LMFDB - Embedded newform 570.2.bb.b.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.b.431.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-1.01882 + 1.40072i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.68082 - 0.418131i) q^{6} +(0.0247885 + 0.0429350i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.924029 - 2.85415i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.01882 + 1.40072i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.68082 - 0.418131i) q^{6} +(0.0247885 + 0.0429350i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.924029 - 2.85415i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(-3.95269 - 2.28209i) q^{11} +(-1.55635 - 0.760105i) q^{12} +(1.88266 - 5.17256i) q^{13} +(0.00860897 - 0.0488239i) q^{14} +(-1.24657 + 1.20252i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.54568 - 1.84207i) q^{17} +(-1.12677 + 2.78036i) q^{18} +(1.29242 + 4.16289i) q^{19} +1.00000i q^{20} +(-0.0853949 - 0.00902109i) q^{21} +(1.56104 + 4.28892i) q^{22} +(7.43226 - 1.31051i) q^{23} +(0.703651 + 1.58268i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-4.76706 + 2.75226i) q^{26} +(4.93928 + 1.61355i) q^{27} +(-0.0379783 + 0.0318675i) q^{28} +(0.178067 - 0.149416i) q^{29} +(1.72790 - 0.119907i) q^{30} +(-3.24992 + 1.87634i) q^{31} +(0.939693 + 0.342020i) q^{32} +(7.22363 - 3.21159i) q^{33} +(-2.36812 + 0.417563i) q^{34} +(0.0169564 + 0.0465872i) q^{35} +(2.65033 - 1.40561i) q^{36} -4.36974i q^{37} +(1.68581 - 4.01971i) q^{38} +(5.32722 + 7.90696i) q^{39} +(0.642788 - 0.766044i) q^{40} +(1.98626 - 0.722940i) q^{41} +(0.0596176 + 0.0618013i) q^{42} +(2.01451 - 11.4249i) q^{43} +(1.56104 - 4.28892i) q^{44} +(-0.414373 - 2.97124i) q^{45} +(-6.53582 - 3.77346i) q^{46} +(-1.05055 - 1.25200i) q^{47} +(0.478300 - 1.66470i) q^{48} +(3.49877 - 6.06005i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.00546 + 4.04179i) q^{51} +(5.42090 + 0.955851i) q^{52} +(0.773243 + 4.38528i) q^{53} +(-2.74654 - 4.41096i) q^{54} +(-3.49636 - 2.93380i) q^{55} +0.0495771 q^{56} +(-7.14778 - 2.43091i) q^{57} -0.232450 q^{58} +(10.2644 + 8.61286i) q^{59} +(-1.40072 - 1.01882i) q^{60} +(-0.950706 - 5.39172i) q^{61} +(3.69567 + 0.651646i) q^{62} +(0.0996377 - 0.110423i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.75226 - 4.76706i) q^{65} +(-7.59799 - 2.18304i) q^{66} +(1.40754 + 1.67745i) q^{67} +(2.08249 + 1.20233i) q^{68} +(-5.73645 + 11.7457i) q^{69} +(0.0169564 - 0.0465872i) q^{70} +(0.580865 - 3.29425i) q^{71} +(-2.93378 - 0.626843i) q^{72} +(8.80341 - 3.20418i) q^{73} +(-2.80882 + 3.34742i) q^{74} +(-1.43645 + 0.967790i) q^{75} +(-3.87522 + 1.99566i) q^{76} -0.226279i q^{77} +(1.00161 - 9.48136i) q^{78} +(-0.806619 - 2.21617i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(-7.29234 + 5.27463i) q^{81} +(-1.98626 - 0.722940i) q^{82} +(-8.15617 + 4.70897i) q^{83} +(-0.00594463 - 0.0856640i) q^{84} +(1.84207 - 1.54568i) q^{85} +(-8.88698 + 7.45706i) q^{86} +(0.0278724 + 0.401650i) q^{87} +(-3.95269 + 2.28209i) q^{88} +(-3.17977 - 1.15734i) q^{89} +(-1.59245 + 2.54246i) q^{90} +(0.268752 - 0.0473883i) q^{91} +(2.58120 + 7.09178i) q^{92} +(0.682841 - 6.46387i) q^{93} +1.63437i q^{94} +(0.549903 + 4.32407i) q^{95} +(-1.43645 + 0.967790i) q^{96} +(-3.76924 + 4.49200i) q^{97} +(-6.57554 + 2.39330i) q^{98} +(-2.86102 + 13.3903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−1.01882	+	1.40072i	−0.588214	+	0.808706i
$3$	−1.01882	+	1.40072i	−0.588214	+	0.808706i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$6$	1.68082	−	0.418131i	0.686193	−	0.170701i
$7$	0.0247885	+	0.0429350i	0.00936919	+	0.0162279i	0.870672	−	0.491864i	$-0.163684\pi$
$7$	0.0247885	+	0.0429350i	0.00936919	+	0.0162279i	−0.861303	+	0.508092i	$0.830351\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.924029	−	2.85415i	−0.308010	−	0.951383i
$10$	−0.642788	−	0.766044i	−0.203267	−	0.242245i
$11$	−3.95269	−	2.28209i	−1.19178	−	0.688076i	−0.233071	−	0.972460i	$-0.574878\pi$
$11$	−3.95269	−	2.28209i	−1.19178	−	0.688076i	−0.958710	+	0.284384i	$0.908211\pi$
$12$	−1.55635	−	0.760105i	−0.449281	−	0.219424i
$13$	1.88266	−	5.17256i	0.522155	−	1.43461i	−0.345961	−	0.938249i	$-0.612447\pi$
$13$	1.88266	−	5.17256i	0.522155	−	1.43461i	0.868116	−	0.496361i	$-0.165331\pi$
$14$	0.00860897	−	0.0488239i	0.00230084	−	0.0130487i
$15$	−1.24657	+	1.20252i	−0.321863	+	0.310490i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.54568	−	1.84207i	0.374882	−	0.446768i	−0.545310	−	0.838235i	$-0.683588\pi$
$17$	1.54568	−	1.84207i	0.374882	−	0.446768i	0.920192	+	0.391467i	$0.128032\pi$
$18$	−1.12677	+	2.78036i	−0.265581	+	0.655337i
$19$	1.29242	+	4.16289i	0.296501	+	0.955033i
$19$	1.29242	+	4.16289i	0.296501	+	0.955033i
$20$			1.00000i			0.223607i
$21$	−0.0853949	−	0.00902109i	−0.0186347	−	0.00196856i
$22$	1.56104	+	4.28892i	0.332815	+	0.914402i
$23$	7.43226	−	1.31051i	1.54973	−	0.273260i	0.667694	−	0.744436i	$-0.267281\pi$
$23$	7.43226	−	1.31051i	1.54973	−	0.273260i	0.882039	+	0.471176i	$0.156170\pi$
$24$	0.703651	+	1.58268i	0.143632	+	0.323063i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−4.76706	+	2.75226i	−0.934897	+	0.539763i
$27$	4.93928	+	1.61355i	0.950564	+	0.310528i
$28$	−0.0379783	+	0.0318675i	−0.00717722	+	0.00602240i
$29$	0.178067	−	0.149416i	0.0330663	−	0.0277459i	−0.626105	−	0.779739i	$-0.715352\pi$
$29$	0.178067	−	0.149416i	0.0330663	−	0.0277459i	0.659171	+	0.751993i	$0.270907\pi$
$30$	1.72790	−	0.119907i	0.315469	−	0.0218919i
$31$	−3.24992	+	1.87634i	−0.583702	+	0.337001i	−0.762603	−	0.646866i	$-0.776079\pi$
$31$	−3.24992	+	1.87634i	−0.583702	+	0.337001i	0.178901	+	0.983867i	$0.442746\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	7.22363	−	3.21159i	1.25747	−	0.559065i
$34$	−2.36812	+	0.417563i	−0.406129	+	0.0716115i
$35$	0.0169564	+	0.0465872i	0.00286615	+	0.00787468i
$36$	2.65033	−	1.40561i	0.441722	−	0.234268i
$37$		−	4.36974i		−	0.718382i	−0.933264	−	0.359191i	$-0.883053\pi$
$37$		−	4.36974i		−	0.718382i	0.933264	−	0.359191i	$-0.116947\pi$
$38$	1.68581	−	4.01971i	0.273474	−	0.652083i
$39$	5.32722	+	7.90696i	0.853038	+	1.26613i
$40$	0.642788	−	0.766044i	0.101634	−	0.121122i
$41$	1.98626	−	0.722940i	0.310202	−	0.112904i	−0.182228	−	0.983256i	$-0.558331\pi$
$41$	1.98626	−	0.722940i	0.310202	−	0.112904i	0.492430	+	0.870352i	$0.336109\pi$
$42$	0.0596176	+	0.0618013i	0.00919920	+	0.00953615i
$43$	2.01451	−	11.4249i	0.307211	−	1.74228i	−0.305702	−	0.952127i	$-0.598891\pi$
$43$	2.01451	−	11.4249i	0.307211	−	1.74228i	0.612913	−	0.790151i	$-0.289998\pi$
$44$	1.56104	−	4.28892i	0.235336	−	0.646580i
$45$	−0.414373	−	2.97124i	−0.0617710	−	0.442927i
$46$	−6.53582	−	3.77346i	−0.963654	−	0.556366i
$47$	−1.05055	−	1.25200i	−0.153239	−	0.182623i	0.683964	−	0.729516i	$-0.260255\pi$
$47$	−1.05055	−	1.25200i	−0.153239	−	0.182623i	−0.837202	+	0.546893i	$0.815810\pi$
$48$	0.478300	−	1.66470i	0.0690366	−	0.240279i
$49$	3.49877	−	6.06005i	0.499824	−	0.865721i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.00546	+	4.04179i	0.140792	+	0.565964i
$52$	5.42090	+	0.955851i	0.751743	+	0.132553i
$53$	0.773243	+	4.38528i	0.106213	+	0.602364i	0.990729	+	0.135854i	$0.0433778\pi$
$53$	0.773243	+	4.38528i	0.106213	+	0.602364i	−0.884516	+	0.466510i	$0.845511\pi$
$54$	−2.74654	−	4.41096i	−0.373756	−	0.600255i
$55$	−3.49636	−	2.93380i	−0.471449	−	0.395593i
$56$	0.0495771			0.00662502
$57$	−7.14778	−	2.43091i	−0.946746	−	0.321982i
$58$	−0.232450			−0.0305222
$59$	10.2644	+	8.61286i	1.33631	+	1.12130i	0.982557	+	0.185960i	$0.0595396\pi$
$59$	10.2644	+	8.61286i	1.33631	+	1.12130i	0.353754	+	0.935338i	$0.384905\pi$
$60$	−1.40072	−	1.01882i	−0.180832	−	0.131529i
$61$	−0.950706	−	5.39172i	−0.121725	−	0.690339i	−0.983199	−	0.182537i	$-0.941569\pi$
$61$	−0.950706	−	5.39172i	−0.121725	−	0.690339i	0.861474	−	0.507802i	$-0.169542\pi$
$62$	3.69567	+	0.651646i	0.469351	+	0.0827592i
$63$	0.0996377	−	0.110423i	0.0125532	−	0.0139120i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.75226	−	4.76706i	0.341376	−	0.591281i
$66$	−7.59799	−	2.18304i	−0.935248	−	0.268714i
$67$	1.40754	+	1.67745i	0.171959	+	0.204933i	0.845140	−	0.534545i	$-0.179517\pi$
$67$	1.40754	+	1.67745i	0.171959	+	0.204933i	−0.673181	+	0.739478i	$0.735073\pi$
$68$	2.08249	+	1.20233i	0.252539	+	0.145803i
$69$	−5.73645	+	11.7457i	−0.690588	+	1.41401i
$70$	0.0169564	−	0.0465872i	0.00202667	−	0.00556824i
$71$	0.580865	−	3.29425i	0.0689360	−	0.390956i	−0.930744	−	0.365671i	$-0.880840\pi$
$71$	0.580865	−	3.29425i	0.0689360	−	0.390956i	0.999680	−	0.0252848i	$-0.00804927\pi$
$72$	−2.93378	−	0.626843i	−0.345749	−	0.0738741i
$73$	8.80341	−	3.20418i	1.03036	−	0.375021i	0.229143	−	0.973393i	$-0.426408\pi$
$73$	8.80341	−	3.20418i	1.03036	−	0.375021i	0.801218	+	0.598372i	$0.204185\pi$
$74$	−2.80882	+	3.34742i	−0.326518	+	0.389130i
$75$	−1.43645	+	0.967790i	−0.165867	+	0.111751i
$76$	−3.87522	+	1.99566i	−0.444518	+	0.228918i
$77$		−	0.226279i		−	0.0257868i
$78$	1.00161	−	9.48136i	0.113410	−	1.07355i
$79$	−0.806619	−	2.21617i	−0.0907517	−	0.249338i	0.886010	−	0.463666i	$-0.153466\pi$
$79$	−0.806619	−	2.21617i	−0.0907517	−	0.249338i	−0.976762	+	0.214328i	$0.931244\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	−7.29234	+	5.27463i	−0.810260	+	0.586070i
$82$	−1.98626	−	0.722940i	−0.219346	−	0.0798354i
$83$	−8.15617	+	4.70897i	−0.895256	+	0.516877i	−0.875658	−	0.482931i	$-0.839572\pi$
$83$	−8.15617	+	4.70897i	−0.895256	+	0.516877i	−0.0195983	+	0.999808i	$0.506239\pi$
$84$	−0.00594463	−	0.0856640i	−0.000648612	−	0.00934671i
$85$	1.84207	−	1.54568i	0.199801	−	0.167653i
$86$	−8.88698	+	7.45706i	−0.958308	+	0.804116i
$87$	0.0278724	+	0.401650i	0.00298823	+	0.0430614i
$88$	−3.95269	+	2.28209i	−0.421359	+	0.243271i
$89$	−3.17977	−	1.15734i	−0.337055	−	0.122678i	0.167947	−	0.985796i	$-0.446286\pi$
$89$	−3.17977	−	1.15734i	−0.337055	−	0.122678i	−0.505002	+	0.863118i	$0.668508\pi$
$90$	−1.59245	+	2.54246i	−0.167859	+	0.267999i
$91$	0.268752	−	0.0473883i	0.0281729	−	0.00496764i
$92$	2.58120	+	7.09178i	0.269108	+	0.739369i
$93$	0.682841	−	6.46387i	0.0708073	−	0.670272i
$94$			1.63437i			0.168572i
$95$	0.549903	+	4.32407i	0.0564188	+	0.443641i
$96$	−1.43645	+	0.967790i	−0.146607	+	0.0987747i
$97$	−3.76924	+	4.49200i	−0.382708	+	0.456094i	−0.922667	−	0.385597i	$-0.873995\pi$
$97$	−3.76924	+	4.49200i	−0.382708	+	0.456094i	0.539959	+	0.841691i	$0.318440\pi$
$98$	−6.57554	+	2.39330i	−0.664230	+	0.241760i
$99$	−2.86102	+	13.3903i	−0.287543	+	1.34578i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−2.45398	+	6.74225i	−0.244180	+	0.670879i	0.755693	+	0.654926i	$0.227300\pi$
$101$	−2.45398	+	6.74225i	−0.244180	+	0.670879i	−0.999873	+	0.0159526i	$0.994922\pi$
$102$	1.82779	−	3.74249i	0.180978	−	0.370562i
$103$	−4.52136	−	2.61041i	−0.445502	−	0.257211i	0.260426	−	0.965494i	$-0.416137\pi$
$103$	−4.52136	−	2.61041i	−0.445502	−	0.257211i	−0.705929	+	0.708283i	$0.749470\pi$
$104$	−3.53824	−	4.21671i	−0.346953	−	0.413482i
$105$	−0.0825310	−	0.0237127i	−0.00805421	−	0.00231412i
$106$	2.22646	−	3.85635i	0.216253	−	0.374562i
$107$	−8.35051	−	14.4635i	−0.807274	−	1.39824i	−0.914745	−	0.404032i	$-0.867609\pi$
$107$	−8.35051	−	14.4635i	−0.807274	−	1.39824i	0.107471	−	0.994208i	$-0.465725\pi$
$108$	−0.731338	+	5.14443i	−0.0703731	+	0.495023i
$109$	−15.2871	−	2.69553i	−1.46424	−	0.258185i	−0.615979	−	0.787762i	$-0.711240\pi$
$109$	−15.2871	−	2.69553i	−1.46424	−	0.258185i	−0.848262	+	0.529577i	$0.822351\pi$
$110$	0.792561	+	4.49484i	0.0755677	+	0.428566i
$111$	6.12079	+	4.45197i	0.580959	+	0.422562i
$112$	−0.0379783	−	0.0318675i	−0.00358861	−	0.00301120i
$113$	19.2917			1.81481			0.907407	−	0.420252i	$-0.138058\pi$
$113$	19.2917			1.81481			0.907407	+	0.420252i	$0.138058\pi$
$114$	3.91296	+	6.45668i	0.366482	+	0.604724i
$115$	7.54692			0.703754
$116$	0.178067	+	0.149416i	0.0165331	+	0.0138729i
$117$	−16.5029	−	0.593794i	−1.52569	−	0.0548963i
$118$	−2.32675	−	13.1957i	−0.214195	−	1.21476i
$119$	0.117404	+	0.0207016i	0.0107625	+	0.00189771i
$120$	0.418131	+	1.68082i	0.0381700	+	0.153437i
$121$	4.91586	+	8.51451i	0.446896	+	0.774046i
$122$	−2.73745	+	4.74140i	−0.247837	+	0.429266i
$123$	−1.01100	+	3.51874i	−0.0911587	+	0.317274i
$124$	−2.41218	−	2.87472i	−0.216620	−	0.258158i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	−0.147306	+	0.0205434i	−0.0131230	+	0.00183015i
$127$	−3.62343	+	9.95530i	−0.321528	+	0.883390i	0.668650	+	0.743577i	$0.266872\pi$
$127$	−3.62343	+	9.95530i	−0.321528	+	0.883390i	−0.990178	+	0.139813i	$0.955350\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	13.9506	+	14.4616i	1.22828	+	1.27327i
$130$	−5.17256	+	1.88266i	−0.453664	+	0.165120i
$131$	8.21698	−	9.79262i	0.717921	−	0.855585i	−0.276506	−	0.961012i	$-0.589176\pi$
$131$	8.21698	−	9.79262i	0.717921	−	0.855585i	0.994427	+	0.105427i	$0.0336209\pi$
$132$	4.41716	+	6.55620i	0.384465	+	0.570644i
$133$	−0.146697	+	0.158682i	−0.0127202	+	0.0137595i
$134$		−	2.18975i		−	0.189166i
$135$	4.58405	+	2.44673i	0.394532	+	0.210581i
$136$	−0.822439	−	2.25963i	−0.0705236	−	0.193762i
$137$	−0.811168	+	0.143031i	−0.0693027	+	0.0122199i	−0.208192	−	0.978088i	$-0.566758\pi$
$137$	−0.811168	+	0.143031i	−0.0693027	+	0.0122199i	0.138889	+	0.990308i	$0.455647\pi$
$138$	11.9444	−	5.31039i	1.01677	−	0.452051i
$139$	−7.35362	−	2.67650i	−0.623726	−	0.227018i	0.0107722	−	0.999942i	$-0.496571\pi$
$139$	−7.35362	−	2.67650i	−0.623726	−	0.227018i	−0.634498	+	0.772924i	$0.718793\pi$
$140$	−0.0429350	+	0.0247885i	−0.00362867	+	0.00209501i
$141$	2.82402	−	0.195972i	0.237825	−	0.0165038i
$142$	−2.56247	+	2.15017i	−0.215038	+	0.180438i
$143$	−19.2458	+	16.1492i	−1.60942	+	1.35046i
$144$	1.84448	+	2.36599i	0.153707	+	0.197166i
$145$	0.201308	−	0.116225i	0.0167177	−	0.00965197i
$146$	−8.80341	−	3.20418i	−0.728576	−	0.265180i
$147$	4.92382	+	11.0749i	0.406110	+	0.913440i
$148$	4.30336	−	0.758798i	0.353734	−	0.0623728i
$149$	−7.84295	−	21.5483i	−0.642519	−	1.76531i	−0.643664	−	0.765308i	$-0.722587\pi$
$149$	−7.84295	−	21.5483i	−0.642519	−	1.76531i	0.00114461	−	0.999999i	$-0.499636\pi$
$150$	1.72247	+	0.181961i	0.140639	+	0.0148570i
$151$			19.7299i			1.60560i	0.596251	+	0.802798i	$0.296656\pi$
$151$			19.7299i			1.60560i	−0.596251	+	0.802798i	$0.703344\pi$
$152$	4.25138	+	0.962180i	0.344832	+	0.0780431i
$153$	−6.68580	−	2.70948i	−0.540515	−	0.219048i
$154$	−0.145449	+	0.173340i	−0.0117206	+	0.0139681i
$155$	−3.52637	+	1.28349i	−0.283245	+	0.103093i
$156$	−6.86178	+	6.61932i	−0.549382	+	0.529970i
$157$	0.672713	−	3.81515i	0.0536884	−	0.304482i	−0.946125	−	0.323802i	$-0.895039\pi$
$157$	0.672713	−	3.81515i	0.0536884	−	0.304482i	0.999813	+	0.0193198i	$0.00615006\pi$
$158$	−0.806619	+	2.21617i	−0.0641711	+	0.176309i
$159$	−6.93034	−	3.38470i	−0.549611	−	0.268424i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	0.240502	+	0.286619i	0.0189542	+	0.0225887i
$162$	8.97673	+	0.646824i	0.705278	+	0.0508193i
$163$	1.46788	−	2.54244i	0.114973	−	0.199140i	−0.802796	−	0.596254i	$-0.796655\pi$
$163$	1.46788	−	2.54244i	0.114973	−	0.199140i	0.917769	+	0.397114i	$0.129988\pi$
$164$	1.05687	+	1.83055i	0.0825275	+	0.142942i
$165$	7.67157	−	1.90842i	0.597231	−	0.148571i
$166$	9.27486	+	1.63541i	0.719869	+	0.126932i
$167$	4.12337	+	23.3848i	0.319076	+	1.80957i	0.548397	+	0.836218i	$0.315238\pi$
$167$	4.12337	+	23.3848i	0.319076	+	1.80957i	−0.229321	+	0.973351i	$0.573651\pi$
$168$	−0.0505099	+	0.0694436i	−0.00389693	+	0.00535769i
$169$	−13.2524	−	11.1201i	−1.01942	−	0.855392i
$170$	−2.40465			−0.184428
$171$	10.6873	−	7.53538i	0.817277	−	0.576245i
$172$	11.6011			0.884578
$173$	6.37777	+	5.35159i	0.484893	+	0.406874i	0.852192	−	0.523229i	$-0.175273\pi$
$173$	6.37777	+	5.35159i	0.484893	+	0.406874i	−0.367299	+	0.930103i	$0.619717\pi$
$174$	0.236824	−	0.325598i	0.0179536	−	0.0246835i
$175$	0.00860897	+	0.0488239i	0.000650777	+	0.00369074i
$176$	4.49484	+	0.792561i	0.338811	+	0.0597415i
$177$	−22.5217	+	5.60263i	−1.69284	+	0.421120i
$178$	1.69192	+	2.93049i	0.126815	+	0.219650i
$179$	−3.90407	+	6.76205i	−0.291804	+	0.505420i	−0.974236	−	0.225529i	$-0.927589\pi$
$179$	−3.90407	+	6.76205i	−0.291804	+	0.505420i	0.682432	+	0.730949i	$0.260922\pi$
$180$	2.85415	−	0.924029i	0.212736	−	0.0688730i
$181$	5.26113	+	6.26997i	0.391057	+	0.466044i	0.925272	−	0.379305i	$-0.123837\pi$
$181$	5.26113	+	6.26997i	0.391057	+	0.466044i	−0.534215	+	0.845349i	$0.679393\pi$
$182$	−0.236337	−	0.136449i	−0.0175185	−	0.0101143i
$183$	8.52088	+	4.16150i	0.629882	+	0.307627i
$184$	2.58120	−	7.09178i	0.190288	−	0.522813i
$185$	0.758798	−	4.30336i	0.0557880	−	0.316389i
$186$	−4.67798	+	4.51269i	−0.343006	+	0.330886i
$187$	−10.3134	+	3.75376i	−0.754188	+	0.274502i
$188$	1.05055	−	1.25200i	0.0766193	−	0.0913113i
$189$	0.0531598	+	0.252066i	0.00386681	+	0.0183351i
$190$	2.35821	−	3.66590i	0.171083	−	0.265953i
$191$		−	7.26429i		−	0.525626i	−0.964847	−	0.262813i	$-0.915350\pi$
$191$		−	7.26429i		−	0.525626i	0.964847	−	0.262813i	$-0.0846502\pi$
$192$	1.72247	+	0.181961i	0.124308	+	0.0131319i
$193$	−8.68254	−	23.8551i	−0.624983	−	1.71713i	−0.694449	−	0.719542i	$-0.744352\pi$
$193$	−8.68254	−	23.8551i	−0.624983	−	1.71713i	0.0694661	−	0.997584i	$-0.477870\pi$
$194$	5.77481	−	1.01825i	0.414607	−	0.0731064i
$195$	3.87326	+	8.71190i	0.277370	+	0.623872i
$196$	6.57554	+	2.39330i	0.469681	+	0.170950i
$197$	1.83631	−	1.06019i	0.130832	−	0.0755357i	−0.433156	−	0.901319i	$-0.642600\pi$
$197$	1.83631	−	1.06019i	0.130832	−	0.0755357i	0.563987	+	0.825783i	$0.309267\pi$
$198$	10.7988	−	8.41853i	0.767436	−	0.598279i
$199$	12.5108	−	10.4978i	0.886866	−	0.744169i	−0.0807131	−	0.996737i	$-0.525720\pi$
$199$	12.5108	−	10.4978i	0.886866	−	0.744169i	0.967579	+	0.252568i	$0.0812753\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	−3.78366	+	0.262566i	−0.266879	+	0.0185200i
$202$	6.21369	−	3.58748i	0.437194	−	0.252414i
$203$	0.0108292	+	0.00394151i	0.000760062	+	0.000276640i
$204$	−3.80579	+	1.69203i	−0.266459	+	0.118466i
$205$	2.08162	−	0.367046i	0.145387	−	0.0256356i
$206$	1.78562	+	4.90596i	0.124410	+	0.341814i
$207$	−10.6080	−	20.0018i	−0.737308	−	1.39022i
$208$			5.50452i			0.381670i
$209$	4.39156	−	19.4040i	0.303771	−	1.34221i
$210$	0.0479802	+	0.0712149i	0.00331095	+	0.00491430i
$211$	−13.1703	+	15.6958i	−0.906683	+	1.08054i	0.0897339	+	0.995966i	$0.471398\pi$
$211$	−13.1703	+	15.6958i	−0.906683	+	1.08054i	−0.996417	+	0.0845770i	$0.973046\pi$
$212$	−4.18438	+	1.52299i	−0.287385	+	0.104599i
$213$	4.02253	+	4.16986i	0.275619	+	0.285714i
$214$	−2.90010	+	16.4473i	−0.198247	+	1.12431i
$215$	3.96782	−	10.9015i	0.270603	−	0.743476i
$216$	3.86701	−	3.47077i	0.263117	−	0.236156i
$217$	−0.161122	−	0.0930235i	−0.0109376	−	0.00631485i
$218$	9.97796	+	11.8913i	0.675793	+	0.805379i
$219$	−4.48090	+	15.5956i	−0.302791	+	1.05385i
$220$	2.28209	−	3.95269i	0.153858	−	0.266491i
$221$	−6.61823	−	11.4631i	−0.445190	−	0.771092i
$222$	−1.82713	−	7.34477i	−0.122629	−	0.492949i
$223$	20.9549	+	3.69492i	1.40325	+	0.247430i	0.823477	−	0.567350i	$-0.192031\pi$
$223$	20.9549	+	3.69492i	1.40325	+	0.247430i	0.579770	+	0.814780i	$0.303142\pi$
$224$	0.00860897	+	0.0488239i	0.000575211	+	0.00326218i
$225$	0.107874	−	2.99806i	0.00719159	−	0.199871i
$226$	−14.7783	−	12.4005i	−0.983040	−	0.824869i
$227$	−27.4056			−1.81897			−0.909486	−	0.415735i	$-0.863524\pi$
$227$	−27.4056			−1.81897			−0.909486	+	0.415735i	$0.863524\pi$
$228$	1.15278	−	7.46131i	0.0763446	−	0.494137i
$229$	−2.61998			−0.173133			−0.0865666	−	0.996246i	$-0.527590\pi$
$229$	−2.61998			−0.173133			−0.0865666	+	0.996246i	$0.527590\pi$
$230$	−5.78127	−	4.85106i	−0.381206	−	0.319870i
$231$	0.316953	+	0.230536i	0.0208540	+	0.0151682i
$232$	−0.0403646	−	0.228919i	−0.00265006	−	0.0150293i
$233$	15.9958	+	2.82049i	1.04792	+	0.184776i	0.670990	−	0.741466i	$-0.265869\pi$
$233$	15.9958	+	2.82049i	1.04792	+	0.184776i	0.376928	+	0.926242i	$0.376980\pi$
$234$	12.2603	+	11.0627i	0.801479	+	0.723193i
$235$	−0.817184	−	1.41540i	−0.0533072	−	0.0923308i
$236$	−6.69961	+	11.6041i	−0.436108	+	0.755361i
$237$	3.92602	+	1.12802i	0.255023	+	0.0732727i
$238$	−0.0766303	−	0.0913245i	−0.00496721	−	0.00591969i
$239$	−10.1435	−	5.85634i	−0.656127	−	0.378815i	0.134672	−	0.990890i	$-0.457002\pi$
$239$	−10.1435	−	5.85634i	−0.656127	−	0.378815i	−0.790800	+	0.612075i	$0.790335\pi$
$240$	0.760105	−	1.55635i	0.0490646	−	0.100462i
$241$	−7.37806	+	20.2710i	−0.475263	+	1.30577i	0.438210	+	0.898873i	$0.355613\pi$
$241$	−7.37806	+	20.2710i	−0.475263	+	1.30577i	−0.913473	+	0.406900i	$0.866610\pi$
$242$	1.70726	−	9.68234i	0.109747	−	0.622405i
$243$	0.0412748	−	15.5884i	0.00264778	−	0.999996i
$244$	5.14472	−	1.87253i	0.329357	−	0.119876i
$245$	4.49793	−	5.36043i	0.287362	−	0.342465i
$246$	3.03627	−	2.04565i	0.193586	−	0.130426i
$247$	23.9660	+	1.15220i	1.52492	+	0.0733127i
$248$			3.75268i			0.238296i
$249$	1.71370	−	16.2221i	0.108601	−	1.02803i
$250$	−0.342020	−	0.939693i	−0.0216313	−	0.0594314i
$251$	−2.50779	+	0.442190i	−0.158290	+	0.0279108i	−0.252232	−	0.967667i	$-0.581164\pi$
$251$	−2.50779	+	0.442190i	−0.158290	+	0.0279108i	0.0939415	+	0.995578i	$0.470053\pi$
$252$	0.126048	+	0.0789491i	0.00794026	+	0.00497333i
$253$	−32.3681	−	11.7810i	−2.03497	−	0.740668i
$254$	9.17485	−	5.29710i	0.575681	−	0.332370i
$255$	0.288334	+	4.15499i	0.0180562	+	0.260195i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	4.03396	−	3.38490i	0.251632	−	0.211144i	−0.508243	−	0.861214i	$-0.669705\pi$
$257$	4.03396	−	3.38490i	0.251632	−	0.211144i	0.759875	+	0.650070i	$0.225260\pi$
$258$	−1.39105	−	20.0455i	−0.0866032	−	1.24798i
$259$	0.187615	−	0.108320i	0.0116578	−	0.00673065i
$260$	5.17256	+	1.88266i	0.320789	+	0.116758i
$261$	−0.590995	−	0.370166i	−0.0365817	−	0.0229127i
$262$	−12.5892	+	2.21981i	−0.777760	+	0.137140i
$263$	−7.58236	−	20.8324i	−0.467548	−	1.28458i	−0.919695	−	0.392634i	$-0.871564\pi$
$263$	−7.58236	−	20.8324i	−0.467548	−	1.28458i	0.452147	−	0.891944i	$-0.350658\pi$
$264$	0.830501	−	7.86164i	0.0511138	−	0.483851i
$265$			4.45293i			0.273541i
$266$	0.214375	−	0.0272626i	0.0131442	−	0.00167158i
$267$	4.86072	−	3.27485i	0.297471	−	0.200418i
$268$	−1.40754	+	1.67745i	−0.0859794	+	0.102466i
$269$	−11.3349	+	4.12558i	−0.691103	+	0.251541i	−0.663607	−	0.748081i	$-0.730975\pi$
$269$	−11.3349	+	4.12558i	−0.691103	+	0.251541i	−0.0274954	+	0.999622i	$0.508753\pi$
$270$	−1.93886	−	4.82087i	−0.117995	−	0.293389i
$271$	2.49521	−	14.1511i	0.151573	−	0.859616i	−0.810279	−	0.586045i	$-0.800684\pi$
$271$	2.49521	−	14.1511i	0.151573	−	0.859616i	0.961852	−	0.273571i	$-0.0882047\pi$
$272$	−0.822439	+	2.25963i	−0.0498677	+	0.137010i
$273$	−0.207432	+	0.424727i	−0.0125543	+	0.0257056i
$274$	0.713329	+	0.411841i	0.0430938	+	0.0248802i
$275$	−2.93380	−	3.49636i	−0.176915	−	0.210839i
$276$	−12.5634	−	3.60969i	−0.756225	−	0.217278i
$277$	−13.2547	+	22.9578i	−0.796396	+	1.37940i	0.125553	+	0.992087i	$0.459930\pi$
$277$	−13.2547	+	22.9578i	−0.796396	+	1.37940i	−0.921949	+	0.387312i	$0.873404\pi$
$278$	3.91278	+	6.77714i	0.234673	+	0.406466i
$279$	8.35838	+	7.54196i	0.500403	+	0.451525i
$280$	0.0488239	+	0.00860897i	0.00291779	+	0.000514485i
$281$	1.57453	+	8.92958i	0.0939283	+	0.532694i	0.995070	+	0.0991702i	$0.0316188\pi$
$281$	1.57453	+	8.92958i	0.0939283	+	0.532694i	−0.901142	+	0.433524i	$0.857270\pi$
$282$	−2.28929	−	1.66512i	−0.136325	−	0.0991564i
$283$	17.6352	+	14.7977i	1.04830	+	0.879629i	0.992914	−	0.118836i	$-0.0379162\pi$
$283$	17.6352	+	14.7977i	1.04830	+	0.879629i	0.0553872	+	0.998465i	$0.482361\pi$
$284$	3.34507			0.198493
$285$	−6.61706	−	3.63517i	−0.391961	−	0.215329i
$286$	25.1236			1.48559
$287$	0.0802760	+	0.0673596i	0.00473854	+	0.00397611i
$288$	0.107874	−	2.99806i	0.00635653	−	0.176662i
$289$	1.94792	+	11.0472i	0.114584	+	0.649837i
$290$	−0.228919	−	0.0403646i	−0.0134426	−	0.00237029i
$291$	−2.45188	−	9.85617i	−0.143732	−	0.577779i
$292$	4.68420	+	8.11327i	0.274122	+	0.474793i
$293$	4.55814	−	7.89493i	0.266289	−	0.461227i	−0.701611	−	0.712560i	$-0.747536\pi$
$293$	4.55814	−	7.89493i	0.266289	−	0.461227i	0.967901	+	0.251333i	$0.0808690\pi$
$294$	3.34692	−	11.6488i	0.195196	−	0.679373i
$295$	8.61286	+	10.2644i	0.501460	+	0.597617i
$296$	−3.78431	−	2.18487i	−0.219959	−	0.126993i
$297$	−15.8412	−	17.6497i	−0.919199	−	1.02414i
$298$	−7.84295	+	21.5483i	−0.454330	+	1.24826i
$299$	7.21373	−	40.9111i	0.417181	−	2.36595i
$300$	−1.20252	−	1.24657i	−0.0694277	−	0.0719708i
$301$	0.540464	−	0.196713i	0.0311519	−	0.0113383i
$302$	12.6821	−	15.1140i	0.729775	−	0.869712i
$303$	−6.94385	−	10.3064i	−0.398913	−	0.592090i
$304$	−2.63827	−	3.46981i	−0.151315	−	0.199007i
$305$		−	5.47490i		−	0.313492i
$306$	3.38000	+	6.37313i	0.193222	+	0.364327i
$307$	−8.94795	−	24.5843i	−0.510687	−	1.40310i	−0.880523	−	0.474003i	$-0.842809\pi$
$307$	−8.94795	−	24.5843i	−0.510687	−	1.40310i	0.369837	−	0.929097i	$-0.379414\pi$
$308$	0.222841	−	0.0392929i	0.0126975	−	0.00223892i
$309$	8.26288	−	3.67363i	0.470059	−	0.208985i
$310$	3.52637	+	1.28349i	0.200284	+	0.0728975i
$311$	−8.63775	+	4.98701i	−0.489802	+	0.282787i	−0.724492	−	0.689283i	$-0.757926\pi$
$311$	−8.63775	+	4.98701i	−0.489802	+	0.282787i	0.234691	+	0.972070i	$0.424592\pi$
$312$	9.51124	−	0.660030i	0.538468	−	0.0373668i
$313$	−13.1661	+	11.0477i	−0.744192	+	0.624451i	−0.933960	−	0.357378i	$-0.883671\pi$
$313$	−13.1661	+	11.0477i	−0.744192	+	0.624451i	0.189768	+	0.981829i	$0.439226\pi$
$314$	−2.96766	+	2.49016i	−0.167475	+	0.140528i
$315$	0.117299	−	0.0914439i	0.00660904	−	0.00515228i
$316$	2.04243	−	1.17920i	0.114896	−	0.0663350i
$317$	0.0341637	+	0.0124346i	0.00191883	+	0.000698395i	0.342979	−	0.939343i	$-0.388564\pi$
$317$	0.0341637	+	0.0124346i	0.00191883	+	0.000698395i	−0.341061	+	0.940041i	$0.610786\pi$
$318$	3.13331	+	7.04756i	0.175707	+	0.395208i
$319$	−1.04483	+	0.184231i	−0.0584990	+	0.0103150i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	28.7669	+	3.03893i	1.60561	+	0.169617i
$322$		−	0.374154i		−	0.0208508i
$323$	9.66600	+	4.05378i	0.537830	+	0.225558i
$324$	−6.46080	−	6.26562i	−0.358933	−	0.348090i
$325$	3.53824	−	4.21671i	0.196266	−	0.233901i
$326$	−2.75871	+	1.00409i	−0.152791	+	0.0556114i
$327$	19.3505	−	18.6667i	1.07008	−	1.03227i
$328$	0.367046	−	2.08162i	0.0202667	−	0.114938i
$329$	0.0277129	−	0.0761407i	0.00152786	−	0.00419777i
$330$	−7.10348	−	3.46926i	−0.391034	−	0.190976i
$331$	22.7917	+	13.1588i	1.25275	+	0.723273i	0.971654	−	0.236408i	$-0.0759702\pi$
$331$	22.7917	+	13.1588i	1.25275	+	0.723273i	0.281092	+	0.959681i	$0.409304\pi$
$332$	−6.05373	−	7.21456i	−0.332242	−	0.395950i
$333$	−12.4719	+	4.03777i	−0.683456	+	0.221268i
$334$	11.8728	−	20.5642i	0.649649	−	1.12522i
$335$	1.09487	+	1.89638i	0.0598194	+	0.103610i
$336$	0.0833303	−	0.0207297i	0.00454604	−	0.00113090i
$337$	8.03363	+	1.41655i	0.437620	+	0.0771641i	0.388118	−	0.921610i	$-0.373125\pi$
$337$	8.03363	+	1.41655i	0.437620	+	0.0771641i	0.0495020	+	0.998774i	$0.484237\pi$
$338$	3.00408	+	17.0370i	0.163400	+	0.926689i
$339$	−19.6547	+	27.0223i	−1.06750	+	1.46765i
$340$	1.84207	+	1.54568i	0.0999003	+	0.0838263i
$341$	17.1279			0.927528
$342$	−13.0306	−	1.09722i	−0.704613	−	0.0593308i
$343$	0.693958			0.0374702
$344$	−8.88698	−	7.45706i	−0.479154	−	0.402058i
$345$	−7.68892	+	10.5711i	−0.413957	+	0.569129i
$346$	−1.44572	−	8.19911i	−0.0777226	−	0.440787i
$347$	8.23054	+	1.45127i	0.441838	+	0.0779080i	0.390142	−	0.920755i	$-0.372426\pi$
$347$	8.23054	+	1.45127i	0.441838	+	0.0779080i	0.0516967	+	0.998663i	$0.483537\pi$
$348$	−0.390708	+	0.0971947i	−0.0209441	+	0.00521018i
$349$	8.18925	+	14.1842i	0.438360	+	0.759263i	0.997563	−	0.0697683i	$-0.0222260\pi$
$349$	8.18925	+	14.1842i	0.438360	+	0.759263i	−0.559203	+	0.829031i	$0.688893\pi$
$350$	0.0247885	−	0.0429350i	0.00132500	−	0.00229497i
$351$	17.6451	−	22.5110i	0.941828	−	1.20155i
$352$	−2.93380	−	3.49636i	−0.156372	−	0.186357i
$353$	22.7758	+	13.1496i	1.21223	+	0.699884i	0.963246	−	0.268622i	$-0.0865684\pi$
$353$	22.7758	+	13.1496i	1.21223	+	0.699884i	0.248989	+	0.968506i	$0.419902\pi$
$354$	20.8540	+	10.1848i	1.10838	+	0.541317i
$355$	1.14408	−	3.14334i	0.0607215	−	0.166831i
$356$	0.587598	−	3.33244i	0.0311426	−	0.176619i
$357$	−0.148611	+	0.143360i	−0.00786531	+	0.00758740i
$358$	7.33726	−	2.67054i	0.387786	−	0.141143i
$359$	−4.81363	+	5.73667i	−0.254054	+	0.302770i	−0.877964	−	0.478726i	$-0.841099\pi$
$359$	−4.81363	+	5.73667i	−0.254054	+	0.302770i	0.623910	+	0.781496i	$0.285543\pi$
$360$	−2.78036	−	1.12677i	−0.146538	−	0.0593857i
$361$	−15.6593	+	10.7604i	−0.824175	+	0.566335i
$362$		−	8.18487i		−	0.430187i
$363$	−16.9348	−	1.78899i	−0.888846	−	0.0938974i
$364$	0.0933367	+	0.256441i	0.00489217	+	0.0134411i
$365$	9.22607	−	1.62680i	0.482914	−	0.0851508i
$366$	−3.85241	−	8.66501i	−0.201369	−	0.452927i
$367$	11.1858	+	4.07128i	0.583892	+	0.212519i	0.617041	−	0.786931i	$-0.288331\pi$
$367$	11.1858	+	4.07128i	0.583892	+	0.212519i	−0.0331490	+	0.999450i	$0.510554\pi$
$368$	−6.53582	+	3.77346i	−0.340703	+	0.196705i
$369$	−3.89874	−	5.00107i	−0.202960	−	0.260345i
$370$	−3.34742	+	2.80882i	−0.174024	+	0.146023i
$371$	−0.169115	+	0.141904i	−0.00877999	+	0.00736728i
$372$	6.48424	−	0.449972i	0.336192	−	0.0233300i
$373$	8.09048	−	4.67104i	0.418909	−	0.241857i	−0.275701	−	0.961243i	$-0.588910\pi$
$373$	8.09048	−	4.67104i	0.418909	−	0.241857i	0.694611	+	0.719386i	$0.255577\pi$
$374$	10.3134	+	3.75376i	0.533291	+	0.194102i
$375$	−1.58268	+	0.703651i	−0.0817292	+	0.0363364i
$376$	−1.60954	+	0.283805i	−0.0830056	+	0.0146361i
$377$	−0.437624	−	1.20236i	−0.0225388	−	0.0619249i
$378$	0.121302	−	0.227264i	0.00623909	−	0.0116892i
$379$			18.3649i			0.943339i	0.881775	+	0.471670i	$0.156349\pi$
$379$			18.3649i			0.943339i	−0.881775	+	0.471670i	$0.843651\pi$
$380$	−4.16289	+	1.29242i	−0.213552	+	0.0662995i
$381$	−10.2530	−	15.2180i	−0.525275	−	0.779643i
$382$	−4.66940	+	5.56477i	−0.238907	+	0.284718i
$383$	−11.7518	+	4.27730i	−0.600488	+	0.218560i	−0.624336	−	0.781156i	$-0.714630\pi$
$383$	−11.7518	+	4.27730i	−0.600488	+	0.218560i	0.0238481	+	0.999716i	$0.492408\pi$
$384$	−1.20252	−	1.24657i	−0.0613660	−	0.0636138i
$385$	0.0392929	−	0.222841i	0.00200255	−	0.0113570i
$386$	−8.68254	+	23.8551i	−0.441930	+	1.21419i
$387$	−34.4698	+	4.80719i	−1.75220	+	0.244363i
$388$	−5.07828	−	2.93195i	−0.257811	−	0.148847i
$389$	−19.5601	−	23.3109i	−0.991738	−	1.18191i	−0.983309	−	0.181943i	$-0.941762\pi$
$389$	−19.5601	−	23.3109i	−0.991738	−	1.18191i	−0.00842858	−	0.999964i	$-0.502683\pi$
$390$	2.63281	−	9.16339i	0.133318	−	0.464006i
$391$	9.07385	−	15.7164i	0.458884	−	0.794811i
$392$	−3.49877	−	6.06005i	−0.176715	−	0.306079i
$393$	5.34512	+	21.4866i	0.269626	+	1.08385i
$394$	−2.08817	−	0.368201i	−0.105201	−	0.0185497i
$395$	−0.409531	−	2.32257i	−0.0206057	−	0.116861i
$396$	−13.6837	−	0.492355i	−0.687631	−	0.0247418i
$397$	3.99026	+	3.34823i	0.200266	+	0.168043i	0.737405	−	0.675450i	$-0.236051\pi$
$397$	3.99026	+	3.34823i	0.200266	+	0.168043i	−0.537140	+	0.843493i	$0.680495\pi$
$398$	−16.3317			−0.818633
$399$	−0.0728119	−	0.367149i	−0.00364515	−	0.0183804i
$400$	−1.00000			−0.0500000
$401$	14.0231	+	11.7668i	0.700281	+	0.587605i	0.921853	−	0.387539i	$-0.126675\pi$
$401$	14.0231	+	11.7668i	0.700281	+	0.587605i	−0.221573	+	0.975144i	$0.571119\pi$
$402$	3.06722	+	2.23095i	0.152979	+	0.111270i
$403$	3.58700	+	20.3429i	0.178681	+	1.01335i
$404$	−7.06595	−	1.24592i	−0.351544	−	0.0619867i
$405$	−8.09749	+	3.92820i	−0.402367	+	0.195194i
$406$	−0.00576210	−	0.00998026i	−0.000285968	−	0.000495312i
$407$	−9.97214	+	17.2723i	−0.494301	+	0.856154i
$408$	4.00303	+	1.15014i	0.198179	+	0.0569406i
$409$	18.1015	+	21.5726i	0.895063	+	1.06669i	0.997409	+	0.0719460i	$0.0229209\pi$
$409$	18.1015	+	21.5726i	0.895063	+	1.06669i	−0.102345	+	0.994749i	$0.532635\pi$
$410$	−1.83055	−	1.05687i	−0.0904044	−	0.0521950i
$411$	0.626085	−	1.28194i	0.0308825	−	0.0632334i
$412$	1.78562	−	4.90596i	0.0879713	−	0.241699i
$413$	−0.115354	+	0.654203i	−0.00567618	+	0.0321912i
$414$	−4.73073	+	22.1410i	−0.232503	+	1.08817i
$415$	−8.84997	+	3.22112i	−0.434428	+	0.158119i
$416$	3.53824	−	4.21671i	0.173476	−	0.206741i
$417$	11.2410	−	7.57350i	0.550475	−	0.370876i
$418$	−15.8368	+	12.0415i	−0.774604	+	0.588970i
$419$		−	0.152253i		−	0.00743803i	−0.999993	−	0.00371901i	$-0.998816\pi$
$419$		−	0.152253i		−	0.00743803i	0.999993	−	0.00371901i	$-0.00118380\pi$
$420$	0.00902109	−	0.0853949i	0.000440184	−	0.00416684i
$421$	−10.0386	−	27.5808i	−0.489251	−	1.34421i	−0.901360	−	0.433071i	$-0.857430\pi$
$421$	−10.0386	−	27.5808i	−0.489251	−	1.34421i	0.412109	−	0.911135i	$-0.364792\pi$
$422$	20.1781	−	3.55795i	0.982255	−	0.173198i
$423$	−2.60265	+	4.15531i	−0.126545	+	0.202038i
$424$	4.18438	+	1.52299i	0.203212	+	0.0739630i
$425$	2.08249	−	1.20233i	0.101016	−	0.0583214i
$426$	−0.401096	−	5.77993i	−0.0194332	−	0.280039i
$427$	0.207927	−	0.174472i	0.0100623	−	0.00844327i
$428$	12.7937	−	10.7352i	0.618408	−	0.518906i
$429$	−3.01249	−	43.4110i	−0.145444	−	2.09590i
$430$	−10.0469	+	5.80056i	−0.484503	+	0.279728i
$431$	34.7067	+	12.6322i	1.67177	+	0.608473i	0.992145	−	0.125091i	$-0.0399224\pi$
$431$	34.7067	+	12.6322i	1.67177	+	0.608473i	0.679620	+	0.733564i	$0.262145\pi$
$432$	−5.19327	+	0.173093i	−0.249861	+	0.00832794i
$433$	1.32642	−	0.233884i	0.0637439	−	0.0112398i	−0.141685	−	0.989912i	$-0.545252\pi$
$433$	1.32642	−	0.233884i	0.0637439	−	0.0112398i	0.205429	+	0.978672i	$0.434141\pi$
$434$	0.0636319	+	0.174827i	0.00305443	+	0.00839197i
$435$	−0.0422968	+	0.400388i	−0.00202798	+	0.0191971i
$436$		−	15.5230i		−	0.743415i
$437$	15.0611	+	29.2460i	0.720469	+	1.39902i
$438$	13.4572	−	9.06664i	0.643010	−	0.433221i
$439$	18.4829	−	22.0271i	0.882142	−	1.05130i	−0.116171	−	0.993229i	$-0.537062\pi$
$439$	18.4829	−	22.0271i	0.882142	−	1.05130i	0.998313	−	0.0580668i	$-0.0184936\pi$
$440$	−4.28892	+	1.56104i	−0.204466	+	0.0744197i
$441$	−20.5293	−	4.38636i	−0.977583	−	0.208874i
$442$	−2.29849	+	13.0354i	−0.109328	+	0.620029i
$443$	−12.5486	+	34.4769i	−0.596200	+	1.63805i	0.162578	+	0.986696i	$0.448019\pi$
$443$	−12.5486	+	34.4769i	−0.596200	+	1.63805i	−0.758778	+	0.651350i	$0.774203\pi$
$444$	−3.32147	+	6.80087i	−0.157630	+	0.322755i
$445$	−2.93049	−	1.69192i	−0.138919	−	0.0802048i
$446$	−13.6774	−	16.3001i	−0.647642	−	0.771830i
$447$	38.1737	+	10.9680i	1.80555	+	0.518769i
$448$	0.0247885	−	0.0429350i	0.00117115	−	0.00202849i
$449$	2.39895	+	4.15511i	0.113214	+	0.196092i	0.917064	−	0.398740i	$-0.130552\pi$
$449$	2.39895	+	4.15511i	0.113214	+	0.196092i	−0.803851	+	0.594831i	$0.797219\pi$
$450$	−2.00975	+	2.22731i	−0.0947406	+	0.104996i
$451$	−9.50090	−	1.67526i	−0.447380	−	0.0788851i
$452$	3.34998	+	18.9987i	0.157570	+	0.893622i
$453$	−27.6361	−	20.1011i	−1.29846	−	0.944434i
$454$	20.9939	+	17.6160i	0.985292	+	0.826758i
$455$	0.272898			0.0127937
$456$	−5.67911	+	4.97470i	−0.265949	+	0.232962i
$457$	24.2731			1.13545			0.567723	−	0.823219i	$-0.307824\pi$
$457$	24.2731			1.13545			0.567723	+	0.823219i	$0.307824\pi$
$458$	2.00702	+	1.68409i	0.0937820	+	0.0786924i
$459$	10.6068	−	6.60446i	0.495084	−	0.308270i
$460$	1.31051	+	7.43226i	0.0611028	+	0.346531i
$461$	24.0953	+	4.24866i	1.12223	+	0.197880i	0.703820	−	0.710378i	$-0.251476\pi$
$461$	24.0953	+	4.24866i	1.12223	+	0.197880i	0.418411	+	0.908258i	$0.362587\pi$
$462$	−0.0946141	−	0.380334i	−0.00440185	−	0.0176948i
$463$	11.7691	+	20.3847i	0.546956	+	0.947356i	0.998481	+	0.0550973i	$0.0175469\pi$
$463$	11.7691	+	20.3847i	0.546956	+	0.947356i	−0.451525	+	0.892259i	$0.649120\pi$
$464$	−0.116225	+	0.201308i	−0.00539562	+	0.00934548i
$465$	1.79491	−	6.24709i	0.0832368	−	0.289702i
$466$	−10.4405	−	12.4425i	−0.483647	−	0.576388i
$467$	−14.6101	−	8.43512i	−0.676073	−	0.390331i	0.122301	−	0.992493i	$-0.460973\pi$
$467$	−14.6101	−	8.43512i	−0.676073	−	0.390331i	−0.798374	+	0.602162i	$0.794306\pi$
$468$	−2.28092	−	16.3553i	−0.105436	−	0.756024i
$469$	−0.0371302	+	0.102014i	−0.00171451	+	0.00471059i
$470$	−0.283805	+	1.60954i	−0.0130909	+	0.0742424i
$471$	4.65858	+	4.82921i	0.214656	+	0.222518i
$472$	12.5912	−	4.58281i	0.579555	−	0.210941i
$473$	−34.0353	+	40.5617i	−1.56495	+	1.86503i
$474$	−2.28243	−	3.38771i	−0.104836	−	0.155603i
$475$	−0.209319	+	4.35387i	−0.00960420	+	0.199769i
$476$			0.119216i			0.00546424i
$477$	11.8017	−	6.25908i	0.540365	−	0.286583i
$478$	4.00597	+	11.0063i	0.183229	+	0.503418i
$479$	28.2285	−	4.97744i	1.28979	−	0.227425i	0.513659	−	0.857994i	$-0.328289\pi$
$479$	28.2285	−	4.97744i	1.28979	−	0.227425i	0.776133	+	0.630569i	$0.217178\pi$
$480$	−1.58268	+	0.703651i	−0.0722391	+	0.0321171i
$481$	−22.6028	−	8.22674i	−1.03060	−	0.375107i
$482$	18.6819	−	10.7860i	0.850937	−	0.491289i
$483$	−0.646499	+	0.0448636i	−0.0294167	+	0.00204137i
$484$	−7.53153	+	6.31970i	−0.342342	+	0.287259i
$485$	−4.49200	+	3.76924i	−0.203971	+	0.171152i
$486$	−10.0517	+	11.9149i	−0.455952	+	0.540470i
$487$	−2.94898	+	1.70259i	−0.133631	+	0.0771519i	−0.565325	−	0.824868i	$-0.691249\pi$
$487$	−2.94898	+	1.70259i	−0.133631	+	0.0771519i	0.431694	+	0.902020i	$0.357916\pi$
$488$	−5.14472	−	1.87253i	−0.232891	−	0.0847652i
$489$	2.06575	+	4.64637i	0.0934165	+	0.210116i
$490$	−6.89123	+	1.21511i	−0.311314	+	0.0548931i
$491$	2.67289	+	7.34370i	0.120626	+	0.331417i	0.985279	−	0.170952i	$-0.0546843\pi$
$491$	2.67289	+	7.34370i	0.120626	+	0.331417i	−0.864654	+	0.502369i	$0.832462\pi$
$492$	−3.64084	−	0.384617i	−0.164142	−	0.0173399i
$493$		−	0.558962i		−	0.0251744i
$494$	−17.6184	−	16.2877i	−0.792689	−	0.732817i
$495$	−5.14276	+	12.6901i	−0.231150	+	0.570375i
$496$	2.41218	−	2.87472i	0.108310	−	0.129079i
$497$	0.155838	−	0.0567202i	0.00699027	−	0.00254425i
$498$	−11.7401	+	11.3253i	−0.526087	+	0.507499i
$499$	−6.93748	+	39.3444i	−0.310564	+	1.76130i	0.285519	+	0.958373i	$0.407834\pi$
$499$	−6.93748	+	39.3444i	−0.310564	+	1.76130i	−0.596083	+	0.802923i	$0.703277\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	−36.9565	−	18.0491i	−1.65109	−	0.806375i
$502$	2.20531	+	1.27324i	0.0984278	+	0.0568273i
$503$	−21.6749	−	25.8312i	−0.966438	−	1.15176i	−0.988381	−	0.151996i	$-0.951430\pi$
$503$	−21.6749	−	25.8312i	−0.966438	−	1.15176i	0.0219435	−	0.999759i	$-0.493015\pi$
$504$	−0.0458107	−	0.141500i	−0.00204057	−	0.00630293i
$505$	−3.58748	+	6.21369i	−0.159641	+	0.276506i
$506$	17.2227	+	29.8306i	0.765644	+	1.32613i
$507$	29.0779	−	7.23358i	1.29139	−	0.321254i
$508$	−10.4333	−	1.83966i	−0.462901	−	0.0816219i
$509$	1.55533	+	8.82074i	0.0689390	+	0.390972i	0.999680	+	0.0252935i	$0.00805203\pi$
$509$	1.55533	+	8.82074i	0.0689390	+	0.390972i	−0.930741	+	0.365679i	$0.880837\pi$
$510$	2.44990	−	3.36824i	0.108483	−	0.149148i
$511$	0.355795	+	0.298548i	0.0157395	+	0.0132070i
$512$	−1.00000			−0.0441942
$513$	−0.333424	+	22.6470i	−0.0147210	+	0.999892i
$514$	−5.26596			−0.232272
$515$	−3.99937	−	3.35587i	−0.176233	−	0.147877i
$516$	−11.8194	+	16.2499i	−0.520321	+	0.715363i
$517$	1.29534	+	7.34621i	0.0569688	+	0.323086i
$518$	−0.213348	−	0.0376190i	−0.00937397	−	0.00165288i
$519$	−13.9938	+	3.48119i	−0.614262	+	0.152807i
$520$	−2.75226	−	4.76706i	−0.120695	−	0.209049i
$521$	−7.80314	+	13.5154i	−0.341862	+	0.592122i	−0.984778	−	0.173814i	$-0.944391\pi$
$521$	−7.80314	+	13.5154i	−0.341862	+	0.592122i	0.642917	+	0.765936i	$0.277724\pi$
$522$	0.214791	+	0.663448i	0.00940113	+	0.0290383i
$523$	−16.1601	−	19.2588i	−0.706631	−	0.842130i	0.286629	−	0.958042i	$-0.407465\pi$
$523$	−16.1601	−	19.2588i	−0.706631	−	0.842130i	−0.993259	+	0.115912i	$0.963021\pi$
$524$	11.0707	+	6.39168i	0.483626	+	0.279222i
$525$	−0.0771595	−	0.0376838i	−0.00336752	−	0.00164466i
$526$	−7.58236	+	20.8324i	−0.330606	+	0.908334i
$527$	−1.56698	+	8.88680i	−0.0682588	+	0.387115i
$528$	−5.68957	+	5.48853i	−0.247607	+	0.238858i
$529$	31.9082	−	11.6136i	1.38731	−	0.504940i
$530$	2.86229	−	3.41114i	0.124330	−	0.148171i
$531$	15.0978	−	37.2547i	0.655188	−	1.61672i
$532$	−0.181745	−	0.116913i	−0.00787964	−	0.00506883i
$533$		−	11.6351i		−	0.503973i
$534$	−5.82856	−	0.615727i	−0.252226	−	0.0266451i
$535$	−5.71208	−	15.6938i	−0.246955	−	0.678503i
$536$	2.15648	−	0.380246i	0.0931458	−	0.0164241i
$537$	−5.49421	−	12.3578i	−0.237093	−	0.533278i
$538$	11.3349	+	4.12558i	0.488683	+	0.177866i
$539$	−27.6591	+	15.9690i	−1.19136	+	0.687834i
$540$	−1.61355	+	4.93928i	−0.0694361	+	0.212553i
$541$	−16.1354	+	13.5392i	−0.693716	+	0.582096i	−0.919978	−	0.391970i	$-0.871794\pi$
$541$	−16.1354	+	13.5392i	−0.693716	+	0.582096i	0.226263	+	0.974066i	$0.427349\pi$
$542$	−11.0076	+	9.23645i	−0.472816	+	0.396739i
$543$	−14.1426	+	0.981421i	−0.606917	+	0.0421168i
$544$	2.08249	−	1.20233i	0.0892860	−	0.0515493i
$545$	−14.5868	−	5.30916i	−0.624830	−	0.227420i
$546$	0.431911	−	0.192025i	0.0184841	−	0.00821791i
$547$	−36.2930	+	6.39943i	−1.55178	+	0.273620i	−0.882831	−	0.469691i	$-0.844365\pi$
$547$	−36.2930	+	6.39943i	−1.55178	+	0.273620i	−0.668946	+	0.743311i	$0.733254\pi$
$548$	−0.281716	−	0.774007i	−0.0120343	−	0.0330640i
$549$	−14.5103	+	7.69556i	−0.619285	+	0.328439i
$550$			4.56418i			0.194617i
$551$	0.852140	+	0.548167i	0.0363024	+	0.0233527i
$552$	7.30383	+	10.8408i	0.310872	+	0.461413i
$553$	0.0751563	−	0.0895677i	0.00319597	−	0.00380881i
$554$	24.9106	−	9.06673i	1.05835	−	0.385208i
$555$	5.25472	+	5.44719i	0.223051	+	0.231220i
$556$	1.35889	−	7.70667i	0.0576300	−	0.326836i
$557$	−5.70792	+	15.6824i	−0.241852	+	0.664484i	0.758072	+	0.652171i	$0.226142\pi$
$557$	−5.70792	+	15.6824i	−0.241852	+	0.664484i	−0.999924	+	0.0123129i	$0.996081\pi$
$558$	−1.55501	−	11.1501i	−0.0658288	−	0.472023i
$559$	−55.3032	−	31.9293i	−2.33908	−	1.35047i
$560$	−0.0318675	−	0.0379783i	−0.00134665	−	0.00160487i
$561$	5.24946	−	18.2705i	0.221632	−	0.771382i
$562$	4.53366	−	7.85254i	0.191241	−	0.331239i
$563$	−6.55133	−	11.3472i	−0.276106	−	0.478229i	0.694308	−	0.719678i	$-0.255711\pi$
$563$	−6.55133	−	11.3472i	−0.276106	−	0.478229i	−0.970413	+	0.241449i	$0.922377\pi$
$564$	0.683380	+	2.74708i	0.0287755	+	0.115673i
$565$	18.9987	+	3.34998i	0.799280	+	0.140935i
$566$	−3.99757	−	22.6713i	−0.168030	−	0.952947i
$567$	−0.407233	−	0.182346i	−0.0171022	−	0.00765783i
$568$	−2.56247	−	2.15017i	−0.107519	−	0.0902191i
$569$	4.24123			0.177802			0.0889008	−	0.996040i	$-0.471665\pi$
$569$	4.24123			0.177802			0.0889008	+	0.996040i	$0.471665\pi$
$570$	2.73232	+	7.03807i	0.114444	+	0.294792i
$571$	6.84855			0.286603			0.143302	−	0.989679i	$-0.454228\pi$
$571$	6.84855			0.286603			0.143302	+	0.989679i	$0.454228\pi$
$572$	−19.2458	−	16.1492i	−0.804708	−	0.675230i
$573$	10.1752	+	7.40098i	0.425077	+	0.309180i
$574$	−0.0181971	−	0.103201i	−0.000759532	−	0.00430752i
$575$	7.43226	+	1.31051i	0.309947	+	0.0546520i
$576$	−2.00975	+	2.22731i	−0.0837397	+	0.0928045i
$577$	−5.49206	−	9.51253i	−0.228637	−	0.396012i	0.728767	−	0.684762i	$-0.240094\pi$
$577$	−5.49206	−	9.51253i	−0.228637	−	0.396012i	−0.957405	+	0.288750i	$0.906760\pi$
$578$	5.60883	−	9.71477i	0.233296	−	0.404081i
$579$	42.2602	+	12.1421i	1.75627	+	0.504610i
$580$	0.149416	+	0.178067i	0.00620417	+	0.00739384i
$581$	−0.404359	−	0.233457i	−0.0167757	−	0.00968543i
$582$	−4.45718	+	9.12630i	−0.184756	+	0.378297i
$583$	6.95120	−	19.0983i	0.287889	−	0.790970i
$584$	1.62680	−	9.22607i	0.0673177	−	0.381777i
$585$	−16.1491	−	3.45047i	−0.667682	−	0.142659i
$586$	−8.56650	+	3.11795i	−0.353879	+	0.128801i
$587$	0.101358	−	0.120794i	0.00418349	−	0.00498568i	−0.763949	−	0.645277i	$-0.776742\pi$
$587$	0.101358	−	0.120794i	0.00418349	−	0.00498568i	0.768132	+	0.640291i	$0.221186\pi$
$588$	−10.0516	+	6.77215i	−0.414521	+	0.279279i
$589$	−12.0112	−	11.1040i	−0.494915	−	0.457534i
$590$		−	13.3992i		−	0.551638i
$591$	−0.385827	+	3.65230i	−0.0158708	+	0.150235i
$592$	1.49454	+	4.10622i	0.0614252	+	0.168764i
$593$	−1.76611	+	0.311414i	−0.0725256	+	0.0127882i	−0.209793	−	0.977746i	$-0.567279\pi$
$593$	−1.76611	+	0.311414i	−0.0725256	+	0.0127882i	0.137268	+	0.990534i	$0.456168\pi$
$594$	0.790027	+	23.7030i	0.0324152	+	0.972546i
$595$	0.112026	+	0.0407741i	0.00459262	+	0.00167158i
$596$	19.8590	−	11.4656i	0.813458	−	0.469650i
$597$	1.95828	+	28.2194i	0.0801470	+	1.15494i
$598$	−31.8232	+	26.7028i	−1.30135	+	1.09196i
$599$	22.0694	−	18.5184i	0.901731	−	0.756642i	−0.0687967	−	0.997631i	$-0.521916\pi$
$599$	22.0694	−	18.5184i	0.901731	−	0.756642i	0.970528	+	0.240988i	$0.0774716\pi$
$600$	0.119907	+	1.72790i	0.00489517	+	0.0705410i
$601$	9.18577	−	5.30341i	0.374695	−	0.216330i	−0.300812	−	0.953683i	$-0.597258\pi$
$601$	9.18577	−	5.30341i	0.374695	−	0.216330i	0.675508	+	0.737353i	$0.263924\pi$
$602$	−0.540464	−	0.196713i	−0.0220277	−	0.00801742i
$603$	3.48707	−	5.56735i	0.142004	−	0.226720i
$604$	−19.4302	+	3.42606i	−0.790602	+	0.139404i
$605$	3.36264	+	9.23879i	0.136711	+	0.375610i
$606$	−1.30556	+	12.3586i	−0.0530347	+	0.502034i
$607$			3.77417i			0.153189i	0.997062	+	0.0765945i	$0.0244047\pi$
$607$			3.77417i			0.153189i	−0.997062	+	0.0765945i	$0.975595\pi$
$608$	−0.209319	+	4.35387i	−0.00848900	+	0.176573i
$609$	−0.0165539	+	0.0111530i	−0.000670799	+	0.000451943i
$610$	−3.51920	+	4.19401i	−0.142488	+	0.169811i
$611$	−8.45386	+	3.07696i	−0.342007	+	0.124480i
$612$	1.50734	−	7.05472i	0.0609305	−	0.285170i
$613$	−1.71903	+	9.74910i	−0.0694309	+	0.393762i	0.930212	+	0.367024i	$0.119623\pi$
$613$	−1.71903	+	9.74910i	−0.0694309	+	0.393762i	−0.999642	+	0.0267386i	$0.991488\pi$
$614$	−8.94795	+	24.5843i	−0.361110	+	0.992141i
$615$	−1.60666	+	3.28972i	−0.0647869	+	0.132654i
$616$	−0.195963	−	0.113139i	−0.00789558	−	0.00455851i
$617$	19.9225	+	23.7427i	0.802051	+	0.955847i	0.999702	−	0.0244258i	$-0.00777575\pi$
$617$	19.9225	+	23.7427i	0.802051	+	0.955847i	−0.197651	+	0.980272i	$0.563331\pi$
$618$	−8.69109	−	2.49711i	−0.349607	−	0.100449i
$619$	−9.58849	+	16.6078i	−0.385394	+	0.667522i	−0.991824	−	0.127615i	$-0.959268\pi$
$619$	−9.58849	+	16.6078i	−0.385394	+	0.667522i	0.606430	+	0.795137i	$0.292601\pi$
$620$	−1.87634	−	3.24992i	−0.0753557	−	0.130520i
$621$	38.8246	+	5.51935i	1.55798	+	0.221484i
$622$	9.82248	+	1.73197i	0.393846	+	0.0694456i
$623$	−0.0291314	−	0.165212i	−0.00116713	−	0.00661910i
$624$	−7.71029	−	5.60810i	−0.308659	−	0.224504i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	17.1871			0.686936
$627$	22.7054	+	25.9205i	0.906767	+	1.03516i
$628$	3.87400			0.154589
$629$	−8.04938	−	6.75423i	−0.320950	−	0.269309i
$630$	−0.148635	−	0.00534807i	−0.00592176	−	0.000213072i
$631$	−3.56077	−	20.1941i	−0.141752	−	0.803916i	−0.969918	−	0.243433i	$-0.921727\pi$
$631$	−3.56077	−	20.1941i	−0.141752	−	0.803916i	0.828166	−	0.560483i	$-0.189385\pi$
$632$	−2.32257	−	0.409531i	−0.0923867	−	0.0162903i
$633$	−8.56725	−	34.4391i	−0.340518	−	1.36883i
$634$	−0.0181781	−	0.0314855i	−0.000721946	−	0.00125045i
$635$	−5.29710	+	9.17485i	−0.210209	+	0.364093i
$636$	2.12983	−	7.41280i	0.0844534	−	0.293936i
$637$	−24.7590	−	29.5066i	−0.980987	−	1.16909i
$638$	0.918805	+	0.530472i	0.0363758	+	0.0210016i
$639$	−9.93902	+	1.38611i	−0.393182	+	0.0548335i
$640$	−0.342020	+	0.939693i	−0.0135195	+	0.0371446i
$641$	−4.57705	+	25.9577i	−0.180782	+	1.02527i	0.750473	+	0.660901i	$0.229826\pi$
$641$	−4.57705	+	25.9577i	−0.180782	+	1.02527i	−0.931255	+	0.364367i	$0.881285\pi$
$642$	−20.0834	−	20.8190i	−0.792627	−	0.821660i
$643$	5.70532	−	2.07656i	0.224996	−	0.0818917i	−0.227062	−	0.973880i	$-0.572912\pi$
$643$	5.70532	−	2.07656i	0.224996	−	0.0818917i	0.452058	+	0.891988i	$0.350690\pi$
$644$	−0.240502	+	0.286619i	−0.00947710	+	0.0112944i
$645$	11.2275	+	16.6644i	0.442081	+	0.656161i
$646$	−4.79887	−	9.31856i	−0.188809	−	0.366634i
$647$		−	22.0438i		−	0.866633i	−0.901242	−	0.433317i	$-0.857343\pi$
$647$		−	22.0438i		−	0.866633i	0.901242	−	0.433317i	$-0.142657\pi$
$648$	0.921794	+	8.95267i	0.0362115	+	0.351694i
$649$	−20.9167	−	57.4683i	−0.821054	−	2.25583i
$650$	−5.42090	+	0.955851i	−0.212625	+	0.0374915i
$651$	0.294453	−	0.130912i	0.0115405	−	0.00513085i
$652$	2.75871	+	1.00409i	0.108040	+	0.0393232i
$653$	0.412733	−	0.238292i	0.0161515	−	0.00932507i	−0.491903	−	0.870650i	$-0.663698\pi$
$653$	0.412733	−	0.238292i	0.0161515	−	0.00932507i	0.508054	+	0.861325i	$0.330365\pi$
$654$	−26.8220	+	1.86131i	−1.04882	+	0.0727829i
$655$	9.79262	−	8.21698i	0.382629	−	0.321064i
$656$	−1.61922	+	1.35868i	−0.0632197	+	0.0530477i
$657$	−17.2798	−	22.1655i	−0.674150	−	0.864759i
$658$	−0.0701716	+	0.0405136i	−0.00273557	+	0.00157938i
$659$	1.91490	+	0.696967i	0.0745939	+	0.0271500i	0.379048	−	0.925377i	$-0.376252\pi$
$659$	1.91490	+	0.696967i	0.0745939	+	0.0271500i	−0.304454	+	0.952527i	$0.598474\pi$
$660$	3.21159	+	7.22363i	0.125011	+	0.281179i
$661$	49.5896	−	8.74399i	1.92881	−	0.340102i	0.929244	−	0.369468i	$-0.120460\pi$
$661$	49.5896	−	8.74399i	1.92881	−	0.340102i	0.999569	+	0.0293661i	$0.00934886\pi$
$662$	−9.00115	−	24.7305i	−0.349840	−	0.961176i
$663$	22.7994	+	2.40852i	0.885454	+	0.0935390i
$664$			9.41794i			0.365487i
$665$	−0.172023	+	0.130798i	−0.00667076	+	0.00507211i
$666$	12.1495	+	4.92368i	0.470782	+	0.190789i
$667$	1.12763	−	1.34386i	0.0436621	−	0.0520344i
$668$	−22.3135	+	8.12145i	−0.863335	+	0.314228i
$669$	−26.5248	+	25.5875i	−1.02551	+	0.989272i
$670$	0.380246	−	2.15648i	0.0146902	−	0.0833122i
$671$	−8.54654	+	23.4814i	−0.329935	+	0.906490i
$672$	−0.0771595	−	0.0376838i	−0.00297649	−	0.00145368i
$673$	35.2180	+	20.3331i	1.35755	+	0.783783i	0.989293	−	0.145940i	$-0.0466207\pi$
$673$	35.2180	+	20.3331i	1.35755	+	0.783783i	0.368259	+	0.929723i	$0.379954\pi$
$674$	−5.24358	−	6.24905i	−0.201975	−	0.240705i
$675$	4.08954	+	3.20557i	0.157406	+	0.123383i
$676$	8.64989	−	14.9821i	0.332688	−	0.576233i
$677$	−2.83215	−	4.90542i	−0.108848	−	0.188531i	0.806456	−	0.591295i	$-0.201383\pi$
$677$	−2.83215	−	4.90542i	−0.108848	−	0.188531i	−0.915304	+	0.402764i	$0.868050\pi$
$678$	32.4260	−	8.06648i	1.24531	−	0.309791i
$679$	−0.286298	−	0.0504821i	−0.0109871	−	0.00193733i
$680$	−0.417563	−	2.36812i	−0.0160128	−	0.0908132i
$681$	27.9212	−	38.3875i	1.06994	−	1.47101i
$682$	−13.1207	−	11.0096i	−0.502419	−	0.421580i
$683$	−9.55529			−0.365623			−0.182812	−	0.983148i	$-0.558520\pi$
$683$	−9.55529			−0.365623			−0.182812	+	0.983148i	$0.558520\pi$
$684$	9.27673	+	9.21642i	0.354705	+	0.352398i
$685$	−0.823681			−0.0314712
$686$	−0.531602	−	0.446067i	−0.0202967	−	0.0170309i
$687$	2.66928	−	3.66986i	0.101839	−	0.140014i
$688$	2.01451	+	11.4249i	0.0768027	+	0.435569i
$689$	24.1389	+	4.25634i	0.919618	+	0.162153i
$690$	12.6850	−	3.15560i	0.482911	−	0.120132i
$691$	8.27849	+	14.3388i	0.314929	+	0.545473i	0.979422	−	0.201821i	$-0.0646860\pi$
$691$	8.27849	+	14.3388i	0.314929	+	0.545473i	−0.664494	+	0.747294i	$0.731353\pi$
$692$	−4.16280	+	7.21017i	−0.158246	+	0.274090i
$693$	−0.645833	+	0.209088i	−0.0245332	+	0.00794259i
$694$	−5.37210	−	6.40222i	−0.203922	−	0.243025i
$695$	−6.77714	−	3.91278i	−0.257071	−	0.148420i
$696$	0.361775	+	0.176687i	0.0137130	+	0.00669729i
$697$	1.73842	−	4.77627i	0.0658473	−	0.180914i
$698$	2.84410	−	16.1297i	0.107651	−	0.610517i
$699$	−20.2475	+	19.5320i	−0.765830	+	0.738770i
$700$	−0.0465872	+	0.0169564i	−0.00176083	+	0.000640890i
$701$	5.90415	−	7.03629i	0.222997	−	0.265757i	−0.642934	−	0.765922i	$-0.722283\pi$
$701$	5.90415	−	7.03629i	0.222997	−	0.265757i	0.865930	+	0.500165i	$0.166727\pi$
$702$	−27.9867	+	5.90231i	−1.05629	+	0.222768i
$703$	18.1908	−	5.64753i	0.686078	−	0.213001i
$704$			4.56418i			0.172019i
$705$	2.81514	+	0.297391i	0.106024	+	0.0112004i
$706$	−8.99487	−	24.7132i	−0.338527	−	0.930094i
$707$	−0.350309	+	0.0617690i	−0.0131747	+	0.00232306i
$708$	−9.42837	−	21.2067i	−0.354340	−	0.796996i
$709$	25.4820	+	9.27468i	0.956995	+	0.348318i	0.772855	−	0.634582i	$-0.218828\pi$
$709$	25.4820	+	9.27468i	0.956995	+	0.348318i	0.184140	+	0.982900i	$0.441050\pi$
$710$	−2.89692	+	1.67253i	−0.108719	+	0.0627691i
$711$	−5.57993	+	4.35001i	−0.209264	+	0.163138i
$712$	−2.59217	+	2.17509i	−0.0971459	+	0.0815150i
$713$	−21.6953	+	18.2045i	−0.812495	+	0.681764i
$714$	0.205992	−	0.0142948i	0.00770906	−	0.000534968i
$715$	−21.7577	+	12.5618i	−0.813692	+	0.469785i
$716$	−7.33726	−	2.67054i	−0.274206	−	0.0998029i
$717$	18.5374	−	8.24164i	0.692293	−	0.307790i
$718$	7.37491	−	1.30040i	0.275229	−	0.0485304i
$719$	5.95669	+	16.3659i	0.222147	+	0.610344i	0.999832	−	0.0183099i	$-0.00582855\pi$
$719$	5.95669	+	16.3659i	0.222147	+	0.610344i	−0.777685	+	0.628654i	$0.783606\pi$
$720$	1.40561	+	2.65033i	0.0523839	+	0.0987721i
$721$		−	0.258833i		−	0.00963943i
$722$	18.9124	+	1.82269i	0.703846	+	0.0678336i
$723$	−20.8772	−	30.9871i	−0.776430	−	1.15242i
$724$	−5.26113	+	6.26997i	−0.195528	+	0.233022i
$725$	0.218432	−	0.0795027i	0.00811235	−	0.00295266i
$726$	11.8229	+	12.2559i	0.438788	+	0.454860i
$727$	3.77532	−	21.4109i	0.140019	−	0.794087i	−0.831214	−	0.555953i	$-0.812353\pi$
$727$	3.77532	−	21.4109i	0.140019	−	0.794087i	0.971232	−	0.238133i	$-0.0765356\pi$
$728$	0.0933367	−	0.256441i	0.00345929	−	0.00950432i
$729$	21.7929	+	15.9395i	0.807145	+	0.590353i
$730$	−8.11327	−	4.68420i	−0.300286	−	0.173370i
$731$	−17.9316	−	21.3701i	−0.663225	−	0.790401i
$732$	−2.61864	+	9.11407i	−0.0967877	+	0.336866i
$733$	−13.0209	+	22.5529i	−0.480939	+	0.833011i	−0.999761	−	0.0218712i	$-0.993038\pi$
$733$	−13.0209	+	22.5529i	−0.480939	+	0.833011i	0.518821	+	0.854883i	$0.326371\pi$
$734$	−5.95182	−	10.3088i	−0.219686	−	0.380507i
$735$	2.92589	+	11.7616i	0.107923	+	0.433834i
$736$	7.43226	+	1.31051i	0.273957	+	0.0483060i
$737$	−1.73551	−	9.84257i	−0.0639283	−	0.362556i
$738$	−0.228017	+	6.33711i	−0.00839341	+	0.233272i
$739$	5.49042	+	4.60701i	0.201968	+	0.169472i	0.738162	−	0.674623i	$-0.235694\pi$
$739$	5.49042	+	4.60701i	0.201968	+	0.169472i	−0.536194	+	0.844095i	$0.680138\pi$
$740$	4.36974			0.160635
$741$	−26.0308	+	32.3957i	−0.956267	+	1.19009i
$742$	0.220763			0.00810448
$743$	14.6356	+	12.2807i	0.536928	+	0.450536i	0.870486	−	0.492193i	$-0.163805\pi$
$743$	14.6356	+	12.2807i	0.536928	+	0.450536i	−0.333558	+	0.942730i	$0.608249\pi$
$744$	−5.25645	−	3.82329i	−0.192711	−	0.140169i
$745$	−3.98197	−	22.5829i	−0.145888	−	0.827372i
$746$	−9.20016	−	1.62224i	−0.336842	−	0.0593943i
$747$	20.9766	+	18.9277i	0.767495	+	0.692529i
$748$	−5.48763	−	9.50485i	−0.200648	−	0.347532i
$749$	0.413994	−	0.717059i	0.0151270	−	0.0262008i
$750$	1.66470	+	0.478300i	0.0607863	+	0.0174650i
$751$	−10.2967	−	12.2712i	−0.375733	−	0.447781i	0.544730	−	0.838612i	$-0.316632\pi$
$751$	−10.2967	−	12.2712i	−0.375733	−	0.447781i	−0.920463	+	0.390831i	$0.872188\pi$
$752$	1.41540	+	0.817184i	0.0516145	+	0.0297996i
$753$	1.93559	−	3.96321i	0.0705367	−	0.144428i
$754$	−0.437624	+	1.20236i	−0.0159373	+	0.0437875i
$755$	−3.42606	+	19.4302i	−0.124687	+	0.707136i
$756$	−0.239005	+	0.0961229i	−0.00869253	+	0.00349596i
$757$	23.8438	−	8.67842i	0.866616	−	0.315422i	0.129820	−	0.991538i	$-0.458560\pi$
$757$	23.8438	−	8.67842i	0.866616	−	0.315422i	0.736796	+	0.676115i	$0.236338\pi$
$758$	11.8047	−	14.0683i	0.428766	−	0.510984i
$759$	49.4791	−	33.3360i	1.79598	−	1.21002i
$760$	4.01971	+	1.68581i	0.145810	+	0.0611506i
$761$		−	39.9883i		−	1.44957i	−0.688973	−	0.724787i	$-0.741938\pi$
$761$		−	39.9883i		−	1.44957i	0.688973	−	0.724787i	$-0.258062\pi$
$762$	−1.92773	+	18.2482i	−0.0698343	+	0.661061i
$763$	−0.263213	−	0.723172i	−0.00952895	−	0.0261806i
$764$	7.15393	−	1.26143i	0.258820	−	0.0456370i
$765$	−6.11373	−	3.82929i	−0.221042	−	0.138448i
$766$	11.7518	+	4.27730i	0.424609	+	0.154545i
$767$	63.8749	−	36.8782i	2.30639	−	1.33159i
$768$	0.119907	+	1.72790i	0.00432676	+	0.0623501i
$769$	1.69997	−	1.42644i	0.0613023	−	0.0514388i	−0.611622	−	0.791150i	$-0.709483\pi$
$769$	1.69997	−	1.42644i	0.0613023	−	0.0514388i	0.672924	+	0.739712i	$0.265038\pi$
$770$	−0.173340	+	0.145449i	−0.00624672	+	0.00524162i
$771$	0.631425	+	9.09903i	0.0227402	+	0.327694i
$772$	21.9850	−	12.6930i	0.791256	−	0.456832i
$773$	38.4365	+	13.9898i	1.38247	+	0.503176i	0.922925	−	0.384980i	$-0.125792\pi$
$773$	38.4365	+	13.9898i	1.38247	+	0.503176i	0.459541	+	0.888157i	$0.348014\pi$
$774$	29.4954	+	18.4742i	1.06019	+	0.664043i
$775$	−3.69567	+	0.651646i	−0.132752	+	0.0234078i
$776$	2.00557	+	5.51026i	0.0719958	+	0.197807i
$777$	−0.0394199	+	0.373154i	−0.00141418	+	0.0133868i
$778$			30.4302i			1.09097i
$779$	5.57660	+	7.33425i	0.199802	+	0.262777i
$780$	−7.90696	+	5.32722i	−0.283115	+	0.190745i
$781$	−9.81375	+	11.6956i	−0.351164	+	0.418501i
$782$	−17.0533	+	6.20688i	−0.609823	+	0.221958i
$783$	1.12061	−	0.450688i	0.0400475	−	0.0161063i
$784$	−1.21511	+	6.89123i	−0.0433968	+	0.246115i
$785$	1.32499	−	3.64037i	0.0472908	−	0.129930i
$786$	9.71670	−	19.8954i	0.346583	−	0.709647i
$787$	−18.8142	−	10.8624i	−0.670652	−	0.387201i	0.125672	−	0.992072i	$-0.459891\pi$
$787$	−18.8142	−	10.8624i	−0.670652	−	0.387201i	−0.796324	+	0.604871i	$0.793225\pi$
$788$	1.36296	+	1.62431i	0.0485534	+	0.0578637i
$789$	36.9053	+	10.6036i	1.31386	+	0.377497i
$790$	−1.17920	+	2.04243i	−0.0419540	+	0.0726664i
$791$	0.478214	+	0.828292i	0.0170033	+	0.0294507i
$792$	10.1658	+	9.17286i	0.361227	+	0.325944i
$793$	−29.6789	−	5.23318i	−1.05393	−	0.185836i
$794$	−0.904519	−	5.12978i	−0.0321002	−	0.182049i
$795$	−6.23730	−	4.53671i	−0.221214	−	0.160901i
$796$	12.5108	+	10.4978i	0.443433	+	0.372084i
$797$	24.8634			0.880708			0.440354	−	0.897824i	$-0.354853\pi$
$797$	24.8634			0.880708			0.440354	+	0.897824i	$0.354853\pi$
$798$	−0.180221	+	0.328055i	−0.00637977	+	0.0116130i
$799$	−3.93008			−0.139036
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−0.365028	+	10.1450i	−0.0128976	+	0.358455i
$802$	−3.17878	−	18.0278i	−0.112247	−	0.636582i
$803$	−42.1094	−	7.42502i	−1.48601	−	0.262023i
$804$	−0.915602	−	3.68058i	−0.0322908	−	0.129804i
$805$	0.187077	+	0.324027i	0.00659360	+	0.0114205i
$806$	10.3284	−	17.8893i	0.363801	−	0.630122i
$807$	5.76943	−	20.0803i	0.203094	−	0.706858i
$808$	4.61197	+	5.49633i	0.162249	+	0.193360i
$809$	8.75419	+	5.05423i	0.307781	+	0.177697i	0.645933	−	0.763394i	$-0.276469\pi$
$809$	8.75419	+	5.05423i	0.307781	+	0.177697i	−0.338152	+	0.941091i	$0.609802\pi$
$810$	8.72803	+	2.19579i	0.306672	+	0.0771522i
$811$	11.4816	−	31.5453i	0.403172	−	1.10771i	−0.557538	−	0.830151i	$-0.688254\pi$
$811$	11.4816	−	31.5453i	0.403172	−	1.10771i	0.960710	−	0.277554i	$-0.0895238\pi$
$812$	−0.00200116	+	0.0113491i	−7.02269e−5	+	0.000398276i
$813$	17.2795	+	17.9124i	0.606018	+	0.628216i
$814$	18.7415	−	6.82135i	0.656889	−	0.239088i
$815$	1.88707	−	2.24892i	0.0661012	−	0.0787764i
$816$	−2.32720	−	3.45416i	−0.0814682	−	0.120920i
$817$	50.1641	−	6.37949i	1.75502	−	0.223190i
$818$		−	28.1610i		−	0.984626i
$819$	−0.383588	−	0.723272i	−0.0134037	−	0.0252732i
$820$	0.722940	+	1.98626i	0.0252462	+	0.0693633i
$821$	18.9298	−	3.33784i	0.660655	−	0.116491i	0.166739	−	0.986001i	$-0.446676\pi$
$821$	18.9298	−	3.33784i	0.660655	−	0.116491i	0.493916	+	0.869510i	$0.335565\pi$
$822$	−1.30362	+	0.579584i	−0.0454691	+	0.0202153i
$823$	−39.4357	−	14.3534i	−1.37464	−	0.500329i	−0.454093	−	0.890954i	$-0.650037\pi$
$823$	−39.4357	−	14.3534i	−1.37464	−	0.500329i	−0.920550	+	0.390625i	$0.872259\pi$
$824$	−4.52136	+	2.61041i	−0.157509	+	0.0909378i
$825$	7.88642	−	0.547276i	0.274570	−	0.0190537i
$826$	0.508879	−	0.427001i	0.0177062	−	0.0148572i
$827$	−32.5078	+	27.2773i	−1.13041	+	0.948524i	−0.999083	−	0.0428160i	$-0.986367\pi$
$827$	−32.5078	+	27.2773i	−1.13041	+	0.948524i	−0.131323	+	0.991340i	$0.541923\pi$
$828$	17.8559	−	13.9201i	0.620536	−	0.483758i
$829$	−9.39697	+	5.42534i	−0.326370	+	0.188430i	−0.654228	−	0.756297i	$-0.727006\pi$
$829$	−9.39697	+	5.42534i	−0.326370	+	0.188430i	0.327858	+	0.944727i	$0.393673\pi$
$830$	8.84997	+	3.22112i	0.307187	+	0.111807i
$831$	−18.6533	−	41.9558i	−0.647076	−	1.45543i
$832$	−5.42090	+	0.955851i	−0.187936	+	0.0331382i
$833$	−5.75505	−	15.8119i	−0.199401	−	0.547849i
$834$	−13.4793	−	1.42395i	−0.466749	−	0.0493072i
$835$			23.7455i			0.821748i
$836$	19.8718	+	0.955368i	0.687282	+	0.0330421i
$837$	−19.0798	+	4.02387i	−0.659495	+	0.139085i
$838$	−0.0978661	+	0.116632i	−0.00338073	+	0.00402900i
$839$	−27.7645	+	10.1054i	−0.958536	+	0.348879i	−0.773460	−	0.633846i	$-0.781475\pi$
$839$	−27.7645	+	10.1054i	−0.958536	+	0.348879i	−0.185076	+	0.982724i	$0.559253\pi$
$840$	−0.0618013	+	0.0596176i	−0.00213235	+	0.00205700i
$841$	−5.02641	+	28.5062i	−0.173325	+	0.982973i
$842$	−10.0386	+	27.5808i	−0.345953	+	0.950497i
$843$	−14.1120	−	6.89213i	−0.486042	−	0.237377i
$844$	−17.7443	−	10.2447i	−0.610785	−	0.352637i
$845$	−11.1201	−	13.2524i	−0.382543	−	0.455897i
$846$	4.66473	−	1.51020i	0.160377	−	0.0519218i
$847$	−0.243714	+	0.422125i	−0.00837411	+	0.0145044i
$848$	−2.22646	−	3.85635i	−0.0764571	−	0.132428i
$849$	−38.6943	+	9.62582i	−1.32799	+	0.330357i
$850$	−2.36812	−	0.417563i	−0.0812258	−	0.0143223i
$851$	−5.72659	−	32.4771i	−0.196305	−	1.11330i
$852$	−3.40801	+	4.68550i	−0.116756	+	0.160523i
$853$	34.9167	+	29.2986i	1.19553	+	1.00317i	0.999746	+	0.0225181i	$0.00716834\pi$
$853$	34.9167	+	29.2986i	1.19553	+	1.00317i	0.195780	+	0.980648i	$0.437276\pi$
$854$	−0.271430			−0.00928813
$855$	11.8334	−	5.56507i	0.404695	−	0.190321i
$856$	−16.7010			−0.570829
$857$	−34.2949	−	28.7768i	−1.17149	−	0.982997i	−0.171493	−	0.985185i	$-0.554859\pi$
$857$	−34.2949	−	28.7768i	−1.17149	−	0.982997i	−0.999998	+	0.00218838i	$0.999303\pi$
$858$	−25.5963	+	35.1911i	−0.873845	+	1.20141i
$859$	1.44530	+	8.19669i	0.0493129	+	0.279667i	0.999486	−	0.0320551i	$-0.0102052\pi$
$859$	1.44530	+	8.19669i	0.0493129	+	0.279667i	−0.950173	+	0.311722i	$0.899094\pi$
$860$	11.4249	+	2.01451i	0.389585	+	0.0686944i
$861$	−0.176138	+	0.0438172i	−0.00600278	+	0.00149328i
$862$	−18.4671	−	31.9859i	−0.628991	−	1.08944i
$863$	−2.76152	+	4.78310i	−0.0940034	+	0.162819i	−0.909192	−	0.416377i	$-0.863300\pi$
$863$	−2.76152	+	4.78310i	−0.0940034	+	0.162819i	0.815189	+	0.579195i	$0.196633\pi$
$864$	4.08954	+	3.20557i	0.139129	+	0.109056i
$865$	5.35159	+	6.37777i	0.181959	+	0.216851i
$866$	−1.16644	−	0.673443i	−0.0396372	−	0.0228845i
$867$	−17.4586	−	8.52660i	−0.592927	−	0.289578i
$868$	0.0636319	−	0.174827i	0.00215981	−	0.00593402i
$869$	−1.86917	+	10.6006i	−0.0634073	+	0.359601i
$870$	0.289766	−	0.279527i	0.00982397	−	0.00947685i
$871$	11.3266	−	4.12255i	0.383788	−	0.139687i
$872$	−9.97796	+	11.8913i	−0.337897	+	0.402689i
$873$	16.3037	+	6.60723i	0.551798	+	0.223621i
$874$	7.26150	−	32.0848i	0.245624	−	1.08528i
$875$			0.0495771i			0.00167601i
$876$	−16.1367	−	1.70468i	−0.545210	−	0.0575958i
$877$	12.5573	+	34.5008i	0.424029	+	1.16501i	0.949381	+	0.314126i	$0.101711\pi$
$877$	12.5573	+	34.5008i	0.424029	+	1.16501i	−0.525352	+	0.850885i	$0.676067\pi$
$878$	−28.3175	+	4.99314i	−0.955669	+	0.168510i
$879$	6.41467	+	14.4281i	0.216362	+	0.486649i
$880$	4.28892	+	1.56104i	0.144580	+	0.0526227i
$881$	−27.3206	+	15.7736i	−0.920456	+	0.531425i	−0.883780	−	0.467902i	$-0.845010\pi$
$881$	−27.3206	+	15.7736i	−0.920456	+	0.531425i	−0.0366754	+	0.999327i	$0.511677\pi$
$882$	12.9068	+	16.5561i	0.434595	+	0.557473i
$883$	−1.50592	+	1.26362i	−0.0506782	+	0.0425240i	−0.667775	−	0.744363i	$-0.732753\pi$
$883$	−1.50592	+	1.26362i	−0.0506782	+	0.0425240i	0.617097	+	0.786887i	$0.288309\pi$
$884$	10.1397	−	8.50823i	0.341036	−	0.286163i
$885$	−23.1525	+	1.60666i	−0.778262	+	0.0540072i
$886$	31.7741	−	18.3448i	1.06747	−	0.616304i
$887$	2.67042	+	0.971954i	0.0896640	+	0.0326350i	0.386463	−	0.922305i	$-0.373697\pi$
$887$	2.67042	+	0.971954i	0.0896640	+	0.0326350i	−0.296799	+	0.954940i	$0.595919\pi$
$888$	6.91591	−	3.07477i	0.232083	−	0.103183i
$889$	−0.517251	+	0.0912052i	−0.0173480	+	0.00305893i
$890$	1.15734	+	3.17977i	0.0387942	+	0.106586i
$891$	40.8616	−	4.20723i	1.36891	−	0.140948i
$892$			21.2782i			0.712447i
$893$	3.85418	−	5.99143i	0.128975	−	0.200496i
$894$	−22.1926	−	32.9395i	−0.742233	−	1.10166i
$895$	−5.01898	+	5.98139i	−0.167766	+	0.199936i
$896$	−0.0465872	+	0.0169564i	−0.00155637	+	0.000566472i
$897$	49.9555	+	51.7852i	1.66796	+	1.72906i
$898$	0.833147	−	4.72501i	0.0278025	−	0.157676i
$899$	−0.298348	+	0.819705i	−0.00995047	+	0.0273387i
$900$	2.97124	−	0.414373i	0.0990415	−	0.0138124i
$901$	9.27318	+	5.35387i	0.308934	+	0.178363i
$902$	6.20127	+	7.39039i	0.206480	+	0.246073i
$903$	−0.275094	+	0.957453i	−0.00915456	+	0.0318620i
$904$	9.64587	−	16.7071i	0.320817	−	0.555671i
$905$	4.09244	+	7.08831i	0.136037	+	0.235623i
$906$	8.24968	+	33.1625i	0.274077	+	1.10175i
$907$	−31.8990	−	5.62465i	−1.05919	−	0.186763i	−0.383192	−	0.923669i	$-0.625175\pi$
$907$	−31.8990	−	5.62465i	−1.05919	−	0.186763i	−0.675996	+	0.736905i	$0.736286\pi$
$908$	−4.75893	−	26.9892i	−0.157931	−	0.895669i
$909$	21.5109	+	0.773989i	0.713473	+	0.0256716i
$910$	−0.209052	−	0.175416i	−0.00693002	−	0.00581497i
$911$	−7.82569			−0.259277			−0.129638	−	0.991561i	$-0.541382\pi$
$911$	−7.82569			−0.259277			−0.129638	+	0.991561i	$0.541382\pi$
$912$	7.54813	−	0.160378i	0.249944	−	0.00531063i
$913$	42.9851			1.42260
$914$	−18.5943	−	15.6024i	−0.615043	−	0.516083i
$915$	7.66879	+	5.57791i	0.253522	+	0.184400i
$916$	−0.454955	−	2.58018i	−0.0150321	−	0.0852515i
$917$	0.624134	+	0.110052i	0.0206107	+	0.00363422i
$918$	−12.3706	−	1.75861i	−0.408289	−	0.0580429i
$919$	27.9633	+	48.4339i	0.922425	+	1.59769i	0.795652	+	0.605755i	$0.207129\pi$
$919$	27.9633	+	48.4339i	0.922425	+	1.59769i	0.126773	+	0.991932i	$0.459538\pi$
$920$	3.77346	−	6.53582i	0.124407	−	0.215480i
$921$	43.5520	+	12.5133i	1.43509	+	0.412327i
$922$	−15.7271	−	18.7428i	−0.517945	−	0.617262i
$923$	−15.9461	−	9.20651i	−0.524874	−	0.303036i
$924$	−0.171996	+	0.352170i	−0.00565824	+	0.0115855i
$925$	1.49454	−	4.10622i	0.0491402	−	0.135012i
$926$	4.08736	−	23.1806i	0.134319	−	0.761761i
$927$	−3.27263	+	15.3167i	−0.107487	+	0.503067i
$928$	0.218432	−	0.0795027i	0.00717037	−	0.00260980i
$929$	−30.8764	+	36.7971i	−1.01302	+	1.20727i	−0.0348691	+	0.999392i	$0.511101\pi$
$929$	−30.8764	+	36.7971i	−1.01302	+	1.20727i	−0.978154	+	0.207882i	$0.933343\pi$
$930$	−5.39053	+	3.63181i	−0.176763	+	0.119092i
$931$	29.7492	+	6.73290i	0.974990	+	0.220662i
$932$			16.2425i			0.532042i
$933$	1.81488	−	17.1799i	0.0594165	−	0.562445i
$934$	5.76996	+	15.8528i	0.188799	+	0.518721i
$935$	−10.8085	+	1.90583i	−0.353476	+	0.0623274i
$936$	−8.76569	+	13.9950i	−0.286515	+	0.457442i
$937$	−29.4595	−	10.7224i	−0.962400	−	0.350285i	−0.187426	−	0.982279i	$-0.560015\pi$
$937$	−29.4595	−	10.7224i	−0.962400	−	0.350285i	−0.774974	+	0.631994i	$0.782237\pi$
$938$	0.0940170	−	0.0542807i	0.00306976	−	0.00177233i
$939$	−2.06085	−	29.6976i	−0.0672534	−	0.969143i
$940$	1.25200	−	1.05055i	0.0408357	−	0.0342652i
$941$	−10.2979	+	8.64100i	−0.335703	+	0.281688i	−0.795019	−	0.606585i	$-0.792539\pi$
$941$	−10.2979	+	8.64100i	−0.335703	+	0.281688i	0.459316	+	0.888273i	$0.348095\pi$
$942$	−0.464519	−	6.69387i	−0.0151348	−	0.218098i
$943$	13.8150	−	7.97609i	0.449878	−	0.259737i
$944$	−12.5912	−	4.58281i	−0.409807	−	0.149158i
$945$	0.00858145	+	0.257467i	0.000279154	+	0.00837541i
$946$	52.1452	−	9.19460i	1.69539	−	0.298942i
$947$	−11.4782	−	31.5360i	−0.372991	−	1.02478i	−0.974199	−	0.225691i	$-0.927536\pi$
$947$	−11.4782	−	31.5360i	−0.372991	−	1.02478i	0.601208	−	0.799093i	$-0.294686\pi$
$948$	−0.429135	+	4.06226i	−0.0139377	+	0.131936i
$949$		−	51.5686i		−	1.67399i
$950$	2.95896	−	3.20071i	0.0960014	−	0.103845i
$951$	−0.0522239	+	0.0351852i	−0.00169348	+	0.00114096i
$952$	0.0766303	−	0.0913245i	0.00248360	−	0.00295984i
$953$	26.0956	−	9.49800i	0.845318	−	0.307671i	0.117188	−	0.993110i	$-0.462612\pi$
$953$	26.0956	−	9.49800i	0.845318	−	0.307671i	0.728130	+	0.685439i	$0.240390\pi$
$954$	−13.0639	−	2.79129i	−0.422960	−	0.0903712i
$955$	1.26143	−	7.15393i	0.0408190	−	0.231496i
$956$	4.00597	−	11.0063i	0.129562	−	0.355970i
$957$	0.806429	−	1.65121i	0.0260682	−	0.0533759i
$958$	−24.8237	−	14.3320i	−0.802018	−	0.463045i
$959$	−0.0262487	−	0.0312820i	−0.000847615	−	0.00101015i
$960$	1.66470	+	0.478300i	0.0537280	+	0.0154371i
$961$	−8.45869	+	14.6509i	−0.272861	+	0.472609i
$962$	12.0267	+	20.8308i	0.387756	+	0.671613i
$963$	−33.5649	+	37.1983i	−1.08161	+	1.19870i
$964$	−21.2443	−	3.74594i	−0.684232	−	0.120649i
$965$	−4.40824	−	25.0004i	−0.141906	−	0.804791i
$966$	0.524085	+	0.381194i	0.0168622	+	0.0122647i
$967$	−32.0591	−	26.9008i	−1.03095	−	0.865071i	−0.0399881	−	0.999200i	$-0.512732\pi$
$967$	−32.0591	−	26.9008i	−1.03095	−	0.865071i	−0.990964	+	0.134129i	$0.957176\pi$
$968$	9.83171			0.316003
$969$	−15.5261	+	9.40930i	−0.498769	+	0.302270i
$970$	5.86390			0.188278
$971$	−12.2234	−	10.2566i	−0.392266	−	0.329150i	0.425229	−	0.905086i	$-0.360194\pi$
$971$	−12.2234	−	10.2566i	−0.392266	−	0.329150i	−0.817495	+	0.575935i	$0.804638\pi$
$972$	15.3587	−	2.66625i	0.492632	−	0.0855200i
$973$	−0.0673701	−	0.382075i	−0.00215978	−	0.0122487i
$974$	3.35346	+	0.591305i	0.107452	+	0.0189466i
$975$	2.30161	+	9.25213i	0.0737106	+	0.296305i
$976$	2.73745	+	4.74140i	0.0876236	+	0.151769i
$977$	−13.0402	+	22.5863i	−0.417193	+	0.722599i	−0.995656	−	0.0931096i	$-0.970319\pi$
$977$	−13.0402	+	22.5863i	−0.417193	+	0.722599i	0.578463	+	0.815708i	$0.303653\pi$
$978$	1.40417	−	4.88717i	0.0449005	−	0.156274i
$979$	9.92751	+	11.8311i	0.317285	+	0.378125i
$980$	6.06005	+	3.49877i	0.193581	+	0.111764i
$981$	6.43229	+	46.1225i	0.205367	+	1.47258i
$982$	2.67289	−	7.34370i	0.0852953	−	0.234347i
$983$	6.64869	−	37.7066i	0.212060	−	1.20265i	−0.673875	−	0.738845i	$-0.735372\pi$
$983$	6.64869	−	37.7066i	0.212060	−	1.20265i	0.885936	−	0.463808i	$-0.153517\pi$
$984$	2.54182	+	2.63492i	0.0810302	+	0.0839982i
$985$	1.99251	−	0.725215i	0.0634867	−	0.0231073i
$986$	−0.359294	+	0.428190i	−0.0114422	+	0.0136363i
$987$	0.0784173	+	0.116391i	0.00249605	+	0.00370478i
$988$	3.02695	+	23.8020i	0.0963002	+	0.757241i
$989$		−	87.5527i		−	2.78402i
$990$	12.0966	−	6.41545i	0.384455	−	0.203896i
$991$	−4.65302	−	12.7841i	−0.147808	−	0.406099i	0.843589	−	0.536990i	$-0.180439\pi$
$991$	−4.65302	−	12.7841i	−0.147808	−	0.406099i	−0.991397	+	0.130890i	$0.958216\pi$
$992$	−3.69567	+	0.651646i	−0.117338	+	0.0206898i
$993$	−41.6523	+	18.5184i	−1.32180	+	0.587663i
$994$	−0.155838	−	0.0567202i	−0.00494287	−	0.00179906i
$995$	14.1436	−	8.16583i	0.448384	−	0.258874i
$996$	16.2732	−	1.12927i	0.515636	−	0.0357824i
$997$	−11.6231	+	9.75292i	−0.368107	+	0.308878i	−0.808012	−	0.589166i	$-0.799456\pi$
$997$	−11.6231	+	9.75292i	−0.368107	+	0.308878i	0.439905	+	0.898044i	$0.355012\pi$
$998$	30.6045	−	25.6802i	0.968768	−	0.812893i
$999$	7.05079	−	21.5834i	0.223077	−	0.682868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.41.5	yes	84
3.2	odd	2		570.2.bb.a.41.13	✓	84
19.13	odd	18		570.2.bb.a.431.13	yes	84
57.32	even	18	inner	570.2.bb.b.431.5	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.13	✓	84	3.2	odd	2
570.2.bb.a.431.13	yes	84	19.13	odd	18
570.2.bb.b.41.5	yes	84	1.1	even	1	trivial
570.2.bb.b.431.5	yes	84	57.32	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.01882 + 1.40072i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.68082 - 0.418131i) q^{6} +(0.0247885 + 0.0429350i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.924029 - 2.85415i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.01882 + 1.40072i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.68082 - 0.418131i) q^{6} +(0.0247885 + 0.0429350i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.924029 - 2.85415i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(-3.95269 - 2.28209i) q^{11} +(-1.55635 - 0.760105i) q^{12} +(1.88266 - 5.17256i) q^{13} +(0.00860897 - 0.0488239i) q^{14} +(-1.24657 + 1.20252i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.54568 - 1.84207i) q^{17} +(-1.12677 + 2.78036i) q^{18} +(1.29242 + 4.16289i) q^{19} +1.00000i q^{20} +(-0.0853949 - 0.00902109i) q^{21} +(1.56104 + 4.28892i) q^{22} +(7.43226 - 1.31051i) q^{23} +(0.703651 + 1.58268i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-4.76706 + 2.75226i) q^{26} +(4.93928 + 1.61355i) q^{27} +(-0.0379783 + 0.0318675i) q^{28} +(0.178067 - 0.149416i) q^{29} +(1.72790 - 0.119907i) q^{30} +(-3.24992 + 1.87634i) q^{31} +(0.939693 + 0.342020i) q^{32} +(7.22363 - 3.21159i) q^{33} +(-2.36812 + 0.417563i) q^{34} +(0.0169564 + 0.0465872i) q^{35} +(2.65033 - 1.40561i) q^{36} -4.36974i q^{37} +(1.68581 - 4.01971i) q^{38} +(5.32722 + 7.90696i) q^{39} +(0.642788 - 0.766044i) q^{40} +(1.98626 - 0.722940i) q^{41} +(0.0596176 + 0.0618013i) q^{42} +(2.01451 - 11.4249i) q^{43} +(1.56104 - 4.28892i) q^{44} +(-0.414373 - 2.97124i) q^{45} +(-6.53582 - 3.77346i) q^{46} +(-1.05055 - 1.25200i) q^{47} +(0.478300 - 1.66470i) q^{48} +(3.49877 - 6.06005i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.00546 + 4.04179i) q^{51} +(5.42090 + 0.955851i) q^{52} +(0.773243 + 4.38528i) q^{53} +(-2.74654 - 4.41096i) q^{54} +(-3.49636 - 2.93380i) q^{55} +0.0495771 q^{56} +(-7.14778 - 2.43091i) q^{57} -0.232450 q^{58} +(10.2644 + 8.61286i) q^{59} +(-1.40072 - 1.01882i) q^{60} +(-0.950706 - 5.39172i) q^{61} +(3.69567 + 0.651646i) q^{62} +(0.0996377 - 0.110423i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.75226 - 4.76706i) q^{65} +(-7.59799 - 2.18304i) q^{66} +(1.40754 + 1.67745i) q^{67} +(2.08249 + 1.20233i) q^{68} +(-5.73645 + 11.7457i) q^{69} +(0.0169564 - 0.0465872i) q^{70} +(0.580865 - 3.29425i) q^{71} +(-2.93378 - 0.626843i) q^{72} +(8.80341 - 3.20418i) q^{73} +(-2.80882 + 3.34742i) q^{74} +(-1.43645 + 0.967790i) q^{75} +(-3.87522 + 1.99566i) q^{76} -0.226279i q^{77} +(1.00161 - 9.48136i) q^{78} +(-0.806619 - 2.21617i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(-7.29234 + 5.27463i) q^{81} +(-1.98626 - 0.722940i) q^{82} +(-8.15617 + 4.70897i) q^{83} +(-0.00594463 - 0.0856640i) q^{84} +(1.84207 - 1.54568i) q^{85} +(-8.88698 + 7.45706i) q^{86} +(0.0278724 + 0.401650i) q^{87} +(-3.95269 + 2.28209i) q^{88} +(-3.17977 - 1.15734i) q^{89} +(-1.59245 + 2.54246i) q^{90} +(0.268752 - 0.0473883i) q^{91} +(2.58120 + 7.09178i) q^{92} +(0.682841 - 6.46387i) q^{93} +1.63437i q^{94} +(0.549903 + 4.32407i) q^{95} +(-1.43645 + 0.967790i) q^{96} +(-3.76924 + 4.49200i) q^{97} +(-6.57554 + 2.39330i) q^{98} +(-2.86102 + 13.3903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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