LMFDB - Embedded newform 882.2.y.a.457.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(193,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([14, 22]))

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

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

chi := DirichletCharacter("882.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.y (of order $21$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			457.23
Character	$\chi$	$=$	882.457
Dual form			882.2.y.a.193.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 + 0.149042i) q^{2} +(1.51433 - 0.840718i) q^{3} +(0.955573 + 0.294755i) q^{4} +(2.33528 + 1.12461i) q^{5} +(1.62272 - 0.605629i) q^{6} +(-0.864156 - 2.50065i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.58638 - 2.54625i) q^{9} +O(q^{10})$	\(q+(0.988831 + 0.149042i) q^{2} +(1.51433 - 0.840718i) q^{3} +(0.955573 + 0.294755i) q^{4} +(2.33528 + 1.12461i) q^{5} +(1.62272 - 0.605629i) q^{6} +(-0.864156 - 2.50065i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.58638 - 2.54625i) q^{9} +(2.14159 + 1.46011i) q^{10} +(-1.09122 + 1.36834i) q^{11} +(1.69486 - 0.357011i) q^{12} +(-2.76424 - 0.416643i) q^{13} +(-0.481803 - 2.60151i) q^{14} +(4.48187 - 0.260281i) q^{15} +(0.826239 + 0.563320i) q^{16} +(5.50495 - 1.69805i) q^{17} +(1.94817 - 2.28137i) q^{18} +(-1.88160 + 3.25903i) q^{19} +(1.90005 + 1.76299i) q^{20} +(-3.41096 - 3.06029i) q^{21} +(-1.28297 + 1.19042i) q^{22} +(-0.0798894 - 0.350018i) q^{23} +(1.72914 - 0.100418i) q^{24} +(1.07134 + 1.34342i) q^{25} +(-2.67127 - 0.823979i) q^{26} +(0.261631 - 5.18956i) q^{27} +(-0.0886859 - 2.64426i) q^{28} +(-0.00727862 - 0.00675357i) q^{29} +(4.47060 + 0.410614i) q^{30} +(-1.75965 + 3.04780i) q^{31} +(0.733052 + 0.680173i) q^{32} +(-0.502071 + 2.98953i) q^{33} +(5.69654 - 0.858615i) q^{34} +(0.794210 - 6.81156i) q^{35} +(2.26643 - 1.96553i) q^{36} +(-0.698826 - 0.648416i) q^{37} +(-2.34632 + 2.94219i) q^{38} +(-4.53626 + 1.69302i) q^{39} +(1.61607 + 2.02648i) q^{40} +(0.239044 + 3.18982i) q^{41} +(-2.91675 - 3.53449i) q^{42} +(-0.537681 + 7.17485i) q^{43} +(-1.44606 + 0.985910i) q^{44} +(6.56820 - 4.16214i) q^{45} +(-0.0268296 - 0.358016i) q^{46} +(-7.97634 - 1.20224i) q^{47} +(1.72479 + 0.158418i) q^{48} +(-5.50647 + 4.32190i) q^{49} +(0.859151 + 1.48809i) q^{50} +(6.90872 - 7.19952i) q^{51} +(-2.51863 - 1.21291i) q^{52} +(-0.700447 + 0.649920i) q^{53} +(1.03217 - 5.09260i) q^{54} +(-4.08716 + 1.96827i) q^{55} +(0.306412 - 2.62795i) q^{56} +(-0.109438 + 6.51714i) q^{57} +(-0.00619076 - 0.00776296i) q^{58} +(-0.992564 + 13.2448i) q^{59} +(4.35947 + 1.07234i) q^{60} +(0.775640 - 0.239253i) q^{61} +(-2.19424 + 2.75149i) q^{62} +(-7.73815 - 1.76663i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-5.98673 - 4.08168i) q^{65} +(-0.942029 + 2.88131i) q^{66} +(-0.519222 + 0.899320i) q^{67} +5.76089 q^{68} +(-0.415246 - 0.462878i) q^{69} +(1.80055 - 6.61711i) q^{70} +(-1.04058 - 4.55906i) q^{71} +(2.53406 - 1.60578i) q^{72} +(5.86366 - 14.9404i) q^{73} +(-0.594379 - 0.745328i) q^{74} +(2.75181 + 1.13369i) q^{75} +(-2.75862 + 2.55963i) q^{76} +(4.36473 + 1.54629i) q^{77} +(-4.73792 + 0.998014i) q^{78} +(5.03667 + 8.72376i) q^{79} +(1.29598 + 2.24471i) q^{80} +(-3.96677 - 8.07866i) q^{81} +(-0.239044 + 3.18982i) q^{82} +(3.62283 - 0.546053i) q^{83} +(-2.35738 - 3.92973i) q^{84} +(14.7653 + 2.22550i) q^{85} +(-1.60103 + 7.01458i) q^{86} +(-0.0167001 - 0.00410786i) q^{87} +(-1.57686 + 0.759373i) q^{88} +(1.37605 - 0.207407i) q^{89} +(7.11518 - 3.13671i) q^{90} +(1.34686 + 7.27244i) q^{91} +(0.0268296 - 0.358016i) q^{92} +(-0.102345 + 6.09473i) q^{93} +(-7.70806 - 2.37762i) q^{94} +(-8.05921 + 5.49468i) q^{95} +(1.68192 + 0.413715i) q^{96} +(4.98514 - 8.63452i) q^{97} +(-6.08911 + 3.45293i) q^{98} +(1.75305 + 4.94923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9}+O(q^{10}) $ 336 * q - 28 * q^2 - 13 * q^3 + 28 * q^4 - 4 * q^5 - 5 * q^6 - q^7 + 56 * q^8 + 29 * q^9	\( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9} - 2 q^{10} + q^{12} - 23 q^{13} + q^{14} + q^{15} + 28 q^{16} + 7 q^{17} - q^{18} + 38 q^{19} + 2 q^{20} + 13 q^{21} + 21 q^{23} - q^{24} - 48 q^{25} + 9 q^{26} - 28 q^{27} + 2 q^{28} + 11 q^{29} - 7 q^{30} + 44 q^{31} - 28 q^{32} - 25 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} - 22 q^{38} - 51 q^{39} + 4 q^{40} + 3 q^{41} + 13 q^{42} + q^{43} - 75 q^{45} - 42 q^{46} - 33 q^{47} - 2 q^{48} - 41 q^{49} + 172 q^{50} + 4 q^{51} + 11 q^{52} - 78 q^{53} + 11 q^{54} + 23 q^{55} + q^{56} - 30 q^{57} - 13 q^{58} + 14 q^{59} - 8 q^{60} + 92 q^{61} - 24 q^{62} - 22 q^{63} - 56 q^{64} + 7 q^{65} + 29 q^{66} + 29 q^{67} + 42 q^{68} + 19 q^{69} - 34 q^{70} + 7 q^{71} - q^{72} - 8 q^{73} - 8 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{77} + 4 q^{78} - 9 q^{79} - 12 q^{80} + 45 q^{81} - 3 q^{82} - 109 q^{83} + 28 q^{84} + 93 q^{85} + 2 q^{86} - 15 q^{87} + 47 q^{89} - 3 q^{90} + 45 q^{91} + 42 q^{92} + 155 q^{93} - 9 q^{94} - 13 q^{95} - q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q - 28 * q^2 - 13 * q^3 + 28 * q^4 - 4 * q^5 - 5 * q^6 - q^7 + 56 * q^8 + 29 * q^9 - 2 * q^10 + q^12 - 23 * q^13 + q^14 + q^15 + 28 * q^16 + 7 * q^17 - q^18 + 38 * q^19 + 2 * q^20 + 13 * q^21 + 21 * q^23 - q^24 - 48 * q^25 + 9 * q^26 - 28 * q^27 + 2 * q^28 + 11 * q^29 - 7 * q^30 + 44 * q^31 - 28 * q^32 - 25 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 - 22 * q^38 - 51 * q^39 + 4 * q^40 + 3 * q^41 + 13 * q^42 + q^43 - 75 * q^45 - 42 * q^46 - 33 * q^47 - 2 * q^48 - 41 * q^49 + 172 * q^50 + 4 * q^51 + 11 * q^52 - 78 * q^53 + 11 * q^54 + 23 * q^55 + q^56 - 30 * q^57 - 13 * q^58 + 14 * q^59 - 8 * q^60 + 92 * q^61 - 24 * q^62 - 22 * q^63 - 56 * q^64 + 7 * q^65 + 29 * q^66 + 29 * q^67 + 42 * q^68 + 19 * q^69 - 34 * q^70 + 7 * q^71 - q^72 - 8 * q^73 - 8 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^77 + 4 * q^78 - 9 * q^79 - 12 * q^80 + 45 * q^81 - 3 * q^82 - 109 * q^83 + 28 * q^84 + 93 * q^85 + 2 * q^86 - 15 * q^87 + 47 * q^89 - 3 * q^90 + 45 * q^91 + 42 * q^92 + 155 * q^93 - 9 * q^94 - 13 * q^95 - q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$2$	0.988831	+	0.149042i	0.699209	+	0.105389i
$3$	1.51433	−	0.840718i	0.874298	−	0.485389i
$3$	1.51433	−	0.840718i	0.874298	−	0.485389i
$4$	0.955573	+	0.294755i	0.477786	+	0.147378i
$5$	2.33528	+	1.12461i	1.04437	+	0.502942i	0.875763	−	0.482741i	$-0.160359\pi$
$5$	2.33528	+	1.12461i	1.04437	+	0.502942i	0.168607	+	0.985683i	$0.446073\pi$
$6$	1.62272	−	0.605629i	0.662472	−	0.247247i
$7$	−0.864156	−	2.50065i	−0.326620	−	0.945156i
$7$	−0.864156	−	2.50065i	−0.326620	−	0.945156i
$8$	0.900969	+	0.433884i	0.318541	+	0.153401i
$9$	1.58638	−	2.54625i	0.528795	−	0.848750i
$10$	2.14159	+	1.46011i	0.677229	+	0.461727i
$11$	−1.09122	+	1.36834i	−0.329015	+	0.412571i	−0.918634	−	0.395110i	$-0.870706\pi$
$11$	−1.09122	+	1.36834i	−0.329015	+	0.412571i	0.589619	+	0.807681i	$0.299278\pi$
$12$	1.69486	−	0.357011i	0.489263	−	0.103060i
$13$	−2.76424	−	0.416643i	−0.766664	−	0.115556i	−0.245944	−	0.969284i	$-0.579098\pi$
$13$	−2.76424	−	0.416643i	−0.766664	−	0.115556i	−0.520719	+	0.853728i	$0.674336\pi$
$14$	−0.481803	−	2.60151i	−0.128767	−	0.695283i
$15$	4.48187	−	0.260281i	1.15721	−	0.0672044i
$16$	0.826239	+	0.563320i	0.206560	+	0.140830i
$17$	5.50495	−	1.69805i	1.33515	−	0.411838i	0.456675	−	0.889634i	$-0.349040\pi$
$17$	5.50495	−	1.69805i	1.33515	−	0.411838i	0.878471	+	0.477796i	$0.158564\pi$
$18$	1.94817	−	2.28137i	0.459187	−	0.537724i
$19$	−1.88160	+	3.25903i	−0.431669	+	0.747672i	−0.997017	−	0.0771801i	$-0.975408\pi$
$19$	−1.88160	+	3.25903i	−0.431669	+	0.747672i	0.565348	+	0.824852i	$0.308742\pi$
$20$	1.90005	+	1.76299i	0.424864	+	0.394216i
$21$	−3.41096	−	3.06029i	−0.744332	−	0.667810i
$22$	−1.28297	+	1.19042i	−0.273530	+	0.253799i
$23$	−0.0798894	−	0.350018i	−0.0166581	−	0.0729839i	0.965916	−	0.258857i	$-0.0833458\pi$
$23$	−0.0798894	−	0.350018i	−0.0166581	−	0.0729839i	−0.982574	+	0.185873i	$0.940489\pi$
$24$	1.72914	−	0.100418i	0.352959	−	0.0204978i
$25$	1.07134	+	1.34342i	0.214269	+	0.268685i
$26$	−2.67127	−	0.823979i	−0.523880	−	0.161595i
$27$	0.261631	−	5.18956i	0.0503508	−	0.998732i
$28$	−0.0886859	−	2.64426i	−0.0167601	−	0.499719i
$29$	−0.00727862	−	0.00675357i	−0.00135161	−	0.00125411i	0.679497	−	0.733679i	$-0.262198\pi$
$29$	−0.00727862	−	0.00675357i	−0.00135161	−	0.00125411i	−0.680848	+	0.732425i	$0.738389\pi$
$30$	4.47060	+	0.410614i	0.816217	+	0.0749675i
$31$	−1.75965	+	3.04780i	−0.316042	+	0.547400i	−0.979658	−	0.200672i	$-0.935687\pi$
$31$	−1.75965	+	3.04780i	−0.316042	+	0.547400i	0.663617	+	0.748073i	$0.269021\pi$
$32$	0.733052	+	0.680173i	0.129586	+	0.120239i
$33$	−0.502071	+	2.98953i	−0.0873993	+	0.520410i
$34$	5.69654	−	0.858615i	0.976949	−	0.147251i
$35$	0.794210	−	6.81156i	0.134246	−	1.15136i
$36$	2.26643	−	1.96553i	0.377738	−	0.327588i
$37$	−0.698826	−	0.648416i	−0.114886	−	0.106599i	0.620638	−	0.784097i	$-0.286874\pi$
$37$	−0.698826	−	0.648416i	−0.114886	−	0.106599i	−0.735524	+	0.677498i	$0.763064\pi$
$38$	−2.34632	+	2.94219i	−0.380623	+	0.477286i
$39$	−4.53626	+	1.69302i	−0.726382	+	0.271100i
$40$	1.61607	+	2.02648i	0.255522	+	0.320415i
$41$	0.239044	+	3.18982i	0.0373324	+	0.498166i	0.984261	+	0.176722i	$0.0565493\pi$
$41$	0.239044	+	3.18982i	0.0373324	+	0.498166i	−0.946928	+	0.321445i	$0.895832\pi$
$42$	−2.91675	−	3.53449i	−0.450064	−	0.545383i
$43$	−0.537681	+	7.17485i	−0.0819956	+	1.09416i	0.792742	+	0.609558i	$0.208653\pi$
$43$	−0.537681	+	7.17485i	−0.0819956	+	1.09416i	−0.874737	+	0.484597i	$0.838966\pi$
$44$	−1.44606	+	0.985910i	−0.218002	+	0.148632i
$45$	6.56820	−	4.16214i	0.979130	−	0.620456i
$46$	−0.0268296	−	0.358016i	−0.00395580	−	0.0527865i
$47$	−7.97634	−	1.20224i	−1.16347	−	0.175365i	−0.461213	−	0.887290i	$-0.652585\pi$
$47$	−7.97634	−	1.20224i	−1.16347	−	0.175365i	−0.702255	+	0.711925i	$0.747824\pi$
$48$	1.72479	+	0.158418i	0.248952	+	0.0228656i
$49$	−5.50647	+	4.32190i	−0.786638	+	0.617414i
$50$	0.859151	+	1.48809i	0.121502	+	0.210448i
$51$	6.90872	−	7.19952i	0.967414	−	1.00813i
$52$	−2.51863	−	1.21291i	−0.349271	−	0.168200i
$53$	−0.700447	+	0.649920i	−0.0962138	+	0.0892734i	−0.726813	−	0.686835i	$-0.759000\pi$
$53$	−0.700447	+	0.649920i	−0.0962138	+	0.0892734i	0.630600	+	0.776108i	$0.282809\pi$
$54$	1.03217	−	5.09260i	0.140461	−	0.693016i
$55$	−4.08716	+	1.96827i	−0.551112	+	0.265402i
$56$	0.306412	−	2.62795i	0.0409460	−	0.351174i
$57$	−0.109438	+	6.51714i	−0.0144954	+	0.863216i
$58$	−0.00619076	−	0.00776296i	−0.000812886	−	0.00101933i
$59$	−0.992564	+	13.2448i	−0.129221	+	1.72433i	0.436473	+	0.899717i	$0.356227\pi$
$59$	−0.992564	+	13.2448i	−0.129221	+	1.72433i	−0.565694	+	0.824615i	$0.691392\pi$
$60$	4.35947	+	1.07234i	0.562805	+	0.138438i
$61$	0.775640	−	0.239253i	0.0993105	−	0.0306332i	−0.244702	−	0.969598i	$-0.578690\pi$
$61$	0.775640	−	0.239253i	0.0993105	−	0.0306332i	0.344012	+	0.938965i	$0.388214\pi$
$62$	−2.19424	+	2.75149i	−0.278669	+	0.349440i
$63$	−7.73815	−	1.76663i	−0.974916	−	0.222575i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−5.98673	−	4.08168i	−0.742563	−	0.506271i
$66$	−0.942029	+	2.88131i	−0.115956	+	0.354665i
$67$	−0.519222	+	0.899320i	−0.0634331	+	0.109869i	−0.895998	−	0.444058i	$-0.853538\pi$
$67$	−0.519222	+	0.899320i	−0.0634331	+	0.109869i	0.832565	+	0.553928i	$0.186872\pi$
$68$	5.76089			0.698610
$69$	−0.415246	−	0.462878i	−0.0499897	−	0.0557240i
$70$	1.80055	−	6.61711i	0.215207	−	0.790896i
$71$	−1.04058	−	4.55906i	−0.123494	−	0.541061i	−0.998389	−	0.0567482i	$-0.981927\pi$
$71$	−1.04058	−	4.55906i	−0.123494	−	0.541061i	0.874895	−	0.484313i	$-0.160930\pi$
$72$	2.53406	−	1.60578i	0.298642	−	0.189243i
$73$	5.86366	−	14.9404i	0.686290	−	1.74864i	0.0236269	−	0.999721i	$-0.492479\pi$
$73$	5.86366	−	14.9404i	0.686290	−	1.74864i	0.662663	−	0.748918i	$-0.269426\pi$
$74$	−0.594379	−	0.745328i	−0.0690952	−	0.0866426i
$75$	2.75181	+	1.13369i	0.317751	+	0.130907i
$76$	−2.75862	+	2.55963i	−0.316436	+	0.293609i
$77$	4.36473	+	1.54629i	0.497407	+	0.176216i
$78$	−4.73792	+	0.998014i	−0.536464	+	0.113003i
$79$	5.03667	+	8.72376i	0.566669	+	0.981500i	0.996892	+	0.0787774i	$0.0251016\pi$
$79$	5.03667	+	8.72376i	0.566669	+	0.981500i	−0.430223	+	0.902723i	$0.641565\pi$
$80$	1.29598	+	2.24471i	0.144895	+	0.250966i
$81$	−3.96677	−	8.07866i	−0.440752	−	0.897629i
$82$	−0.239044	+	3.18982i	−0.0263980	+	0.352257i
$83$	3.62283	−	0.546053i	0.397657	−	0.0599372i	0.0528303	−	0.998604i	$-0.483176\pi$
$83$	3.62283	−	0.546053i	0.397657	−	0.0599372i	0.344827	+	0.938666i	$0.387938\pi$
$84$	−2.35738	−	3.92973i	−0.257211	−	0.428768i
$85$	14.7653	+	2.22550i	1.60152	+	0.241390i
$86$	−1.60103	+	7.01458i	−0.172644	+	0.756402i
$87$	−0.0167001	−	0.00410786i	−0.00179044	−	0.000440409i
$88$	−1.57686	+	0.759373i	−0.168093	+	0.0809495i
$89$	1.37605	−	0.207407i	0.145862	−	0.0219851i	−0.0757056	−	0.997130i	$-0.524121\pi$
$89$	1.37605	−	0.207407i	0.145862	−	0.0219851i	0.221567	+	0.975145i	$0.428883\pi$
$90$	7.11518	−	3.13671i	0.750005	−	0.330639i
$91$	1.34686	+	7.27244i	0.141190	+	0.762359i
$92$	0.0268296	−	0.358016i	0.00279718	−	0.0373257i
$93$	−0.102345	+	6.09473i	−0.0106126	+	0.631995i
$94$	−7.70806	−	2.37762i	−0.795026	−	0.245233i
$95$	−8.05921	+	5.49468i	−0.826858	+	0.563742i
$96$	1.68192	+	0.413715i	0.171660	+	0.0422246i
$97$	4.98514	−	8.63452i	0.506164	−	0.876702i	−0.493810	−	0.869570i	$-0.664396\pi$
$97$	4.98514	−	8.63452i	0.506164	−	0.876702i	0.999975	−	0.00713253i	$-0.00227037\pi$
$98$	−6.08911	+	3.45293i	−0.615093	+	0.348799i
$99$	1.75305	+	4.94923i	0.176188	+	0.497416i
$100$	0.627766	+	1.59952i	0.0627766	+	0.159952i
$101$	−8.66360	−	4.17217i	−0.862060	−	0.415146i	−0.0500203	−	0.998748i	$-0.515929\pi$
$101$	−8.66360	−	4.17217i	−0.862060	−	0.415146i	−0.812040	+	0.583602i	$0.801643\pi$
$102$	7.90458	−	6.08941i	0.782670	−	0.602942i
$103$	−9.33496	−	4.49548i	−0.919801	−	0.442953i	−0.0868009	−	0.996226i	$-0.527664\pi$
$103$	−9.33496	−	4.49548i	−0.919801	−	0.442953i	−0.833000	+	0.553273i	$0.813379\pi$
$104$	−2.30972	−	1.57474i	−0.226487	−	0.154416i
$105$	−4.52391	−	10.9826i	−0.441488	−	1.07180i
$106$	−0.789490	+	0.538265i	−0.0766820	+	0.0522809i
$107$	−16.9597	+	2.55626i	−1.63955	+	0.247123i	−0.903121	−	0.429386i	$-0.858730\pi$
$107$	−16.9597	+	2.55626i	−1.63955	+	0.247123i	−0.736434	+	0.676510i	$0.763492\pi$
$108$	1.77966	−	4.88189i	0.171248	−	0.469760i
$109$	4.45235	+	0.671083i	0.426457	+	0.0642781i	0.358765	−	0.933428i	$-0.383198\pi$
$109$	4.45235	+	0.671083i	0.426457	+	0.0642781i	0.0676929	+	0.997706i	$0.478436\pi$
$110$	−4.33487	+	1.33713i	−0.413313	+	0.127490i
$111$	−1.60339	−	0.394399i	−0.152187	−	0.0374347i
$112$	0.694665	−	2.55293i	0.0656397	−	0.241229i
$113$	5.04725	−	12.8602i	0.474805	−	1.20978i	−0.470151	−	0.882586i	$-0.655801\pi$
$113$	5.04725	−	12.8602i	0.474805	−	1.20978i	0.944956	−	0.327197i	$-0.106104\pi$
$114$	−1.07954	+	6.42803i	−0.101109	+	0.602041i
$115$	0.207071	−	0.907236i	0.0193095	−	0.0846002i
$116$	−0.00496460	−	0.00859894i	−0.000460952	−	0.000798392i
$117$	−5.44603	+	6.37750i	−0.503486	+	0.589600i
$118$	−2.95552	+	12.9490i	−0.272078	+	1.19205i
$119$	−9.00336	−	12.2985i	−0.825337	−	1.12741i
$120$	4.15096	+	1.71011i	0.378929	+	0.156111i
$121$	1.76612	+	7.73789i	0.160557	+	0.703444i
$122$	0.802635	−	0.120978i	0.0726672	−	0.0109528i
$123$	3.04373	+	4.62947i	0.274444	+	0.417425i
$124$	−2.57982	+	2.39373i	−0.231675	+	0.214963i
$125$	−1.89278	−	8.29279i	−0.169295	−	0.741730i
$126$	−7.38842	−	2.90021i	−0.658213	−	0.258371i
$127$	1.08123	−	4.73719i	0.0959439	−	0.420358i	−0.904031	−	0.427467i	$-0.859406\pi$
$127$	1.08123	−	4.73719i	0.0959439	−	0.420358i	0.999975	+	0.00710962i	$0.00226308\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.21781	+	11.3171i	0.459402	+	0.996418i
$130$	−5.31152	−	4.92837i	−0.465851	−	0.432247i
$131$	11.8483	−	5.70584i	1.03519	−	0.498521i	0.162456	−	0.986716i	$-0.448059\pi$
$131$	11.8483	−	5.70584i	1.03519	−	0.498521i	0.872735	+	0.488194i	$0.162344\pi$
$132$	−1.36094	+	2.70873i	−0.118455	+	0.235764i
$133$	9.77567	+	1.88891i	0.847658	+	0.163789i
$134$	−0.647460	+	0.811889i	−0.0559320	+	0.0701365i
$135$	6.44723	−	11.8249i	0.554889	−	1.01772i
$136$	5.69654	+	0.858615i	0.488474	+	0.0736257i
$137$	−16.8773	+	8.12769i	−1.44193	+	0.694396i	−0.981173	−	0.193132i	$-0.938136\pi$
$137$	−16.8773	+	8.12769i	−1.44193	+	0.694396i	−0.460755	+	0.887527i	$0.652421\pi$
$138$	−0.341619	−	0.519598i	−0.0290806	−	0.0442311i
$139$	0.713257	+	9.51776i	0.0604977	+	0.807286i	0.942108	+	0.335308i	$0.108840\pi$
$139$	0.713257	+	9.51776i	0.0604977	+	0.807286i	−0.881611	+	0.471977i	$0.843540\pi$
$140$	2.76667	−	6.27484i	0.233826	−	0.530321i
$141$	−13.0895	+	4.88527i	−1.10234	+	0.411414i
$142$	−0.349461	−	4.66323i	−0.0293261	−	0.391330i
$143$	3.58650	−	3.32779i	0.299918	−	0.278284i
$144$	2.74509	−	1.21017i	0.228757	−	0.100847i
$145$	−0.00940249	−	0.0239571i	−0.000780834	−	0.00198953i
$146$	8.02492	−	13.8996i	0.664147	−	1.15034i
$147$	−4.70510	+	11.1742i	−0.388070	+	0.921630i
$148$	−0.476655	−	0.825591i	−0.0391808	−	0.0678632i
$149$	1.05150	−	1.31854i	0.0861424	−	0.108019i	−0.736893	−	0.676010i	$-0.763708\pi$
$149$	1.05150	−	1.31854i	0.0861424	−	0.108019i	0.823035	+	0.567991i	$0.192279\pi$
$150$	2.55210	+	1.53116i	0.208378	+	0.125019i
$151$	2.53609	+	11.1113i	0.206384	+	0.904228i	0.966950	+	0.254967i	$0.0820645\pi$
$151$	2.53609	+	11.1113i	0.206384	+	0.904228i	−0.760566	+	0.649261i	$0.775078\pi$
$152$	−3.10930	+	2.11989i	−0.252198	+	0.171945i
$153$	4.40930	−	16.7107i	0.356471	−	1.35098i
$154$	4.08551	+	2.17954i	0.329220	+	0.175633i
$155$	−7.53686	+	5.13855i	−0.605376	+	0.412738i
$156$	−4.83375	+	0.280716i	−0.387010	+	0.0224753i
$157$	0.444440	−	5.93064i	0.0354702	−	0.473317i	−0.950980	−	0.309254i	$-0.899921\pi$
$157$	0.444440	−	5.93064i	0.0354702	−	0.473317i	0.986450	−	0.164063i	$-0.0524602\pi$
$158$	3.68020	+	9.37700i	0.292781	+	0.745994i
$159$	−0.514308	+	1.57307i	−0.0407873	+	0.124753i
$160$	0.946953	+	2.41280i	0.0748632	+	0.190748i
$161$	−0.806235	+	0.502246i	−0.0635402	+	0.0395825i
$162$	−2.71840	−	8.57965i	−0.213577	−	0.674081i
$163$	−0.934878	+	12.4751i	−0.0732253	+	0.977124i	0.832710	+	0.553709i	$0.186788\pi$
$163$	−0.934878	+	12.4751i	−0.0732253	+	0.977124i	−0.905936	+	0.423415i	$0.860831\pi$
$164$	−0.711792	+	3.11857i	−0.0555816	+	0.243519i
$165$	−4.53454	+	6.41676i	−0.353014	+	0.499544i
$166$	3.66375			0.284362
$167$	5.23785	−	1.61566i	0.405317	−	0.125024i	−0.0853918	−	0.996347i	$-0.527214\pi$
$167$	5.23785	−	1.61566i	0.405317	−	0.125024i	0.490709	+	0.871324i	$0.336738\pi$
$168$	−1.74536	−	4.23718i	−0.134657	−	0.326906i
$169$	−4.95499	−	1.52841i	−0.381153	−	0.117570i
$170$	14.2686	+	4.40129i	1.09436	+	0.337564i
$171$	5.31335	+	9.96109i	0.406322	+	0.761744i
$172$	−2.62862	+	6.69761i	−0.200430	+	0.510688i
$173$	−5.50629	+	5.10909i	−0.418635	+	0.388437i	−0.861172	−	0.508314i	$-0.830269\pi$
$173$	−5.50629	+	5.10909i	−0.418635	+	0.388437i	0.442537	+	0.896750i	$0.354079\pi$
$174$	−0.0159013	−	0.00655100i	−0.00120548	−	0.000496630i
$175$	2.43362	−	3.83998i	0.183964	−	0.290275i
$176$	−1.67242	+	0.515874i	−0.126064	+	0.0388855i
$177$	9.63212	+	20.8915i	0.723995	+	1.57030i
$178$	1.39160			0.104305
$179$	−16.4698	+	5.08027i	−1.23101	+	0.379717i	−0.840971	−	0.541080i	$-0.818016\pi$
$179$	−16.4698	+	5.08027i	−1.23101	+	0.379717i	−0.390042	+	0.920797i	$0.627540\pi$
$180$	7.50321	−	2.04122i	0.559256	−	0.152143i
$181$	11.0002	+	13.7938i	0.817640	+	1.02529i	0.999122	+	0.0418941i	$0.0133392\pi$
$181$	11.0002	+	13.7938i	0.817640	+	1.02529i	−0.181482	+	0.983394i	$0.558089\pi$
$182$	0.247919	+	7.39196i	0.0183769	+	0.547928i
$183$	0.973429	−	1.01440i	0.0719579	−	0.0749868i
$184$	0.0798894	−	0.350018i	0.00588952	−	0.0258037i
$185$	−0.902740	−	2.30014i	−0.0663707	−	0.169110i
$186$	−1.00957	+	6.01141i	−0.0740256	+	0.440778i
$187$	−3.68358	+	9.38560i	−0.269370	+	0.686343i
$188$	−7.26760	−	3.49989i	−0.530044	−	0.255256i
$189$	−13.2033	+	3.83035i	−0.960402	+	0.278617i
$190$	−8.78814	+	4.23214i	−0.637559	+	0.307032i
$191$	−0.360782	−	4.81430i	−0.0261052	−	0.348350i	−0.994928	−	0.100594i	$-0.967926\pi$
$191$	−0.360782	−	4.81430i	−0.0261052	−	0.348350i	0.968822	−	0.247757i	$-0.0796933\pi$
$192$	1.60147	+	0.659771i	0.115576	+	0.0476149i
$193$	−10.1804	+	6.94090i	−0.732803	+	0.499617i	−0.871303	−	0.490746i	$-0.836724\pi$
$193$	−10.1804	+	6.94090i	−0.732803	+	0.499617i	0.138500	+	0.990362i	$0.455772\pi$
$194$	6.21637	−	7.79508i	0.446309	−	0.559654i
$195$	−12.4974	−	1.14786i	−0.894960	−	0.0821998i
$196$	−6.53573	+	2.50683i	−0.466838	+	0.179059i
$197$	5.23516			0.372990			0.186495	−	0.982456i	$-0.440287\pi$
$197$	5.23516			0.372990			0.186495	+	0.982456i	$0.440287\pi$
$198$	0.995827	+	5.15523i	0.0707704	+	0.366366i
$199$	−1.73511	−	23.1534i	−0.122999	−	1.64130i	−0.628021	−	0.778196i	$-0.716135\pi$
$199$	−1.73511	−	23.1534i	−0.122999	−	1.64130i	0.505023	−	0.863106i	$-0.331484\pi$
$200$	0.382358	+	1.67522i	0.0270368	+	0.118456i
$201$	−0.0301990	+	1.79839i	−0.00213007	+	0.126848i
$202$	−7.94500	−	5.41681i	−0.559008	−	0.381126i
$203$	−0.0105984	+	0.0240374i	−0.000743864	+	0.00168710i
$204$	8.72388	−	4.84328i	0.610794	−	0.339098i
$205$	−3.02908	+	7.71797i	−0.211560	+	0.539046i
$206$	−8.56068	−	5.83657i	−0.596451	−	0.406653i
$207$	−1.01797	−	0.351845i	−0.0707537	−	0.0244550i
$208$	−2.04922	−	1.90140i	−0.142088	−	0.131838i
$209$	−2.40623	−	6.13098i	−0.166443	−	0.424089i
$210$	−2.83650	−	11.5342i	−0.195737	−	0.795938i
$211$	−5.99416	+	15.2729i	−0.412655	+	1.05143i	0.561885	+	0.827215i	$0.310076\pi$
$211$	−5.99416	+	15.2729i	−0.412655	+	1.05143i	−0.974540	+	0.224213i	$0.928019\pi$
$212$	−0.860896	+	0.414586i	−0.0591266	+	0.0284739i
$213$	−5.40866	−	6.02909i	−0.370595	−	0.413106i
$214$	−17.1513			−1.17244
$215$	−9.32457	+	16.1506i	−0.635931	+	1.10146i
$216$	2.48739	−	4.56212i	0.169245	−	0.310413i
$217$	9.14207	+	1.76648i	0.620604	+	0.119916i
$218$	4.30260	+	1.32718i	0.291409	+	0.0898877i
$219$	−3.68113	−	27.5543i	−0.248748	−	1.86195i
$220$	−4.48574	+	0.676116i	−0.302428	+	0.0455837i
$221$	−15.9245	+	2.40023i	−1.07120	+	0.161457i
$222$	−1.52670	−	0.628966i	−0.102465	−	0.0422135i
$223$	15.3038	+	4.72058i	1.02482	+	0.316114i	0.761202	−	0.648515i	$-0.224610\pi$
$223$	15.3038	+	4.72058i	1.02482	+	0.316114i	0.263613	+	0.964628i	$0.415086\pi$
$224$	1.06740	−	2.42088i	0.0713187	−	0.161752i
$225$	5.12025	−	0.596722i	0.341350	−	0.0397815i
$226$	6.90758	−	11.9643i	0.459485	−	0.795852i
$227$	21.8450			1.44990			0.724951	−	0.688800i	$-0.241862\pi$
$227$	21.8450			1.44990			0.724951	+	0.688800i	$0.241862\pi$
$228$	−2.02554	+	6.19534i	−0.134144	+	0.410296i
$229$	−13.6190	+	6.55856i	−0.899968	+	0.433402i	−0.825877	−	0.563850i	$-0.809320\pi$
$229$	−13.6190	+	6.55856i	−0.899968	+	0.433402i	−0.0740905	+	0.997252i	$0.523605\pi$
$230$	0.339975	−	0.866241i	0.0224173	−	0.0571182i
$231$	7.90962	−	1.32792i	0.520415	−	0.0873707i
$232$	−0.00362755	−	0.00924284i	−0.000238160	−	0.000606822i
$233$	19.1960	+	17.8112i	1.25757	+	1.16685i	0.978425	+	0.206604i	$0.0662413\pi$
$233$	19.1960	+	17.8112i	1.25757	+	1.16685i	0.279144	+	0.960249i	$0.409949\pi$
$234$	−6.33572	+	5.49458i	−0.414179	+	0.359192i
$235$	−17.2749	−	11.7779i	−1.12689	−	0.768303i
$236$	−4.85246	+	12.3639i	−0.315868	+	0.804818i
$237$	14.9614	+	8.97623i	0.971847	+	0.583069i
$238$	−7.06980	−	13.5031i	−0.458267	−	0.875273i
$239$	−19.4302	−	13.2473i	−1.25683	−	0.856894i	−0.262680	−	0.964883i	$-0.584606\pi$
$239$	−19.4302	−	13.2473i	−1.25683	−	0.856894i	−0.994152	+	0.107989i	$0.965559\pi$
$240$	3.84972	+	2.30967i	0.248498	+	0.149089i
$241$	−1.07126	−	4.69349i	−0.0690059	−	0.302335i	0.928634	−	0.370997i	$-0.120984\pi$
$241$	−1.07126	−	4.69349i	−0.0690059	−	0.302335i	−0.997640	+	0.0686625i	$0.978127\pi$
$242$	0.593124	+	7.91469i	0.0381274	+	0.508775i
$243$	−12.7989	−	8.89882i	−0.821048	−	0.570860i
$244$	0.811701			0.0519638
$245$	−17.7196	+	3.90021i	−1.13207	+	0.249176i
$246$	2.31975	+	5.03141i	0.147902	+	0.320791i
$247$	6.55905	−	8.22479i	0.417343	−	0.523331i
$248$	−2.90778	+	1.98249i	−0.184644	+	0.125888i
$249$	5.02708	−	3.87268i	0.318578	−	0.245421i
$250$	−0.635659	−	8.48227i	−0.0402026	−	0.536466i
$251$	14.1772	−	6.82740i	0.894859	−	0.430942i	0.0708298	−	0.997488i	$-0.477435\pi$
$251$	14.1772	−	6.82740i	0.894859	−	0.430942i	0.824029	+	0.566547i	$0.191721\pi$
$252$	−6.87365	−	3.96901i	−0.432999	−	0.250024i
$253$	0.566122	+	0.272630i	0.0355918	+	0.0171401i
$254$	1.77520	−	4.52313i	0.111386	−	0.283806i
$255$	24.2305	−	9.04328i	1.51737	−	0.566312i
$256$	0.365341	+	0.930874i	0.0228338	+	0.0581796i
$257$	5.24647	−	22.9863i	0.327266	−	1.43384i	−0.497054	−	0.867720i	$-0.665585\pi$
$257$	5.24647	−	22.9863i	0.327266	−	1.43384i	0.824320	−	0.566125i	$-0.191558\pi$
$258$	3.47280	+	11.9684i	0.216207	+	0.745120i
$259$	−1.01756	+	2.30785i	−0.0632283	+	0.143403i
$260$	−4.51766	−	5.66497i	−0.280173	−	0.351326i
$261$	−0.0287430	+	0.00781941i	−0.00177915	+	0.000484010i
$262$	12.5664	−	3.87621i	0.776353	−	0.239473i
$263$	0.743896			0.0458706			0.0229353	−	0.999737i	$-0.492699\pi$
$263$	0.743896			0.0458706			0.0229353	+	0.999737i	$0.492699\pi$
$264$	−1.74946	+	2.47563i	−0.107672	+	0.152365i
$265$	−2.36665	+	0.730015i	−0.145382	+	0.0448445i
$266$	9.38496	+	3.32480i	0.575429	+	0.203856i
$267$	1.90943	−	1.47096i	0.116855	−	0.0900211i
$268$	−0.761234	+	0.706322i	−0.0464998	+	0.0431455i
$269$	9.14496	−	23.3010i	0.557578	−	1.42069i	−0.322824	−	0.946459i	$-0.604632\pi$
$269$	9.14496	−	23.3010i	0.557578	−	1.42069i	0.880402	−	0.474227i	$-0.157272\pi$
$270$	8.13762	−	10.7319i	0.495240	−	0.653121i
$271$	24.7185	+	7.62466i	1.50154	+	0.463165i	0.933118	−	0.359569i	$-0.117076\pi$
$271$	24.7185	+	7.62466i	1.50154	+	0.463165i	0.568426	+	0.822734i	$0.307553\pi$
$272$	5.50495	+	1.69805i	0.333786	+	0.102959i
$273$	8.15367	+	9.88054i	0.493483	+	0.597997i
$274$	−17.9002	+	5.52148i	−1.08139	+	0.333565i
$275$	−3.00733			−0.181349
$276$	−0.260362	−	0.564710i	−0.0156719	−	0.0339915i
$277$	1.73290	−	7.59234i	0.104120	−	0.456179i	−0.895811	−	0.444435i	$-0.853404\pi$
$277$	1.73290	−	7.59234i	0.104120	−	0.456179i	0.999931	−	0.0117443i	$-0.00373842\pi$
$278$	−0.713257	+	9.51776i	−0.0427783	+	0.570837i
$279$	4.96897	+	9.31548i	0.297485	+	0.557703i
$280$	3.67098	−	5.79241i	0.219383	−	0.346163i
$281$	−1.38938	−	3.54008i	−0.0828833	−	0.211183i	0.883424	−	0.468575i	$-0.155232\pi$
$281$	−1.38938	−	3.54008i	−0.0828833	−	0.211183i	−0.966307	+	0.257391i	$0.917137\pi$
$282$	−13.6715	+	2.87981i	−0.814123	+	0.171490i
$283$	−10.2986	−	26.2404i	−0.612188	−	1.55983i	−0.814286	−	0.580463i	$-0.802871\pi$
$283$	−10.2986	−	26.2404i	−0.612188	−	1.55983i	0.202099	−	0.979365i	$-0.435224\pi$
$284$	0.349461	−	4.66323i	0.0207367	−	0.276712i
$285$	−7.58482	+	15.0963i	−0.449286	+	0.894227i
$286$	4.04243	−	2.75608i	0.239034	−	0.162970i
$287$	7.77004	−	3.35427i	0.458651	−	0.197996i
$288$	2.89479	−	0.787517i	0.170577	−	0.0464049i
$289$	13.3750	−	9.11891i	0.786764	−	0.536407i
$290$	−0.00572684	−	0.0250909i	−0.000336292	−	0.00147339i
$291$	0.289946	−	17.2666i	0.0169969	−	1.01219i
$292$	10.0069	−	12.5483i	0.585610	−	0.734332i
$293$	−13.8753	−	24.0326i	−0.810601	−	1.40400i	−0.912444	−	0.409202i	$-0.865807\pi$
$293$	−13.8753	−	24.0326i	−0.810601	−	1.40400i	0.101843	−	0.994801i	$-0.467526\pi$
$294$	−6.31797	+	10.3481i	−0.368472	+	0.603514i
$295$	−17.2133	+	29.8142i	−1.00219	+	1.73585i
$296$	−0.348283	−	0.887412i	−0.0202436	−	0.0515797i
$297$	6.81561	+	6.02094i	0.395482	+	0.349370i
$298$	1.23628	−	1.14710i	0.0716155	−	0.0664495i
$299$	0.0750012	+	1.00082i	0.00433743	+	0.0578790i
$300$	2.29539	+	1.89443i	0.132525	+	0.109375i
$301$	18.4064	−	4.85565i	1.06093	−	0.279875i
$302$	0.851705	+	11.3652i	0.0490101	+	0.653995i
$303$	−16.6272	+	0.965610i	−0.955205	+	0.0554728i
$304$	−3.39053	+	1.63279i	−0.194460	+	0.0936470i
$305$	2.08041	+	0.313571i	0.119124	+	0.0179550i
$306$	6.85066	−	15.8669i	0.391626	−	0.907051i
$307$	−3.86107	+	4.84162i	−0.220363	+	0.276326i	−0.879708	−	0.475514i	$-0.842262\pi$
$307$	−3.86107	+	4.84162i	−0.220363	+	0.276326i	0.659345	+	0.751840i	$0.270833\pi$
$308$	3.71504	+	2.76412i	0.211684	+	0.157500i
$309$	−17.9156	+	1.04044i	−1.01918	+	0.0591884i
$310$	−8.21854	+	3.95784i	−0.466782	+	0.224790i
$311$	−20.5710	−	19.0871i	−1.16648	−	1.08233i	−0.995275	−	0.0970964i	$-0.969045\pi$
$311$	−20.5710	−	19.0871i	−1.16648	−	1.08233i	−0.171202	−	0.985236i	$-0.554765\pi$
$312$	−4.82160	−	0.442852i	−0.272969	−	0.0250715i
$313$	7.25309	+	12.5627i	0.409969	+	0.710087i	0.994886	−	0.101006i	$-0.0322062\pi$
$313$	7.25309	+	12.5627i	0.409969	+	0.710087i	−0.584917	+	0.811093i	$0.698873\pi$
$314$	1.32339	−	5.79816i	0.0746834	−	0.327209i
$315$	−16.0840	−	12.8280i	−0.906231	−	0.722777i
$316$	2.24153	+	9.82078i	0.126096	+	0.552462i
$317$	−3.75077	+	3.48021i	−0.210664	+	0.195468i	−0.778447	−	0.627711i	$-0.783992\pi$
$317$	−3.75077	+	3.48021i	−0.210664	+	0.195468i	0.567782	+	0.823179i	$0.307802\pi$
$318$	−0.743018	+	1.47885i	−0.0416664	+	0.0829297i
$319$	0.0171838	−	0.00259004i	0.000962106	−	0.000145014i
$320$	0.576767	+	2.52698i	0.0322423	+	0.141263i
$321$	−23.5334	+	18.1293i	−1.31351	+	1.01188i
$322$	−0.872086	+	0.376473i	−0.0485994	+	0.0209800i
$323$	−4.82411	+	21.1358i	−0.268421	+	1.17603i
$324$	−1.40931	−	8.88897i	−0.0782948	−	0.493832i
$325$	−2.40173	−	4.15992i	−0.133224	−	0.230751i
$326$	−2.78375	+	12.1964i	−0.154178	+	0.675497i
$327$	7.30651	−	2.72693i	0.404051	−	0.150799i
$328$	−1.16864	+	2.97765i	−0.0645274	+	0.164413i
$329$	3.88643	+	20.9849i	0.214266	+	1.15694i
$330$	−5.44026	+	5.66925i	−0.299477	+	0.312082i
$331$	19.5253	−	6.02275i	1.07321	−	0.331040i	0.292711	−	0.956201i	$-0.405443\pi$
$331$	19.5253	−	6.02275i	1.07321	−	0.331040i	0.780496	+	0.625161i	$0.214967\pi$
$332$	3.62283	+	0.546053i	0.198829	+	0.0299686i
$333$	−2.75963	+	0.750748i	−0.151227	+	0.0411407i
$334$	5.42015	−	0.816956i	0.296577	−	0.0447018i
$335$	−2.22392	+	1.51624i	−0.121506	+	0.0828411i
$336$	−1.09434	−	4.44999i	−0.0597013	−	0.242767i
$337$	7.66210	+	5.22393i	0.417381	+	0.284566i	0.753746	−	0.657166i	$-0.228245\pi$
$337$	7.66210	+	5.22393i	0.417381	+	0.284566i	−0.336365	+	0.941732i	$0.609197\pi$
$338$	−4.67185	−	2.24984i	−0.254115	−	0.122375i
$339$	−3.16859	−	23.7178i	−0.172094	−	1.28818i
$340$	13.4533	+	6.47877i	0.729608	+	0.351360i
$341$	−2.25028	−	5.73361i	−0.121859	−	0.310492i
$342$	3.76938	+	10.6418i	0.203825	+	0.575440i
$343$	15.5660	+	10.0349i	0.840485	+	0.541835i
$344$	−3.59749	+	6.23103i	−0.193963	+	0.335955i
$345$	−0.449157	−	1.54794i	−0.0241818	−	0.0833384i
$346$	−6.20626	+	4.23135i	−0.333650	+	0.227479i
$347$	−27.0679	−	8.34934i	−1.45308	−	0.448216i	−0.535082	−	0.844800i	$-0.679719\pi$
$347$	−27.0679	−	8.34934i	−1.45308	−	0.448216i	−0.917998	+	0.396584i	$0.870195\pi$
$348$	−0.0147473	−	0.00884780i	−0.000790540	−	0.000474292i
$349$	−2.42913	+	32.4145i	−0.130028	+	1.73511i	0.426684	+	0.904401i	$0.359682\pi$
$349$	−2.42913	+	32.4145i	−0.130028	+	1.73511i	−0.556712	+	0.830705i	$0.687937\pi$
$350$	2.97875	−	3.43438i	0.159221	−	0.183575i
$351$	−2.88540	+	14.2362i	−0.154012	+	0.759873i
$352$	−1.73063	+	0.260850i	−0.0922428	+	0.0139034i
$353$	26.4497	−	12.7375i	1.40778	−	0.677949i	0.433053	−	0.901368i	$-0.357436\pi$
$353$	26.4497	−	12.7375i	1.40778	−	0.677949i	0.974722	+	0.223419i	$0.0717219\pi$
$354$	6.41082	+	22.0938i	0.340731	+	1.17427i
$355$	2.69714	−	11.8169i	0.143149	−	0.627178i
$356$	1.37605	+	0.207407i	0.0729308	+	0.0109925i
$357$	−23.9737	−	11.0547i	−1.26882	−	0.585079i
$358$	−17.0431	+	2.56883i	−0.900754	+	0.135767i
$359$	−0.0244431	+	0.326170i	−0.00129006	+	0.0172146i	−0.997812	−	0.0661200i	$-0.978938\pi$
$359$	−0.0244431	+	0.326170i	−0.00129006	+	0.0172146i	0.996522	+	0.0833346i	$0.0265570\pi$
$360$	7.72363	−	0.900124i	0.407071	−	0.0474407i
$361$	2.41916	+	4.19011i	0.127324	+	0.220532i
$362$	8.82150	+	15.2793i	0.463647	+	0.803061i
$363$	9.17987	+	10.2329i	0.481818	+	0.537088i
$364$	−0.856564	+	7.34634i	−0.0448962	+	0.385053i
$365$	30.4955	−	28.2956i	1.59621	−	1.48106i
$366$	1.11375	−	0.857990i	0.0582164	−	0.0448479i
$367$	−16.3514	−	20.5040i	−0.853536	−	1.07030i	−0.996746	−	0.0806078i	$-0.974314\pi$
$367$	−16.3514	−	20.5040i	−0.853536	−	1.07030i	0.143210	−	0.989692i	$-0.454258\pi$
$368$	0.131165	−	0.334202i	0.00683743	−	0.0174215i
$369$	8.50129	+	4.45162i	0.442560	+	0.231742i
$370$	−0.549838	−	2.40900i	−0.0285847	−	0.125238i
$371$	2.23052	+	1.18994i	0.115803	+	0.0617785i
$372$	−1.89425	+	5.79380i	−0.0982124	+	0.300394i
$373$	−14.2494			−0.737808			−0.368904	−	0.929467i	$-0.620267\pi$
$373$	−14.2494			−0.737808			−0.368904	+	0.929467i	$0.620267\pi$
$374$	−5.04129	+	8.73176i	−0.260679	+	0.451509i
$375$	−9.83819	−	10.9667i	−0.508042	−	0.566319i
$376$	−6.66480	−	4.54398i	−0.343711	−	0.234338i
$377$	0.0173061	+	0.0217011i	0.000891308	+	0.00111766i
$378$	−13.6268	+	1.81971i	−0.700885	+	0.0935957i
$379$	14.6762	−	18.4033i	0.753863	−	0.945315i	−0.245849	−	0.969308i	$-0.579067\pi$
$379$	14.6762	−	18.4033i	0.753863	−	0.945315i	0.999712	+	0.0239936i	$0.00763813\pi$
$380$	−9.32075	+	2.87507i	−0.478144	+	0.147488i
$381$	−2.34530	−	8.08268i	−0.120153	−	0.414088i
$382$	0.360782	−	4.81430i	0.0184592	−	0.246321i
$383$	16.7130	+	20.9574i	0.853995	+	1.07088i	0.996705	+	0.0811110i	$0.0258468\pi$
$383$	16.7130	+	20.9574i	0.853995	+	1.07088i	−0.142710	+	0.989764i	$0.545582\pi$
$384$	1.48525	+	0.891088i	0.0757937	+	0.0454732i
$385$	8.45390	+	8.51965i	0.430851	+	0.434201i
$386$	−11.1012	+	5.34606i	−0.565036	+	0.272107i
$387$	17.4160	+	12.7512i	0.885305	+	0.648177i
$388$	7.30873	−	6.78151i	0.371045	−	0.344279i
$389$	−26.1300	−	12.5836i	−1.32485	−	0.638012i	−0.368330	−	0.929695i	$-0.620070\pi$
$389$	−26.1300	−	12.5836i	−1.32485	−	0.638012i	−0.956515	+	0.291683i	$0.905785\pi$
$390$	−12.1868	−	2.99768i	−0.617101	−	0.151794i
$391$	−1.03414	−	1.79118i	−0.0522985	−	0.0905836i
$392$	−6.83636	+	1.50473i	−0.345288	+	0.0760004i
$393$	13.1452	−	18.6016i	0.663088	−	0.938327i
$394$	5.17669	+	0.780260i	0.260798	+	0.0393089i
$395$	1.95119	+	26.0368i	0.0981748	+	1.31005i
$396$	0.216357	+	5.24607i	0.0108724	+	0.263625i
$397$	29.7697	−	20.2966i	1.49410	−	1.01866i	0.506399	−	0.862300i	$-0.330976\pi$
$397$	29.7697	−	20.2966i	1.49410	−	1.01866i	0.987700	−	0.156360i	$-0.0499759\pi$
$398$	1.73511	−	23.1534i	0.0869731	−	1.16058i
$399$	16.3916	−	5.35816i	0.820608	−	0.268244i
$400$	0.128409	+	1.71350i	0.00642044	+	0.0856749i
$401$	4.32429	+	5.42249i	0.215945	+	0.270786i	0.877991	−	0.478676i	$-0.158883\pi$
$401$	4.32429	+	5.42249i	0.215945	+	0.270786i	−0.662047	+	0.749463i	$0.730312\pi$
$402$	−0.297897	+	1.77380i	−0.0148578	+	0.0884690i
$403$	6.13394	−	7.69171i	0.305553	−	0.383151i
$404$	−7.04893	−	6.54045i	−0.350697	−	0.325400i
$405$	−0.178151	−	23.3270i	−0.00885242	−	1.15913i
$406$	−0.0140626	+	0.0221893i	−0.000697918	+	0.00110124i
$407$	1.64983	−	0.248671i	0.0817789	−	0.0123262i
$408$	9.34829	−	3.48896i	0.462809	−	0.172729i
$409$	11.5512	+	10.7179i	0.571168	+	0.529966i	0.912017	−	0.410151i	$-0.134524\pi$
$409$	11.5512	+	10.7179i	0.571168	+	0.529966i	−0.340849	+	0.940118i	$0.610715\pi$
$410$	−4.14555	+	7.18030i	−0.204734	+	0.354610i
$411$	−18.7247	+	26.4971i	−0.923623	+	1.30700i
$412$	−7.59517	−	7.04729i	−0.374187	−	0.347195i
$413$	33.9784	−	8.96357i	1.67197	−	0.441068i
$414$	−0.954159	−	0.499636i	−0.0468944	−	0.0245558i
$415$	9.07443	+	2.79909i	0.445446	+	0.137402i
$416$	−1.74295	−	2.18558i	−0.0854549	−	0.107157i
$417$	9.08186	+	13.8134i	0.444741	+	0.676443i
$418$	−1.46558	−	6.42114i	−0.0716840	−	0.314068i
$419$	2.65630	−	2.46469i	0.129769	−	0.120408i	−0.612619	−	0.790379i	$-0.709884\pi$
$419$	2.65630	−	2.46469i	0.129769	−	0.120408i	0.742387	+	0.669971i	$0.233693\pi$
$420$	−1.08573	−	11.8282i	−0.0529783	−	0.577155i
$421$	9.78347	+	9.07774i	0.476817	+	0.442422i	0.881604	−	0.471989i	$-0.156464\pi$
$421$	9.78347	+	9.07774i	0.476817	+	0.442422i	−0.404787	+	0.914411i	$0.632654\pi$
$422$	−8.20352	+	14.2089i	−0.399341	+	0.691679i
$423$	−15.7147	+	18.4025i	−0.764077	+	0.894761i
$424$	−0.913071	+	0.281645i	−0.0443427	+	0.0136779i
$425$	8.17889	+	5.57627i	0.396734	+	0.270489i
$426$	−4.44966	−	6.76787i	−0.215587	−	0.327904i
$427$	−1.26856	−	1.73285i	−0.0613900	−	0.0838584i
$428$	−16.9597	−	2.55626i	−0.819777	−	0.123562i
$429$	2.63341	−	8.05461i	0.127142	−	0.388880i
$430$	−11.6276	+	14.5805i	−0.560730	+	0.703134i
$431$	7.95982	+	5.42692i	0.383411	+	0.261405i	0.739653	−	0.672989i	$-0.234990\pi$
$431$	7.95982	+	5.42692i	0.383411	+	0.261405i	−0.356242	+	0.934394i	$0.615942\pi$
$432$	3.13955	−	4.14044i	0.151052	−	0.199207i
$433$	−4.09547	−	1.97227i	−0.196816	−	0.0947815i	0.332880	−	0.942969i	$-0.391980\pi$
$433$	−4.09547	−	1.97227i	−0.196816	−	0.0947815i	−0.529696	+	0.848188i	$0.677694\pi$
$434$	8.77668	+	3.10931i	0.421294	+	0.149251i
$435$	−0.0343797	−	0.0283742i	−0.00164838	−	0.00136044i
$436$	4.05674	+	1.95362i	0.194282	+	0.0935615i
$437$	1.29104	+	0.398233i	0.0617588	+	0.0190501i
$438$	0.466745	−	27.7952i	0.0223020	−	1.32811i
$439$	1.78715	+	0.269369i	0.0852960	+	0.0128563i	0.191552	−	0.981483i	$-0.438648\pi$
$439$	1.78715	+	0.269369i	0.0852960	+	0.0128563i	−0.106256	+	0.994339i	$0.533886\pi$
$440$	−4.53640			−0.216265
$441$	2.26926	+	20.8770i	0.108060	+	0.994144i
$442$	−16.1044			−0.766007
$443$	5.16153	+	0.777975i	0.245231	+	0.0369627i	0.270508	−	0.962718i	$-0.412808\pi$
$443$	5.16153	+	0.777975i	0.245231	+	0.0369627i	−0.0252762	+	0.999681i	$0.508047\pi$
$444$	−1.41590	−	0.849484i	−0.0671957	−	0.0403147i
$445$	3.44673	+	1.06318i	0.163391	+	0.0503993i
$446$	14.4293	+	6.94877i	0.683245	+	0.329034i
$447$	0.483798	−	2.88072i	0.0228828	−	0.136254i
$448$	1.41629	−	2.23475i	0.0669135	−	0.105582i
$449$	32.5651	+	15.6825i	1.53684	+	0.740105i	0.994953	−	0.100343i	$-0.0319941\pi$
$449$	32.5651	+	15.6825i	1.53684	+	0.740105i	0.541891	+	0.840448i	$0.317708\pi$
$450$	5.15200	+	0.173077i	0.242868	+	0.00815891i
$451$	−4.62562	−	3.15370i	−0.217812	−	0.148502i
$452$	8.61361	−	10.8011i	0.405150	−	0.508042i
$453$	13.1820	+	14.6941i	0.619343	+	0.690388i
$454$	21.6010	+	3.25583i	1.01378	+	0.152803i
$455$	−5.03338	+	18.4979i	−0.235968	+	0.867196i
$456$	−2.92628	+	5.82425i	−0.137036	+	0.272746i
$457$	19.5115	+	13.3027i	0.912711	+	0.622276i	0.925954	−	0.377637i	$-0.123263\pi$
$457$	19.5115	+	13.3027i	0.912711	+	0.622276i	−0.0132432	+	0.999912i	$0.504216\pi$
$458$	−14.4444	+	4.45550i	−0.674941	+	0.208192i
$459$	−7.37188	−	29.0125i	−0.344090	−	1.35419i
$460$	0.465284	−	0.805895i	0.0216940	−	0.0375751i
$461$	20.1374	+	18.6847i	0.937890	+	0.870235i	0.991734	−	0.128314i	$-0.0409566\pi$
$461$	20.1374	+	18.6847i	0.937890	+	0.870235i	−0.0538431	+	0.998549i	$0.517147\pi$
$462$	8.01920	−	0.134219i	0.373087	−	0.00624444i
$463$	22.9423	−	21.2873i	1.06622	−	0.989306i	0.0662542	−	0.997803i	$-0.478895\pi$
$463$	22.9423	−	21.2873i	1.06622	−	0.989306i	0.999964	+	0.00849699i	$0.00270471\pi$
$464$	−0.00220946	−	0.00968026i	−0.000102571	−	0.000449395i
$465$	−7.09322	+	14.1178i	−0.328940	+	0.654699i
$466$	16.3269	+	20.4733i	0.756330	+	0.948408i
$467$	4.93353	+	1.52179i	0.228297	+	0.0704202i	0.406793	−	0.913520i	$-0.366647\pi$
$467$	4.93353	+	1.52179i	0.228297	+	0.0704202i	−0.178496	+	0.983941i	$0.557123\pi$
$468$	−7.08388	+	4.48892i	−0.327453	+	0.207500i
$469$	2.69757	+	0.521239i	0.124562	+	0.0240686i
$470$	−15.3266	−	14.2210i	−0.706963	−	0.655966i
$471$	−4.31297	−	9.35460i	−0.198731	−	0.431037i
$472$	−6.64099	+	11.5025i	−0.305677	+	0.529447i
$473$	−9.23094	−	8.56506i	−0.424439	−	0.393822i
$474$	13.4565	+	11.1059i	0.618076	+	0.510109i
$475$	−6.39409	+	0.963754i	−0.293381	+	0.0442201i
$476$	−4.97831	−	14.4059i	−0.228180	−	0.660295i
$477$	0.543679	+	2.81454i	0.0248934	+	0.128869i
$478$	−17.2387	−	15.9952i	−0.788481	−	0.731604i
$479$	18.4730	−	23.1645i	0.844055	−	1.05841i	−0.153474	−	0.988153i	$-0.549046\pi$
$479$	18.4730	−	23.1645i	0.844055	−	1.05841i	0.997529	−	0.0702584i	$-0.0223824\pi$
$480$	3.46248	+	2.85765i	0.158040	+	0.130433i
$481$	1.66157	+	2.08354i	0.0757610	+	0.0950013i
$482$	−0.359765	−	4.80074i	−0.0163869	−	0.218667i
$483$	−0.798658	+	1.43838i	−0.0363402	+	0.0654486i
$484$	−0.593124	+	7.91469i	−0.0269602	+	0.359758i
$485$	21.3522	−	14.5577i	0.969554	−	0.661030i
$486$	−11.3296	−	10.7070i	−0.513922	−	0.485679i
$487$	−3.10600	−	41.4467i	−0.140746	−	1.87813i	−0.405891	−	0.913921i	$-0.633039\pi$
$487$	−3.10600	−	41.4467i	−0.140746	−	1.87813i	0.265145	−	0.964209i	$-0.414580\pi$
$488$	0.802635	+	0.120978i	0.0363336	+	0.00547641i
$489$	9.07232	+	19.6773i	0.410264	+	0.889840i
$490$	−18.1030	+	1.21568i	−0.817811	+	0.0549188i
$491$	7.91211	+	13.7042i	0.357069	+	0.618461i	0.987470	−	0.157808i	$-0.0504429\pi$
$491$	7.91211	+	13.7042i	0.357069	+	0.618461i	−0.630401	+	0.776270i	$0.717110\pi$
$492$	1.54395	+	5.32095i	0.0696066	+	0.239887i
$493$	−0.0515363	−	0.0248186i	−0.00232108	−	0.00111777i
$494$	7.71164	−	7.15535i	0.346963	−	0.321935i
$495$	−1.47210	+	13.5294i	−0.0661659	+	0.608100i
$496$	−3.17077	+	1.52696i	−0.142372	+	0.0685627i
$497$	−10.5014	+	6.54185i	−0.471051	+	0.293442i
$498$	5.54812	−	3.08018i	0.248617	−	0.138026i
$499$	−20.7029	−	25.9606i	−0.926789	−	1.16216i	−0.986470	−	0.163939i	$-0.947580\pi$
$499$	−20.7029	−	25.9606i	−0.926789	−	1.16216i	0.0596812	−	0.998217i	$-0.480992\pi$
$500$	0.635659	−	8.48227i	0.0284275	−	0.379339i
$501$	6.57351	−	6.85020i	0.293683	−	0.306044i
$502$	15.0365	−	4.63813i	0.671110	−	0.207010i
$503$	5.18137	−	6.49724i	0.231026	−	0.289697i	−0.652783	−	0.757545i	$-0.726399\pi$
$503$	5.18137	−	6.49724i	0.231026	−	0.289697i	0.883809	+	0.467847i	$0.154970\pi$
$504$	−6.20532	−	4.94914i	−0.276407	−	0.220452i
$505$	−15.5399	−	19.4864i	−0.691516	−	0.867133i
$506$	0.519165	+	0.353961i	0.0230797	+	0.0157355i
$507$	−8.78845	+	1.85123i	−0.390309	+	0.0822161i
$508$	2.42951	−	4.20803i	0.107792	−	0.186701i
$509$	11.7504			0.520826			0.260413	−	0.965497i	$-0.416141\pi$
$509$	11.7504			0.520826			0.260413	+	0.965497i	$0.416141\pi$
$510$	25.3077	−	5.33091i	1.12064	−	0.236056i
$511$	−42.4277	−	1.75213i	−1.87689	−	0.0775098i
$512$	0.222521	+	0.974928i	0.00983413	+	0.0430861i
$513$	16.4206	+	10.6173i	0.724989	+	0.468767i
$514$	8.61379	−	21.9476i	0.379938	−	0.968067i
$515$	−16.7441	−	20.9964i	−0.737833	−	0.925214i
$516$	1.65021	+	12.3523i	0.0726465	+	0.543780i
$517$	10.3490	−	9.60246i	0.455148	−	0.422316i
$518$	−1.35017	+	2.13041i	−0.0593229	+	0.0936050i
$519$	−4.04303	+	12.3661i	−0.177469	+	0.542811i
$520$	−3.62288	−	6.27502i	−0.158874	−	0.275178i
$521$	−0.0883182	−	0.152972i	−0.00386929	−	0.00670181i	0.864084	−	0.503347i	$-0.167898\pi$
$521$	−0.0883182	−	0.152972i	−0.00386929	−	0.00670181i	−0.867954	+	0.496645i	$0.834565\pi$
$522$	−0.0295874	+	0.00344816i	−0.00129500	+	0.000150922i
$523$	−0.639131	+	8.52862i	−0.0279473	+	0.372930i	0.965642	+	0.259877i	$0.0836821\pi$
$523$	−0.639131	+	8.52862i	−0.0279473	+	0.372930i	−0.993589	+	0.113053i	$0.963937\pi$
$524$	13.0037	−	1.96000i	0.568071	−	0.0856229i
$525$	0.456955	−	7.86098i	0.0199431	−	0.343081i
$526$	0.735588	+	0.110872i	0.0320731	+	0.00483425i
$527$	−4.51144	+	19.7659i	−0.196522	+	0.861017i
$528$	−2.09889	+	2.18724i	−0.0913426	+	0.0951873i
$529$	20.6062	−	9.92340i	0.895920	−	0.431452i
$530$	−2.44902	+	0.369131i	−0.106379	+	0.0160340i
$531$	32.1501	+	23.5387i	1.39520	+	1.02149i
$532$	8.78460	+	4.68642i	0.380861	+	0.203182i
$533$	0.668240	−	8.91704i	0.0289447	−	0.386240i
$534$	2.10734	−	1.16994i	0.0911934	−	0.0506283i
$535$	−42.4805	−	13.1035i	−1.83659	−	0.566513i
$536$	−0.858003	+	0.584977i	−0.0370601	+	0.0252671i
$537$	−20.6697	+	21.5397i	−0.891962	+	0.929507i
$538$	12.5157	−	21.6777i	0.539588	−	0.934594i
$539$	0.0949099	−	12.2509i	0.00408806	−	0.527682i
$540$	9.64624	−	9.39916i	0.415108	−	0.404476i
$541$	14.2208	+	36.2341i	0.611401	+	1.55782i	0.815428	+	0.578858i	$0.196502\pi$
$541$	14.2208	+	36.2341i	0.611401	+	1.55782i	−0.204027	+	0.978965i	$0.565403\pi$
$542$	23.3061	+	11.2236i	1.00108	+	0.482095i
$543$	28.2547	+	11.6403i	1.21253	+	0.499534i
$544$	5.19038	+	2.49955i	0.222536	+	0.107168i
$545$	9.64278	+	6.57434i	0.413051	+	0.281614i
$546$	6.58998	+	10.9854i	0.282025	+	0.470133i
$547$	−36.7633	+	25.0648i	−1.57189	+	1.07169i	−0.612169	+	0.790727i	$0.709703\pi$
$547$	−36.7633	+	25.0648i	−1.57189	+	1.07169i	−0.959717	+	0.280967i	$0.909345\pi$
$548$	−18.5232	+	2.79192i	−0.791272	+	0.119265i
$549$	0.621265	−	2.35452i	0.0265149	−	0.100488i
$550$	−2.97374	−	0.448220i	−0.126801	−	0.0191122i
$551$	0.0357055	−	0.0110137i	0.00152111	−	0.000469199i
$552$	−0.173288	−	0.597207i	−0.00737563	−	0.0254188i
$553$	17.4626	−	20.1336i	0.742585	−	0.856169i
$554$	2.84513	−	7.24926i	0.120878	−	0.307992i
$555$	−3.30082	−	2.72422i	−0.140112	−	0.115637i
$556$	−2.12384	+	9.30515i	−0.0900708	+	0.394626i
$557$	−0.00208915	−	0.00361852i	−8.85202e−5	−	0.000153322i	0.865981	−	0.500077i	$-0.166695\pi$
$557$	−0.00208915	−	0.00361852i	−8.85202e−5	−	0.000153322i	−0.866070	+	0.499923i	$0.833362\pi$
$558$	3.52507	+	9.95202i	0.149228	+	0.421302i
$559$	4.47563	−	19.6090i	0.189299	−	0.829374i
$560$	4.49330	−	5.18058i	0.189876	−	0.218919i
$561$	2.31250	+	17.3097i	0.0976338	+	0.730818i
$562$	−0.846238	−	3.70761i	−0.0356964	−	0.156396i
$563$	26.2384	−	3.95481i	1.10582	−	0.166675i	0.429344	−	0.903141i	$-0.358745\pi$
$563$	26.2384	−	3.95481i	1.10582	−	0.166675i	0.676475	+	0.736466i	$0.263507\pi$
$564$	−13.9480	+	0.810018i	−0.587315	+	0.0341079i
$565$	26.2495	−	24.3559i	1.10432	−	1.02466i
$566$	−6.27264	−	27.4822i	−0.263659	−	1.15516i
$567$	−16.7740	+	16.9007i	−0.704441	+	0.709763i
$568$	1.04058	−	4.55906i	0.0436616	−	0.191294i
$569$	4.22721	+	7.32174i	0.177214	+	0.306943i	0.940925	−	0.338615i	$-0.109958\pi$
$569$	4.22721	+	7.32174i	0.177214	+	0.306943i	−0.763711	+	0.645558i	$0.776625\pi$
$570$	−9.75009	+	13.7972i	−0.408386	+	0.577902i
$571$	17.7907	+	16.5074i	0.744520	+	0.690813i	0.958203	−	0.286090i	$-0.0923555\pi$
$571$	17.7907	+	16.5074i	0.744520	+	0.690813i	−0.213683	+	0.976903i	$0.568546\pi$
$572$	4.40805	−	2.12280i	0.184310	−	0.0887589i
$573$	−4.59381	−	6.98711i	−0.191909	−	0.291891i
$574$	8.18319	−	2.15874i	0.341560	−	0.0901041i
$575$	0.384633	−	0.482315i	0.0160403	−	0.0201139i
$576$	2.97983	−	0.347274i	0.124160	−	0.0144698i
$577$	−26.2848	−	3.96180i	−1.09425	−	0.164932i	−0.422977	−	0.906140i	$-0.639015\pi$
$577$	−26.2848	−	3.96180i	−1.09425	−	0.164932i	−0.671275	+	0.741208i	$0.734253\pi$
$578$	14.5847	−	7.02362i	0.606644	−	0.292144i
$579$	−9.58117	+	19.0697i	−0.398180	+	0.792509i
$580$	−0.00192327	−	0.0256642i	−7.98593e−5	−	0.00106565i
$581$	−4.49618	−	8.58754i	−0.186533	−	0.356271i
$582$	2.86016	−	17.0305i	0.118557	−	0.705938i
$583$	−0.124974	−	1.66766i	−0.00517588	−	0.0690673i
$584$	11.7654	−	10.9167i	0.486854	−	0.451735i
$585$	−19.8902	+	8.76859i	−0.822360	+	0.362536i
$586$	−10.1384	−	25.8322i	−0.418813	−	1.06712i
$587$	−4.89208	+	8.47333i	−0.201918	+	0.349732i	−0.949146	−	0.314835i	$-0.898051\pi$
$587$	−4.89208	+	8.47333i	−0.201918	+	0.349732i	0.747229	+	0.664567i	$0.231384\pi$
$588$	−7.78971	+	9.29088i	−0.321242	+	0.383149i
$589$	−6.62190	−	11.4695i	−0.272851	−	0.472591i
$590$	−21.4646	+	26.9157i	−0.883682	+	1.10810i
$591$	7.92776	−	4.40130i	0.326104	−	0.181045i
$592$	−0.212132	−	0.929409i	−0.00871855	−	0.0381985i
$593$	−5.84579	+	3.98559i	−0.240058	+	0.163669i	−0.677373	−	0.735640i	$-0.736882\pi$
$593$	−5.84579	+	3.98559i	−0.240058	+	0.163669i	0.437315	+	0.899308i	$0.355929\pi$
$594$	5.84211	+	6.96951i	0.239705	+	0.285962i
$595$	−7.19429	−	38.8459i	−0.294937	−	1.59253i
$596$	1.39343	−	0.950027i	0.0570773	−	0.0389146i
$597$	−22.0930	−	33.6032i	−0.904208	−	1.37529i
$598$	−0.0750012	+	1.00082i	−0.00306703	+	0.0409266i
$599$	−12.7705	−	32.5386i	−0.521787	−	1.32949i	−0.912537	−	0.408995i	$-0.865879\pi$
$599$	−12.7705	−	32.5386i	−0.521787	−	1.32949i	0.390749	−	0.920497i	$-0.372216\pi$
$600$	1.98741	+	2.21538i	0.0811355	+	0.0904425i
$601$	−5.23901	−	13.3488i	−0.213704	−	0.544508i	0.783319	−	0.621620i	$-0.213525\pi$
$601$	−5.23901	−	13.3488i	−0.213704	−	0.544508i	−0.997022	+	0.0771124i	$0.975430\pi$
$602$	18.9245	−	2.05808i	0.771306	−	0.0838810i
$603$	1.46620	+	2.74874i	0.0597085	+	0.111937i
$604$	−0.851705	+	11.3652i	−0.0346554	+	0.462444i
$605$	−4.57773	+	20.0564i	−0.186111	+	0.815407i
$606$	−16.5854	−	1.52332i	−0.673734	−	0.0618808i
$607$	−29.3849			−1.19270			−0.596349	−	0.802726i	$-0.703382\pi$
$607$	−29.3849			−1.19270			−0.596349	+	0.802726i	$0.703382\pi$
$608$	−3.59601	+	1.10922i	−0.145838	+	0.0449849i
$609$	0.00415917	+	0.0453108i	0.000168538	+	0.00183609i
$610$	2.01043	+	0.620137i	0.0814001	+	0.0251086i
$611$	21.5476	+	6.64657i	0.871724	+	0.268891i
$612$	9.13898	−	14.6686i	0.369421	−	0.592945i
$613$	−5.11338	+	13.0287i	−0.206527	+	0.526223i	−0.996179	−	0.0873320i	$-0.972166\pi$
$613$	−5.11338	+	13.0287i	−0.206527	+	0.526223i	0.789652	+	0.613555i	$0.210261\pi$
$614$	−4.53955	+	4.21208i	−0.183201	+	0.169986i
$615$	1.90162	+	14.2341i	0.0766805	+	0.573976i
$616$	3.26157	+	3.28694i	0.131413	+	0.132435i
$617$	41.2038	−	12.7097i	1.65880	−	0.511673i	0.683018	−	0.730402i	$-0.260667\pi$
$617$	41.2038	−	12.7097i	1.65880	−	0.511673i	0.975786	+	0.218729i	$0.0701910\pi$
$618$	−17.8706	−	1.64137i	−0.718861	−	0.0660256i
$619$	−44.8130			−1.80119			−0.900593	−	0.434664i	$-0.856867\pi$
$619$	−44.8130			−1.80119			−0.900593	+	0.434664i	$0.856867\pi$
$620$	−8.71664	+	2.68873i	−0.350069	+	0.107982i
$621$	−1.83734	+	0.323015i	−0.0737300	+	0.0129622i
$622$	−17.4965	−	21.9399i	−0.701545	−	0.879710i
$623$	−1.70778	−	3.26179i	−0.0684207	−	0.130681i
$624$	−4.70174	−	1.15653i	−0.188220	−	0.0462981i
$625$	6.81781	−	29.8708i	0.272712	−	1.19483i
$626$	5.29970	+	13.5034i	0.211819	+	0.539705i
$627$	−8.79826	−	7.26136i	−0.351369	−	0.289991i
$628$	2.17278	−	5.53616i	0.0867035	−	0.220917i
$629$	−4.94804	−	2.38285i	−0.197291	−	0.0950105i
$630$	−13.9924	−	15.0819i	−0.557472	−	0.600878i
$631$	−30.9653	+	14.9121i	−1.23271	+	0.593642i	−0.932824	−	0.360333i	$-0.882663\pi$
$631$	−30.9653	+	14.9121i	−1.23271	+	0.593642i	−0.299886	+	0.953975i	$0.596949\pi$
$632$	0.752781	+	10.0452i	0.0299440	+	0.399575i
$633$	3.76306	+	28.1676i	0.149568	+	1.11956i
$634$	−4.22758	+	2.88231i	−0.167899	+	0.114471i
$635$	7.85249	−	9.84671i	0.311617	−	0.390755i
$636$	−0.955130	+	1.35159i	−0.0378734	+	0.0535940i
$637$	17.0219	−	9.65256i	0.674433	−	0.382448i
$638$	0.0173779			0.000687996
$639$	−13.2593	−	4.58286i	−0.524528	−	0.181295i
$640$	0.193698	+	2.58472i	0.00765659	+	0.102170i
$641$	5.33357	+	23.3679i	0.210664	+	0.922977i	0.964117	+	0.265476i	$0.0855292\pi$
$641$	5.33357	+	23.3679i	0.210664	+	0.922977i	−0.753454	+	0.657501i	$0.771614\pi$
$642$	−25.9726	+	14.4194i	−1.02506	+	0.569087i
$643$	36.9638	+	25.2015i	1.45771	+	0.993850i	0.994176	+	0.107772i	$0.0343715\pi$
$643$	36.9638	+	25.2015i	1.45771	+	0.993850i	0.463535	+	0.886079i	$0.346581\pi$
$644$	−0.918456	+	0.242290i	−0.0361922	+	0.00954758i
$645$	−0.542336	+	32.2967i	−0.0213545	+	1.27168i
$646$	−7.92036	+	20.1808i	−0.311622	+	0.794001i
$647$	−14.6333	−	9.97681i	−0.575294	−	0.392229i	0.240433	−	0.970666i	$-0.422711\pi$
$647$	−14.6333	−	9.97681i	−0.575294	−	0.392229i	−0.815727	+	0.578437i	$0.803663\pi$
$648$	−0.0687321	−	8.99974i	−0.00270005	−	0.353543i
$649$	−17.0404	−	15.8112i	−0.668894	−	0.620643i
$650$	−1.75490	−	4.47141i	−0.0688329	−	0.175383i
$651$	15.3292	−	5.01088i	0.600799	−	0.196392i
$652$	−4.57044	+	11.6453i	−0.178992	+	0.456065i
$653$	34.8324	−	16.7744i	1.36310	−	0.656433i	0.397771	−	0.917485i	$-0.369784\pi$
$653$	34.8324	−	16.7744i	1.36310	−	0.656433i	0.965325	+	0.261052i	$0.0840694\pi$
$654$	7.63133	−	1.60749i	0.298409	−	0.0628579i
$655$	34.0860			1.33185
$656$	−1.59938	+	2.77021i	−0.0624454	+	0.108159i
$657$	−28.7399	−	38.6315i	−1.12125	−	1.50716i
$658$	0.715378	+	21.3298i	0.0278884	+	0.831521i
$659$	4.81299	+	1.48461i	0.187487	+	0.0578322i	0.387077	−	0.922047i	$-0.373485\pi$
$659$	4.81299	+	1.48461i	0.187487	+	0.0578322i	−0.199590	+	0.979880i	$0.563961\pi$
$660$	−6.22446	+	4.79510i	−0.242287	+	0.186649i
$661$	−15.9850	+	2.40935i	−0.621745	+	0.0937129i	−0.452357	−	0.891837i	$-0.649417\pi$
$661$	−15.9850	+	2.40935i	−0.621745	+	0.0937129i	−0.169387	+	0.985550i	$0.554179\pi$
$662$	20.2049	−	3.04539i	0.785284	−	0.118362i
$663$	−22.0970	+	17.0228i	−0.858177	+	0.661109i
$664$	3.50098	+	1.07991i	0.135864	+	0.0419086i
$665$	20.7047	+	15.4050i	0.802893	+	0.597380i
$666$	−2.84070	+	0.331060i	−0.110075	+	0.0128283i
$667$	−0.00178239	+	0.00308719i	−6.90144e−5	+	0.000119536i
$668$	5.48137			0.212081
$669$	27.1436	−	5.71763i	1.04943	−	0.221057i
$670$	−2.42506	+	1.16785i	−0.0936883	+	0.0451179i
$671$	−0.519011	+	1.32242i	−0.0200362	+	0.0510514i
$672$	−0.418883	−	4.56339i	−0.0161588	−	0.176037i
$673$	−2.35337	−	5.99628i	−0.0907156	−	0.231140i	0.878314	−	0.478084i	$-0.158669\pi$
$673$	−2.35337	−	5.99628i	−0.0907156	−	0.231140i	−0.969030	+	0.246945i	$0.920573\pi$
$674$	6.79793	+	6.30756i	0.261847	+	0.242958i
$675$	7.25207	−	5.20832i	0.279132	−	0.200469i
$676$	−4.28435	−	2.92102i	−0.164783	−	0.112347i
$677$	12.4400	−	31.6965i	0.478107	−	1.21820i	−0.464883	−	0.885372i	$-0.653903\pi$
$677$	12.4400	−	31.6965i	0.478107	−	1.21820i	0.942989	−	0.332823i	$-0.108001\pi$
$678$	0.401759	−	23.9252i	0.0154295	−	0.918841i
$679$	−25.8998	−	5.00450i	−0.993944	−	0.192055i
$680$	12.3374	+	8.41151i	0.473119	+	0.322567i
$681$	33.0805	−	18.3655i	1.26765	−	0.703767i
$682$	−1.37059	−	6.00496i	−0.0524827	−	0.229942i
$683$	0.391131	+	5.21927i	0.0149662	+	0.199710i	0.999675	+	0.0255005i	$0.00811794\pi$
$683$	0.391131	+	5.21927i	0.0149662	+	0.199710i	−0.984709	+	0.174209i	$0.944263\pi$
$684$	2.14121	+	11.0847i	0.0818712	+	0.423834i
$685$	−48.5539			−1.85515
$686$	13.8965	+	12.2428i	0.530571	+	0.467434i
$687$	−15.1097	+	21.3815i	−0.576472	+	0.815757i
$688$	−4.48599	+	5.62526i	−0.171027	+	0.214461i
$689$	2.20699	−	1.50470i	0.0840797	−	0.0573246i
$690$	−0.213431	−	1.59760i	−0.00812520	−	0.0608195i
$691$	−2.28903	−	30.5450i	−0.0870788	−	1.16199i	−0.854010	−	0.520257i	$-0.825836\pi$
$691$	−2.28903	−	30.5450i	−0.0870788	−	1.16199i	0.766931	−	0.641730i	$-0.221783\pi$
$692$	−6.76759	+	3.25910i	−0.257265	+	0.123892i
$693$	10.8614	−	8.66067i	0.412589	−	0.328992i
$694$	−25.5212	−	12.2903i	−0.968770	−	0.466535i
$695$	−9.03814	+	23.0288i	−0.342836	+	0.873532i
$696$	−0.0132639	−	0.0109470i	−0.000502768	−	0.000414943i
$697$	6.73240	+	17.1539i	0.255008	+	0.649750i
$698$	−7.23312	+	31.6904i	−0.273778	+	1.19950i
$699$	44.0432	+	10.8337i	1.66587	+	0.409768i
$700$	3.45735	−	2.95206i	0.130676	−	0.111577i
$701$	3.61595	+	4.53425i	0.136572	+	0.171256i	0.845414	−	0.534111i	$-0.179354\pi$
$701$	3.61595	+	4.53425i	0.136572	+	0.171256i	−0.708842	+	0.705367i	$0.750782\pi$
$702$	−4.97497	+	13.6472i	−0.187768	+	0.515079i
$703$	3.42812	−	1.05743i	0.129294	−	0.0398819i
$704$	−1.75018			−0.0659623
$705$	−36.0618	−	3.31219i	−1.35817	−	0.124744i
$706$	28.0527	−	8.65311i	1.05578	−	0.325664i
$707$	−2.94642	+	25.2700i	−0.110811	+	0.950376i
$708$	3.04631	+	22.8025i	0.114487	+	0.856970i
$709$	−16.8287	+	15.6147i	−0.632014	+	0.586423i	−0.929735	−	0.368230i	$-0.879964\pi$
$709$	−16.8287	+	15.6147i	−0.632014	+	0.586423i	0.297721	+	0.954653i	$0.403774\pi$
$710$	4.42824	−	11.2830i	0.166189	−	0.423442i
$711$	30.2030	+	1.01464i	1.13270	+	0.0380520i
$712$	1.32977	+	0.410181i	0.0498353	+	0.0153722i
$713$	1.20736	+	0.372422i	0.0452160	+	0.0139473i
$714$	−22.0583	−	14.5044i	−0.825510	−	0.542812i
$715$	12.1180	−	3.73790i	0.453187	−	0.139790i
$716$	−17.2356			−0.644123
$717$	−40.5609	−	3.72541i	−1.51477	−	0.139128i
$718$	−0.0727832	+	0.318884i	−0.00271624	+	0.0119006i
$719$	−1.92529	+	25.6912i	−0.0718012	+	0.958121i	0.838695	+	0.544602i	$0.183319\pi$
$719$	−1.92529	+	25.6912i	−0.0718012	+	0.958121i	−0.910496	+	0.413518i	$0.864300\pi$
$720$	7.77152	+	0.261077i	0.289628	+	0.00972976i
$721$	−3.17474	+	27.2282i	−0.118234	+	1.01403i
$722$	1.76764	+	4.50387i	0.0657847	+	0.167617i
$723$	−5.56815	−	6.20687i	−0.207082	−	0.230836i
$724$	6.44571	+	16.4234i	0.239553	+	0.610371i
$725$	0.00127500	−	0.0170137i	4.73522e−5	−	0.000631872i
$726$	7.55221	+	11.4868i	0.280289	+	0.426315i
$727$	−18.8295	+	12.8378i	−0.698349	+	0.476126i	−0.859719	−	0.510768i	$-0.829361\pi$
$727$	−18.8295	+	12.8378i	−0.698349	+	0.476126i	0.161370	+	0.986894i	$0.448409\pi$
$728$	−1.94191	+	7.13663i	−0.0719721	+	0.264501i
$729$	−26.8631	−	2.71550i	−0.994930	−	0.100574i
$730$	34.3721	−	23.4345i	1.27217	−	0.867350i
$731$	9.22336	+	40.4102i	0.341138	+	1.49462i
$732$	1.22918	−	0.682412i	0.0454319	−	0.0252227i
$733$	−19.9460	+	25.0115i	−0.736723	+	0.923822i	−0.999154	−	0.0411289i	$-0.986905\pi$
$733$	−19.9460	+	25.0115i	−0.736723	+	0.923822i	0.262430	+	0.964951i	$0.415476\pi$
$734$	−13.1128	−	22.7120i	−0.484002	−	0.838317i
$735$	−23.5544	+	20.8034i	−0.868816	+	0.767346i
$736$	0.179510	−	0.310920i	0.00661682	−	0.0114607i
$737$	−0.663994	−	1.69183i	−0.0244585	−	0.0623193i
$738$	7.74286	+	5.66895i	0.285019	+	0.208677i
$739$	17.6425	−	16.3699i	0.648990	−	0.602175i	−0.285407	−	0.958406i	$-0.592129\pi$
$739$	17.6425	−	16.3699i	0.648990	−	0.602175i	0.934398	+	0.356231i	$0.115938\pi$
$740$	−0.184654	−	2.46404i	−0.00678803	−	0.0905800i
$741$	3.01783	−	17.9694i	0.110863	−	0.660121i
$742$	2.02825	+	1.50909i	0.0744595	+	0.0554004i
$743$	0.161906	+	2.16049i	0.00593976	+	0.0792607i	0.999386	−	0.0350407i	$-0.0111561\pi$
$743$	0.161906	+	2.16049i	0.00593976	+	0.0792607i	−0.993446	+	0.114301i	$0.963537\pi$
$744$	−2.73662	+	5.44676i	−0.100329	+	0.199688i
$745$	3.93840	−	1.89664i	0.144292	−	0.0694873i
$746$	−14.0903	−	2.12377i	−0.515882	−	0.0777567i
$747$	4.35681	−	10.0909i	0.159407	−	0.369206i
$748$	−6.28638	+	7.88287i	−0.229853	+	0.288226i
$749$	21.0481	+	40.2012i	0.769082	+	1.46892i
$750$	−8.09380	−	12.3105i	−0.295544	−	0.449517i
$751$	8.18847	−	3.94336i	0.298801	−	0.143895i	−0.278476	−	0.960443i	$-0.589829\pi$
$751$	8.18847	−	3.94336i	0.298801	−	0.143895i	0.577278	+	0.816548i	$0.304115\pi$
$752$	−5.91311	−	5.48657i	−0.215629	−	0.200074i
$753$	15.7291	−	22.2580i	0.573200	−	0.811126i
$754$	0.0138784	+	0.0240381i	0.000505421	+	0.000875415i
$755$	−6.57347	+	28.8002i	−0.239233	+	1.04815i
$756$	−13.7458	−	0.231580i	−0.499929	−	0.00842247i
$757$	6.20261	+	27.1754i	0.225438	+	0.987707i	0.953310	+	0.301994i	$0.0976522\pi$
$757$	6.20261	+	27.1754i	0.225438	+	0.987707i	−0.727872	+	0.685713i	$0.759491\pi$
$758$	17.2551	−	16.0104i	0.626734	−	0.581524i
$759$	1.08650	−	0.0630977i	0.0394375	−	0.00229030i
$760$	−9.64515	+	1.45377i	−0.349866	+	0.0527339i
$761$	−5.01683	−	21.9802i	−0.181860	−	0.796781i	−0.980744	−	0.195296i	$-0.937433\pi$
$761$	−5.01683	−	21.9802i	−0.181860	−	0.796781i	0.798884	−	0.601485i	$-0.205424\pi$
$762$	−1.11445	−	8.34195i	−0.0403721	−	0.302197i
$763$	−2.16938	−	11.7137i	−0.0785369	−	0.424063i
$764$	1.07429	−	4.70675i	0.0388663	−	0.170284i
$765$	29.0901	−	34.0655i	1.05175	−	1.23164i
$766$	13.4028	+	23.2143i	0.484262	+	0.838767i
$767$	8.26206	−	36.1985i	0.298326	−	1.30705i
$768$	1.33585	+	1.10250i	0.0482033	+	0.0397831i
$769$	12.3023	−	31.3456i	0.443631	−	1.13035i	−0.517848	−	0.855473i	$-0.673267\pi$
$769$	12.3023	−	31.3456i	0.443631	−	1.13035i	0.961479	−	0.274880i	$-0.0886381\pi$
$770$	7.08969	+	9.68448i	0.255495	+	0.349004i
$771$	−11.3801	−	39.2196i	−0.409844	−	1.41246i
$772$	−11.7740	+	3.63180i	−0.423756	+	0.130711i
$773$	−40.0205	−	6.03211i	−1.43944	−	0.216960i	−0.617514	−	0.786560i	$-0.711860\pi$
$773$	−40.0205	−	6.03211i	−1.43944	−	0.216960i	−0.821922	+	0.569600i	$0.807098\pi$
$774$	15.3210	+	15.2045i	0.550702	+	0.546513i
$775$	−5.97967	+	0.901290i	−0.214796	+	0.0323753i
$776$	8.23783	−	5.61646i	0.295721	−	0.201619i
$777$	0.399325	+	4.35033i	0.0143257	+	0.156067i
$778$	−23.9627	−	16.3375i	−0.859104	−	0.585727i
$779$	−10.8455	−	5.22292i	−0.388580	−	0.187130i
$780$	−11.6039	−	4.78054i	−0.415485	−	0.171171i
$781$	7.37386	+	3.55106i	0.263857	+	0.127067i
$782$	−0.755624	−	1.92530i	−0.0270211	−	0.0688486i
$783$	−0.0369524	+	0.0360059i	−0.00132057	+	0.00128675i
$784$	−6.98427	+	0.469018i	−0.249438	+	0.0167506i
$785$	7.70758	−	13.3499i	0.275095	−	0.476479i
$786$	15.7708	−	16.4346i	0.562526	−	0.586204i
$787$	12.2939	−	8.38184i	0.438230	−	0.298780i	−0.324035	−	0.946045i	$-0.605040\pi$
$787$	12.2939	−	8.38184i	0.438230	−	0.298780i	0.762265	+	0.647265i	$0.224087\pi$
$788$	5.00258	+	1.54309i	0.178209	+	0.0549703i
$789$	1.12650	−	0.625407i	0.0401046	−	0.0222651i
$790$	−1.95119	+	26.0368i	−0.0694201	+	0.926346i
$791$	−36.5204	−	1.50818i	−1.29851	−	0.0536246i
$792$	−0.567946	+	5.21972i	−0.0201811	+	0.185475i
$793$	−2.24374	+	0.338190i	−0.0796776	+	0.0120095i
$794$	32.4623	−	15.6330i	1.15204	−	0.554794i
$795$	−2.97015	+	3.09517i	−0.105340	+	0.109774i
$796$	5.16657	−	22.6362i	0.183124	−	0.802319i
$797$	−45.5878	−	6.87126i	−1.61480	−	0.243392i	−0.721357	−	0.692563i	$-0.756481\pi$
$797$	−45.5878	−	6.87126i	−1.61480	−	0.243392i	−0.893446	+	0.449171i	$0.851719\pi$
$798$	17.0071	−	2.85527i	0.602046	−	0.101075i
$799$	−45.9508	+	6.92596i	−1.62562	+	0.245023i
$800$	−0.128409	+	1.71350i	−0.00453994	+	0.0605813i
$801$	1.65484	−	3.83280i	0.0584710	−	0.135426i
$802$	3.46781	+	6.00643i	0.122453	+	0.212094i
$803$	14.0450	+	24.3267i	0.495638	+	0.858471i
$804$	−0.558941	+	1.70959i	−0.0197123	+	0.0602925i
$805$	−2.44762	+	0.266183i	−0.0862672	+	0.00938173i
$806$	7.21181	−	6.69159i	0.254025	−	0.235701i
$807$	−5.74109	−	42.9737i	−0.202096	−	1.51275i
$808$	−5.99540	−	7.51799i	−0.210917	−	0.264482i
$809$	−4.86216	+	12.3886i	−0.170944	+	0.435559i	−0.990513	−	0.137423i	$-0.956118\pi$
$809$	−4.86216	+	12.3886i	−0.170944	+	0.435559i	0.819568	+	0.572982i	$0.194213\pi$
$810$	3.30055	−	23.0930i	0.115970	−	0.811407i
$811$	6.64878	+	29.1302i	0.233470	+	1.02290i	0.946737	+	0.322008i	$0.104358\pi$
$811$	6.64878	+	29.1302i	0.233470	+	1.02290i	−0.713267	+	0.700893i	$0.752785\pi$
$812$	−0.0172127	+	0.0198455i	−0.000604048	+	0.000696442i
$813$	43.8422	−	9.23509i	1.53761	−	0.323889i
$814$	1.66846			0.0584796
$815$	−16.2128	+	28.0815i	−0.567911	+	0.983651i
$816$	9.76388	−	2.05670i	0.341804	−	0.0719990i
$817$	−22.3713	−	15.2525i	−0.782674	−	0.533618i
$818$	9.82472	+	12.3198i	0.343513	+	0.430752i
$819$	20.6541	+	8.10745i	0.721712	+	0.283297i
$820$	−5.16942	+	6.48224i	−0.180524	+	0.226370i
$821$	−13.5766	+	4.18783i	−0.473827	+	0.146156i	−0.522466	−	0.852660i	$-0.674988\pi$
$821$	−13.5766	+	4.18783i	−0.473827	+	0.146156i	0.0486390	+	0.998816i	$0.484512\pi$
$822$	−22.4648	+	23.4104i	−0.783549	+	0.816530i
$823$	1.20775	−	16.1163i	0.0420995	−	0.561779i	−0.935777	−	0.352594i	$-0.885300\pi$
$823$	1.20775	−	16.1163i	0.0420995	−	0.561779i	0.977876	−	0.209185i	$-0.0670811\pi$
$824$	−6.45999	−	8.10057i	−0.225045	−	0.282197i
$825$	−4.55409	+	2.52832i	−0.158553	+	0.0880248i
$826$	34.9349	−	3.79923i	1.21554	−	0.132192i
$827$	−10.1938	+	4.90907i	−0.354473	+	0.170705i	−0.602642	−	0.798012i	$-0.705885\pi$
$827$	−10.1938	+	4.90907i	−0.354473	+	0.170705i	0.248169	+	0.968717i	$0.420171\pi$
$828$	−0.869035	−	0.636266i	−0.0302011	−	0.0221118i
$829$	−9.05618	+	8.40291i	−0.314534	+	0.291845i	−0.821603	−	0.570061i	$-0.806920\pi$
$829$	−9.05618	+	8.40291i	−0.314534	+	0.291845i	0.507068	+	0.861906i	$0.330729\pi$
$830$	8.55589	+	4.12030i	0.296979	+	0.143018i
$831$	−3.75884	−	12.9542i	−0.130393	−	0.449376i
$832$	−1.39773	−	2.42095i	−0.0484577	−	0.0839312i
$833$	−22.9740	+	33.1421i	−0.796002	+	1.14831i
$834$	6.92165	+	15.0127i	0.239677	+	0.519846i
$835$	14.0488	+	2.11752i	0.486180	+	0.0732799i
$836$	−0.492192	−	6.56785i	−0.0170228	−	0.227154i
$837$	15.3564	+	9.92919i	0.530793	+	0.343203i
$838$	2.99397	−	2.04126i	0.103425	−	0.0705141i
$839$	2.44129	−	32.5767i	0.0842826	−	1.12467i	−0.781384	−	0.624051i	$-0.785486\pi$
$839$	2.44129	−	32.5767i	0.0842826	−	1.12467i	0.865666	−	0.500622i	$-0.166895\pi$
$840$	0.689292	−	11.8579i	0.0237828	−	0.409136i
$841$	−2.16717	−	28.9188i	−0.0747298	−	0.997200i
$842$	8.32123	+	10.4345i	0.286769	+	0.359596i
$843$	−5.08018	−	4.19276i	−0.174971	−	0.144406i
$844$	−10.2296	+	12.8275i	−0.352118	+	0.441542i
$845$	−9.85243	−	9.14172i	−0.338934	−	0.314485i
$846$	−18.2820	+	15.8548i	−0.628547	+	0.545100i
$847$	17.8235	−	11.1032i	0.612423	−	0.381510i
$848$	−0.944850	+	0.142413i	−0.0324463	+	0.00489049i
$849$	−37.6562	−	31.0783i	−1.29236	−	1.06661i
$850$	7.25644	+	6.73299i	0.248894	+	0.230940i
$851$	−0.171129	+	0.296403i	−0.00586621	+	0.0101606i
$852$	−3.39126	−	7.35546i	−0.116183	−	0.251994i
$853$	26.0897	+	24.2077i	0.893293	+	0.828854i	0.985984	−	0.166840i	$-0.0533565\pi$
$853$	26.0897	+	24.2077i	0.893293	+	0.828854i	−0.0926913	+	0.995695i	$0.529547\pi$
$854$	−0.996125	−	1.90256i	−0.0340867	−	0.0651044i
$855$	1.20580	+	29.2374i	0.0412376	+	0.999899i
$856$	−16.3893	−	5.05542i	−0.560174	−	0.172791i
$857$	30.2895	+	37.9819i	1.03467	+	1.29744i	0.953713	+	0.300719i	$0.0972266\pi$
$857$	30.2895	+	37.9819i	1.03467	+	1.29744i	0.0809581	+	0.996718i	$0.474202\pi$
$858$	3.80448	−	7.57215i	0.129883	−	0.258509i
$859$	4.00849	+	17.5623i	0.136768	+	0.599219i	0.996133	+	0.0878566i	$0.0280017\pi$
$859$	4.00849	+	17.5623i	0.136768	+	0.599219i	−0.859365	+	0.511362i	$0.829141\pi$
$860$	−13.6708	+	12.6846i	−0.466170	+	0.432543i
$861$	8.94641	−	11.6119i	0.304893	−	0.395732i
$862$	7.06208	+	6.55265i	0.240535	+	0.223184i
$863$	−14.1714	+	24.5455i	−0.482399	+	0.835540i	−0.999796	−	0.0202057i	$-0.993568\pi$
$863$	−14.1714	+	24.5455i	−0.482399	+	0.835540i	0.517397	+	0.855746i	$0.326901\pi$
$864$	3.72159	−	3.62626i	0.126611	−	0.123368i
$865$	−18.6045	+	5.73872i	−0.632572	+	0.195122i
$866$	−3.75578	−	2.56064i	−0.127626	−	0.0870142i
$867$	12.5877	−	25.0536i	0.427501	−	0.850866i
$868$	8.21524	+	4.38267i	0.278843	+	0.148758i
$869$	−17.4332	−	2.62763i	−0.591381	−	0.0891364i
$870$	−0.0297667	−	0.0331813i	−0.00100919	−	0.00112495i
$871$	1.80995	−	2.26961i	0.0613279	−	0.0769028i
$872$	3.72025	+	2.53643i	0.125984	+	0.0858942i
$873$	−14.0773	−	26.3911i	−0.476443	−	0.893202i
$874$	1.21727	+	0.586204i	0.0411746	+	0.0198287i
$875$	−19.1017	+	11.8994i	−0.645755	+	0.402274i
$876$	4.60419	−	27.4152i	0.155561	−	0.926274i
$877$	−30.3917	−	14.6359i	−1.02626	−	0.494219i	−0.156488	−	0.987680i	$-0.550017\pi$
$877$	−30.3917	−	14.6359i	−1.02626	−	0.494219i	−0.869768	+	0.493461i	$0.835732\pi$
$878$	1.72704	+	0.532722i	0.0582848	+	0.0179785i
$879$	−41.2164	−	24.7282i	−1.39019	−	0.834060i
$880$	−4.48574	−	0.676116i	−0.151214	−	0.0227919i
$881$	−29.5268			−0.994782			−0.497391	−	0.867526i	$-0.665709\pi$
$881$	−29.5268			−0.994782			−0.497391	+	0.867526i	$0.665709\pi$
$882$	−0.867651	+	20.9821i	−0.0292153	+	0.706503i
$883$	11.5375			0.388269			0.194134	−	0.980975i	$-0.437810\pi$
$883$	11.5375			0.388269			0.194134	+	0.980975i	$0.437810\pi$
$884$	−15.9245	−	2.40023i	−0.535599	−	0.0807285i
$885$	−1.00116	+	59.6200i	−0.0336535	+	2.00411i
$886$	4.98792	+	1.53857i	0.167573	+	0.0516893i
$887$	−13.1386	−	6.32721i	−0.441151	−	0.212447i	0.200105	−	0.979775i	$-0.435872\pi$
$887$	−13.1386	−	6.32721i	−0.441151	−	0.212447i	−0.641255	+	0.767328i	$0.721586\pi$
$888$	−1.27348	−	1.05102i	−0.0427352	−	0.0352701i
$889$	−12.7804	+	1.38989i	−0.428641	+	0.0466155i
$890$	3.24977	+	1.56501i	0.108933	+	0.0524592i
$891$	15.3830	+	3.38768i	0.515350	+	0.113492i
$892$	13.2324	+	9.02172i	0.443055	+	0.302070i
$893$	18.9264	−	23.7330i	0.633348	−	0.794193i
$894$	0.907743	−	2.77644i	0.0303595	−	0.0928581i
$895$	−44.1751	−	6.65832i	−1.47661	−	0.222563i
$896$	1.73355	−	1.99870i	0.0579137	−	0.0667720i
$897$	0.954986	+	1.45252i	0.0318860	+	0.0484982i
$898$	29.8641	+	20.3610i	0.996577	+	0.679454i
$899$	0.0333913	−	0.0102999i	0.00111366	−	0.000343520i
$900$	5.06866	+	0.939009i	0.168955	+	0.0313003i
$901$	−2.75233	+	4.76717i	−0.0916933	+	0.158817i
$902$	−4.10392	−	3.80788i	−0.136646	−	0.126789i
$903$	23.7911	−	22.8277i	0.791720	−	0.759657i
$904$	10.1272	−	9.39670i	0.336827	−	0.312529i
$905$	10.1759	+	44.5835i	0.338258	+	1.48201i
$906$	10.8447	+	16.4946i	0.360291	+	0.547997i
$907$	−12.4263	−	15.5821i	−0.412608	−	0.517394i	0.531488	−	0.847066i	$-0.321633\pi$
$907$	−12.4263	−	15.5821i	−0.412608	−	0.517394i	−0.944095	+	0.329672i	$0.893062\pi$
$908$	20.8745	+	6.43892i	0.692744	+	0.213683i
$909$	−24.3672	+	15.4410i	−0.808208	+	0.512146i
$910$	−7.73413	+	17.5411i	−0.256384	+	0.581483i
$911$	14.0467	+	13.0334i	0.465388	+	0.431817i	0.877689	−	0.479231i	$-0.159084\pi$
$911$	14.0467	+	13.0334i	0.465388	+	0.431817i	−0.412301	+	0.911048i	$0.635275\pi$
$912$	−3.76165	+	5.32306i	−0.124561	+	0.176264i
$913$	−3.20611	+	5.55314i	−0.106107	+	0.183782i
$914$	17.3109	+	16.0622i	0.572595	+	0.531290i
$915$	3.41404	−	1.27419i	0.112865	−	0.0421233i
$916$	−14.9471	+	2.25291i	−0.493866	+	0.0744383i
$917$	−24.5071	−	24.6977i	−0.809295	−	0.815589i
$918$	−2.96545	−	29.7872i	−0.0978744	−	0.983124i
$919$	12.0702	+	11.1995i	0.398158	+	0.369436i	0.853689	−	0.520784i	$-0.174360\pi$
$919$	12.0702	+	11.1995i	0.398158	+	0.369436i	−0.455531	+	0.890220i	$0.650551\pi$
$920$	0.580199	−	0.727547i	0.0191286	−	0.0239865i
$921$	−1.77648	+	10.5779i	−0.0585371	+	0.348553i
$922$	17.1276	+	21.4774i	0.564068	+	0.707319i
$923$	0.976906	+	13.0359i	0.0321553	+	0.429082i
$924$	7.94963	+	1.06248i	0.261524	+	0.0349530i
$925$	0.122414	−	1.63349i	0.00402493	−	0.0537090i
$926$	25.8587	−	17.6302i	0.849771	−	0.579364i
$927$	−26.2555	+	16.6376i	−0.862342	+	0.546449i
$928$	−0.000742010	−	0.00990144i	−2.43577e−5	−	0.000325031i
$929$	−13.1238	−	1.97809i	−0.430578	−	0.0648992i	−0.0698220	−	0.997559i	$-0.522243\pi$
$929$	−13.1238	−	1.97809i	−0.430578	−	0.0648992i	−0.360756	+	0.932660i	$0.617481\pi$
$930$	−9.11815	+	12.9030i	−0.298996	+	0.423105i
$931$	−3.72422	−	26.0778i	−0.122056	−	0.854666i
$932$	13.0932	+	22.6780i	0.428881	+	0.742844i
$933$	−47.1982	−	11.6098i	−1.54520	−	0.380086i
$934$	4.65162	+	2.24010i	0.152206	+	0.0732983i
$935$	−19.1574	+	17.7754i	−0.626513	+	0.581319i
$936$	−7.67380	+	3.38298i	−0.250826	+	0.110576i
$937$	−41.6818	+	20.0729i	−1.36168	+	0.655753i	−0.965012	−	0.262207i	$-0.915550\pi$
$937$	−41.6818	+	20.0729i	−1.36168	+	0.655753i	−0.396673	+	0.917960i	$0.629835\pi$
$938$	2.58975	+	0.917469i	0.0845585	+	0.0299564i
$939$	21.5453	+	12.9263i	0.703103	+	0.421833i
$940$	−13.0359	−	16.3465i	−0.425184	−	0.533163i
$941$	1.50833	−	20.1273i	0.0491703	−	0.656131i	−0.917109	−	0.398636i	$-0.869484\pi$
$941$	1.50833	−	20.1273i	0.0491703	−	0.656131i	0.966280	−	0.257495i	$-0.0828972\pi$
$942$	−2.87057	−	9.89293i	−0.0935283	−	0.322329i
$943$	1.09740	−	0.338503i	0.0357362	−	0.0110232i
$944$	−8.28118	+	10.3843i	−0.269530	+	0.337979i
$945$	−35.1412	−	5.90371i	−1.14314	−	0.192048i
$946$	−7.85128	−	9.84520i	−0.255267	−	0.320095i
$947$	−8.00457	−	5.45742i	−0.260113	−	0.177342i	0.426241	−	0.904610i	$-0.359838\pi$
$947$	−8.00457	−	5.45742i	−0.260113	−	0.177342i	−0.686354	+	0.727267i	$0.740790\pi$
$948$	11.6509	+	12.9874i	0.378404	+	0.421811i
$949$	−22.4334	+	38.8558i	−0.728219	+	1.26131i
$950$	−6.46632			−0.209795
$951$	−2.75403	+	8.42352i	−0.0893055	+	0.273151i
$952$	−2.77561	−	14.9870i	−0.0899580	−	0.485732i
$953$	−3.30873	−	14.4965i	−0.107180	−	0.469588i	−0.999823	−	0.0188225i	$-0.994008\pi$
$953$	−3.30873	−	14.4965i	−0.107180	−	0.469588i	0.892642	−	0.450765i	$-0.148849\pi$
$954$	0.118122	+	2.86413i	0.00382434	+	0.0927297i
$955$	4.57169	−	11.6485i	0.147937	−	0.376936i
$956$	−14.6622	−	18.3859i	−0.474210	−	0.594641i
$957$	0.0238444	−	0.0183689i	0.000770780	−	0.000593782i
$958$	21.7192	−	20.1525i	0.701715	−	0.651097i
$959$	34.9091	+	35.1806i	1.12728	+	1.13604i
$960$	2.99790	+	3.34178i	0.0967567	+	0.107856i
$961$	9.30729	+	16.1207i	0.300235	+	0.520023i
$962$	1.33247	+	2.30791i	0.0429607	+	0.0744101i
$963$	−20.3957	+	47.2388i	−0.657243	+	1.52225i
$964$	0.359765	−	4.80074i	0.0115873	−	0.154621i
$965$	−31.5800	+	4.75992i	−1.01660	+	0.153227i
$966$	−1.00412	+	1.30328i	−0.0323069	+	0.0419324i
$967$	−32.7264	−	4.93271i	−1.05241	−	0.158625i	−0.400018	−	0.916507i	$-0.630996\pi$
$967$	−32.7264	−	4.93271i	−1.05241	−	0.158625i	−0.652391	+	0.757882i	$0.726234\pi$
$968$	−1.76612	+	7.73789i	−0.0567653	+	0.248705i
$969$	10.4640	+	36.0623i	0.336151	+	1.15849i
$970$	23.2834	−	11.2127i	0.747586	−	0.360018i
$971$	38.4999	−	5.80292i	1.23552	−	0.186225i	0.501382	−	0.865226i	$-0.332825\pi$
$971$	38.4999	−	5.80292i	1.23552	−	0.186225i	0.734137	+	0.679001i	$0.237587\pi$
$972$	−9.60728	−	12.2760i	−0.308154	−	0.393753i
$973$	23.1842	−	10.0084i	0.743251	−	0.320856i
$974$	3.10600	−	41.4467i	0.0995227	−	1.32804i
$975$	−7.13433	−	4.28031i	−0.228481	−	0.137079i
$976$	0.775640	+	0.239253i	0.0248276	+	0.00765831i
$977$	−0.618007	+	0.421350i	−0.0197718	+	0.0134802i	−0.573166	−	0.819440i	$-0.694285\pi$
$977$	−0.618007	+	0.421350i	−0.0197718	+	0.0134802i	0.553394	+	0.832920i	$0.313332\pi$
$978$	6.03823	+	20.8097i	0.193081	+	0.665422i
$979$	−1.21777	+	2.10924i	−0.0389201	+	0.0674117i
$980$	−18.0820	−	1.49601i	−0.577608	−	0.0477884i
$981$	8.77188	−	10.2722i	0.280065	−	0.327966i
$982$	5.78124	+	14.7304i	0.184487	+	0.470065i
$983$	17.2655	+	8.31461i	0.550683	+	0.265195i	0.688467	−	0.725267i	$-0.258284\pi$
$983$	17.2655	+	8.31461i	0.550683	+	0.265195i	−0.137785	+	0.990462i	$0.543998\pi$
$984$	0.733657	+	5.49164i	0.0233881	+	0.175067i
$985$	12.2256	+	5.88753i	0.389539	+	0.187592i
$986$	−0.0472617	−	0.0322225i	−0.00150512	−	0.00102617i
$987$	23.5277	+	28.5107i	0.748896	+	0.907505i
$988$	8.69195	−	5.92607i	0.276528	−	0.188534i
$989$	2.55429	−	0.384997i	0.0812215	−	0.0122422i
$990$	−3.47210	+	13.1588i	−0.110351	+	0.418216i
$991$	0.642609	+	0.0968578i	0.0204132	+	0.00307679i	0.159241	−	0.987240i	$-0.449095\pi$
$991$	0.642609	+	0.0968578i	0.0204132	+	0.00307679i	−0.138828	+	0.990317i	$0.544333\pi$
$992$	−3.36294	+	1.03733i	−0.106773	+	0.0329353i
$993$	24.5043	−	25.5357i	0.777620	−	0.810351i
$994$	−11.3591	+	4.90364i	−0.360289	+	0.155534i
$995$	21.9867	−	56.0211i	0.697024	−	1.77599i
$996$	5.94523	−	2.21887i	0.188382	−	0.0703077i
$997$	0.874490	−	3.83139i	0.0276954	−	0.121341i	−0.959191	−	0.282760i	$-0.908750\pi$
$997$	0.874490	−	3.83139i	0.0276954	−	0.121341i	0.986886	+	0.161419i	$0.0516070\pi$
$998$	−16.6024	−	28.7563i	−0.525541	−	0.910264i
$999$	−3.54783	+	3.45695i	−0.112248	+	0.109373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.y.a.457.23	yes	336
9.4	even	3		882.2.bb.b.751.4	yes	336
49.46	even	21		882.2.bb.b.781.4	yes	336
441.193	even	21	inner	882.2.y.a.193.23	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.193.23	✓	336	441.193	even	21	inner
882.2.y.a.457.23	yes	336	1.1	even	1	trivial
882.2.bb.b.751.4	yes	336	9.4	even	3
882.2.bb.b.781.4	yes	336	49.46	even	21

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988831 + 0.149042i) q^{2} +(1.51433 - 0.840718i) q^{3} +(0.955573 + 0.294755i) q^{4} +(2.33528 + 1.12461i) q^{5} +(1.62272 - 0.605629i) q^{6} +(-0.864156 - 2.50065i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.58638 - 2.54625i) q^{9} +O(q^{10})\)	\(q+(0.988831 + 0.149042i) q^{2} +(1.51433 - 0.840718i) q^{3} +(0.955573 + 0.294755i) q^{4} +(2.33528 + 1.12461i) q^{5} +(1.62272 - 0.605629i) q^{6} +(-0.864156 - 2.50065i) q^{7} +(0.900969 + 0.433884i) q^{8} +(1.58638 - 2.54625i) q^{9} +(2.14159 + 1.46011i) q^{10} +(-1.09122 + 1.36834i) q^{11} +(1.69486 - 0.357011i) q^{12} +(-2.76424 - 0.416643i) q^{13} +(-0.481803 - 2.60151i) q^{14} +(4.48187 - 0.260281i) q^{15} +(0.826239 + 0.563320i) q^{16} +(5.50495 - 1.69805i) q^{17} +(1.94817 - 2.28137i) q^{18} +(-1.88160 + 3.25903i) q^{19} +(1.90005 + 1.76299i) q^{20} +(-3.41096 - 3.06029i) q^{21} +(-1.28297 + 1.19042i) q^{22} +(-0.0798894 - 0.350018i) q^{23} +(1.72914 - 0.100418i) q^{24} +(1.07134 + 1.34342i) q^{25} +(-2.67127 - 0.823979i) q^{26} +(0.261631 - 5.18956i) q^{27} +(-0.0886859 - 2.64426i) q^{28} +(-0.00727862 - 0.00675357i) q^{29} +(4.47060 + 0.410614i) q^{30} +(-1.75965 + 3.04780i) q^{31} +(0.733052 + 0.680173i) q^{32} +(-0.502071 + 2.98953i) q^{33} +(5.69654 - 0.858615i) q^{34} +(0.794210 - 6.81156i) q^{35} +(2.26643 - 1.96553i) q^{36} +(-0.698826 - 0.648416i) q^{37} +(-2.34632 + 2.94219i) q^{38} +(-4.53626 + 1.69302i) q^{39} +(1.61607 + 2.02648i) q^{40} +(0.239044 + 3.18982i) q^{41} +(-2.91675 - 3.53449i) q^{42} +(-0.537681 + 7.17485i) q^{43} +(-1.44606 + 0.985910i) q^{44} +(6.56820 - 4.16214i) q^{45} +(-0.0268296 - 0.358016i) q^{46} +(-7.97634 - 1.20224i) q^{47} +(1.72479 + 0.158418i) q^{48} +(-5.50647 + 4.32190i) q^{49} +(0.859151 + 1.48809i) q^{50} +(6.90872 - 7.19952i) q^{51} +(-2.51863 - 1.21291i) q^{52} +(-0.700447 + 0.649920i) q^{53} +(1.03217 - 5.09260i) q^{54} +(-4.08716 + 1.96827i) q^{55} +(0.306412 - 2.62795i) q^{56} +(-0.109438 + 6.51714i) q^{57} +(-0.00619076 - 0.00776296i) q^{58} +(-0.992564 + 13.2448i) q^{59} +(4.35947 + 1.07234i) q^{60} +(0.775640 - 0.239253i) q^{61} +(-2.19424 + 2.75149i) q^{62} +(-7.73815 - 1.76663i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-5.98673 - 4.08168i) q^{65} +(-0.942029 + 2.88131i) q^{66} +(-0.519222 + 0.899320i) q^{67} +5.76089 q^{68} +(-0.415246 - 0.462878i) q^{69} +(1.80055 - 6.61711i) q^{70} +(-1.04058 - 4.55906i) q^{71} +(2.53406 - 1.60578i) q^{72} +(5.86366 - 14.9404i) q^{73} +(-0.594379 - 0.745328i) q^{74} +(2.75181 + 1.13369i) q^{75} +(-2.75862 + 2.55963i) q^{76} +(4.36473 + 1.54629i) q^{77} +(-4.73792 + 0.998014i) q^{78} +(5.03667 + 8.72376i) q^{79} +(1.29598 + 2.24471i) q^{80} +(-3.96677 - 8.07866i) q^{81} +(-0.239044 + 3.18982i) q^{82} +(3.62283 - 0.546053i) q^{83} +(-2.35738 - 3.92973i) q^{84} +(14.7653 + 2.22550i) q^{85} +(-1.60103 + 7.01458i) q^{86} +(-0.0167001 - 0.00410786i) q^{87} +(-1.57686 + 0.759373i) q^{88} +(1.37605 - 0.207407i) q^{89} +(7.11518 - 3.13671i) q^{90} +(1.34686 + 7.27244i) q^{91} +(0.0268296 - 0.358016i) q^{92} +(-0.102345 + 6.09473i) q^{93} +(-7.70806 - 2.37762i) q^{94} +(-8.05921 + 5.49468i) q^{95} +(1.68192 + 0.413715i) q^{96} +(4.98514 - 8.63452i) q^{97} +(-6.08911 + 3.45293i) q^{98} +(1.75305 + 4.94923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9}+O(q^{10}) \) 336 * q - 28 * q^2 - 13 * q^3 + 28 * q^4 - 4 * q^5 - 5 * q^6 - q^7 + 56 * q^8 + 29 * q^9	\( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9} - 2 q^{10} + q^{12} - 23 q^{13} + q^{14} + q^{15} + 28 q^{16} + 7 q^{17} - q^{18} + 38 q^{19} + 2 q^{20} + 13 q^{21} + 21 q^{23} - q^{24} - 48 q^{25} + 9 q^{26} - 28 q^{27} + 2 q^{28} + 11 q^{29} - 7 q^{30} + 44 q^{31} - 28 q^{32} - 25 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} - 22 q^{38} - 51 q^{39} + 4 q^{40} + 3 q^{41} + 13 q^{42} + q^{43} - 75 q^{45} - 42 q^{46} - 33 q^{47} - 2 q^{48} - 41 q^{49} + 172 q^{50} + 4 q^{51} + 11 q^{52} - 78 q^{53} + 11 q^{54} + 23 q^{55} + q^{56} - 30 q^{57} - 13 q^{58} + 14 q^{59} - 8 q^{60} + 92 q^{61} - 24 q^{62} - 22 q^{63} - 56 q^{64} + 7 q^{65} + 29 q^{66} + 29 q^{67} + 42 q^{68} + 19 q^{69} - 34 q^{70} + 7 q^{71} - q^{72} - 8 q^{73} - 8 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{77} + 4 q^{78} - 9 q^{79} - 12 q^{80} + 45 q^{81} - 3 q^{82} - 109 q^{83} + 28 q^{84} + 93 q^{85} + 2 q^{86} - 15 q^{87} + 47 q^{89} - 3 q^{90} + 45 q^{91} + 42 q^{92} + 155 q^{93} - 9 q^{94} - 13 q^{95} - q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q - 28 * q^2 - 13 * q^3 + 28 * q^4 - 4 * q^5 - 5 * q^6 - q^7 + 56 * q^8 + 29 * q^9 - 2 * q^10 + q^12 - 23 * q^13 + q^14 + q^15 + 28 * q^16 + 7 * q^17 - q^18 + 38 * q^19 + 2 * q^20 + 13 * q^21 + 21 * q^23 - q^24 - 48 * q^25 + 9 * q^26 - 28 * q^27 + 2 * q^28 + 11 * q^29 - 7 * q^30 + 44 * q^31 - 28 * q^32 - 25 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 - 22 * q^38 - 51 * q^39 + 4 * q^40 + 3 * q^41 + 13 * q^42 + q^43 - 75 * q^45 - 42 * q^46 - 33 * q^47 - 2 * q^48 - 41 * q^49 + 172 * q^50 + 4 * q^51 + 11 * q^52 - 78 * q^53 + 11 * q^54 + 23 * q^55 + q^56 - 30 * q^57 - 13 * q^58 + 14 * q^59 - 8 * q^60 + 92 * q^61 - 24 * q^62 - 22 * q^63 - 56 * q^64 + 7 * q^65 + 29 * q^66 + 29 * q^67 + 42 * q^68 + 19 * q^69 - 34 * q^70 + 7 * q^71 - q^72 - 8 * q^73 - 8 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^77 + 4 * q^78 - 9 * q^79 - 12 * q^80 + 45 * q^81 - 3 * q^82 - 109 * q^83 + 28 * q^84 + 93 * q^85 + 2 * q^86 - 15 * q^87 + 47 * q^89 - 3 * q^90 + 45 * q^91 + 42 * q^92 + 155 * q^93 - 9 * q^94 - 13 * q^95 - q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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