LMFDB - Embedded newform 372.2.ba.a.43.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(43,372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("372.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 0, 19])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			43.15
Character	$\chi$	$=$	372.43
Dual form			372.2.ba.a.199.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38712 - 0.275519i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(1.84818 - 0.764352i) q^{4} +(1.01376 - 1.75588i) q^{5} +(-1.37926 - 0.312492i) q^{6} +(-2.45297 - 2.20866i) q^{7} +(2.35304 - 1.56945i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.922421 - 2.71492i) q^{10} +(-2.37540 - 0.504907i) q^{11} +(-1.99929 - 0.0534516i) q^{12} +(-0.470290 + 0.0494294i) q^{13} +(-4.01108 - 2.38783i) q^{14} +(-1.64029 + 1.19174i) q^{15} +(2.83153 - 2.82532i) q^{16} +(0.729809 + 3.43348i) q^{17} +(1.13291 + 0.846470i) q^{18} +(4.36627 + 0.458914i) q^{19} +(0.531494 - 4.02004i) q^{20} +(1.34256 + 3.01543i) q^{21} +(-3.43406 - 0.0458972i) q^{22} +(0.249732 - 0.768596i) q^{23} +(-2.78797 + 0.476697i) q^{24} +(0.444594 + 0.770060i) q^{25} +(-0.638727 + 0.198138i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-6.22173 - 2.20707i) q^{28} +(4.56381 - 6.28155i) q^{29} +(-1.94693 + 2.10502i) q^{30} +(5.56134 - 0.267292i) q^{31} +(3.14923 - 4.69918i) q^{32} +(1.96467 + 1.42742i) q^{33} +(1.95832 + 4.56156i) q^{34} +(-6.36486 + 2.06807i) q^{35} +(1.80470 + 0.862013i) q^{36} +(-8.90837 + 5.14325i) q^{37} +(6.18296 - 0.566423i) q^{38} +(0.449736 + 0.146128i) q^{39} +(-0.370353 - 5.72270i) q^{40} +(1.77354 - 0.789632i) q^{41} +(2.69309 + 3.81285i) q^{42} +(-1.25308 + 11.9223i) q^{43} +(-4.77609 + 0.882484i) q^{44} +(1.98321 - 0.421544i) q^{45} +(0.134645 - 1.13494i) q^{46} +(3.12976 + 4.30774i) q^{47} +(-3.73589 + 1.42937i) q^{48} +(0.407166 + 3.87392i) q^{49} +(0.828869 + 0.945668i) q^{50} +(0.729809 - 3.43348i) q^{51} +(-0.831398 + 0.450821i) q^{52} +(3.68658 - 3.31941i) q^{53} +(-0.690676 - 1.23409i) q^{54} +(-3.29463 + 3.65906i) q^{55} +(-9.23834 - 1.34726i) q^{56} +(-3.80213 - 2.19516i) q^{57} +(4.59985 - 9.97065i) q^{58} +(0.745769 - 1.67503i) q^{59} +(-2.12064 + 3.45632i) q^{60} -1.82153i q^{61} +(7.64058 - 1.90302i) q^{62} -3.30080i q^{63} +(3.07364 - 7.38598i) q^{64} +(-0.389967 + 0.875881i) q^{65} +(3.11851 + 1.43869i) q^{66} +(6.39130 + 3.69002i) q^{67} +(3.97321 + 5.78786i) q^{68} +(-0.540758 + 0.600572i) q^{69} +(-8.25901 + 4.62229i) q^{70} +(-8.78095 + 7.90640i) q^{71} +(2.74082 + 0.698484i) q^{72} +(-2.41912 + 11.3811i) q^{73} +(-10.9399 + 9.58870i) q^{74} +(-0.0929455 - 0.884317i) q^{75} +(8.42042 - 2.48921i) q^{76} +(4.71161 + 6.48498i) q^{77} +(0.664096 + 0.0787859i) q^{78} +(-13.8017 + 2.93364i) q^{79} +(-2.09043 - 7.83601i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.24255 - 1.58395i) q^{82} +(7.40839 - 3.29843i) q^{83} +(4.78613 + 4.54687i) q^{84} +(6.76863 + 2.19926i) q^{85} +(1.54664 + 16.8828i) q^{86} +(-6.72419 + 3.88221i) q^{87} +(-6.38185 + 2.54001i) q^{88} +(-2.50874 + 0.815138i) q^{89} +(2.63479 - 1.13114i) q^{90} +(1.26278 + 0.917463i) q^{91} +(-0.125929 - 1.61139i) q^{92} +(-5.18926 - 2.01782i) q^{93} +(5.52819 + 5.11303i) q^{94} +(5.23213 - 7.20141i) q^{95} +(-4.78830 + 3.01201i) q^{96} +(-0.792875 - 2.44022i) q^{97} +(1.63212 + 5.26139i) q^{98} +(-1.21423 - 2.10311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{30}\right)$

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 $

$2$	1.38712	−	0.275519i	0.980839	−	0.194821i
$2$	1.38712	−	0.275519i	0.980839	−	0.194821i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	1.84818	−	0.764352i	0.924089	−	0.382176i
$5$	1.01376	−	1.75588i	0.453366	−	0.785253i	−0.545227	−	0.838289i	$-0.683556\pi$
$5$	1.01376	−	1.75588i	0.453366	−	0.785253i	0.998593	+	0.0530359i	$0.0168898\pi$
$6$	−1.37926	−	0.312492i	−0.563079	−	0.127574i
$7$	−2.45297	−	2.20866i	−0.927136	−	0.834797i	0.0594183	−	0.998233i	$-0.481075\pi$
$7$	−2.45297	−	2.20866i	−0.927136	−	0.834797i	−0.986554	+	0.163437i	$0.947742\pi$
$8$	2.35304	−	1.56945i	0.831927	−	0.554885i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	0.922421	−	2.71492i	0.291695	−	0.858532i
$11$	−2.37540	−	0.504907i	−0.716210	−	0.152235i	−0.164628	−	0.986356i	$-0.552642\pi$
$11$	−2.37540	−	0.504907i	−0.716210	−	0.152235i	−0.551582	+	0.834121i	$0.685976\pi$
$12$	−1.99929	−	0.0534516i	−0.577144	−	0.0154301i
$13$	−0.470290	+	0.0494294i	−0.130435	+	0.0137093i	−0.169521	−	0.985527i	$-0.554222\pi$
$13$	−0.470290	+	0.0494294i	−0.130435	+	0.0137093i	0.0390860	+	0.999236i	$0.487555\pi$
$14$	−4.01108	−	2.38783i	−1.07201	−	0.638175i
$15$	−1.64029	+	1.19174i	−0.423522	+	0.307707i
$16$	2.83153	−	2.82532i	0.707883	−	0.706330i
$17$	0.729809	+	3.43348i	0.177005	+	0.832742i	0.973606	+	0.228236i	$0.0732959\pi$
$17$	0.729809	+	3.43348i	0.177005	+	0.832742i	−0.796601	+	0.604506i	$0.793371\pi$
$18$	1.13291	+	0.846470i	0.267030	+	0.199515i
$19$	4.36627	+	0.458914i	1.00169	+	0.105282i	0.591151	−	0.806561i	$-0.298674\pi$
$19$	4.36627	+	0.458914i	1.00169	+	0.105282i	0.410540	+	0.911843i	$0.365340\pi$
$20$	0.531494	−	4.02004i	0.118846	−	0.898909i
$21$	1.34256	+	3.01543i	0.292970	+	0.658020i
$22$	−3.43406	−	0.0458972i	−0.732145	−	0.00978532i
$23$	0.249732	−	0.768596i	0.0520727	−	0.160263i	−0.921638	−	0.388050i	$-0.873149\pi$
$23$	0.249732	−	0.768596i	0.0520727	−	0.160263i	0.973711	+	0.227786i	$0.0731488\pi$
$24$	−2.78797	+	0.476697i	−0.569091	+	0.0973053i
$25$	0.444594	+	0.770060i	0.0889188	+	0.154012i
$26$	−0.638727	+	0.198138i	−0.125265	+	0.0388580i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−6.22173	−	2.20707i	−1.17580	−	0.417098i
$29$	4.56381	−	6.28155i	0.847479	−	1.16645i	−0.136934	−	0.990580i	$-0.543725\pi$
$29$	4.56381	−	6.28155i	0.847479	−	1.16645i	0.984413	−	0.175874i	$-0.0562752\pi$
$30$	−1.94693	+	2.10502i	−0.355459	+	0.384322i
$31$	5.56134	−	0.267292i	0.998847	−	0.0480070i
$31$	5.56134	−	0.267292i	0.998847	−	0.0480070i
$32$	3.14923	−	4.69918i	0.556711	−	0.830706i
$33$	1.96467	+	1.42742i	0.342005	+	0.248481i
$34$	1.95832	+	4.56156i	0.335849	+	0.782301i
$35$	−6.36486	+	2.06807i	−1.07586	+	0.349567i
$36$	1.80470	+	0.862013i	0.300783	+	0.143669i
$37$	−8.90837	+	5.14325i	−1.46453	+	0.845545i	−0.999216	−	0.0396020i	$-0.987391\pi$
$37$	−8.90837	+	5.14325i	−1.46453	+	0.845545i	−0.465311	+	0.885147i	$0.654058\pi$
$38$	6.18296	−	0.566423i	1.00301	−	0.0918859i
$39$	0.449736	+	0.146128i	0.0720154	+	0.0233992i
$40$	−0.370353	−	5.72270i	−0.0585579	−	0.904839i
$41$	1.77354	−	0.789632i	0.276981	−	0.123320i	−0.263545	−	0.964647i	$-0.584892\pi$
$41$	1.77354	−	0.789632i	0.276981	−	0.123320i	0.540526	+	0.841327i	$0.318225\pi$
$42$	2.69309	+	3.81285i	0.415552	+	0.588335i
$43$	−1.25308	+	11.9223i	−0.191093	+	1.81813i	0.307781	+	0.951457i	$0.400414\pi$
$43$	−1.25308	+	11.9223i	−0.191093	+	1.81813i	−0.498874	+	0.866675i	$0.666253\pi$
$44$	−4.77609	+	0.882484i	−0.720023	+	0.133039i
$45$	1.98321	−	0.421544i	0.295639	−	0.0628400i
$46$	0.134645	−	1.13494i	0.0198523	−	0.167337i
$47$	3.12976	+	4.30774i	0.456522	+	0.628348i	0.973783	−	0.227479i	$-0.0730484\pi$
$47$	3.12976	+	4.30774i	0.456522	+	0.628348i	−0.517261	+	0.855828i	$0.673048\pi$
$48$	−3.73589	+	1.42937i	−0.539230	+	0.206312i
$49$	0.407166	+	3.87392i	0.0581665	+	0.553417i
$50$	0.828869	+	0.945668i	0.117220	+	0.133738i
$51$	0.729809	−	3.43348i	0.102194	−	0.480784i
$52$	−0.831398	+	0.450821i	−0.115294	+	0.0625177i
$53$	3.68658	−	3.31941i	0.506391	−	0.455957i	−0.375900	−	0.926660i	$-0.622667\pi$
$53$	3.68658	−	3.31941i	0.506391	−	0.455957i	0.882291	+	0.470704i	$0.156000\pi$
$54$	−0.690676	−	1.23409i	−0.0939891	−	0.167938i
$55$	−3.29463	+	3.65906i	−0.444248	+	0.493388i
$56$	−9.23834	−	1.34726i	−1.23453	−	0.180036i
$57$	−3.80213	−	2.19516i	−0.503604	−	0.290756i
$58$	4.59985	−	9.97065i	0.603990	−	1.30921i
$59$	0.745769	−	1.67503i	0.0970909	−	0.218070i	−0.858470	−	0.512864i	$-0.828584\pi$
$59$	0.745769	−	1.67503i	0.0970909	−	0.218070i	0.955561	+	0.294794i	$0.0952512\pi$
$60$	−2.12064	+	3.45632i	−0.273774	+	0.446208i
$61$		−	1.82153i		−	0.233223i	−0.993178	−	0.116611i	$-0.962797\pi$
$61$		−	1.82153i		−	0.233223i	0.993178	−	0.116611i	$-0.0372032\pi$
$62$	7.64058	−	1.90302i	0.970355	−	0.241684i
$63$		−	3.30080i		−	0.415861i
$64$	3.07364	−	7.38598i	0.384205	−	0.923248i
$65$	−0.389967	+	0.875881i	−0.0483695	+	0.108640i
$66$	3.11851	+	1.43869i	0.383862	+	0.177090i
$67$	6.39130	+	3.69002i	0.780821	+	0.450807i	0.836721	−	0.547629i	$-0.184470\pi$
$67$	6.39130	+	3.69002i	0.780821	+	0.450807i	−0.0559001	+	0.998436i	$0.517803\pi$
$68$	3.97321	+	5.78786i	0.481822	+	0.701881i
$69$	−0.540758	+	0.600572i	−0.0650996	+	0.0723004i
$70$	−8.25901	+	4.62229i	−0.987140	+	0.552469i
$71$	−8.78095	+	7.90640i	−1.04211	+	0.938317i	−0.998155	−	0.0607161i	$-0.980662\pi$
$71$	−8.78095	+	7.90640i	−1.04211	+	0.938317i	−0.0439521	+	0.999034i	$0.513995\pi$
$72$	2.74082	+	0.698484i	0.323009	+	0.0823171i
$73$	−2.41912	+	11.3811i	−0.283137	+	1.33205i	0.574798	+	0.818295i	$0.305081\pi$
$73$	−2.41912	+	11.3811i	−0.283137	+	1.33205i	−0.857935	+	0.513758i	$0.828253\pi$
$74$	−10.9399	+	9.58870i	−1.27173	+	1.11466i
$75$	−0.0929455	−	0.884317i	−0.0107324	−	0.102112i
$76$	8.42042	−	2.48921i	0.965889	−	0.285532i
$77$	4.71161	+	6.48498i	0.536938	+	0.739032i
$78$	0.664096	+	0.0787859i	0.0751941	+	0.00892074i
$79$	−13.8017	+	2.93364i	−1.55281	+	0.330060i	−0.902866	−	0.429922i	$-0.858541\pi$
$79$	−13.8017	+	2.93364i	−1.55281	+	0.330060i	−0.649944	+	0.759982i	$0.725208\pi$
$80$	−2.09043	−	7.83601i	−0.233718	−	0.876093i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	2.24255	−	1.58395i	0.247648	−	0.174919i
$83$	7.40839	−	3.29843i	0.813176	−	0.362049i	0.0423562	−	0.999103i	$-0.486514\pi$
$83$	7.40839	−	3.29843i	0.813176	−	0.362049i	0.770820	+	0.637053i	$0.219847\pi$
$84$	4.78613	+	4.54687i	0.522210	+	0.496104i
$85$	6.76863	+	2.19926i	0.734161	+	0.238543i
$86$	1.54664	+	16.8828i	0.166779	+	1.82052i
$87$	−6.72419	+	3.88221i	−0.720908	+	0.416217i
$88$	−6.38185	+	2.54001i	−0.680307	+	0.270766i
$89$	−2.50874	+	0.815138i	−0.265926	+	0.0864045i	−0.438945	−	0.898514i	$-0.644648\pi$
$89$	−2.50874	+	0.815138i	−0.265926	+	0.0864045i	0.173019	+	0.984918i	$0.444648\pi$
$90$	2.63479	−	1.13114i	0.277732	−	0.119233i
$91$	1.26278	+	0.917463i	0.132375	+	0.0961763i
$92$	−0.125929	−	1.61139i	−0.0131290	−	0.167999i
$93$	−5.18926	−	2.01782i	−0.538101	−	0.209238i
$94$	5.52819	+	5.11303i	0.570190	+	0.527368i
$95$	5.23213	−	7.20141i	0.536806	−	0.738849i
$96$	−4.78830	+	3.01201i	−0.488704	+	0.307412i
$97$	−0.792875	−	2.44022i	−0.0805043	−	0.247767i	0.902701	−	0.430268i	$-0.141581\pi$
$97$	−0.792875	−	2.44022i	−0.0805043	−	0.247767i	−0.983206	+	0.182501i	$0.941581\pi$
$98$	1.63212	+	5.26139i	0.164869	+	0.531481i
$99$	−1.21423	−	2.10311i	−0.122035	−	0.211371i
$100$	1.41029	+	1.08338i	0.141029	+	0.108338i
$101$	5.85448	−	18.0182i	0.582542	−	1.79288i	−0.0263810	−	0.999652i	$-0.508398\pi$
$101$	5.85448	−	18.0182i	0.582542	−	1.79288i	0.608923	−	0.793229i	$-0.291602\pi$
$102$	0.0663414	−	4.96371i	0.00656878	−	0.491481i
$103$	1.32164	+	2.96845i	0.130225	+	0.292490i	0.966876	−	0.255246i	$-0.0821564\pi$
$103$	1.32164	+	2.96845i	0.130225	+	0.292490i	−0.836651	+	0.547736i	$0.815490\pi$
$104$	−1.02904	+	0.854407i	−0.100905	+	0.0837815i
$105$	6.65575	+	0.699547i	0.649535	+	0.0682688i
$106$	4.19916	−	5.62013i	0.407858	−	0.545876i
$107$	−0.668465	−	3.14488i	−0.0646230	−	0.304027i	0.933952	−	0.357399i	$-0.116336\pi$
$107$	−0.668465	−	3.14488i	−0.0646230	−	0.304027i	−0.998575	+	0.0533720i	$0.983003\pi$
$108$	−1.29806	−	1.52152i	−0.124906	−	0.146409i
$109$	−8.06544	+	5.85988i	−0.772529	+	0.561275i	−0.902728	−	0.430213i	$-0.858439\pi$
$109$	−8.06544	+	5.85988i	−0.772529	+	0.561275i	0.130199	+	0.991488i	$0.458439\pi$
$110$	−3.56190	+	5.98327i	−0.339613	+	0.570483i
$111$	10.2301	−	1.07523i	0.971003	−	0.102056i
$112$	−13.1858	+	0.676523i	−1.24595	+	0.0639254i
$113$	−11.3478	−	2.41205i	−1.06751	−	0.226906i	−0.359526	−	0.933135i	$-0.617062\pi$
$113$	−11.3478	−	2.41205i	−1.06751	−	0.226906i	−0.707984	+	0.706229i	$0.750395\pi$
$114$	−5.87880	−	1.99738i	−0.550600	−	0.187072i
$115$	−1.09639	−	1.21767i	−0.102239	−	0.113548i
$116$	3.63343	−	15.0978i	0.337355	−	1.40179i
$117$	−0.351418	−	0.316419i	−0.0324886	−	0.0292529i
$118$	0.572967	−	2.52893i	0.0527459	−	0.232807i
$119$	5.79321	−	10.0341i	0.531063	−	0.919828i
$120$	−1.98930	+	5.37859i	−0.181597	+	0.490995i
$121$	−4.66141	−	2.07539i	−0.423764	−	0.188672i
$122$	−0.501865	−	2.52667i	−0.0454367	−	0.228754i
$123$	−1.94138			−0.175049
$124$	10.0741	−	4.74483i	0.904677	−	0.426098i
$125$	11.9404			1.06798
$126$	−0.909431	−	4.57859i	−0.0810185	−	0.407893i
$127$	10.2295	+	4.55448i	0.907723	+	0.404144i	0.806851	−	0.590755i	$-0.201170\pi$
$127$	10.2295	+	4.55448i	0.907723	+	0.404144i	0.100872	+	0.994899i	$0.467837\pi$
$128$	2.22851	−	11.0921i	0.196975	−	0.980409i
$129$	5.99398	−	10.3819i	0.527741	−	0.914073i
$130$	−0.299608	+	1.32239i	−0.0262774	+	0.115981i
$131$	−3.77513	−	3.39915i	−0.329835	−	0.296985i	0.487528	−	0.873107i	$-0.337899\pi$
$131$	−3.77513	−	3.39915i	−0.329835	−	0.296985i	−0.817364	+	0.576122i	$0.804565\pi$
$132$	4.72211	+	1.13642i	0.411007	+	0.0989128i
$133$	−9.69675	−	10.7693i	−0.840814	−	0.933819i
$134$	9.88213	+	3.35756i	0.853686	+	0.290049i
$135$	−1.98321	−	0.421544i	−0.170687	−	0.0362807i
$136$	7.10596	+	6.93374i	0.609331	+	0.594563i
$137$	0.712853	−	0.0749239i	0.0609031	−	0.00640118i	−0.0740279	−	0.997256i	$-0.523585\pi$
$137$	0.712853	−	0.0749239i	0.0609031	−	0.00640118i	0.134931	+	0.990855i	$0.456919\pi$
$138$	−0.584625	+	0.982052i	−0.0497666	+	0.0835978i
$139$	4.47998	−	3.25489i	0.379987	−	0.276077i	−0.381353	−	0.924429i	$-0.624542\pi$
$139$	4.47998	−	3.25489i	0.379987	−	0.276077i	0.761340	+	0.648353i	$0.224542\pi$
$140$	−10.1827	+	8.68716i	−0.860593	+	0.734199i
$141$	−1.10706	−	5.20830i	−0.0932312	−	0.438618i
$142$	−10.0018	+	13.3864i	−0.839335	+	1.12336i
$143$	1.14208	+	0.120038i	0.0955058	+	0.0100381i
$144$	3.99429	+	0.213730i	0.332857	+	0.0178108i
$145$	−6.40304	−	14.3815i	−0.531743	−	1.19432i
$146$	−0.219904	+	16.4534i	−0.0181994	+	1.36169i
$147$	1.20370	−	3.70461i	0.0992796	−	0.305551i
$148$	−12.5330	+	16.3148i	−1.03021	+	1.34107i
$149$	−10.5690	−	18.3061i	−0.865847	−	1.49969i	−0.866204	−	0.499691i	$-0.833447\pi$
$149$	−10.5690	−	18.3061i	−0.865847	−	1.49969i	0.000356622	−	1.00000i	$-0.499886\pi$
$150$	−0.372572	−	1.20104i	−0.0304204	−	0.0980647i
$151$	1.58350	+	4.87351i	0.128863	+	0.396601i	0.994585	−	0.103925i	$-0.0331401\pi$
$151$	1.58350	+	4.87351i	0.128863	+	0.396601i	−0.865722	+	0.500526i	$0.833140\pi$
$152$	10.9943	−	5.77281i	0.891753	−	0.468237i
$153$	−2.06324	+	2.83980i	−0.166803	+	0.229584i
$154$	8.32229	+	7.69728i	0.670629	+	0.620264i
$155$	5.16852	−	10.0360i	0.415146	−	0.806112i
$156$	0.942886	−	0.0736858i	0.0754913	−	0.00589959i
$157$	8.67297	+	6.30128i	0.692178	+	0.502897i	0.877375	−	0.479805i	$-0.159292\pi$
$157$	8.67297	+	6.30128i	0.692178	+	0.502897i	−0.185197	+	0.982701i	$0.559292\pi$
$158$	−18.3363	+	7.87191i	−1.45875	+	0.626256i
$159$	−4.71799	+	1.53297i	−0.374161	+	0.121572i
$160$	−5.05864	−	10.2935i	−0.399921	−	0.813773i
$161$	−2.31016	+	1.33377i	−0.182066	+	0.105116i
$162$	0.129016	+	1.40832i	0.0101365	+	0.110648i
$163$	−11.1226	−	3.61395i	−0.871189	−	0.283067i	−0.160895	−	0.986972i	$-0.551438\pi$
$163$	−11.1226	−	3.61395i	−0.871189	−	0.283067i	−0.710294	+	0.703905i	$0.751438\pi$
$164$	2.67427	−	2.81499i	0.208825	−	0.219814i
$165$	4.49807	−	2.00267i	0.350174	−	0.155908i
$166$	9.36751	−	6.61645i	0.727060	−	0.513536i
$167$	1.32121	−	12.5705i	0.102238	−	0.972731i	−0.816361	−	0.577541i	$-0.804012\pi$
$167$	1.32121	−	12.5705i	0.102238	−	0.972731i	0.918600	−	0.395190i	$-0.129321\pi$
$168$	7.89166	+	4.98836i	0.608855	+	0.384860i
$169$	−12.4972	+	2.65636i	−0.961322	+	0.204335i
$170$	9.99481	+	1.18575i	0.766567	+	0.0909425i
$171$	2.58057	+	3.55184i	0.197341	+	0.271616i
$172$	6.79691	+	22.9923i	0.518259	+	1.75315i
$173$	2.16050	+	20.5557i	0.164259	+	1.56282i	0.697328	+	0.716752i	$0.254372\pi$
$173$	2.16050	+	20.5557i	0.164259	+	1.56282i	−0.533068	+	0.846072i	$0.678961\pi$
$174$	−8.25760	+	7.23771i	−0.626007	+	0.548690i
$175$	0.610227	−	2.87089i	0.0461288	−	0.217019i
$176$	−8.15254	+	5.28160i	−0.614521	+	0.398116i
$177$	−1.36259	+	1.22688i	−0.102418	+	0.0922179i
$178$	−3.25532	+	1.82189i	−0.243997	+	0.136557i
$179$	2.67139	−	2.96688i	0.199669	−	0.221755i	−0.634992	−	0.772518i	$-0.718997\pi$
$179$	2.67139	−	2.96688i	0.199669	−	0.221755i	0.834661	+	0.550764i	$0.185663\pi$
$180$	3.34311	−	2.29496i	0.249181	−	0.171056i
$181$	0.363506	+	0.209870i	0.0270192	+	0.0155995i	0.513449	−	0.858120i	$-0.328368\pi$
$181$	0.363506	+	0.209870i	0.0270192	+	0.0155995i	−0.486430	+	0.873720i	$0.661701\pi$
$182$	2.00440	+	0.924708i	0.148576	+	0.0685439i
$183$	−0.740882	+	1.66405i	−0.0547676	+	0.123010i
$184$	−0.618645	−	2.20048i	−0.0456071	−	0.162222i
$185$			20.8560i			1.53336i
$186$	−7.75405	−	1.36921i	−0.568554	−	0.100395i
$187$		−	8.52438i		−	0.623364i
$188$	9.07698	+	5.56924i	0.662007	+	0.406178i
$189$	−1.34256	+	3.01543i	−0.0976565	+	0.219340i
$190$	5.27345	−	11.4307i	0.382576	−	0.829273i
$191$	5.89101	+	3.40118i	0.426259	+	0.246100i	0.697751	−	0.716340i	$-0.254184\pi$
$191$	5.89101	+	3.40118i	0.426259	+	0.246100i	−0.271493	+	0.962440i	$0.587517\pi$
$192$	−5.81206	+	5.49727i	−0.419449	+	0.396731i
$193$	−10.1925	+	11.3199i	−0.733673	+	0.814826i	−0.988350	−	0.152200i	$-0.951364\pi$
$193$	−10.1925	+	11.3199i	−0.733673	+	0.814826i	0.254677	+	0.967026i	$0.418031\pi$
$194$	−1.77214	−	3.16641i	−0.127232	−	0.227335i
$195$	0.712506	−	0.641543i	0.0510236	−	0.0459419i
$196$	3.71356	+	6.84848i	0.265254	+	0.489177i
$197$	0.834414	−	3.92561i	0.0594496	−	0.279688i	−0.938375	−	0.345620i	$-0.887669\pi$
$197$	0.834414	−	3.92561i	0.0594496	−	0.279688i	0.997824	+	0.0659318i	$0.0210020\pi$
$198$	−2.26373	−	2.58272i	−0.160876	−	0.183546i
$199$	−1.04264	−	9.92004i	−0.0739107	−	0.703213i	−0.967249	−	0.253829i	$-0.918310\pi$
$199$	−1.04264	−	9.92004i	−0.0739107	−	0.703213i	0.893339	−	0.449384i	$-0.148357\pi$
$200$	2.25472	+	1.11422i	0.159433	+	0.0787869i
$201$	−4.33787	−	5.97057i	−0.305970	−	0.421132i
$202$	3.15648	−	26.6064i	0.222089	−	1.87202i
$203$	−25.0687	+	5.32852i	−1.75948	+	0.373989i
$204$	−1.27557	−	6.90352i	−0.0893079	−	0.483343i
$205$	0.411443	−	3.91462i	0.0287364	−	0.273409i
$206$	2.65113	+	3.75345i	0.184713	+	0.261515i
$207$	0.738282	−	0.328704i	0.0513141	−	0.0228465i
$208$	−1.19199	+	1.46868i	−0.0826494	+	0.101835i
$209$	−10.1399	−	3.29466i	−0.701393	−	0.227897i
$210$	9.42503	−	0.863430i	0.650389	−	0.0595823i
$211$	23.2785	−	13.4398i	1.60256	−	0.925237i	0.611583	−	0.791180i	$-0.290533\pi$
$211$	23.2785	−	13.4398i	1.60256	−	0.925237i	0.990974	−	0.134056i	$-0.0428003\pi$
$212$	4.27626	−	8.95272i	0.293695	−	0.614875i
$213$	11.2376	−	3.65132i	0.769989	−	0.250185i
$214$	−1.79371	−	4.17814i	−0.122616	−	0.285612i
$215$	19.6638	+	14.2866i	1.34106	+	0.974336i
$216$	−2.21977	−	1.75289i	−0.151036	−	0.119269i
$217$	−14.2322	−	11.6275i	−0.966143	−	0.789325i
$218$	−9.57319	+	10.3505i	−0.648378	+	0.701025i
$219$	6.83907	−	9.41318i	0.462142	−	0.636084i
$220$	−3.29226	+	9.28086i	−0.221964	+	0.625715i
$221$	−0.512937	−	1.57866i	−0.0345039	−	0.106192i
$222$	13.8942	−	4.31007i	0.932514	−	0.289273i
$223$	−8.89106	−	15.3998i	−0.595389	−	1.03124i	−0.993492	−	0.113904i	$-0.963664\pi$
$223$	−8.89106	−	15.3998i	−0.595389	−	1.03124i	0.398102	−	0.917341i	$-0.369669\pi$
$224$	−18.1039	+	4.57136i	−1.20962	+	0.305437i
$225$	−0.274774	+	0.845668i	−0.0183183	+	0.0563779i
$226$	−16.4053	−	0.219261i	−1.09126	−	0.0145850i
$227$	1.47765	+	3.31886i	0.0980751	+	0.220280i	0.955919	−	0.293630i	$-0.0948632\pi$
$227$	1.47765	+	3.31886i	0.0980751	+	0.220280i	−0.857844	+	0.513910i	$0.828197\pi$
$228$	−8.70489	−	1.15088i	−0.576496	−	0.0762191i
$229$	12.8820	+	1.35395i	0.851264	+	0.0894714i	0.520104	−	0.854103i	$-0.325893\pi$
$229$	12.8820	+	1.35395i	0.851264	+	0.0894714i	0.331160	+	0.943575i	$0.392560\pi$
$230$	−1.85632	−	1.38697i	−0.122402	−	0.0914541i
$231$	−1.66659	−	7.84071i	−0.109654	−	0.515881i
$232$	0.880260	−	21.9434i	0.0577919	−	1.44066i
$233$	−21.7523	+	15.8040i	−1.42504	+	1.03535i	−0.434127	+	0.900852i	$0.642943\pi$
$233$	−21.7523	+	15.8040i	−1.42504	+	1.03535i	−0.990913	+	0.134501i	$0.957057\pi$
$234$	−0.574637	−	0.342087i	−0.0375652	−	0.0223629i
$235$	10.7367	−	1.12847i	0.700384	−	0.0736133i
$236$	0.0980057	−	3.66578i	0.00637963	−	0.238622i
$237$	13.8017	+	2.93364i	0.896515	+	0.190560i
$238$	5.27126	−	15.5146i	0.341685	−	1.00566i
$239$	2.39233	+	2.65695i	0.154747	+	0.171864i	0.815533	−	0.578710i	$-0.196444\pi$
$239$	2.39233	+	2.65695i	0.154747	+	0.171864i	−0.660786	+	0.750574i	$0.729777\pi$
$240$	−1.27749	+	8.00881i	−0.0824614	+	0.516966i
$241$	17.4840	+	15.7426i	1.12624	+	1.01407i	0.999756	+	0.0221029i	$0.00703614\pi$
$241$	17.4840	+	15.7426i	1.12624	+	1.01407i	0.126485	+	0.991969i	$0.459631\pi$
$242$	−7.03772	−	1.59450i	−0.452402	−	0.102499i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−1.39229	−	3.36651i	−0.0891321	−	0.215519i
$245$	7.21490	+	3.21228i	0.460943	+	0.205225i
$246$	−2.69292	+	0.534887i	−0.171695	+	0.0341032i
$247$	−2.07610			−0.132099
$248$	12.6666	−	9.35722i	0.804329	−	0.594184i
$249$	−8.10949			−0.513918
$250$	16.5627	−	3.28981i	1.04752	−	0.208066i
$251$	−19.3724	−	8.62515i	−1.22277	−	0.544414i	−0.309166	−	0.951008i	$-0.600050\pi$
$251$	−19.3724	−	8.62515i	−1.22277	−	0.544414i	−0.913609	+	0.406594i	$0.866716\pi$
$252$	−2.52297	−	6.10046i	−0.158932	−	0.384293i
$253$	−0.981283	+	1.69963i	−0.0616927	+	0.106855i
$254$	15.4444	+	3.49916i	0.969066	+	0.219557i
$255$	−5.28893	−	4.76217i	−0.331206	−	0.298219i
$256$	0.0351374	−	16.0000i	0.00219609	−	0.999998i
$257$	1.01090	+	1.12272i	0.0630583	+	0.0700333i	0.773849	−	0.633371i	$-0.218329\pi$
$257$	1.01090	+	1.12272i	0.0630583	+	0.0700333i	−0.710790	+	0.703404i	$0.751662\pi$
$258$	5.45394	−	16.0523i	0.339548	−	0.999374i
$259$	33.2117	+	7.05936i	2.06367	+	0.438647i
$260$	−0.0512478	+	1.91686i	−0.00317825	+	0.118878i
$261$	7.72189	−	0.811603i	0.477973	−	0.0502370i
$262$	−6.17308	−	3.67489i	−0.381374	−	0.227035i
$263$	−14.5019	+	10.5363i	−0.894226	+	0.649693i	−0.936976	−	0.349393i	$-0.886388\pi$
$263$	−14.5019	+	10.5363i	−0.894226	+	0.649693i	0.0427505	+	0.999086i	$0.486388\pi$
$264$	6.86322	+	0.275318i	0.422402	+	0.0169446i
$265$	−2.09119	−	9.83827i	−0.128461	−	0.604360i
$266$	−16.4177	−	12.2667i	−1.00663	−	0.752118i
$267$	2.62339	+	0.275730i	0.160549	+	0.0168744i
$268$	14.6327	+	1.93461i	0.893836	+	0.118175i
$269$	1.27123	+	2.85523i	0.0775082	+	0.174086i	0.948143	−	0.317843i	$-0.102959\pi$
$269$	1.27123	+	2.85523i	0.0775082	+	0.174086i	−0.870635	+	0.491929i	$0.836292\pi$
$270$	−2.86708	−	0.0383193i	−0.174485	−	0.00233204i
$271$	−4.99506	+	15.3732i	−0.303428	+	0.933856i	0.676831	+	0.736139i	$0.263353\pi$
$271$	−4.99506	+	15.3732i	−0.303428	+	0.933856i	−0.980259	+	0.197717i	$0.936647\pi$
$272$	11.7672	+	7.66007i	0.713489	+	0.464460i
$273$	−0.780441	−	1.35176i	−0.0472344	−	0.0818124i
$274$	0.968166	−	0.300332i	0.0584891	−	0.0181437i
$275$	−0.667280	−	2.05368i	−0.0402385	−	0.123841i
$276$	−0.540368	+	1.52329i	−0.0325264	+	0.0916916i
$277$	18.2869	−	25.1697i	1.09875	−	1.51230i	0.261725	−	0.965142i	$-0.415709\pi$
$277$	18.2869	−	25.1697i	1.09875	−	1.51230i	0.837027	−	0.547161i	$-0.184291\pi$
$278$	5.31746	−	5.74923i	0.318920	−	0.344816i
$279$	3.91990	+	3.95403i	0.234678	+	0.236722i
$280$	−11.7311	+	14.8556i	−0.701065	+	0.887792i
$281$	4.21711	+	3.06391i	0.251572	+	0.182777i	0.706423	−	0.707790i	$-0.250308\pi$
$281$	4.21711	+	3.06391i	0.251572	+	0.182777i	−0.454851	+	0.890567i	$0.650308\pi$
$282$	−2.97060	−	6.91950i	−0.176897	−	0.412050i
$283$	−19.6141	+	6.37301i	−1.16594	+	0.378836i	−0.827125	−	0.562018i	$-0.810025\pi$
$283$	−19.6141	+	6.37301i	−1.16594	+	0.378836i	−0.338812	+	0.940854i	$0.610025\pi$
$284$	−10.1855	+	21.3242i	−0.604398	+	1.26536i
$285$	−7.70887	+	4.45072i	−0.456634	+	0.263638i
$286$	1.61727	−	0.148159i	0.0956314	−	0.00876082i
$287$	−6.09448	−	1.98022i	−0.359746	−	0.116888i
$288$	5.59942	−	0.804032i	0.329949	−	0.0473780i
$289$	4.27409	−	1.90295i	0.251417	−	0.111938i
$290$	−12.8441	−	18.1846i	−0.754232	−	1.06784i
$291$	−0.268199	+	2.55174i	−0.0157221	+	0.149586i
$292$	4.22818	+	22.8833i	0.247435	+	1.33914i
$293$	−18.1468	+	3.85721i	−1.06014	+	0.225341i	−0.704808	−	0.709398i	$-0.748967\pi$
$293$	−18.1468	+	3.85721i	−1.06014	+	0.225341i	−0.355336	+	0.934738i	$0.615634\pi$
$294$	0.648983	−	5.47037i	0.0378495	−	0.319038i
$295$	−2.18511	−	3.00755i	−0.127222	−	0.175106i
$296$	−12.8897	+	26.0836i	−0.749199	+	1.51608i
$297$	0.253844	+	2.41516i	0.0147295	+	0.140142i
$298$	−19.7041	−	22.4807i	−1.14143	−	1.30227i
$299$	−0.0794551	+	0.373807i	−0.00459501	+	0.0216178i
$300$	−0.847710	−	1.56333i	−0.0489425	−	0.0902591i
$301$	29.4061	−	26.4774i	1.69494	−	1.52613i
$302$	3.53924	+	6.32384i	0.203660	+	0.363896i
$303$	−12.6770	+	14.0792i	−0.728275	+	0.808831i
$304$	13.6598	−	11.0367i	0.783444	−	0.632997i
$305$	−3.19838	−	1.84659i	−0.183139	−	0.105735i
$306$	−2.07953	+	4.50759i	−0.118879	+	0.257682i
$307$	3.02219	−	6.78796i	0.172486	−	0.387409i	−0.806530	−	0.591193i	$-0.798657\pi$
$307$	3.02219	−	6.78796i	0.172486	−	0.387409i	0.979016	+	0.203784i	$0.0653239\pi$
$308$	13.6647	+	8.38407i	0.778619	+	0.477727i
$309$		−	3.24938i		−	0.184851i
$310$	4.40423	−	15.3451i	0.250143	−	0.871545i
$311$			11.4780i			0.650856i	0.945567	+	0.325428i	$0.105508\pi$
$311$			11.4780i			0.650856i	−0.945567	+	0.325428i	$0.894492\pi$
$312$	1.28759	−	0.361993i	0.0728954	−	0.0204938i
$313$	−1.93620	+	4.34878i	−0.109441	+	0.245807i	−0.959961	−	0.280135i	$-0.909621\pi$
$313$	−1.93620	+	4.34878i	−0.109441	+	0.245807i	0.850520	+	0.525943i	$0.176287\pi$
$314$	13.7665	+	6.35104i	0.776890	+	0.358410i
$315$	−5.79580	−	3.34621i	−0.326556	−	0.188537i
$316$	−23.2656	+	15.9712i	−1.30879	+	0.898452i
$317$	9.91979	−	11.0170i	0.557151	−	0.618779i	−0.397104	−	0.917774i	$-0.629985\pi$
$317$	9.91979	−	11.0170i	0.557151	−	0.618779i	0.954255	+	0.298995i	$0.0966514\pi$
$318$	−6.12203	+	3.42630i	−0.343307	+	0.192137i
$319$	−14.0125	+	12.6169i	−0.784548	+	0.706410i
$320$	−9.85297	−	12.8845i	−0.550798	−	0.720267i
$321$	−0.668465	+	3.14488i	−0.0373101	+	0.175530i
$322$	−2.83698	+	2.48658i	−0.158098	+	0.138572i
$323$	1.61087	+	15.3264i	0.0896314	+	0.852786i
$324$	0.566978	+	1.91795i	0.0314988	+	0.106553i
$325$	−0.247152	−	0.340175i	−0.0137095	−	0.0188695i
$326$	−16.4240	−	1.94849i	−0.909644	−	0.107917i
$327$	9.75158	−	2.07276i	0.539263	−	0.114624i
$328$	2.93393	−	4.64153i	0.161999	−	0.256286i
$329$	1.83715	−	17.4793i	0.101285	−	0.963667i
$330$	5.68757	−	4.01724i	0.313090	−	0.221142i
$331$	−24.5963	+	10.9510i	−1.35193	+	0.601920i	−0.949569	−	0.313559i	$-0.898479\pi$
$331$	−24.5963	+	10.9510i	−1.35193	+	0.601920i	−0.402366	+	0.915479i	$0.631812\pi$
$332$	11.1709	−	11.7587i	0.613081	−	0.645342i
$333$	−9.78304	−	3.17870i	−0.536107	−	0.174192i
$334$	−1.63073	−	17.8007i	−0.0892294	−	0.974011i
$335$	12.9584	−	7.48156i	0.707995	−	0.408761i
$336$	12.3210	+	4.74513i	0.672168	+	0.258868i
$337$	−6.46706	+	2.10127i	−0.352283	+	0.114464i	−0.479812	−	0.877371i	$-0.659295\pi$
$337$	−6.46706	+	2.10127i	−0.352283	+	0.114464i	0.127529	+	0.991835i	$0.459295\pi$
$338$	−16.6032	+	7.12789i	−0.903093	+	0.387706i
$339$	9.38565	+	6.81907i	0.509759	+	0.370361i
$340$	14.1906	−	1.10899i	0.769596	−	0.0601434i
$341$	−13.3454	−	2.17304i	−0.722692	−	0.117677i
$342$	4.55814	+	4.21582i	0.246476	+	0.227966i
$343$	−6.02369	+	8.29090i	−0.325249	+	0.447667i
$344$	15.7629	+	30.0203i	0.849879	+	1.61859i
$345$	0.506335	+	1.55834i	0.0272602	+	0.0838982i
$346$	8.66035	+	27.9179i	0.465583	+	1.50088i
$347$	−0.412927	−	0.715211i	−0.0221671	−	0.0383945i	0.854729	−	0.519074i	$-0.173723\pi$
$347$	−0.412927	−	0.715211i	−0.0221671	−	0.0383945i	−0.876896	+	0.480680i	$0.840390\pi$
$348$	−9.46012	+	12.3147i	−0.507116	+	0.660135i
$349$	−6.15715	+	18.9498i	−0.329585	+	1.01436i	0.639744	+	0.768588i	$0.279041\pi$
$349$	−6.15715	+	18.9498i	−0.329585	+	1.01436i	−0.969328	+	0.245769i	$0.920959\pi$
$350$	0.0554711	−	4.15039i	0.00296505	−	0.221848i
$351$	0.192338	+	0.431998i	0.0102662	+	0.0230583i
$352$	−9.85334	+	9.57237i	−0.525185	+	0.510209i
$353$	16.2263	+	1.70545i	0.863638	+	0.0907720i	0.525980	−	0.850497i	$-0.323699\pi$
$353$	16.2263	+	1.70545i	0.863638	+	0.0907720i	0.337658	+	0.941269i	$0.390365\pi$
$354$	−1.55204	+	2.07724i	−0.0824899	+	0.110404i
$355$	4.98093	+	23.4335i	0.264361	+	1.24372i
$356$	−4.01354	+	3.42408i	−0.212717	+	0.181476i
$357$	−9.37361	+	6.81033i	−0.496104	+	0.360441i
$358$	2.88810	−	4.85142i	0.152641	−	0.256406i
$359$	19.3571	−	2.03451i	1.02163	−	0.107378i	0.421128	−	0.907001i	$-0.361634\pi$
$359$	19.3571	−	2.03451i	1.02163	−	0.107378i	0.600501	+	0.799624i	$0.294968\pi$
$360$	4.00498	−	4.10446i	0.211081	−	0.216324i
$361$	0.268912	+	0.0571591i	0.0141533	+	0.00300837i
$362$	0.562047	+	0.190961i	0.0295406	+	0.0100367i
$363$	3.41427	+	3.79193i	0.179203	+	0.199025i
$364$	3.03511	+	0.730428i	0.159083	+	0.0382848i
$365$	17.5314	+	15.7853i	0.917634	+	0.826241i
$366$	−0.569213	+	2.51235i	−0.0297532	+	0.131323i
$367$	4.14820	−	7.18489i	0.216534	−	0.375048i	−0.737212	−	0.675662i	$-0.763858\pi$
$367$	4.14820	−	7.18489i	0.216534	−	0.375048i	0.953746	+	0.300613i	$0.0971914\pi$
$368$	−1.46441	−	2.88188i	−0.0763374	−	0.150228i
$369$	1.77354	+	0.789632i	0.0923269	+	0.0411066i
$370$	5.74622	+	28.9297i	0.298732	+	1.50398i
$371$	−16.3745			−0.850124
$372$	−11.1330	+	0.237130i	−0.577219	+	0.0122946i
$373$	27.3026			1.41367			0.706837	−	0.707377i	$-0.250122\pi$
$373$	27.3026			1.41367			0.706837	+	0.707377i	$0.250122\pi$
$374$	−2.34863	−	11.8243i	−0.121445	−	0.611420i
$375$	−10.9081	−	4.85660i	−0.563292	−	0.250794i
$376$	14.1252	+	5.22430i	0.728454	+	0.269423i
$377$	−1.83582	+	3.17973i	−0.0945496	+	0.163765i
$378$	−1.03147	+	4.55265i	−0.0530532	+	0.234163i
$379$	0.912013	+	0.821180i	0.0468470	+	0.0421812i	0.692222	−	0.721685i	$-0.256632\pi$
$379$	0.912013	+	0.821180i	0.0468470	+	0.0421812i	−0.645375	+	0.763866i	$0.723299\pi$
$380$	4.16550	−	17.3087i	0.213686	−	0.887917i
$381$	−7.49266	−	8.32144i	−0.383861	−	0.426320i
$382$	9.10860	+	3.09474i	0.466036	+	0.158341i
$383$	−18.8533	−	4.00740i	−0.963360	−	0.204769i	−0.300725	−	0.953711i	$-0.597229\pi$
$383$	−18.8533	−	4.00740i	−0.963360	−	0.204769i	−0.662635	+	0.748942i	$0.730562\pi$
$384$	−6.54739	+	9.22668i	−0.334120	+	0.470847i
$385$	16.1633	−	1.69883i	0.823756	−	0.0865803i
$386$	−11.0193	+	18.5103i	−0.560870	+	0.942148i
$387$	−9.69846	+	7.04635i	−0.493001	+	0.358186i
$388$	−3.33056	−	3.90393i	−0.169084	−	0.198192i
$389$	8.06682	+	37.9514i	0.409004	+	1.92421i	0.380925	+	0.924606i	$0.375606\pi$
$389$	8.06682	+	37.9514i	0.409004	+	1.92421i	0.0280790	+	0.999606i	$0.491061\pi$
$390$	0.811571	−	1.08620i	0.0410955	−	0.0550020i
$391$	2.82122	+	0.296522i	0.142675	+	0.0149958i
$392$	7.03801	+	8.47648i	0.355473	+	0.428127i
$393$	2.06620	+	4.64076i	0.104226	+	0.234095i
$394$	0.0758503	−	5.67517i	0.00382128	−	0.285911i
$395$	−8.84044	+	27.2081i	−0.444811	+	1.36899i
$396$	−3.85164	−	2.95883i	−0.193552	−	0.148687i
$397$	8.09600	+	14.0227i	0.406326	+	0.703778i	0.994475	−	0.104975i	$-0.0334763\pi$
$397$	8.09600	+	14.0227i	0.406326	+	0.703778i	−0.588148	+	0.808753i	$0.700143\pi$
$398$	−4.17942	−	13.4730i	−0.209495	−	0.675339i
$399$	4.47814	+	13.7823i	0.224187	+	0.689978i
$400$	3.43455	+	0.924327i	0.171727	+	0.0462164i
$401$	−20.7676	+	28.5842i	−1.03709	+	1.42743i	−0.137593	+	0.990489i	$0.543937\pi$
$401$	−20.7676	+	28.5842i	−1.03709	+	1.42743i	−0.899492	+	0.436936i	$0.856063\pi$
$402$	−7.66214	−	7.08671i	−0.382153	−	0.353453i
$403$	−2.60223	+	0.400599i	−0.129626	+	0.0199552i
$404$	−2.95215	−	37.7758i	−0.146875	−	1.87942i
$405$	1.64029	+	1.19174i	0.0815068	+	0.0592182i
$406$	−33.3051	+	14.2982i	−1.65290	+	0.709607i
$407$	23.7578	−	7.71938i	1.17763	−	0.382635i
$408$	−3.67142	−	9.22454i	−0.181762	−	0.456683i
$409$	−7.54666	+	4.35707i	−0.373158	+	0.215443i	−0.674837	−	0.737967i	$-0.735786\pi$
$409$	−7.54666	+	4.35707i	−0.373158	+	0.215443i	0.301679	+	0.953410i	$0.402453\pi$
$410$	−0.507831	−	5.54339i	−0.0250800	−	0.273768i
$411$	−0.681698	−	0.221497i	−0.0336257	−	0.0109256i
$412$	4.71157	+	4.47603i	0.232123	+	0.220518i
$413$	−5.52892	+	2.46163i	−0.272060	+	0.121129i
$414$	0.933518	−	0.659361i	0.0458799	−	0.0324058i
$415$	1.71867	−	16.3520i	0.0843660	−	0.802689i
$416$	−1.24877	+	2.36564i	−0.0612262	+	0.115985i
$417$	−5.41655	+	1.15132i	−0.265250	+	0.0563805i
$418$	−14.9730	−	1.77634i	−0.732353	−	0.0868835i
$419$	18.4123	+	25.3423i	0.899499	+	1.23805i	0.970628	+	0.240587i	$0.0773398\pi$
$419$	18.4123	+	25.3423i	0.899499	+	1.23805i	−0.0711289	+	0.997467i	$0.522660\pi$
$420$	12.8357	−	3.79445i	0.626319	−	0.185150i
$421$	−2.54985	−	24.2602i	−0.124272	−	1.18237i	−0.861870	−	0.507130i	$-0.830706\pi$
$421$	−2.54985	−	24.2602i	−0.124272	−	1.18237i	0.737597	−	0.675241i	$-0.235960\pi$
$422$	28.5870	−	25.0563i	1.39159	−	1.21972i
$423$	−1.10706	+	5.20830i	−0.0538270	+	0.253236i
$424$	3.46503	−	13.5966i	0.168277	−	0.660311i
$425$	−2.31952	+	2.08850i	−0.112513	+	0.101307i
$426$	14.5819	−	8.16098i	0.706494	−	0.395401i
$427$	−4.02314	+	4.46815i	−0.194694	+	0.216229i
$428$	−3.63924	−	5.30136i	−0.175909	−	0.256251i
$429$	−0.994521	−	0.574187i	−0.0480159	−	0.0277220i
$430$	31.2121	+	14.3994i	1.50518	+	0.694400i
$431$	5.64780	−	12.6852i	0.272045	−	0.611023i	−0.724923	−	0.688829i	$-0.758125\pi$
$431$	5.64780	−	12.6852i	0.272045	−	0.611023i	0.996969	+	0.0778062i	$0.0247915\pi$
$432$	−3.56203	−	1.81987i	−0.171378	−	0.0875587i
$433$			33.0577i			1.58865i	0.607492	+	0.794326i	$0.292176\pi$
$433$			33.0577i			1.58865i	−0.607492	+	0.794326i	$0.707824\pi$
$434$	−22.9453	−	12.2074i	−1.10141	−	0.585976i
$435$			15.7425i			0.754794i
$436$	−10.4274	+	16.9950i	−0.499380	+	0.813911i
$437$	1.44312	−	3.24129i	0.0690336	−	0.155052i
$438$	6.89308	−	14.9415i	0.329364	−	0.713931i
$439$	−3.52501	−	2.03516i	−0.168239	−	0.0971331i	0.413516	−	0.910497i	$-0.364301\pi$
$439$	−3.52501	−	2.03516i	−0.168239	−	0.0971331i	−0.581755	+	0.813364i	$0.697634\pi$
$440$	−2.00970	+	13.7807i	−0.0958085	+	0.656969i
$441$	−2.60644	+	2.89474i	−0.124116	+	0.137845i
$442$	−1.14645	−	2.04846i	−0.0545312	−	0.0974352i
$443$	−9.84936	+	8.86841i	−0.467957	+	0.421351i	−0.869078	−	0.494674i	$-0.835287\pi$
$443$	−9.84936	+	8.86841i	−0.467957	+	0.421351i	0.401121	+	0.916025i	$0.368621\pi$
$444$	18.0853	−	9.80666i	0.858290	−	0.465403i
$445$	−1.11197	+	5.23139i	−0.0527122	+	0.247992i
$446$	−16.5759	−	18.9116i	−0.784889	−	0.895490i
$447$	2.20952	+	21.0222i	0.104507	+	0.994317i
$448$	−23.8527	+	11.3290i	−1.12693	+	0.535243i
$449$	−5.54398	−	7.63064i	−0.261637	−	0.360112i	0.657907	−	0.753099i	$-0.271442\pi$
$449$	−5.54398	−	7.63064i	−0.261637	−	0.360112i	−0.919544	+	0.392987i	$0.871442\pi$
$450$	−0.148146	+	1.24874i	−0.00698368	+	0.0588664i
$451$	−4.61156	+	0.980218i	−0.217150	+	0.0461566i
$452$	−22.8164	+	4.21581i	−1.07319	+	0.198295i
$453$	0.535637	−	5.09624i	0.0251664	−	0.239442i
$454$	2.96408	+	4.19652i	0.139111	+	0.196952i
$455$	2.89111	−	1.28720i	0.135537	−	0.0603450i
$456$	−12.3918	+	0.801952i	−0.580298	+	0.0375548i
$457$	−24.7117	−	8.02932i	−1.15597	−	0.375596i	−0.332578	−	0.943076i	$-0.607918\pi$
$457$	−24.7117	−	8.02932i	−1.15597	−	0.375596i	−0.823387	+	0.567480i	$0.807918\pi$
$458$	18.2418	−	1.67114i	0.852383	−	0.0780871i
$459$	3.03991	−	1.75509i	0.141891	−	0.0819208i
$460$	−2.95706	−	1.41244i	−0.137874	−	0.0658553i
$461$	40.2204	−	13.0684i	1.87325	−	0.608655i	0.882995	−	0.469383i	$-0.155524\pi$
$461$	40.2204	−	13.0684i	1.87325	−	0.608655i	0.990254	−	0.139273i	$-0.0444764\pi$
$462$	−4.47202	−	10.4168i	−0.208057	−	0.484633i
$463$	−30.6969	−	22.3026i	−1.42661	−	1.03649i	−0.990636	−	0.136530i	$-0.956405\pi$
$463$	−30.6969	−	22.3026i	−1.42661	−	1.03649i	−0.435971	−	0.899960i	$-0.643595\pi$
$464$	−4.82481	−	30.6806i	−0.223986	−	1.42431i
$465$	−8.80369	+	7.06613i	−0.408261	+	0.327684i
$466$	−25.8187	+	27.9151i	−1.19603	+	1.29314i
$467$	−23.6741	+	32.5846i	−1.09551	+	1.50783i	−0.254296	+	0.967127i	$0.581844\pi$
$467$	−23.6741	+	32.5846i	−1.09551	+	1.50783i	−0.841210	+	0.540708i	$0.818156\pi$
$468$	−0.891340	−	0.316191i	−0.0412022	−	0.0146159i
$469$	−7.52765	−	23.1677i	−0.347595	−	1.06979i
$470$	14.5821	−	4.52347i	0.672622	−	0.208652i
$471$	−5.36019	−	9.28412i	−0.246984	−	0.427790i
$472$	−0.874044	−	5.11186i	−0.0402312	−	0.235292i
$473$	8.99622	−	27.6875i	0.413646	−	1.27307i
$474$	19.9528	+	0.266675i	0.916462	+	0.0122488i
$475$	1.58783	+	3.56632i	0.0728545	+	0.163634i
$476$	3.03728	−	22.9729i	0.139213	−	1.05296i
$477$	4.93361	+	0.518543i	0.225895	+	0.0237425i
$478$	4.05048	+	3.02637i	0.185265	+	0.138423i
$479$	−6.75315	−	31.7711i	−0.308559	−	1.45166i	−0.809982	−	0.586454i	$-0.800523\pi$
$479$	−6.75315	−	31.7711i	−0.308559	−	1.45166i	0.501423	−	0.865202i	$-0.332810\pi$
$480$	0.434554	+	11.4611i	0.0198346	+	0.523126i
$481$	3.93529	−	2.85915i	0.179434	−	0.130366i
$482$	28.5896	+	17.0197i	1.30222	+	0.775225i
$483$	2.65293	−	0.278834i	0.120712	−	0.0126874i
$484$	−10.2014	−	0.272739i	−0.463702	−	0.0123972i
$485$	−5.08851	−	1.08160i	−0.231057	−	0.0491128i
$486$	0.454952	−	1.33904i	0.0206370	−	0.0607399i
$487$	−9.76910	−	10.8497i	−0.442680	−	0.491646i	0.479970	−	0.877285i	$-0.340648\pi$
$487$	−9.76910	−	10.8497i	−0.442680	−	0.491646i	−0.922650	+	0.385639i	$0.873981\pi$
$488$	−2.85880	−	4.28614i	−0.129412	−	0.194024i
$489$	8.69107	+	7.82548i	0.393024	+	0.353880i
$490$	10.8929	+	2.46797i	0.492093	+	0.111491i
$491$	11.5748	−	20.0482i	0.522364	−	0.904761i	−0.477297	−	0.878742i	$-0.658383\pi$
$491$	11.5748	−	20.0482i	0.522364	−	0.904761i	0.999661	−	0.0260195i	$-0.00828320\pi$
$492$	−3.58802	+	1.48390i	−0.161761	+	0.0668994i
$493$	24.8983	+	11.0854i	1.12136	+	0.499263i
$494$	−2.87978	+	0.572003i	−0.129568	+	0.0257356i
$495$	−4.92375			−0.221306
$496$	14.9919	−	16.4694i	0.673158	−	0.739499i
$497$	39.0020			1.74948
$498$	−11.2488	+	2.23431i	−0.504071	+	0.100122i
$499$	−28.6639	−	12.7620i	−1.28317	−	0.571305i	−0.352039	−	0.935985i	$-0.614512\pi$
$499$	−28.6639	−	12.7620i	−1.28317	−	0.571305i	−0.931133	+	0.364680i	$0.881178\pi$
$500$	22.0680	−	9.12668i	0.986912	−	0.408158i
$501$	−6.31985	+	10.9463i	−0.282350	+	0.489045i
$502$	−29.2481	−	6.62662i	−1.30541	−	0.295760i
$503$	21.2325	+	19.1179i	0.946713	+	0.852424i	0.989185	−	0.146674i	$-0.0468568\pi$
$503$	21.2325	+	19.1179i	0.946713	+	0.852424i	−0.0424723	+	0.999098i	$0.513523\pi$
$504$	−5.18044	−	7.76692i	−0.230755	−	0.345966i
$505$	−25.7028	−	28.5459i	−1.14376	−	1.27027i
$506$	−0.892872	+	2.62795i	−0.0396930	+	0.116826i
$507$	12.4972	+	2.65636i	0.555020	+	0.117973i
$508$	22.3872	+	0.598529i	0.993272	+	0.0265555i
$509$	−12.9193	+	1.35788i	−0.572639	+	0.0601868i	−0.386422	−	0.922322i	$-0.626289\pi$
$509$	−12.9193	+	1.35788i	−0.572639	+	0.0601868i	−0.186217	+	0.982509i	$0.559623\pi$
$510$	−8.64842	−	5.14849i	−0.382959	−	0.227979i
$511$	31.0710	−	22.5744i	1.37450	−	0.998632i
$512$	−4.35955	−	22.2035i	−0.192667	−	0.981264i
$513$	−0.912799	−	4.29438i	−0.0403011	−	0.189602i
$514$	1.71157	+	1.27882i	0.0754940	+	0.0564063i
$515$	6.55207	+	0.688650i	0.288719	+	0.0303455i
$516$	3.14254	−	23.7691i	0.138342	−	1.04638i
$517$	−5.25941	−	11.8128i	−0.231309	−	0.519528i
$518$	48.0134	+	0.641713i	2.10959	+	0.0281952i
$519$	6.38706	−	19.6574i	0.280361	−	0.862862i
$520$	0.457043	+	2.67302i	0.0200427	+	0.117220i
$521$	−16.4847	−	28.5523i	−0.722206	−	1.25090i	−0.960114	−	0.279609i	$-0.909795\pi$
$521$	−16.4847	−	28.5523i	−0.722206	−	1.25090i	0.237908	−	0.971288i	$-0.423538\pi$
$522$	10.4875	−	3.25331i	0.459027	−	0.142394i
$523$	−6.05370	−	18.6314i	−0.264710	−	0.814693i	−0.991760	−	0.128109i	$-0.959109\pi$
$523$	−6.05370	−	18.6314i	−0.264710	−	0.814693i	0.727050	−	0.686584i	$-0.240891\pi$
$524$	−9.57527	−	3.39670i	−0.418298	−	0.148385i
$525$	−1.72517	+	2.37449i	−0.0752925	+	0.103631i
$526$	−17.2129	+	18.6105i	−0.750518	+	0.811458i
$527$	4.97646	+	18.8997i	0.216778	+	0.823284i
$528$	9.59594	−	1.50905i	0.417610	−	0.0656729i
$529$	18.0790	+	13.1352i	0.786044	+	0.571095i
$530$	−5.61135	−	13.0707i	−0.243741	−	0.567753i
$531$	1.74380	−	0.566596i	0.0756746	−	0.0245882i
$532$	−26.1529	−	12.4919i	−1.13387	−	0.541593i
$533$	−0.795048	+	0.459021i	−0.0344373	+	0.0198824i
$534$	3.71492	−	0.340324i	0.160760	−	0.0147273i
$535$	−6.19969	−	2.01440i	−0.268036	−	0.0870902i
$536$	20.8303	−	1.34806i	0.899732	−	0.0582275i
$537$	−3.64717	+	1.62383i	−0.157387	+	0.0700733i
$538$	2.55001	+	3.61028i	0.109939	+	0.155650i
$539$	0.988788	−	9.40769i	0.0425901	−	0.405218i
$540$	−3.98753	+	0.736781i	−0.171596	+	0.0317060i
$541$	−24.2643	+	5.15754i	−1.04321	+	0.221740i	−0.697486	−	0.716598i	$-0.745698\pi$
$541$	−24.2643	+	5.15754i	−1.04321	+	0.221740i	−0.345719	+	0.938338i	$0.612365\pi$
$542$	−2.69312	+	22.7007i	−0.115679	+	0.975076i
$543$	−0.246717	−	0.339577i	−0.0105876	−	0.0145726i
$544$	18.4329	+	7.38333i	0.790304	+	0.316558i
$545$	2.11285	+	20.1024i	0.0905046	+	0.861093i
$546$	−1.45500	−	1.66003i	−0.0622681	−	0.0710425i
$547$	1.71133	−	8.05119i	0.0731713	−	0.344244i	−0.926299	−	0.376789i	$-0.877028\pi$
$547$	1.71133	−	8.05119i	0.0731713	−	0.344244i	0.999470	+	0.0325455i	$0.0103614\pi$
$548$	1.26021	−	0.683343i	0.0538336	−	0.0291910i
$549$	1.35366	−	1.21884i	0.0577727	−	0.0520188i
$550$	−1.49142	−	2.66484i	−0.0635944	−	0.113629i
$551$	22.8095	−	25.3325i	0.971718	−	1.07920i
$552$	−0.329857	+	2.26187i	−0.0140397	+	0.0962715i
$553$	40.3345	+	23.2871i	1.71520	+	0.990270i
$554$	18.4313	−	39.9517i	0.783071	−	1.69739i
$555$	8.48291	−	19.0529i	0.360079	−	0.808751i
$556$	5.79191	−	9.43991i	0.245632	−	0.400341i
$557$		−	40.8982i		−	1.73291i	−0.499254	−	0.866456i	$-0.666392\pi$
$557$		−	40.8982i		−	1.73291i	0.499254	−	0.866456i	$-0.333608\pi$
$558$	6.52677	+	4.40469i	0.276300	+	0.186466i
$559$		−	5.66887i		−	0.239768i
$560$	−12.1793	+	23.8386i	−0.514671	+	1.00736i
$561$	−3.46718	+	7.78741i	−0.146384	+	0.328785i
$562$	6.69378	+	3.08810i	0.282360	+	0.130264i
$563$	−38.7607	−	22.3785i	−1.63357	−	0.943141i	−0.982981	−	0.183709i	$-0.941190\pi$
$563$	−38.7607	−	22.3785i	−1.63357	−	0.943141i	−0.650587	−	0.759432i	$-0.725477\pi$
$564$	−6.02702	−	8.77969i	−0.253783	−	0.369692i
$565$	−15.7392	+	17.4801i	−0.662151	+	0.735394i
$566$	−25.4511	+	14.2441i	−1.06979	+	0.598726i
$567$	2.45297	−	2.20866i	0.103015	−	0.0927552i
$568$	−8.25324	+	32.3854i	−0.346298	+	1.35886i
$569$	−3.06700	+	14.4291i	−0.128575	+	0.604899i	0.865926	+	0.500173i	$0.166730\pi$
$569$	−3.06700	+	14.4291i	−0.128575	+	0.604899i	−0.994501	+	0.104727i	$0.966603\pi$
$570$	−9.46684	+	8.29760i	−0.396522	+	0.347548i
$571$	1.60953	+	15.3136i	0.0673567	+	0.640856i	0.975166	+	0.221474i	$0.0710867\pi$
$571$	1.60953	+	15.3136i	0.0673567	+	0.640856i	−0.907810	+	0.419382i	$0.862247\pi$
$572$	2.20253	−	0.651103i	0.0920922	−	0.0272240i
$573$	−3.99832	−	5.50322i	−0.167032	−	0.229900i
$574$	−8.99933	−	1.06765i	−0.375625	−	0.0445627i
$575$	0.702894	−	0.149405i	0.0293127	−	0.00623061i
$576$	7.54552	−	2.65803i	0.314397	−	0.110751i
$577$	−3.07974	+	29.3017i	−0.128211	+	1.21985i	0.721430	+	0.692487i	$0.243485\pi$
$577$	−3.07974	+	29.3017i	−0.128211	+	1.21985i	−0.849642	+	0.527361i	$0.823182\pi$
$578$	5.40436	−	3.81720i	0.224792	−	0.158775i
$579$	13.9156	−	6.19560i	0.578311	−	0.257480i
$580$	−22.8265	−	21.6853i	−0.947817	−	0.900435i
$581$	−25.4577	−	8.27170i	−1.05616	−	0.343168i
$582$	0.331030	+	3.61346i	0.0137216	+	0.149783i
$583$	−10.4331	+	6.02355i	−0.432095	+	0.249470i
$584$	12.1697	+	30.5769i	0.503588	+	1.26528i
$585$	−0.911845	+	0.296277i	−0.0377002	+	0.0122495i
$586$	−24.1089	+	10.3502i	−0.995930	+	0.427562i
$587$	4.23099	+	3.07399i	0.174631	+	0.126877i	0.671668	−	0.740853i	$-0.265578\pi$
$587$	4.23099	+	3.07399i	0.174631	+	0.126877i	−0.497036	+	0.867730i	$0.665578\pi$
$588$	−0.606973	−	7.76684i	−0.0250311	−	0.320299i
$589$	24.4050	+	1.38511i	1.00559	+	0.0570724i
$590$	−3.85964	−	3.56978i	−0.158899	−	0.146965i
$591$	−2.35897	+	3.24684i	−0.0970349	+	0.133557i
$592$	−10.6930	+	39.7323i	−0.439480	+	1.63299i
$593$	−12.0646	−	37.1309i	−0.495432	−	1.52478i	−0.816282	−	0.577653i	$-0.803969\pi$
$593$	−12.0646	−	37.1309i	−0.495432	−	1.52478i	0.320850	−	0.947130i	$-0.396031\pi$
$594$	1.01753	+	3.28017i	0.0417499	+	0.134587i
$595$	−11.7458	−	20.3443i	−0.481531	−	0.834037i
$596$	−33.5257	−	25.7544i	−1.37327	−	1.05494i
$597$	−3.08235	+	9.48649i	−0.126152	+	0.388256i
$598$	−0.00722266	+	0.540405i	−0.000295357	+	0.0220988i
$599$	6.88318	+	15.4599i	0.281239	+	0.631673i	0.997832	−	0.0658190i	$-0.0209660\pi$
$599$	6.88318	+	15.4599i	0.281239	+	0.631673i	−0.716593	+	0.697492i	$0.754299\pi$
$600$	−1.60660	−	1.93496i	−0.0655891	−	0.0789946i
$601$	17.1734	+	1.80500i	0.700517	+	0.0736273i	0.448090	−	0.893989i	$-0.352104\pi$
$601$	17.1734	+	1.80500i	0.700517	+	0.0736273i	0.252427	+	0.967616i	$0.418771\pi$
$602$	33.4947	−	44.8291i	1.36514	−	1.82710i
$603$	1.53440	+	7.21876i	0.0624854	+	0.293971i
$604$	6.65167	+	7.79677i	0.270653	+	0.317246i
$605$	−8.36967	+	6.08092i	−0.340276	+	0.247225i
$606$	−13.7054	+	23.0223i	−0.556743	+	0.935216i
$607$	35.1910	−	3.69873i	1.42836	−	0.150127i	0.641436	−	0.767177i	$-0.278339\pi$
$607$	35.1910	−	3.69873i	1.42836	−	0.150127i	0.786924	+	0.617050i	$0.211672\pi$
$608$	15.9069	−	19.0727i	0.645111	−	0.773500i
$609$	25.0687	+	5.32852i	1.01584	+	0.215923i
$610$	−4.94529	−	1.68021i	−0.200229	−	0.0680299i
$611$	−1.68482	−	1.87118i	−0.0681606	−	0.0757000i
$612$	−1.64262	+	6.82550i	−0.0663991	+	0.275905i
$613$	−9.57314	−	8.61970i	−0.386656	−	0.348146i	0.452764	−	0.891631i	$-0.350438\pi$
$613$	−9.57314	−	8.61970i	−0.386656	−	0.348146i	−0.839419	+	0.543484i	$0.817105\pi$
$614$	2.32192	−	10.2484i	0.0937052	−	0.413590i
$615$	−1.96809	+	3.40883i	−0.0793611	+	0.137457i
$616$	21.2645	+	7.86479i	0.856771	+	0.316882i
$617$	38.5708	+	17.1728i	1.55280	+	0.691352i	0.990744	−	0.135746i	$-0.0433430\pi$
$617$	38.5708	+	17.1728i	1.55280	+	0.691352i	0.562058	+	0.827098i	$0.310010\pi$
$618$	−0.895264	−	4.50726i	−0.0360128	−	0.181309i
$619$	4.65384			0.187054			0.0935268	−	0.995617i	$-0.470186\pi$
$619$	4.65384			0.187054			0.0935268	+	0.995617i	$0.470186\pi$
$620$	1.88130	−	22.4989i	0.0755548	−	0.903578i
$621$	−0.808150			−0.0324299
$622$	3.16239	+	15.9213i	0.126800	+	0.638385i
$623$	7.95422	+	3.54145i	0.318679	+	0.141885i
$624$	1.68630	−	0.856881i	0.0675060	−	0.0343027i
$625$	9.88170	−	17.1156i	0.395268	−	0.684624i
$626$	−1.48756	+	6.56572i	−0.0594550	+	0.262419i
$627$	7.92323	+	7.13410i	0.316423	+	0.284909i
$628$	20.8456	+	5.01669i	0.831830	+	0.200188i
$629$	−24.1607	−	26.8331i	−0.963349	−	1.06991i
$630$	−8.96138	−	3.04472i	−0.357030	−	0.121305i
$631$	15.8365	+	3.36616i	0.630442	+	0.134005i	0.512041	−	0.858961i	$-0.328890\pi$
$631$	15.8365	+	3.36616i	0.630442	+	0.134005i	0.118401	+	0.992966i	$0.462223\pi$
$632$	−27.8718	+	28.5641i	−1.10868	+	1.13622i
$633$	−26.7324	+	2.80969i	−1.06252	+	0.111675i
$634$	10.7245	−	18.0150i	0.425924	−	0.715467i
$635$	18.3674	−	13.3447i	0.728886	−	0.529567i
$636$	−7.54796	+	6.43940i	−0.299296	+	0.255339i
$637$	−0.382972	−	1.80174i	−0.0151739	−	0.0713875i
$638$	−15.9607	+	21.3618i	−0.631891	+	0.845721i
$639$	−11.7512	−	1.23510i	−0.464871	−	0.0488599i
$640$	−17.2171	−	15.1576i	−0.680567	−	0.599159i
$641$	−4.39682	−	9.87542i	−0.173664	−	0.390056i	0.805653	−	0.592388i	$-0.201815\pi$
$641$	−4.39682	−	9.87542i	−0.173664	−	0.390056i	−0.979317	+	0.202332i	$0.935148\pi$
$642$	−0.0607651	+	4.54649i	−0.00239821	+	0.179436i
$643$	9.67955	−	29.7906i	0.381724	−	1.17483i	−0.557105	−	0.830442i	$-0.688088\pi$
$643$	9.67955	−	29.7906i	0.381724	−	1.17483i	0.938829	−	0.344384i	$-0.111912\pi$
$644$	−3.25011	+	4.23082i	−0.128072	+	0.166718i
$645$	−12.1529	−	21.0494i	−0.478519	−	0.828819i
$646$	6.45719	+	20.8157i	0.254055	+	0.818983i
$647$	−8.74903	−	26.9267i	−0.343960	−	1.05860i	−0.962138	−	0.272562i	$-0.912129\pi$
$647$	−8.74903	−	26.9267i	−0.343960	−	1.05860i	0.618178	−	0.786038i	$-0.287871\pi$
$648$	1.31489	+	2.50421i	0.0516539	+	0.0983745i
$649$	−2.61723	+	3.60231i	−0.102735	+	0.141403i
$650$	−0.436552	−	0.403767i	−0.0171230	−	0.0158371i
$651$	8.27241	+	16.4110i	0.324221	+	0.643197i
$652$	−23.3189	+	1.82236i	−0.913238	+	0.0713689i
$653$	5.03737	+	3.65987i	0.197128	+	0.143222i	0.681971	−	0.731380i	$-0.261123\pi$
$653$	5.03737	+	3.65987i	0.197128	+	0.143222i	−0.484843	+	0.874601i	$0.661123\pi$
$654$	12.9555	−	5.56190i	0.506599	−	0.217487i
$655$	−9.79556	+	3.18277i	−0.382744	+	0.124361i
$656$	2.79088	−	7.24669i	0.108965	−	0.282936i
$657$	−10.0765	+	5.81766i	−0.393121	+	0.226969i
$658$	−2.26754	−	24.7520i	−0.0883979	−	0.964934i
$659$	39.3631	+	12.7898i	1.53337	+	0.498221i	0.949537	−	0.313655i	$-0.101553\pi$
$659$	39.3631	+	12.7898i	1.53337	+	0.498221i	0.583830	+	0.811876i	$0.301553\pi$
$660$	6.78249	−	7.13940i	0.264008	−	0.277901i
$661$	−13.6514	+	6.07800i	−0.530979	+	0.236407i	−0.654671	−	0.755914i	$-0.727193\pi$
$661$	−13.6514	+	6.07800i	−0.530979	+	0.236407i	0.123693	+	0.992321i	$0.460526\pi$
$662$	−31.1007	+	21.9670i	−1.20876	+	0.853772i
$663$	−0.173507	+	1.65081i	−0.00673844	+	0.0641120i
$664$	12.2555	−	19.3885i	0.475607	−	0.752418i
$665$	−28.7398	+	6.10883i	−1.11448	+	0.236890i
$666$	−14.4460	−	1.71382i	−0.559771	−	0.0664091i
$667$	−3.68824	−	5.07643i	−0.142809	−	0.196560i
$668$	−7.16643	−	24.2423i	−0.277277	−	0.937964i
$669$	1.85874	+	17.6847i	0.0718630	+	0.683730i
$670$	15.9135	−	13.9481i	0.614794	−	0.538861i
$671$	−0.919701	+	4.32686i	−0.0355047	+	0.167036i
$672$	18.3981	+	3.18737i	0.709721	+	0.122955i
$673$	33.1094	−	29.8118i	1.27627	−	1.14916i	0.295219	−	0.955430i	$-0.404607\pi$
$673$	33.1094	−	29.8118i	1.27627	−	1.14916i	0.981055	−	0.193732i	$-0.0620592\pi$
$674$	−8.39162	+	4.69651i	−0.323233	+	0.180903i
$675$	0.594983	−	0.660796i	0.0229009	−	0.0254340i
$676$	−21.0666	+	14.4617i	−0.810256	+	0.556219i
$677$	−25.0218	−	14.4464i	−0.961667	−	0.555219i	−0.0649814	−	0.997886i	$-0.520699\pi$
$677$	−25.0218	−	14.4464i	−0.961667	−	0.555219i	−0.896686	+	0.442668i	$0.854032\pi$
$678$	14.8978	+	6.87292i	0.572145	+	0.263953i
$679$	−3.44473	+	7.73698i	−0.132196	+	0.296918i
$680$	19.3785	−	5.44808i	0.743132	−	0.208924i
$681$		−	3.63294i		−	0.139215i
$682$	−19.1103	+	0.662646i	−0.731771	+	0.0253740i
$683$		−	9.31040i		−	0.356253i	−0.984008	−	0.178126i	$-0.942996\pi$
$683$		−	9.31040i		−	0.356253i	0.984008	−	0.178126i	$-0.0570036\pi$
$684$	7.48421	+	4.59198i	0.286166	+	0.175579i
$685$	0.591102	−	1.32764i	0.0225849	−	0.0507264i
$686$	−6.07126	+	13.1601i	−0.231802	+	0.502454i
$687$	−11.2176	−	6.47646i	−0.427976	−	0.247092i
$688$	30.1361	+	37.2987i	1.14893	+	1.42200i
$689$	−1.56969	+	1.74331i	−0.0598002	+	0.0664149i
$690$	1.13170	+	2.02209i	0.0430830	+	0.0769797i
$691$	20.1448	−	18.1385i	0.766346	−	0.690021i	−0.190154	−	0.981754i	$-0.560899\pi$
$691$	20.1448	−	18.1385i	0.766346	−	0.690021i	0.956500	+	0.291734i	$0.0942321\pi$
$692$	19.7048	+	36.3393i	0.749065	+	1.38141i
$693$	−1.66659	+	7.84071i	−0.0633087	+	0.297844i
$694$	−0.769831	−	0.878311i	−0.0292224	−	0.0333402i
$695$	−1.17359	−	11.1660i	−0.0445168	−	0.423549i
$696$	−9.72936	+	19.6883i	−0.368791	+	0.746283i
$697$	4.00554	+	5.51315i	0.151720	+	0.208825i
$698$	−3.31967	+	27.9819i	−0.125651	+	1.05913i
$699$	26.2998	−	5.59019i	0.994749	−	0.211440i
$700$	−1.06656	−	5.77235i	−0.0403123	−	0.218174i
$701$	−2.45397	+	23.3480i	−0.0926852	+	0.881841i	0.845096	+	0.534615i	$0.179543\pi$
$701$	−2.45397	+	23.3480i	−0.0926852	+	0.881841i	−0.937781	+	0.347227i	$0.887123\pi$
$702$	0.385818	+	0.546238i	0.0145618	+	0.0206164i
$703$	−41.2567	+	18.3686i	−1.55602	+	0.692787i
$704$	−11.0303	+	15.9928i	−0.415722	+	0.602750i
$705$	−10.2674	−	3.33609i	−0.386694	−	0.125644i
$706$	22.9776	−	2.10498i	0.864774	−	0.0792222i
$707$	−54.1571	+	31.2676i	−2.03679	+	1.17594i
$708$	−1.58054	+	3.30899i	−0.0594003	+	0.124359i
$709$	−1.34986	+	0.438595i	−0.0506949	+	0.0164718i	−0.334255	−	0.942483i	$-0.608485\pi$
$709$	−1.34986	+	0.438595i	−0.0506949	+	0.0164718i	0.283560	+	0.958955i	$0.408485\pi$
$710$	13.3655	+	31.1326i	0.501598	+	1.16838i
$711$	−11.4152	−	8.29366i	−0.428105	−	0.311037i
$712$	−4.62385	+	5.85540i	−0.173286	+	0.219440i
$713$	1.18341	−	4.34118i	0.0443189	−	0.162578i
$714$	−11.1259	+	12.0293i	−0.416377	+	0.450186i
$715$	1.36857	−	1.88367i	0.0511815	−	0.0704453i
$716$	2.66947	−	7.52521i	0.0997626	−	0.281230i
$717$	−1.10482	−	3.40029i	−0.0412604	−	0.126986i
$718$	26.2900	−	8.15535i	0.981134	−	0.304355i
$719$	−1.28898	−	2.23257i	−0.0480707	−	0.0832608i	0.840989	−	0.541052i	$-0.181974\pi$
$719$	−1.28898	−	2.23257i	−0.0480707	−	0.0832608i	−0.889060	+	0.457792i	$0.848641\pi$
$720$	4.42452	−	6.79681i	0.164892	−	0.253302i
$721$	3.31437	−	10.2006i	0.123434	−	0.379890i
$722$	0.388761	+	0.00519590i	0.0144682	+	0.000193371i
$723$	−9.56928	−	21.4930i	−0.355886	−	0.799332i
$724$	0.832238	+	0.110031i	0.0309299	+	0.00408927i
$725$	6.86621	+	0.721668i	0.255005	+	0.0268021i
$726$	5.78074	+	4.31915i	0.214543	+	0.160299i
$727$	5.34964	+	25.1681i	0.198407	+	0.933432i	0.958825	+	0.283998i	$0.0916609\pi$
$727$	5.34964	+	25.1681i	0.198407	+	0.933432i	−0.760418	+	0.649434i	$0.775006\pi$
$728$	4.41129	+	0.176959i	0.163493	+	0.00655853i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	28.6672	+	17.0658i	1.06102	+	0.631635i
$731$	−41.8495	+	4.39856i	−1.54786	+	0.162687i
$732$	−0.0973635	+	3.64175i	−0.00359866	+	0.134603i
$733$	20.8190	+	4.42522i	0.768968	+	0.163449i	0.575660	−	0.817689i	$-0.304745\pi$
$733$	20.8190	+	4.42522i	0.768968	+	0.163449i	0.193308	+	0.981138i	$0.438078\pi$
$734$	3.77446	−	11.1092i	0.139318	−	0.410047i
$735$	−5.28459	−	5.86913i	−0.194925	−	0.216486i
$736$	−2.82531	−	3.59403i	−0.104142	−	0.132478i
$737$	−13.3188	−	11.9923i	−0.490603	−	0.441741i
$738$	2.67767	+	0.606667i	0.0985663	+	0.0223317i
$739$	−7.81137	+	13.5297i	−0.287346	+	0.497698i	−0.973175	−	0.230065i	$-0.926106\pi$
$739$	−7.81137	+	13.5297i	−0.287346	+	0.497698i	0.685829	+	0.727762i	$0.259440\pi$
$740$	15.9413	+	38.5457i	0.586015	+	1.41697i
$741$	1.89661	+	0.844424i	0.0696736	+	0.0310207i
$742$	−22.7134	+	4.51149i	−0.833835	+	0.165622i
$743$	23.7764			0.872272			0.436136	−	0.899881i	$-0.356347\pi$
$743$	23.7764			0.872272			0.436136	+	0.899881i	$0.356347\pi$
$744$	−15.3774	+	3.39628i	−0.563764	+	0.124514i
$745$	−42.8576			−1.57018
$746$	37.8718	−	7.52237i	1.38659	−	0.275413i
$747$	7.40839	+	3.29843i	0.271059	+	0.120683i
$748$	−6.51563	−	15.7546i	−0.238235	−	0.576044i
$749$	−5.30626	+	9.19072i	−0.193887	+	0.335821i
$750$	−16.4689	−	3.73128i	−0.601359	−	0.136247i
$751$	15.2162	+	13.7007i	0.555248	+	0.499947i	0.898308	−	0.439366i	$-0.144797\pi$
$751$	15.2162	+	13.7007i	0.555248	+	0.499947i	−0.343060	+	0.939313i	$0.611464\pi$
$752$	21.0327	+	3.35494i	0.766985	+	0.122342i
$753$	14.1894	+	15.7589i	0.517091	+	0.574287i
$754$	−1.67042	+	4.91646i	−0.0608331	+	0.179047i
$755$	10.1626	+	2.16012i	0.369854	+	0.0786149i
$756$	−0.176433	+	6.59924i	−0.00641680	+	0.240012i
$757$	−31.1112	+	3.26992i	−1.13076	+	0.118847i	−0.651373	−	0.758758i	$-0.725807\pi$
$757$	−31.1112	+	3.26992i	−1.13076	+	0.118847i	−0.479384	+	0.877605i	$0.659140\pi$
$758$	1.49132	+	0.887795i	0.0541671	+	0.0322462i
$759$	1.58775	−	1.15357i	0.0576316	−	0.0418718i
$760$	1.00916	−	25.1568i	0.0366063	−	0.912534i
$761$	−5.59614	−	26.3278i	−0.202860	−	0.954380i	−0.955281	−	0.295698i	$-0.904448\pi$
$761$	−5.59614	−	26.3278i	−0.202860	−	0.954380i	0.752422	−	0.658682i	$-0.228886\pi$
$762$	−12.6859	−	9.47843i	−0.459562	−	0.343367i
$763$	32.7268	+	3.43973i	1.18479	+	0.124526i
$764$	13.4873	+	1.78318i	0.487955	+	0.0645130i
$765$	2.89473	+	6.50166i	0.104659	+	0.235068i
$766$	−27.2559	−	0.364282i	−0.984795	−	0.0131621i
$767$	−0.267932	+	0.824610i	−0.00967446	+	0.0297749i
$768$	−6.53987	+	14.6024i	−0.235987	+	0.526919i
$769$	−25.2984	−	43.8182i	−0.912285	−	1.58012i	−0.810828	−	0.585285i	$-0.800983\pi$
$769$	−25.2984	−	43.8182i	−0.912285	−	1.58012i	−0.101457	−	0.994840i	$-0.532351\pi$
$770$	21.9523	−	6.80975i	0.791105	−	0.245406i
$771$	−0.466853	−	1.43683i	−0.0168133	−	0.0517460i
$772$	−10.1852	+	28.7119i	−0.366572	+	1.03336i
$773$	−15.2185	+	20.9465i	−0.547371	+	0.753391i	−0.989653	−	0.143485i	$-0.954169\pi$
$773$	−15.2185	+	20.9465i	−0.547371	+	0.753391i	0.442282	+	0.896876i	$0.354169\pi$
$774$	−11.5115	+	12.4462i	−0.413772	+	0.447370i
$775$	2.67837	+	4.16373i	0.0962099	+	0.149566i
$776$	−5.69548	−	4.49757i	−0.204456	−	0.161453i
$777$	−27.4691	−	19.9575i	−0.985448	−	0.715970i
$778$	21.6459	+	50.4204i	0.776044	+	1.80766i
$779$	8.10614	−	2.63384i	0.290433	−	0.0943673i
$780$	0.826473	−	1.73029i	0.0295925	−	0.0619544i
$781$	24.8503	−	14.3473i	0.889212	−	0.513387i
$782$	3.99505	−	0.365988i	0.142863	−	0.0130877i
$783$	−7.38440	−	2.39934i	−0.263897	−	0.0857453i
$784$	12.0980	+	9.81876i	0.432070	+	0.350670i
$785$	19.8566	−	8.84071i	0.708711	−	0.315538i
$786$	4.14467	+	5.86799i	0.147836	+	0.209304i
$787$	5.75305	−	54.7366i	0.205074	−	1.95115i	−0.0906698	−	0.995881i	$-0.528901\pi$
$787$	5.75305	−	54.7366i	0.205074	−	1.95115i	0.295744	−	0.955267i	$-0.404433\pi$
$788$	−1.45840	−	7.89302i	−0.0519534	−	0.281177i
$789$	17.5336	−	3.72689i	0.624214	−	0.132681i
$790$	−4.76638	+	40.1764i	−0.169580	+	1.42941i
$791$	22.5084	+	30.9801i	0.800306	+	1.10153i
$792$	−6.15788	−	3.04304i	−0.218811	−	0.108130i
$793$	0.0900371	+	0.856646i	0.00319731	+	0.0304204i
$794$	15.0936	+	17.2205i	0.535652	+	0.611132i
$795$	−2.09119	+	9.83827i	−0.0741668	+	0.348927i
$796$	−9.50939	−	17.5371i	−0.337051	−	0.621585i
$797$	4.11930	−	3.70903i	0.145913	−	0.131381i	−0.592942	−	0.805245i	$-0.702034\pi$
$797$	4.11930	−	3.70903i	0.145913	−	0.131381i	0.738855	+	0.673865i	$0.235367\pi$
$798$	10.0090	+	17.8838i	0.354314	+	0.633080i
$799$	−12.5064	+	13.8898i	−0.442445	+	0.491385i
$800$	5.01878	+	0.335867i	0.177441	+	0.0118747i
$801$	−2.28444	−	1.31892i	−0.0807166	−	0.0466018i
$802$	−20.9316	+	45.3714i	−0.739121	+	1.60212i
$803$	11.4928	−	25.8132i	0.405571	−	0.910926i
$804$	−12.5808	−	7.71902i	−0.443690	−	0.272229i
$805$			5.40847i			0.190624i
$806$	−3.49922	+	1.27264i	−0.123255	+	0.0448268i
$807$		−	3.12543i		−	0.110020i
$808$	−14.5029	−	51.5860i	−0.510211	−	1.81479i
$809$	3.57013	−	8.01864i	0.125519	−	0.281920i	−0.839845	−	0.542826i	$-0.817354\pi$
$809$	3.57013	−	8.01864i	0.125519	−	0.281920i	0.965364	+	0.260905i	$0.0840210\pi$
$810$	2.60362	+	1.20115i	0.0914820	+	0.0422042i
$811$	27.9915	+	16.1609i	0.982913	+	0.567485i	0.903148	−	0.429329i	$-0.141250\pi$
$811$	27.9915	+	16.1609i	0.982913	+	0.567485i	0.0797645	+	0.996814i	$0.474583\pi$
$812$	−42.2586	+	29.0094i	−1.48299	+	1.01803i
$813$	10.8161	−	12.0125i	0.379336	−	0.421295i
$814$	30.8280	−	17.2534i	1.08052	−	0.604731i
$815$	−17.6213	+	15.8663i	−0.617246	+	0.555771i
$816$	−7.63421	−	11.7840i	−0.267251	−	0.412521i
$817$	−10.9426	+	51.4809i	−0.382833	+	1.80109i
$818$	−9.26764	+	8.12300i	−0.324035	+	0.284014i
$819$	0.163157	+	1.55233i	0.00570115	+	0.0542428i
$820$	−2.23173	−	7.54940i	−0.0779353	−	0.263637i
$821$	−12.0341	−	16.5635i	−0.419992	−	0.578070i	0.545628	−	0.838028i	$-0.316291\pi$
$821$	−12.0341	−	16.5635i	−0.419992	−	0.578070i	−0.965620	+	0.259958i	$0.916291\pi$
$822$	−1.00662	−	0.119422i	−0.0351099	−	0.00416530i
$823$	−8.84889	+	1.88089i	−0.308453	+	0.0655637i	−0.359537	−	0.933131i	$-0.617066\pi$
$823$	−8.84889	+	1.88089i	−0.308453	+	0.0655637i	0.0510847	+	0.998694i	$0.483732\pi$
$824$	7.76873	+	4.91065i	0.270636	+	0.171071i
$825$	−0.225715	+	2.14754i	−0.00785839	+	0.0747676i
$826$	−6.99102	+	4.93789i	−0.243249	+	0.171811i
$827$	−8.48118	+	3.77607i	−0.294920	+	0.131307i	−0.548863	−	0.835912i	$-0.684939\pi$
$827$	−8.48118	+	3.77607i	−0.294920	+	0.131307i	0.253943	+	0.967219i	$0.418272\pi$
$828$	1.11323	−	1.17181i	0.0386874	−	0.0407233i
$829$	−16.1792	−	5.25693i	−0.561926	−	0.182581i	0.0142618	−	0.999898i	$-0.495460\pi$
$829$	−16.1792	−	5.25693i	−0.561926	−	0.182581i	−0.576187	+	0.817318i	$0.695460\pi$
$830$	−2.12130	−	23.1557i	−0.0736313	−	0.803745i
$831$	−26.9434	+	15.5558i	−0.934655	+	0.539623i
$832$	−1.08041	+	3.62548i	−0.0374566	+	0.125691i
$833$	−13.0039	+	4.22522i	−0.450558	+	0.146395i
$834$	−7.19617	+	3.08938i	−0.249183	+	0.106976i
$835$	−20.7328	−	15.0633i	−0.717488	−	0.521286i
$836$	−21.2587	+	1.66135i	−0.735247	+	0.0574590i
$837$	−1.97276	−	5.20656i	−0.0681885	−	0.179965i
$838$	32.5222	+	30.0798i	1.12346	+	1.03909i
$839$	−7.91951	+	10.9003i	−0.273412	+	0.376319i	−0.923538	−	0.383507i	$-0.874716\pi$
$839$	−7.91951	+	10.9003i	−0.273412	+	0.376319i	0.650126	+	0.759826i	$0.274716\pi$
$840$	16.7592	−	8.79982i	0.578247	−	0.303623i
$841$	−9.66798	−	29.7550i	−0.333378	−	1.02603i
$842$	−10.2211	−	32.9492i	−0.352242	−	1.13550i
$843$	−2.60632	−	4.51427i	−0.0897663	−	0.155480i
$844$	32.7500	−	42.6322i	1.12730	−	1.46746i
$845$	−8.00487	+	24.6364i	−0.275376	+	0.847520i
$846$	−0.100634	+	7.52953i	−0.00345988	+	0.258871i
$847$	6.85045	+	15.3864i	0.235384	+	0.528682i
$848$	1.06027	−	19.8148i	0.0364098	−	0.680443i
$849$	20.5105	+	2.15574i	0.703919	+	0.0739848i
$850$	−2.64202	+	3.53607i	−0.0906205	+	0.121286i
$851$	1.72838	+	8.13137i	0.0592480	+	0.278740i
$852$	17.9782	−	15.3378i	0.615924	−	0.525464i
$853$	−33.4633	+	24.3125i	−1.14576	+	0.832445i	−0.987912	−	0.155018i	$-0.950457\pi$
$853$	−33.4633	+	24.3125i	−1.14576	+	0.832445i	−0.157851	+	0.987463i	$0.550457\pi$
$854$	−4.34950	+	7.30629i	−0.148837	+	0.250016i
$855$	8.85267	−	0.930453i	0.302755	−	0.0318208i
$856$	−6.50867	−	6.35092i	−0.222462	−	0.217070i
$857$	24.4235	+	5.19138i	0.834291	+	0.177334i	0.605203	−	0.796072i	$-0.293092\pi$
$857$	24.4235	+	5.19138i	0.834291	+	0.177334i	0.229089	+	0.973406i	$0.426425\pi$
$858$	−1.53771	−	0.522455i	−0.0524967	−	0.0178363i
$859$	20.3186	+	22.5661i	0.693261	+	0.769945i	0.982288	−	0.187376i	$-0.0599984\pi$
$859$	20.3186	+	22.5661i	0.693261	+	0.769945i	−0.289027	+	0.957321i	$0.593332\pi$
$860$	47.2621	+	11.3741i	1.61163	+	0.387853i
$861$	4.76216	+	4.28786i	0.162294	+	0.146130i
$862$	4.33915	−	19.1519i	0.147792	−	0.652315i
$863$	−15.4884	+	26.8267i	−0.527232	+	0.913193i	0.472264	+	0.881457i	$0.343437\pi$
$863$	−15.4884	+	26.8267i	−0.527232	+	0.913193i	−0.999496	+	0.0317358i	$0.989896\pi$
$864$	−5.44236	−	1.54297i	−0.185153	−	0.0524929i
$865$	38.2836	+	17.0450i	1.30168	+	0.579546i
$866$	9.10801	+	45.8548i	0.309503	+	1.55821i
$867$	−4.67857			−0.158893
$868$	−35.1911	−	10.6113i	−1.19446	−	0.360170i
$869$	34.2657			1.16238
$870$	4.33734	+	21.8366i	0.147050	+	0.740331i
$871$	−3.18816	−	1.41946i	−0.108027	−	0.0480965i
$872$	−9.78153	+	26.4469i	−0.331244	+	0.895605i
$873$	1.28290	−	2.22205i	0.0434196	−	0.0752049i
$874$	1.10873	−	4.89365i	0.0375035	−	0.165530i
$875$	−29.2895	−	26.3724i	−0.990165	−	0.891548i
$876$	5.44485	−	22.6247i	0.183964	−	0.764418i
$877$	−31.5493	−	35.0390i	−1.06534	−	1.18318i	−0.982431	−	0.186626i	$-0.940245\pi$
$877$	−31.5493	−	35.0390i	−1.06534	−	1.18318i	−0.0829121	−	0.996557i	$-0.526422\pi$
$878$	−5.45032	−	1.85180i	−0.183939	−	0.0624953i
$879$	18.1468	+	3.85721i	0.612075	+	0.130101i
$880$	1.00916	+	19.6691i	0.0340188	+	0.663046i
$881$	28.5764	−	3.00350i	0.962764	−	0.101191i	0.389915	−	0.920851i	$-0.372505\pi$
$881$	28.5764	−	3.00350i	0.962764	−	0.101191i	0.572850	+	0.819660i	$0.305838\pi$
$882$	−2.81787	+	4.73346i	−0.0948828	+	0.159384i
$883$	−8.38760	+	6.09395i	−0.282265	+	0.205078i	−0.719905	−	0.694073i	$-0.755815\pi$
$883$	−8.38760	+	6.09395i	−0.282265	+	0.205078i	0.437640	+	0.899150i	$0.355815\pi$
$884$	−2.15465	−	2.52558i	−0.0724687	−	0.0849444i
$885$	0.772919	+	3.63630i	0.0259814	+	0.122233i
$886$	−11.2188	+	15.0152i	−0.376903	+	0.504445i
$887$	51.6195	+	5.42543i	1.73321	+	0.182168i	0.917890	−	0.396836i	$-0.129892\pi$
$887$	51.6195	+	5.42543i	1.73321	+	0.182168i	0.815325	+	0.579004i	$0.196558\pi$
$888$	22.3845	−	18.5858i	0.751174	−	0.623699i
$889$	−15.0334	−	33.7656i	−0.504204	−	1.13246i
$890$	−0.101080	+	7.56291i	−0.00338822	+	0.253509i
$891$	0.750438	−	2.30961i	0.0251406	−	0.0773748i
$892$	−28.2031	−	21.6656i	−0.944310	−	0.725419i
$893$	11.6885	+	20.2450i	0.391140	+	0.677474i
$894$	8.85688	+	28.5515i	0.296218	+	0.954905i
$895$	−2.50134	−	7.69833i	−0.0836105	−	0.257327i
$896$	−29.9651	+	22.2864i	−1.00106	+	0.744538i
$897$	0.224627	−	0.309172i	0.00750007	−	0.0103230i
$898$	−9.79253	−	9.05711i	−0.326781	−	0.302240i
$899$	23.7019	−	36.1537i	0.790504	−	1.20579i
$900$	0.138556	+	1.77297i	0.00461855	+	0.0590990i
$901$	14.0877	+	10.2353i	0.469328	+	0.340987i
$902$	−6.12670	+	2.63025i	−0.203997	+	0.0875776i
$903$	−37.6331	+	12.2277i	−1.25235	+	0.406914i
$904$	−30.4874	+	12.1342i	−1.01400	+	0.403576i
$905$	0.737013	−	0.425514i	0.0244991	−	0.0141446i
$906$	−0.661120	−	7.21666i	−0.0219642	−	0.239757i
$907$	23.0634	+	7.49376i	0.765808	+	0.248826i	0.665770	−	0.746157i	$-0.268103\pi$
$907$	23.0634	+	7.49376i	0.765808	+	0.248826i	0.100039	+	0.994984i	$0.468103\pi$
$908$	5.26774	+	5.00440i	0.174816	+	0.166077i
$909$	17.3076	−	7.70582i	0.574056	−	0.255586i
$910$	3.65565	−	2.58205i	0.121184	−	0.0855942i
$911$	1.99940	−	19.0230i	0.0662431	−	0.630261i	−0.910153	−	0.414272i	$-0.864036\pi$
$911$	1.99940	−	19.0230i	0.0662431	−	0.630261i	0.976396	−	0.215988i	$-0.0692973\pi$
$912$	−16.9679	+	4.52657i	−0.561863	+	0.149890i
$913$	−19.2633	+	4.09453i	−0.637521	+	0.135509i
$914$	−36.4902	−	4.32906i	−1.20699	−	0.143193i
$915$	2.17079	+	2.98784i	0.0717642	+	0.0987749i
$916$	24.8431	−	7.34401i	0.820838	−	0.242653i
$917$	1.75272	+	16.6760i	0.0578799	+	0.550690i
$918$	3.73315	−	3.27207i	0.123212	−	0.107994i
$919$	−3.29588	+	15.5059i	−0.108721	+	0.511493i	0.889761	+	0.456426i	$0.150871\pi$
$919$	−3.29588	+	15.5059i	−0.108721	+	0.511493i	−0.998483	+	0.0550672i	$0.982463\pi$
$920$	−4.49094	−	1.14449i	−0.148062	−	0.0377327i
$921$	−5.52182	+	4.97187i	−0.181950	+	0.163829i
$922$	52.1897	−	29.2088i	1.71878	−	0.961941i
$923$	3.73878	−	4.15234i	0.123063	−	0.136676i
$924$	−9.07323	−	13.2172i	−0.298487	−	0.434813i
$925$	−7.92122	−	4.57332i	−0.260448	−	0.150370i
$926$	−48.7250	−	22.4787i	−1.60120	−	0.738697i
$927$	−1.32164	+	2.96845i	−0.0434084	+	0.0974968i
$928$	−15.1456	−	41.2283i	−0.497180	−	1.35338i
$929$			39.9758i			1.31156i	0.754950	+	0.655782i	$0.227661\pi$
$929$			39.9758i			1.31156i	−0.754950	+	0.655782i	$0.772339\pi$
$930$	−10.2649	+	12.2271i	−0.336599	+	0.400943i
$931$			17.1014i			0.560477i
$932$	−28.1223	+	45.8350i	−0.921178	+	1.50138i
$933$	4.66851	−	10.4856i	0.152840	−	0.343285i
$934$	−23.8610	+	51.7212i	−0.780757	+	1.69237i
$935$	−14.9678	−	8.64165i	−0.489499	−	0.282612i
$936$	−1.32351	−	0.193012i	−0.0432602	−	0.00630881i
$937$	15.2513	−	16.9383i	0.498238	−	0.553349i	−0.440602	−	0.897702i	$-0.645235\pi$
$937$	15.2513	−	16.9383i	0.498238	−	0.553349i	0.938840	+	0.344353i	$0.111902\pi$
$938$	−16.8249	−	30.0623i	−0.549351	−	0.981569i
$939$	3.53761	−	3.18528i	0.115446	−	0.103948i
$940$	18.9808	−	10.2922i	0.619084	−	0.335695i
$941$	−5.12116	+	24.0932i	−0.166945	+	0.785415i	0.812381	+	0.583127i	$0.198171\pi$
$941$	−5.12116	+	24.0932i	−0.166945	+	0.785415i	−0.979326	+	0.202288i	$0.935162\pi$
$942$	−9.99315	−	11.4013i	−0.325594	−	0.371475i
$943$	−0.163998	−	1.56033i	−0.00534050	−	0.0508115i
$944$	−2.62081	−	6.84992i	−0.0853002	−	0.222946i
$945$	3.93370	+	5.41427i	0.127963	+	0.176126i
$946$	4.85037	−	40.8844i	0.157699	−	1.32927i
$947$	−2.80157	+	0.595493i	−0.0910389	+	0.0193509i	−0.253206	−	0.967412i	$-0.581485\pi$
$947$	−2.80157	+	0.595493i	−0.0910389	+	0.0193509i	0.162167	+	0.986763i	$0.448152\pi$
$948$	27.7503	−	5.12746i	0.901288	−	0.166532i
$949$	0.575128	−	5.47198i	0.0186694	−	0.177628i
$950$	3.18509	+	4.50942i	0.103338	+	0.146305i
$951$	−13.5432	+	6.02983i	−0.439169	+	0.195531i
$952$	−2.11642	−	32.7029i	−0.0685935	−	1.05991i
$953$	25.5144	+	8.29013i	0.826492	+	0.268543i	0.691567	−	0.722312i	$-0.256921\pi$
$953$	25.5144	+	8.29013i	0.826492	+	0.268543i	0.134925	+	0.990856i	$0.456921\pi$
$954$	6.98636	−	0.640022i	0.226192	−	0.0207215i
$955$	11.9441	−	6.89593i	0.386502	−	0.223147i
$956$	6.45230	+	3.08194i	0.208682	+	0.0996770i
$957$	17.9328	−	5.82671i	0.579684	−	0.188351i
$958$	−18.1209	−	42.2095i	−0.585460	−	1.36373i
$959$	−1.91409	−	1.39067i	−0.0618091	−	0.0449070i
$960$	3.76053	+	15.7782i	0.121370	+	0.509238i
$961$	30.8571	−	2.97300i	0.995391	−	0.0959032i
$962$	4.67095	−	5.05022i	0.150597	−	0.162826i
$963$	1.88981	−	2.60110i	0.0608983	−	0.0838194i
$964$	44.3464	+	15.7313i	1.42830	+	0.506671i
$965$	9.54369	+	29.3725i	0.307222	+	0.945533i
$966$	3.60309	−	1.11770i	0.115928	−	0.0359616i
$967$	−7.26599	−	12.5851i	−0.233658	−	0.404708i	0.725223	−	0.688514i	$-0.241736\pi$
$967$	−7.26599	−	12.5851i	−0.233658	−	0.404708i	−0.958882	+	0.283805i	$0.908403\pi$
$968$	−14.2257	+	2.43237i	−0.457232	+	0.0781793i
$969$	4.76222	−	14.6566i	0.152984	−	0.470838i
$970$	−7.35635	−	0.0983197i	−0.236198	−	0.00315686i
$971$	10.8598	+	24.3916i	0.348509	+	0.782764i	0.999715	+	0.0238629i	$0.00759653\pi$
$971$	10.8598	+	24.3916i	0.348509	+	0.782764i	−0.651206	+	0.758901i	$0.725737\pi$
$972$	0.262141	−	1.98275i	0.00840818	−	0.0635966i
$973$	−18.1782	−	1.91061i	−0.582767	−	0.0612513i
$974$	−16.5402	−	12.3582i	−0.529981	−	0.395982i
$975$	0.0874226	+	0.411291i	0.00279976	+	0.0131719i
$976$	−5.14640	−	5.15771i	−0.164732	−	0.165094i
$977$	32.1061	−	23.3264i	1.02716	−	0.746278i	0.0594246	−	0.998233i	$-0.481073\pi$
$977$	32.1061	−	23.3264i	1.02716	−	0.746278i	0.967739	+	0.251955i	$0.0810734\pi$
$978$	14.2116	+	8.46029i	0.454437	+	0.270530i
$979$	6.37082	−	0.669600i	0.203612	−	0.0214005i
$980$	15.7897	+	0.422144i	0.504385	+	0.0134849i
$981$	−9.75158	−	2.07276i	−0.311344	−	0.0661782i
$982$	10.5320	−	30.9982i	0.336089	−	0.989193i
$983$	−36.5511	−	40.5941i	−1.16580	−	1.29475i	−0.947824	−	0.318795i	$-0.896722\pi$
$983$	−36.5511	−	40.5941i	−1.16580	−	1.29475i	−0.217974	−	0.975955i	$-0.569945\pi$
$984$	−4.56816	+	3.04691i	−0.145628	+	0.0971319i
$985$	−6.04700	−	5.44475i	−0.192674	−	0.173484i
$986$	37.5911	+	8.51684i	1.19714	+	0.271231i
$987$	−8.78781	+	15.2209i	−0.279719	+	0.484487i
$988$	−3.83700	+	1.58687i	−0.122071	+	0.0504850i
$989$	8.85049	+	3.94049i	0.281429	+	0.125300i
$990$	−6.82981	+	1.35658i	−0.217066	+	0.0431151i
$991$	28.3427			0.900334			0.450167	−	0.892944i	$-0.351364\pi$
$991$	28.3427			0.900334			0.450167	+	0.892944i	$0.351364\pi$
$992$	16.2579	−	26.9755i	0.516189	−	0.856474i
$993$	26.9240			0.854407
$994$	54.1003	−	10.7458i	1.71596	−	0.340835i
$995$	−18.4754	−	8.22576i	−0.585708	−	0.260774i
$996$	−14.9878	+	6.19850i	−0.474906	+	0.196407i
$997$	−8.84541	+	15.3207i	−0.280137	+	0.485212i	−0.971418	−	0.237374i	$-0.923713\pi$
$997$	−8.84541	+	15.3207i	−0.280137	+	0.485212i	0.691281	+	0.722586i	$0.257047\pi$
$998$	−43.2763	−	9.80491i	−1.36989	−	0.310369i
$999$	7.64436	+	6.88301i	0.241857	+	0.217769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.ba.a.43.15	✓	128
4.3	odd	2		372.2.ba.b.43.9	yes	128
31.13	odd	30		372.2.ba.b.199.9	yes	128
124.75	even	30	inner	372.2.ba.a.199.15	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.ba.a.43.15	✓	128	1.1	even	1	trivial
372.2.ba.a.199.15	yes	128	124.75	even	30	inner
372.2.ba.b.43.9	yes	128	4.3	odd	2
372.2.ba.b.199.9	yes	128	31.13	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38712 - 0.275519i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(1.84818 - 0.764352i) q^{4} +(1.01376 - 1.75588i) q^{5} +(-1.37926 - 0.312492i) q^{6} +(-2.45297 - 2.20866i) q^{7} +(2.35304 - 1.56945i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.922421 - 2.71492i) q^{10} +(-2.37540 - 0.504907i) q^{11} +(-1.99929 - 0.0534516i) q^{12} +(-0.470290 + 0.0494294i) q^{13} +(-4.01108 - 2.38783i) q^{14} +(-1.64029 + 1.19174i) q^{15} +(2.83153 - 2.82532i) q^{16} +(0.729809 + 3.43348i) q^{17} +(1.13291 + 0.846470i) q^{18} +(4.36627 + 0.458914i) q^{19} +(0.531494 - 4.02004i) q^{20} +(1.34256 + 3.01543i) q^{21} +(-3.43406 - 0.0458972i) q^{22} +(0.249732 - 0.768596i) q^{23} +(-2.78797 + 0.476697i) q^{24} +(0.444594 + 0.770060i) q^{25} +(-0.638727 + 0.198138i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-6.22173 - 2.20707i) q^{28} +(4.56381 - 6.28155i) q^{29} +(-1.94693 + 2.10502i) q^{30} +(5.56134 - 0.267292i) q^{31} +(3.14923 - 4.69918i) q^{32} +(1.96467 + 1.42742i) q^{33} +(1.95832 + 4.56156i) q^{34} +(-6.36486 + 2.06807i) q^{35} +(1.80470 + 0.862013i) q^{36} +(-8.90837 + 5.14325i) q^{37} +(6.18296 - 0.566423i) q^{38} +(0.449736 + 0.146128i) q^{39} +(-0.370353 - 5.72270i) q^{40} +(1.77354 - 0.789632i) q^{41} +(2.69309 + 3.81285i) q^{42} +(-1.25308 + 11.9223i) q^{43} +(-4.77609 + 0.882484i) q^{44} +(1.98321 - 0.421544i) q^{45} +(0.134645 - 1.13494i) q^{46} +(3.12976 + 4.30774i) q^{47} +(-3.73589 + 1.42937i) q^{48} +(0.407166 + 3.87392i) q^{49} +(0.828869 + 0.945668i) q^{50} +(0.729809 - 3.43348i) q^{51} +(-0.831398 + 0.450821i) q^{52} +(3.68658 - 3.31941i) q^{53} +(-0.690676 - 1.23409i) q^{54} +(-3.29463 + 3.65906i) q^{55} +(-9.23834 - 1.34726i) q^{56} +(-3.80213 - 2.19516i) q^{57} +(4.59985 - 9.97065i) q^{58} +(0.745769 - 1.67503i) q^{59} +(-2.12064 + 3.45632i) q^{60} -1.82153i q^{61} +(7.64058 - 1.90302i) q^{62} -3.30080i q^{63} +(3.07364 - 7.38598i) q^{64} +(-0.389967 + 0.875881i) q^{65} +(3.11851 + 1.43869i) q^{66} +(6.39130 + 3.69002i) q^{67} +(3.97321 + 5.78786i) q^{68} +(-0.540758 + 0.600572i) q^{69} +(-8.25901 + 4.62229i) q^{70} +(-8.78095 + 7.90640i) q^{71} +(2.74082 + 0.698484i) q^{72} +(-2.41912 + 11.3811i) q^{73} +(-10.9399 + 9.58870i) q^{74} +(-0.0929455 - 0.884317i) q^{75} +(8.42042 - 2.48921i) q^{76} +(4.71161 + 6.48498i) q^{77} +(0.664096 + 0.0787859i) q^{78} +(-13.8017 + 2.93364i) q^{79} +(-2.09043 - 7.83601i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.24255 - 1.58395i) q^{82} +(7.40839 - 3.29843i) q^{83} +(4.78613 + 4.54687i) q^{84} +(6.76863 + 2.19926i) q^{85} +(1.54664 + 16.8828i) q^{86} +(-6.72419 + 3.88221i) q^{87} +(-6.38185 + 2.54001i) q^{88} +(-2.50874 + 0.815138i) q^{89} +(2.63479 - 1.13114i) q^{90} +(1.26278 + 0.917463i) q^{91} +(-0.125929 - 1.61139i) q^{92} +(-5.18926 - 2.01782i) q^{93} +(5.52819 + 5.11303i) q^{94} +(5.23213 - 7.20141i) q^{95} +(-4.78830 + 3.01201i) q^{96} +(-0.792875 - 2.44022i) q^{97} +(1.63212 + 5.26139i) q^{98} +(-1.21423 - 2.10311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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