LMFDB - Embedded newform 380.2.bb.a.59.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.10
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08636 - 0.905441i) q^{2} +(-1.75425 + 2.09063i) q^{3} +(0.360351 + 1.96727i) q^{4} +(-2.18548 - 0.472930i) q^{5} +(3.79868 - 0.682806i) q^{6} +(-1.59127 - 2.75617i) q^{7} +(1.38978 - 2.46344i) q^{8} +(-0.772405 - 4.38052i) q^{9} +O(q^{10})$	\(q+(-1.08636 - 0.905441i) q^{2} +(-1.75425 + 2.09063i) q^{3} +(0.360351 + 1.96727i) q^{4} +(-2.18548 - 0.472930i) q^{5} +(3.79868 - 0.682806i) q^{6} +(-1.59127 - 2.75617i) q^{7} +(1.38978 - 2.46344i) q^{8} +(-0.772405 - 4.38052i) q^{9} +(1.94601 + 2.49260i) q^{10} +(0.876762 + 0.506199i) q^{11} +(-4.74497 - 2.69771i) q^{12} +(-3.83232 + 3.21570i) q^{13} +(-0.766853 + 4.43499i) q^{14} +(4.82259 - 3.73940i) q^{15} +(-3.74029 + 1.41782i) q^{16} +(5.77829 + 1.01887i) q^{17} +(-3.12720 + 5.45819i) q^{18} +(0.956248 - 4.25272i) q^{19} +(0.142839 - 4.46985i) q^{20} +(8.55360 + 1.50823i) q^{21} +(-0.494145 - 1.34377i) q^{22} +(5.67498 + 2.06552i) q^{23} +(2.71212 + 7.22698i) q^{24} +(4.55267 + 2.06716i) q^{25} +(7.07491 - 0.0234611i) q^{26} +(3.42257 + 1.97602i) q^{27} +(4.84870 - 4.12365i) q^{28} +(2.84576 - 0.501783i) q^{29} +(-8.62487 - 0.304251i) q^{30} +(0.591422 + 1.02437i) q^{31} +(5.34705 + 1.84636i) q^{32} +(-2.59633 + 0.944987i) q^{33} +(-5.35477 - 6.33876i) q^{34} +(2.17423 + 6.77612i) q^{35} +(8.33933 - 3.09806i) q^{36} -6.25121 q^{37} +(-4.88941 + 3.75415i) q^{38} -13.6531i q^{39} +(-4.20237 + 4.72653i) q^{40} +(4.05794 - 4.83606i) q^{41} +(-7.92667 - 9.38326i) q^{42} +(4.48584 - 1.63271i) q^{43} +(-0.679887 + 1.90724i) q^{44} +(-0.383606 + 9.93886i) q^{45} +(-4.29485 - 7.38226i) q^{46} +(-1.20896 - 6.85637i) q^{47} +(3.59727 - 10.3068i) q^{48} +(-1.56430 + 2.70945i) q^{49} +(-3.07414 - 6.36786i) q^{50} +(-12.2666 + 10.2929i) q^{51} +(-7.70713 - 6.38043i) q^{52} +(7.88929 + 2.87147i) q^{53} +(-1.92897 - 5.24561i) q^{54} +(-1.67675 - 1.52094i) q^{55} +(-9.00115 + 0.0895490i) q^{56} +(7.21335 + 9.45947i) q^{57} +(-3.54585 - 2.03155i) q^{58} +(-0.555649 + 3.15124i) q^{59} +(9.09423 + 8.13984i) q^{60} +(-8.86603 - 3.22697i) q^{61} +(0.285013 - 1.64833i) q^{62} +(-10.8443 + 9.09949i) q^{63} +(-4.13705 - 6.84725i) q^{64} +(9.89628 - 5.21544i) q^{65} +(3.67618 + 1.32423i) q^{66} +(5.98040 - 1.05451i) q^{67} +(0.0778272 + 11.7346i) q^{68} +(-14.2735 + 8.24083i) q^{69} +(3.77339 - 9.32993i) q^{70} +(1.39936 - 0.509326i) q^{71} +(-11.8646 - 4.18518i) q^{72} +(9.08468 - 10.8267i) q^{73} +(6.79106 + 5.66010i) q^{74} +(-12.3082 + 5.89164i) q^{75} +(8.71082 + 0.348725i) q^{76} -3.22200i q^{77} +(-12.3621 + 14.8322i) q^{78} +(4.30164 + 3.60950i) q^{79} +(8.84488 - 1.32972i) q^{80} +(2.40439 - 0.875127i) q^{81} +(-8.78714 + 1.57947i) q^{82} +(-4.37900 - 7.58465i) q^{83} +(0.115208 + 17.3707i) q^{84} +(-12.1465 - 4.95945i) q^{85} +(-6.35156 - 2.28795i) q^{86} +(-3.94311 + 6.82967i) q^{87} +(2.46549 - 1.45635i) q^{88} +(-3.27166 - 3.89901i) q^{89} +(9.41579 - 10.4498i) q^{90} +(14.9613 + 5.44546i) q^{91} +(-2.01845 + 11.9085i) q^{92} +(-3.17908 - 0.560558i) q^{93} +(-4.89467 + 8.54312i) q^{94} +(-4.10110 + 8.84200i) q^{95} +(-13.2401 + 7.93973i) q^{96} +(-2.56292 + 14.5350i) q^{97} +(4.15264 - 1.52705i) q^{98} +(1.54020 - 4.23167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.08636	−	0.905441i	−0.768172	−	0.640244i
$2$	−1.08636	−	0.905441i	−0.768172	−	0.640244i
$3$	−1.75425	+	2.09063i	−1.01281	+	1.20702i	−0.0346051	+	0.999401i	$0.511017\pi$
$3$	−1.75425	+	2.09063i	−1.01281	+	1.20702i	−0.978209	+	0.207624i	$0.933427\pi$
$4$	0.360351	+	1.96727i	0.180176	+	0.983634i
$5$	−2.18548	−	0.472930i	−0.977378	−	0.211501i
$5$	−2.18548	−	0.472930i	−0.977378	−	0.211501i
$6$	3.79868	−	0.682806i	1.55081	−	0.278754i
$7$	−1.59127	−	2.75617i	−0.601445	−	1.04173i	−0.992603	−	0.121409i	$-0.961259\pi$
$7$	−1.59127	−	2.75617i	−0.601445	−	1.04173i	0.391158	−	0.920324i	$-0.372075\pi$
$8$	1.38978	−	2.46344i	0.491360	−	0.870957i
$9$	−0.772405	−	4.38052i	−0.257468	−	1.46017i
$10$	1.94601	+	2.49260i	0.615382	+	0.788229i
$11$	0.876762	+	0.506199i	0.264354	+	0.152625i	0.626319	−	0.779567i	$-0.284561\pi$
$11$	0.876762	+	0.506199i	0.264354	+	0.152625i	−0.361965	+	0.932192i	$0.617894\pi$
$12$	−4.74497	−	2.69771i	−1.36976	−	0.778762i
$13$	−3.83232	+	3.21570i	−1.06289	+	0.891875i	−0.994390	−	0.105776i	$-0.966267\pi$
$13$	−3.83232	+	3.21570i	−1.06289	+	0.891875i	−0.0685050	+	0.997651i	$0.521823\pi$
$14$	−0.766853	+	4.43499i	−0.204950	+	1.18530i
$15$	4.82259	−	3.73940i	1.24519	−	0.965508i
$16$	−3.74029	+	1.41782i	−0.935073	+	0.354454i
$17$	5.77829	+	1.01887i	1.40144	+	0.247112i	0.822735	−	0.568425i	$-0.192447\pi$
$17$	5.77829	+	1.01887i	1.40144	+	0.247112i	0.578706	+	0.815537i	$0.303558\pi$
$18$	−3.12720	+	5.45819i	−0.737088	+	1.28651i
$19$	0.956248	−	4.25272i	0.219378	−	0.975640i
$19$	0.956248	−	4.25272i	0.219378	−	0.975640i
$20$	0.142839	−	4.46985i	0.0319398	−	0.999490i
$21$	8.55360	+	1.50823i	1.86655	+	0.329123i
$22$	−0.494145	−	1.34377i	−0.105352	−	0.286493i
$23$	5.67498	+	2.06552i	1.18331	+	0.430691i	0.857371	−	0.514698i	$-0.172096\pi$
$23$	5.67498	+	2.06552i	1.18331	+	0.430691i	0.325943	+	0.945389i	$0.394318\pi$
$24$	2.71212	+	7.22698i	0.553610	+	1.47520i
$25$	4.55267	+	2.06716i	0.910535	+	0.413433i
$26$	7.07491	−	0.0234611i	1.38750	−	0.00460111i
$27$	3.42257	+	1.97602i	0.658674	+	0.380286i
$28$	4.84870	−	4.12365i	0.916318	−	0.779297i
$29$	2.84576	−	0.501783i	0.528444	−	0.0931789i	0.0969402	−	0.995290i	$-0.469094\pi$
$29$	2.84576	−	0.501783i	0.528444	−	0.0931789i	0.431503	+	0.902111i	$0.357983\pi$
$30$	−8.62487	−	0.304251i	−1.57468	−	0.0555483i
$31$	0.591422	+	1.02437i	0.106223	+	0.183983i	0.914237	−	0.405180i	$-0.132791\pi$
$31$	0.591422	+	1.02437i	0.106223	+	0.183983i	−0.808014	+	0.589163i	$0.799458\pi$
$32$	5.34705	+	1.84636i	0.945234	+	0.326393i
$33$	−2.59633	+	0.944987i	−0.451963	+	0.164501i
$34$	−5.35477	−	6.33876i	−0.918335	−	1.08709i
$35$	2.17423	+	6.77612i	0.367511	+	1.14537i
$36$	8.33933	−	3.09806i	1.38989	−	0.516343i
$37$	−6.25121			−1.02769			−0.513846	−	0.857882i	$-0.671780\pi$
$37$	−6.25121			−1.02769			−0.513846	+	0.857882i	$0.671780\pi$
$38$	−4.88941	+	3.75415i	−0.793168	+	0.609003i
$39$		−	13.6531i		−	2.18624i
$40$	−4.20237	+	4.72653i	−0.664452	+	0.747331i
$41$	4.05794	−	4.83606i	0.633743	−	0.755266i	−0.349625	−	0.936890i	$-0.613691\pi$
$41$	4.05794	−	4.83606i	0.633743	−	0.755266i	0.983368	+	0.181624i	$0.0581354\pi$
$42$	−7.92667	−	9.38326i	−1.22311	−	1.44787i
$43$	4.48584	−	1.63271i	0.684084	−	0.248986i	0.0234840	−	0.999724i	$-0.492524\pi$
$43$	4.48584	−	1.63271i	0.684084	−	0.248986i	0.660600	+	0.750738i	$0.270302\pi$
$44$	−0.679887	+	1.90724i	−0.102497	+	0.287527i
$45$	−0.383606	+	9.93886i	−0.0571846	+	1.48160i
$46$	−4.29485	−	7.38226i	−0.633241	−	1.08845i
$47$	−1.20896	−	6.85637i	−0.176345	−	1.00010i	−0.936580	−	0.350455i	$-0.886027\pi$
$47$	−1.20896	−	6.85637i	−0.176345	−	1.00010i	0.760234	−	0.649649i	$-0.225084\pi$
$48$	3.59727	−	10.3068i	0.519220	−	1.48765i
$49$	−1.56430	+	2.70945i	−0.223471	+	0.387064i
$50$	−3.07414	−	6.36786i	−0.434749	−	0.900551i
$51$	−12.2666	+	10.2929i	−1.71767	+	1.44130i
$52$	−7.70713	−	6.38043i	−1.06879	−	0.884806i
$53$	7.88929	+	2.87147i	1.08368	+	0.394426i	0.821275	−	0.570532i	$-0.193263\pi$
$53$	7.88929	+	2.87147i	1.08368	+	0.394426i	0.262402	+	0.964959i	$0.415485\pi$
$54$	−1.92897	−	5.24561i	−0.262499	−	0.713837i
$55$	−1.67675	−	1.52094i	−0.226093	−	0.205083i
$56$	−9.00115	+	0.0895490i	−1.20283	+	0.0119665i
$57$	7.21335	+	9.45947i	0.955432	+	1.25294i
$58$	−3.54585	−	2.03155i	−0.465593	−	0.266755i
$59$	−0.555649	+	3.15124i	−0.0723393	+	0.410257i	0.927038	+	0.374968i	$0.122346\pi$
$59$	−0.555649	+	3.15124i	−0.0723393	+	0.410257i	−0.999377	+	0.0352889i	$0.988765\pi$
$60$	9.09423	+	8.13984i	1.17406	+	1.05085i
$61$	−8.86603	−	3.22697i	−1.13518	−	0.413171i	−0.295009	−	0.955494i	$-0.595323\pi$
$61$	−8.86603	−	3.22697i	−1.13518	−	0.413171i	−0.840170	+	0.542323i	$0.817545\pi$
$62$	0.285013	−	1.64833i	0.0361967	−	0.209339i
$63$	−10.8443	+	9.09949i	−1.36626	+	1.14643i
$64$	−4.13705	−	6.84725i	−0.517131	−	0.855906i
$65$	9.89628	−	5.21544i	1.22748	−	0.646895i
$66$	3.67618	+	1.32423i	0.452506	+	0.163001i
$67$	5.98040	−	1.05451i	0.730623	−	0.128828i	0.204052	−	0.978960i	$-0.434589\pi$
$67$	5.98040	−	1.05451i	0.730623	−	0.128828i	0.526570	+	0.850132i	$0.323478\pi$
$68$	0.0778272	+	11.7346i	0.00943794	+	1.42303i
$69$	−14.2735	+	8.24083i	−1.71833	+	0.992080i
$70$	3.77339	−	9.32993i	0.451006	−	1.11514i
$71$	1.39936	−	0.509326i	0.166074	−	0.0604458i	−0.257645	−	0.966240i	$-0.582947\pi$
$71$	1.39936	−	0.509326i	0.166074	−	0.0604458i	0.423719	+	0.905794i	$0.360724\pi$
$72$	−11.8646	−	4.18518i	−1.39826	−	0.493228i
$73$	9.08468	−	10.8267i	1.06328	−	1.26717i	0.101066	−	0.994880i	$-0.467775\pi$
$73$	9.08468	−	10.8267i	1.06328	−	1.26717i	0.962215	−	0.272289i	$-0.0877808\pi$
$74$	6.79106	+	5.66010i	0.789444	+	0.657974i
$75$	−12.3082	+	5.89164i	−1.42123	+	0.680308i
$76$	8.71082	+	0.348725i	0.999200	+	0.0400015i
$77$		−	3.22200i		−	0.367181i
$78$	−12.3621	+	14.8322i	−1.39973	+	1.67941i
$79$	4.30164	+	3.60950i	0.483972	+	0.406101i	0.851860	−	0.523769i	$-0.175475\pi$
$79$	4.30164	+	3.60950i	0.483972	+	0.406101i	−0.367888	+	0.929870i	$0.619919\pi$
$80$	8.84488	−	1.32972i	0.988887	−	0.148667i
$81$	2.40439	−	0.875127i	0.267154	−	0.0972363i
$82$	−8.78714	+	1.57947i	−0.970378	+	0.174424i
$83$	−4.37900	−	7.58465i	−0.480658	−	0.832523i	0.519096	−	0.854716i	$-0.326269\pi$
$83$	−4.37900	−	7.58465i	−0.480658	−	0.832523i	−0.999754	+	0.0221925i	$0.992935\pi$
$84$	0.115208	+	17.3707i	0.0125702	+	1.89530i
$85$	−12.1465	−	4.95945i	−1.31747	−	0.537928i
$86$	−6.35156	−	2.28795i	−0.684906	−	0.246716i
$87$	−3.94311	+	6.82967i	−0.422746	+	0.732217i
$88$	2.46549	−	1.45635i	0.262822	−	0.155247i
$89$	−3.27166	−	3.89901i	−0.346795	−	0.413294i	0.564248	−	0.825605i	$-0.309166\pi$
$89$	−3.27166	−	3.89901i	−0.346795	−	0.413294i	−0.911043	+	0.412311i	$0.864722\pi$
$90$	9.41579	−	10.4498i	0.992511	−	1.10151i
$91$	14.9613	+	5.44546i	1.56837	+	0.570839i
$92$	−2.01845	+	11.9085i	−0.210438	+	1.24155i
$93$	−3.17908	−	0.560558i	−0.329655	−	0.0581271i
$94$	−4.89467	+	8.54312i	−0.504847	+	0.881155i
$95$	−4.10110	+	8.84200i	−0.420764	+	0.907170i
$96$	−13.2401	+	7.93973i	−1.35131	+	0.810345i
$97$	−2.56292	+	14.5350i	−0.260225	+	1.47581i	0.522071	+	0.852902i	$0.325160\pi$
$97$	−2.56292	+	14.5350i	−0.260225	+	1.47581i	−0.782296	+	0.622907i	$0.785951\pi$
$98$	4.15264	−	1.52705i	0.419480	−	0.154255i
$99$	1.54020	−	4.23167i	0.154796	−	0.425299i
$100$	−2.42610	+	9.70124i	−0.242610	+	0.970124i
$101$	3.64320	−	3.05701i	0.362512	−	0.304183i	−0.443279	−	0.896384i	$-0.646185\pi$
$101$	3.64320	−	3.05701i	0.362512	−	0.304183i	0.805791	+	0.592200i	$0.201741\pi$
$102$	22.6456	−	0.0750951i	2.24224	−	0.00743552i
$103$	−13.2887	−	7.67222i	−1.30937	−	0.755967i	−0.327381	−	0.944892i	$-0.606166\pi$
$103$	−13.2887	−	7.67222i	−1.30937	−	0.755967i	−0.981991	+	0.188926i	$0.939499\pi$
$104$	2.59561	+	13.9098i	0.254520	+	1.36397i
$105$	−17.9805	−	7.34147i	−1.75471	−	0.716454i
$106$	−5.97065	−	10.2627i	−0.579921	−	0.996805i
$107$	16.3092	−	9.41614i	1.57667	−	0.910292i	0.581353	−	0.813651i	$-0.302524\pi$
$107$	16.3092	−	9.41614i	1.57667	−	0.910292i	0.995319	−	0.0966407i	$-0.0308098\pi$
$108$	−2.65404	+	7.44518i	−0.255385	+	0.716413i
$109$	2.57700	+	7.08026i	0.246832	+	0.678166i	0.999798	+	0.0201062i	$0.00640043\pi$
$109$	2.57700	+	7.08026i	0.246832	+	0.678166i	−0.752966	+	0.658060i	$0.771377\pi$
$110$	0.444436	+	3.17048i	0.0423753	+	0.302294i
$111$	10.9662	−	13.0690i	1.04086	−	1.24045i
$112$	9.85957	+	8.05274i	0.931641	+	0.760912i
$113$	−5.34794			−0.503092			−0.251546	−	0.967845i	$-0.580939\pi$
$113$	−5.34794			−0.503092			−0.251546	+	0.967845i	$0.580939\pi$
$114$	0.728703	−	16.8076i	0.0682493	−	1.57418i
$115$	−11.4257	−	7.19803i	−1.06545	−	0.671220i
$116$	2.01262	+	5.41755i	0.186867	+	0.503007i
$117$	17.0466	+	14.3038i	1.57595	+	1.32238i
$118$	3.45690	−	2.92027i	0.318233	−	0.268833i
$119$	−6.38667	−	17.5472i	−0.585465	−	1.60855i
$120$	−2.50944	−	17.0771i	−0.229080	−	1.55892i
$121$	−4.98753	−	8.63865i	−0.453411	−	0.785332i
$122$	6.70986	+	11.5333i	0.607482	+	1.04418i
$123$	2.99179	+	16.9673i	0.269760	+	1.52989i
$124$	−1.80210	+	1.53262i	−0.161833	+	0.137633i
$125$	−8.97217	−	6.67085i	−0.802495	−	0.596659i
$126$	20.0199	−	0.0663881i	1.78351	−	0.00591433i
$127$	5.15197	+	6.13988i	0.457163	+	0.544826i	0.944553	−	0.328358i	$-0.106495\pi$
$127$	5.15197	+	6.13988i	0.457163	+	0.544826i	−0.487390	+	0.873185i	$0.662051\pi$
$128$	−1.70547	+	11.1844i	−0.150743	+	0.988573i
$129$	−4.45587	+	12.2424i	−0.392317	+	1.07788i
$130$	−15.4732	−	3.29466i	−1.35709	−	0.288961i
$131$	10.1411	+	1.78815i	0.886033	+	0.156232i	0.598103	−	0.801420i	$-0.295922\pi$
$131$	10.1411	+	1.78815i	0.886033	+	0.156232i	0.287931	+	0.957651i	$0.407033\pi$
$132$	−2.79463	−	4.76715i	−0.243242	−	0.414927i
$133$	−13.2428	+	4.13165i	−1.14830	+	0.358260i
$134$	−7.45166	−	4.26933i	−0.643725	−	0.368814i
$135$	−6.54545	−	5.93720i	−0.563343	−	0.510993i
$136$	10.5404	−	12.8185i	0.903836	−	1.09917i
$137$	−2.05984	+	5.65936i	−0.175984	+	0.483512i	−0.996054	−	0.0887514i	$-0.971712\pi$
$137$	−2.05984	+	5.65936i	−0.175984	+	0.483512i	0.820070	+	0.572264i	$0.193935\pi$
$138$	22.9678	+	3.97135i	1.95515	+	0.338064i
$139$	10.4465	+	12.4496i	0.886060	+	1.05597i	0.998060	+	0.0622569i	$0.0198298\pi$
$139$	10.4465	+	12.4496i	0.886060	+	1.05597i	−0.112000	+	0.993708i	$0.535726\pi$
$140$	−12.5470	+	6.71907i	−1.06041	+	0.567865i
$141$	16.4549	+	9.50026i	1.38575	+	0.800066i
$142$	−1.98137	−	0.713729i	−0.166273	−	0.0598948i
$143$	−4.98782	+	0.879487i	−0.417102	+	0.0735464i
$144$	9.09980	+	15.2893i	0.758317	+	1.27411i
$145$	−6.45666	−	0.249205i	−0.536196	−	0.0206954i
$146$	−19.6722	+	3.53604i	−1.62808	+	0.292644i
$147$	−2.92028	−	8.02340i	−0.240861	−	0.661759i
$148$	−2.25263	−	12.2978i	−0.185165	−	1.01087i
$149$	−5.67929	−	4.76549i	−0.465266	−	0.390404i	0.379798	−	0.925069i	$-0.375993\pi$
$149$	−5.67929	−	4.76549i	−0.465266	−	0.390404i	−0.845064	+	0.534665i	$0.820438\pi$
$150$	18.7056	+	4.74390i	1.52731	+	0.387338i
$151$	1.70219			0.138522			0.0692612	−	0.997599i	$-0.477936\pi$
$151$	1.70219			0.138522			0.0692612	+	0.997599i	$0.477936\pi$
$152$	−9.14733	−	8.26598i	−0.741946	−	0.670459i
$153$		−	26.0989i		−	2.10997i
$154$	−2.91734	+	3.50025i	−0.235086	+	0.282058i
$155$	−0.808086	−	2.51845i	−0.0649070	−	0.202287i
$156$	26.8593	−	4.91991i	2.15046	−	0.393908i
$157$	−2.94835	−	8.10052i	−0.235304	−	0.646492i	−0.999998	−	0.00209846i	$-0.999332\pi$
$157$	−2.94835	−	8.10052i	−0.235304	−	0.646492i	0.764694	−	0.644394i	$-0.222890\pi$
$158$	−1.40493	−	7.81609i	−0.111770	−	0.621815i
$159$	−19.8429	+	11.4563i	−1.57365	+	0.908545i
$160$	−10.8127	−	6.56397i	−0.854818	−	0.518927i
$161$	−3.33752	−	18.9280i	−0.263033	−	1.49173i
$162$	−3.40441	−	1.22633i	−0.267475	−	0.0963498i
$163$	4.92357	−	8.52788i	0.385644	−	0.667955i	−0.606214	−	0.795301i	$-0.707313\pi$
$163$	4.92357	−	8.52788i	0.385644	−	0.667955i	0.991858	+	0.127346i	$0.0406460\pi$
$164$	10.9761	+	6.24037i	0.857090	+	0.487291i
$165$	6.12115	−	0.837369i	0.476531	−	0.0651891i
$166$	−2.11029	+	12.2046i	−0.163790	+	0.947259i
$167$	−4.79605	+	13.1770i	−0.371129	+	1.01967i	0.603796	+	0.797139i	$0.293654\pi$
$167$	−4.79605	+	13.1770i	−0.371129	+	1.01967i	−0.974926	+	0.222531i	$0.928568\pi$
$168$	15.6030	−	18.9752i	1.20380	−	1.46397i
$169$	2.08854	−	11.8447i	0.160657	−	0.911131i
$170$	8.70497	+	16.3857i	0.667641	+	1.25672i
$171$	−19.3677	−	0.904052i	−1.48109	−	0.0691346i
$172$	4.82846	+	8.23650i	0.368167	+	0.628027i
$173$	0.862887	−	4.89368i	0.0656041	−	0.372059i	−0.934276	−	0.356552i	$-0.883952\pi$
$173$	0.862887	−	4.89368i	0.0656041	−	0.372059i	0.999880	−	0.0155078i	$-0.00493648\pi$
$174$	10.4675	−	3.84921i	0.793539	−	0.291808i
$175$	−1.54710	−	15.8373i	−0.116950	−	1.19719i
$176$	−3.99705	−	0.650245i	−0.301289	−	0.0490140i
$177$	−5.61333	−	6.68971i	−0.421924	−	0.502829i
$178$	0.0238694	+	7.19802i	0.00178909	+	0.539514i
$179$	5.78145	−	10.0138i	0.432126	−	0.748464i	−0.564930	−	0.825139i	$-0.691097\pi$
$179$	5.78145	−	10.0138i	0.432126	−	0.748464i	0.997056	+	0.0766749i	$0.0244304\pi$
$180$	−19.6906	+	2.82683i	−1.46765	+	0.210699i
$181$	14.5003	−	2.55679i	1.07780	−	0.190044i	0.393555	−	0.919301i	$-0.371245\pi$
$181$	14.5003	−	2.55679i	1.07780	−	0.190044i	0.684240	+	0.729257i	$0.260134\pi$
$182$	−11.3228	−	19.4623i	−0.839300	−	1.44264i
$183$	22.2996	−	12.8747i	1.64843	−	0.951723i
$184$	12.9752	−	11.1093i	0.956547	−	0.818991i
$185$	13.6619	+	2.95639i	1.00444	+	0.217358i
$186$	2.94607	+	3.48744i	0.216016	+	0.255711i
$187$	4.55044	+	3.81827i	0.332761	+	0.279219i
$188$	13.0527	−	4.84906i	0.951963	−	0.353654i
$189$		−	12.5776i		−	0.914883i
$190$	12.4612	−	5.89228i	0.904029	−	0.427471i
$191$			16.3660i			1.18420i	0.805865	+	0.592100i	$0.201701\pi$
$191$			16.3660i			1.18420i	−0.805865	+	0.592100i	$0.798299\pi$
$192$	21.5724	+	3.36273i	1.55686	+	0.242684i
$193$	−5.14586	−	4.31789i	−0.370407	−	0.310809i	0.438515	−	0.898724i	$-0.355504\pi$
$193$	−5.14586	−	4.31789i	−0.370407	−	0.310809i	−0.808923	+	0.587915i	$0.799949\pi$
$194$	15.9449	−	13.4697i	1.14478	−	0.967068i
$195$	−6.45696	+	29.8386i	−0.462393	+	2.13679i
$196$	−5.89391	−	2.10105i	−0.420993	−	0.150075i
$197$	15.3393	−	8.85613i	1.09288	−	0.630973i	0.158536	−	0.987353i	$-0.449322\pi$
$197$	15.3393	−	8.85613i	1.09288	−	0.630973i	0.934341	+	0.356380i	$0.115989\pi$
$198$	−5.50474	+	3.20255i	−0.391205	+	0.227595i
$199$	−12.1491	+	2.14222i	−0.861227	+	0.151858i	−0.586782	−	0.809745i	$-0.699605\pi$
$199$	−12.1491	+	2.14222i	−0.861227	+	0.151858i	−0.274445	+	0.961603i	$0.588494\pi$
$200$	11.4195	−	8.34233i	0.807482	−	0.589892i
$201$	−8.28651	+	14.3527i	−0.584486	+	1.01236i
$202$	−6.72576	+	0.0223033i	−0.473223	+	0.00156926i
$203$	−5.91137	−	7.04490i	−0.414897	−	0.494455i
$204$	−24.6692	−	20.4227i	−1.72719	−	1.42987i
$205$	−11.1557	+	8.65000i	−0.779146	+	0.604143i
$206$	7.48953	+	20.3669i	0.521820	+	1.41903i
$207$	4.66469	−	26.4548i	0.324219	−	1.83874i
$208$	9.77474	−	17.4612i	0.677756	−	1.21072i
$209$	2.99112	−	3.24457i	0.206900	−	0.224431i
$210$	12.8860	+	24.2557i	0.889216	+	1.67380i
$211$	1.15829	−	6.56899i	0.0797400	−	0.452228i	−0.918628	−	0.395123i	$-0.870702\pi$
$211$	1.15829	−	6.56899i	0.0797400	−	0.452228i	0.998368	−	0.0571048i	$-0.0181869\pi$
$212$	−2.80603	+	16.5551i	−0.192719	+	1.13701i
$213$	−1.39001	+	3.81902i	−0.0952420	+	0.261675i
$214$	−26.2434	−	4.53775i	−1.79396	−	0.310194i
$215$	−10.5759	+	1.44677i	−0.721269	+	0.0986692i
$216$	9.62441	−	5.68506i	0.654858	−	0.386819i
$217$	1.88223	−	3.26011i	0.127774	−	0.221311i
$218$	3.61121	−	10.0250i	0.244582	−	0.678981i
$219$	6.69785	+	37.9854i	0.452598	+	2.56681i
$220$	2.38787	−	3.84669i	0.160990	−	0.259344i
$221$	−25.4206	+	14.6766i	−1.70998	+	0.987256i
$222$	−23.7464	+	4.26836i	−1.59375	+	0.286474i
$223$	−1.77574	−	4.87879i	−0.118912	−	0.326708i	0.865929	−	0.500167i	$-0.166728\pi$
$223$	−1.77574	−	4.87879i	−0.118912	−	0.326708i	−0.984841	+	0.173459i	$0.944506\pi$
$224$	−3.41975	−	17.6754i	−0.228491	−	1.18099i
$225$	5.53875	−	21.5398i	0.369250	−	1.43599i
$226$	5.80978	+	4.84224i	0.386461	+	0.322101i
$227$		−	5.16817i		−	0.343023i	−0.985182	−	0.171512i	$-0.945135\pi$
$227$		−	5.16817i		−	0.343023i	0.985182	−	0.171512i	$-0.0548651\pi$
$228$	−16.0100	+	17.5993i	−1.06029	+	1.16554i
$229$	14.2247			0.939997			0.469998	−	0.882667i	$-0.344255\pi$
$229$	14.2247			0.939997			0.469998	+	0.882667i	$0.344255\pi$
$230$	5.89503	+	18.1650i	0.388707	+	1.19776i
$231$	6.73601	+	5.65218i	0.443197	+	0.371886i
$232$	2.71885	−	7.70771i	0.178501	−	0.506036i
$233$	−1.56141	−	4.28993i	−0.102291	−	0.281042i	0.877981	−	0.478696i	$-0.158890\pi$
$233$	−1.56141	−	4.28993i	−0.102291	−	0.281042i	−0.980272	+	0.197653i	$0.936668\pi$
$234$	−5.56746	−	30.9737i	−0.363956	−	2.02481i
$235$	−0.600417	+	15.5562i	−0.0391669	+	1.01478i
$236$	−6.39957	+	0.0424438i	−0.416576	+	0.00276285i
$237$	−15.0922	+	2.66117i	−0.980347	+	0.172862i
$238$	−8.94977	+	24.8453i	−0.580127	+	1.61048i
$239$	5.83611	+	3.36948i	0.377506	+	0.217953i	0.676733	−	0.736229i	$-0.263395\pi$
$239$	5.83611	+	3.36948i	0.377506	+	0.217953i	−0.299226	+	0.954182i	$0.596729\pi$
$240$	−12.7361	+	20.8240i	−0.822114	+	1.34418i
$241$	4.41428	+	5.26074i	0.284349	+	0.338874i	0.889246	−	0.457430i	$-0.151230\pi$
$241$	4.41428	+	5.26074i	0.284349	+	0.338874i	−0.604897	+	0.796304i	$0.706786\pi$
$242$	−2.40355	+	13.9006i	−0.154506	+	0.893563i
$243$	−6.44336	+	17.7030i	−0.413342	+	1.13565i
$244$	3.15343	−	18.6047i	0.201878	−	1.19104i
$245$	4.70013	−	5.18165i	0.300280	−	0.331043i
$246$	12.1127	−	21.1414i	0.772278	−	1.34793i
$247$	10.0108	+	19.3728i	0.636972	+	1.23266i
$248$	3.34542	−	0.0332823i	0.212435	−	0.00211343i
$249$	23.5385	+	4.15048i	1.49169	+	0.263026i
$250$	3.70693	+	15.3707i	0.234447	+	0.972129i
$251$	−6.81952	+	18.7365i	−0.430444	+	1.18264i	0.515096	+	0.857132i	$0.327756\pi$
$251$	−6.81952	+	18.7365i	−0.430444	+	1.18264i	−0.945541	+	0.325504i	$0.894466\pi$
$252$	−21.8089	−	18.0547i	−1.37383	−	1.13734i
$253$	3.93004	+	4.68364i	0.247080	+	0.294458i
$254$	−0.0375878	−	11.3349i	−0.00235847	−	0.711216i
$255$	31.6763	−	16.6937i	1.98365	−	1.04540i
$256$	11.9796	−	10.6061i	0.748725	−	0.662881i
$257$	2.71289	+	15.3856i	0.169225	+	0.959725i	0.944600	+	0.328224i	$0.106450\pi$
$257$	2.71289	+	15.3856i	0.169225	+	0.959725i	−0.775375	+	0.631502i	$0.782439\pi$
$258$	15.9254	−	9.26511i	0.991475	−	0.576821i
$259$	9.94738	+	17.2294i	0.618100	+	1.07058i
$260$	13.8263	+	17.5893i	0.857471	+	1.09084i
$261$	−4.39615	−	12.0783i	−0.272115	−	0.747629i
$262$	−9.39783	−	11.1248i	−0.580600	−	0.687290i
$263$	3.34770	+	2.80906i	0.206428	+	0.173214i	0.740140	−	0.672452i	$-0.234759\pi$
$263$	3.34770	+	2.80906i	0.206428	+	0.173214i	−0.533712	+	0.845666i	$0.679203\pi$
$264$	−1.28040	+	7.70921i	−0.0788032	+	0.474469i
$265$	−15.8839	−	10.0066i	−0.975740	−	0.614702i
$266$	18.1274	+	7.50216i	1.11147	+	0.459987i
$267$	13.8907			0.850095
$268$	4.22955	+	11.3851i	0.258361	+	0.695454i
$269$	−12.9509	+	15.4343i	−0.789631	+	0.941046i	−0.999326	−	0.0367211i	$-0.988309\pi$
$269$	−12.9509	+	15.4343i	−0.789631	+	0.941046i	0.209694	+	0.977767i	$0.432753\pi$
$270$	1.73492	+	12.3765i	0.105584	+	0.753207i
$271$	−5.37440	−	14.7660i	−0.326472	−	0.896973i	−0.988997	−	0.147934i	$-0.952738\pi$
$271$	−5.37440	−	14.7660i	−0.326472	−	0.896973i	0.662526	−	0.749039i	$-0.269485\pi$
$272$	−23.0571	+	4.38169i	−1.39804	+	0.265679i
$273$	−37.6302	+	21.7258i	−2.27748	+	1.31490i
$274$	7.36195	−	4.28304i	0.444752	−	0.258748i
$275$	2.94522	+	4.11697i	0.177603	+	0.248263i
$276$	−21.3554	−	25.1103i	−1.28545	−	1.51146i
$277$	17.1663	+	9.91100i	1.03143	+	0.595494i	0.917393	−	0.397983i	$-0.130290\pi$
$277$	17.1663	+	9.91100i	1.03143	+	0.595494i	0.114033	+	0.993477i	$0.463623\pi$
$278$	−0.0762156	−	22.9835i	−0.00457111	−	1.37846i
$279$	4.03047	−	3.38197i	0.241298	−	0.202473i
$280$	19.7142	+	4.06121i	1.17815	+	0.242704i
$281$	0.694607	−	1.90842i	0.0414368	−	0.113847i	−0.917249	−	0.398315i	$-0.869595\pi$
$281$	0.694607	−	1.90842i	0.0414368	−	0.113847i	0.958685	+	0.284469i	$0.0918172\pi$
$282$	−9.27403	−	25.2197i	−0.552260	−	1.50181i
$283$	−0.898453	+	5.09538i	−0.0534075	+	0.302889i	−0.999797	−	0.0201382i	$-0.993589\pi$
$283$	−0.898453	+	5.09538i	−0.0534075	+	0.302889i	0.946390	+	0.323027i	$0.104701\pi$
$284$	1.50624	+	2.56938i	0.0893790	+	0.152465i
$285$	−11.2910	−	24.0849i	−0.668821	−	1.42667i
$286$	6.21489	+	3.56074i	0.367494	+	0.210551i
$287$	−19.7863	−	3.48885i	−1.16795	−	0.205940i
$288$	3.95793	−	24.8490i	0.233224	−	1.46424i
$289$	16.3757	+	5.96029i	0.963279	+	0.350605i
$290$	6.78861	+	6.11685i	0.398641	+	0.359194i
$291$	−25.8914	−	30.8561i	−1.51778	−	1.80882i
$292$	24.5727	+	13.9706i	1.43801	+	0.817567i
$293$	13.3016	−	23.0390i	0.777085	−	1.34595i	−0.156530	−	0.987673i	$-0.550031\pi$
$293$	13.3016	−	23.0390i	0.777085	−	1.34595i	0.933615	−	0.358278i	$-0.116636\pi$
$294$	−4.09225	+	11.3604i	−0.238665	+	0.662554i
$295$	2.70468	−	6.62420i	0.157473	−	0.385676i
$296$	−8.68778	+	15.3995i	−0.504967	+	0.895076i
$297$	2.00052	+	3.46500i	0.116082	+	0.201060i
$298$	1.85488	+	10.3193i	0.107450	+	0.597781i
$299$	−28.3904	+	10.3333i	−1.64186	+	0.597589i
$300$	−16.0257	−	22.0904i	−0.925244	−	1.27539i
$301$	−11.6382	−	9.76563i	−0.670816	−	0.562881i
$302$	−1.84919	−	1.54124i	−0.106409	−	0.0886882i
$303$			12.9793i			0.745642i
$304$	2.45292	+	17.2622i	0.140685	+	0.990054i
$305$	17.8504	+	11.2455i	1.02211	+	0.643916i
$306$	−23.6310	+	28.3528i	−1.35090	+	1.62082i
$307$	−7.12390	+	8.48994i	−0.406583	+	0.484546i	−0.930015	−	0.367521i	$-0.880207\pi$
$307$	−7.12390	+	8.48994i	−0.406583	+	0.484546i	0.523433	+	0.852067i	$0.324651\pi$
$308$	6.33855	−	1.16105i	0.361172	−	0.0661572i
$309$	39.3514	−	14.3227i	2.23862	−	0.814791i
$310$	−1.40244	+	3.46762i	−0.0796532	+	0.196947i
$311$	−1.45863	+	0.842142i	−0.0827115	+	0.0477535i	−0.540785	−	0.841161i	$-0.681873\pi$
$311$	−1.45863	+	0.842142i	−0.0827115	+	0.0477535i	0.458074	+	0.888914i	$0.348540\pi$
$312$	−33.6335	−	18.9747i	−1.90412	−	1.07423i
$313$	30.1296	−	5.31267i	1.70303	−	0.300290i	0.764278	−	0.644887i	$-0.223096\pi$
$313$	30.1296	−	5.31267i	1.70303	−	0.300290i	0.938751	+	0.344597i	$0.111985\pi$
$314$	−4.13158	+	11.4696i	−0.233159	+	0.647269i
$315$	28.0036	−	14.7582i	1.57782	−	0.831528i
$316$	−5.55076	+	9.76316i	−0.312254	+	0.549221i
$317$	14.9318	−	12.5293i	0.838652	−	0.703713i	−0.118608	−	0.992941i	$-0.537843\pi$
$317$	14.9318	−	12.5293i	0.838652	−	0.703713i	0.957260	+	0.289228i	$0.0933987\pi$
$318$	31.9295	+	5.52093i	1.79052	+	0.309598i
$319$	2.74905	+	1.00057i	0.153917	+	0.0560214i
$320$	5.80317	+	16.9211i	0.324407	+	0.945918i
$321$	−8.92474	+	50.6147i	−0.498131	+	2.82504i
$322$	−13.5124	+	23.5845i	−0.753019	+	1.31431i
$323$	9.85844	−	23.5991i	0.548538	−	1.31309i
$324$	2.58803	+	4.41473i	0.143780	+	0.245263i
$325$	−24.0947	+	6.71800i	−1.33653	+	0.372648i
$326$	−13.0703	+	4.80633i	−0.723895	+	0.266198i
$327$	−19.3229	−	7.03296i	−1.06856	−	0.388923i
$328$	−6.27371	−	16.7175i	−0.346408	−	0.923070i
$329$	−16.9735	+	14.2424i	−0.935779	+	0.785212i
$330$	−7.40795	−	4.63266i	−0.407794	−	0.255019i
$331$	16.1667	−	28.0016i	0.888605	−	1.53911i	0.0470793	−	0.998891i	$-0.485009\pi$
$331$	16.1667	−	28.0016i	0.888605	−	1.53911i	0.841525	−	0.540217i	$-0.181658\pi$
$332$	13.3431	−	11.3478i	0.732296	−	0.622792i
$333$	4.82846	+	27.3836i	0.264598	+	1.50061i
$334$	17.1413	−	9.97245i	0.937928	−	0.545668i
$335$	−13.5688	−	0.523709i	−0.741342	−	0.0286133i
$336$	−34.1314	+	6.48621i	−1.86202	+	0.353852i
$337$	−18.7486	+	6.82393i	−1.02130	+	0.371723i	−0.797762	−	0.602972i	$-0.793983\pi$
$337$	−18.7486	+	6.82393i	−1.02130	+	0.371723i	−0.223538	+	0.974695i	$0.571761\pi$
$338$	−12.9936	+	10.9765i	−0.706758	+	0.597045i
$339$	9.38159	−	11.1805i	0.509538	−	0.607244i
$340$	5.37956	−	25.6826i	0.291748	−	1.39283i
$341$			1.19751i			0.0648487i
$342$	20.2217	+	18.5185i	1.09347	+	1.00136i
$343$	−12.3209			−0.665267
$344$	2.21223	−	13.3197i	0.119275	−	0.718149i
$345$	35.0919	−	11.2598i	1.88929	−	0.606208i
$346$	−5.36834	+	4.53500i	−0.288604	+	0.243803i
$347$	−28.3000	+	10.3004i	−1.51923	+	0.552953i	−0.960955	−	0.276706i	$-0.910757\pi$
$347$	−28.3000	+	10.3004i	−1.51923	+	0.552953i	−0.558271	+	0.829659i	$0.688535\pi$
$348$	−14.8567	−	5.29608i	−0.796403	−	0.283900i
$349$	9.33083	+	16.1615i	0.499468	+	0.865103i	1.00000		0.000614500i	$-0.000195602\pi$
$349$	9.33083	+	16.1615i	0.499468	+	0.865103i	−0.500532	+	0.865718i	$0.666862\pi$
$350$	−12.6591	+	18.6059i	−0.676656	+	0.994525i
$351$	−19.4707	+	3.43321i	−1.03927	+	0.183251i
$352$	3.75347	+	4.32549i	0.200060	+	0.230549i
$353$	12.6924	+	7.32797i	0.675549	+	0.390029i	0.798176	−	0.602424i	$-0.205798\pi$
$353$	12.6924	+	7.32797i	0.675549	+	0.390029i	−0.122627	+	0.992453i	$0.539132\pi$
$354$	0.0409538	+	12.3500i	0.00217667	+	0.656393i
$355$	−3.29916	+	0.451322i	−0.175101	+	0.0239537i
$356$	6.49145	−	7.84125i	0.344046	−	0.415585i
$357$	47.8885	+	17.4300i	2.53453	+	0.922492i
$358$	−15.3476	+	5.64378i	−0.811146	+	0.298283i
$359$	11.5786	+	2.04163i	0.611097	+	0.107753i	0.470627	−	0.882332i	$-0.344028\pi$
$359$	11.5786	+	2.04163i	0.611097	+	0.107753i	0.140470	+	0.990085i	$0.455139\pi$
$360$	23.9506	+	14.7578i	1.26231	+	0.777803i
$361$	−17.1712	−	8.13330i	−0.903746	−	0.428069i
$362$	−18.0675	−	10.3515i	−0.949607	−	0.544065i
$363$	26.8095	+	4.72725i	1.40714	+	0.248116i
$364$	−5.32136	+	31.3951i	−0.278915	+	1.64555i
$365$	−24.9747	+	19.3651i	−1.30723	+	1.01362i
$366$	−35.8826	−	6.20446i	−1.87561	−	0.324312i
$367$	21.6629	−	18.1774i	1.13080	−	0.948851i	0.131698	−	0.991290i	$-0.457957\pi$
$367$	21.6629	−	18.1774i	1.13080	−	0.948851i	0.999099	+	0.0424388i	$0.0135128\pi$
$368$	−24.1546	+	0.320415i	−1.25915	+	0.0167028i
$369$	−24.3188	−	14.0405i	−1.26599	−	0.730919i
$370$	−12.1649	−	15.5818i	−0.632423	−	0.810057i
$371$	−4.63978	−	26.3135i	−0.240885	−	1.36613i
$372$	−0.0428188	−	6.45611i	−0.00222005	−	0.334734i
$373$	−0.535283	−	0.927138i	−0.0277159	−	0.0480054i	0.851835	−	0.523811i	$-0.175490\pi$
$373$	−0.535283	−	0.927138i	−0.0277159	−	0.0480054i	−0.879551	+	0.475805i	$0.842157\pi$
$374$	−1.48619	−	8.26816i	−0.0768489	−	0.427537i
$375$	29.6856	−	7.05516i	1.53296	−	0.364327i
$376$	−18.5704	−	6.55061i	−0.957696	−	0.337822i
$377$	−9.29227	+	11.0741i	−0.478576	+	0.570345i
$378$	−11.3882	+	13.6637i	−0.585748	+	0.702787i
$379$	−34.8984			−1.79261			−0.896305	−	0.443438i	$-0.853759\pi$
$379$	−34.8984			−1.79261			−0.896305	+	0.443438i	$0.853759\pi$
$380$	−18.8724	−	4.88175i	−0.968135	−	0.250428i
$381$	−21.8740			−1.12064
$382$	14.8184	−	17.7793i	0.758176	−	0.909668i
$383$	15.6669	−	18.6711i	0.800543	−	0.954050i	−0.199121	−	0.979975i	$-0.563809\pi$
$383$	15.6669	−	18.6711i	0.800543	−	0.954050i	0.999664	+	0.0259253i	$0.00825321\pi$
$384$	−20.3907	−	23.1857i	−1.04056	−	1.18319i
$385$	−1.52378	+	7.04163i	−0.0776592	+	0.358875i
$386$	1.68066	+	9.35005i	0.0855431	+	0.475905i
$387$	−10.6170	−	18.3892i	−0.539693	−	0.934776i
$388$	−29.5179	+	0.195771i	−1.49854	+	0.00993877i
$389$	−4.84237	−	27.4624i	−0.245518	−	1.39240i	−0.819287	−	0.573383i	$-0.805631\pi$
$389$	−4.84237	−	27.4624i	−0.245518	−	1.39240i	0.573770	−	0.819017i	$-0.305480\pi$
$390$	34.0317	−	26.5690i	1.72326	−	1.34537i
$391$	30.6872	+	17.7172i	1.55192	+	0.895999i
$392$	4.50053	+	7.61908i	0.227311	+	0.384822i
$393$	−21.5284	+	18.0644i	−1.08596	+	0.911231i
$394$	−24.6827	−	4.26787i	−1.24349	−	0.215012i
$395$	−7.69411	−	9.92288i	−0.387133	−	0.499274i
$396$	8.87984	+	1.50510i	0.446229	+	0.0756342i
$397$	−25.3341	−	4.46708i	−1.27148	−	0.224196i	−0.503122	−	0.864216i	$-0.667815\pi$
$397$	−25.3341	−	4.46708i	−1.27148	−	0.224196i	−0.768359	+	0.640019i	$0.778926\pi$
$398$	15.1379	+	8.67309i	0.758796	+	0.434743i
$399$	14.5934	−	34.9338i	0.730586	−	1.74888i
$400$	−19.9592	−	1.27694i	−0.997960	−	0.0638470i
$401$	14.0961	+	2.48552i	0.703924	+	0.124121i	0.514142	−	0.857705i	$-0.328111\pi$
$401$	14.0961	+	2.48552i	0.703924	+	0.124121i	0.189782	+	0.981826i	$0.439222\pi$
$402$	21.9976	−	8.08919i	1.09714	−	0.403452i
$403$	−5.56060	−	2.02389i	−0.276993	−	0.100817i
$404$	7.32678	+	6.06555i	0.364521	+	0.301773i
$405$	−5.66863	+	0.775465i	−0.281676	+	0.0385332i
$406$	0.0431283	+	13.0057i	0.00214042	+	0.645462i
$407$	−5.48082	−	3.16436i	−0.271674	−	0.156851i
$408$	8.30810	+	44.5229i	0.411312	+	2.20421i
$409$	−19.5699	+	3.45070i	−0.967670	+	0.170626i	−0.635081	−	0.772446i	$-0.719033\pi$
$409$	−19.5699	+	3.45070i	−0.967670	+	0.170626i	−0.332589	+	0.943072i	$0.607922\pi$
$410$	19.9511	+	0.703796i	0.985316	+	0.0347580i
$411$	−8.21816	−	14.2343i	−0.405372	−	0.702125i
$412$	10.3047	−	28.9071i	0.507678	−	1.42415i
$413$	9.56953	−	3.48303i	0.470886	−	0.171388i
$414$	−29.0208	+	24.5158i	−1.42629	+	1.20489i
$415$	5.98322	+	18.6471i	0.293705	+	0.915349i
$416$	−26.4290	+	10.1187i	−1.29579	+	0.496109i
$417$	−44.3533			−2.17199
$418$	−6.18720	+	0.816480i	−0.302626	+	0.0399353i
$419$			12.1981i			0.595914i	0.954579	+	0.297957i	$0.0963053\pi$
$419$			12.1981i			0.595914i	−0.954579	+	0.297957i	$0.903695\pi$
$420$	7.96336	−	38.0179i	0.388572	−	1.85508i
$421$	−9.20196	+	10.9665i	−0.448476	+	0.534473i	−0.942158	−	0.335170i	$-0.891206\pi$
$421$	−9.20196	+	10.9665i	−0.448476	+	0.534473i	0.493682	+	0.869643i	$0.335651\pi$
$422$	−7.20615	+	6.08751i	−0.350790	+	0.296336i
$423$	−29.1007	+	10.5918i	−1.41492	+	0.514990i
$424$	18.0380	−	15.4441i	0.876004	−	0.750030i
$425$	24.2005	+	16.5832i	1.17390	+	0.804405i
$426$	4.96795	−	2.89026i	0.240698	−	0.140033i
$427$	5.21421	+	29.5712i	0.252333	+	1.43105i
$428$	24.4011	+	28.6915i	1.17947	+	1.38686i
$429$	6.91118	−	11.9705i	0.333675	−	0.577942i
$430$	12.7992	+	8.00413i	0.617231	+	0.385993i
$431$	−2.80631	+	2.35477i	−0.135175	+	0.113425i	−0.707868	−	0.706344i	$-0.750343\pi$
$431$	−2.80631	+	2.35477i	−0.135175	+	0.113425i	0.572693	+	0.819770i	$0.305899\pi$
$432$	−15.6031	−	2.53833i	−0.750702	−	0.122125i
$433$	−1.22220	−	0.444844i	−0.0587351	−	0.0213778i	0.312486	−	0.949923i	$-0.398838\pi$
$433$	−1.22220	−	0.444844i	−0.0587351	−	0.0213778i	−0.371221	+	0.928545i	$0.621061\pi$
$434$	−4.99662	+	1.83741i	−0.239845	+	0.0881984i
$435$	11.8476	−	13.0613i	0.568047	−	0.626242i
$436$	−13.0002	+	7.62104i	−0.622594	+	0.364982i
$437$	14.2108	−	22.1589i	0.679793	−	1.06000i
$438$	27.1173	−	47.3302i	1.29571	−	2.26153i
$439$	1.03416	−	5.86503i	0.0493579	−	0.279922i	−0.950132	−	0.311847i	$-0.899052\pi$
$439$	1.03416	−	5.86503i	0.0493579	−	0.279922i	0.999490	+	0.0319243i	$0.0101636\pi$
$440$	−6.07704	+	2.01681i	−0.289712	+	0.0961478i
$441$	13.0771	+	4.75967i	0.622718	+	0.226651i
$442$	40.9048	+	7.07283i	1.94564	+	0.336420i
$443$	−18.5732	+	15.5848i	−0.882440	+	0.740455i	−0.966679	−	0.255990i	$-0.917599\pi$
$443$	−18.5732	+	15.5848i	−0.882440	+	0.740455i	0.0842389	+	0.996446i	$0.473154\pi$
$444$	29.6618	+	16.8640i	1.40769	+	0.800328i
$445$	5.30619	+	10.0685i	0.251538	+	0.477292i
$446$	−2.48838	+	6.90795i	−0.117828	+	0.327101i
$447$	19.9257	−	3.51345i	0.942455	−	0.166180i
$448$	−12.2890	+	22.2982i	−0.580600	+	1.05349i
$449$	13.8669	−	8.00608i	0.654421	−	0.377830i	−0.135727	−	0.990746i	$-0.543337\pi$
$449$	13.8669	−	8.00608i	0.654421	−	0.377830i	0.790148	+	0.612916i	$0.210004\pi$
$450$	−25.5201	+	18.3849i	−1.20303	+	0.866674i
$451$	6.00585	−	2.18595i	0.282805	−	0.102932i
$452$	−1.92714	−	10.5208i	−0.0906449	−	0.494858i
$453$	−2.98606	+	3.55865i	−0.140298	+	0.167200i
$454$	−4.67947	+	5.61449i	−0.219619	+	0.263501i
$455$	−30.1223	−	18.9766i	−1.41215	−	0.889637i
$456$	33.3277	−	4.62310i	1.56071	−	0.216497i
$457$			34.6973i			1.62307i	0.584303	+	0.811535i	$0.301368\pi$
$457$			34.6973i			1.62307i	−0.584303	+	0.811535i	$0.698632\pi$
$458$	−15.4532	−	12.8797i	−0.722079	−	0.601827i
$459$	17.7633	+	14.9052i	0.829119	+	0.695714i
$460$	10.0432	−	25.0713i	0.468266	−	1.16895i
$461$	29.0943	−	10.5895i	1.35506	−	0.493201i	0.440536	−	0.897735i	$-0.354789\pi$
$461$	29.0943	−	10.5895i	1.35506	−	0.493201i	0.914523	+	0.404534i	$0.132566\pi$
$462$	−2.20000	−	12.2394i	−0.102353	−	0.569427i
$463$	−13.6653	−	23.6690i	−0.635079	−	1.09999i	−0.986498	−	0.163771i	$-0.947634\pi$
$463$	−13.6653	−	23.6690i	−0.635079	−	1.09999i	0.351419	−	0.936218i	$-0.385699\pi$
$464$	−9.93252	+	5.91158i	−0.461106	+	0.274438i
$465$	6.68273	+	2.72857i	0.309904	+	0.126535i
$466$	−2.18803	+	6.07416i	−0.101359	+	0.281380i
$467$	12.3956	−	21.4697i	0.573598	−	0.993502i	−0.422594	−	0.906319i	$-0.638880\pi$
$467$	12.3956	−	21.4697i	0.573598	−	0.993502i	0.996192	−	0.0871824i	$-0.0277863\pi$
$468$	−21.9966	+	38.6895i	−1.01679	+	1.78842i
$469$	−12.4229	−	14.8050i	−0.573634	−	0.683630i
$470$	14.7375	−	16.3560i	0.679791	−	0.754446i
$471$	22.1073	+	8.04640i	1.01865	+	0.370759i
$472$	6.99066	+	5.74833i	0.321771	+	0.264588i
$473$	4.75949	+	0.839227i	0.218842	+	0.0385877i
$474$	18.8051	+	10.7742i	0.863748	+	0.494873i
$475$	13.1445	−	17.3845i	0.603113	−	0.797656i
$476$	32.2187	−	18.8875i	1.47674	−	0.865705i
$477$	6.48480	−	36.7772i	0.296919	−	1.68391i
$478$	−3.28924	−	8.94472i	−0.150446	−	0.409122i
$479$	4.49014	−	12.3366i	0.205160	−	0.563671i	−0.793852	−	0.608110i	$-0.791928\pi$
$479$	4.49014	−	12.3366i	0.205160	−	0.563671i	0.999012	+	0.0444390i	$0.0141500\pi$
$480$	32.6909	−	11.0905i	1.49213	−	0.506210i
$481$	23.9567	−	20.1020i	1.09233	−	0.916573i
$482$	−0.0322058	−	9.71193i	−0.00146693	−	0.442366i
$483$	45.4262	+	26.2268i	2.06696	+	1.19336i
$484$	15.1973	−	12.9248i	0.690785	−	0.587489i
$485$	12.4753	−	30.5540i	0.566473	−	1.38739i
$486$	23.0288	−	13.3977i	1.04461	−	0.607733i
$487$	17.4027	−	10.0475i	0.788594	−	0.455295i	−0.0508736	−	0.998705i	$-0.516201\pi$
$487$	17.4027	−	10.0475i	0.788594	−	0.455295i	0.839467	+	0.543410i	$0.182867\pi$
$488$	−20.2712	+	17.3561i	−0.917636	+	0.785676i
$489$	9.19146	+	25.2533i	0.415652	+	1.14200i
$490$	−9.79771	+	1.37343i	−0.442615	+	0.0620454i
$491$	−11.7701	+	14.0271i	−0.531177	+	0.633032i	−0.963186	−	0.268837i	$-0.913361\pi$
$491$	−11.7701	+	14.0271i	−0.531177	+	0.633032i	0.432009	+	0.901870i	$0.357805\pi$
$492$	−32.3011	+	11.9998i	−1.45625	+	0.540994i
$493$	16.9548			0.763608
$494$	6.66559	−	30.1100i	0.299899	−	1.35471i
$495$	−5.36737	+	8.51983i	−0.241245	+	0.382938i
$496$	−3.66446	−	2.99293i	−0.164539	−	0.134386i
$497$	−3.63055	−	3.04639i	−0.162852	−	0.136649i
$498$	−21.8133	−	25.8217i	−0.977476	−	1.15710i
$499$	−1.02077	−	2.80453i	−0.0456958	−	0.125548i	0.914746	−	0.404030i	$-0.132391\pi$
$499$	−1.02077	−	2.80453i	−0.0456958	−	0.125548i	−0.960441	+	0.278482i	$0.910169\pi$
$500$	9.89022	−	20.0545i	0.442304	−	0.896865i
$501$	−19.1348	−	33.1425i	−0.854881	−	1.48070i
$502$	24.3732	−	14.1799i	1.08783	−	0.632879i
$503$	1.40030	+	7.94152i	0.0624365	+	0.354095i	0.999981	+	0.00622852i	$0.00198261\pi$
$503$	1.40030	+	7.94152i	0.0624365	+	0.354095i	−0.937544	+	0.347866i	$0.886906\pi$
$504$	7.34481	+	39.3606i	0.327164	+	1.75326i
$505$	−9.40790	+	4.95806i	−0.418646	+	0.220631i
$506$	−0.0286728	−	8.64654i	−0.00127466	−	0.384385i
$507$	21.0990	+	25.1449i	0.937042	+	1.11672i
$508$	−10.2223	+	12.3478i	−0.453540	+	0.547846i
$509$	−0.0677817	+	0.186229i	−0.00300437	+	0.00825444i	−0.941186	−	0.337890i	$-0.890287\pi$
$509$	−0.0677817	+	0.186229i	−0.00300437	+	0.00825444i	0.938181	+	0.346144i	$0.112509\pi$
$510$	−49.5270	−	10.5457i	−2.19309	−	0.466970i
$511$	−44.2964	−	7.81065i	−1.95956	−	0.345523i
$512$	−22.6173	+	0.675212i	−0.999555	+	0.0298404i
$513$	11.6763	−	12.6656i	0.515521	−	0.559202i
$514$	10.9836	−	19.1706i	0.484464	−	0.845579i
$515$	25.4138	+	23.0521i	1.11986	+	1.01580i
$516$	−25.6898	−	4.35433i	−1.13093	−	0.191688i
$517$	2.41071	−	6.62338i	0.106023	−	0.291296i
$518$	4.79376	−	27.7241i	0.210626	−	1.21812i
$519$	8.71714	+	10.3887i	0.382640	+	0.456013i
$520$	0.905706	−	31.6271i	0.0397178	−	1.38694i
$521$	3.04886	+	1.76026i	0.133573	+	0.0771184i	0.565297	−	0.824887i	$-0.308761\pi$
$521$	3.04886	+	1.76026i	0.133573	+	0.0771184i	−0.431725	+	0.902006i	$0.642095\pi$
$522$	−6.16042	+	17.1018i	−0.269634	+	0.748528i
$523$	−22.4405	+	3.95686i	−0.981254	+	0.173022i	−0.641191	−	0.767381i	$-0.721559\pi$
$523$	−22.4405	+	3.95686i	−0.981254	+	0.173022i	−0.340063	+	0.940403i	$0.610448\pi$
$524$	0.136590	+	20.5947i	0.00596695	+	0.899682i
$525$	35.8240	+	24.5482i	1.56349	+	1.07137i
$526$	−1.09337	−	6.08279i	−0.0476733	−	0.265222i
$527$	2.37371	+	6.52170i	0.103400	+	0.284090i
$528$	8.37122	−	7.21565i	0.364310	−	0.314021i
$529$	10.3200	+	8.65947i	0.448694	+	0.376499i
$530$	8.19521	+	25.2527i	0.355977	+	1.09691i
$531$	14.2333			0.617672
$532$	−12.9001	−	24.5634i	−0.559292	−	1.06496i
$533$			31.5824i			1.36799i
$534$	−15.0903	−	12.5772i	−0.653019	−	0.544268i
$535$	−40.0967	+	12.8657i	−1.73353	+	0.556232i
$536$	5.71371	−	16.1979i	0.246795	−	0.699642i
$537$	10.7930	+	29.6534i	0.465751	+	1.27964i
$538$	28.0442	−	5.04089i	1.20907	−	0.217328i
$539$	−2.74304	+	1.58369i	−0.118151	+	0.0682145i
$540$	9.32141	−	15.0161i	0.401129	−	0.646192i
$541$	6.52643	+	37.0132i	0.280593	+	1.59132i	0.720614	+	0.693336i	$0.243860\pi$
$541$	6.52643	+	37.0132i	0.280593	+	1.59132i	−0.440021	+	0.897987i	$0.645029\pi$
$542$	−7.53126	+	20.9074i	−0.323495	+	0.898051i
$543$	−20.0917	+	34.7999i	−0.862218	+	1.49341i
$544$	29.0156	+	16.1167i	1.24403	+	0.690999i
$545$	−2.28353	−	16.6925i	−0.0978156	−	0.715030i
$546$	60.5513	+	10.4699i	2.59136	+	0.448071i
$547$	0.645066	−	1.77230i	0.0275810	−	0.0757783i	−0.925138	−	0.379631i	$-0.876051\pi$
$547$	0.645066	−	1.77230i	0.0275810	−	0.0757783i	0.952719	+	0.303853i	$0.0982731\pi$
$548$	−11.8758	−	2.01290i	−0.507307	−	0.0859868i
$549$	−7.28766	+	41.3304i	−0.311030	+	1.76394i
$550$	0.528112	−	7.13923i	0.0225188	−	0.304418i
$551$	0.587307	−	12.5820i	0.0250201	−	0.536012i
$552$	0.463753	+	46.6149i	0.0197387	+	1.98406i
$553$	3.10331	−	17.5997i	0.131966	−	0.748416i
$554$	−9.67499	−	26.3100i	−0.411051	−	1.11781i
$555$	−30.1471	+	23.3758i	−1.27967	+	0.992245i
$556$	−20.7274	+	25.0373i	−0.879037	+	1.06182i
$557$	−6.84446	−	8.15691i	−0.290009	−	0.345620i	0.601293	−	0.799028i	$-0.294652\pi$
$557$	−6.84446	−	8.15691i	−0.290009	−	0.345620i	−0.891303	+	0.453409i	$0.850208\pi$
$558$	−7.44072	+	0.0246742i	−0.314991	+	0.00104454i
$559$	−11.9409	+	20.6822i	−0.505045	+	0.874764i
$560$	−17.7395	−	22.2620i	−0.749632	−	0.940742i
$561$	−15.9652	+	2.81509i	−0.674049	+	0.118853i
$562$	−2.48255	+	1.44430i	−0.104720	+	0.0609241i
$563$	4.42841	−	2.55674i	0.186635	−	0.107754i	−0.403771	−	0.914860i	$-0.632301\pi$
$563$	4.42841	−	2.55674i	0.186635	−	0.107754i	0.590406	+	0.807106i	$0.298968\pi$
$564$	−12.7600	+	35.7947i	−0.537293	+	1.50723i
$565$	11.6878	+	2.52920i	0.491711	+	0.106404i
$566$	5.58961	−	4.72192i	0.234949	−	0.198477i
$567$	−6.23804	−	5.23433i	−0.261973	−	0.219821i
$568$	0.690106	−	4.15509i	0.0289562	−	0.174344i
$569$		−	30.2550i		−	1.26836i	−0.773187	−	0.634178i	$-0.781339\pi$
$569$		−	30.2550i		−	1.26836i	0.773187	−	0.634178i	$-0.218661\pi$
$570$	−9.54141	+	36.3882i	−0.399646	+	1.52413i
$571$			17.3053i			0.724204i	0.932138	+	0.362102i	$0.117941\pi$
$571$			17.3053i			0.724204i	−0.932138	+	0.362102i	$0.882059\pi$
$572$	−3.52756	−	9.49546i	−0.147495	−	0.397025i
$573$	−34.2151	−	28.7099i	−1.42936	−	1.19937i
$574$	18.3360	+	21.7055i	0.765331	+	0.905968i
$575$	21.5665	+	21.1348i	0.899387	+	0.881380i
$576$	−26.7991	+	23.4113i	−1.11663	+	0.975470i
$577$	−16.4813	+	9.51548i	−0.686125	+	0.396135i	−0.802159	−	0.597111i	$-0.796315\pi$
$577$	−16.4813	+	9.51548i	−0.686125	+	0.396135i	0.116034	+	0.993245i	$0.462982\pi$
$578$	−12.3933	−	21.3023i	−0.515491	−	0.886059i
$579$	18.0542	−	3.18344i	0.750307	−	0.132299i
$580$	−1.83641	−	12.7918i	−0.0762529	−	0.531150i
$581$	−13.9364	+	24.1385i	−0.578178	+	1.00143i
$582$	0.188899	+	56.9639i	0.00783010	+	2.36123i
$583$	5.46350	+	6.51114i	0.226275	+	0.269664i
$584$	−14.0452	−	37.4262i	−0.581196	−	1.54871i
$585$	−30.4903	−	39.3225i	−1.26062	−	1.62578i
$586$	−35.3107	+	12.9848i	−1.45867	+	0.536398i
$587$	1.03703	−	5.88130i	0.0428029	−	0.242747i	−0.955898	−	0.293698i	$-0.905114\pi$
$587$	1.03703	−	5.88130i	0.0428029	−	0.242747i	0.998701	+	0.0509507i	$0.0162251\pi$
$588$	14.7319	−	8.63622i	0.607532	−	0.356152i
$589$	4.92191	−	1.53559i	0.202804	−	0.0632731i
$590$	−8.93608	+	4.74733i	−0.367893	+	0.195445i
$591$	−8.39396	+	47.6045i	−0.345281	+	1.95819i
$592$	23.3814	−	8.86307i	0.960968	−	0.364270i
$593$	2.27169	−	6.24141i	0.0932870	−	0.256304i	−0.884270	−	0.466977i	$-0.845343\pi$
$593$	2.27169	−	6.24141i	0.0932870	−	0.256304i	0.977557	+	0.210673i	$0.0675654\pi$
$594$	0.964074	−	5.57559i	0.0395564	−	0.228769i
$595$	5.65934	+	41.3696i	0.232010	+	1.69599i
$596$	7.32846	−	12.8899i	0.300185	−	0.527993i
$597$	16.8339	−	29.1572i	0.688967	−	1.19333i
$598$	40.1984	+	14.4802i	1.64383	+	0.592141i
$599$	−5.78001	−	32.7801i	−0.236165	−	1.33936i	−0.840146	−	0.542360i	$-0.817531\pi$
$599$	−5.78001	−	32.7801i	−0.236165	−	1.33936i	0.603981	−	0.796998i	$-0.293580\pi$
$600$	−2.59193	+	38.5085i	−0.105815	+	1.57210i
$601$	17.6568	−	10.1942i	0.720236	−	0.415828i	−0.0946036	−	0.995515i	$-0.530158\pi$
$601$	17.6568	−	10.1942i	0.720236	−	0.415828i	0.814840	+	0.579687i	$0.196825\pi$
$602$	3.80108	+	21.1467i	0.154921	+	0.861875i
$603$	−9.23858	−	25.3828i	−0.376224	−	1.03367i
$604$	0.613388	+	3.34867i	0.0249584	+	0.136255i
$605$	6.81467	+	21.2384i	0.277056	+	0.863463i
$606$	11.7520	−	14.1002i	0.477393	−	0.572781i
$607$			11.2024i			0.454692i	0.973814	+	0.227346i	$0.0730048\pi$
$607$			11.2024i			0.454692i	−0.973814	+	0.227346i	$0.926995\pi$
$608$	12.9651	−	20.9739i	0.525806	−	0.850604i
$609$	25.0983			1.01703
$610$	−9.20982	−	28.3792i	−0.372895	−	1.14904i
$611$	26.6811	+	22.3881i	1.07940	+	0.905727i
$612$	51.3436	−	9.40478i	2.07544	−	0.380166i
$613$	−9.57534	−	26.3080i	−0.386744	−	1.06257i	−0.968458	−	0.249178i	$-0.919840\pi$
$613$	−9.57534	−	26.3080i	−0.386744	−	1.06257i	0.581713	−	0.813394i	$-0.302382\pi$
$614$	15.4263	−	2.77284i	0.622553	−	0.111903i
$615$	1.48584	−	38.4966i	0.0599147	−	1.55233i
$616$	−7.93720	−	4.47786i	−0.319799	−	0.180418i
$617$	7.96463	−	1.40438i	0.320644	−	0.0565382i	−0.0110097	−	0.999939i	$-0.503505\pi$
$617$	7.96463	−	1.40438i	0.320644	−	0.0565382i	0.331654	+	0.943401i	$0.392393\pi$
$618$	−55.7181	−	20.0707i	−2.24131	−	0.807363i
$619$	−30.5329	−	17.6282i	−1.22722	−	0.708537i	−0.260774	−	0.965400i	$-0.583978\pi$
$619$	−30.5329	−	17.6282i	−1.22722	−	0.708537i	−0.966448	+	0.256863i	$0.917311\pi$
$620$	4.66328	−	2.49725i	0.187282	−	0.100292i
$621$	15.3415	+	18.2833i	0.615633	+	0.733683i
$622$	2.34711	+	0.405838i	0.0941105	+	0.0162726i
$623$	−5.54022	+	15.2216i	−0.221964	+	0.609841i
$624$	19.3576	+	51.0666i	0.774923	+	2.04430i
$625$	16.4537	+	18.8222i	0.658147	+	0.752889i
$626$	−37.5419	−	21.5092i	−1.50048	−	0.859679i
$627$	1.53602	+	11.9451i	0.0613429	+	0.477041i
$628$	14.8735	−	8.71923i	0.593516	−	0.347935i
$629$	−36.1213	−	6.36916i	−1.44025	−	0.253955i
$630$	−43.7846	−	9.32293i	−1.74442	−	0.371434i
$631$	5.27370	−	14.4894i	0.209943	−	0.576813i	−0.789368	−	0.613920i	$-0.789592\pi$
$631$	5.27370	−	14.4894i	0.209943	−	0.576813i	0.999311	+	0.0371065i	$0.0118141\pi$
$632$	14.8701	−	5.58041i	0.591500	−	0.221977i
$633$	11.7014	+	13.9452i	0.465088	+	0.554271i
$634$	−27.5658	+	0.0914111i	−1.09478	+	0.00363040i
$635$	−8.35581	−	15.8551i	−0.331590	−	0.629192i
$636$	−29.6881	−	34.9080i	−1.17721	−	1.38419i
$637$	−2.71787	−	15.4138i	−0.107686	−	0.610717i
$638$	−2.08050	−	3.57609i	−0.0823677	−	0.141579i
$639$	−3.31199	−	5.73653i	−0.131020	−	0.226934i
$640$	9.01673	−	23.6368i	0.356417	−	0.934327i
$641$	−11.9777	−	32.9083i	−0.473089	−	1.29980i	−0.915258	−	0.402869i	$-0.868013\pi$
$641$	−11.9777	−	32.9083i	−0.473089	−	1.29980i	0.442169	−	0.896932i	$-0.354209\pi$
$642$	55.5242	−	46.9049i	2.19136	−	1.85119i
$643$	7.57663	+	6.35754i	0.298793	+	0.250717i	0.779842	−	0.625977i	$-0.215300\pi$
$643$	7.57663	+	6.35754i	0.298793	+	0.250717i	−0.481049	+	0.876694i	$0.659744\pi$
$644$	36.0338	−	13.3865i	1.41993	−	0.527503i
$645$	15.5280	−	24.6482i	0.611416	−	0.970524i
$646$	−32.0774	+	16.7109i	−1.26207	+	0.657481i
$647$	−19.5672			−0.769267			−0.384634	−	0.923069i	$-0.625672\pi$
$647$	−19.5672			−0.769267			−0.384634	+	0.923069i	$0.625672\pi$
$648$	1.18574	−	7.13929i	0.0465804	−	0.280458i
$649$	−2.08233	+	2.48162i	−0.0817385	+	0.0974121i
$650$	32.2582	+	14.5182i	1.26527	+	0.569450i
$651$	3.51380	+	9.65408i	0.137717	+	0.378373i
$652$	18.5508	+	6.61296i	0.726507	+	0.258983i
$653$	−10.6278	+	6.13596i	−0.415898	+	0.240119i	−0.693321	−	0.720629i	$-0.743853\pi$
$653$	−10.6278	+	6.13596i	−0.415898	+	0.240119i	0.277423	+	0.960748i	$0.410520\pi$
$654$	14.6237	+	25.1361i	0.571831	+	0.982898i
$655$	−21.3176	−	8.70402i	−0.832946	−	0.340094i
$656$	−8.32123	+	23.8417i	−0.324889	+	0.930862i
$657$	−54.4437	−	31.4331i	−2.12405	−	1.22632i
$658$	31.3350	−	0.103910i	1.22157	−	0.00405084i
$659$	−4.11927	+	3.45648i	−0.160464	+	0.134645i	−0.719484	−	0.694509i	$-0.755622\pi$
$659$	−4.11927	+	3.45648i	−0.160464	+	0.134645i	0.559020	+	0.829154i	$0.311177\pi$
$660$	3.85310	+	11.7402i	0.149982	+	0.456987i
$661$	3.24416	−	8.91326i	0.126183	−	0.346686i	−0.860475	−	0.509493i	$-0.829833\pi$
$661$	3.24416	−	8.91326i	0.126183	−	0.346686i	0.986658	+	0.162808i	$0.0520550\pi$
$662$	−42.9167	+	15.7818i	−1.66801	+	0.613376i
$663$	13.9107	−	78.8915i	0.540247	−	3.06389i
$664$	−24.7701	+	0.246428i	−0.961268	+	0.00956328i
$665$	30.8960	−	2.76671i	1.19810	−	0.107289i
$666$	19.5488	−	34.1203i	0.757500	−	1.32213i
$667$	17.1860	+	3.03036i	0.665446	+	0.117336i
$668$	−27.6510	−	4.68675i	−1.06985	−	0.181336i
$669$	13.3148	+	4.84620i	0.514781	+	0.187365i
$670$	14.2664	+	12.8547i	0.551158	+	0.496619i
$671$	−6.13991	−	7.31726i	−0.237029	−	0.282480i
$672$	42.9518	+	23.8576i	1.65690	+	0.920327i
$673$	−9.22356	+	15.9757i	−0.355542	+	0.615817i	−0.987211	−	0.159422i	$-0.949037\pi$
$673$	−9.22356	+	15.9757i	−0.355542	+	0.615817i	0.631668	+	0.775239i	$0.282370\pi$
$674$	26.5464	+	9.56251i	1.02253	+	0.368334i
$675$	11.4971	+	16.0712i	0.442523	+	0.618580i
$676$	24.0543	−	0.159535i	0.925166	−	0.00613597i
$677$	−14.3471	−	24.8499i	−0.551404	−	0.955060i	−0.998174	−	0.0604107i	$-0.980759\pi$
$677$	−14.3471	−	24.8499i	−0.551404	−	0.955060i	0.446770	−	0.894649i	$-0.352574\pi$
$678$	−20.3151	+	3.65160i	−0.780197	+	0.140239i
$679$	44.1393	−	16.0654i	1.69391	−	0.616533i
$680$	−29.0982	+	23.0296i	−1.11586	+	0.883145i
$681$	10.8047	+	9.06624i	0.414038	+	0.347419i
$682$	1.08427	−	1.30092i	0.0415190	−	0.0498150i
$683$			14.8522i			0.568305i	0.958779	+	0.284152i	$0.0917121\pi$
$683$			14.8522i			0.568305i	−0.958779	+	0.284152i	$0.908288\pi$
$684$	−5.20068	−	38.4273i	−0.198853	−	1.46931i
$685$	7.17823	−	11.3943i	0.274266	−	0.435353i
$686$	13.3849	+	11.1559i	0.511039	+	0.425933i
$687$	−24.9537	+	29.7386i	−0.952042	+	1.13460i
$688$	−14.4635	+	12.4669i	−0.551415	+	0.475297i
$689$	−39.4681	+	14.3652i	−1.50361	+	0.547271i
$690$	−48.3175	−	19.5415i	−1.83942	−	0.743932i
$691$	−6.56188	+	3.78851i	−0.249626	+	0.144122i	−0.619593	−	0.784923i	$-0.712702\pi$
$691$	−6.56188	+	3.78851i	−0.249626	+	0.144122i	0.369967	+	0.929045i	$0.379369\pi$
$692$	9.93812	−	0.0659125i	0.377791	−	0.00250562i
$693$	−14.1141	+	2.48869i	−0.536149	+	0.0945375i
$694$	40.0704	+	14.4341i	1.52105	+	0.547912i
$695$	−16.9428	−	32.1490i	−0.642678	−	1.21948i
$696$	11.3444	+	19.2053i	0.430009	+	0.727975i
$697$	28.3752	−	23.8096i	1.07479	−	0.901855i
$698$	4.49663	−	26.0057i	0.170200	−	0.984329i
$699$	11.7077	+	4.26126i	0.442827	+	0.161176i
$700$	30.5988	−	8.75058i	1.15653	−	0.330741i
$701$	5.52325	−	31.3239i	0.208610	−	1.18309i	−0.683046	−	0.730375i	$-0.739345\pi$
$701$	5.52325	−	31.3239i	0.208610	−	1.18309i	0.891657	−	0.452712i	$-0.149544\pi$
$702$	24.2607	+	13.8999i	0.915662	+	0.524617i
$703$	−5.97771	+	26.5846i	−0.225454	+	1.00266i
$704$	−0.161135	−	8.09758i	−0.00607302	−	0.305189i
$705$	−31.4690	−	28.5447i	−1.18519	−	1.07505i
$706$	−7.15347	−	19.4530i	−0.269224	−	0.732125i
$707$	−14.2229	−	5.17673i	−0.534909	−	0.194691i
$708$	11.1377	−	13.4536i	0.418580	−	0.505616i
$709$	10.9687	−	9.20381i	0.411937	−	0.345656i	−0.413149	−	0.910663i	$-0.635571\pi$
$709$	10.9687	−	9.20381i	0.411937	−	0.345656i	0.825086	+	0.565007i	$0.191127\pi$
$710$	3.99271	+	2.49689i	0.149844	+	0.0937068i
$711$	12.4889	−	21.6314i	0.468370	−	0.811241i
$712$	−14.1518	+	2.64077i	−0.530363	+	0.0989672i
$713$	1.24044	+	7.03489i	0.0464549	+	0.263459i
$714$	−36.2423	−	62.2954i	−1.35633	−	2.33135i
$715$	11.3167	+	0.436787i	0.423222	+	0.0163349i
$716$	21.7831	+	7.76519i	0.814073	+	0.290199i
$717$	−17.2823	+	6.29024i	−0.645419	+	0.234913i
$718$	−10.7300	−	12.7017i	−0.400439	−	0.474024i
$719$	13.9296	−	16.6007i	0.519487	−	0.619101i	−0.440972	−	0.897521i	$-0.645366\pi$
$719$	13.9296	−	16.6007i	0.519487	−	0.619101i	0.960459	+	0.278420i	$0.0898106\pi$
$720$	−12.6567	−	37.7181i	−0.471686	−	1.40567i
$721$			48.8344i			1.81869i
$722$	11.2898	+	24.3832i	0.420164	+	0.907448i
$723$	−18.7420			−0.697022
$724$	10.2551	+	27.6046i	0.381127	+	1.02592i
$725$	13.9931	+	3.59818i	0.519689	+	0.133633i
$726$	−24.8445	−	29.4100i	−0.922067	−	1.09151i
$727$	10.9802	−	3.99646i	0.407232	−	0.148220i	−0.130278	−	0.991477i	$-0.541587\pi$
$727$	10.9802	−	3.99646i	0.407232	−	0.148220i	0.537511	+	0.843257i	$0.319365\pi$
$728$	34.2074	−	29.2882i	1.26781	−	1.08549i
$729$	−21.8691	−	37.8784i	−0.809966	−	1.40290i
$730$	44.6655	+	1.57562i	1.65314	+	0.0583162i
$731$	27.5840	−	4.86380i	1.02023	−	0.179894i
$732$	33.3636	+	39.2299i	1.23316	+	1.44998i
$733$	40.8347	+	23.5759i	1.50826	+	0.870796i	0.999954	+	0.00962065i	$0.00306240\pi$
$733$	40.8347	+	23.5759i	1.50826	+	0.870796i	0.508309	+	0.861175i	$0.330271\pi$
$734$	−39.9923	+	0.132619i	−1.47614	+	0.00489505i
$735$	2.58771	+	18.9161i	0.0954492	+	0.697731i
$736$	26.5307	+	21.5225i	0.977934	+	0.793330i
$737$	5.77718	+	2.10272i	0.212805	+	0.0774548i
$738$	13.7062	+	37.2723i	0.504530	+	1.37201i
$739$	−3.69363	−	0.651286i	−0.135872	−	0.0239580i	0.105298	−	0.994441i	$-0.466420\pi$
$739$	−3.69363	−	0.651286i	−0.135872	−	0.0239580i	−0.241171	+	0.970483i	$0.577531\pi$
$740$	−0.892918	+	27.9420i	−0.0328243	+	1.02717i
$741$	−58.0627	−	13.0557i	−2.13299	−	0.479615i
$742$	−18.7848	+	32.7869i	−0.689613	+	1.20365i
$743$	−7.67090	−	1.35259i	−0.281418	−	0.0496216i	0.0311575	−	0.999514i	$-0.490081\pi$
$743$	−7.67090	−	1.35259i	−0.281418	−	0.0496216i	−0.312576	+	0.949893i	$0.601192\pi$
$744$	−5.79911	+	7.05242i	−0.212606	+	0.258554i
$745$	10.1582	+	13.1008i	0.372169	+	0.479977i
$746$	−0.257959	+	1.49187i	−0.00944456	+	0.0546213i
$747$	−29.8424	+	25.0407i	−1.09188	+	0.916192i
$748$	−5.87180	+	10.3278i	−0.214694	+	0.377624i
$749$	−51.9049	−	29.9673i	−1.89656	−	1.09498i
$750$	−38.6373	−	19.2142i	−1.41083	−	0.701602i
$751$	2.93202	+	16.6283i	0.106991	+	0.606775i	0.990406	+	0.138185i	$0.0441268\pi$
$751$	2.93202	+	16.6283i	0.106991	+	0.606775i	−0.883416	+	0.468590i	$0.844762\pi$
$752$	14.2429	+	23.9307i	0.519387	+	0.872664i
$753$	−27.2079	−	47.1255i	−0.991511	−	1.71735i
$754$	20.1217	−	3.61684i	0.732788	−	0.131717i
$755$	−3.72011	−	0.805019i	−0.135389	−	0.0292976i
$756$	24.7434	−	4.53234i	0.899910	−	0.164840i
$757$	3.27044	−	3.89756i	0.118866	−	0.141659i	−0.703330	−	0.710864i	$-0.748304\pi$
$757$	3.27044	−	3.89756i	0.118866	−	0.141659i	0.822196	+	0.569204i	$0.192749\pi$
$758$	37.9122	+	31.5984i	1.37703	+	1.14771i
$759$	−16.6860			−0.605664
$760$	16.0821	+	22.3912i	0.583359	+	0.812214i
$761$	−42.1085			−1.52643			−0.763216	−	0.646143i	$-0.776381\pi$
$761$	−42.1085			−1.52643			−0.763216	+	0.646143i	$0.776381\pi$
$762$	23.7630	+	19.8056i	0.860844	+	0.717483i
$763$	15.4137	−	18.3693i	0.558012	−	0.665013i
$764$	−32.1962	+	5.89750i	−1.16482	+	0.213364i
$765$	−12.3430	+	57.0387i	−0.446261	+	2.06224i
$766$	−33.9255	+	6.09805i	−1.22578	+	0.220331i
$767$	−8.00402	−	13.8634i	−0.289009	−	0.500577i
$768$	1.15827	+	43.6506i	0.0417954	+	1.57510i
$769$	7.07342	+	40.1154i	0.255074	+	1.44660i	0.795882	+	0.605451i	$0.207007\pi$
$769$	7.07342	+	40.1154i	0.255074	+	1.44660i	−0.540808	+	0.841146i	$0.681881\pi$
$770$	8.03116	−	6.27004i	0.289423	−	0.225957i
$771$	−36.9246	−	21.3184i	−1.32981	−	0.767764i
$772$	6.64013	−	11.6792i	0.238984	−	0.420345i
$773$	−37.5695	+	31.5245i	−1.35128	+	1.13386i	−0.372709	+	0.927948i	$0.621571\pi$
$773$	−37.5695	+	31.5245i	−1.35128	+	1.13386i	−0.978571	+	0.205911i	$0.933984\pi$
$774$	−5.11647	+	29.5904i	−0.183908	+	1.06360i
$775$	0.575005	+	5.88620i	0.0206548	+	0.211439i
$776$	32.2443	+	26.5140i	1.15750	+	0.951798i
$777$	−53.4704	−	9.42827i	−1.91824	−	0.338237i
$778$	−19.6051	+	34.2185i	−0.702876	+	1.22679i
$779$	−16.6860	−	21.8817i	−0.597838	−	0.783994i
$780$	−61.0273	−	1.95020i	−2.18513	−	0.0698282i
$781$	1.48473	+	0.261797i	0.0531277	+	0.00936785i
$782$	−17.2953	−	47.0327i	−0.618480	−	1.68189i
$783$	10.7313	+	3.90589i	0.383507	+	0.139585i
$784$	2.00944	−	12.3520i	0.0717658	−	0.441144i
$785$	2.61258	+	19.0979i	0.0932471	+	0.681634i
$786$	39.7438	−	0.131795i	1.41762	−	0.00470097i
$787$	−21.5339	−	12.4326i	−0.767601	−	0.443175i	0.0644170	−	0.997923i	$-0.479481\pi$
$787$	−21.5339	−	12.4326i	−0.767601	−	0.443175i	−0.832018	+	0.554748i	$0.812815\pi$
$788$	22.9499	+	26.9851i	0.817557	+	0.961306i
$789$	−11.7454	+	2.07103i	−0.418147	+	0.0737306i
$790$	−0.626020	+	17.7464i	−0.0222728	+	0.631388i
$791$	8.51003	+	14.7398i	0.302582	+	0.524087i
$792$	−8.28392	−	9.67526i	−0.294356	−	0.343795i
$793$	44.3545	−	16.1437i	1.57507	−	0.573280i
$794$	23.4772	+	27.7914i	0.833175	+	0.986279i
$795$	48.7844	−	15.6533i	1.73020	−	0.555164i
$796$	−8.59226	−	23.1286i	−0.304545	−	0.819772i
$797$	8.97206			0.317807			0.158903	−	0.987294i	$-0.449204\pi$
$797$	8.97206			0.317807			0.158903	+	0.987294i	$0.449204\pi$
$798$	−47.4842	+	24.7371i	−1.68092	+	0.875685i
$799$		−	40.8498i		−	1.44516i
$800$	20.5267	+	19.4591i	0.725727	+	0.687983i
$801$	−14.5527	+	17.3432i	−0.514193	+	0.612792i
$802$	−13.0629	−	15.4633i	−0.461267	−	0.546029i
$803$	13.4456	−	4.89379i	0.474484	−	0.172698i
$804$	−31.2216	−	11.1298i	−1.10110	−	0.392518i
$805$	−1.65754	+	42.9452i	−0.0584206	+	1.51362i
$806$	4.20829	+	7.23347i	0.148231	+	0.254788i
$807$	−9.54830	−	54.1511i	−0.336116	−	1.90621i
$808$	−2.46751	−	13.2233i	−0.0868069	−	0.465196i
$809$	18.5059	−	32.0532i	0.650633	−	1.12693i	−0.332336	−	0.943161i	$-0.607837\pi$
$809$	18.5059	−	32.0532i	0.650633	−	1.12693i	0.982970	−	0.183769i	$-0.0588298\pi$
$810$	6.86030	+	4.29018i	0.241047	+	0.150742i
$811$	12.1404	−	10.1870i	0.426306	−	0.357713i	−0.404250	−	0.914649i	$-0.632467\pi$
$811$	12.1404	−	10.1870i	0.426306	−	0.357713i	0.830556	+	0.556935i	$0.188023\pi$
$812$	11.7290	−	14.1679i	0.411609	−	0.497196i
$813$	40.2983	+	14.6674i	1.41332	+	0.514408i
$814$	3.08900	+	8.40019i	0.108270	+	0.294427i
$815$	−14.7935	+	16.3090i	−0.518193	+	0.571280i
$816$	31.2873	−	55.8903i	1.09527	−	1.95655i
$817$	−2.65388	−	20.6383i	−0.0928476	−	0.722042i
$818$	24.3844	+	13.9707i	0.852579	+	0.488474i
$819$	12.2978	−	69.7443i	0.429720	−	2.43706i
$820$	−21.0368	−	18.8292i	−0.734639	−	0.657543i
$821$	20.0936	+	7.31349i	0.701273	+	0.255243i	0.667954	−	0.744202i	$-0.267170\pi$
$821$	20.0936	+	7.31349i	0.701273	+	0.255243i	0.0333187	+	0.999445i	$0.489392\pi$
$822$	−3.96043	+	22.9046i	−0.138136	+	0.798889i
$823$	−11.4317	+	9.59236i	−0.398485	+	0.334369i	−0.819908	−	0.572496i	$-0.805975\pi$
$823$	−11.4317	+	9.59236i	−0.398485	+	0.334369i	0.421423	+	0.906864i	$0.361531\pi$
$824$	−37.3683	+	22.0732i	−1.30179	+	0.768955i
$825$	−13.7737	−	1.06482i	−0.479538	−	0.0370723i
$826$	−13.5496	−	4.88084i	−0.471452	−	0.169826i
$827$	−21.7491	+	3.83495i	−0.756289	+	0.133354i	−0.538481	−	0.842638i	$-0.681002\pi$
$827$	−21.7491	+	3.83495i	−0.756289	+	0.133354i	−0.217808	+	0.975992i	$0.569891\pi$
$828$	53.7246	−	0.356317i	1.86706	−	0.0123829i
$829$	−20.9998	+	12.1242i	−0.729352	+	0.421091i	−0.818185	−	0.574955i	$-0.805019\pi$
$829$	−20.9998	+	12.1242i	−0.729352	+	0.421091i	0.0888333	+	0.996047i	$0.471686\pi$
$830$	10.3839	−	25.6749i	0.360431	−	0.891188i
$831$	−50.8342	+	18.5021i	−1.76342	+	0.641832i
$832$	37.8732	+	12.9374i	1.31302	+	0.448523i
$833$	−11.7995	+	14.0622i	−0.408830	+	0.487225i
$834$	48.1836	+	40.1593i	1.66846	+	1.39060i
$835$	16.7135	−	26.5300i	0.578395	−	0.918108i
$836$	7.46079	+	4.71516i	0.258037	+	0.163077i
$837$			4.67465i			0.161580i
$838$	11.0446	−	13.2515i	0.381530	−	0.457765i
$839$	17.6583	+	14.8171i	0.609631	+	0.511541i	0.894525	−	0.447018i	$-0.147514\pi$
$839$	17.6583	+	14.8171i	0.609631	+	0.511541i	−0.284894	+	0.958559i	$0.591958\pi$
$840$	−43.0741	+	34.0907i	−1.48620	+	1.17624i
$841$	−19.4045	+	7.06268i	−0.669122	+	0.243541i
$842$	19.9261	−	3.58168i	0.686700	−	0.123433i
$843$	2.77128	+	4.80000i	0.0954479	+	0.165321i
$844$	13.3404	−	0.0884771i	0.459194	−	0.00304551i
$845$	−10.1662	+	24.8987i	−0.349727	+	0.856540i
$846$	41.2040	+	14.8425i	1.41662	+	0.510295i
$847$	−15.8730	+	27.4929i	−0.545404	+	0.944667i
$848$	−33.5795	+	0.445437i	−1.15312	+	0.0152964i
$849$	−9.07644	−	10.8169i	−0.311503	−	0.371234i
$850$	−11.2753	−	39.9275i	−0.386739	−	1.36950i
$851$	−35.4755	−	12.9120i	−1.21608	−	0.442618i
$852$	−8.01394	−	1.35833i	−0.274553	−	0.0465358i
$853$	−42.1116	−	7.42540i	−1.44187	−	0.254241i	−0.602640	−	0.798013i	$-0.705884\pi$
$853$	−42.1116	−	7.42540i	−1.44187	−	0.254241i	−0.839233	+	0.543772i	$0.816995\pi$
$854$	21.1105	−	36.8461i	0.722387	−	1.26085i
$855$	41.9003	+	11.1354i	1.43296	+	0.380822i
$856$	−0.529894	−	53.2631i	−0.0181114	−	1.82049i
$857$	−7.16915	+	40.6583i	−0.244894	+	1.38886i	0.575846	+	0.817558i	$0.304673\pi$
$857$	−7.16915	+	40.6583i	−0.244894	+	1.38886i	−0.820740	+	0.571302i	$0.806438\pi$
$858$	−18.3466	+	6.74660i	−0.626343	+	0.230325i
$859$	0.761865	−	2.09321i	0.0259945	−	0.0714193i	−0.926017	−	0.377483i	$-0.876790\pi$
$859$	0.761865	−	2.09321i	0.0259945	−	0.0714193i	0.952011	+	0.306063i	$0.0990120\pi$
$860$	−6.65723	−	20.2843i	−0.227010	−	0.691688i
$861$	42.0039	−	35.2454i	1.43149	−	1.20116i
$862$	5.18077	−	0.0171800i	0.176458	−	0.000585153i
$863$	30.3873	+	17.5441i	1.03440	+	0.597208i	0.918241	−	0.396023i	$-0.129610\pi$
$863$	30.3873	+	17.5441i	1.03440	+	0.597208i	0.116155	+	0.993231i	$0.462943\pi$
$864$	14.6522	+	16.8852i	0.498478	+	0.574446i
$865$	−4.20019	+	10.2870i	−0.142811	+	0.349767i
$866$	0.924966	+	1.58989i	0.0314316	+	0.0540266i
$867$	−41.1878	+	23.7798i	−1.39881	+	0.807604i
$868$	7.09178	+	2.52806i	0.240711	+	0.0858080i
$869$	1.94439	+	5.34216i	0.0659588	+	0.181220i
$870$	−24.6969	+	3.46200i	−0.837305	+	0.117373i
$871$	−19.5279	+	23.2724i	−0.661676	+	0.788555i
$872$	21.0232	+	3.49169i	0.711937	+	0.118243i
$873$	65.6507			2.22194
$874$	−35.5016	+	11.2055i	−1.20086	+	0.379032i
$875$	−4.10880	+	35.3439i	−0.138903	+	1.19484i
$876$	−72.3139	+	26.8645i	−2.44326	+	0.907669i
$877$	23.0259	+	19.3211i	0.777531	+	0.652426i	0.942626	−	0.333852i	$-0.108349\pi$
$877$	23.0259	+	19.3211i	0.777531	+	0.652426i	−0.165095	+	0.986278i	$0.552793\pi$
$878$	−6.43391	+	5.43515i	−0.217134	+	0.183427i
$879$	24.8317	+	68.2246i	0.837553	+	2.30116i
$880$	8.42796	+	3.31142i	0.284106	+	0.111628i
$881$	17.9777	+	31.1383i	0.605684	+	1.04907i	0.991943	+	0.126684i	$0.0404336\pi$
$881$	17.9777	+	31.1383i	0.605684	+	1.04907i	−0.386260	+	0.922390i	$0.626233\pi$
$882$	−9.89680	−	17.0112i	−0.333242	−	0.572798i
$883$	−9.57315	−	54.2921i	−0.322162	−	1.82707i	−0.528909	−	0.848679i	$-0.677399\pi$
$883$	−9.57315	−	54.2921i	−0.322162	−	1.82707i	0.206747	−	0.978395i	$-0.433712\pi$
$884$	−38.0332	−	44.7205i	−1.27920	−	1.50411i
$885$	9.10407	+	17.2750i	0.306030	+	0.580691i
$886$	34.2883	−	0.113704i	1.15194	−	0.00381995i
$887$	7.55590	+	9.00477i	0.253702	+	0.302351i	0.877831	−	0.478971i	$-0.158990\pi$
$887$	7.55590	+	9.00477i	0.253702	+	0.302351i	−0.624128	+	0.781322i	$0.714546\pi$
$888$	−16.9541	−	45.1773i	−0.568941	−	1.51605i
$889$	8.72433	−	23.9699i	0.292605	−	0.803925i
$890$	3.35200	−	15.7424i	0.112359	−	0.527688i
$891$	2.55107	+	0.449822i	0.0854640	+	0.0150696i
$892$	8.95801	−	5.25143i	0.299936	−	0.175831i
$893$	−30.3142	−	1.41502i	−1.01443	−	0.0473517i
$894$	−24.8277	−	14.2247i	−0.830363	−	0.475746i
$895$	−17.3711	+	19.1507i	−0.580651	+	0.640137i
$896$	33.5400	−	13.0969i	1.12049	−	0.437538i
$897$	28.2008	−	77.4810i	0.941596	−	2.58701i
$898$	−22.3135	−	3.85822i	−0.744611	−	0.128751i
$899$	2.19706	+	2.61835i	0.0732759	+	0.0873268i
$900$	44.3704	+	3.13432i	1.47901	+	0.104477i
$901$	42.6609	+	24.6303i	1.42124	+	0.820554i
$902$	−8.50376	−	3.06322i	−0.283144	−	0.101994i
$903$	40.8326	−	7.19989i	1.35882	−	0.239597i
$904$	−7.43243	+	13.1743i	−0.247199	+	0.438171i
$905$	−32.8992	−	1.26980i	−1.09361	−	0.0422095i
$906$	6.46609	−	1.16227i	0.214821	−	0.0386138i
$907$	1.37212	+	3.76986i	0.0455604	+	0.125176i	0.960386	−	0.278673i	$-0.0898944\pi$
$907$	1.37212	+	3.76986i	0.0455604	+	0.125176i	−0.914826	+	0.403849i	$0.867672\pi$
$908$	10.1672	−	1.86236i	0.337410	−	0.0618045i
$909$	−16.2053	−	13.5979i	−0.537496	−	0.451013i
$910$	15.5414	+	47.8894i	0.515193	+	1.58752i
$911$	33.6859			1.11606			0.558031	−	0.829820i	$-0.311557\pi$
$911$	33.6859			1.11606			0.558031	+	0.829820i	$0.311557\pi$
$912$	−40.3918	−	25.1540i	−1.33751	−	0.832931i
$913$		−	8.86658i		−	0.293441i
$914$	31.4164	−	37.6937i	1.03916	−	1.24680i
$915$	−54.8242	+	17.5912i	−1.81243	+	0.581548i
$916$	5.12590	+	27.9839i	0.169365	+	0.924613i
$917$	−11.2088	−	30.7960i	−0.370149	−	1.01697i
$918$	−5.80155	−	32.2760i	−0.191480	−	1.06527i
$919$	−22.6234	+	13.0616i	−0.746278	+	0.430864i	−0.824347	−	0.566084i	$-0.808458\pi$
$919$	−22.6234	+	13.0616i	−0.746278	+	0.430864i	0.0780696	+	0.996948i	$0.475124\pi$
$920$	−33.6111	+	18.1429i	−1.10812	+	0.598153i
$921$	−5.25223	−	29.7869i	−0.173067	−	0.981511i
$922$	−41.1950	−	14.8393i	−1.35669	−	0.488705i
$923$	−3.72496	+	6.45183i	−0.122609	+	0.212364i
$924$	−8.69203	+	15.2883i	−0.285947	+	0.502949i
$925$	−28.4597	−	12.9223i	−0.935750	−	0.424882i
$926$	−6.58546	+	38.0861i	−0.216412	+	1.25159i
$927$	−23.3441	+	64.1375i	−0.766722	+	2.10655i
$928$	16.1429	+	2.57123i	0.529916	+	0.0844046i
$929$	1.14542	−	6.49598i	0.0375799	−	0.213126i	−0.960235	−	0.279192i	$-0.909934\pi$
$929$	1.14542	−	6.49598i	0.0375799	−	0.213126i	0.997815	+	0.0660656i	$0.0210446\pi$
$930$	−4.78927	−	9.01503i	−0.157046	−	0.295614i
$931$	10.0266	+	9.24343i	0.328610	+	0.302941i
$932$	7.87678	−	4.61758i	0.258013	−	0.151254i
$933$	0.798194	−	4.52678i	0.0261317	−	0.148200i
$934$	−32.9056	+	12.1004i	−1.07671	+	0.395937i
$935$	−8.13912	−	10.4968i	−0.266178	−	0.343282i
$936$	58.9273	−	22.1141i	1.92610	−	0.722822i
$937$	−17.0227	−	20.2869i	−0.556108	−	0.662744i	0.412610	−	0.910908i	$-0.364617\pi$
$937$	−17.0227	−	20.2869i	−0.556108	−	0.662744i	−0.968718	+	0.248164i	$0.920173\pi$
$938$	0.0906348	+	27.3317i	0.00295933	+	0.892411i
$939$	−41.7480	+	72.3096i	−1.36239	+	2.35973i
$940$	−30.8196	+	4.42453i	−1.00523	+	0.144312i
$941$	42.6087	−	7.51307i	1.38900	−	0.244919i	0.571387	−	0.820681i	$-0.306406\pi$
$941$	42.6087	−	7.51307i	1.38900	−	0.244919i	0.817618	+	0.575762i	$0.195294\pi$
$942$	−16.7309	−	28.7582i	−0.545123	−	0.936991i
$943$	33.0177	−	19.0628i	1.07520	−	0.620769i
$944$	−2.38959	−	12.5744i	−0.0777746	−	0.409261i
$945$	−5.94831	+	27.4880i	−0.193499	+	0.894186i
$946$	−4.41065	−	5.22114i	−0.143402	−	0.169754i
$947$	38.9709	+	32.7004i	1.26638	+	1.06262i	0.994972	+	0.100158i	$0.0319348\pi$
$947$	38.9709	+	32.7004i	1.26638	+	1.06262i	0.271411	+	0.962463i	$0.412510\pi$
$948$	−10.6737	−	28.7315i	−0.346667	−	0.933157i
$949$			70.7050i			2.29518i
$950$	−30.0203	+	6.98420i	−0.973989	+	0.226597i
$951$			53.1962i			1.72500i
$952$	−52.1025	−	8.65355i	−1.68865	−	0.280463i
$953$	1.73315	+	1.45429i	0.0561424	+	0.0471091i	0.670427	−	0.741975i	$-0.266111\pi$
$953$	1.73315	+	1.45429i	0.0561424	+	0.0471091i	−0.614285	+	0.789084i	$0.710555\pi$
$954$	−40.3444	+	34.0816i	−1.30620	+	1.10343i
$955$	7.73996	−	35.7675i	0.250459	−	1.15741i
$956$	−4.52562	+	12.6954i	−0.146369	+	0.410598i
$957$	−6.91434	+	3.99200i	−0.223509	+	0.129043i
$958$	−16.0479	+	9.33637i	−0.518485	+	0.301644i
$959$	18.8759	−	3.32833i	0.609535	−	0.107477i
$960$	−45.5559	−	17.5515i	−1.47031	−	0.566471i
$961$	14.8004	−	25.6351i	0.477434	−	0.826939i
$962$	−44.2267	+	0.146661i	−1.42593	+	0.00472853i
$963$	−53.8449	−	64.1699i	−1.73513	−	2.06785i
$964$	−8.75859	+	10.5798i	−0.282095	+	0.340752i
$965$	9.20413	+	11.8703i	0.296291	+	0.382119i
$966$	−25.6023	−	69.6225i	−0.823741	−	2.24007i
$967$	−1.32336	+	7.50513i	−0.0425563	+	0.241349i	−0.998664	−	0.0516652i	$-0.983547\pi$
$967$	−1.32336	+	7.50513i	−0.0425563	+	0.241349i	0.956108	+	0.293014i	$0.0946582\pi$
$968$	−28.2123	+	0.280673i	−0.906778	+	0.00902118i
$969$	32.0429	+	62.0090i	1.02937	+	1.99202i
$970$	−41.2175	+	21.8970i	−1.32341	+	0.703069i
$971$	8.96489	−	50.8424i	0.287697	−	1.63161i	−0.407793	−	0.913074i	$-0.633701\pi$
$971$	8.96489	−	50.8424i	0.287697	−	1.63161i	0.695490	−	0.718536i	$-0.255187\pi$
$972$	−37.1484	−	6.29653i	−1.19154	−	0.201961i
$973$	17.6901	−	48.6030i	0.567117	−	1.55814i
$974$	−28.0030	−	4.84200i	−0.897275	−	0.155148i
$975$	28.2232	−	62.1580i	0.903864	−	1.99065i
$976$	37.7368	−	0.500585i	1.20793	−	0.0160233i
$977$	−0.423996	+	0.734383i	−0.0135648	+	0.0234950i	−0.872728	−	0.488207i	$-0.837651\pi$
$977$	−0.423996	+	0.734383i	−0.0135648	+	0.0234950i	0.859163	+	0.511701i	$0.170985\pi$
$978$	12.8802	−	35.7565i	0.411863	−	1.14337i
$979$	−0.894791	−	5.07461i	−0.0285977	−	0.162185i
$980$	11.8874	+	7.37921i	0.379729	+	0.235720i
$981$	29.0248	−	16.7575i	0.926690	−	0.535025i
$982$	25.4872	−	4.58128i	0.813330	−	0.146195i
$983$	9.92979	+	27.2819i	0.316711	+	0.870157i	0.991260	+	0.131926i	$0.0421162\pi$
$983$	9.92979	+	27.2819i	0.316711	+	0.870157i	−0.674548	+	0.738231i	$0.735662\pi$
$984$	45.9557	+	16.2106i	1.46501	+	0.516776i
$985$	−37.7120	+	12.1005i	−1.20161	+	0.385554i
$986$	−18.4190	−	15.3516i	−0.586582	−	0.488895i
$987$		−	60.4700i		−	1.92478i
$988$	−34.5041	+	26.6750i	−1.09772	+	0.848644i
$989$	28.8294			0.916723
$990$	13.5451	−	4.39576i	0.430492	−	0.139706i
$991$	45.7935	+	38.4253i	1.45468	+	1.22062i	0.929074	+	0.369893i	$0.120606\pi$
$991$	45.7935	+	38.4253i	1.45468	+	1.22062i	0.525606	+	0.850728i	$0.323839\pi$
$992$	1.27100	+	6.56935i	0.0403544	+	0.208577i
$993$	30.1805	+	82.9204i	0.957751	+	2.63140i
$994$	1.18575	+	6.59673i	0.0376097	+	0.209236i
$995$	27.5648	+	1.06391i	0.873862	+	0.0337281i
$996$	0.317038	+	47.8022i	0.0100457	+	1.51467i
$997$	−2.95030	+	0.520217i	−0.0934368	+	0.0164754i	−0.220171	−	0.975461i	$-0.570662\pi$
$997$	−2.95030	+	0.520217i	−0.0934368	+	0.0164754i	0.126734	+	0.991937i	$0.459550\pi$
$998$	−1.43042	+	3.97097i	−0.0452792	+	0.125699i
$999$	−21.3952	−	12.3525i	−0.676914	−	0.390817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.10	yes	336
4.3	odd	2	inner	380.2.bb.a.59.51	yes	336
5.4	even	2	inner	380.2.bb.a.59.47	yes	336
19.10	odd	18	inner	380.2.bb.a.219.6	yes	336
20.19	odd	2	inner	380.2.bb.a.59.6	✓	336
76.67	even	18	inner	380.2.bb.a.219.47	yes	336
95.29	odd	18	inner	380.2.bb.a.219.51	yes	336
380.219	even	18	inner	380.2.bb.a.219.10	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.6	✓	336	20.19	odd	2	inner
380.2.bb.a.59.10	yes	336	1.1	even	1	trivial
380.2.bb.a.59.47	yes	336	5.4	even	2	inner
380.2.bb.a.59.51	yes	336	4.3	odd	2	inner
380.2.bb.a.219.6	yes	336	19.10	odd	18	inner
380.2.bb.a.219.10	yes	336	380.219	even	18	inner
380.2.bb.a.219.47	yes	336	76.67	even	18	inner
380.2.bb.a.219.51	yes	336	95.29	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08636 - 0.905441i) q^{2} +(-1.75425 + 2.09063i) q^{3} +(0.360351 + 1.96727i) q^{4} +(-2.18548 - 0.472930i) q^{5} +(3.79868 - 0.682806i) q^{6} +(-1.59127 - 2.75617i) q^{7} +(1.38978 - 2.46344i) q^{8} +(-0.772405 - 4.38052i) q^{9} +O(q^{10})\)	\(q+(-1.08636 - 0.905441i) q^{2} +(-1.75425 + 2.09063i) q^{3} +(0.360351 + 1.96727i) q^{4} +(-2.18548 - 0.472930i) q^{5} +(3.79868 - 0.682806i) q^{6} +(-1.59127 - 2.75617i) q^{7} +(1.38978 - 2.46344i) q^{8} +(-0.772405 - 4.38052i) q^{9} +(1.94601 + 2.49260i) q^{10} +(0.876762 + 0.506199i) q^{11} +(-4.74497 - 2.69771i) q^{12} +(-3.83232 + 3.21570i) q^{13} +(-0.766853 + 4.43499i) q^{14} +(4.82259 - 3.73940i) q^{15} +(-3.74029 + 1.41782i) q^{16} +(5.77829 + 1.01887i) q^{17} +(-3.12720 + 5.45819i) q^{18} +(0.956248 - 4.25272i) q^{19} +(0.142839 - 4.46985i) q^{20} +(8.55360 + 1.50823i) q^{21} +(-0.494145 - 1.34377i) q^{22} +(5.67498 + 2.06552i) q^{23} +(2.71212 + 7.22698i) q^{24} +(4.55267 + 2.06716i) q^{25} +(7.07491 - 0.0234611i) q^{26} +(3.42257 + 1.97602i) q^{27} +(4.84870 - 4.12365i) q^{28} +(2.84576 - 0.501783i) q^{29} +(-8.62487 - 0.304251i) q^{30} +(0.591422 + 1.02437i) q^{31} +(5.34705 + 1.84636i) q^{32} +(-2.59633 + 0.944987i) q^{33} +(-5.35477 - 6.33876i) q^{34} +(2.17423 + 6.77612i) q^{35} +(8.33933 - 3.09806i) q^{36} -6.25121 q^{37} +(-4.88941 + 3.75415i) q^{38} -13.6531i q^{39} +(-4.20237 + 4.72653i) q^{40} +(4.05794 - 4.83606i) q^{41} +(-7.92667 - 9.38326i) q^{42} +(4.48584 - 1.63271i) q^{43} +(-0.679887 + 1.90724i) q^{44} +(-0.383606 + 9.93886i) q^{45} +(-4.29485 - 7.38226i) q^{46} +(-1.20896 - 6.85637i) q^{47} +(3.59727 - 10.3068i) q^{48} +(-1.56430 + 2.70945i) q^{49} +(-3.07414 - 6.36786i) q^{50} +(-12.2666 + 10.2929i) q^{51} +(-7.70713 - 6.38043i) q^{52} +(7.88929 + 2.87147i) q^{53} +(-1.92897 - 5.24561i) q^{54} +(-1.67675 - 1.52094i) q^{55} +(-9.00115 + 0.0895490i) q^{56} +(7.21335 + 9.45947i) q^{57} +(-3.54585 - 2.03155i) q^{58} +(-0.555649 + 3.15124i) q^{59} +(9.09423 + 8.13984i) q^{60} +(-8.86603 - 3.22697i) q^{61} +(0.285013 - 1.64833i) q^{62} +(-10.8443 + 9.09949i) q^{63} +(-4.13705 - 6.84725i) q^{64} +(9.89628 - 5.21544i) q^{65} +(3.67618 + 1.32423i) q^{66} +(5.98040 - 1.05451i) q^{67} +(0.0778272 + 11.7346i) q^{68} +(-14.2735 + 8.24083i) q^{69} +(3.77339 - 9.32993i) q^{70} +(1.39936 - 0.509326i) q^{71} +(-11.8646 - 4.18518i) q^{72} +(9.08468 - 10.8267i) q^{73} +(6.79106 + 5.66010i) q^{74} +(-12.3082 + 5.89164i) q^{75} +(8.71082 + 0.348725i) q^{76} -3.22200i q^{77} +(-12.3621 + 14.8322i) q^{78} +(4.30164 + 3.60950i) q^{79} +(8.84488 - 1.32972i) q^{80} +(2.40439 - 0.875127i) q^{81} +(-8.78714 + 1.57947i) q^{82} +(-4.37900 - 7.58465i) q^{83} +(0.115208 + 17.3707i) q^{84} +(-12.1465 - 4.95945i) q^{85} +(-6.35156 - 2.28795i) q^{86} +(-3.94311 + 6.82967i) q^{87} +(2.46549 - 1.45635i) q^{88} +(-3.27166 - 3.89901i) q^{89} +(9.41579 - 10.4498i) q^{90} +(14.9613 + 5.44546i) q^{91} +(-2.01845 + 11.9085i) q^{92} +(-3.17908 - 0.560558i) q^{93} +(-4.89467 + 8.54312i) q^{94} +(-4.10110 + 8.84200i) q^{95} +(-13.2401 + 7.93973i) q^{96} +(-2.56292 + 14.5350i) q^{97} +(4.15264 - 1.52705i) q^{98} +(1.54020 - 4.23167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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