LMFDB - Embedded newform 392.2.z.a.109.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.26
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.158727 - 1.40528i) q^{2} +(0.331575 + 2.19985i) q^{3} +(-1.94961 + 0.446111i) q^{4} +(-2.18080 - 0.855902i) q^{5} +(3.03878 - 0.815131i) q^{6} +(0.239753 - 2.63487i) q^{7} +(0.936366 + 2.66894i) q^{8} +(-1.86270 + 0.574567i) q^{9} +(-0.856628 + 3.20049i) q^{10} +(0.946675 - 3.06904i) q^{11} +(-1.62782 - 4.14094i) q^{12} +(6.29115 - 1.43591i) q^{13} +(-3.74077 + 0.0813049i) q^{14} +(1.15976 - 5.08125i) q^{15} +(3.60197 - 1.73949i) q^{16} +(1.11924 - 0.763087i) q^{17} +(1.10309 + 2.52641i) q^{18} +(-2.56973 + 1.48363i) q^{19} +(4.63355 + 0.695797i) q^{20} +(5.87582 - 0.346233i) q^{21} +(-4.46312 - 0.843201i) q^{22} +(-0.865154 - 0.589852i) q^{23} +(-5.56080 + 2.94482i) q^{24} +(0.358077 + 0.332247i) q^{25} +(-3.01643 - 8.61289i) q^{26} +(1.01420 + 2.10601i) q^{27} +(0.708018 + 5.24392i) q^{28} +(4.05674 - 8.42391i) q^{29} +(-7.32465 - 0.823256i) q^{30} +(3.06500 - 5.30874i) q^{31} +(-3.01619 - 4.78567i) q^{32} +(7.06534 + 1.06493i) q^{33} +(-1.25000 - 1.45173i) q^{34} +(-2.77804 + 5.54092i) q^{35} +(3.37522 - 1.95115i) q^{36} +(2.51352 - 0.188362i) q^{37} +(2.49280 + 3.37569i) q^{38} +(5.24479 + 13.3635i) q^{39} +(0.242319 - 6.62186i) q^{40} +(1.42183 + 1.78292i) q^{41} +(-1.41921 - 8.20220i) q^{42} +(-1.45388 - 1.15943i) q^{43} +(-0.476514 + 6.40577i) q^{44} +(4.55396 + 0.341272i) q^{45} +(-0.691583 + 1.30941i) q^{46} +(-5.07237 + 4.70647i) q^{47} +(5.02094 + 7.34704i) q^{48} +(-6.88504 - 1.26343i) q^{49} +(0.410063 - 0.555935i) q^{50} +(2.04979 + 2.20915i) q^{51} +(-11.6247 + 5.60602i) q^{52} +(-13.1369 - 0.984473i) q^{53} +(2.79854 - 1.75951i) q^{54} +(-4.69131 + 5.88272i) q^{55} +(7.25678 - 1.82731i) q^{56} +(-4.11584 - 5.16109i) q^{57} +(-12.4818 - 4.36375i) q^{58} +(-3.35496 + 1.31672i) q^{59} +(0.00571593 + 10.4238i) q^{60} +(8.59410 - 0.644039i) q^{61} +(-7.94676 - 3.46454i) q^{62} +(1.06732 + 5.04572i) q^{63} +(-6.24644 + 4.99820i) q^{64} +(-14.9488 - 2.25316i) q^{65} +(0.375061 - 10.0978i) q^{66} +(5.87497 + 3.39191i) q^{67} +(-1.84167 + 1.98703i) q^{68} +(1.01073 - 2.09879i) q^{69} +(8.22748 + 3.02443i) q^{70} +(-11.1501 + 5.36960i) q^{71} +(-3.27765 - 4.43342i) q^{72} +(6.95014 + 6.44879i) q^{73} +(-0.663664 - 3.50229i) q^{74} +(-0.612166 + 0.897883i) q^{75} +(4.34811 - 4.03889i) q^{76} +(-7.85955 - 3.23017i) q^{77} +(17.9469 - 9.49153i) q^{78} +(3.16216 + 5.47702i) q^{79} +(-9.34402 + 0.710544i) q^{80} +(-9.12839 + 6.22363i) q^{81} +(2.27981 - 2.28106i) q^{82} +(6.04232 + 1.37912i) q^{83} +(-11.3011 + 3.29629i) q^{84} +(-3.09398 + 0.706181i) q^{85} +(-1.39856 + 2.22715i) q^{86} +(19.8765 + 6.13109i) q^{87} +(9.07752 - 0.347134i) q^{88} +(9.55075 - 2.94602i) q^{89} +(-0.243254 - 6.45375i) q^{90} +(-2.27512 - 16.9206i) q^{91} +(1.94985 + 0.764028i) q^{92} +(12.6947 + 4.98232i) q^{93} +(7.41902 + 6.38104i) q^{94} +(6.87392 - 1.03608i) q^{95} +(9.52768 - 8.22199i) q^{96} +0.651035 q^{97} +(-0.682634 + 9.87593i) q^{98} +6.26064i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

Coefficient data

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

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

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

$2$	−0.158727	−	1.40528i	−0.112237	−	0.993681i
$2$	−0.158727	−	1.40528i	−0.112237	−	0.993681i
$3$	0.331575	+	2.19985i	0.191435	+	1.27009i	0.853679	+	0.520799i	$0.174366\pi$
$3$	0.331575	+	2.19985i	0.191435	+	1.27009i	−0.662245	+	0.749288i	$0.730396\pi$
$4$	−1.94961	+	0.446111i	−0.974806	+	0.223056i
$5$	−2.18080	−	0.855902i	−0.975285	−	0.382771i	−0.176442	−	0.984311i	$-0.556459\pi$
$5$	−2.18080	−	0.855902i	−0.975285	−	0.382771i	−0.798843	+	0.601540i	$0.794554\pi$
$6$	3.03878	−	0.815131i	1.24058	−	0.332776i
$7$	0.239753	−	2.63487i	0.0906181	−	0.995886i
$7$	0.239753	−	2.63487i	0.0906181	−	0.995886i
$8$	0.936366	+	2.66894i	0.331055	+	0.943611i
$9$	−1.86270	+	0.574567i	−0.620900	+	0.191522i
$10$	−0.856628	+	3.20049i	−0.270890	+	1.01208i
$11$	0.946675	−	3.06904i	0.285433	−	0.925352i	−0.693376	−	0.720576i	$-0.743877\pi$
$11$	0.946675	−	3.06904i	0.285433	−	0.925352i	0.978809	−	0.204775i	$-0.0656464\pi$
$12$	−1.62782	−	4.14094i	−0.469912	−	1.19539i
$13$	6.29115	−	1.43591i	1.74485	−	0.398251i	0.773104	−	0.634279i	$-0.218703\pi$
$13$	6.29115	−	1.43591i	1.74485	−	0.398251i	0.971746	+	0.236029i	$0.0758459\pi$
$14$	−3.74077	+	0.0813049i	−0.999764	+	0.0217296i
$15$	1.15976	−	5.08125i	0.299449	−	1.31197i
$16$	3.60197	−	1.73949i	0.900492	−	0.434872i
$17$	1.11924	−	0.763087i	0.271456	−	0.185076i	−0.419939	−	0.907552i	$-0.637949\pi$
$17$	1.11924	−	0.763087i	0.271456	−	0.185076i	0.691396	+	0.722476i	$0.256996\pi$
$18$	1.10309	+	2.52641i	0.260000	+	0.595481i
$19$	−2.56973	+	1.48363i	−0.589536	+	0.340369i	−0.764914	−	0.644132i	$-0.777219\pi$
$19$	−2.56973	+	1.48363i	−0.589536	+	0.340369i	0.175378	+	0.984501i	$0.443885\pi$
$20$	4.63355	+	0.695797i	1.03609	+	0.155585i
$21$	5.87582	−	0.346233i	1.28221	−	0.0755543i
$22$	−4.46312	−	0.843201i	−0.951541	−	0.179771i
$23$	−0.865154	−	0.589852i	−0.180397	−	0.122993i	0.469755	−	0.882797i	$-0.344342\pi$
$23$	−0.865154	−	0.589852i	−0.180397	−	0.122993i	−0.650152	+	0.759804i	$0.725295\pi$
$24$	−5.56080	+	2.94482i	−1.13509	+	0.601109i
$25$	0.358077	+	0.332247i	0.0716155	+	0.0664495i
$26$	−3.01643	−	8.61289i	−0.591571	−	1.68913i
$27$	1.01420	+	2.10601i	0.195183	+	0.405301i
$28$	0.708018	+	5.24392i	0.133803	+	0.991008i
$29$	4.05674	−	8.42391i	0.753318	−	1.56428i	−0.0705559	−	0.997508i	$-0.522477\pi$
$29$	4.05674	−	8.42391i	0.753318	−	1.56428i	0.823874	−	0.566773i	$-0.191808\pi$
$30$	−7.32465	−	0.823256i	−1.33729	−	0.150305i
$31$	3.06500	−	5.30874i	0.550491	−	0.953478i	−0.447748	−	0.894160i	$-0.647774\pi$
$31$	3.06500	−	5.30874i	0.550491	−	0.953478i	0.998239	−	0.0593186i	$-0.0188928\pi$
$32$	−3.01619	−	4.78567i	−0.533192	−	0.845994i
$33$	7.06534	+	1.06493i	1.22992	+	0.185380i
$34$	−1.25000	−	1.45173i	−0.214374	−	0.248969i
$35$	−2.77804	+	5.54092i	−0.469575	+	0.936587i
$36$	3.37522	−	1.95115i	0.562537	−	0.325192i
$37$	2.51352	−	0.188362i	0.413220	−	0.0309665i	0.133501	−	0.991049i	$-0.457378\pi$
$37$	2.51352	−	0.188362i	0.413220	−	0.0309665i	0.279718	+	0.960082i	$0.409759\pi$
$38$	2.49280	+	3.37569i	0.404386	+	0.547609i
$39$	5.24479	+	13.3635i	0.839838	+	2.13987i
$40$	0.242319	−	6.62186i	0.0383139	−	1.04701i
$41$	1.42183	+	1.78292i	0.222052	+	0.278445i	0.880362	−	0.474303i	$-0.157300\pi$
$41$	1.42183	+	1.78292i	0.222052	+	0.278445i	−0.658310	+	0.752747i	$0.728728\pi$
$42$	−1.41921	−	8.20220i	−0.218988	−	1.26563i
$43$	−1.45388	−	1.15943i	−0.221715	−	0.176812i	0.506333	−	0.862338i	$-0.331001\pi$
$43$	−1.45388	−	1.15943i	−0.221715	−	0.176812i	−0.728048	+	0.685526i	$0.759572\pi$
$44$	−0.476514	+	6.40577i	−0.0718371	+	0.965705i
$45$	4.55396	+	0.341272i	0.678864	+	0.0508738i
$46$	−0.691583	+	1.30941i	−0.101968	+	0.193062i
$47$	−5.07237	+	4.70647i	−0.739881	+	0.686509i	−0.957147	−	0.289604i	$-0.906477\pi$
$47$	−5.07237	+	4.70647i	−0.739881	+	0.686509i	0.217266	+	0.976112i	$0.430286\pi$
$48$	5.02094	+	7.34704i	0.724710	+	1.06045i
$49$	−6.88504	−	1.26343i	−0.983577	−	0.180490i
$50$	0.410063	−	0.555935i	0.0579917	−	0.0786211i
$51$	2.04979	+	2.20915i	0.287029	+	0.309343i
$52$	−11.6247	+	5.60602i	−1.61206	+	0.777415i
$53$	−13.1369	−	0.984473i	−1.80449	−	0.135228i	−0.870418	−	0.492314i	$-0.836151\pi$
$53$	−13.1369	−	0.984473i	−1.80449	−	0.135228i	−0.934071	+	0.357086i	$0.883770\pi$
$54$	2.79854	−	1.75951i	0.380833	−	0.239439i
$55$	−4.69131	+	5.88272i	−0.632577	+	0.793226i
$56$	7.25678	−	1.82731i	0.969729	−	0.244185i
$57$	−4.11584	−	5.16109i	−0.545156	−	0.683604i
$58$	−12.4818	−	4.36375i	−1.63895	−	0.572988i
$59$	−3.35496	+	1.31672i	−0.436778	+	0.171423i	−0.573534	−	0.819182i	$-0.694428\pi$
$59$	−3.35496	+	1.31672i	−0.436778	+	0.171423i	0.136755	+	0.990605i	$0.456333\pi$
$60$	0.00571593	+	10.4238i	0.000737923	+	1.34571i
$61$	8.59410	−	0.644039i	1.10036	−	0.0824607i	0.487854	−	0.872925i	$-0.337780\pi$
$61$	8.59410	−	0.644039i	1.10036	−	0.0824607i	0.612508	+	0.790465i	$0.290161\pi$
$62$	−7.94676	−	3.46454i	−1.00924	−	0.439997i
$63$	1.06732	+	5.04572i	0.134470	+	0.635701i
$64$	−6.24644	+	4.99820i	−0.780805	+	0.624775i
$65$	−14.9488	−	2.25316i	−1.85417	−	0.279470i
$66$	0.375061	−	10.0978i	0.0461668	−	1.24295i
$67$	5.87497	+	3.39191i	0.717741	+	0.414388i	0.813921	−	0.580976i	$-0.197329\pi$
$67$	5.87497	+	3.39191i	0.717741	+	0.414388i	−0.0961795	+	0.995364i	$0.530662\pi$
$68$	−1.84167	+	1.98703i	−0.223335	+	0.240963i
$69$	1.01073	−	2.09879i	0.121677	−	0.252665i
$70$	8.22748	+	3.02443i	0.983372	+	0.361488i
$71$	−11.1501	+	5.36960i	−1.32327	+	0.637255i	−0.956139	−	0.292913i	$-0.905375\pi$
$71$	−11.1501	+	5.36960i	−1.32327	+	0.637255i	−0.367134	+	0.930168i	$0.619661\pi$
$72$	−3.27765	−	4.43342i	−0.386275	−	0.522484i
$73$	6.95014	+	6.44879i	0.813452	+	0.754774i	0.972601	−	0.232481i	$-0.0746844\pi$
$73$	6.95014	+	6.44879i	0.813452	+	0.754774i	−0.159148	+	0.987255i	$0.550875\pi$
$74$	−0.663664	−	3.50229i	−0.0771494	−	0.407133i
$75$	−0.612166	+	0.897883i	−0.0706869	+	0.103679i
$76$	4.34811	−	4.03889i	0.498762	−	0.463293i
$77$	−7.85955	−	3.23017i	−0.895679	−	0.368112i
$78$	17.9469	−	9.49153i	2.03209	−	1.07470i
$79$	3.16216	+	5.47702i	0.355770	+	0.616212i	0.987250	−	0.159180i	$-0.0508852\pi$
$79$	3.16216	+	5.47702i	0.355770	+	0.616212i	−0.631479	+	0.775393i	$0.717552\pi$
$80$	−9.34402	+	0.710544i	−1.04469	+	0.0794412i
$81$	−9.12839	+	6.22363i	−1.01427	+	0.691515i
$82$	2.27981	−	2.28106i	0.251763	−	0.251901i
$83$	6.04232	+	1.37912i	0.663230	+	0.151378i	0.540868	−	0.841107i	$-0.318096\pi$
$83$	6.04232	+	1.37912i	0.663230	+	0.151378i	0.122362	+	0.992485i	$0.460953\pi$
$84$	−11.3011	+	3.29629i	−1.23305	+	0.359655i
$85$	−3.09398	+	0.706181i	−0.335589	+	0.0765960i
$86$	−1.39856	+	2.22715i	−0.150810	+	0.240159i
$87$	19.8765	+	6.13109i	2.13098	+	0.657321i
$88$	9.07752	−	0.347134i	0.967666	−	0.0370046i
$89$	9.55075	−	2.94602i	1.01238	−	0.312277i	0.256186	−	0.966627i	$-0.417534\pi$
$89$	9.55075	−	2.94602i	1.01238	−	0.312277i	0.756192	+	0.654350i	$0.227058\pi$
$90$	−0.243254	−	6.45375i	−0.0256412	−	0.680285i
$91$	−2.27512	−	16.9206i	−0.238497	−	1.77376i
$92$	1.94985	+	0.764028i	0.203286	+	0.0796554i
$93$	12.6947	+	4.98232i	1.31638	+	0.516642i
$94$	7.41902	+	6.38104i	0.765213	+	0.658154i
$95$	6.87392	−	1.03608i	0.705249	−	0.106299i
$96$	9.52768	−	8.22199i	0.972414	−	0.839153i
$97$	0.651035			0.0661026			0.0330513	−	0.999454i	$-0.489478\pi$
$97$	0.651035			0.0661026			0.0330513	+	0.999454i	$0.489478\pi$
$98$	−0.682634	+	9.87593i	−0.0689564	+	0.997620i
$99$			6.26064i			0.629218i
$100$	−0.846331	−	0.488011i	−0.0846331	−	0.0488011i
$101$	−2.05372	−	13.6256i	−0.204353	−	1.35579i	−0.822067	−	0.569391i	$-0.807179\pi$
$101$	−2.05372	−	13.6256i	−0.204353	−	1.35579i	0.617714	−	0.786403i	$-0.288059\pi$
$102$	2.77912	−	3.23118i	0.275173	−	0.319935i
$103$	3.27594	−	8.34696i	0.322788	−	0.822451i	−0.673723	−	0.738984i	$-0.735306\pi$
$103$	3.27594	−	8.34696i	0.322788	−	0.822451i	0.996511	−	0.0834662i	$-0.0265990\pi$
$104$	9.72318	+	15.4461i	0.953436	+	1.51462i
$105$	−13.1103	−	4.27406i	−1.27944	−	0.417106i
$106$	0.701719	+	18.6172i	0.0681570	+	1.80826i
$107$	−0.563209	−	1.82588i	−0.0544475	−	0.176515i	0.924265	−	0.381753i	$-0.124679\pi$
$107$	−0.563209	−	1.82588i	−0.0544475	−	0.176515i	−0.978712	+	0.205238i	$0.934203\pi$
$108$	−2.91681	−	3.65345i	−0.280670	−	0.351553i
$109$	−2.47727	+	8.03112i	−0.237280	+	0.769242i	0.756109	+	0.654445i	$0.227098\pi$
$109$	−2.47727	+	8.03112i	−0.237280	+	0.769242i	−0.993389	+	0.114796i	$0.963378\pi$
$110$	9.01150	+	5.65885i	0.859213	+	0.539550i
$111$	1.24779	+	5.46692i	0.118435	+	0.518897i
$112$	−3.71973	−	9.90775i	−0.351481	−	0.936195i
$113$	3.34055	−	14.6359i	0.314253	−	1.37683i	−0.533213	−	0.845981i	$-0.679016\pi$
$113$	3.34055	−	14.6359i	0.314253	−	1.37683i	0.847466	−	0.530850i	$-0.178127\pi$
$114$	−6.59948	+	6.60310i	−0.618098	+	0.618437i
$115$	1.38188	+	2.02684i	0.128861	+	0.189004i
$116$	−4.15107	+	18.2331i	−0.385417	+	1.69290i
$117$	−10.8935	+	6.28936i	−1.00710	+	0.581452i
$118$	2.38289	+	4.50565i	0.219362	+	0.414779i
$119$	−1.74229	−	3.13201i	−0.159716	−	0.287111i
$120$	14.6475	−	1.66258i	1.33713	−	0.151772i
$121$	0.565789	+	0.385748i	0.0514353	+	0.0350680i
$122$	−2.26917	−	11.9749i	−0.205441	−	1.08415i
$123$	−3.45071	+	3.71898i	−0.311140	+	0.335330i
$124$	−3.60728	+	11.7173i	−0.323943	+	1.05225i
$125$	4.58588	+	9.52268i	0.410173	+	0.851734i
$126$	6.92123	−	2.30077i	0.616592	−	0.204969i
$127$	−0.777755	−	0.374547i	−0.0690146	−	0.0332357i	0.399058	−	0.916926i	$-0.369337\pi$
$127$	−0.777755	−	0.374547i	−0.0690146	−	0.0332357i	−0.468073	+	0.883690i	$0.655051\pi$
$128$	8.01534	+	7.98463i	0.708463	+	0.705748i
$129$	2.06852	−	3.58277i	0.182123	−	0.315446i
$130$	−0.793548	+	21.3648i	−0.0695988	+	1.87382i
$131$	−3.16382	+	20.9906i	−0.276424	+	1.83395i	0.231843	+	0.972753i	$0.425525\pi$
$131$	−3.16382	+	20.9906i	−0.276424	+	1.83395i	−0.508267	+	0.861200i	$0.669714\pi$
$132$	−14.2498	+	1.07573i	−1.24028	+	0.0936302i
$133$	3.29308	+	7.12660i	0.285546	+	0.617954i
$134$	3.83406	−	8.79435i	0.331213	−	0.759716i
$135$	−0.409233	−	5.46084i	−0.0352212	−	0.469994i
$136$	3.08465	+	2.27266i	0.264507	+	0.194879i
$137$	−5.09075	−	12.9710i	−0.434932	−	1.10819i	−0.965467	−	0.260526i	$-0.916104\pi$
$137$	−5.09075	−	12.9710i	−0.434932	−	1.10819i	0.530535	−	0.847663i	$-0.321991\pi$
$138$	−3.10982	−	1.08722i	−0.264725	−	0.0925499i
$139$	0.416390	−	0.332060i	0.0353178	−	0.0281650i	−0.605672	−	0.795715i	$-0.707096\pi$
$139$	0.416390	−	0.332060i	0.0353178	−	0.0281650i	0.640990	+	0.767550i	$0.278524\pi$
$140$	2.94424	−	12.0420i	0.248833	−	1.01773i
$141$	−12.0354	−	9.59792i	−1.01356	−	0.808291i
$142$	9.31561	+	14.8167i	0.781748	+	1.24339i
$143$	1.54879	−	20.6671i	0.129516	−	1.72827i
$144$	−5.70994	+	5.30972i	−0.475828	+	0.442476i
$145$	−16.0570	+	14.8987i	−1.33346	+	1.23727i
$146$	7.95916	−	10.7905i	0.658705	−	0.893026i
$147$	0.496466	−	15.5650i	0.0409478	−	1.28378i
$148$	−4.81635	+	1.48854i	−0.395902	+	0.122357i
$149$	−0.0519054	−	0.0559407i	−0.00425225	−	0.00458284i	0.730922	−	0.682461i	$-0.239090\pi$
$149$	−0.0519054	−	0.0559407i	−0.00425225	−	0.00458284i	−0.735174	+	0.677878i	$0.762900\pi$
$150$	1.35894	+	0.717746i	0.110957	+	0.0586037i
$151$	−0.378344	+	5.04865i	−0.0307892	+	0.410854i	0.960421	+	0.278554i	$0.0898551\pi$
$151$	−0.378344	+	5.04865i	−0.0307892	+	0.410854i	−0.991210	+	0.132300i	$0.957764\pi$
$152$	−6.36593	−	5.46922i	−0.516345	−	0.443612i
$153$	−1.64637	+	2.06448i	−0.133101	+	0.166904i
$154$	−3.29177	+	11.5576i	−0.265258	+	0.931335i
$155$	−11.2279	+	8.95398i	−0.901850	+	0.719201i
$156$	−16.1869	−	23.7139i	−1.29599	−	1.89863i
$157$	19.8907	−	7.80653i	1.58745	−	0.623029i	0.602853	−	0.797853i	$-0.294031\pi$
$157$	19.8907	−	7.80653i	1.58745	−	0.623029i	0.984600	+	0.174823i	$0.0559355\pi$
$158$	7.19481	−	5.31306i	0.572388	−	0.422684i
$159$	−2.19016	−	29.2256i	−0.173691	−	2.31774i
$160$	2.48166	+	13.0182i	0.196192	+	1.02918i
$161$	−1.76161	+	2.13815i	−0.138834	+	0.168510i
$162$	10.1949	+	11.8401i	0.800983	+	0.930244i
$163$	−2.81236	+	18.6588i	−0.220281	+	1.46147i	0.556053	+	0.831147i	$0.312315\pi$
$163$	−2.81236	+	18.6588i	−0.220281	+	1.46147i	−0.776334	+	0.630322i	$0.782923\pi$
$164$	−3.56739	−	2.84170i	−0.278566	−	0.221899i
$165$	−14.4967	−	8.36965i	−1.12856	−	0.651576i
$166$	0.978967	−	8.71004i	0.0759826	−	0.676030i
$167$	8.16374	+	3.93145i	0.631729	+	0.304225i	0.722210	−	0.691674i	$-0.243126\pi$
$167$	8.16374	+	3.93145i	0.631729	+	0.304225i	−0.0904814	+	0.995898i	$0.528841\pi$
$168$	6.42599	+	15.3580i	0.495776	+	1.18489i
$169$	25.8041	−	12.4266i	1.98493	−	0.955892i
$170$	1.48348	+	4.23581i	0.113778	+	0.324872i
$171$	3.93419	−	4.24005i	0.300855	−	0.324244i
$172$	3.35175	+	1.61185i	0.255568	+	0.122903i
$173$	−9.66485	+	14.1757i	−0.734805	+	1.07776i	0.258919	+	0.965899i	$0.416634\pi$
$173$	−9.66485	+	14.1757i	−0.734805	+	1.07776i	−0.993724	+	0.111862i	$0.964319\pi$
$174$	5.46094	−	28.9052i	0.413993	−	2.19129i
$175$	0.961277	−	0.863829i	0.0726657	−	0.0652993i
$176$	−1.92867	−	12.7013i	−0.145379	−	0.957399i
$177$	−4.00902	−	6.94383i	−0.301337	−	0.521930i
$178$	−5.65593	−	12.9538i	−0.423930	−	0.970932i
$179$	−3.20282	−	4.69767i	−0.239390	−	0.351121i	0.687677	−	0.726017i	$-0.258631\pi$
$179$	−3.20282	−	4.69767i	−0.239390	−	0.351121i	−0.927067	+	0.374896i	$0.877678\pi$
$180$	−9.03069	+	1.36622i	−0.673108	+	0.101832i
$181$	−6.22657	−	1.42117i	−0.462818	−	0.105635i	−0.0152471	−	0.999884i	$-0.504853\pi$
$181$	−6.22657	−	1.42117i	−0.462818	−	0.105635i	−0.447570	+	0.894249i	$0.647711\pi$
$182$	−23.4170	+	5.88293i	−1.73578	+	0.436072i
$183$	4.26638	+	18.6922i	0.315380	+	1.38177i
$184$	0.764177	−	2.86136i	0.0563359	−	0.210942i
$185$	−5.64271	−	1.74054i	−0.414860	−	0.127967i
$186$	4.98654	−	18.6305i	0.365631	−	1.36605i
$187$	−1.28239	−	4.15740i	−0.0937776	−	0.304019i
$188$	7.78953	−	11.4386i	0.568110	−	0.834247i
$189$	5.79220	−	2.16736i	0.421320	−	0.157652i
$190$	−2.54705	−	9.49531i	−0.184783	−	0.688863i
$191$	0.415330	−	1.05824i	0.0300522	−	0.0765718i	−0.915060	−	0.403318i	$-0.867857\pi$
$191$	0.415330	−	1.05824i	0.0300522	−	0.0765718i	0.945112	+	0.326746i	$0.105952\pi$
$192$	−13.0665	−	12.0840i	−0.942992	−	0.872086i
$193$	23.2508	−	3.50450i	1.67363	−	0.252259i	0.757412	−	0.652937i	$-0.226464\pi$
$193$	23.2508	−	3.50450i	1.67363	−	0.252259i	0.916219	+	0.400678i	$0.131225\pi$
$194$	−0.103337	−	0.914886i	−0.00741916	−	0.0656850i
$195$		−	33.6322i		−	2.40845i
$196$	13.9868	−	0.608286i	0.999056	−	0.0434490i
$197$			14.9248i			1.06335i	0.846949	+	0.531673i	$0.178437\pi$
$197$			14.9248i			1.06335i	−0.846949	+	0.531673i	$0.821563\pi$
$198$	8.79794	−	0.993732i	0.625242	−	0.0706215i
$199$	−21.0921	+	3.17913i	−1.49518	+	0.225363i	−0.845144	−	0.534539i	$-0.820485\pi$
$199$	−21.0921	+	3.17913i	−1.49518	+	0.225363i	−0.650039	+	0.759901i	$0.725247\pi$
$200$	−0.551455	+	1.26679i	−0.0389938	+	0.0895756i
$201$	−5.51373	+	14.0487i	−0.388908	+	0.990922i
$202$	−18.8217	+	5.04880i	−1.32429	+	0.355232i
$203$	−21.2233	−	12.7086i	−1.48958	−	0.891971i
$204$	−4.98183	−	3.39255i	−0.348798	−	0.237526i
$205$	−1.57473	−	5.10514i	−0.109984	−	0.356558i
$206$	−12.2498	−	3.27872i	−0.853483	−	0.228439i
$207$	1.95043	+	0.601629i	0.135565	+	0.0418161i
$208$	20.1628	−	16.1155i	1.39804	−	1.11741i
$209$	2.12064	+	9.29113i	0.146688	+	0.642681i
$210$	−3.92528	+	19.1021i	−0.270870	+	1.31817i
$211$	−13.1609	−	3.00389i	−0.906034	−	0.206796i	−0.255978	−	0.966683i	$-0.582397\pi$
$211$	−13.1609	−	3.00389i	−0.906034	−	0.206796i	−0.650056	+	0.759886i	$0.725255\pi$
$212$	26.0510	−	3.94117i	1.78919	−	0.270680i
$213$	−15.5094	−	22.7482i	−1.06269	−	1.55868i
$214$	−2.47647	+	1.08128i	−0.169288	+	0.0739149i
$215$	2.17827	+	3.77288i	0.148557	+	0.257308i
$216$	−4.67113	+	4.67882i	−0.317830	+	0.318354i
$217$	−13.2530	−	9.34866i	−0.899671	−	0.634628i
$218$	11.6792	+	2.20650i	0.791013	+	0.149443i
$219$	−11.8819	+	17.4276i	−0.802905	+	1.17765i
$220$	6.52189	−	13.5619i	0.439706	−	0.914341i
$221$	5.94560	−	6.40783i	0.399944	−	0.431037i
$222$	7.48448	−	2.62124i	0.502325	−	0.175926i
$223$	−19.9855	+	9.62450i	−1.33833	+	0.644504i	−0.959695	−	0.281043i	$-0.909320\pi$
$223$	−19.9855	+	9.62450i	−1.33833	+	0.644504i	−0.378632	+	0.925547i	$0.623605\pi$
$224$	−13.3327	+	6.79988i	−0.890830	+	0.454336i
$225$	−0.857889	−	0.413138i	−0.0571926	−	0.0275425i
$226$	−21.0978	−	2.37129i	−1.40340	−	0.157736i
$227$	−2.26112	−	1.30546i	−0.150076	−	0.0866463i	0.423082	−	0.906092i	$-0.360948\pi$
$227$	−2.26112	−	1.30546i	−0.150076	−	0.0866463i	−0.573157	+	0.819445i	$0.694282\pi$
$228$	10.3267	+	8.22601i	0.683903	+	0.544781i
$229$	−0.816283	+	5.41568i	−0.0539415	+	0.357878i	0.945535	+	0.325521i	$0.105540\pi$
$229$	−0.816283	+	5.41568i	−0.0539415	+	0.357878i	−0.999476	+	0.0323575i	$0.989698\pi$
$230$	2.62893	−	2.26363i	0.173347	−	0.149260i
$231$	4.49988	−	18.3609i	0.296071	−	1.20806i
$232$	26.2815	+	2.93932i	1.72546	+	0.192976i
$233$	−0.246981	−	3.29573i	−0.0161802	−	0.215910i	−0.999433	−	0.0336643i	$-0.989282\pi$
$233$	−0.246981	−	3.29573i	−0.0161802	−	0.215910i	0.983253	−	0.182246i	$-0.0583368\pi$
$234$	10.5674	+	14.3101i	0.690812	+	0.935480i
$235$	15.0901	−	5.92243i	0.984370	−	0.386337i
$236$	5.95346	−	4.06379i	0.387537	−	0.264530i
$237$	−11.0001	+	8.77233i	−0.714536	+	0.569824i
$238$	−4.12479	+	2.94554i	−0.267371	+	0.190931i
$239$	−4.39410	+	5.51003i	−0.284231	+	0.356414i	−0.903366	−	0.428870i	$-0.858912\pi$
$239$	−4.39410	+	5.51003i	−0.284231	+	0.356414i	0.619135	+	0.785284i	$0.287483\pi$
$240$	−4.66133	−	20.3199i	−0.300888	−	1.31164i
$241$	−0.906022	+	12.0900i	−0.0583620	+	0.778787i	0.888854	+	0.458191i	$0.151502\pi$
$241$	−0.906022	+	12.0900i	−0.0583620	+	0.778787i	−0.947216	+	0.320596i	$0.896117\pi$
$242$	0.452277	−	0.856319i	0.0290735	−	0.0550463i
$243$	−11.9481	−	12.8770i	−0.766474	−	0.826062i
$244$	−16.4678	+	5.08955i	−1.05425	+	0.325825i
$245$	13.9335	+	8.64822i	0.890181	+	0.552515i
$246$	5.77393	+	4.25891i	0.368132	+	0.271538i
$247$	−14.0362	+	13.0237i	−0.893100	+	0.828676i
$248$	17.0387	+	3.20937i	1.08196	+	0.203795i
$249$	−1.03038	+	13.7495i	−0.0652978	+	0.871339i
$250$	12.6541	−	7.95594i	0.800316	−	0.503178i
$251$	20.6129	+	16.4383i	1.30108	+	1.03757i	0.996370	+	0.0851265i	$0.0271294\pi$
$251$	20.6129	+	16.4383i	1.30108	+	1.03757i	0.304705	+	0.952447i	$0.401442\pi$
$252$	−4.33181	−	9.36105i	−0.272878	−	0.589691i
$253$	−2.62930	+	2.09680i	−0.165303	+	0.131825i
$254$	−0.402892	+	1.15241i	−0.0252797	+	0.0723088i
$255$	−2.57938	−	6.57215i	−0.161527	−	0.411564i
$256$	9.94837	−	12.5312i	0.621773	−	0.783197i
$257$	−0.735837	−	9.81907i	−0.0459003	−	0.612497i	−0.971964	−	0.235129i	$-0.924449\pi$
$257$	−0.735837	−	9.81907i	−0.0459003	−	0.612497i	0.926064	−	0.377367i	$-0.123170\pi$
$258$	−5.36312	−	2.33816i	−0.333893	−	0.145567i
$259$	0.106314	−	6.66794i	0.00660604	−	0.414326i
$260$	30.1494	−	2.27601i	1.86979	−	0.141152i
$261$	−2.71639	+	18.0221i	−0.168141	+	1.11554i
$262$	29.9997	+	1.11427i	1.85339	+	0.0688401i
$263$	13.6122	−	23.5770i	0.839364	−	1.45382i	−0.0510630	−	0.998695i	$-0.516261\pi$
$263$	13.6122	−	23.5770i	0.839364	−	1.45382i	0.890427	−	0.455126i	$-0.150406\pi$
$264$	3.77352	+	19.8541i	0.232244	+	1.22194i
$265$	27.8063	+	13.3908i	1.70813	+	0.822592i
$266$	9.49215	−	5.75887i	0.582001	−	0.353099i
$267$	9.64760	+	20.0334i	0.590423	+	1.22603i
$268$	−12.9671	−	3.99203i	−0.792090	−	0.243852i
$269$	−4.00260	+	4.31378i	−0.244043	+	0.263016i	−0.843181	−	0.537630i	$-0.819320\pi$
$269$	−4.00260	+	4.31378i	−0.244043	+	0.263016i	0.599138	+	0.800646i	$0.295510\pi$
$270$	−7.60904	+	1.44187i	−0.463071	+	0.0877494i
$271$	−12.7804	−	8.71353i	−0.776354	−	0.529309i	0.109103	−	0.994030i	$-0.465202\pi$
$271$	−12.7804	−	8.71353i	−0.776354	−	0.529309i	−0.885457	+	0.464721i	$0.846155\pi$
$272$	2.70410	−	4.69553i	0.163960	−	0.284708i
$273$	36.4685	−	10.6154i	2.20717	−	0.642471i
$274$	−17.4198	+	9.21277i	−1.05237	+	0.556563i
$275$	1.35866	−	0.784425i	0.0819305	−	0.0473026i
$276$	−1.03423	+	4.54273i	−0.0622532	+	0.273440i
$277$	−8.61782	−	12.6400i	−0.517795	−	0.759465i	0.474910	−	0.880034i	$-0.342481\pi$
$277$	−8.61782	−	12.6400i	−0.517795	−	0.759465i	−0.992705	+	0.120569i	$0.961528\pi$
$278$	−0.532729	−	0.532437i	−0.0319510	−	0.0319335i
$279$	−2.65896	+	11.6496i	−0.159188	+	0.697446i
$280$	−17.3896	−	2.22609i	−1.03923	−	0.133034i
$281$	5.35738	+	23.4722i	0.319595	+	1.40024i	0.838266	+	0.545262i	$0.183570\pi$
$281$	5.35738	+	23.4722i	0.319595	+	1.40024i	−0.518671	+	0.854974i	$0.673573\pi$
$282$	−11.5774	+	18.4365i	−0.689424	+	1.09788i
$283$	−1.55078	+	5.02750i	−0.0921842	+	0.298854i	−0.989909	−	0.141702i	$-0.954742\pi$
$283$	−1.55078	+	5.02750i	−0.0921842	+	0.298854i	0.897725	+	0.440556i	$0.145219\pi$
$284$	19.3429	−	15.4428i	1.14779	−	0.916363i
$285$	4.55844	+	14.7781i	0.270018	+	0.875378i
$286$	−29.2889	+	1.10396i	−1.73189	+	0.0652783i
$287$	5.03863	−	3.31887i	0.297421	−	0.195906i
$288$	8.36795	+	7.18126i	0.493086	+	0.423160i
$289$	−5.54039	+	14.1167i	−0.325905	+	0.830394i
$290$	23.4855	+	20.1997i	1.37912	+	1.18617i
$291$	0.215867	+	1.43218i	0.0126543	+	0.0839561i
$292$	−16.4269	−	9.47210i	−0.961315	−	0.554313i
$293$		−	0.0280075i		−	0.00163622i	−1.00000		0.000818108i	$-0.999740\pi$
$293$		−	0.0280075i		−	0.00163622i	1.00000		0.000818108i	$-0.000260412\pi$
$294$	−21.9520	+	1.77291i	−1.28026	+	0.103398i
$295$	8.44350			0.491599
$296$	2.85630	+	6.53204i	0.166019	+	0.379667i
$297$	7.42354	−	1.11892i	0.430757	−	0.0649262i
$298$	−0.0703734	+	0.0818207i	−0.00407662	+	0.00473975i
$299$	−6.28979	−	2.46856i	−0.363748	−	0.142761i
$300$	0.792931	−	2.02362i	0.0457799	−	0.116834i
$301$	−3.40353	+	3.55281i	−0.196176	+	0.204781i
$302$	7.15481	−	0.269679i	0.411713	−	0.0155183i
$303$	29.2933	−	9.03578i	1.68286	−	0.519092i
$304$	−6.67533	+	9.81401i	−0.382856	+	0.562872i
$305$	−19.2933	−	5.95119i	−1.10473	−	0.340764i
$306$	3.16250	+	1.98592i	0.180788	+	0.113527i
$307$	17.0810	−	3.89864i	0.974867	−	0.222507i	0.294721	−	0.955583i	$-0.404773\pi$
$307$	17.0810	−	3.89864i	0.974867	−	0.222507i	0.680146	+	0.733076i	$0.261916\pi$
$308$	16.7641	+	2.79135i	0.955223	+	0.159052i
$309$	19.4483	+	4.43895i	1.10638	+	0.252523i
$310$	14.3650	+	14.3571i	0.815878	+	0.815430i
$311$	−13.9928	+	9.54016i	−0.793461	+	0.540973i	−0.890863	−	0.454272i	$-0.849899\pi$
$311$	−13.9928	+	9.54016i	−0.793461	+	0.540973i	0.0974015	+	0.995245i	$0.468947\pi$
$312$	−30.7553	+	26.5111i	−1.74117	+	1.50090i
$313$	0.399195	+	0.691426i	0.0225638	+	0.0390817i	0.877087	−	0.480332i	$-0.159484\pi$
$313$	0.399195	+	0.691426i	0.0225638	+	0.0390817i	−0.854523	+	0.519414i	$0.826150\pi$
$314$	−14.1275	−	26.7129i	−0.797263	−	1.50750i
$315$	1.99103	−	11.9172i	0.112182	−	0.671461i
$316$	−8.60833	−	9.26738i	−0.484257	−	0.521331i
$317$	6.15543	−	9.02835i	0.345723	−	0.507083i	−0.613514	−	0.789684i	$-0.710245\pi$
$317$	6.15543	−	9.02835i	0.345723	−	0.507083i	0.959238	+	0.282601i	$0.0911971\pi$
$318$	−40.7225	+	7.71668i	−2.28361	+	0.432730i
$319$	−22.0129	−	20.4250i	−1.23249	−	1.14358i
$320$	17.9002	−	5.55375i	1.00065	−	0.310464i
$321$	3.82993	−	1.84439i	0.213766	−	0.102944i
$322$	3.28431	+	2.13616i	0.183027	+	0.119044i
$323$	−1.74401	+	3.62148i	−0.0970393	+	0.201504i
$324$	15.0204	−	16.2059i	0.834466	−	0.900330i
$325$	2.72980	+	1.57605i	0.151422	+	0.0874234i
$326$	26.6672	+	0.990493i	1.47696	+	0.0548584i
$327$	−18.4887	−	2.78672i	−1.02243	−	0.154106i
$328$	−3.42714	+	5.46423i	−0.189232	+	0.301712i
$329$	11.1848	+	14.4934i	0.616638	+	0.799047i
$330$	−9.46067	+	21.7003i	−0.520793	+	1.19456i
$331$	32.6020	−	2.44318i	1.79197	−	0.134289i	0.863178	−	0.504900i	$-0.168471\pi$
$331$	32.6020	−	2.44318i	1.79197	−	0.134289i	0.928788	+	0.370610i	$0.120851\pi$
$332$	−12.3954	+	0.00679704i	−0.680286	+	0.000373036i
$333$	−4.57370	+	1.79505i	−0.250637	+	0.0983679i
$334$	4.22897	−	12.0963i	0.231399	−	0.661883i
$335$	−9.90900	−	12.4255i	−0.541387	−	0.678877i
$336$	20.5623	−	11.4680i	1.12176	−	0.625632i
$337$	8.97445	−	11.2536i	0.488869	−	0.613023i	−0.474809	−	0.880089i	$-0.657483\pi$
$337$	8.97445	−	11.2536i	0.488869	−	0.613023i	0.963678	+	0.267066i	$0.0860543\pi$
$338$	−21.5586	−	34.2895i	−1.17263	−	1.86510i
$339$	33.3045	+	2.49583i	1.80885	+	0.135555i
$340$	5.71702	−	2.75704i	0.310049	−	0.149521i
$341$	−13.3912	−	14.4323i	−0.725174	−	0.781552i
$342$	−6.58291	−	4.85562i	−0.355963	−	0.262562i
$343$	−4.97969	+	17.8382i	−0.268878	+	0.963174i
$344$	1.73309	−	4.96598i	0.0934418	−	0.267748i
$345$	−4.00056	+	3.71198i	−0.215383	+	0.199846i
$346$	21.4549	+	11.3317i	1.15342	+	0.609198i
$347$	4.44654	+	0.333222i	0.238703	+	0.0178883i	0.193544	−	0.981092i	$-0.438002\pi$
$347$	4.44654	+	0.333222i	0.238703	+	0.0178883i	0.0451585	+	0.998980i	$0.485621\pi$
$348$	−41.4866	−	3.08611i	−2.22391	−	0.165433i
$349$	6.66851	+	5.31796i	0.356957	+	0.284664i	0.785505	−	0.618855i	$-0.212403\pi$
$349$	6.66851	+	5.31796i	0.356957	+	0.284664i	−0.428548	+	0.903519i	$0.640975\pi$
$350$	−1.36650	−	1.21375i	−0.0730425	−	0.0648776i
$351$	9.40451	+	11.7929i	0.501976	+	0.629458i
$352$	−17.5428	+	4.72636i	−0.935033	+	0.251916i
$353$	6.43677	+	16.4006i	0.342595	+	0.872917i	0.993508	+	0.113765i	$0.0362911\pi$
$353$	6.43677	+	16.4006i	0.342595	+	0.872917i	−0.650913	+	0.759152i	$0.725614\pi$
$354$	−9.12167	+	6.73596i	−0.484811	+	0.358012i
$355$	28.9120	−	2.16666i	1.53449	−	0.114994i
$356$	−17.3060	+	10.0043i	−0.917216	+	0.530226i
$357$	6.31227	−	4.87128i	0.334081	−	0.257816i
$358$	−6.09316	+	5.24650i	−0.322034	+	0.277286i
$359$	19.9933	+	3.01350i	1.05520	+	0.159046i	0.653656	−	0.756792i	$-0.273234\pi$
$359$	19.9933	+	3.01350i	1.05520	+	0.159046i	0.401548	+	0.915838i	$0.368472\pi$
$360$	3.35334	+	12.4738i	0.176736	+	0.657426i
$361$	−5.09766	+	8.82941i	−0.268298	+	0.464706i
$362$	−1.00882	+	8.97564i	−0.0530224	+	0.471749i
$363$	−0.660989	+	1.37256i	−0.0346929	+	0.0720406i
$364$	11.9841	+	31.9736i	0.628135	+	1.67587i
$365$	−9.63736	−	20.0122i	−0.504443	−	1.04749i
$366$	25.5906	−	8.96241i	1.33764	−	0.468473i
$367$	7.14256	+	6.62733i	0.372839	+	0.345944i	0.844231	−	0.535980i	$-0.180058\pi$
$367$	7.14256	+	6.62733i	0.372839	+	0.345944i	−0.471392	+	0.881924i	$0.656248\pi$
$368$	−4.14230	−	0.619706i	−0.215932	−	0.0323044i
$369$	−3.67284	−	2.50410i	−0.191201	−	0.130358i
$370$	−1.55030	+	8.20584i	−0.0805962	+	0.426602i
$371$	−5.74356	+	34.3779i	−0.298191	+	1.78481i
$372$	−26.9725	−	4.05032i	−1.39846	−	0.209999i
$373$	−28.2037	+	16.2834i	−1.46033	+	0.843123i	−0.999026	−	0.0441186i	$-0.985952\pi$
$373$	−28.2037	+	16.2834i	−1.46033	+	0.843123i	−0.461305	+	0.887241i	$0.652619\pi$
$374$	−5.63876	+	2.46201i	−0.291573	+	0.127307i
$375$	−19.4279	+	13.2457i	−1.00325	+	0.684007i
$376$	−17.3108	−	9.13084i	−0.892739	−	0.470887i
$377$	13.4256	−	58.8212i	0.691451	−	3.02945i
$378$	−3.96512	−	7.79563i	−0.203944	−	0.400964i
$379$	−26.8342	+	6.12472i	−1.37838	+	0.314606i	−0.846578	−	0.532264i	$-0.821341\pi$
$379$	−26.8342	+	6.12472i	−1.37838	+	0.314606i	−0.531800	+	0.846870i	$0.678484\pi$
$380$	−12.9393	+	5.08648i	−0.663770	+	0.260931i
$381$	0.566065	−	1.83514i	0.0290004	−	0.0940170i
$382$	−1.55305	−	0.415682i	−0.0794610	−	0.0212682i
$383$	−16.3078	+	5.03028i	−0.833288	+	0.257035i	−0.681906	−	0.731440i	$-0.738849\pi$
$383$	−16.3078	+	5.03028i	−0.833288	+	0.257035i	−0.151382	+	0.988475i	$0.548372\pi$
$384$	−14.9073	+	20.2801i	−0.760737	+	1.03491i
$385$	14.3754	+	13.7714i	0.732640	+	0.701855i
$386$	−8.61533	−	32.1176i	−0.438509	−	1.63474i
$387$	3.37432	+	1.32432i	0.171527	+	0.0673192i
$388$	−1.26927	+	0.290434i	−0.0644372	+	0.0147446i
$389$	1.39952	+	9.28518i	0.0709582	+	0.470777i	0.995885	+	0.0906307i	$0.0288883\pi$
$389$	1.39952	+	9.28518i	0.0709582	+	0.470777i	−0.924926	+	0.380146i	$0.875874\pi$
$390$	−47.2626	+	5.33834i	−2.39323	+	0.270317i
$391$	−1.41843			−0.0717330
$392$	−3.07489	−	19.5588i	−0.155305	−	0.987867i
$393$	−47.2252			−2.38220
$394$	20.9735	−	2.36897i	1.05663	−	0.119347i
$395$	−2.20825	−	14.6508i	−0.111109	−	0.737162i
$396$	−2.79294	−	12.2058i	−0.140350	−	0.613365i
$397$	18.5253	+	7.27063i	0.929757	+	0.364903i	0.781399	−	0.624031i	$-0.214506\pi$
$397$	18.5253	+	7.27063i	0.929757	+	0.364903i	0.148357	+	0.988934i	$0.452601\pi$
$398$	7.81545	+	29.1357i	0.391753	+	1.46044i
$399$	−14.5856	+	9.60729i	−0.730192	+	0.480966i
$400$	1.86772	+	0.573874i	0.0933862	+	0.0286937i
$401$	3.95988	−	1.22146i	0.197747	−	0.0609969i	−0.194300	−	0.980942i	$-0.562243\pi$
$401$	3.95988	−	1.22146i	0.197747	−	0.0609969i	0.392047	+	0.919945i	$0.371767\pi$
$402$	20.6176	+	5.51840i	1.02831	+	0.275233i
$403$	11.6595	−	37.7992i	0.580801	−	1.88291i
$404$	10.0825	+	25.6484i	0.501622	+	1.27605i
$405$	25.2341	−	5.75951i	1.25389	−	0.286192i
$406$	−14.4904	+	31.8418i	−0.719149	+	1.58028i
$407$	1.80139	−	7.89241i	0.0892917	−	0.391212i
$408$	−3.97673	+	7.53934i	−0.196877	+	0.373253i
$409$	−24.9895	+	17.0375i	−1.23565	+	0.842452i	−0.991855	−	0.127375i	$-0.959345\pi$
$409$	−24.9895	+	17.0375i	−1.23565	+	0.842452i	−0.243796	+	0.969827i	$0.578393\pi$
$410$	−6.92418	+	3.02325i	−0.341961	+	0.149308i
$411$	26.8464	−	15.4998i	1.32423	−	0.764547i
$412$	−2.66314	+	17.7348i	−0.131204	+	0.873729i
$413$	2.66503	+	9.15556i	0.131138	+	0.450515i
$414$	0.535870	−	2.83640i	0.0263366	−	0.139401i
$415$	−11.9967	−	8.17922i	−0.588896	−	0.401502i
$416$	−25.8471	−	25.7763i	−1.26726	−	1.26379i
$417$	0.868549	+	0.805896i	0.0425330	+	0.0394649i
$418$	12.7200	−	4.45484i	0.622156	−	0.217893i
$419$	−4.09982	−	8.51336i	−0.200289	−	0.415905i	0.776497	−	0.630121i	$-0.216995\pi$
$419$	−4.09982	−	8.51336i	−0.200289	−	0.415905i	−0.976786	+	0.214216i	$0.931280\pi$
$420$	27.4668	+	2.48409i	1.34024	+	0.121211i
$421$	−4.92545	+	10.2278i	−0.240052	+	0.498472i	−0.985835	−	0.167716i	$-0.946361\pi$
$421$	−4.92545	+	10.2278i	−0.240052	+	0.498472i	0.745784	+	0.666188i	$0.232075\pi$
$422$	−2.13231	+	18.9715i	−0.103799	+	0.923519i
$423$	6.74412	−	11.6812i	0.327910	−	0.567957i
$424$	−9.67343	−	35.9833i	−0.469783	−	1.74750i
$425$	0.654310	+	0.0986213i	0.0317387	+	0.00478384i
$426$	−29.5057	+	25.4058i	−1.42956	+	1.23092i
$427$	0.363505	−	22.7987i	0.0175912	−	1.10331i
$428$	1.91258	+	3.30850i	0.0924483	+	0.159923i
$429$	45.9783	−	3.44559i	2.21985	−	0.166355i
$430$	4.95620	−	3.65994i	0.239009	−	0.176498i
$431$	−8.33205	−	21.2297i	−0.401341	−	1.02260i	−0.978551	−	0.206004i	$-0.933954\pi$
$431$	−8.33205	−	21.2297i	−0.401341	−	1.02260i	0.577211	−	0.816595i	$-0.304141\pi$
$432$	7.31648	+	5.82158i	0.352014	+	0.280091i
$433$	16.6804	+	20.9165i	0.801607	+	1.00518i	0.999688	+	0.0249979i	$0.00795789\pi$
$433$	16.6804	+	20.9165i	0.801607	+	1.00518i	−0.198080	+	0.980186i	$0.563471\pi$
$434$	−11.0339	+	20.1080i	−0.529642	+	0.965215i
$435$	−38.0991	−	30.3830i	−1.82671	−	1.45676i
$436$	1.24695	−	16.7627i	0.0597180	−	0.802788i
$437$	3.09834	+	0.232188i	0.148214	+	0.0111071i
$438$	26.3765	+	13.9312i	1.26032	+	0.665656i
$439$	12.4158	−	11.5202i	0.592574	−	0.549828i	−0.325852	−	0.945421i	$-0.605651\pi$
$439$	12.4158	−	11.5202i	0.592574	−	0.549828i	0.918426	+	0.395592i	$0.129461\pi$
$440$	−20.0934	−	7.01244i	−0.957915	−	0.334305i
$441$	13.5507	−	1.60252i	0.645271	−	0.0763103i
$442$	−9.94851	−	7.33812i	−0.473202	−	0.349039i
$443$	−4.75525	−	5.12494i	−0.225929	−	0.243493i	0.609907	−	0.792473i	$-0.291207\pi$
$443$	−4.75525	−	5.12494i	−0.225929	−	0.243493i	−0.835836	+	0.548980i	$0.815016\pi$
$444$	−4.87155	−	10.1017i	−0.231194	−	0.479406i
$445$	−23.3498	−	1.74983i	−1.10689	−	0.0829498i
$446$	16.6973	+	26.5575i	0.790642	+	1.25753i
$447$	0.105851	−	0.132733i	0.00500657	−	0.00627804i
$448$	11.6720	+	17.6569i	0.551450	+	0.834208i
$449$	3.64239	+	4.56742i	0.171895	+	0.215550i	0.860315	−	0.509763i	$-0.170267\pi$
$449$	3.64239	+	4.56742i	0.171895	+	0.215550i	−0.688420	+	0.725312i	$0.741695\pi$
$450$	−0.444403	+	1.27115i	−0.0209494	+	0.0599225i
$451$	6.81785	−	2.67581i	0.321040	−	0.125999i
$452$	0.0164640	+	30.0246i	0.000774403	+	1.41224i
$453$	−11.2318	+	0.841704i	−0.527714	+	0.0395467i
$454$	−1.47563	+	3.38471i	−0.0692548	+	0.158853i
$455$	−9.52079	+	38.8478i	−0.446342	+	1.82121i
$456$	9.92070	−	15.8176i	0.464579	−	0.740726i
$457$	−26.6297	−	4.01378i	−1.24569	−	0.187757i	−0.507083	−	0.861897i	$-0.669276\pi$
$457$	−26.6297	−	4.01378i	−1.24569	−	0.187757i	−0.738603	+	0.674141i	$0.764514\pi$
$458$	7.74010	+	0.287489i	0.361671	+	0.0134335i
$459$	2.74220	+	1.58321i	0.127995	+	0.0738979i
$460$	−3.59832	−	3.33508i	−0.167772	−	0.155499i
$461$	−14.5018	+	30.1133i	−0.675415	+	1.40251i	0.227963	+	0.973670i	$0.426794\pi$
$461$	−14.5018	+	30.1133i	−0.675415	+	1.40251i	−0.903378	+	0.428845i	$0.858921\pi$
$462$	−26.5164	−	3.40921i	−1.23366	−	0.158611i
$463$	15.6609	−	7.54187i	0.727822	−	0.350500i	−0.0330054	−	0.999455i	$-0.510508\pi$
$463$	15.6609	−	7.54187i	0.727822	−	0.350500i	0.760827	+	0.648955i	$0.224794\pi$
$464$	−0.0410159	−	37.3993i	−0.00190412	−	1.73622i
$465$	−23.4204	−	21.7309i	−1.08609	−	1.00775i
$466$	−4.59221	+	0.870198i	−0.212730	+	0.0403111i
$467$	3.93586	−	5.77285i	0.182130	−	0.267135i	−0.724306	−	0.689478i	$-0.757840\pi$
$467$	3.93586	−	5.77285i	0.182130	−	0.267135i	0.906436	+	0.422343i	$0.138792\pi$
$468$	18.4323	−	17.1215i	0.852035	−	0.791443i
$469$	10.3458	−	14.6665i	0.477724	−	0.677237i
$470$	−10.7179	−	20.2657i	−0.494378	−	0.934789i
$471$	23.7685	+	41.1682i	1.09519	+	1.89693i
$472$	−6.65572	−	7.72124i	−0.306354	−	0.355399i
$473$	−4.93471	+	3.36443i	−0.226898	+	0.154697i
$474$	14.0736	+	14.0659i	0.646421	+	0.646066i
$475$	−1.41310	−	0.322530i	−0.0648372	−	0.0147987i
$476$	4.79401	+	5.32895i	0.219733	+	0.244252i
$477$	25.0357	−	5.71424i	1.14631	−	0.261637i
$478$	8.44058	+	5.30034i	0.386063	+	0.242432i
$479$	31.6861	+	9.77386i	1.44777	+	0.446579i	0.916299	−	0.400495i	$-0.131162\pi$
$479$	31.6861	+	9.77386i	1.44777	+	0.446579i	0.531475	+	0.847074i	$0.321638\pi$
$480$	−27.8152	+	9.77578i	−1.26958	+	0.446201i
$481$	15.5424	−	4.79421i	0.708674	−	0.218597i
$482$	17.1336	−	0.645800i	0.780416	−	0.0294154i
$483$	−5.28772	−	3.16632i	−0.240599	−	0.144073i
$484$	−1.27515	−	0.499655i	−0.0579616	−	0.0227116i
$485$	−1.41978	−	0.557223i	−0.0644689	−	0.0253022i
$486$	−16.1993	+	18.8344i	−0.734816	+	0.854345i
$487$	7.08183	−	1.06741i	0.320908	−	0.0483692i	0.0133872	−	0.999910i	$-0.495739\pi$
$487$	7.08183	−	1.06741i	0.320908	−	0.0483692i	0.307521	+	0.951541i	$0.400500\pi$
$488$	9.76612	+	22.3340i	0.442092	+	1.01101i
$489$	−41.9791			−1.89836
$490$	9.94152	−	20.9532i	0.449112	−	0.946569i
$491$		−	8.94020i		−	0.403465i	−0.979441	−	0.201733i	$-0.935343\pi$
$491$		−	8.94020i		−	0.403465i	0.979441	−	0.201733i	$-0.0646572\pi$
$492$	5.06847	−	8.78998i	0.228504	−	0.396283i
$493$	−1.88770	−	12.5241i	−0.0850176	−	0.564055i
$494$	20.5298	+	17.6575i	0.923679	+	0.794449i
$495$	5.35850	−	13.6532i	0.240846	−	0.613667i
$496$	1.80557	−	24.4535i	0.0810724	−	1.09799i
$497$	11.4749	+	30.6664i	0.514720	+	1.37558i
$498$	19.4854	−	0.734443i	0.873162	−	0.0329112i
$499$	−1.66958	−	5.41266i	−0.0747408	−	0.242304i	0.910491	−	0.413529i	$-0.135704\pi$
$499$	−1.66958	−	5.41266i	−0.0747408	−	0.242304i	−0.985232	+	0.171225i	$0.945228\pi$
$500$	−13.1889	−	16.5197i	−0.589823	−	0.738784i
$501$	−5.94173	+	19.2626i	−0.265457	+	0.860590i
$502$	19.8285	−	31.5761i	0.884988	−	1.40931i
$503$	−5.13476	−	22.4968i	−0.228947	−	1.00308i	−0.950500	−	0.310725i	$-0.899428\pi$
$503$	−5.13476	−	22.4968i	−0.228947	−	1.00308i	0.721552	−	0.692360i	$-0.243429\pi$
$504$	−12.4673	+	7.57325i	−0.555338	+	0.337339i
$505$	−7.18338	+	31.4725i	−0.319656	+	1.40051i
$506$	3.36393	+	3.36208i	0.149545	+	0.149463i
$507$	35.8927	+	52.6449i	1.59405	+	2.33804i
$508$	1.68341	+	0.383256i	0.0746892	+	0.0170042i
$509$	−11.1169	+	6.41833i	−0.492747	+	0.284488i	−0.725713	−	0.687997i	$-0.758490\pi$
$509$	−11.1169	+	6.41833i	−0.492747	+	0.284488i	0.232966	+	0.972485i	$0.425157\pi$
$510$	−8.82628	+	4.66792i	−0.390834	+	0.206699i
$511$	18.6580	−	16.7666i	0.825382	−	0.741710i
$512$	−19.1888	−	11.9912i	−0.848034	−	0.529941i
$513$	−5.73076	−	3.90716i	−0.253019	−	0.172505i
$514$	−13.6817	+	2.59261i	−0.603475	+	0.114355i
$515$	−14.2884	+	15.3992i	−0.629621	+	0.678570i
$516$	−2.43449	+	7.90781i	−0.107172	+	0.348122i
$517$	9.64247	+	20.0228i	0.424076	+	0.880602i
$518$	−9.38719	+	0.908981i	−0.412449	+	0.0399383i
$519$	−34.3892	−	16.5610i	−1.50952	−	0.726945i
$520$	−7.98396	−	42.0071i	−0.350120	−	1.84213i
$521$	3.47831	−	6.02461i	0.152388	−	0.263943i	−0.779717	−	0.626132i	$-0.784637\pi$
$521$	3.47831	−	6.02461i	0.152388	−	0.263943i	0.932105	+	0.362189i	$0.117970\pi$
$522$	25.7572	+	0.956695i	1.12736	+	0.0418734i
$523$	5.55490	−	36.8544i	0.242899	−	1.61153i	−0.451726	−	0.892157i	$-0.649191\pi$
$523$	5.55490	−	36.8544i	0.242899	−	1.61153i	0.694625	−	0.719372i	$-0.255571\pi$
$524$	−3.19590	−	42.3348i	−0.139614	−	1.84941i
$525$	2.21903	+	1.82825i	0.0968465	+	0.0797912i
$526$	−35.2929	−	15.3866i	−1.53884	−	0.670888i
$527$	−0.620548	−	8.28064i	−0.0270315	−	0.360710i
$528$	27.3016	−	8.45423i	1.18815	−	0.367923i
$529$	−8.00228	−	20.3895i	−0.347925	−	0.886499i
$530$	14.4042	−	41.2011i	0.625679	−	1.78966i
$531$	5.49274	−	4.38031i	0.238365	−	0.190089i
$532$	−9.59947	−	12.4250i	−0.416190	−	0.538693i
$533$	11.5050	+	9.17496i	0.498339	+	0.397412i
$534$	26.6212	−	16.7374i	1.15201	−	0.724298i
$535$	−0.334526	+	4.46394i	−0.0144628	+	0.192993i
$536$	−3.55168	+	18.8560i	−0.153409	+	0.814454i
$537$	9.27223	−	8.60337i	0.400126	−	0.371263i
$538$	6.69738	+	4.94006i	0.288745	+	0.212981i
$539$	−10.3954	+	19.9344i	−0.447763	+	0.858636i
$540$	3.23399	+	10.4640i	0.139169	+	0.450297i
$541$	−2.02537	−	2.18283i	−0.0870776	−	0.0938473i	0.688010	−	0.725701i	$-0.258485\pi$
$541$	−2.02537	−	2.18283i	−0.0870776	−	0.0938473i	−0.775087	+	0.631854i	$0.782294\pi$
$542$	−10.2163	+	19.3431i	−0.438829	+	0.830857i
$543$	1.06180	−	14.1688i	0.0455663	−	0.608041i
$544$	−7.02773	−	3.05471i	−0.301312	−	0.130970i
$545$	12.2763	−	15.3940i	0.525859	−	0.659406i
$546$	−20.7061	−	49.5634i	−0.886138	−	2.12112i
$547$	13.7087	−	10.9323i	0.586140	−	0.467431i	−0.284958	−	0.958540i	$-0.591980\pi$
$547$	13.7087	−	10.9323i	0.586140	−	0.467431i	0.871098	+	0.491109i	$0.163408\pi$
$548$	15.7115	+	23.0174i	0.671162	+	0.983255i
$549$	−15.6382	+	6.13754i	−0.667422	+	0.261944i
$550$	−1.31799	−	1.78479i	−0.0561994	−	0.0761038i
$551$	2.07327	+	27.6659i	0.0883243	+	1.17861i
$552$	6.54796	+	0.732324i	0.278700	+	0.0311698i
$553$	15.1893	−	7.01873i	0.645916	−	0.298467i
$554$	−16.3949	+	14.1167i	−0.696551	+	0.599763i
$555$	1.95797	−	12.9903i	0.0831110	−	0.551406i
$556$	−0.663664	+	0.833145i	−0.0281456	+	0.0353332i
$557$	−18.2718	−	10.5492i	−0.774200	−	0.446984i	0.0601710	−	0.998188i	$-0.480835\pi$
$557$	−18.2718	−	10.5492i	−0.774200	−	0.446984i	−0.834371	+	0.551204i	$0.814169\pi$
$558$	16.7930	+	1.88746i	0.710906	+	0.0799025i
$559$	−10.8114	−	5.20652i	−0.457276	−	0.220212i
$560$	−0.368069	+	24.7906i	−0.0155538	+	1.04759i
$561$	8.72048	−	4.19956i	0.368179	−	0.177306i
$562$	32.1346	−	11.2543i	1.35552	−	0.474734i
$563$	−4.54036	+	4.89334i	−0.191353	+	0.206230i	−0.821440	−	0.570295i	$-0.806829\pi$
$563$	−4.54036	+	4.89334i	−0.191353	+	0.206230i	0.630087	+	0.776525i	$0.283019\pi$
$564$	27.7461	+	13.3431i	1.16832	+	0.561845i
$565$	−19.8120	+	29.0589i	−0.833497	+	1.22252i
$566$	7.31118	+	1.38127i	0.307312	+	0.0580593i
$567$	14.2099	+	25.5442i	0.596759	+	1.07276i
$568$	−24.7717	−	24.7310i	−1.03940	−	1.03769i
$569$	9.99539	+	17.3125i	0.419029	+	0.725779i	0.995842	−	0.0910971i	$-0.0290373\pi$
$569$	9.99539	+	17.3125i	0.419029	+	0.725779i	−0.576813	+	0.816876i	$0.695704\pi$
$570$	20.0438	−	8.75155i	0.839541	−	0.366562i
$571$	9.97349	+	14.6284i	0.417378	+	0.612181i	0.976139	−	0.217148i	$-0.0696755\pi$
$571$	9.97349	+	14.6284i	0.417378	+	0.612181i	−0.558761	+	0.829329i	$0.688723\pi$
$572$	6.20031	+	40.9838i	0.259248	+	1.71362i
$573$	2.46570	+	0.562779i	0.103006	+	0.0235104i
$574$	−5.46370	−	6.55388i	−0.228050	−	0.273554i
$575$	−0.113815	−	0.498658i	−0.00474643	−	0.0207955i
$576$	8.76344	−	12.8991i	0.365143	−	0.537465i
$577$	28.1819	+	8.69298i	1.17323	+	0.361893i	0.819293	−	0.573376i	$-0.194366\pi$
$577$	28.1819	+	8.69298i	1.17323	+	0.361893i	0.353937	+	0.935269i	$0.384843\pi$
$578$	20.7173	+	5.54509i	0.861725	+	0.230645i
$579$	15.4188	+	49.9864i	0.640782	+	2.07737i
$580$	24.6584	−	36.2099i	1.02389	−	1.50354i
$581$	5.08246	−	15.5900i	0.210856	−	0.646784i
$582$	1.97835	−	0.530679i	0.0820053	−	0.0219974i
$583$	−15.4577	+	39.3857i	−0.640194	+	1.63119i
$584$	−10.7035	+	24.5879i	−0.442915	+	1.01745i
$585$	29.1397	−	4.39210i	1.20478	−	0.181591i
$586$	−0.0393583	+	0.00444555i	−0.00162588	+	0.000183644i
$587$			2.82726i			0.116694i	0.998296	+	0.0583468i	$0.0185829\pi$
$587$			2.82726i			0.116694i	−0.998296	+	0.0583468i	$0.981417\pi$
$588$	5.97580	+	30.5672i	0.246438	+	1.26057i
$589$			18.1894i			0.749480i
$590$	−1.34021	−	11.8655i	−0.0551756	−	0.488493i
$591$	−32.8324	+	4.94868i	−1.35054	+	0.203562i
$592$	8.72596	−	5.05070i	0.358635	−	0.207583i
$593$	−2.56532	+	6.53634i	−0.105345	+	0.268415i	−0.973821	−	0.227316i	$-0.927005\pi$
$593$	−2.56532	+	6.53634i	−0.105345	+	0.268415i	0.868476	+	0.495732i	$0.165100\pi$
$594$	−2.75071	−	10.2545i	−0.112863	−	0.420748i
$595$	1.11890	+	8.32153i	0.0458705	+	0.341149i
$596$	0.126151	+	0.0859070i	0.00516735	+	0.00351889i
$597$	−13.9872	−	45.3455i	−0.572460	−	1.85587i
$598$	−2.47065	+	9.23073i	−0.101033	+	0.377473i
$599$	28.3664	+	8.74987i	1.15902	+	0.357510i	0.813875	−	0.581040i	$-0.197354\pi$
$599$	28.3664	+	8.74987i	1.15902	+	0.357510i	0.345144	+	0.938550i	$0.387830\pi$
$600$	−2.96960	−	0.793086i	−0.121234	−	0.0323776i
$601$	1.15592	+	5.06441i	0.0471509	+	0.206582i	0.993016	−	0.117978i	$-0.0376411\pi$
$601$	1.15592	+	5.06441i	0.0471509	+	0.206582i	−0.945865	+	0.324559i	$0.894784\pi$
$602$	5.53292	+	4.21897i	0.225505	+	0.171953i
$603$	−12.8922	−	2.94256i	−0.525010	−	0.119830i
$604$	−1.51464	−	10.0117i	−0.0616296	−	0.407370i
$605$	−0.903711	−	1.32550i	−0.0367411	−	0.0538893i
$606$	−17.3474	−	39.7310i	−0.704691	−	1.61396i
$607$	13.0390	+	22.5842i	0.529237	+	0.916665i	0.999419	+	0.0340953i	$0.0108550\pi$
$607$	13.0390	+	22.5842i	0.529237	+	0.916665i	−0.470182	+	0.882570i	$0.655812\pi$
$608$	14.8510	+	7.82294i	0.602286	+	0.317262i
$609$	20.9200	−	50.9019i	0.847723	−	2.06265i
$610$	−5.30071	+	28.0570i	−0.214619	+	1.13600i
$611$	−25.1529	+	36.8926i	−1.01758	+	1.49251i
$612$	2.28879	−	4.75941i	0.0925190	−	0.192388i
$613$	24.5387	−	26.4465i	0.991110	−	1.06816i	−0.00656305	−	0.999978i	$-0.502089\pi$
$613$	24.5387	−	26.4465i	0.991110	−	1.06816i	0.997673	−	0.0681838i	$-0.0217204\pi$
$614$	−8.18989	−	23.3848i	−0.330517	−	0.943734i
$615$	10.7084	−	5.15690i	0.431805	−	0.207946i
$616$	1.26171	−	24.0013i	0.0508357	−	0.967038i
$617$	−10.4431	−	5.02915i	−0.420425	−	0.202466i	0.211696	−	0.977335i	$-0.432101\pi$
$617$	−10.4431	−	5.02915i	−0.420425	−	0.202466i	−0.632121	+	0.774870i	$0.717815\pi$
$618$	3.15099	−	28.0349i	0.126751	−	1.12773i
$619$	−20.7200	−	11.9627i	−0.832807	−	0.480821i	0.0220060	−	0.999758i	$-0.492995\pi$
$619$	−20.7200	−	11.9627i	−0.832807	−	0.480821i	−0.854813	+	0.518937i	$0.826328\pi$
$620$	17.8956	−	22.4657i	0.718707	−	0.902244i
$621$	0.364794	−	2.42025i	0.0146387	−	0.0971212i
$622$	15.6276	+	18.1496i	0.626610	+	0.727731i
$623$	−5.47254	−	25.8713i	−0.219253	−	1.03651i
$624$	42.1372	+	39.0117i	1.68684	+	1.56172i
$625$	−2.03294	−	27.1277i	−0.0813176	−	1.08511i
$626$	0.908283	−	0.670728i	0.0363023	−	0.0268077i
$627$	−19.7360	+	7.74580i	−0.788179	+	0.309338i
$628$	−35.2966	+	24.0932i	−1.40849	+	0.961422i
$629$	2.66950	−	2.12886i	0.106440	−	0.0848831i
$630$	−17.0631	−	0.906362i	−0.679809	−	0.0361103i
$631$	11.9526	−	14.9881i	0.475824	−	0.596665i	−0.484762	−	0.874646i	$-0.661094\pi$
$631$	11.9526	−	14.9881i	0.475824	−	0.596665i	0.960587	+	0.277981i	$0.0896653\pi$
$632$	−11.6569	+	13.5681i	−0.463685	+	0.539709i
$633$	2.24430	−	29.9481i	0.0892029	−	1.19033i
$634$	−13.6644	−	7.21704i	−0.542682	−	0.286625i
$635$	1.37556	+	1.48250i	0.0545872	+	0.0588311i
$636$	17.3078	+	56.0016i	0.686301	+	2.22061i
$637$	−45.1290	+	1.93787i	−1.78807	+	0.0767812i
$638$	−25.2088	+	34.1763i	−0.998025	+	1.35305i
$639$	17.6841	−	16.4084i	0.699572	−	0.649108i
$640$	−10.6458	−	24.2733i	−0.420813	−	0.959485i
$641$	−2.95229	+	39.3955i	−0.116608	+	1.55603i	0.565481	+	0.824761i	$0.308691\pi$
$641$	−2.95229	+	39.3955i	−0.116608	+	1.55603i	−0.682089	+	0.731269i	$0.738928\pi$
$642$	−3.19980	−	5.08935i	−0.126286	−	0.200861i
$643$	−31.4283	−	25.0633i	−1.23941	−	0.988399i	−0.999847	−	0.0175185i	$-0.994423\pi$
$643$	−31.4283	−	25.0633i	−1.23941	−	0.988399i	−0.239566	−	0.970880i	$-0.577005\pi$
$644$	2.48059	−	4.95443i	0.0977491	−	0.195232i
$645$	−7.57753	+	6.04288i	−0.298365	+	0.237938i
$646$	5.36600	+	1.87599i	0.211122	+	0.0738100i
$647$	12.8194	+	32.6633i	0.503983	+	1.28413i	0.925995	+	0.377537i	$0.123229\pi$
$647$	12.8194	+	32.6633i	0.503983	+	1.28413i	−0.422012	+	0.906590i	$0.638676\pi$
$648$	−25.1580	−	18.5355i	−0.988299	−	0.728143i
$649$	0.865030	+	11.5430i	0.0339554	+	0.453103i
$650$	1.78149	−	4.08628i	0.0698759	−	0.160277i
$651$	16.1713	−	32.2544i	0.633805	−	1.26415i
$652$	−2.84088	−	37.6320i	−0.111257	−	1.47378i
$653$	6.17330	−	40.9572i	0.241580	−	1.60278i	−0.458488	−	0.888701i	$-0.651609\pi$
$653$	6.17330	−	40.9572i	0.241580	−	1.60278i	0.700067	−	0.714077i	$-0.253153\pi$
$654$	−0.981465	+	26.4241i	−0.0383783	+	1.03326i
$655$	24.8655	−	43.0684i	0.971577	−	1.68282i
$656$	8.22274	+	3.94876i	0.321044	+	0.154173i
$657$	−16.6513	−	8.01884i	−0.649629	−	0.312845i
$658$	18.5919	−	18.0182i	0.724788	−	0.702424i
$659$	−0.467810	−	0.971418i	−0.0182233	−	0.0378411i	0.891659	−	0.452709i	$-0.149542\pi$
$659$	−0.467810	−	0.971418i	−0.0182233	−	0.0378411i	−0.909882	+	0.414868i	$0.863828\pi$
$660$	31.9966	+	9.85044i	1.24547	+	0.383428i
$661$	5.57621	−	6.00973i	0.216890	−	0.233751i	−0.615230	−	0.788348i	$-0.710937\pi$
$661$	5.57621	−	6.00973i	0.216890	−	0.233751i	0.832120	+	0.554596i	$0.187127\pi$
$662$	−8.60816	−	45.4270i	−0.334566	−	1.76557i
$663$	16.0677	+	10.9548i	0.624018	+	0.425448i
$664$	1.97704	+	17.4179i	0.0767239	+	0.675946i
$665$	−1.08188	−	18.3603i	−0.0419536	−	0.711980i
$666$	3.24851	+	6.14240i	0.125877	+	0.238013i
$667$	−8.47857	+	4.89511i	−0.328292	+	0.189539i
$668$	−17.6700	−	4.02286i	−0.683672	−	0.155649i
$669$	−27.7992	−	40.7739i	−1.07478	−	1.57641i
$670$	−15.8884	+	15.8972i	−0.613824	+	0.614161i
$671$	6.15923	−	26.9854i	0.237775	−	1.04176i
$672$	−19.3795	−	27.0754i	−0.747582	−	1.04446i
$673$	−9.62877	−	42.1864i	−0.371162	−	1.62617i	−0.723522	−	0.690301i	$-0.757478\pi$
$673$	−9.62877	−	42.1864i	−0.371162	−	1.62617i	0.352360	−	0.935864i	$-0.385379\pi$
$674$	−17.2389	−	10.8253i	−0.664018	−	0.416977i
$675$	−0.336553	+	1.09108i	−0.0129539	+	0.0419956i
$676$	−44.7643	+	35.7385i	−1.72170	+	1.37456i
$677$	0.356285	+	1.15505i	0.0136931	+	0.0443921i	0.962162	−	0.272480i	$-0.0878437\pi$
$677$	0.356285	+	1.15505i	0.0136931	+	0.0443921i	−0.948468	+	0.316872i	$0.897368\pi$
$678$	−1.77899	−	47.1983i	−0.0683218	−	1.81264i
$679$	0.156088	−	1.71539i	0.00599009	−	0.0658307i
$680$	−4.78185	−	7.59639i	−0.183375	−	0.291308i
$681$	2.12209	−	5.40699i	0.0813186	−	0.207196i
$682$	−18.1558	+	21.1092i	−0.695222	+	0.808311i
$683$	0.260529	+	1.72850i	0.00996886	+	0.0661391i	0.993262	−	0.115889i	$-0.0369718\pi$
$683$	0.260529	+	1.72850i	0.00996886	+	0.0661391i	−0.983293	+	0.182028i	$0.941734\pi$
$684$	−5.77861	+	10.0215i	−0.220951	+	0.383183i
$685$			32.6444i			1.24728i
$686$	25.8581	+	4.16643i	0.987266	+	0.159075i
$687$	−12.1844			−0.464863
$688$	−7.25367	−	1.64724i	−0.276544	−	0.0628002i
$689$	−84.0596	+	12.6700i	−3.20242	+	0.482687i
$690$	5.85135	+	5.03271i	0.222757	+	0.191592i
$691$	−0.955175	−	0.374879i	−0.0363366	−	0.0142611i	0.347103	−	0.937827i	$-0.387165\pi$
$691$	−0.955175	−	0.374879i	−0.0363366	−	0.0142611i	−0.383440	+	0.923566i	$0.625261\pi$
$692$	12.5188	−	31.9488i	0.475892	−	1.21451i
$693$	16.4959	+	1.50101i	0.626629	+	0.0570185i
$694$	−0.237516	−	6.30152i	−0.00901600	−	0.239202i
$695$	−1.19228	+	0.367769i	−0.0452256	+	0.0139503i
$696$	2.24819	+	58.7900i	0.0852175	+	2.22843i
$697$	2.95189	+	0.910538i	0.111811	+	0.0344891i
$698$	6.41474	−	10.2152i	0.242801	−	0.386652i
$699$	7.16823	−	1.63610i	0.271127	−	0.0618831i
$700$	−1.48875	+	2.11297i	−0.0562696	+	0.0798626i
$701$	20.1966	+	4.60973i	0.762813	+	0.174107i	0.586192	−	0.810172i	$-0.300626\pi$
$701$	20.1966	+	4.60973i	0.762813	+	0.174107i	0.176621	+	0.984279i	$0.443483\pi$
$702$	15.0795	−	15.0878i	0.569140	−	0.569452i
$703$	−6.17960	+	4.21318i	−0.233068	+	0.158903i
$704$	9.42635	+	23.9023i	0.355269	+	0.900850i
$705$	18.0320	+	31.2323i	0.679124	+	1.17628i
$706$	22.0258	−	11.6487i	0.828950	−	0.438404i
$707$	−36.3939	+	2.14452i	−1.36873	+	0.0806529i
$708$	10.9138	+	11.7493i	0.410164	+	0.441566i
$709$	−3.33382	+	4.88982i	−0.125204	+	0.183641i	−0.883723	−	0.468010i	$-0.844971\pi$
$709$	−3.33382	+	4.88982i	−0.125204	+	0.183641i	0.758519	+	0.651651i	$0.225923\pi$
$710$	−7.63388	−	40.2855i	−0.286494	−	1.51189i
$711$	−9.03707	−	8.38517i	−0.338916	−	0.314468i
$712$	16.8057	+	22.7318i	0.629821	+	0.851910i
$713$	−5.78308	+	2.78498i	−0.216578	+	0.104298i
$714$	−7.84743	−	8.09728i	−0.293683	−	0.303033i
$715$	−21.0667	+	43.7454i	−0.787849	+	1.63598i
$716$	8.33994	+	7.72983i	0.311678	+	0.288877i
$717$	−13.5782	−	7.83940i	−0.507088	−	0.292768i
$718$	1.06133	−	28.5744i	0.0396086	−	1.06639i
$719$	−5.99525	−	0.903638i	−0.223585	−	0.0337000i	0.0362942	−	0.999341i	$-0.488445\pi$
$719$	−5.99525	−	0.903638i	−0.223585	−	0.0337000i	−0.259879	+	0.965641i	$0.583683\pi$
$720$	16.9969	−	6.69230i	0.633436	−	0.249407i
$721$	−21.2077	−	10.6329i	−0.789816	−	0.395989i
$722$	13.2169	+	5.76217i	0.491883	+	0.214446i
$723$	−26.8967	+	2.01563i	−1.00030	+	0.0749621i
$724$	12.7734	−	0.00700431i	0.474720	−	0.000260313i
$725$	4.25145	−	1.66857i	0.157895	−	0.0619692i
$726$	2.03374	+	0.711011i	0.0754792	+	0.0263881i
$727$	−20.7488	−	26.0182i	−0.769531	−	0.964961i	0.230436	−	0.973087i	$-0.425985\pi$
$727$	−20.7488	−	26.0182i	−0.769531	−	0.964961i	−0.999967	+	0.00812660i	$0.997413\pi$
$728$	43.0296	−	21.9160i	1.59478	−	0.812261i
$729$	3.70072	−	4.64055i	0.137064	−	0.171872i
$730$	−26.5930	+	16.7196i	−0.984250	+	0.618822i
$731$	−2.51200	−	0.188248i	−0.0929097	−	0.00696262i
$732$	−16.6566	−	34.5393i	−0.615645	−	1.27661i
$733$	−18.9561	−	20.4299i	−0.700161	−	0.754594i	0.278419	−	0.960460i	$-0.410190\pi$
$733$	−18.9561	−	20.4299i	−0.700161	−	0.754594i	−0.978580	+	0.205866i	$0.933999\pi$
$734$	8.17952	−	11.0892i	0.301912	−	0.409311i
$735$	−14.4048	+	33.5193i	−0.531330	+	1.23638i
$736$	−0.213364	+	5.91945i	−0.00786471	+	0.218194i
$737$	15.9716	−	14.8195i	0.588322	−	0.545883i
$738$	−2.93598	+	5.55883i	−0.108075	+	0.204624i
$739$	−0.888123	−	0.0665556i	−0.0326701	−	0.00244829i	0.0583850	−	0.998294i	$-0.481405\pi$
$739$	−0.888123	−	0.0665556i	−0.0326701	−	0.00244829i	−0.0910551	+	0.995846i	$0.529024\pi$
$740$	11.7776	+	0.876112i	0.432952	+	0.0322065i
$741$	−33.3042	−	26.5592i	−1.22346	−	0.975677i
$742$	49.2221	+	2.61460i	1.80700	+	0.0959849i
$743$	24.8005	+	31.0989i	0.909843	+	1.14091i	0.989565	+	0.144090i	$0.0460255\pi$
$743$	24.8005	+	31.0989i	0.909843	+	1.14091i	−0.0797215	+	0.996817i	$0.525403\pi$
$744$	−1.41057	+	38.5467i	−0.0517139	+	1.41319i
$745$	0.0653157	+	0.166422i	0.00239298	+	0.00609721i
$746$	27.3594	+	37.0494i	1.00170	+	1.35647i
$747$	−12.0474	+	0.902830i	−0.440792	+	0.0330328i
$748$	4.35482	+	7.53323i	0.159228	+	0.275442i
$749$	−4.94598	+	1.04622i	−0.180722	+	0.0382281i
$750$	21.6977	+	25.1992i	0.792288	+	0.920145i
$751$	−28.3152	−	4.26782i	−1.03324	−	0.155735i	−0.389534	−	0.921012i	$-0.627364\pi$
$751$	−28.3152	−	4.26782i	−1.03324	−	0.155735i	−0.643701	+	0.765277i	$0.722602\pi$
$752$	−10.0837	+	25.7759i	−0.367714	+	0.939949i
$753$	−29.3270	+	50.7959i	−1.06874	+	1.85111i
$754$	−84.7911	−	9.53012i	−3.08791	−	0.347067i
$755$	5.14625	−	10.6863i	0.187291	−	0.388914i
$756$	−10.3257	+	6.80947i	−0.375540	+	0.247658i
$757$	12.5078	+	25.9727i	0.454604	+	0.943994i	0.994741	+	0.102418i	$0.0326579\pi$
$757$	12.5078	+	25.9727i	0.454604	+	0.943994i	−0.540138	+	0.841577i	$0.681628\pi$
$758$	12.8662	+	36.7373i	0.467323	+	1.33436i
$759$	−5.48446	−	5.08884i	−0.199073	−	0.184713i
$760$	9.20173	+	17.3759i	0.333782	+	0.630290i
$761$	−3.21684	−	2.19321i	−0.116610	−	0.0795037i	0.503610	−	0.863931i	$-0.332005\pi$
$761$	−3.21684	−	2.19321i	−0.116610	−	0.0795037i	−0.620221	+	0.784427i	$0.712957\pi$
$762$	−2.66873	−	0.504193i	−0.0966779	−	0.0182650i
$763$	20.5670	+	8.45276i	0.744575	+	0.306011i
$764$	−0.337638	+	2.24845i	−0.0122153	+	0.0813460i
$765$	5.35741	−	3.09310i	0.193698	−	0.111831i
$766$	9.65743	+	22.1185i	0.348937	+	0.799174i
$767$	−19.2158	+	13.1011i	−0.693844	+	0.473055i
$768$	30.8653	+	17.7300i	1.11376	+	0.639775i
$769$	−2.26104	+	9.90626i	−0.0815351	+	0.357229i	−0.999194	−	0.0401402i	$-0.987220\pi$
$769$	−2.26104	+	9.90626i	−0.0815351	+	0.357229i	0.917659	+	0.397369i	$0.130077\pi$
$770$	17.0709	−	22.3874i	0.615191	−	0.806784i
$771$	21.3565	−	4.87449i	0.769137	−	0.175550i
$772$	−43.7667	+	17.2049i	−1.57520	+	0.619216i
$773$	10.6386	−	34.4896i	0.382645	−	1.24051i	−0.535593	−	0.844476i	$-0.679912\pi$
$773$	10.6386	−	34.4896i	0.382645	−	1.24051i	0.918238	−	0.396029i	$-0.129612\pi$
$774$	1.32545	−	4.95207i	0.0476422	−	0.177998i
$775$	2.86132	−	0.882602i	0.102782	−	0.0317040i
$776$	0.609607	+	1.73757i	0.0218836	+	0.0623752i
$777$	14.7038	−	1.97705i	0.527494	−	0.0709261i
$778$	12.8261	−	3.44052i	0.459838	−	0.123348i
$779$	−6.29891	−	2.47214i	−0.225682	−	0.0885735i
$780$	15.0037	+	65.5697i	0.537218	+	2.34777i
$781$	5.92404	+	39.3034i	0.211979	+	1.40639i
$782$	0.225143	+	1.99328i	0.00805109	+	0.0712797i
$783$	21.8551			0.781039
$784$	−26.9974	+	7.42558i	−0.964194	+	0.265199i
$785$	−50.0594			−1.78670
$786$	7.49591	+	66.3645i	0.267370	+	2.36714i
$787$	5.89418	+	39.1054i	0.210105	+	1.39396i	0.806486	+	0.591254i	$0.201367\pi$
$787$	5.89418	+	39.1054i	0.210105	+	1.39396i	−0.596381	+	0.802702i	$0.703395\pi$
$788$	−6.65811	−	29.0975i	−0.237185	−	1.03656i
$789$	56.3795	+	22.1273i	2.00716	+	0.787753i
$790$	−20.2379	+	5.42868i	−0.720033	+	0.193144i
$791$	−37.7628	−	12.3109i	−1.34269	−	0.437725i
$792$	−16.7092	+	5.86225i	−0.593737	+	0.208306i
$793$	53.1420	−	16.3921i	1.88713	−	0.582101i
$794$	7.27680	−	27.1872i	0.258244	−	0.964837i
$795$	−20.2380	+	65.6100i	−0.717768	+	2.32695i
$796$	39.7032	−	15.6075i	1.40724	−	0.553193i
$797$	21.3138	−	4.86474i	0.754974	−	0.172318i	0.172323	−	0.985040i	$-0.444873\pi$
$797$	21.3138	−	4.86474i	0.754974	−	0.172318i	0.582651	+	0.812723i	$0.302016\pi$
$798$	15.8160	+	18.9719i	0.559881	+	0.671596i
$799$	−2.08577	+	9.13834i	−0.0737891	+	0.323291i
$800$	0.509994	−	2.71576i	0.0180310	−	0.0960166i
$801$	−16.0975	+	10.9751i	−0.568777	+	0.387786i
$802$	−2.34503	−	5.37086i	−0.0828060	−	0.189652i
$803$	26.3711	−	15.2254i	0.930617	−	0.537292i
$804$	4.48232	−	29.8493i	0.158079	−	1.05270i
$805$	5.67176	−	3.15512i	0.199903	−	0.111203i
$806$	−54.9690	−	10.3851i	−1.93620	−	0.365799i
$807$	−10.8169	−	7.37481i	−0.380771	−	0.259605i
$808$	34.4427	−	18.2398i	1.21169	−	0.641673i
$809$	18.6243	+	17.2808i	0.654796	+	0.607562i	0.935964	−	0.352096i	$-0.114531\pi$
$809$	18.6243	+	17.2808i	0.654796	+	0.607562i	−0.281167	+	0.959659i	$0.590722\pi$
$810$	−12.0990	−	34.5467i	−0.425117	−	1.21385i
$811$	−3.58014	−	7.43424i	−0.125716	−	0.261051i	0.828606	−	0.559832i	$-0.189134\pi$
$811$	−3.58014	−	7.43424i	−0.125716	−	0.261051i	−0.954322	+	0.298781i	$0.903420\pi$
$812$	47.0466	+	15.3090i	1.65101	+	0.537239i
$813$	14.9308	−	31.0042i	0.523648	−	1.08737i
$814$	−11.3770	−	1.27872i	−0.398762	−	0.0448190i
$815$	22.1033	−	38.2840i	0.774245	−	1.34103i
$816$	11.2261	+	4.39171i	0.392992	+	0.153741i
$817$	5.45626	+	0.822400i	0.190891	+	0.0287721i
$818$	27.9090	+	32.4128i	0.975815	+	1.13329i
$819$	13.9599	+	30.2108i	0.487798	+	1.05565i
$820$	5.34756	+	9.25053i	0.186745	+	0.323042i
$821$	30.8833	−	2.31438i	1.07783	−	0.0807725i	0.476040	−	0.879424i	$-0.342072\pi$
$821$	30.8833	−	2.31438i	1.07783	−	0.0807725i	0.601794	+	0.798651i	$0.294453\pi$
$822$	−26.0427	−	35.2664i	−0.908344	−	1.23006i
$823$	−13.0639	−	33.2862i	−0.455378	−	1.16028i	−0.955673	−	0.294429i	$-0.904870\pi$
$823$	−13.0639	−	33.2862i	−0.455378	−	1.16028i	0.500295	−	0.865855i	$-0.333225\pi$
$824$	25.3450	+	0.927467i	0.882934	+	0.0323098i
$825$	2.17612	+	2.72877i	0.0757628	+	0.0950035i
$826$	12.4431	−	5.19834i	0.432950	−	0.180873i
$827$	22.3737	+	17.8424i	0.778009	+	0.620441i	0.929840	−	0.367965i	$-0.119945\pi$
$827$	22.3737	+	17.8424i	0.778009	+	0.620441i	−0.151831	+	0.988406i	$0.548517\pi$
$828$	−4.07098	−	0.302833i	−0.141476	−	0.0105242i
$829$	−24.2911	−	1.82037i	−0.843665	−	0.0632239i	−0.354118	−	0.935201i	$-0.615219\pi$
$829$	−24.2911	−	1.82037i	−0.843665	−	0.0632239i	−0.489547	+	0.871977i	$0.662838\pi$
$830$	−9.58988	+	18.1570i	−0.332870	+	0.630238i
$831$	24.9488	−	23.1491i	0.865463	−	0.803032i
$832$	−32.1203	+	40.4138i	−1.11357	+	1.40109i
$833$	−8.67014	+	3.83980i	−0.300403	+	0.133041i
$834$	0.994645	−	1.34847i	0.0344417	−	0.0466937i
$835$	−14.4386	−	15.5611i	−0.499667	−	0.538513i
$836$	−8.27930	−	17.1681i	−0.286346	−	0.593769i
$837$	14.2888	+	1.07079i	0.493892	+	0.0370121i
$838$	−11.3129	+	7.11268i	−0.390797	+	0.245703i
$839$	−26.9308	+	33.7702i	−0.929755	+	1.16588i	0.0561256	+	0.998424i	$0.482125\pi$
$839$	−26.9308	+	33.7702i	−0.929755	+	1.16588i	−0.985880	+	0.167452i	$0.946446\pi$
$840$	−0.868891	−	38.9928i	−0.0299796	−	1.34538i
$841$	−36.4239	−	45.6741i	−1.25600	−	1.57497i
$842$	15.1547	+	5.29819i	0.522265	+	0.182588i
$843$	−49.8591	+	19.5683i	−1.71724	+	0.673967i
$844$	26.9987	−	0.0148048i	0.929334	−	0.000509602i
$845$	−66.9096	+	5.01418i	−2.30176	+	0.172493i
$846$	−17.4857	−	7.62324i	−0.601172	−	0.262093i
$847$	1.15204	−	1.39829i	0.0395847	−	0.0480459i
$848$	−49.0311	+	19.3054i	−1.68374	+	0.662949i
$849$	−11.5740	−	1.74449i	−0.397217	−	0.0598709i
$850$	0.0347337	−	0.935141i	0.00119136	−	0.0320751i
$851$	−2.28569	−	1.31964i	−0.0783523	−	0.0452367i
$852$	40.3856	+	37.4312i	1.38359	+	1.28237i
$853$	17.2307	−	35.7800i	0.589969	−	1.22508i	−0.365726	−	0.930723i	$-0.619179\pi$
$853$	17.2307	−	35.7800i	0.589969	−	1.22508i	0.955695	−	0.294360i	$-0.0951065\pi$
$854$	−32.0962	+	3.10795i	−1.09831	+	0.106352i
$855$	−12.2088	+	5.87943i	−0.417531	+	0.201072i
$856$	4.34579	−	3.21286i	0.148536	−	0.109813i
$857$	26.2518	+	24.3581i	0.896745	+	0.832058i	0.986476	−	0.163908i	$-0.0524101\pi$
$857$	26.2518	+	24.3581i	0.896745	+	0.832058i	−0.0897305	+	0.995966i	$0.528601\pi$
$858$	−12.1400	−	64.0653i	−0.414453	−	2.18715i
$859$	−21.7040	+	31.8339i	−0.740529	+	1.08616i	0.252420	+	0.967618i	$0.418774\pi$
$859$	−21.7040	+	31.8339i	−0.740529	+	1.08616i	−0.992949	+	0.118539i	$0.962179\pi$
$860$	−5.92991	−	6.38390i	−0.202208	−	0.217689i
$861$	8.97171	+	9.98380i	0.305755	+	0.340247i
$862$	−28.5111	+	15.0786i	−0.971093	+	0.513578i
$863$	−0.376277	−	0.651732i	−0.0128086	−	0.0221852i	0.859550	−	0.511052i	$-0.170744\pi$
$863$	−0.376277	−	0.651732i	−0.0128086	−	0.0221852i	−0.872359	+	0.488866i	$0.837411\pi$
$864$	7.01962	−	11.2057i	0.238812	−	0.381227i
$865$	33.2102	−	22.6423i	1.12918	−	0.769862i
$866$	26.7459	−	26.7606i	0.908862	−	0.909361i
$867$	−32.8917	−	7.50732i	−1.11706	−	0.254962i
$868$	30.0087	+	12.3140i	1.01856	+	0.417963i
$869$	19.8027	−	4.51985i	0.671762	−	0.153325i
$870$	−36.6492	+	58.3625i	−1.24253	+	1.97867i
$871$	41.8308	+	12.9031i	1.41738	+	0.437204i
$872$	−23.7542	+	0.908385i	−0.804418	+	0.0307618i
$873$	−1.21268	+	0.374063i	−0.0410431	+	0.0126601i
$874$	−0.165501	−	4.39088i	−0.00559814	−	0.148524i
$875$	26.1905	−	9.80009i	0.885399	−	0.331303i
$876$	15.3905	−	39.2776i	0.519996	−	1.32707i
$877$	−17.4731	−	6.85767i	−0.590023	−	0.231567i	0.0514969	−	0.998673i	$-0.483601\pi$
$877$	−17.4731	−	6.85767i	−0.590023	−	0.231567i	−0.641520	+	0.767106i	$0.721696\pi$
$878$	−18.1598	−	15.6191i	−0.612863	−	0.527119i
$879$	0.0616124	−	0.00928658i	0.00207814	−	0.000313229i
$880$	−6.66506	+	29.3499i	−0.224679	+	0.989384i
$881$	2.07603			0.0699432			0.0349716	−	0.999388i	$-0.488866\pi$
$881$	2.07603			0.0699432			0.0349716	+	0.999388i	$0.488866\pi$
$882$	−4.40284	−	18.7881i	−0.148251	−	0.632629i
$883$		−	47.3024i		−	1.59185i	−0.605394	−	0.795926i	$-0.706984\pi$
$883$		−	47.3024i		−	1.59185i	0.605394	−	0.795926i	$-0.293016\pi$
$884$	−8.73300	+	15.1452i	−0.293723	+	0.509387i
$885$	2.79965	+	18.5745i	0.0941092	+	0.624374i
$886$	−6.44717	+	7.49591i	−0.216597	+	0.251830i
$887$	−19.5230	+	49.7438i	−0.655518	+	1.67023i	0.0834676	+	0.996510i	$0.473400\pi$
$887$	−19.5230	+	49.7438i	−0.655518	+	1.67023i	−0.738985	+	0.673721i	$0.764695\pi$
$888$	−13.4225	+	8.44930i	−0.450428	+	0.283540i
$889$	−1.17335	+	1.95948i	−0.0393529	+	0.0657189i
$890$	1.24725	+	33.0907i	0.0418080	+	1.10920i
$891$	10.4590	+	33.9072i	0.350389	+	1.13593i
$892$	34.6703	−	27.6798i	1.16085	−	0.926788i
$893$	6.05193	−	19.6199i	0.202520	−	0.656554i
$894$	−0.203328	−	0.127682i	−0.00680030	−	0.00427031i
$895$	2.96397	+	12.9860i	0.0990746	+	0.434074i
$896$	22.9601	−	19.2050i	0.767044	−	0.641594i
$897$	3.34494	−	14.6551i	0.111684	−	0.489321i
$898$	5.84034	−	5.84355i	0.194895	−	0.195002i
$899$	−32.2864	−	47.3555i	−1.07681	−	1.57939i
$900$	1.85686	+	0.422744i	0.0618952	+	0.0140915i
$901$	−15.4546	+	8.92272i	−0.514868	+	0.297259i
$902$	−4.84243	−	9.15626i	−0.161235	−	0.304870i
$903$	−8.94420	−	6.30924i	−0.297644	−	0.209958i
$904$	42.1903	−	4.78885i	1.40323	−	0.159275i
$905$	12.3625	+	8.42864i	0.410945	+	0.280178i
$906$	2.96561	+	15.6501i	0.0985258	+	0.519941i
$907$	−0.894078	+	0.963587i	−0.0296874	+	0.0319954i	−0.747721	−	0.664013i	$-0.768852\pi$
$907$	−0.894078	+	0.963587i	−0.0296874	+	0.0319954i	0.718034	+	0.696008i	$0.245042\pi$
$908$	4.99069	+	1.53643i	0.165622	+	0.0509881i
$909$	11.6543	+	24.2003i	0.386548	+	0.802675i
$910$	56.1031	+	7.21317i	1.85980	+	0.239114i
$911$	−20.1109	−	9.68490i	−0.666304	−	0.320875i	0.0699792	−	0.997548i	$-0.477707\pi$
$911$	−20.1109	−	9.68490i	−0.666304	−	0.320875i	−0.736283	+	0.676673i	$0.763421\pi$
$912$	−23.8028	−	11.4307i	−0.788188	−	0.378507i
$913$	9.95269	−	17.2386i	0.329386	−	0.570513i
$914$	−1.41363	+	38.0592i	−0.0467586	+	1.25889i
$915$	6.69459	−	44.4157i	0.221316	−	1.46834i
$916$	−0.824561	−	10.9226i	−0.0272443	−	0.360894i
$917$	54.5488	+	13.3688i	1.80136	+	0.441476i
$918$	1.78959	−	4.10485i	0.0590653	−	0.135480i
$919$	−3.94516	−	52.6445i	−0.130139	−	1.73658i	−0.555464	−	0.831540i	$-0.687459\pi$
$919$	−3.94516	−	52.6445i	−0.130139	−	1.73658i	0.425326	−	0.905040i	$-0.360160\pi$
$920$	−4.11556	+	5.58600i	−0.135686	+	0.184165i
$921$	14.2401	+	36.2831i	0.469227	+	1.19557i
$922$	44.6193	+	15.5992i	1.46946	+	0.513734i
$923$	−62.4366	+	49.7915i	−2.05513	+	1.63891i
$924$	−0.582017	+	37.8041i	−0.0191469	+	1.24366i
$925$	0.962617	+	0.767661i	0.0316506	+	0.0252405i
$926$	−13.0842	−	20.8108i	−0.429974	−	0.683884i
$927$	−1.30621	+	17.4301i	−0.0429015	+	0.572481i
$928$	−52.5499	+	5.99392i	−1.72504	+	0.196760i
$929$	−24.3427	+	22.5867i	−0.798658	+	0.741047i	−0.969722	−	0.244213i	$-0.921470\pi$
$929$	−24.3427	+	22.5867i	−0.798658	+	0.741047i	0.171063	+	0.985260i	$0.445280\pi$
$930$	−26.8205	+	36.3614i	−0.879480	+	1.19234i
$931$	19.5672	−	6.96819i	0.641287	−	0.228373i
$932$	1.95178	+	6.31521i	0.0639326	+	0.206862i
$933$	−25.6266	−	27.6189i	−0.838978	−	0.904204i
$934$	−8.73718	−	4.61467i	−0.285889	−	0.150997i
$935$	−0.761693	+	10.1641i	−0.0249100	+	0.332401i
$936$	−26.9862	−	23.1849i	−0.882072	−	0.757822i
$937$	1.85452	−	2.32550i	0.0605847	−	0.0759708i	−0.750616	−	0.660739i	$-0.770243\pi$
$937$	1.85452	−	2.32550i	0.0605847	−	0.0759708i	0.811201	+	0.584768i	$0.198814\pi$
$938$	−22.2527	−	12.2107i	−0.726576	−	0.398694i
$939$	−1.38867	+	1.10743i	−0.0453177	+	0.0361396i
$940$	−26.7778	+	18.2783i	−0.873395	+	0.596173i
$941$	−16.0511	+	6.29960i	−0.523252	+	0.205361i	−0.612241	−	0.790671i	$-0.709732\pi$
$941$	−16.0511	+	6.29960i	−0.523252	+	0.205361i	0.0889889	+	0.996033i	$0.471636\pi$
$942$	54.0801	−	39.9359i	1.76203	−	1.30118i
$943$	−0.178444	−	2.38117i	−0.00581093	−	0.0775414i
$944$	−9.79404	+	10.5787i	−0.318769	+	0.344308i
$945$	−14.4867	−	0.230977i	−0.471252	−	0.00751368i
$946$	5.51123	+	6.40061i	0.179186	+	0.208102i
$947$	−3.84311	+	25.4973i	−0.124884	+	0.828552i	0.835423	+	0.549607i	$0.185223\pi$
$947$	−3.84311	+	25.4973i	−0.124884	+	0.828552i	−0.960307	+	0.278945i	$0.910015\pi$
$948$	17.5326	−	22.0099i	0.569432	−	0.714849i
$949$	52.9843	+	30.5905i	1.71994	+	0.993009i
$950$	−0.228948	+	2.03699i	−0.00742804	+	0.0660885i
$951$	21.9021	+	10.5475i	0.710223	+	0.342025i
$952$	6.72771	−	7.58277i	0.218046	−	0.245759i
$953$	11.5768	−	5.57512i	0.375011	−	0.180596i	−0.236878	−	0.971539i	$-0.576124\pi$
$953$	11.5768	−	5.57512i	0.375011	−	0.180596i	0.611889	+	0.790944i	$0.290410\pi$
$954$	−12.0039	−	34.2751i	−0.388642	−	1.10970i
$955$	−1.81151	+	1.95234i	−0.0586190	+	0.0631763i
$956$	6.10871	−	12.7027i	0.197570	−	0.410834i
$957$	37.6331	−	55.1977i	1.21651	−	1.78429i
$958$	8.70556	−	46.0791i	0.281264	−	1.48875i
$959$	−35.3974	+	10.3036i	−1.14304	+	0.332721i
$960$	18.1527	+	37.5364i	0.585876	+	1.21148i
$961$	−3.28850	−	5.69585i	−0.106081	−	0.183737i
$962$	−9.20420	−	21.0805i	−0.296755	−	0.679662i
$963$	2.09818	+	3.07747i	0.0676129	+	0.0991700i
$964$	−3.62710	−	23.9750i	−0.116821	−	0.772184i
$965$	−53.7050	−	12.2578i	−1.72882	−	0.394593i
$966$	−3.61026	+	7.93329i	−0.116158	+	0.255249i
$967$	7.95236	+	34.8416i	0.255731	+	1.12043i	0.925765	+	0.378100i	$0.123422\pi$
$967$	7.95236	+	34.8416i	0.255731	+	1.12043i	−0.670034	+	0.742330i	$0.733721\pi$
$968$	−0.499752	+	1.87126i	−0.0160626	+	0.0601444i
$969$	−8.54499	−	2.63578i	−0.274505	−	0.0846735i
$970$	−0.557695	+	2.08363i	−0.0179065	+	0.0669014i
$971$	−12.1425	−	39.3650i	−0.389671	−	1.26328i	−0.911877	−	0.410463i	$-0.865367\pi$
$971$	−12.1425	−	39.3650i	−0.389671	−	1.26328i	0.522206	−	0.852819i	$-0.325109\pi$
$972$	29.0388	+	19.7750i	0.931420	+	0.634284i
$973$	−0.775104	−	1.17675i	−0.0248487	−	0.0377247i
$974$	−2.62409	−	9.78251i	−0.0840813	−	0.313452i
$975$	−2.56195	+	6.52773i	−0.0820479	+	0.209055i
$976$	29.8354	−	17.2691i	0.955008	−	0.552771i
$977$	−10.2062	+	1.53834i	−0.326526	+	0.0492159i	−0.310260	−	0.950652i	$-0.600416\pi$
$977$	−10.2062	+	1.53834i	−0.326526	+	0.0492159i	−0.0162663	+	0.999868i	$0.505178\pi$
$978$	6.66322	+	58.9923i	0.213066	+	1.88637i
$979$		−	32.1006i		−	1.02594i
$980$	−31.0231	−	10.6448i	−0.990995	−	0.340035i
$981$		−	16.3829i		−	0.523067i
$982$	−12.5635	+	1.41905i	−0.400916	+	0.0452837i
$983$	15.2456	−	2.29790i	0.486259	−	0.0732918i	0.0986627	−	0.995121i	$-0.468543\pi$
$983$	15.2456	−	2.29790i	0.486259	−	0.0732918i	0.387596	+	0.921829i	$0.373305\pi$
$984$	−13.1569	−	5.72740i	−0.419425	−	0.182583i
$985$	12.7742	−	32.5480i	0.407019	−	1.03707i
$986$	−17.3002	+	4.64065i	−0.550949	+	0.147788i
$987$	−28.1748	+	29.4106i	−0.896813	+	0.936149i
$988$	21.5551	−	31.6528i	0.685759	−	1.00701i
$989$	0.573940	+	1.86067i	0.0182502	+	0.0591658i
$990$	−20.0371	−	5.36304i	−0.636821	−	0.170449i
$991$	26.8574	+	8.28441i	0.853153	+	0.263163i	0.690332	−	0.723493i	$-0.257465\pi$
$991$	26.8574	+	8.28441i	0.853153	+	0.263163i	0.162821	+	0.986656i	$0.447941\pi$
$992$	−34.6505	+	1.34410i	−1.10015	+	0.0426752i
$993$	16.1846	+	70.9095i	0.513604	+	2.25025i
$994$	41.2734	−	20.9930i	1.30911	−	0.665859i
$995$	48.7189	+	11.1198i	1.54449	+	0.352520i
$996$	−4.12496	−	27.2658i	−0.130704	−	0.863951i
$997$	15.9157	+	23.3441i	0.504056	+	0.739315i	0.990962	−	0.134139i	$-0.0428270\pi$
$997$	15.9157	+	23.3441i	0.504056	+	0.739315i	−0.486906	+	0.873454i	$0.661875\pi$
$998$	−7.34128	+	3.20536i	−0.232384	+	0.101464i
$999$	2.94590	+	5.10244i	0.0932041	+	0.161434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.26	✓	648
8.5	even	2	inner	392.2.z.a.109.53	yes	648
49.9	even	21	inner	392.2.z.a.205.53	yes	648
392.205	even	42	inner	392.2.z.a.205.26	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.26	✓	648	1.1	even	1	trivial
392.2.z.a.109.53	yes	648	8.5	even	2	inner
392.2.z.a.205.26	yes	648	392.205	even	42	inner
392.2.z.a.205.53	yes	648	49.9	even	21	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.158727 - 1.40528i) q^{2} +(0.331575 + 2.19985i) q^{3} +(-1.94961 + 0.446111i) q^{4} +(-2.18080 - 0.855902i) q^{5} +(3.03878 - 0.815131i) q^{6} +(0.239753 - 2.63487i) q^{7} +(0.936366 + 2.66894i) q^{8} +(-1.86270 + 0.574567i) q^{9} +(-0.856628 + 3.20049i) q^{10} +(0.946675 - 3.06904i) q^{11} +(-1.62782 - 4.14094i) q^{12} +(6.29115 - 1.43591i) q^{13} +(-3.74077 + 0.0813049i) q^{14} +(1.15976 - 5.08125i) q^{15} +(3.60197 - 1.73949i) q^{16} +(1.11924 - 0.763087i) q^{17} +(1.10309 + 2.52641i) q^{18} +(-2.56973 + 1.48363i) q^{19} +(4.63355 + 0.695797i) q^{20} +(5.87582 - 0.346233i) q^{21} +(-4.46312 - 0.843201i) q^{22} +(-0.865154 - 0.589852i) q^{23} +(-5.56080 + 2.94482i) q^{24} +(0.358077 + 0.332247i) q^{25} +(-3.01643 - 8.61289i) q^{26} +(1.01420 + 2.10601i) q^{27} +(0.708018 + 5.24392i) q^{28} +(4.05674 - 8.42391i) q^{29} +(-7.32465 - 0.823256i) q^{30} +(3.06500 - 5.30874i) q^{31} +(-3.01619 - 4.78567i) q^{32} +(7.06534 + 1.06493i) q^{33} +(-1.25000 - 1.45173i) q^{34} +(-2.77804 + 5.54092i) q^{35} +(3.37522 - 1.95115i) q^{36} +(2.51352 - 0.188362i) q^{37} +(2.49280 + 3.37569i) q^{38} +(5.24479 + 13.3635i) q^{39} +(0.242319 - 6.62186i) q^{40} +(1.42183 + 1.78292i) q^{41} +(-1.41921 - 8.20220i) q^{42} +(-1.45388 - 1.15943i) q^{43} +(-0.476514 + 6.40577i) q^{44} +(4.55396 + 0.341272i) q^{45} +(-0.691583 + 1.30941i) q^{46} +(-5.07237 + 4.70647i) q^{47} +(5.02094 + 7.34704i) q^{48} +(-6.88504 - 1.26343i) q^{49} +(0.410063 - 0.555935i) q^{50} +(2.04979 + 2.20915i) q^{51} +(-11.6247 + 5.60602i) q^{52} +(-13.1369 - 0.984473i) q^{53} +(2.79854 - 1.75951i) q^{54} +(-4.69131 + 5.88272i) q^{55} +(7.25678 - 1.82731i) q^{56} +(-4.11584 - 5.16109i) q^{57} +(-12.4818 - 4.36375i) q^{58} +(-3.35496 + 1.31672i) q^{59} +(0.00571593 + 10.4238i) q^{60} +(8.59410 - 0.644039i) q^{61} +(-7.94676 - 3.46454i) q^{62} +(1.06732 + 5.04572i) q^{63} +(-6.24644 + 4.99820i) q^{64} +(-14.9488 - 2.25316i) q^{65} +(0.375061 - 10.0978i) q^{66} +(5.87497 + 3.39191i) q^{67} +(-1.84167 + 1.98703i) q^{68} +(1.01073 - 2.09879i) q^{69} +(8.22748 + 3.02443i) q^{70} +(-11.1501 + 5.36960i) q^{71} +(-3.27765 - 4.43342i) q^{72} +(6.95014 + 6.44879i) q^{73} +(-0.663664 - 3.50229i) q^{74} +(-0.612166 + 0.897883i) q^{75} +(4.34811 - 4.03889i) q^{76} +(-7.85955 - 3.23017i) q^{77} +(17.9469 - 9.49153i) q^{78} +(3.16216 + 5.47702i) q^{79} +(-9.34402 + 0.710544i) q^{80} +(-9.12839 + 6.22363i) q^{81} +(2.27981 - 2.28106i) q^{82} +(6.04232 + 1.37912i) q^{83} +(-11.3011 + 3.29629i) q^{84} +(-3.09398 + 0.706181i) q^{85} +(-1.39856 + 2.22715i) q^{86} +(19.8765 + 6.13109i) q^{87} +(9.07752 - 0.347134i) q^{88} +(9.55075 - 2.94602i) q^{89} +(-0.243254 - 6.45375i) q^{90} +(-2.27512 - 16.9206i) q^{91} +(1.94985 + 0.764028i) q^{92} +(12.6947 + 4.98232i) q^{93} +(7.41902 + 6.38104i) q^{94} +(6.87392 - 1.03608i) q^{95} +(9.52768 - 8.22199i) q^{96} +0.651035 q^{97} +(-0.682634 + 9.87593i) q^{98} +6.26064i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25}+ \cdots + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

L-functions

Modular forms

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Database

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