i	$0.695872\pi$
$588$	20.8124	+	41.8893i	0.858287	+	1.72748i
$589$	−2.16207	−	0.189157i	−0.0890866	−	0.00779407i
$590$	7.12951	−	43.5853i	0.293517	−	1.79438i
$591$	59.4118			2.44387
$592$	23.9349	+	4.37284i	0.983717	+	0.179722i
$593$	29.9130			1.22838			0.614189	−	0.789159i	$-0.289483\pi$
$593$	29.9130			1.22838			0.614189	+	0.789159i	$0.289483\pi$
$594$	−9.16047	+	56.0013i	−0.375859	+	2.29776i
$595$	−0.521143	−	0.0455941i	−0.0213648	−	0.00186918i
$596$	−17.1379	+	8.51483i	−0.701996	+	0.348781i
$597$	16.8353	+	6.12755i	0.689024	+	0.250784i
$598$	0.370396	−	1.45419i	0.0151466	−	0.0594662i
$599$	14.2941	+	5.20264i	0.584043	+	0.212574i	0.617107	−	0.786879i	$-0.288304\pi$
$599$	14.2941	+	5.20264i	0.584043	+	0.212574i	−0.0330646	+	0.999453i	$0.510527\pi$
$600$	13.2192	+	42.8891i	0.539670	+	1.75094i
$601$	28.7182	+	5.06379i	1.17144	+	0.206556i	0.725317	−	0.688415i	$-0.241693\pi$
$601$	28.7182	+	5.06379i	1.17144	+	0.206556i	0.446123	+	0.894972i	$0.352804\pi$
$602$	−0.111814	+	0.199333i	−0.00455722	+	0.00812421i
$603$	16.0197	+	59.7862i	0.652371	+	2.43468i
$604$	−13.0307	−	33.2161i	−0.530212	−	1.35155i
$605$	−17.2200	+	3.03634i	−0.700091	+	0.123445i
$606$	23.6963	−	42.2436i	0.962595	−	1.71603i
$607$	5.08497	+	2.37116i	0.206393	+	0.0962425i	0.523066	−	0.852292i	$-0.324788\pi$
$607$	5.08497	+	2.37116i	0.206393	+	0.0962425i	−0.316673	+	0.948535i	$0.602566\pi$
$608$	3.03102	+	0.342645i	0.122924	+	0.0138961i
$609$	0.591219	−	0.413976i	0.0239574	−	0.0167752i
$610$	−17.2700	+	49.3431i	−0.699241	+	1.99784i
$611$	−13.5034	+	11.3307i	−0.546287	+	0.458390i
$612$	70.8351	−	7.97062i	2.86334	−	0.322193i
$613$	35.9611	+	16.7690i	1.45246	+	0.677292i	0.979063	−	0.203559i	$-0.0652510\pi$
$613$	35.9611	+	16.7690i	1.45246	+	0.677292i	0.473394	+	0.880851i	$0.343029\pi$
$614$	−24.9880	+	2.49857i	−1.00843	+	0.100834i
$615$	28.7690	−	107.367i	1.16008	−	4.32946i
$616$	0.136958	−	0.211950i	0.00551820	−	0.00853970i
$617$	−6.57259	−	5.51506i	−0.264603	−	0.222028i	0.500827	−	0.865547i	$-0.333029\pi$
$617$	−6.57259	−	5.51506i	−0.264603	−	0.222028i	−0.765430	+	0.643519i	$0.777474\pi$
$618$	−0.640287	−	51.6629i	−0.0257561	−	2.07819i
$619$	22.3354	+	5.98476i	0.897737	+	0.240548i	0.678044	−	0.735021i	$-0.262828\pi$
$619$	22.3354	+	5.98476i	0.897737	+	0.240548i	0.219693	+	0.975569i	$0.429494\pi$
$620$	−2.81035	−	24.9756i	−0.112866	−	1.00305i
$621$	6.08450	−	10.5387i	0.244163	−	0.422902i
$622$	−0.319258	+	0.468192i	−0.0128011	+	0.0187728i
$623$	0.266007	+	0.266007i	0.0106573	+	0.0106573i
$624$	−17.0385	−	10.7130i	−0.682085	−	0.428863i
$625$	−4.54877	−	25.7973i	−0.181951	−	1.03189i
$626$	2.74392	+	5.69888i	0.109669	+	0.227773i
$627$	3.20760	+	2.69150i	0.128099	+	0.107488i
$628$	−33.9006	+	9.99042i	−1.35278	+	0.398661i
$629$	12.5411	−	23.3951i	0.500046	−	0.932823i
$630$	0.707118	+	1.19045i	0.0281723	+	0.0474285i
$631$	−7.52030	+	0.657941i	−0.299379	+	0.0261922i	−0.235856	−	0.971788i	$-0.575789\pi$
$631$	−7.52030	+	0.657941i	−0.299379	+	0.0261922i	−0.0635231	+	0.997980i	$0.520234\pi$
$632$	−17.5260	−	0.878571i	−0.697146	−	0.0349477i
$633$	16.5282	+	93.7359i	0.656935	+	3.72567i
$634$	15.6081	−	22.8892i	0.619875	−	0.909046i
$635$		−	13.8014i		−	0.547691i
$636$	−37.6135	+	33.1842i	−1.49147	+	1.31584i
$637$	−9.12584	−	5.26881i	−0.361579	−	0.208758i
$638$	16.8491	+	7.60410i	0.667062	+	0.301049i
$639$	−77.0908	+	44.5084i	−3.04967	+	1.76073i
$640$	3.06052	+	35.1911i	0.120978	+	1.39105i
$641$	−15.0429	−	12.6225i	−0.594159	−	0.498559i	0.295403	−	0.955373i	$-0.404546\pi$
$641$	−15.0429	−	12.6225i	−0.594159	−	0.498559i	−0.889562	+	0.456814i	$0.848990\pi$
$642$	−13.3064	+	11.4494i	−0.525163	+	0.451872i
$643$	−40.5604	+	23.4176i	−1.59955	+	0.923498i	−0.607971	+	0.793959i	$0.708016\pi$
$643$	−40.5604	+	23.4176i	−1.59955	+	0.923498i	−0.991574	+	0.129539i	$0.958650\pi$
$644$	−0.0435463	+	0.0321287i	−0.00171596	+	0.00126605i
$645$	18.5601	−	39.8023i	0.730804	−	1.56721i
$646$	1.36891	−	3.03322i	0.0538591	−	0.119340i
$647$	2.36701	−	27.0550i	0.0930566	−	1.06364i	−0.795832	−	0.605518i	$-0.792966\pi$
$647$	2.36701	−	27.0550i	0.0930566	−	1.06364i	0.888888	−	0.458124i	$-0.151478\pi$
$648$	−62.9972	−	69.6466i	−2.47476	−	2.73598i
$649$	19.0389	−	13.3312i	0.747342	−	0.523294i
$650$	−7.82528	−	6.40262i	−0.306933	−	0.251131i
$651$	−0.176627	−	0.485277i	−0.00692254	−	0.0190195i
$652$	−0.0671446	−	2.70843i	−0.00262958	−	0.106070i
$653$	−2.76797	−	15.6979i	−0.108319	−	0.614307i	−0.989843	−	0.142167i	$-0.954593\pi$
$653$	−2.76797	−	15.6979i	−0.108319	−	0.614307i	0.881524	−	0.472140i	$-0.156518\pi$
$654$	53.6990	−	38.6010i	2.09980	−	1.50942i
$655$	−22.1222	−	12.7723i	−0.864388	−	0.499054i
$656$	19.4521	−	37.9151i	0.759476	−	1.48034i
$657$	−108.095	−	19.0601i	−4.21719	−	0.743604i
$658$	0.635637	−	0.00787780i	0.0247797	−	0.000307109i
$659$	0.597888	+	1.28217i	0.0232904	+	0.0499464i	0.917609	−	0.397485i	$-0.130117\pi$
$659$	0.597888	+	1.28217i	0.0232904	+	0.0499464i	−0.894318	+	0.447431i	$0.852339\pi$
$660$	−23.1967	+	42.5812i	−0.902928	+	1.65747i
$661$	5.94833	−	16.3429i	0.231363	−	0.635665i	−0.768629	−	0.639695i	$-0.779061\pi$
$661$	5.94833	−	16.3429i	0.231363	−	0.635665i	0.999992	+	0.00403027i	$0.00128288\pi$
$662$	−32.7748	+	28.2008i	−1.27383	+	1.09606i
$663$	−16.8204	+	14.1140i	−0.653251	+	0.548143i
$664$	2.47068	+	19.7509i	0.0958809	+	0.766485i
$665$	0.0646413			0.00250668
$666$	−69.6539	+	9.19017i	−2.69903	+	0.356112i
$667$	−2.80310	−	2.80310i	−0.108537	−	0.108537i
$668$	24.8605	+	10.8509i	0.961880	+	0.419833i
$669$	−3.19648	+	36.5359i	−0.123583	+	1.41256i
$670$	−2.50312	+	33.3688i	−0.0967038	+	1.28915i
$671$	−24.9344	+	11.6271i	−0.962580	+	0.448859i
$672$	0.230908	+	0.688102i	0.00890746	+	0.0265441i
$673$	−7.35827	−	2.67819i	−0.283641	−	0.103237i	0.196282	−	0.980547i	$-0.437113\pi$
$673$	−7.35827	−	2.67819i	−0.283641	−	0.103237i	−0.479923	+	0.877311i	$0.659335\pi$
$674$	−12.6721	+	0.157052i	−0.488110	+	0.00604942i
$675$	−47.0286	−	67.1638i	−1.81013	−	2.58513i
$676$	−21.4592	+	0.531993i	−0.825354	+	0.0204613i
$677$	−3.51415	+	0.941614i	−0.135060	+	0.0361892i	−0.325716	−	0.945468i	$-0.605605\pi$
$677$	−3.51415	+	0.941614i	−0.135060	+	0.0361892i	0.190656	+	0.981657i	$0.438939\pi$
$678$	−5.12105	−	0.837681i	−0.196673	−	0.0321710i
$679$	0.0143054	−	0.0204302i	0.000548990	−	0.000784039i
$680$	37.5693	+	8.58368i	1.44072	+	0.329169i
$681$	9.52604	+	4.44207i	0.365039	+	0.170220i
$682$	8.37575	−	10.2368i	0.320724	−	0.391989i
$683$	1.39403	+	0.245805i	0.0533411	+	0.00940547i	0.200255	−	0.979744i	$-0.435823\pi$
$683$	1.39403	+	0.245805i	0.0533411	+	0.00940547i	−0.146914	+	0.989149i	$0.546934\pi$
$684$	−8.63363	+	1.74400i	−0.330115	+	0.0666835i
$685$	6.26646	+	7.46808i	0.239429	+	0.285341i
$686$	0.268802	+	0.710987i	0.0102629	+	0.0271456i
$687$	10.6671	−	3.88251i	0.406975	−	0.148127i
$688$	10.1700	−	13.4180i	0.387727	−	0.511557i
$689$	2.92470	−	10.9151i	0.111422	−	0.415833i
$690$	7.88229	−	6.78225i	0.300074	−	0.258196i
$691$	−1.79649	−	20.5340i	−0.0683418	−	0.781150i	−0.950607	−	0.310397i	$-0.899538\pi$
$691$	−1.79649	−	20.5340i	−0.0683418	−	0.781150i	0.882265	−	0.470753i	$-0.156018\pi$
$692$	10.7446	+	2.59539i	0.408447	+	0.0986618i
$693$	−0.188595	+	0.703847i	−0.00716414	+	0.0267369i
$694$	3.95133	+	10.4513i	0.149991	+	0.396728i
$695$	14.9319	+	55.7267i	0.566400	+	2.11383i
$696$	−47.3184	+	24.2455i	−1.79360	+	0.919024i
$697$	−32.8737	−	32.8737i	−1.24518	−	1.24518i
$698$	−6.64716	−	4.53267i	−0.251599	−	0.171564i
$699$	15.0305	−	21.4658i	0.568507	−	0.811912i
$700$	0.0721954	+	0.357401i	0.00272873	+	0.0135085i
$701$	10.0720	−	12.0033i	0.380413	−	0.453358i	−0.541532	−	0.840680i	$-0.682155\pi$
$701$	10.0720	−	12.0033i	0.380413	−	0.453358i	0.921944	+	0.387322i	$0.126600\pi$
$702$	35.6317	+	9.07574i	1.34483	+	0.342542i
$703$	−1.29180	+	3.01489i	−0.0487211	+	0.113709i
$704$	−12.1320	+	14.0851i	−0.457244	+	0.530852i
$705$	−121.684	+	10.6460i	−4.58289	+	0.400951i
$706$	−3.86614	−	8.02965i	−0.145504	−	0.302200i
$707$	0.225707	−	0.322344i	0.00848860	−	0.0121230i
$708$	−4.17409	+	66.7192i	−0.156872	+	2.50746i
$709$	30.7049			1.15315			0.576573	−	0.817046i	$-0.304390\pi$
$709$	30.7049			1.15315			0.576573	+	0.817046i	$0.304390\pi$
$710$	−47.2870	+	8.94356i	−1.77465	+	0.335646i
$711$	48.9444	−	13.1146i	1.83556	−	0.491837i
$712$	−16.7281	−	22.0943i	−0.626912	−	0.828020i
$713$	−2.45643	+	1.41822i	−0.0919942	+	0.0531129i
$714$	0.791779	−	0.00981296i	0.0296316	−	0.000367241i
$715$	−0.952089	−	10.8824i	−0.0356061	−	0.406980i
$716$	10.7352	−	31.9362i	0.401194	−	1.19351i
$717$	−0.511747	−	0.886372i	−0.0191115	−	0.0331022i
$718$	0.450571	−	0.550687i	0.0168152	−	0.0205515i
$719$	−1.46870	−	4.03523i	−0.0547734	−	0.150489i	0.909289	−	0.416166i	$-0.136627\pi$
$719$	−1.46870	−	4.03523i	−0.0547734	−	0.150489i	−0.964062	+	0.265678i	$0.914404\pi$
$720$	−39.5927	−	94.0024i	−1.47553	−	3.50326i
$721$	0.0365843	−	0.418161i	0.00136247	−	0.0155731i
$722$	8.74065	−	24.9734i	0.325293	−	0.929415i
$723$	68.7207	+	12.1173i	2.55575	+	0.450648i
$724$	−22.7550	−	30.8415i	−0.845685	−	1.14622i
$725$	−25.0990	+	9.13527i	−0.932152	+	0.339276i
$726$	25.4784	−	7.16647i	0.945591	−	0.265973i
$727$	−4.77605	−	3.34423i	−0.177134	−	0.124031i	0.481647	−	0.876365i	$-0.340039\pi$
$727$	−4.77605	−	3.34423i	−0.177134	−	0.124031i	−0.658781	+	0.752335i	$0.728928\pi$
$728$	−0.129080	−	0.100377i	−0.00478401	−	0.00372020i
$729$	84.9237	+	49.0307i	3.14532	+	1.81595i
$730$	−51.7547	−	29.0314i	−1.91553	−	1.07450i
$731$	−10.5356	−	15.0464i	−0.389674	−	0.556512i
$732$	18.5799	−	76.9184i	0.686734	−	2.84298i
$733$	−38.0791	+	17.7566i	−1.40648	+	0.655855i	−0.969832	−	0.243775i	$-0.921614\pi$
$733$	−38.0791	+	17.7566i	−1.40648	+	0.655855i	−0.436653	+	0.899630i	$0.643836\pi$
$734$	−10.2322	−	17.2261i	−0.377677	−	0.635827i
$735$	−30.8597	−	66.1789i	−1.13828	−	2.44105i
$736$	3.50175	−	1.90528i	0.129076	−	0.0702296i
$737$	−13.4901	+	11.3195i	−0.496915	+	0.416961i
$738$	−19.8641	+	121.436i	−0.731207	+	4.47014i
$739$	−27.7229	−	27.7229i	−1.01980	−	1.01980i	−0.999800	−	0.0200027i	$-0.993633\pi$
$739$	−27.7229	−	27.7229i	−1.01980	−	1.01980i	−0.0200027	−	0.999800i	$-0.506367\pi$
$740$	−37.1843	−	7.75041i	−1.36692	−	0.284911i
$741$	1.91851	−	1.91851i	0.0704784	−	0.0704784i
$742$	−0.330891	+	0.237857i	−0.0121474	+	0.00873202i
$743$	−10.2614	−	12.2291i	−0.376455	−	0.448641i	0.544237	−	0.838931i	$-0.316819\pi$
$743$	−10.2614	−	12.2291i	−0.376455	−	0.448641i	−0.920692	+	0.390290i	$0.872375\pi$
$744$	7.99410	+	37.1935i	0.293078	+	1.36358i
$745$	27.0754	−	12.6255i	0.991965	−	0.462561i
$746$	−16.0880	−	4.09776i	−0.589022	−	0.150030i
$747$	−24.2907	−	52.0916i	−0.888750	−	1.90593i
$748$	10.5726	+	17.3070i	0.386572	+	0.632806i
$749$	−0.116824	+	0.0818012i	−0.00426866	+	0.00298895i
$750$	1.00576	+	3.57568i	0.0367250	+	0.130565i
$751$	9.83240	−	17.0302i	0.358789	−	0.621442i	−0.628969	−	0.777430i	$-0.716523\pi$
$751$	9.83240	−	17.0302i	0.358789	−	0.621442i	0.987759	+	0.155989i	$0.0498563\pi$
$752$	−46.4635	−	5.83655i	−1.69435	−	0.212837i
$753$	−32.3113	+	46.1453i	−1.17749	+	1.68163i
$754$	5.86001	−	10.4467i	0.213409	−	0.380447i
$755$	19.0510	+	52.3423i	0.693338	+	1.90493i
$756$	−0.787244	−	1.06701i	−0.0286318	−	0.0388066i
$757$	−4.03999	+	22.9119i	−0.146836	+	0.832749i	0.819038	+	0.573739i	$0.194507\pi$
$757$	−4.03999	+	22.9119i	−0.146836	+	0.832749i	−0.965875	+	0.259010i	$0.916604\pi$
$758$	34.1108	−	16.4238i	1.23896	−	0.596539i
$759$	5.45154	+	0.476948i	0.197878	+	0.0173121i
$760$	−4.71704	−	0.652011i	−0.171105	−	0.0236509i
$761$	−0.592246	+	0.215560i	−0.0214689	+	0.00781405i	−0.352732	−	0.935724i	$-0.614747\pi$
$761$	−0.592246	+	0.215560i	−0.0214689	+	0.00781405i	0.331263	+	0.943538i	$0.392525\pi$
$762$	2.07848	+	20.7868i	0.0752955	+	0.753026i
$763$	0.465305	−	0.268644i	0.0168452	−	0.00972557i
$764$	−13.1390	+	6.52802i	−0.475353	+	0.236176i
$765$	−110.856	+	9.69863i	−4.00800	+	0.350655i
$766$	22.4164	+	21.8676i	0.809937	+	0.790107i
$767$	−7.53011	−	13.0425i	−0.271896	−	0.470938i
$768$	−9.90933	−	52.5417i	−0.357572	−	1.89593i
$769$	−2.67454	−	9.98153i	−0.0964465	−	0.359943i	0.900788	−	0.434258i	$-0.142990\pi$
$769$	−2.67454	−	9.98153i	−0.0964465	−	0.359943i	−0.997235	+	0.0743153i	$0.976323\pi$
$770$	−0.221941	+	0.325477i	−0.00799821	+	0.0117294i
$771$			37.9619i			1.36716i
$772$	−49.2810	−	3.08312i	−1.77366	−	0.110964i
$773$	1.46524	+	1.02597i	0.0527012	+	0.0369017i	0.599630	−	0.800277i	$-0.295314\pi$
$773$	1.46524	+	1.02597i	0.0527012	+	0.0369017i	−0.546929	+	0.837179i	$0.684203\pi$
$774$	−16.0605	+	45.8875i	−0.577284	+	1.64939i
$775$	1.66566	+	19.0386i	0.0598323	+	0.683886i
$776$	−1.24997	+	1.34655i	−0.0448714	+	0.0483384i
$777$	−0.780071	+	0.0245986i	−0.0279849	+	0.000882472i
$778$	3.70194	−	2.19893i	0.132721	−	0.0788354i
$779$	4.40063	+	3.69257i	0.157669	+	0.132300i
$780$	26.1763	+	17.3783i	0.937262	+	0.622241i
$781$	−20.7463	−	14.5267i	−0.742362	−	0.519807i
$782$	−0.808249	−	4.27342i	−0.0289029	−	0.152817i
$783$	68.6839	−	68.6839i	2.45456	−	2.45456i
$784$	−6.22123	−	27.2941i	−0.222187	−	0.974788i
$785$	53.2928	−	14.2798i	1.90210	−	0.509667i
$786$	35.2426	+	15.9052i	1.25706	+	0.567320i
$787$	−37.1164	−	9.94532i	−1.32306	−	0.354512i	−0.472936	−	0.881097i	$-0.656806\pi$
$787$	−37.1164	−	9.94532i	−1.32306	−	0.354512i	−0.850123	+	0.526585i	$0.823472\pi$
$788$	−34.5633	−	8.34888i	−1.23126	−	0.297417i
$789$	−26.4259	+	2.31197i	−0.940787	+	0.0823082i
$790$	27.3176	+	2.04920i	0.971917	+	0.0729071i
$791$	−0.0407215	−	0.0109113i	−0.00144789	−	0.000387961i
$792$	20.8617	−	49.4593i	0.741289	−	1.75746i
$793$	6.09717	+	16.7518i	0.216517	+	0.594875i
$794$	20.8364	+	9.40361i	0.739458	+	0.333722i
$795$	59.9846	−	50.3331i	2.12743	−	1.78513i
$796$	−8.93300	−	5.93055i	−0.316622	−	0.210203i
$797$	3.17753	−	18.0207i	0.112554	−	0.638325i	−0.875378	−	0.483438i	$-0.839388\pi$
$797$	3.17753	−	18.0207i	0.112554	−	0.638325i	0.987932	−	0.154886i	$-0.0495012\pi$
$798$	−0.0973586	+	0.00973495i	−0.00344646	+	0.000344614i
$799$	−21.5910	+	46.3021i	−0.763836	+	1.63805i
$800$	−1.66332	−	26.8087i	−0.0588072	−	0.947831i
$801$	65.5502	+	45.8988i	2.31610	+	1.62175i
$802$	16.9536	−	12.1869i	0.598652	−	0.430334i
$803$	−8.08268	−	30.1650i	−0.285231	−	1.06450i
$804$	−1.25529	−	50.6349i	−0.0442705	−	1.78576i
$805$	0.0692027	−	0.0484563i	0.00243908	−	0.00170786i
$806$	−6.13489	−	5.98469i	−0.216092	−	0.210802i
$807$	1.19399	−	3.28045i	0.0420303	−	0.115477i
$808$	−19.7218	+	21.2456i	−0.693811	+	0.747419i
$809$	3.50958	+	7.52632i	0.123390	+	0.264611i	0.958294	−	0.285785i	$-0.0922543\pi$
$809$	3.50958	+	7.52632i	0.123390	+	0.264611i	−0.834903	+	0.550397i	$0.814477\pi$
$810$	95.6208	+	111.130i	3.35977	+	3.90471i
$811$	−37.7230	−	3.30034i	−1.32464	−	0.115891i	−0.597214	−	0.802082i	$-0.703726\pi$
$811$	−37.7230	−	3.30034i	−1.32464	−	0.115891i	−0.727421	+	0.686191i	$0.759281\pi$
$812$	−0.402120	+	0.157752i	−0.0141117	+	0.00553602i
$813$	−4.93837	+	4.93837i	−0.173196	+	0.173196i
$814$	−10.7450	−	16.8558i	−0.376613	−	0.590794i
$815$			4.22947i			0.148152i
$816$	−57.8772	−	7.27029i	−2.02611	−	0.254511i
$817$	1.45893	+	1.73868i	0.0510414	+	0.0608287i
$818$	−1.91825	+	25.5719i	−0.0670699	+	0.894102i
$819$	0.443685	+	0.161488i	0.0155036	+	0.00564285i
$820$	−31.8244	+	58.4189i	−1.11136	+	2.04008i
$821$	−16.2645	+	7.58425i	−0.567634	+	0.264692i	−0.685178	−	0.728375i	$-0.740276\pi$
$821$	−16.2645	+	7.58425i	−0.567634	+	0.264692i	0.117544	+	0.993068i	$0.462498\pi$
$822$	−10.5628	−	10.3042i	−0.368422	−	0.359401i
$823$	0.828729	−	4.69996i	0.0288877	−	0.163830i	−0.966951	−	0.254961i	$-0.917937\pi$
$823$	0.828729	−	4.69996i	0.0288877	−	0.163830i	0.995839	+	0.0911314i	$0.0290483\pi$
$824$	−6.88747	+	30.1453i	−0.239936	+	1.05016i
$825$	18.4357	−	31.9316i	0.641850	−	1.11172i
$826$	−0.0876741	+	0.535984i	−0.00305057	+	0.0186493i
$827$	−10.1883	+	1.79646i	−0.354280	+	0.0624692i	−0.347956	−	0.937511i	$-0.613124\pi$
$827$	−10.1883	+	1.79646i	−0.354280	+	0.0624692i	−0.00632416	+	0.999980i	$0.502013\pi$
$828$	−7.93553	+	8.33899i	−0.275779	+	0.289800i
$829$	−41.8602	+	15.2359i	−1.45387	+	0.529164i	−0.943668	−	0.330893i	$-0.892650\pi$
$829$	−41.8602	+	15.2359i	−1.45387	+	0.529164i	−0.510198	+	0.860057i	$0.670428\pi$
$830$	−3.09166	−	30.9195i	−0.107313	−	1.07323i
$831$	9.41624	+	13.4478i	0.326646	+	0.466498i
$832$	8.40682	+	8.62671i	0.291454	+	0.299077i
$833$	−30.4246	−	2.66180i	−1.05415	−	0.0922260i
$834$	−30.8819	−	81.6833i	−1.06935	−	2.82846i
$835$	−38.3782	−	17.8960i	−1.32813	−	0.619318i
$836$	−1.48782	−	2.01655i	−0.0514574	−	0.0697438i
$837$	−34.7505	−	60.1896i	−1.20115	−	2.08046i
$838$	−27.1182	−	2.03424i	−0.936784	−	0.0702717i
$839$	−14.1191	+	16.8264i	−0.487444	+	0.580913i	−0.952565	−	0.304334i	$-0.901566\pi$
$839$	−14.1191	+	16.8264i	−0.487444	+	0.580913i	0.465121	+	0.885247i	$0.346011\pi$
$840$	−0.333740	−	1.08281i	−0.0115151	−	0.0373604i
$841$	−1.32121	−	2.28840i	−0.0455588	−	0.0789102i
$842$	−31.3763	+	11.8624i	−1.08130	+	0.408806i
$843$	−53.4171	+	92.5211i	−1.83978	+	3.18659i
$844$	3.55691	−	56.8542i	0.122434	−	1.95700i
$845$	33.5105			1.15280
$846$	132.866	−	25.1294i	4.56801	−	0.863965i
$847$	0.211760	−	0.0373390i	0.00727616	−	0.00128298i
$848$	26.5451	−	14.0195i	0.911564	−	0.481432i
$849$	1.54985	+	17.7148i	0.0531905	+	0.607971i
$850$	−28.3971	−	7.23302i	−0.974012	−	0.248090i
$851$	0.877059	+	4.19599i	0.0300652	+	0.143837i
$852$	69.8738	−	20.5916i	2.39384	−	0.705458i
$853$	15.1771	−	18.0873i	0.519653	−	0.619298i	−0.440846	−	0.897583i	$-0.645321\pi$
$853$	15.1771	−	18.0873i	0.519653	−	0.619298i	0.960499	+	0.278285i	$0.0897659\pi$
$854$	0.212375	−	0.606790i	0.00726733	−	0.0207639i
$855$	13.5414	−	2.38771i	0.463106	−	0.0816580i
$856$	9.35006	−	4.79089i	0.319578	−	0.163749i
$857$	21.7940	−	21.7940i	0.744469	−	0.744469i	−0.228966	−	0.973435i	$-0.573534\pi$
$857$	21.7940	−	21.7940i	0.744469	−	0.744469i	0.973435	+	0.228966i	$0.0735343\pi$
$858$	3.07287	+	16.2470i	0.104906	+	0.554665i
$859$	30.0072	+	17.3247i	1.02383	+	0.591109i	0.915211	−	0.402974i	$-0.132023\pi$
$859$	30.0072	+	17.3247i	1.02383	+	0.591109i	0.108620	+	0.994083i	$0.465357\pi$
$860$	−16.3907	+	20.5471i	−0.558920	+	0.700651i
$861$	−0.353782	+	1.32033i	−0.0120569	+	0.0449968i
$862$	29.1549	−	29.8867i	0.993021	−	1.01794i
$863$	30.3378	−	36.1552i	1.03271	−	1.23074i	0.0601250	−	0.998191i	$-0.480850\pi$
$863$	30.3378	−	36.1552i	1.03271	−	1.23074i	0.972585	−	0.232546i	$-0.0747055\pi$
$864$	46.6847	+	85.8028i	1.58825	+	2.91907i
$865$	−16.6679	−	4.46614i	−0.566725	−	0.151853i
$866$	−23.0023	+	28.1134i	−0.781651	+	0.955333i
$867$	−2.88600	+	6.18906i	−0.0980138	+	0.210191i
$868$	0.0345599	+	0.307134i	0.00117304	+	0.0104248i
$869$	9.26684	+	11.0438i	0.314356	+	0.374635i
$870$	74.7846	−	36.0076i	2.53544	−	1.22077i
$871$	6.54496	+	9.34717i	0.221768	+	0.316717i
$872$	−36.6642	+	14.9103i	−1.24161	+	0.504927i
$873$	2.24212	−	4.80823i	0.0758842	−	0.162734i
$874$	0.145514	+	0.517334i	0.00492208	+	0.0174991i
$875$	0.00524022	+	0.0297188i	0.000177152	+	0.00100468i
$876$	82.3218	+	35.9311i	2.78140	+	1.21400i
$877$	−23.4243	+	6.27652i	−0.790983	+	0.211943i	−0.631621	−	0.775277i	$-0.717610\pi$
$877$	−23.4243	+	6.27652i	−0.790983	+	0.211943i	−0.159361	+	0.987220i	$0.550944\pi$
$878$	−3.78022	+	1.06329i	−0.127576	+	0.0358843i
$879$	2.50793	−	14.2232i	0.0845905	−	0.479737i
$880$	19.4786	−	21.5122i	0.656623	−	0.725177i
$881$	−12.2312	+	33.6050i	−0.412081	+	1.13218i	0.544002	+	0.839084i	$0.316908\pi$
$881$	−12.2312	+	33.6050i	−0.412081	+	1.13218i	−0.956082	+	0.293098i	$0.905314\pi$
$882$	41.2819	+	69.4988i	1.39003	+	2.34015i
$883$	13.4285	−	36.8946i	0.451906	−	1.24160i	−0.479475	−	0.877556i	$-0.659173\pi$
$883$	13.4285	−	36.8946i	0.451906	−	1.24160i	0.931381	−	0.364046i	$-0.118605\pi$
$884$	11.7688	−	5.84723i	0.395827	−	0.196664i
$885$	9.09554	−	103.963i	0.305743	−	3.49466i
$886$	4.25717	−	3.06022i	0.143023	−	0.102810i
$887$		−	24.8089i		−	0.833001i	−0.909135	−	0.416501i	$-0.863256\pi$
$887$		−	24.8089i		−	0.833001i	0.909135	−	0.416501i	$-0.136744\pi$
$888$	57.1719	+	6.07324i	1.91856	+	0.203805i
$889$			0.169721i			0.00569225i
$890$	25.2516	+	35.1283i	0.846435	+	1.17750i
$891$	−6.72434	+	76.8596i	−0.225274	+	2.57489i
$892$	6.99381	−	20.8058i	0.234170	−	0.696631i
$893$	2.15911	−	5.93210i	0.0722518	−	0.198510i
$894$	−38.8778	+	23.0932i	−1.30027	+	0.772353i
$895$	−17.9893	+	49.4253i	−0.601317	+	1.65210i
$896$	−0.0376363	−	0.432757i	−0.00125734	−	0.0144574i
$897$	0.615743	−	3.49205i	0.0205590	−	0.116596i
$898$	2.01526	+	7.16470i	0.0672502	+	0.239089i
$899$	−21.8692	+	5.85985i	−0.729380	+	0.195437i
$900$	28.3255	+	72.2035i	0.944184	+	2.40678i
$901$	−5.68712	−	32.2532i	−0.189465	−	1.07451i
$902$	−33.7018	+	9.47954i	−1.12215	+	0.315634i
$903$	−0.228240	+	0.489463i	−0.00759537	+	0.0162883i
$904$	2.86150	+	1.20697i	0.0951720	+	0.0401431i
$905$	34.3190	+	49.0126i	1.14080	+	1.62923i
$906$	−36.5762	−	75.9656i	−1.21516	−	2.52379i
$907$	23.3924	+	27.8780i	0.776732	+	0.925673i	0.998781	−	0.0493626i	$-0.0157190\pi$
$907$	23.3924	+	27.8780i	0.776732	+	0.925673i	−0.222049	+	0.975035i	$0.571275\pi$
$908$	−4.91762	−	3.92286i	−0.163197	−	0.130185i
$909$	35.3757	−	75.8633i	1.17334	−	2.51623i
$910$	0.197562	+	0.161645i	0.00654912	+	0.00535847i
$911$	−38.0576	−	10.1975i	−1.26090	−	0.337858i	−0.434364	−	0.900737i	$-0.643027\pi$
$911$	−38.0576	−	10.1975i	−1.26090	−	0.337858i	−0.826539	+	0.562880i	$0.809694\pi$
$912$	7.20271	+	0.271633i	0.238505	+	0.00899467i
$913$	10.5115	−	12.5271i	0.347879	−	0.414586i
$914$	6.48209	+	6.32339i	0.214409	+	0.209159i
$915$	−31.9723	+	119.322i	−1.05697	+	3.94468i
$916$	−6.75126	+	0.759676i	−0.223068	+	0.0251004i
$917$	0.272045	+	0.157065i	0.00898372	+	0.00518675i
$918$	104.711	−	19.8044i	3.45597	−	0.653642i
$919$	9.86029	−	9.86029i	0.325261	−	0.325261i	−0.525520	−	0.850781i	$-0.676129\pi$
$919$	9.86029	−	9.86029i	0.325261	−	0.325261i	0.850781	+	0.525520i	$0.176129\pi$
$920$	−5.53866	+	2.83796i	−0.182604	+	0.0935647i
$921$	−58.4389	+	10.3043i	−1.92563	+	0.339540i
$922$	14.6920	+	5.14216i	0.483855	+	0.169348i
$923$	−10.5487	+	12.5714i	−0.347214	+	0.413793i
$924$	0.285258	−	0.523637i	0.00938428	−	0.0172264i
$925$	28.1202	+	6.59234i	0.924586	+	0.216755i
$926$	−12.1866	+	47.8450i	−0.400476	+	1.57228i
$927$	−7.78210	−	88.9498i	−0.255598	−	2.92149i
$928$	30.9350	−	7.45556i	1.01549	−	0.244741i
$929$	12.0958	−	2.13281i	0.396849	−	0.0699751i	0.0283375	−	0.999598i	$-0.490979\pi$
$929$	12.0958	−	2.13281i	0.396849	−	0.0699751i	0.368511	+	0.929623i	$0.379868\pi$
$930$	−11.0368	−	58.3547i	−0.361912	−	1.91352i
$931$	3.77379			0.123681
$932$	−11.7606	+	10.3757i	−0.385232	+	0.339868i
$933$	−0.669528	+	1.15966i	−0.0219194	+	0.0379654i
$934$	−18.2101	−	48.1661i	−0.595853	−	1.57604i
$935$	−15.8303	−	27.4189i	−0.517706	−	0.896693i
$936$	−30.7480	−	16.2595i	−1.00503	−	0.531457i
$937$	−4.67787	+	5.57487i	−0.152819	+	0.182123i	−0.837023	−	0.547168i	$-0.815706\pi$
$937$	−4.67787	+	5.57487i	−0.152819	+	0.182123i	0.684203	+	0.729292i	$0.260150\pi$
$938$	0.0307817	−	0.410348i	0.00100506	−	0.0133983i
$939$	7.47297	+	12.9436i	0.243871	+	0.422397i
$940$	72.2866	+	10.9064i	2.35773	+	0.355726i
$941$	−30.3683	−	14.1610i	−0.989977	−	0.461634i	−0.140969	−	0.990014i	$-0.545022\pi$
$941$	−30.3683	−	14.1610i	−0.989977	−	0.461634i	−0.849008	+	0.528380i	$0.822800\pi$
$942$	−78.1158	+	29.5332i	−2.54515	+	0.962243i
$943$	7.47918	+	0.654344i	0.243556	+	0.0213084i
$944$	11.8041	−	38.2278i	0.384190	−	1.24421i
$945$	1.18731	+	1.69566i	0.0386234	+	0.0551599i
$946$	−13.7636	+	1.37623i	−0.447493	+	0.0447451i
$947$	55.1688	−	20.0798i	1.79274	−	0.652505i	0.793722	−	0.608281i	$-0.208141\pi$
$947$	55.1688	−	20.0798i	1.79274	−	0.652505i	0.999022	−	0.0442246i	$-0.0140817\pi$
$948$	−41.4527	+	1.02765i	−1.34632	+	0.0333765i
$949$	−19.9280	+	3.51385i	−0.646891	+	0.114064i
$950$	3.57344	+	0.584529i	0.115938	+	0.0189646i
$951$	32.7322	−	56.6939i	1.06141	−	1.83842i
$952$	−0.462003	−	0.105557i	−0.0149736	−	0.00342111i
$953$	1.47496	−	8.36490i	0.0477786	−	0.270966i	−0.951555	−	0.307480i	$-0.900514\pi$
$953$	1.47496	−	8.36490i	0.0477786	−	0.270966i	0.999333	+	0.0365142i	$0.0116254\pi$
$954$	−60.5308	+	62.0500i	−1.95976	+	2.00894i
$955$	20.7577	−	9.67950i	0.671705	−	0.313221i
$956$	0.173155	+	0.587567i	0.00560022	+	0.0190033i
$957$	41.0465	+	14.9397i	1.32684	+	0.482932i
$958$	8.49833	+	0.637492i	0.274569	+	0.0205964i
$959$	−0.0770609	−	0.0918377i	−0.00248843	−	0.00296559i
$960$	13.4320	+	82.3816i	0.433516	+	2.65885i
$961$		−	14.8002i		−	0.477425i
$962$	−11.4873	+	5.98402i	−0.370364	+	0.192933i
$963$	−21.4514	+	21.4514i	−0.691261	+	0.691261i
$964$	−38.2760	−	16.7064i	−1.23279	−	0.538076i
$965$	76.7902	+	6.71827i	2.47196	+	0.216269i
$966$	−0.0969313	+	0.0834037i	−0.00311871	+	0.00268347i
$967$	−6.49010	−	13.9181i	−0.208707	−	0.447575i	0.773891	−	0.633319i	$-0.218308\pi$
$967$	−6.49010	−	13.9181i	−0.208707	−	0.447575i	−0.982598	+	0.185745i	$0.940530\pi$
$968$	−15.8293	+	0.588785i	−0.508773	+	0.0189243i
$969$	2.68949	−	7.38930i	0.0863988	−	0.237379i
$970$	2.00284	−	2.05311i	0.0643074	−	0.0659214i
$971$	−40.8402	+	28.5966i	−1.31062	+	0.917708i	−0.999467	−	0.0326507i	$-0.989605\pi$
$971$	−40.8402	+	28.5966i	−1.31062	+	0.917708i	−0.311156	+	0.950359i	$0.600716\pi$
$972$	−85.7003	−	81.5539i	−2.74884	−	2.61584i
$973$	−0.183623	−	0.685291i	−0.00588669	−	0.0219694i
$974$	7.10855	+	9.88892i	0.227773	+	0.316862i
$975$	−19.5708	−	13.7036i	−0.626768	−	0.438868i
$976$	−21.6180	+	42.1369i	−0.691976	+	1.34877i
$977$	17.4701	−	37.4648i	0.558919	−	1.19861i	−0.400415	−	0.916334i	$-0.631134\pi$
$977$	17.4701	−	37.4648i	0.558919	−	1.19861i	0.959334	−	0.282272i	$-0.0910882\pi$
$978$	−0.636956	−	6.37016i	−0.0203676	−	0.203695i
$979$	−3.95352	+	22.4215i	−0.126355	+	0.716596i
$980$	8.65305	+	42.8367i	0.276411	+	1.36837i
$981$	87.5514	−	73.4643i	2.79530	−	2.34554i
$982$	−6.26311	+	13.8777i	−0.199864	+	0.442857i
$983$	20.2862	+	55.7358i	0.647028	+	1.77769i	0.628428	+	0.777868i	$0.283699\pi$
$983$	20.2862	+	55.7358i	0.647028	+	1.77769i	0.0185996	+	0.999827i	$0.494079\pi$
$984$	39.1341	−	92.7797i	1.24755	−	2.95771i
$985$	53.6175	+	14.3668i	1.70840	+	0.457763i
$986$	2.59684	−	34.6182i	0.0827003	−	1.10247i
$987$	1.49639	−	0.130917i	0.0476307	−	0.00416714i
$988$	−1.38571	+	0.846510i	−0.0440853	+	0.0269311i
$989$	2.86522	+	0.767734i	0.0911088	+	0.0244125i
$990$	−34.4710	+	76.3806i	−1.09556	+	2.42753i
$991$	23.3831	−	6.26549i	0.742789	−	0.199030i	0.132472	−	0.991187i	$-0.457709\pi$
$991$	23.3831	−	6.26549i	0.742789	−	0.199030i	0.610317	+	0.792157i	$0.291042\pi$
$992$	0.576019	−	22.7610i	0.0182886	−	0.722662i
$993$	−72.2443	+	72.2443i	−2.29260	+	2.29260i
$994$	0.581505	−	0.109982i	0.0184442	−	0.00348842i
$995$	13.7117	+	9.60101i	0.434689	+	0.304372i
$996$	9.31294	+	46.1035i	0.295092	+	1.46084i
$997$	−30.5120	−	25.6026i	−0.966324	−	0.810842i	0.0156467	−	0.999878i	$-0.495019\pi$
$997$	−30.5120	−	25.6026i	−0.966324	−	0.810842i	−0.981970	+	0.189036i	$0.939464\pi$
$998$	−12.9299	−	21.7677i	−0.409288	−	0.689044i
$999$	−102.814	+	21.4904i	−3.25288	+	0.679926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.ca.a.19.4	✓	888
16.11	odd	4		592.2.cd.a.315.9	yes	888
37.2	odd	36		592.2.cd.a.483.9	yes	888
592.187	even	36	inner	592.2.ca.a.187.4	yes	888

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.ca.a.19.4	✓	888	1.1	even	1	trivial
592.2.ca.a.187.4	yes	888	592.187	even	36	inner
592.2.cd.a.315.9	yes	888	16.11	odd	4
592.2.cd.a.483.9	yes	888	37.2	odd	36

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.ca (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39566 - 0.228297i) q^{2} +(-3.32903 - 0.291252i) q^{3} +(1.89576 + 0.637253i) q^{4} +(-2.93393 - 1.06786i) q^{5} +(4.57972 + 1.16650i) q^{6} +(0.0360796 + 0.0131319i) q^{7} +(-2.50036 - 1.32219i) q^{8} +(8.04320 + 1.41823i) q^{9} +O(q^{10})\)	\(q+(-1.39566 - 0.228297i) q^{2} +(-3.32903 - 0.291252i) q^{3} +(1.89576 + 0.637253i) q^{4} +(-2.93393 - 1.06786i) q^{5} +(4.57972 + 1.16650i) q^{6} +(0.0360796 + 0.0131319i) q^{7} +(-2.50036 - 1.32219i) q^{8} +(8.04320 + 1.41823i) q^{9} +(3.85099 + 2.16019i) q^{10} +(0.601420 + 2.24453i) q^{11} +(-6.12545 - 2.67358i) q^{12} +(1.48282 - 0.261460i) q^{13} +(-0.0473570 - 0.0265646i) q^{14} +(9.45612 + 4.40946i) q^{15} +(3.18782 + 2.41616i) q^{16} +(3.57469 - 2.50302i) q^{17} +(-10.9018 - 3.81562i) q^{18} +(-0.413071 + 0.346608i) q^{19} +(-4.88153 - 3.89407i) q^{20} +(-0.116285 - 0.0542247i) q^{21} +(-0.326961 - 3.26992i) q^{22} +(-0.182396 + 0.680712i) q^{23} +(7.93870 + 5.12984i) q^{24} +(3.63738 + 3.05213i) q^{25} +(-2.12921 + 0.0263884i) q^{26} +(-16.6794 - 4.46922i) q^{27} +(0.0600299 + 0.0478867i) q^{28} +(-2.81258 + 4.87153i) q^{29} +(-12.1909 - 8.31294i) q^{30} +(2.84603 + 2.84603i) q^{31} +(-3.89752 - 4.09992i) q^{32} +(-1.34842 - 7.64728i) q^{33} +(-5.56050 + 2.67729i) q^{34} +(-0.0918318 - 0.0770560i) q^{35} +(14.3442 + 7.81418i) q^{36} +(5.42909 - 2.74316i) q^{37} +(0.655638 - 0.389445i) q^{38} +(-5.01249 + 0.438536i) q^{39} +(5.92397 + 6.54925i) q^{40} +(-1.84995 - 10.4916i) q^{41} +(0.149916 + 0.102227i) q^{42} -4.20916i q^{43} +(-0.290185 + 4.63835i) q^{44} +(-22.0837 - 12.7500i) q^{45} +(0.409968 - 0.908405i) q^{46} +(-10.1387 + 5.85359i) q^{47} +(-9.90863 - 8.97192i) q^{48} +(-5.36118 - 4.49857i) q^{49} +(-4.37978 - 5.09015i) q^{50} +(-12.6293 + 7.29150i) q^{51} +(2.97768 + 0.449262i) q^{52} +(3.17173 - 6.80181i) q^{53} +(22.2585 + 10.0454i) q^{54} +(0.632327 - 7.22753i) q^{55} +(-0.0728492 - 0.0805385i) q^{56} +(1.47608 - 1.03356i) q^{57} +(5.03758 - 6.15692i) q^{58} +(-3.42095 - 9.39899i) q^{59} +(15.1166 + 14.3852i) q^{60} +(2.05594 + 11.6598i) q^{61} +(-3.32237 - 4.62185i) q^{62} +(0.271571 + 0.156792i) q^{63} +(4.50364 + 6.61190i) q^{64} +(-4.62968 - 0.816338i) q^{65} +(0.136092 + 10.9809i) q^{66} +(3.20279 + 6.86840i) q^{67} +(8.37181 - 2.46715i) q^{68} +(0.805461 - 2.21299i) q^{69} +(0.110575 + 0.128509i) q^{70} +(-8.34927 + 7.00587i) q^{71} +(-18.2357 - 14.1807i) q^{72} -13.4393 q^{73} +(-8.20345 + 2.58909i) q^{74} +(-11.2200 - 11.2200i) q^{75} +(-1.00396 + 0.393855i) q^{76} +(-0.00777595 + 0.0888795i) q^{77} +(7.09588 + 0.532288i) q^{78} +(5.62287 - 2.62199i) q^{79} +(-6.77270 - 10.4930i) q^{80} +(31.2002 + 11.3560i) q^{81} +(0.186710 + 15.0651i) q^{82} +(-4.03651 - 5.76473i) q^{83} +(-0.185894 - 0.176900i) q^{84} +(-13.1608 + 3.52641i) q^{85} +(-0.960939 + 5.87457i) q^{86} +(10.7820 - 15.3983i) q^{87} +(1.46392 - 6.40733i) q^{88} +(8.87990 + 4.14077i) q^{89} +(27.9106 + 22.8364i) q^{90} +(0.0569328 + 0.0100388i) q^{91} +(-0.779565 + 1.17423i) q^{92} +(-8.64562 - 10.3035i) q^{93} +(15.4866 - 5.85500i) q^{94} +(1.58205 - 0.575819i) q^{95} +(11.7809 + 14.7839i) q^{96} +(0.168124 - 0.627446i) q^{97} +(6.45540 + 7.50243i) q^{98} +(1.65407 + 18.9062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 888 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 24 q^{8}+O(q^{10}) \) 888 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 24 * q^7 - 24 * q^8	\( 888 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 24 q^{7} - 24 q^{8} - 6 q^{10} - 18 q^{11} + 18 q^{12} - 12 q^{13} - 12 q^{14} + 18 q^{16} - 24 q^{17} - 120 q^{18} - 12 q^{19} - 12 q^{20} - 12 q^{21} - 42 q^{22} - 24 q^{23} - 24 q^{24} - 6 q^{26} - 18 q^{27} - 42 q^{28} - 6 q^{29} - 78 q^{30} + 24 q^{32} - 24 q^{33} - 12 q^{34} - 12 q^{35} + 36 q^{37} - 108 q^{38} - 24 q^{39} + 18 q^{40} - 30 q^{42} - 96 q^{44} - 18 q^{45} + 48 q^{46} - 18 q^{48} - 24 q^{49} + 30 q^{50} - 198 q^{51} - 12 q^{52} - 36 q^{53} + 18 q^{54} - 24 q^{55} + 156 q^{56} - 84 q^{58} - 12 q^{59} + 144 q^{60} - 12 q^{61} - 12 q^{62} - 144 q^{64} + 24 q^{66} - 12 q^{67} + 138 q^{68} + 6 q^{69} + 60 q^{70} - 24 q^{71} - 180 q^{72} + 48 q^{73} - 54 q^{74} - 24 q^{75} + 96 q^{76} - 30 q^{77} + 60 q^{78} - 144 q^{80} - 24 q^{81} - 36 q^{82} + 48 q^{83} - 12 q^{84} - 18 q^{85} + 12 q^{86} - 192 q^{87} - 120 q^{88} - 48 q^{89} - 78 q^{90} - 12 q^{91} + 336 q^{92} + 24 q^{93} - 60 q^{94} - 126 q^{96} - 24 q^{97} + 42 q^{98} - 210 q^{99}+O(q^{100}) \) 888 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 24 * q^7 - 24 * q^8 - 6 * q^10 - 18 * q^11 + 18 * q^12 - 12 * q^13 - 12 * q^14 + 18 * q^16 - 24 * q^17 - 120 * q^18 - 12 * q^19 - 12 * q^20 - 12 * q^21 - 42 * q^22 - 24 * q^23 - 24 * q^24 - 6 * q^26 - 18 * q^27 - 42 * q^28 - 6 * q^29 - 78 * q^30 + 24 * q^32 - 24 * q^33 - 12 * q^34 - 12 * q^35 + 36 * q^37 - 108 * q^38 - 24 * q^39 + 18 * q^40 - 30 * q^42 - 96 * q^44 - 18 * q^45 + 48 * q^46 - 18 * q^48 - 24 * q^49 + 30 * q^50 - 198 * q^51 - 12 * q^52 - 36 * q^53 + 18 * q^54 - 24 * q^55 + 156 * q^56 - 84 * q^58 - 12 * q^59 + 144 * q^60 - 12 * q^61 - 12 * q^62 - 144 * q^64 + 24 * q^66 - 12 * q^67 + 138 * q^68 + 6 * q^69 + 60 * q^70 - 24 * q^71 - 180 * q^72 + 48 * q^73 - 54 * q^74 - 24 * q^75 + 96 * q^76 - 30 * q^77 + 60 * q^78 - 144 * q^80 - 24 * q^81 - 36 * q^82 + 48 * q^83 - 12 * q^84 - 18 * q^85 + 12 * q^86 - 192 * q^87 - 120 * q^88 - 48 * q^89 - 78 * q^90 - 12 * q^91 + 336 * q^92 + 24 * q^93 - 60 * q^94 - 126 * q^96 - 24 * q^97 + 42 * q^98 - 210 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more