LMFDB - Embedded newform 186.2.p.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [186,2,Mod(11,186)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(186, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 23]))

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

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

chi := DirichletCharacter("186.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.p (of order $30$, degree $8$, 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:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-1.57651 - 0.717375i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.08872 + 1.20592i) q^{5} +(-1.27767 - 1.16943i) q^{6} +(0.0316894 - 0.301504i) q^{7} +(0.587785 + 0.809017i) q^{8} +(1.97075 + 2.26189i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-1.57651 - 0.717375i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.08872 + 1.20592i) q^{5} +(-1.27767 - 1.16943i) q^{6} +(0.0316894 - 0.301504i) q^{7} +(0.587785 + 0.809017i) q^{8} +(1.97075 + 2.26189i) q^{9} +(1.61384 + 1.79235i) q^{10} +(3.75423 - 1.67149i) q^{11} +(-0.853758 - 1.50702i) q^{12} +(0.178771 - 0.841052i) q^{13} +(0.123308 - 0.276955i) q^{14} +(-2.42778 - 3.39954i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.109838 + 0.0489031i) q^{17} +(1.17533 + 2.76018i) q^{18} +(-7.42953 + 1.57920i) q^{19} +(0.980985 + 2.20333i) q^{20} +(-0.266250 + 0.452590i) q^{21} +(4.08700 - 0.429561i) q^{22} +(-0.787971 + 0.572494i) q^{23} +(-0.346279 - 1.69708i) q^{24} +(0.408492 + 0.707530i) q^{25} +(0.429921 - 0.744645i) q^{26} +(-1.48427 - 4.97965i) q^{27} +(0.202857 - 0.225295i) q^{28} +(-1.13592 + 3.49602i) q^{29} +(-1.25844 - 3.98338i) q^{30} +(-2.96549 - 4.71231i) q^{31} +1.00000i q^{32} +(-7.11766 - 0.0580748i) q^{33} +(0.0893503 + 0.0804514i) q^{34} +(0.429780 - 0.591542i) q^{35} +(0.264859 + 2.98829i) q^{36} +(-2.14572 + 1.23883i) q^{37} +(-7.55390 - 0.793947i) q^{38} +(-0.885183 + 1.19768i) q^{39} +(0.252106 + 2.39863i) q^{40} +(-5.77580 + 5.20055i) q^{41} +(-0.393077 + 0.348163i) q^{42} +(-2.37289 - 11.1636i) q^{43} +(4.01971 + 0.854417i) q^{44} +(1.38867 + 7.10102i) q^{45} +(-0.926316 + 0.300978i) q^{46} +(-4.99435 + 1.62276i) q^{47} +(0.195097 - 1.72103i) q^{48} +(6.75713 + 1.43627i) q^{49} +(0.169861 + 0.799132i) q^{50} +(-0.138079 - 0.155891i) q^{51} +(0.638987 - 0.575346i) q^{52} +(-1.15917 - 11.0288i) q^{53} +(0.127175 - 5.19460i) q^{54} +(9.85721 + 1.03603i) q^{55} +(0.262549 - 0.151582i) q^{56} +(12.8456 + 2.84015i) q^{57} +(-2.16066 + 2.97389i) q^{58} +(9.97095 + 8.97788i) q^{59} +(0.0340837 - 4.17729i) q^{60} -3.20415i q^{61} +(-1.36416 - 5.39806i) q^{62} +(0.744422 - 0.522510i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.38764 - 1.54114i) q^{65} +(-6.75135 - 2.25471i) q^{66} +(-0.707708 + 1.22579i) q^{67} +(0.0601164 + 0.104125i) q^{68} +(1.65293 - 0.337270i) q^{69} +(0.591542 - 0.429780i) q^{70} +(9.66655 - 1.01600i) q^{71} +(-0.671535 + 2.92387i) q^{72} +(-1.27184 - 2.85661i) q^{73} +(-2.42353 + 0.515136i) q^{74} +(-0.136427 - 1.40847i) q^{75} +(-6.93884 - 3.08937i) q^{76} +(-0.384992 - 1.18488i) q^{77} +(-1.21196 + 0.865523i) q^{78} +(-6.12085 + 13.7477i) q^{79} +(-0.501450 + 2.35914i) q^{80} +(-1.23232 + 8.91523i) q^{81} +(-7.10017 + 3.16120i) q^{82} +(2.75278 + 3.05728i) q^{83} +(-0.481427 + 0.209655i) q^{84} +(0.170447 + 0.234601i) q^{85} +(1.19298 - 11.3504i) q^{86} +(4.29875 - 4.69661i) q^{87} +(3.55895 + 2.05476i) q^{88} +(1.33414 + 0.969306i) q^{89} +(-0.873636 + 7.18259i) q^{90} +(-0.247916 - 0.0805526i) q^{91} -0.973986 q^{92} +(1.29461 + 9.55636i) q^{93} -5.25137 q^{94} +(-17.4226 - 5.66094i) q^{95} +(0.717375 - 1.57651i) q^{96} +(1.75787 + 1.27717i) q^{97} +(5.98258 + 3.45405i) q^{98} +(11.1794 + 5.19758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−1.57651	−	0.717375i	−0.910196	−	0.414177i
$3$	−1.57651	−	0.717375i	−0.910196	−	0.414177i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	2.08872	+	1.20592i	0.934103	+	0.539304i	0.888107	−	0.459637i	$-0.152021\pi$
$5$	2.08872	+	1.20592i	0.934103	+	0.539304i	0.0459959	+	0.998942i	$0.485354\pi$
$6$	−1.27767	−	1.16943i	−0.521605	−	0.477418i
$7$	0.0316894	−	0.301504i	0.0119775	−	0.113958i	−0.986900	−	0.161336i	$-0.948420\pi$
$7$	0.0316894	−	0.301504i	0.0119775	−	0.113958i	0.998877	+	0.0473778i	$0.0150865\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	1.97075	+	2.26189i	0.656915	+	0.753964i
$10$	1.61384	+	1.79235i	0.510340	+	0.566790i
$11$	3.75423	−	1.67149i	1.13194	−	0.503974i	0.246695	−	0.969093i	$-0.420655\pi$
$11$	3.75423	−	1.67149i	1.13194	−	0.503974i	0.885248	+	0.465120i	$0.153989\pi$
$12$	−0.853758	−	1.50702i	−0.246459	−	0.435038i
$13$	0.178771	−	0.841052i	0.0495822	−	0.233266i	−0.946378	−	0.323061i	$-0.895288\pi$
$13$	0.178771	−	0.841052i	0.0495822	−	0.233266i	0.995960	+	0.0897955i	$0.0286213\pi$
$14$	0.123308	−	0.276955i	0.0329555	−	0.0740193i
$15$	−2.42778	−	3.39954i	−0.626850	−	0.877757i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.109838	+	0.0489031i	0.0266396	+	0.0118607i	0.420013	−	0.907518i	$-0.362025\pi$
$17$	0.109838	+	0.0489031i	0.0266396	+	0.0118607i	−0.393374	+	0.919379i	$0.628692\pi$
$18$	1.17533	+	2.76018i	0.277027	+	0.650581i
$19$	−7.42953	+	1.57920i	−1.70445	+	0.362292i	−0.954271	−	0.298942i	$-0.903366\pi$
$19$	−7.42953	+	1.57920i	−1.70445	+	0.362292i	−0.750180	+	0.661234i	$0.770033\pi$
$20$	0.980985	+	2.20333i	0.219355	+	0.492679i
$21$	−0.266250	+	0.452590i	−0.0581005	+	0.0987633i
$22$	4.08700	−	0.429561i	0.871352	−	0.0915828i
$23$	−0.787971	+	0.572494i	−0.164303	+	0.119373i	−0.666899	−	0.745148i	$-0.732379\pi$
$23$	−0.787971	+	0.572494i	−0.164303	+	0.119373i	0.502595	+	0.864522i	$0.332379\pi$
$24$	−0.346279	−	1.69708i	−0.0706838	−	0.346416i
$25$	0.408492	+	0.707530i	0.0816985	+	0.141506i
$26$	0.429921	−	0.744645i	0.0843144	−	0.146037i
$27$	−1.48427	−	4.97965i	−0.285647	−	0.958335i
$28$	0.202857	−	0.225295i	0.0383364	−	0.0425768i
$29$	−1.13592	+	3.49602i	−0.210936	+	0.649194i	0.788481	+	0.615059i	$0.210868\pi$
$29$	−1.13592	+	3.49602i	−0.210936	+	0.649194i	−0.999417	+	0.0341352i	$0.989132\pi$
$30$	−1.25844	−	3.98338i	−0.229759	−	0.727262i
$31$	−2.96549	−	4.71231i	−0.532617	−	0.846356i
$31$	−2.96549	−	4.71231i	−0.532617	−	0.846356i
$32$			1.00000i			0.176777i
$33$	−7.11766	−	0.0580748i	−1.23902	−	0.0101095i
$34$	0.0893503	+	0.0804514i	0.0153235	+	0.0137973i
$35$	0.429780	−	0.591542i	0.0726462	−	0.0999889i
$36$	0.264859	+	2.98829i	0.0441432	+	0.498048i
$37$	−2.14572	+	1.23883i	−0.352755	+	0.203663i	−0.665898	−	0.746043i	$-0.731951\pi$
$37$	−2.14572	+	1.23883i	−0.352755	+	0.203663i	0.313143	+	0.949706i	$0.398618\pi$
$38$	−7.55390	−	0.793947i	−1.22540	−	0.128795i
$39$	−0.885183	+	1.19768i	−0.141743	+	0.191782i
$40$	0.252106	+	2.39863i	0.0398615	+	0.379257i
$41$	−5.77580	+	5.20055i	−0.902028	+	0.812189i	−0.982825	−	0.184541i	$-0.940920\pi$
$41$	−5.77580	+	5.20055i	−0.902028	+	0.812189i	0.0807971	+	0.996731i	$0.474253\pi$
$42$	−0.393077	+	0.348163i	−0.0606531	+	0.0537227i
$43$	−2.37289	−	11.1636i	−0.361862	−	1.70243i	−0.662811	−	0.748787i	$-0.730637\pi$
$43$	−2.37289	−	11.1636i	−0.361862	−	1.70243i	0.300949	−	0.953640i	$-0.402697\pi$
$44$	4.01971	+	0.854417i	0.605995	+	0.128808i
$45$	1.38867	+	7.10102i	0.207010	+	1.05856i
$46$	−0.926316	+	0.300978i	−0.136578	+	0.0443768i
$47$	−4.99435	+	1.62276i	−0.728500	+	0.236704i	−0.649705	−	0.760187i	$-0.725107\pi$
$47$	−4.99435	+	1.62276i	−0.728500	+	0.236704i	−0.0787956	+	0.996891i	$0.525107\pi$
$48$	0.195097	−	1.72103i	0.0281598	−	0.248409i
$49$	6.75713	+	1.43627i	0.965305	+	0.205182i
$50$	0.169861	+	0.799132i	0.0240219	+	0.113014i
$51$	−0.138079	−	0.155891i	−0.0193349	−	0.0218291i
$52$	0.638987	−	0.575346i	0.0886115	−	0.0797862i
$53$	−1.15917	−	11.0288i	−0.159224	−	1.51492i	−0.724073	−	0.689723i	$-0.757732\pi$
$53$	−1.15917	−	11.0288i	−0.159224	−	1.51492i	0.564849	−	0.825195i	$-0.308935\pi$
$54$	0.127175	−	5.19460i	0.0173063	−	0.706895i
$55$	9.85721	+	1.03603i	1.32915	+	0.139699i
$56$	0.262549	−	0.151582i	0.0350845	−	0.0202561i
$57$	12.8456	+	2.84015i	1.70144	+	0.376187i
$58$	−2.16066	+	2.97389i	−0.283708	+	0.390491i
$59$	9.97095	+	8.97788i	1.29811	+	1.16882i	0.974937	+	0.222480i	$0.0714152\pi$
$59$	9.97095	+	8.97788i	1.29811	+	1.16882i	0.323170	+	0.946341i	$0.395251\pi$
$60$	0.0340837	−	4.17729i	0.00440018	−	0.539286i
$61$		−	3.20415i		−	0.410250i	−0.978736	−	0.205125i	$-0.934240\pi$
$61$		−	3.20415i		−	0.410250i	0.978736	−	0.205125i	$-0.0657601\pi$
$62$	−1.36416	−	5.39806i	−0.173249	−	0.685554i
$63$	0.744422	−	0.522510i	0.0937884	−	0.0658301i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	1.38764	−	1.54114i	0.172116	−	0.191154i
$66$	−6.75135	−	2.25471i	−0.831033	−	0.277535i
$67$	−0.707708	+	1.22579i	−0.0864602	+	0.149754i	−0.906013	−	0.423251i	$-0.860889\pi$
$67$	−0.707708	+	1.22579i	−0.0864602	+	0.149754i	0.819552	+	0.573004i	$0.194222\pi$
$68$	0.0601164	+	0.104125i	0.00729018	+	0.0126270i
$69$	1.65293	−	0.337270i	0.198990	−	0.0406026i
$70$	0.591542	−	0.429780i	0.0707028	−	0.0513686i
$71$	9.66655	−	1.01600i	1.14721	−	0.120576i	0.488214	−	0.872724i	$-0.337649\pi$
$71$	9.66655	−	1.01600i	1.14721	−	0.120576i	0.658995	+	0.752148i	$0.270982\pi$
$72$	−0.671535	+	2.92387i	−0.0791411	+	0.344582i
$73$	−1.27184	−	2.85661i	−0.148858	−	0.334341i	0.823691	−	0.567039i	$-0.191911\pi$
$73$	−1.27184	−	2.85661i	−0.148858	−	0.334341i	−0.972549	+	0.232698i	$0.925244\pi$
$74$	−2.42353	+	0.515136i	−0.281729	+	0.0598834i
$75$	−0.136427	−	1.40847i	−0.0157532	−	0.162636i
$76$	−6.93884	−	3.08937i	−0.795940	−	0.354375i
$77$	−0.384992	−	1.18488i	−0.0438740	−	0.135030i
$78$	−1.21196	+	0.865523i	−0.137228	+	0.0980011i
$79$	−6.12085	+	13.7477i	−0.688650	+	1.54673i	0.141957	+	0.989873i	$0.454660\pi$
$79$	−6.12085	+	13.7477i	−0.688650	+	1.54673i	−0.830607	+	0.556859i	$0.812006\pi$
$80$	−0.501450	+	2.35914i	−0.0560638	+	0.263760i
$81$	−1.23232	+	8.91523i	−0.136925	+	0.990581i
$82$	−7.10017	+	3.16120i	−0.784082	+	0.349096i
$83$	2.75278	+	3.05728i	0.302157	+	0.335580i	0.875034	−	0.484062i	$-0.160839\pi$
$83$	2.75278	+	3.05728i	0.302157	+	0.335580i	−0.572876	+	0.819642i	$0.694172\pi$
$84$	−0.481427	+	0.209655i	−0.0525280	+	0.0228753i
$85$	0.170447	+	0.234601i	0.0184876	+	0.0254460i
$86$	1.19298	−	11.3504i	0.128642	−	1.22395i
$87$	4.29875	−	4.69661i	0.460874	−	0.503529i
$88$	3.55895	+	2.05476i	0.379385	+	0.219038i
$89$	1.33414	+	0.969306i	0.141418	+	0.102746i	0.656245	−	0.754548i	$-0.272144\pi$
$89$	1.33414	+	0.969306i	0.141418	+	0.102746i	−0.514827	+	0.857294i	$0.672144\pi$
$90$	−0.873636	+	7.18259i	−0.0920894	+	0.757112i
$91$	−0.247916	−	0.0805526i	−0.0259886	−	0.00844421i
$92$	−0.973986			−0.101545
$93$	1.29461	+	9.55636i	0.134245	+	0.990948i
$94$	−5.25137			−0.541637
$95$	−17.4226	−	5.66094i	−1.78752	−	0.580800i
$96$	0.717375	−	1.57651i	0.0732168	−	0.160902i
$97$	1.75787	+	1.27717i	0.178485	+	0.129677i	0.673440	−	0.739241i	$-0.264816\pi$
$97$	1.75787	+	1.27717i	0.178485	+	0.129677i	−0.494956	+	0.868918i	$0.664816\pi$
$98$	5.98258	+	3.45405i	0.604332	+	0.348911i
$99$	11.1794	+	5.19758i	1.12357	+	0.522377i
$100$	−0.0853982	+	0.812509i	−0.00853982	+	0.0812509i
$101$	−5.14844	−	7.08622i	−0.512289	−	0.705105i	0.472014	−	0.881591i	$-0.343527\pi$
$101$	−5.14844	−	7.08622i	−0.512289	−	0.705105i	−0.984303	+	0.176486i	$0.943527\pi$
$102$	−0.0831475	−	0.190930i	−0.00823283	−	0.0189049i
$103$	−6.05522	−	6.72501i	−0.596639	−	0.662635i	0.366882	−	0.930267i	$-0.380425\pi$
$103$	−6.05522	−	6.72501i	−0.596639	−	0.662635i	−0.963521	+	0.267633i	$0.913759\pi$
$104$	0.785504	−	0.349729i	0.0770250	−	0.0342938i
$105$	−1.10191	+	0.624256i	−0.107535	+	0.0609212i
$106$	2.30564	−	10.8472i	0.223944	−	1.05357i
$107$	1.66669	−	3.74345i	0.161125	−	0.361893i	−0.814883	−	0.579625i	$-0.803199\pi$
$107$	1.66669	−	3.74345i	0.161125	−	0.361893i	0.976009	+	0.217732i	$0.0698657\pi$
$108$	1.72617	−	4.90106i	0.166101	−	0.471604i
$109$	−0.925478	−	2.84833i	−0.0886447	−	0.272820i	0.896901	−	0.442232i	$-0.145813\pi$
$109$	−0.925478	−	2.84833i	−0.0886447	−	0.272820i	−0.985545	+	0.169412i	$0.945813\pi$
$110$	9.05461	+	4.03137i	0.863323	+	0.384376i
$111$	4.27146	−	0.413742i	0.405429	−	0.0392706i
$112$	0.296540	−	0.0630315i	0.0280204	−	0.00595592i
$113$	6.04634	+	13.5803i	0.568792	+	1.27753i	0.937501	+	0.347983i	$0.113133\pi$
$113$	6.04634	+	13.5803i	0.568792	+	1.27753i	−0.368709	+	0.929545i	$0.620200\pi$
$114$	11.3392	+	6.67064i	1.06201	+	0.624763i
$115$	−2.33623	+	0.245548i	−0.217855	+	0.0228975i
$116$	−2.97389	+	2.16066i	−0.276119	+	0.200612i
$117$	2.25468	−	1.25314i	0.208445	−	0.115853i
$118$	6.70862	+	11.6197i	0.617578	+	1.06968i
$119$	0.0182252	−	0.0315669i	0.00167070	−	0.00289374i
$120$	1.32327	−	3.96231i	0.120798	−	0.361708i
$121$	3.93993	−	4.37573i	0.358175	−	0.397794i
$122$	0.990138	−	3.04733i	0.0896429	−	0.275892i
$123$	12.8363	−	4.05529i	1.15741	−	0.365653i
$124$	0.370698	−	5.55541i	0.0332897	−	0.498891i
$125$		−	10.0888i		−	0.902367i
$126$	0.869452	−	0.266898i	0.0774569	−	0.0237771i
$127$	11.8677	+	10.6857i	1.05308	+	0.948202i	0.998733	−	0.0503202i	$-0.0160242\pi$
$127$	11.8677	+	10.6857i	1.05308	+	0.948202i	0.0543515	+	0.998522i	$0.482691\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−4.26759	+	19.3017i	−0.375740	+	1.69942i
$130$	1.79597	−	1.03690i	0.157517	−	0.0909422i
$131$	−14.2025	−	1.49274i	−1.24088	−	0.130421i	−0.538745	−	0.842469i	$-0.681102\pi$
$131$	−14.2025	−	1.49274i	−1.24088	−	0.130421i	−0.702132	+	0.712047i	$0.747768\pi$
$132$	−5.72417	−	4.23064i	−0.498225	−	0.368230i
$133$	0.240697	+	2.29008i	0.0208711	+	0.198575i
$134$	−1.05186	+	0.947098i	−0.0908667	+	0.0818168i
$135$	2.90485	−	12.1910i	0.250010	−	1.04923i
$136$	0.0249978	+	0.117605i	0.00214354	+	0.0100846i
$137$	−15.3854	−	3.27027i	−1.31446	−	0.279398i	−0.503246	−	0.864143i	$-0.667861\pi$
$137$	−15.3854	−	3.27027i	−1.31446	−	0.279398i	−0.811217	+	0.584746i	$0.801194\pi$
$138$	1.67626	+	0.190022i	0.142692	+	0.0161757i
$139$	11.8588	−	3.85316i	1.00585	−	0.326821i	0.240650	−	0.970612i	$-0.422639\pi$
$139$	11.8588	−	3.85316i	1.00585	−	0.326821i	0.765202	+	0.643791i	$0.222639\pi$
$140$	0.695399	−	0.225949i	0.0587720	−	0.0190962i
$141$	9.03775	+	1.02453i	0.761116	+	0.0862806i
$142$	9.50739	+	2.02086i	0.797843	+	0.169587i
$143$	−0.734663	−	3.45632i	−0.0614356	−	0.289032i
$144$	−1.54219	+	2.57325i	−0.128516	+	0.214438i
$145$	−6.58854	+	5.93235i	−0.547149	+	0.492655i
$146$	−0.326855	−	3.10982i	−0.0270507	−	0.257370i
$147$	−9.62232	−	7.11169i	−0.793635	−	0.586563i
$148$	−2.46410	−	0.258987i	−0.202547	−	0.0212886i
$149$	18.2693	−	10.5478i	1.49668	−	0.864109i	0.496687	−	0.867930i	$-0.334550\pi$
$149$	18.2693	−	10.5478i	1.49668	−	0.864109i	0.999993	+	0.00382108i	$0.00121629\pi$
$150$	0.305491	−	1.38169i	0.0249432	−	0.112815i
$151$	−11.0882	+	15.2616i	−0.902347	+	1.24197i	0.0673664	+	0.997728i	$0.478540\pi$
$151$	−11.0882	+	15.2616i	−0.902347	+	1.24197i	−0.969713	+	0.244246i	$0.921460\pi$
$152$	−5.64456	−	5.08239i	−0.457835	−	0.412236i
$153$	0.105849	+	0.344817i	0.00855742	+	0.0278768i
$154$		−	1.24586i		−	0.100394i
$155$	−0.511386	−	13.4188i	−0.0410755	−	1.07783i
$156$	−1.42011	+	0.448644i	−0.113699	+	0.0359203i
$157$	3.28656	−	10.1150i	0.262296	−	0.807265i	−0.730008	−	0.683439i	$-0.760484\pi$
$157$	3.28656	−	10.1150i	0.262296	−	0.807265i	0.992304	−	0.123826i	$-0.0395165\pi$
$158$	−10.0695	+	11.1834i	−0.801089	+	0.889700i
$159$	−6.08432	+	18.2185i	−0.482518	+	1.44482i
$160$	−1.20592	+	2.08872i	−0.0953365	+	0.165128i
$161$	0.147639	+	0.255719i	0.0116356	+	0.0201534i
$162$	−3.92697	+	8.09808i	−0.308532	+	0.636245i
$163$	8.73131	−	6.34367i	0.683889	−	0.496875i	−0.190756	−	0.981637i	$-0.561094\pi$
$163$	8.73131	−	6.34367i	0.683889	−	0.496875i	0.874646	+	0.484763i	$0.161094\pi$
$164$	−7.72952	+	0.812406i	−0.603574	+	0.0634382i
$165$	−14.7967	−	8.70463i	−1.15192	−	0.677655i
$166$	1.67330	+	3.75830i	0.129873	+	0.291701i
$167$	−18.4855	+	3.92922i	−1.43045	+	0.304052i	−0.857055	−	0.515224i	$-0.827709\pi$
$167$	−18.4855	+	3.92922i	−1.43045	+	0.304052i	−0.573399	+	0.819277i	$0.694375\pi$
$168$	−0.522651	+	0.0506250i	−0.0403234	+	0.00390580i
$169$	11.2007	+	4.98686i	0.861591	+	0.383605i
$170$	0.0896095	+	0.275790i	0.00687273	+	0.0211521i
$171$	−18.2137	−	13.6926i	−1.39284	−	1.04710i
$172$	4.64207	−	10.4263i	0.353955	−	0.794995i
$173$	−4.41924	+	20.7909i	−0.335989	+	1.58070i	0.408301	+	0.912847i	$0.366121\pi$
$173$	−4.41924	+	20.7909i	−0.335989	+	1.58070i	−0.744290	+	0.667856i	$0.767212\pi$
$174$	5.53968	−	3.13835i	0.419962	−	0.237918i
$175$	0.226268	−	0.100741i	0.0171043	−	0.00761530i
$176$	2.74980	+	3.05397i	0.207274	+	0.230201i
$177$	−9.27876	−	21.3066i	−0.697434	−	1.60150i
$178$	0.969306	+	1.33414i	0.0726526	+	0.0999977i
$179$	−0.154133	+	1.46648i	−0.0115205	+	0.109610i	−0.998771	−	0.0495647i	$-0.984217\pi$
$179$	−0.154133	+	1.46648i	−0.0115205	+	0.109610i	0.987250	+	0.159175i	$0.0508833\pi$
$180$	−3.05042	+	6.56108i	−0.227365	+	0.489034i
$181$	−8.11572	−	4.68561i	−0.603236	−	0.348279i	0.167077	−	0.985944i	$-0.446567\pi$
$181$	−8.11572	−	4.68561i	−0.603236	−	0.348279i	−0.770314	+	0.637665i	$0.779900\pi$
$182$	−0.210890	−	0.153220i	−0.0156322	−	0.0113574i
$183$	−2.29858	+	5.05137i	−0.169916	+	0.373408i
$184$	−0.926316	−	0.300978i	−0.0682889	−	0.0221884i
$185$	−5.97575			−0.439346
$186$	−1.72183	+	9.48869i	−0.126250	+	0.695745i
$187$	0.494098			0.0361321
$188$	−4.99435	−	1.62276i	−0.364250	−	0.118352i
$189$	−1.54842	+	0.289711i	−0.112631	+	0.0210734i
$190$	−14.8205	−	10.7677i	−1.07519	−	0.781174i
$191$	16.8170	+	9.70929i	1.21683	+	0.702540i	0.964240	−	0.265032i	$-0.0853826\pi$
$191$	16.8170	+	9.70929i	1.21683	+	0.702540i	0.252595	+	0.967572i	$0.418716\pi$
$192$	1.16943	−	1.27767i	0.0843965	−	0.0922076i
$193$	2.21070	−	21.0334i	0.159130	−	1.51402i	−0.565424	−	0.824800i	$-0.691288\pi$
$193$	2.21070	−	21.0334i	0.159130	−	1.51402i	0.724554	−	0.689218i	$-0.242046\pi$
$194$	1.27717	+	1.75787i	0.0916953	+	0.126208i
$195$	−3.29320	+	1.43415i	−0.235831	+	0.102701i
$196$	4.62242	+	5.13371i	0.330173	+	0.366694i
$197$	5.08696	−	2.26486i	0.362431	−	0.161365i	−0.217439	−	0.976074i	$-0.569770\pi$
$197$	5.08696	−	2.26486i	0.362431	−	0.161365i	0.579870	+	0.814709i	$0.303103\pi$
$198$	9.02607	+	8.39781i	0.641455	+	0.596806i
$199$	−1.18975	+	5.59734i	−0.0843392	+	0.396785i	−0.999986	−	0.00519785i	$-0.998345\pi$
$199$	−1.18975	+	5.59734i	−0.0843392	+	0.396785i	0.915647	+	0.401983i	$0.131679\pi$
$200$	−0.332298	+	0.746353i	−0.0234970	+	0.0527751i
$201$	1.99505	−	1.42477i	0.140720	−	0.100495i
$202$	−2.70670	−	8.33035i	−0.190442	−	0.586122i
$203$	1.01807	+	0.453273i	0.0714543	+	0.0318135i
$204$	−0.0200774	−	0.207279i	−0.00140570	−	0.0145124i
$205$	−18.3355	+	3.89732i	−1.28060	+	0.272201i
$206$	−3.68072	−	8.26703i	−0.256448	−	0.575991i
$207$	−2.84781	−	0.654065i	−0.197937	−	0.0454607i
$208$	0.855131	−	0.0898779i	0.0592927	−	0.00623191i
$209$	−25.2526	+	18.3471i	−1.74676	+	1.26909i
$210$	−1.24088	+	0.253194i	−0.0856291	+	0.0174721i
$211$	0.145338	+	0.251733i	0.0100055	+	0.0173300i	0.870985	−	0.491310i	$-0.163482\pi$
$211$	0.145338	+	0.251733i	0.0100055	+	0.0173300i	−0.860979	+	0.508640i	$0.830148\pi$
$212$	5.54476	−	9.60380i	0.380816	−	0.659592i
$213$	−15.9682	−	5.33282i	−1.09412	−	0.365399i
$214$	2.74191	−	3.04520i	0.187433	−	0.208166i
$215$	8.50609	−	26.1790i	0.580110	−	1.78540i
$216$	3.15619	−	4.12776i	0.214752	−	0.280859i
$217$	−1.51476	+	0.744777i	−0.102828	+	0.0505587i
$218$		−	2.99491i		−	0.202841i
$219$	−0.0441893	+	5.41585i	−0.00298604	+	0.365969i
$220$	7.36569	+	6.63209i	0.496594	+	0.447136i
$221$	0.0607659	−	0.0836370i	0.00408755	−	0.00562604i
$222$	4.19025	+	0.926461i	0.281231	+	0.0621800i
$223$	−18.5103	+	10.6869i	−1.23954	+	0.715648i	−0.969000	−	0.247061i	$-0.920535\pi$
$223$	−18.5103	+	10.6869i	−1.23954	+	0.715648i	−0.270539	+	0.962709i	$0.587202\pi$
$224$	0.301504	+	0.0316894i	0.0201451	+	0.00211733i
$225$	−0.795322	+	2.31833i	−0.0530214	+	0.154555i
$226$	1.55387	+	14.7841i	0.103362	+	0.983421i
$227$	−6.92739	+	6.23745i	−0.459787	+	0.413994i	−0.866202	−	0.499695i	$-0.833446\pi$
$227$	−6.92739	+	6.23745i	−0.459787	+	0.413994i	0.406414	+	0.913689i	$0.366779\pi$
$228$	8.72289	+	9.84817i	0.577688	+	0.652211i
$229$	2.27535	+	10.7047i	0.150359	+	0.707385i	0.987142	+	0.159849i	$0.0511007\pi$
$229$	2.27535	+	10.7047i	0.150359	+	0.707385i	−0.836782	+	0.547536i	$0.815566\pi$
$230$	−2.29777	−	0.488405i	−0.151510	−	0.0322045i
$231$	−0.243064	+	2.14416i	−0.0159924	+	0.141076i
$232$	−3.49602	+	1.13592i	−0.229525	+	0.0745771i
$233$	25.8696	−	8.40554i	1.69477	−	0.550665i	0.707088	−	0.707125i	$-0.250008\pi$
$233$	25.8696	−	8.40554i	1.69477	−	0.550665i	0.987684	+	0.156460i	$0.0500083\pi$
$234$	2.53157	−	0.495070i	0.165494	−	0.0323638i
$235$	−12.3887	−	2.63330i	−0.808150	−	0.171778i
$236$	2.78960	+	13.1240i	0.181588	+	0.854302i
$237$	19.5118	−	17.2823i	1.26743	−	1.12261i
$238$	0.0270879	−	0.0243900i	0.00175585	−	0.00158097i
$239$	0.767125	+	7.29871i	0.0496212	+	0.472114i	0.990911	+	0.134516i	$0.0429479\pi$
$239$	0.767125	+	7.29871i	0.0496212	+	0.472114i	−0.941290	+	0.337598i	$0.890385\pi$
$240$	2.48293	−	3.35947i	0.160272	−	0.216853i
$241$	6.69809	+	0.703998i	0.431462	+	0.0453485i	0.317771	−	0.948168i	$-0.397066\pi$
$241$	6.69809	+	0.703998i	0.431462	+	0.0453485i	0.113691	+	0.993516i	$0.463732\pi$
$242$	5.09927	−	2.94406i	0.327793	−	0.189252i
$243$	8.33833	−	13.1709i	0.534904	−	0.844913i
$244$	1.88335	−	2.59221i	0.120569	−	0.165950i
$245$	12.3817	+	11.1485i	0.791038	+	0.712254i
$246$	13.4612	+	0.109834i	0.858256	+	0.00700274i
$247$			6.53093i			0.415553i
$248$	2.06927	−	5.16896i	0.131399	−	0.328229i
$249$	−2.14657	−	6.79459i	−0.136033	−	0.430590i
$250$	3.11760	−	9.59499i	0.197175	−	0.606841i
$251$	17.6769	−	19.6322i	1.11576	−	1.23918i	0.147544	−	0.989056i	$-0.452863\pi$
$251$	17.6769	−	19.6322i	1.11576	−	1.23918i	0.968215	−	0.250120i	$-0.0804700\pi$
$252$	0.909374	+	0.0148406i	0.0572852	+	0.000934872i
$253$	−2.00131	+	3.46636i	−0.125821	+	0.217928i
$254$	7.98476	+	13.8300i	0.501008	+	0.867772i
$255$	−0.100415	−	0.492124i	−0.00628821	−	0.0308180i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	14.5275	−	1.52691i	0.906203	−	0.0952458i	0.360052	−	0.932932i	$-0.382759\pi$
$257$	14.5275	−	1.52691i	0.906203	−	0.0952458i	0.546151	+	0.837687i	$0.316092\pi$
$258$	−10.0233	+	17.0382i	−0.624021	+	1.06075i
$259$	0.305517	+	0.686203i	0.0189839	+	0.0426386i
$260$	2.02848	−	0.431168i	0.125801	−	0.0267399i
$261$	−10.1462	+	4.32042i	−0.628036	+	0.267427i
$262$	−13.0461	−	5.80849i	−0.805990	−	0.358850i
$263$	5.37029	+	16.5281i	0.331146	+	1.01916i	0.968589	+	0.248666i	$0.0799921\pi$
$263$	5.37029	+	16.5281i	0.331146	+	1.01916i	−0.637443	+	0.770497i	$0.720008\pi$
$264$	−4.13667	−	5.79244i	−0.254594	−	0.356500i
$265$	10.8786	−	24.4338i	0.668270	−	1.50096i
$266$	−0.478757	+	2.25237i	−0.0293545	+	0.138102i
$267$	−1.40792	−	2.48519i	−0.0861632	−	0.152091i
$268$	−1.29305	+	0.575701i	−0.0789854	+	0.0351666i
$269$	1.90640	+	2.11727i	0.116235	+	0.129092i	0.798454	−	0.602056i	$-0.205652\pi$
$269$	1.90640	+	2.11727i	0.116235	+	0.129092i	−0.682219	+	0.731148i	$0.738985\pi$
$270$	6.52991	−	10.6967i	0.397397	−	0.650979i
$271$	13.1066	+	18.0397i	0.796171	+	1.09584i	0.993312	+	0.115460i	$0.0368342\pi$
$271$	13.1066	+	18.0397i	0.796171	+	1.09584i	−0.197141	+	0.980375i	$0.563166\pi$
$272$	−0.0125677	+	0.119574i	−0.000762031	+	0.00725024i
$273$	0.333054	+	0.304840i	0.0201573	+	0.0184498i
$274$	−13.6218	−	7.86456i	−0.822924	−	0.475115i
$275$	2.71620	+	1.97344i	0.163793	+	0.119003i
$276$	1.53549	+	0.698713i	0.0924259	+	0.0420576i
$277$	8.91469	+	2.89656i	0.535632	+	0.174037i	0.564328	−	0.825551i	$-0.309135\pi$
$277$	8.91469	+	2.89656i	0.535632	+	0.174037i	−0.0286958	+	0.999588i	$0.509135\pi$
$278$	12.4691			0.747847
$279$	4.81452	−	15.9944i	0.288238	−	0.957559i
$280$	0.731186			0.0436967
$281$	9.28689	+	3.01749i	0.554010	+	0.180009i	0.572624	−	0.819818i	$-0.305925\pi$
$281$	9.28689	+	3.01749i	0.554010	+	0.180009i	−0.0186144	+	0.999827i	$0.505925\pi$
$282$	8.27881	+	3.76720i	0.492996	+	0.224333i
$283$	1.69039	+	1.22814i	0.100484	+	0.0730055i	0.636892	−	0.770953i	$-0.280220\pi$
$283$	1.69039	+	1.22814i	0.100484	+	0.0730055i	−0.536409	+	0.843958i	$0.680220\pi$
$284$	8.41759	+	4.85990i	0.499492	+	0.288382i
$285$	23.4058	+	21.4230i	1.38644	+	1.26899i
$286$	0.369355	−	3.51418i	0.0218404	−	0.207798i
$287$	1.38496	+	1.90623i	0.0817514	+	0.112521i
$288$	−2.26189	+	1.97075i	−0.133283	+	0.116127i
$289$	−11.3655	−	12.6227i	−0.668562	−	0.742513i
$290$	−8.09928	+	3.60603i	−0.475606	+	0.211753i
$291$	−1.85509	−	3.27452i	−0.108747	−	0.191955i
$292$	0.650129	−	3.05861i	0.0380459	−	0.178992i
$293$	−5.20792	+	11.6972i	−0.304250	+	0.683356i	−0.999368	−	0.0355389i	$-0.988685\pi$
$293$	−5.20792	+	11.6972i	−0.304250	+	0.683356i	0.695118	+	0.718895i	$0.255352\pi$
$294$	−6.95373	−	9.73708i	−0.405550	−	0.567878i
$295$	9.99987	+	30.7764i	0.582215	+	1.79187i
$296$	−2.26346	−	1.00776i	−0.131561	−	0.0585748i
$297$	−13.8957	−	16.2138i	−0.806312	−	0.940822i
$298$	20.6346	−	4.38602i	1.19533	−	0.254075i
$299$	0.340631	+	0.765070i	0.0196992	+	0.0442451i
$300$	0.717505	−	1.21966i	0.0414252	−	0.0704173i
$301$	−3.44106	+	0.361670i	−0.198339	+	0.0208463i
$302$	−15.2616	+	11.0882i	−0.878208	+	0.638056i
$303$	3.03307	+	14.8648i	0.174245	+	0.853963i
$304$	−3.79775	−	6.57790i	−0.217816	−	0.377269i
$305$	3.86396	−	6.69257i	0.221249	−	0.383215i
$306$	−0.00588567	+	0.360650i	−0.000336461	+	0.0206170i
$307$	9.43495	−	10.4786i	0.538481	−	0.598044i	−0.411090	−	0.911595i	$-0.634852\pi$
$307$	9.43495	−	10.4786i	0.538481	−	0.598044i	0.949571	+	0.313551i	$0.101519\pi$
$308$	0.384992	−	1.18488i	0.0219370	−	0.0675151i
$309$	4.72175	+	14.9459i	0.268611	+	0.850242i
$310$	3.66029	−	12.9201i	0.207890	−	0.733812i
$311$		−	0.677244i		−	0.0384030i	−0.999816	−	0.0192015i	$-0.993888\pi$
$311$		−	0.677244i		−	0.0384030i	0.999816	−	0.0192015i	$-0.00611240\pi$
$312$	−1.48924	−	0.0121511i	−0.0843116	−	0.000687921i
$313$	−13.6214	−	12.2648i	−0.769929	−	0.693247i	0.187389	−	0.982286i	$-0.439998\pi$
$313$	−13.6214	−	12.2648i	−0.769929	−	0.693247i	−0.957317	+	0.289039i	$0.906664\pi$
$314$	6.25142	−	8.60434i	0.352788	−	0.485571i
$315$	2.18499	−	0.193662i	0.123110	−	0.0109116i
$316$	−13.0325	+	7.52434i	−0.733138	+	0.423277i
$317$	−15.7906	−	1.65966i	−0.886889	−	0.0932158i	−0.349882	−	0.936794i	$-0.613778\pi$
$317$	−15.7906	−	1.65966i	−0.886889	−	0.0932158i	−0.537007	+	0.843578i	$0.680445\pi$
$318$	−11.4164	+	15.4467i	−0.640198	+	0.866205i
$319$	1.57904	+	15.0235i	0.0884091	+	0.841157i
$320$	−1.79235	+	1.61384i	−0.100195	+	0.0902163i
$321$	−5.31301	+	4.70594i	−0.296544	+	0.262660i
$322$	0.0613918	+	0.288826i	0.00342123	+	0.0160956i
$323$	−0.893272	−	0.189871i	−0.0497030	−	0.0105647i
$324$	−6.23721	+	6.48823i	−0.346512	+	0.360457i
$325$	0.668096	−	0.217077i	0.0370593	−	0.0120413i
$326$	10.2643	−	3.33507i	0.568486	−	0.184712i
$327$	−0.584298	+	5.15432i	−0.0323117	+	0.285035i
$328$	−7.60226	−	1.61591i	−0.419765	−	0.0892237i
$329$	0.331002	+	1.55724i	0.0182487	+	0.0858535i
$330$	−11.3826	−	12.8510i	−0.626594	−	0.707427i
$331$	−3.34709	+	3.01373i	−0.183973	+	0.165650i	−0.755971	−	0.654605i	$-0.772835\pi$
$331$	−3.34709	+	3.01373i	−0.183973	+	0.165650i	0.571998	+	0.820255i	$0.306168\pi$
$332$	0.430027	+	4.09143i	0.0236008	+	0.224547i
$333$	−7.03079	−	2.41197i	−0.385285	−	0.132175i
$334$	−18.7950	−	1.97543i	−1.02842	−	0.108091i
$335$	−2.95640	+	1.70688i	−0.161525	+	0.0932568i
$336$	−0.512715	−	0.113361i	−0.0279709	−	0.00618434i
$337$	−7.85141	+	10.8065i	−0.427694	+	0.588670i	−0.967422	−	0.253169i	$-0.918527\pi$
$337$	−7.85141	+	10.8065i	−0.427694	+	0.588670i	0.539728	+	0.841839i	$0.318527\pi$
$338$	9.11146	+	8.20399i	0.495598	+	0.446238i
$339$	0.210076	−	25.7469i	0.0114098	−	1.39838i
$340$			0.289982i			0.0157265i
$341$	−19.0097	−	12.7343i	−1.02943	−	0.689602i
$342$	−13.0910	−	18.6508i	−0.707880	−	1.00852i
$343$	1.30295	−	4.01008i	0.0703529	−	0.216524i
$344$	7.63676	−	8.48148i	0.411747	−	0.457291i
$345$	3.85923	+	1.28885i	0.207774	+	0.0693892i
$346$	−10.6277	+	18.4077i	−0.571348	+	0.989604i
$347$	1.52237	+	2.63683i	0.0817253	+	0.141552i	0.903991	−	0.427551i	$-0.140624\pi$
$347$	1.52237	+	2.63683i	0.0817253	+	0.141552i	−0.822266	+	0.569104i	$0.807290\pi$
$348$	6.23836	−	1.27290i	0.334411	−	0.0682344i
$349$	2.16241	−	1.57108i	0.115751	−	0.0840981i	−0.528404	−	0.848993i	$-0.677209\pi$
$349$	2.16241	−	1.57108i	0.115751	−	0.0840981i	0.644155	+	0.764895i	$0.277209\pi$
$350$	0.246324	−	0.0258897i	0.0131666	−	0.00138386i
$351$	−4.45349	+	0.358128i	−0.237710	+	0.0191155i
$352$	1.67149	+	3.75423i	0.0890908	+	0.200101i
$353$	15.9127	−	3.38234i	0.846946	−	0.180024i	0.236056	−	0.971740i	$-0.424145\pi$
$353$	15.9127	−	3.38234i	0.846946	−	0.180024i	0.610890	+	0.791716i	$0.290812\pi$
$354$	−2.24052	−	23.1311i	−0.119082	−	1.22940i
$355$	21.4159	+	9.53497i	1.13664	+	0.506064i
$356$	0.509595	+	1.56837i	0.0270085	+	0.0831235i
$357$	−0.0513774	+	0.0366912i	−0.00271918	+	0.00194190i
$358$	−0.599757	+	1.34708i	−0.0316981	+	0.0711952i
$359$	−7.81891	+	36.7851i	−0.412666	+	1.94144i	−0.0860242	+	0.996293i	$0.527416\pi$
$359$	−7.81891	+	36.7851i	−0.412666	+	1.94144i	−0.326642	+	0.945148i	$0.605917\pi$
$360$	−4.92861	+	5.29733i	−0.259760	+	0.279194i
$361$	35.3467	−	15.7374i	1.86035	−	0.828282i
$362$	−6.27057	−	6.96417i	−0.329574	−	0.366029i
$363$	−9.35036	+	4.07197i	−0.490767	+	0.213723i
$364$	−0.153220	−	0.210890i	−0.00803092	−	0.0110536i
$365$	0.788322	−	7.50039i	0.0412627	−	0.392588i
$366$	−3.74704	+	4.09384i	−0.195861	+	0.213988i
$367$	16.5583	+	9.55992i	0.864334	+	0.499024i	0.865461	−	0.500976i	$-0.167025\pi$
$367$	16.5583	+	9.55992i	0.864334	+	0.499024i	−0.00112720	+	0.999999i	$0.500359\pi$
$368$	−0.787971	−	0.572494i	−0.0410758	−	0.0298433i
$369$	−23.1457	−	2.81527i	−1.20492	−	0.146557i
$370$	−5.68327	−	1.84661i	−0.295459	−	0.0960006i
$371$	−3.36195			−0.174544
$372$	−4.56972	+	8.49221i	−0.236929	+	0.440301i
$373$	5.27595			0.273178			0.136589	−	0.990628i	$-0.456386\pi$
$373$	5.27595			0.273178			0.136589	+	0.990628i	$0.456386\pi$
$374$	0.469915	+	0.152685i	0.0242988	+	0.00789514i
$375$	−7.23744	+	15.9050i	−0.373740	+	0.821332i
$376$	−4.24845	−	3.08668i	−0.219097	−	0.159183i
$377$	2.73726	+	1.58036i	0.140976	+	0.0813926i
$378$	−1.56216	−	0.202957i	−0.0803490	−	0.0104390i
$379$	2.12350	−	20.2037i	0.109077	−	1.03779i	−0.793883	−	0.608070i	$-0.791944\pi$
$379$	2.12350	−	20.2037i	0.109077	−	1.03779i	0.902960	−	0.429725i	$-0.141389\pi$
$380$	−10.7677	−	14.8205i	−0.552373	−	0.760277i
$381$	−11.0438	−	25.3596i	−0.565791	−	1.29921i
$382$	12.9936	+	14.4308i	0.664809	+	0.738345i
$383$	26.1814	−	11.6567i	1.33781	−	0.595629i	0.391881	−	0.920016i	$-0.371825\pi$
$383$	26.1814	−	11.6567i	1.33781	−	0.595629i	0.945925	+	0.324387i	$0.105158\pi$
$384$	1.50702	−	0.853758i	0.0769046	−	0.0435682i
$385$	0.624738	−	2.93916i	0.0318396	−	0.149793i
$386$	8.60218	−	19.3208i	0.437840	−	0.983404i
$387$	20.5744	−	27.3678i	1.04586	−	1.39118i
$388$	0.671447	+	2.06650i	0.0340875	+	0.104911i
$389$	−15.9320	−	7.09337i	−0.807783	−	0.359648i	−0.0390654	−	0.999237i	$-0.512438\pi$
$389$	−15.9320	−	7.09337i	−0.807783	−	0.359648i	−0.768717	+	0.639589i	$0.779105\pi$
$390$	−3.57520	+	0.346301i	−0.181037	+	0.0175356i
$391$	−0.114546	+	0.0243475i	−0.00579284	+	0.00123131i
$392$	2.80977	+	6.31086i	0.141915	+	0.318746i
$393$	21.3195	+	12.5418i	1.07542	+	0.632652i
$394$	5.53787	−	0.582054i	0.278994	−	0.0293234i
$395$	−29.3633	+	21.3337i	−1.47743	+	1.07341i
$396$	5.98924	+	10.7760i	0.300970	+	0.541514i
$397$	−2.45723	−	4.25605i	−0.123325	−	0.213605i	0.797752	−	0.602986i	$-0.206022\pi$
$397$	−2.45723	−	4.25605i	−0.123325	−	0.213605i	−0.921077	+	0.389381i	$0.872689\pi$
$398$	−2.86119	+	4.95573i	−0.143419	+	0.248408i
$399$	1.26338	−	3.78299i	0.0632483	−	0.189387i
$400$	−0.546670	+	0.607138i	−0.0273335	+	0.0303569i
$401$	2.28296	−	7.02623i	0.114006	−	0.350873i	−0.877733	−	0.479150i	$-0.840945\pi$
$401$	2.28296	−	7.02623i	0.114006	−	0.350873i	0.991738	+	0.128278i	$0.0409448\pi$
$402$	2.33769	−	0.738529i	0.116593	−	0.0368345i
$403$	−4.49344	+	1.65170i	−0.223834	+	0.0822772i
$404$		−	8.75905i		−	0.435779i
$405$	−13.3250	+	17.1353i	−0.662127	+	0.851461i
$406$	0.828170	+	0.745688i	0.0411014	+	0.0370079i
$407$	−5.98484	+	8.23743i	−0.296658	+	0.408314i
$408$	0.0449580	−	0.203338i	0.00222575	−	0.0100667i
$409$	−17.3470	+	10.0153i	−0.857753	+	0.495224i	−0.863259	−	0.504761i	$-0.831581\pi$
$409$	−17.3470	+	10.0153i	−0.857753	+	0.495224i	0.00550617	+	0.999985i	$0.498247\pi$
$410$	−18.6424	−	1.95939i	−0.920682	−	0.0967676i
$411$	21.9092	+	16.1927i	1.08070	+	0.798727i
$412$	−0.945919	−	8.99982i	−0.0466021	−	0.443389i
$413$	3.02284	−	2.72178i	0.148744	−	0.133930i
$414$	−2.50631	−	1.50208i	−0.123179	−	0.0738230i
$415$	2.06295	+	9.70543i	0.101266	+	0.476421i
$416$	0.841052	+	0.178771i	0.0412360	+	0.00876497i
$417$	−21.4597	−	2.43268i	−1.05088	−	0.119129i
$418$	−29.6862	+	9.64562i	−1.45200	+	0.471783i
$419$	−21.3768	+	6.94574i	−1.04432	+	0.339321i	−0.780438	−	0.625233i	$-0.785004\pi$
$419$	−21.3768	+	6.94574i	−1.04432	+	0.339321i	−0.263885	+	0.964554i	$0.585004\pi$
$420$	−1.25839	−	0.142652i	−0.0614032	−	0.00696071i
$421$	−16.3119	−	3.46720i	−0.794993	−	0.168981i	−0.207527	−	0.978229i	$-0.566541\pi$
$421$	−16.3119	−	3.46720i	−0.794993	−	0.168981i	−0.587467	+	0.809248i	$0.699875\pi$
$422$	0.0604350	+	0.284324i	0.00294193	+	0.0138407i
$423$	−13.5131	−	8.09863i	−0.657029	−	0.393769i
$424$	8.24112	−	7.42034i	0.400224	−	0.360363i
$425$	0.0102677	+	0.0976902i	0.000498054	+	0.00473867i
$426$	−13.5388	−	10.0063i	−0.655955	−	0.484805i
$427$	−0.966066	−	0.101538i	−0.0467512	−	0.00491375i
$428$	3.54873	−	2.04886i	0.171534	−	0.0990354i
$429$	−1.32127	+	5.97593i	−0.0637918	+	0.288521i
$430$	16.1795	−	22.2692i	0.780247	−	1.07392i
$431$	−16.2412	−	14.6236i	−0.782309	−	0.704394i	0.177786	−	0.984069i	$-0.443107\pi$
$431$	−16.2412	−	14.6236i	−0.782309	−	0.704394i	−0.960095	+	0.279675i	$0.909773\pi$
$432$	4.27727	−	2.95042i	0.205790	−	0.141952i
$433$			1.19640i			0.0574954i	0.999587	+	0.0287477i	$0.00915194\pi$
$433$			1.19640i			0.0574954i	−0.999587	+	0.0287477i	$0.990848\pi$
$434$	−1.67077	+	0.240239i	−0.0801994	+	0.0115319i
$435$	14.6426	−	4.62593i	0.702059	−	0.221797i
$436$	0.925478	−	2.84833i	0.0443223	−	0.136410i
$437$	4.95017	−	5.49772i	0.236799	−	0.262992i
$438$	−1.71562	+	5.13712i	−0.0819753	+	0.245461i
$439$	15.0444	−	26.0577i	0.718030	−	1.24366i	−0.243750	−	0.969838i	$-0.578378\pi$
$439$	15.0444	−	26.0577i	0.718030	−	1.24366i	0.961779	−	0.273826i	$-0.0882891\pi$
$440$	4.95575	+	8.58362i	0.236256	+	0.409208i
$441$	10.0679	+	18.1144i	0.479424	+	0.862592i
$442$	0.0836370	−	0.0607659i	0.00397821	−	0.00289034i
$443$	−1.95090	+	0.205048i	−0.0926900	+	0.00974211i	−0.150760	−	0.988570i	$-0.548172\pi$
$443$	−1.95090	+	0.205048i	−0.0926900	+	0.00974211i	0.0580699	+	0.998313i	$0.481505\pi$
$444$	3.69887	+	2.17598i	0.175541	+	0.103267i
$445$	1.61772	+	3.63347i	0.0766875	+	0.172243i
$446$	−20.9067	+	4.44386i	−0.989963	+	0.210423i
$447$	−36.3684	+	3.52271i	−1.72017	+	0.166619i
$448$	0.276955	+	0.123308i	0.0130849	+	0.00582577i
$449$	−0.499839	−	1.53835i	−0.0235889	−	0.0725990i	0.938569	−	0.345091i	$-0.112152\pi$
$449$	−0.499839	−	1.53835i	−0.0235889	−	0.0725990i	−0.962158	+	0.272492i	$0.912152\pi$
$450$	−1.47280	+	1.95909i	−0.0694284	+	0.0923525i
$451$	−12.9910	+	29.1783i	−0.611722	+	1.37395i
$452$	−3.09071	+	14.5407i	−0.145375	+	0.683935i
$453$	28.4290	−	16.1056i	1.33571	−	0.756709i
$454$	−8.51582	+	3.79149i	−0.399667	+	0.177943i
$455$	−0.420685	−	0.467218i	−0.0197220	−	0.0219035i
$456$	5.25271	+	12.0617i	0.245981	+	0.564840i
$457$	−20.5321	−	28.2600i	−0.960452	−	1.32195i	−0.946725	−	0.322044i	$-0.895630\pi$
$457$	−20.5321	−	28.2600i	−0.960452	−	1.32195i	−0.0137275	−	0.999906i	$-0.504370\pi$
$458$	−1.14394	+	10.8839i	−0.0534528	+	0.508570i
$459$	0.0804911	−	0.619541i	0.00375701	−	0.0289177i
$460$	−2.03438	−	1.17455i	−0.0948535	−	0.0547637i
$461$	16.8982	+	12.2773i	0.787029	+	0.571810i	0.907080	−	0.420958i	$-0.138306\pi$
$461$	16.8982	+	12.2773i	0.787029	+	0.571810i	−0.120052	+	0.992768i	$0.538306\pi$
$462$	−0.893750	+	1.96411i	−0.0415810	+	0.0913786i
$463$	0.681116	+	0.221308i	0.0316541	+	0.0102851i	0.324801	−	0.945782i	$-0.394703\pi$
$463$	0.681116	+	0.221308i	0.0316541	+	0.0102851i	−0.293147	+	0.956067i	$0.594703\pi$
$464$	−3.67593			−0.170651
$465$	−8.82013	+	21.5217i	−0.409024	+	0.998046i
$466$	27.2009			1.26006
$467$	28.7101	+	9.32847i	1.32854	+	0.431670i	0.885421	−	0.464791i	$-0.153870\pi$
$467$	28.7101	+	9.32847i	1.32854	+	0.431670i	0.443123	+	0.896461i	$0.353870\pi$
$468$	2.56065	+	0.311458i	0.118366	+	0.0143972i
$469$	0.347153	+	0.252221i	0.0160300	+	0.0116465i
$470$	−10.9686	−	6.33274i	−0.505945	−	0.292107i
$471$	−12.4375	+	13.5887i	−0.573092	+	0.626133i
$472$	−1.40248	+	13.3437i	−0.0645545	+	0.614195i
$473$	−27.5682	−	37.9443i	−1.26759	−	1.74468i
$474$	23.8973	−	10.4070i	1.09764	−	0.478009i
$475$	−4.15223	−	4.61152i	−0.190518	−	0.211591i
$476$	0.0332990	−	0.0148257i	0.00152626	−	0.000679534i
$477$	22.6615	−	24.3568i	1.03760	−	1.11522i
$478$	−1.52585	+	7.17854i	−0.0697905	+	0.328339i
$479$	2.36496	−	5.31180i	0.108058	−	0.242702i	−0.851421	−	0.524483i	$-0.824259\pi$
$479$	2.36496	−	5.31180i	0.108058	−	0.242702i	0.959479	+	0.281781i	$0.0909252\pi$
$480$	3.39954	−	2.42778i	0.155167	−	0.110812i
$481$	0.658331	+	2.02613i	0.0300173	+	0.0923837i
$482$	6.15272	+	2.73937i	0.280249	+	0.124775i
$483$	−0.0493080	−	0.509055i	−0.00224359	−	0.0231628i
$484$	5.75946	−	1.22421i	0.261794	−	0.0556459i
$485$	2.13153	+	4.78749i	0.0967878	+	0.217389i
$486$	12.0003	−	9.94957i	0.544342	−	0.451322i
$487$	15.1685	−	1.59427i	0.687348	−	0.0722432i	0.245585	−	0.969375i	$-0.421020\pi$
$487$	15.1685	−	1.59427i	0.687348	−	0.0722432i	0.441763	+	0.897132i	$0.354353\pi$
$488$	2.59221	−	1.88335i	0.117344	−	0.0852554i
$489$	−18.3158	+	3.73721i	−0.828268	+	0.169003i
$490$	8.33061	+	14.4290i	0.376339	+	0.651838i
$491$	−1.82423	+	3.15966i	−0.0823264	+	0.142593i	−0.904249	−	0.427006i	$-0.859568\pi$
$491$	−1.82423	+	3.15966i	−0.0823264	+	0.142593i	0.821922	+	0.569599i	$0.192902\pi$
$492$	12.7684	+	4.26420i	0.575646	+	0.192245i
$493$	−0.295734	+	0.328445i	−0.0133192	+	0.0147924i
$494$	−2.01817	+	6.21129i	−0.0908017	+	0.279459i
$495$	17.0827	+	24.3377i	0.767808	+	1.09390i
$496$	3.56529	−	4.27653i	0.160086	−	0.192022i
$497$		−	2.94670i		−	0.132178i
$498$	0.0581378	−	7.12537i	0.00260522	−	0.319295i
$499$	−15.8472	−	14.2689i	−0.709417	−	0.638762i	0.233281	−	0.972409i	$-0.425054\pi$
$499$	−15.8472	−	14.2689i	−0.709417	−	0.638762i	−0.942698	+	0.333647i	$0.891721\pi$
$500$	5.93003	−	8.16199i	0.265199	−	0.365015i
$501$	31.9613	+	7.06662i	1.42793	+	0.315713i
$502$	22.8785	−	13.2089i	1.02112	−	0.589541i
$503$	−27.7652	−	2.91824i	−1.23799	−	0.130118i	−0.537181	−	0.843467i	$-0.680511\pi$
$503$	−27.7652	−	2.91824i	−1.23799	−	0.130118i	−0.700809	+	0.713349i	$0.747177\pi$
$504$	0.860280	+	0.295126i	0.0383199	+	0.0131460i
$505$	−2.20821	−	21.0097i	−0.0982641	−	0.934920i
$506$	−2.97452	+	2.67827i	−0.132234	+	0.119064i
$507$	−14.0805	−	15.8969i	−0.625337	−	0.706007i
$508$	3.32025	+	15.6205i	0.147312	+	0.693049i
$509$	8.22359	+	1.74798i	0.364504	+	0.0774778i	0.386523	−	0.922280i	$-0.373676\pi$
$509$	8.22359	+	1.74798i	0.364504	+	0.0774778i	−0.0220186	+	0.999758i	$0.507009\pi$
$510$	0.0565747	−	0.499068i	0.00250517	−	0.0220991i
$511$	−0.901583	+	0.292942i	−0.0398837	+	0.0129590i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	18.8913	+	34.6525i	0.834069	+	1.52995i
$514$	14.2884	+	3.03708i	0.630232	+	0.133960i
$515$	−4.53782	−	21.3488i	−0.199960	−	0.940739i
$516$	−14.7978	+	13.1070i	−0.651437	+	0.577002i
$517$	−16.0375	+	14.4402i	−0.705328	+	0.635080i
$518$	0.0785158	+	0.747028i	0.00344978	+	0.0328225i
$519$	21.8818	−	29.6067i	0.960506	−	1.29959i
$520$	2.06244	+	0.216771i	0.0904441	+	0.00950605i
$521$	17.4940	−	10.1001i	0.766424	−	0.442495i	−0.0651734	−	0.997874i	$-0.520760\pi$
$521$	17.4940	−	10.1001i	0.766424	−	0.442495i	0.831598	+	0.555379i	$0.187427\pi$
$522$	−10.9847	+	0.973605i	−0.480788	+	0.0426135i
$523$	18.3203	−	25.2157i	0.801089	−	1.10261i	−0.191548	−	0.981483i	$-0.561351\pi$
$523$	18.3203	−	25.2157i	0.801089	−	1.10261i	0.992638	−	0.121122i	$-0.0386492\pi$
$524$	−10.6126	−	9.55567i	−0.463615	−	0.417441i
$525$	−0.428982	−	0.00350018i	−0.0187223	−	0.000152760i
$526$			17.3786i			0.757744i
$527$	−0.0952769	−	0.662613i	−0.00415033	−	0.0288639i
$528$	−2.14424	−	6.78724i	−0.0933162	−	0.295377i
$529$	−6.81424	+	20.9721i	−0.296271	+	0.911830i
$530$	17.8967	−	19.8763i	0.777382	−	0.863370i
$531$	−0.656805	+	40.2464i	−0.0285029	+	1.74654i
$532$	−1.15135	+	1.99419i	−0.0499172	+	0.0864591i
$533$	3.34139	+	5.78745i	0.144732	+	0.250682i
$534$	−0.571042	−	2.79863i	−0.0247114	−	0.121109i
$535$	7.99556	−	5.80912i	0.345678	−	0.251150i
$536$	−1.40766	+	0.147951i	−0.0608017	+	0.00639052i
$537$	1.29501	−	2.20134i	0.0558837	−	0.0949950i
$538$	1.15882	+	2.60275i	0.0499602	+	0.112213i
$539$	27.7686	−	5.90239i	1.19608	−	0.254234i
$540$	9.51576	−	8.15529i	0.409493	−	0.350948i
$541$	8.27729	+	3.68529i	0.355868	+	0.158443i	0.576881	−	0.816828i	$-0.304270\pi$
$541$	8.27729	+	3.68529i	0.355868	+	0.158443i	−0.221013	+	0.975271i	$0.570936\pi$
$542$	6.89056	+	21.2070i	0.295975	+	0.910917i
$543$	9.43314	+	13.2089i	0.404815	+	0.566849i
$544$	−0.0489031	+	0.109838i	−0.00209670	+	0.00470927i
$545$	1.50180	−	7.06540i	0.0643299	−	0.302649i
$546$	0.222552	+	0.392840i	0.00952436	+	0.0168120i
$547$	−27.6058	+	12.2909i	−1.18034	+	0.525520i	−0.900639	−	0.434567i	$-0.856901\pi$
$547$	−27.6058	+	12.2909i	−1.18034	+	0.525520i	−0.279699	+	0.960088i	$0.590235\pi$
$548$	−10.5248	−	11.6890i	−0.449598	−	0.499330i
$549$	7.24745	−	6.31457i	0.309314	−	0.269499i
$550$	1.97344	+	2.71620i	0.0841477	+	0.115819i
$551$	2.91849	−	27.7676i	0.124332	−	1.18294i
$552$	1.24443	+	1.13901i	0.0529664	+	0.0484795i
$553$	3.95101	+	2.28112i	0.168014	+	0.0970029i
$554$	7.58329	+	5.50958i	0.322183	+	0.234080i
$555$	9.42081	+	4.28685i	0.399891	+	0.181967i
$556$	11.8588	+	3.85316i	0.502926	+	0.163411i
$557$	−15.6257			−0.662083			−0.331042	−	0.943616i	$-0.607400\pi$
$557$	−15.6257			−0.662083			−0.331042	+	0.943616i	$0.607400\pi$
$558$	9.52142	−	13.7238i	0.403074	−	0.580975i
$559$	−9.81334			−0.415060
$560$	0.695399	+	0.225949i	0.0293860	+	0.00954809i
$561$	−0.778949	−	0.354454i	−0.0328873	−	0.0149651i
$562$	7.89990	+	5.73962i	0.333237	+	0.242111i
$563$	7.97824	+	4.60624i	0.336243	+	0.194130i	0.658609	−	0.752485i	$-0.271145\pi$
$563$	7.97824	+	4.60624i	0.336243	+	0.194130i	−0.322366	+	0.946615i	$0.604478\pi$
$564$	6.70949	+	6.14111i	0.282521	+	0.258588i
$565$	−3.74768	+	35.6568i	−0.157666	+	1.50009i
$566$	1.22814	+	1.69039i	0.0516227	+	0.0710526i
$567$	2.64893	+	0.654068i	0.111245	+	0.0274683i
$568$	6.50381	+	7.22322i	0.272894	+	0.303079i
$569$	−25.6627	+	11.4257i	−1.07583	+	0.478992i	−0.866667	−	0.498888i	$-0.833742\pi$
$569$	−25.6627	+	11.4257i	−1.07583	+	0.478992i	−0.209168	+	0.977880i	$0.567075\pi$
$570$	15.6401	+	27.6073i	0.655093	+	1.15634i
$571$	−0.282296	+	1.32810i	−0.0118137	+	0.0555793i	−0.983660	−	0.180038i	$-0.942378\pi$
$571$	−0.282296	+	1.32810i	−0.0118137	+	0.0555793i	0.971846	+	0.235617i	$0.0757112\pi$
$572$	1.43722	−	3.22804i	0.0600931	−	0.134971i
$573$	−19.5469	−	27.3709i	−0.816583	−	1.14343i
$574$	0.728115	+	2.24091i	0.0303909	+	0.0935336i
$575$	−0.726937	−	0.323653i	−0.0303154	−	0.0134973i
$576$	−2.76018	+	1.17533i	−0.115008	+	0.0489720i
$577$	−31.7388	+	6.74629i	−1.32130	+	0.280852i	−0.813974	−	0.580901i	$-0.802700\pi$
$577$	−31.7388	+	6.74629i	−1.32130	+	0.280852i	−0.507329	+	0.861752i	$0.669367\pi$
$578$	−6.90864	−	15.5171i	−0.287362	−	0.645425i
$579$	−18.5740	+	31.5734i	−0.771910	+	1.31215i
$580$	−8.81719	+	0.926724i	−0.366114	+	0.0384801i
$581$	1.00902	−	0.733093i	0.0418610	−	0.0304138i
$582$	−0.752411	−	3.68750i	−0.0311884	−	0.152852i
$583$	−22.7863	−	39.4670i	−0.943711	−	1.63456i
$584$	1.56347	−	2.70801i	0.0646970	−	0.112058i
$585$	6.22058	+	0.101517i	0.257189	+	0.00419723i
$586$	−8.56765	+	9.51534i	−0.353926	+	0.393075i
$587$	5.81480	−	17.8961i	0.240003	−	0.738652i	−0.756416	−	0.654091i	$-0.773051\pi$
$587$	5.81480	−	17.8961i	0.240003	−	0.738652i	0.996418	−	0.0845608i	$-0.0269487\pi$
$588$	−3.60447	−	11.4093i	−0.148646	−	0.470513i
$589$	29.4738	+	30.3272i	1.21445	+	1.24961i
$590$			32.3603i			1.33225i
$591$	−9.64438	−	0.0786911i	−0.396717	−	0.00323692i
$592$	−1.84127	−	1.65788i	−0.0756756	−	0.0681386i
$593$	−12.2991	+	16.9282i	−0.505062	+	0.695159i	−0.983077	−	0.183193i	$-0.941357\pi$
$593$	−12.2991	+	16.9282i	−0.505062	+	0.695159i	0.478014	+	0.878352i	$0.341357\pi$
$594$	−8.20528	−	19.7143i	−0.336667	−	0.808887i
$595$	0.0761345	−	0.0439562i	0.00312121	−	0.00180203i
$596$	20.9800	+	2.20509i	0.859375	+	0.0903239i
$597$	5.89104	−	7.97074i	0.241104	−	0.326221i
$598$	0.0875398	+	0.832886i	0.00357977	+	0.0340592i
$599$	5.17907	−	4.66326i	0.211611	−	0.190536i	−0.556508	−	0.830842i	$-0.687859\pi$
$599$	5.17907	−	4.66326i	0.211611	−	0.190536i	0.768120	+	0.640306i	$0.221193\pi$
$600$	1.05928	−	0.938248i	0.0432451	−	0.0383038i
$601$	−8.59495	−	40.4360i	−0.350595	−	1.64942i	−0.701250	−	0.712916i	$-0.747374\pi$
$601$	−8.59495	−	40.4360i	−0.350595	−	1.64942i	0.350654	−	0.936505i	$-0.385959\pi$
$602$	−3.38440	−	0.719377i	−0.137938	−	0.0293196i
$603$	−4.16731	+	0.814953i	−0.169706	+	0.0331874i
$604$	−17.9411	+	5.82943i	−0.730014	+	0.237196i
$605$	13.5062	−	4.38842i	0.549104	−	0.178415i
$606$	−1.70886	+	15.0746i	−0.0694179	+	0.612363i
$607$	−37.2280	−	7.91305i	−1.51104	−	0.321181i	−0.623465	−	0.781851i	$-0.714276\pi$
$607$	−37.2280	−	7.91305i	−1.51104	−	0.321181i	−0.887571	+	0.460671i	$0.847609\pi$
$608$	−1.57920	−	7.42953i	−0.0640448	−	0.301307i
$609$	−1.27982	−	1.44492i	−0.0518610	−	0.0585512i
$610$	5.74296	−	5.17098i	0.232526	−	0.209367i
$611$	0.471982	+	4.49061i	0.0190943	+	0.181671i
$612$	−0.117045	+	0.341180i	−0.00473125	+	0.0137914i
$613$	−27.9110	−	2.93356i	−1.12731	−	0.118485i	−0.477538	−	0.878611i	$-0.658471\pi$
$613$	−27.9110	−	2.93356i	−1.12731	−	0.118485i	−0.649776	+	0.760126i	$0.725137\pi$
$614$	12.2112	−	7.05016i	0.492805	−	0.284521i
$615$	31.7018	+	7.00925i	1.27834	+	0.282640i
$616$	0.732299	−	1.00792i	0.0295052	−	0.0406104i
$617$	13.5388	+	12.1904i	0.545051	+	0.490767i	0.895039	−	0.445988i	$-0.147148\pi$
$617$	13.5388	+	12.1904i	0.545051	+	0.490767i	−0.349988	+	0.936754i	$0.613814\pi$
$618$	−0.127884	+	15.6735i	−0.00514425	+	0.630480i
$619$		−	9.89872i		−	0.397863i	−0.980013	−	0.198932i	$-0.936253\pi$
$619$		−	9.89872i		−	0.397863i	0.980013	−	0.198932i	$-0.0637472\pi$
$620$	7.47367	−	11.1566i	0.300150	−	0.448062i
$621$	4.02038	+	3.07409i	0.161332	+	0.123359i
$622$	0.209280	−	0.644097i	0.00839136	−	0.0258260i
$623$	0.334528	−	0.371531i	0.0134026	−	0.0148851i
$624$	−1.41260	−	0.471757i	−0.0565491	−	0.0188854i
$625$	14.2087	−	24.6102i	0.568349	−	0.984410i
$626$	−9.16472	−	15.8738i	−0.366296	−	0.634443i
$627$	52.9725	−	10.8087i	2.11552	−	0.431658i
$628$	8.60434	−	6.25142i	0.343350	−	0.249459i
$629$	−0.296265	+	0.0311387i	−0.0118129	+	0.00124158i
$630$	2.13790	+	0.491017i	0.0851758	+	0.0195626i
$631$	−6.38349	−	14.3376i	−0.254123	−	0.570769i	0.740764	−	0.671765i	$-0.234464\pi$
$631$	−6.38349	−	14.3376i	−0.254123	−	0.570769i	−0.994887	+	0.100996i	$0.967797\pi$
$632$	−14.7198	+	3.12880i	−0.585524	+	0.124457i
$633$	−0.0485395	−	0.501121i	−0.00192927	−	0.0199178i
$634$	−14.5049	−	6.45800i	−0.576063	−	0.256480i
$635$	11.9021	+	36.6308i	0.472320	+	1.45365i
$636$	−15.6309	+	11.1628i	−0.619805	+	0.442633i
$637$	2.41596	−	5.42633i	0.0957238	−	0.214999i
$638$	−3.14077	+	14.7762i	−0.124344	+	0.584995i
$639$	21.3484	+	19.8624i	0.844529	+	0.785746i
$640$	−2.20333	+	0.980985i	−0.0870942	+	0.0387768i
$641$	−26.0981	−	28.9849i	−1.03081	−	1.14483i	−0.989330	−	0.145695i	$-0.953458\pi$
$641$	−26.0981	−	28.9849i	−1.03081	−	1.14483i	−0.0414834	−	0.999139i	$-0.513208\pi$
$642$	−6.50719	+	2.83380i	−0.256818	+	0.111841i
$643$	10.4949	+	14.4449i	0.413877	+	0.569653i	0.964159	−	0.265326i	$-0.0854797\pi$
$643$	10.4949	+	14.4449i	0.413877	+	0.569653i	−0.550282	+	0.834979i	$0.685480\pi$
$644$	−0.0308650	+	0.293661i	−0.00121625	+	0.0115719i
$645$	−32.1901	+	35.1694i	−1.26748	+	1.38479i
$646$	−0.790879	−	0.456614i	−0.0311167	−	0.0179653i
$647$	2.92824	+	2.12749i	0.115121	+	0.0836402i	0.643856	−	0.765147i	$-0.277334\pi$
$647$	2.92824	+	2.12749i	0.115121	+	0.0836402i	−0.528735	+	0.848787i	$0.677334\pi$
$648$	−7.93692	+	4.24327i	−0.311791	+	0.166692i
$649$	52.4397	+	17.0387i	2.05844	+	0.668827i
$650$	0.702477			0.0275534
$651$	2.92231	−	0.0874969i	0.114534	−	0.00342927i
$652$	10.7925			0.422667
$653$	−26.0262	−	8.45641i	−1.01848	−	0.330925i	−0.248255	−	0.968695i	$-0.579857\pi$
$653$	−26.0262	−	8.45641i	−1.01848	−	0.330925i	−0.770227	+	0.637770i	$0.779857\pi$
$654$	−2.14847	+	4.72149i	−0.0840119	+	0.184625i
$655$	−27.8648	−	20.2450i	−1.08877	−	0.791037i
$656$	−6.73084	−	3.88605i	−0.262795	−	0.151725i
$657$	3.95486	−	8.50642i	0.154294	−	0.331867i
$658$	−0.166412	+	1.58331i	−0.00648743	+	0.0617238i
$659$	7.26900	+	10.0049i	0.283160	+	0.389737i	0.926777	−	0.375611i	$-0.122567\pi$
$659$	7.26900	+	10.0049i	0.283160	+	0.389737i	−0.643617	+	0.765348i	$0.722567\pi$
$660$	−6.85435	−	15.7395i	−0.266805	−	0.612659i
$661$	4.88937	+	5.43019i	0.190174	+	0.211210i	0.830690	−	0.556735i	$-0.187946\pi$
$661$	4.88937	+	5.43019i	0.190174	+	0.211210i	−0.640516	+	0.767945i	$0.721279\pi$
$662$	−4.11457	+	1.83192i	−0.159917	+	0.0711997i
$663$	−0.155797	+	0.0882624i	−0.00605065	+	0.00342783i
$664$	−0.855343	+	4.02407i	−0.0331937	+	0.156164i
$665$	−2.25891	+	5.07359i	−0.0875966	+	0.196745i
$666$	−5.94134	−	4.46655i	−0.230222	−	0.173075i
$667$	−1.10637	−	3.40507i	−0.0428390	−	0.131845i
$668$	−17.2647	−	7.68672i	−0.667990	−	0.297408i
$669$	36.8481	−	3.56917i	1.42463	−	0.137992i
$670$	−3.33916	+	0.709760i	−0.129003	+	0.0274204i
$671$	−5.35571	−	12.0291i	−0.206755	−	0.464379i
$672$	−0.452590	−	0.266250i	−0.0174590	−	0.0102708i
$673$	24.2281	−	2.54647i	0.933924	−	0.0981594i	0.374672	−	0.927157i	$-0.377755\pi$
$673$	24.2281	−	2.54647i	0.933924	−	0.0981594i	0.559252	+	0.828998i	$0.311089\pi$
$674$	−10.8065	+	7.85141i	−0.416252	+	0.302425i
$675$	2.91694	−	3.08431i	0.112273	−	0.118715i
$676$	6.13034	+	10.6181i	0.235782	+	0.408387i
$677$	−9.27463	+	16.0641i	−0.356453	+	0.617395i	−0.987366	−	0.158459i	$-0.949347\pi$
$677$	−9.27463	+	16.0641i	−0.356453	+	0.617395i	0.630912	+	0.775854i	$0.282681\pi$
$678$	8.15604	−	24.4219i	0.313231	−	0.937917i
$679$	0.440777	−	0.489533i	0.0169155	−	0.0187865i
$680$	−0.0896095	+	0.275790i	−0.00343637	+	0.0105760i
$681$	15.3957	−	4.86385i	0.589964	−	0.186383i
$682$	−14.1442	−	17.9854i	−0.541609	−	0.688696i
$683$			10.9042i			0.417238i	0.977997	+	0.208619i	$0.0668969\pi$
$683$			10.9042i			0.417238i	−0.977997	+	0.208619i	$0.933103\pi$
$684$	−6.68687	−	21.7833i	−0.255679	−	0.832905i
$685$	−28.1920	−	25.3842i	−1.07716	−	0.969882i
$686$	2.47836	−	3.41118i	0.0946244	−	0.130239i
$687$	4.09216	−	18.5083i	0.156126	−	0.706134i
$688$	9.88392	−	5.70648i	0.376821	−	0.217558i
$689$	−9.48299	−	0.996703i	−0.361273	−	0.0379713i
$690$	3.27207	+	2.41834i	0.124566	+	0.0920644i
$691$	1.31068	+	12.4703i	0.0498605	+	0.474391i	0.990752	+	0.135683i	$0.0433230\pi$
$691$	1.31068	+	12.4703i	0.0498605	+	0.474391i	−0.940892	+	0.338707i	$0.890010\pi$
$692$	−15.7958	+	14.2226i	−0.600467	+	0.540663i
$693$	1.92136	−	3.20592i	0.0729864	−	0.121783i
$694$	0.633039	+	2.97821i	0.0240298	+	0.113051i
$695$	29.4163	+	6.25264i	1.11583	+	0.237176i
$696$	6.32638	+	0.717163i	0.239801	+	0.0271840i
$697$	−0.888725	+	0.288764i	−0.0336629	+	0.0109377i
$698$	2.54206	−	0.825967i	0.0962186	−	0.0312633i
$699$	−46.8135	−	5.30681i	−1.77065	−	0.200722i
$700$	0.242269	+	0.0514958i	0.00915690	+	0.00194636i
$701$	0.398322	+	1.87396i	0.0150444	+	0.0707784i	0.985029	−	0.172386i	$-0.0551478\pi$
$701$	0.398322	+	1.87396i	0.0150444	+	0.0707784i	−0.969985	+	0.243165i	$0.921814\pi$
$702$	−4.34619	−	1.03560i	−0.164036	−	0.0390864i
$703$	13.9854	−	12.5925i	0.527468	−	0.474934i
$704$	0.429561	+	4.08700i	0.0161897	+	0.154035i
$705$	17.6418	+	13.0388i	0.664429	+	0.491068i
$706$	16.1790	+	1.70049i	0.608906	+	0.0639986i
$707$	−2.29968	+	1.32772i	−0.0864882	+	0.0499340i
$708$	5.01704	−	22.6913i	0.188552	−	0.852792i
$709$	−25.1863	+	34.6660i	−0.945891	+	1.30191i	0.00743720	+	0.999972i	$0.497633\pi$
$709$	−25.1863	+	34.6660i	−0.945891	+	1.30191i	−0.953328	+	0.301935i	$0.902367\pi$
$710$	17.4213	+	15.6862i	0.653808	+	0.588692i
$711$	−43.1584	+	13.2484i	−1.61857	+	0.496855i
$712$			1.64908i			0.0618020i
$713$	5.03449	+	2.01544i	0.188543	+	0.0754788i
$714$	−0.0602010	+	0.0190189i	−0.00225297	+	0.000711764i
$715$	2.63354	−	8.10521i	0.0984889	−	0.303118i
$716$	−0.986672	+	1.09581i	−0.0368737	+	0.0409523i
$717$	4.02653	−	12.0568i	0.150374	−	0.450269i
$718$	−18.8034	+	32.5685i	−0.701738	+	1.21545i
$719$	−20.9330	−	36.2569i	−0.780668	−	1.35216i	−0.931553	−	0.363605i	$-0.881546\pi$
$719$	−20.9330	−	36.2569i	−0.780668	−	1.35216i	0.150886	−	0.988551i	$-0.451787\pi$
$720$	−6.32435	+	3.51503i	−0.235695	+	0.130998i
$721$	−2.21950	+	1.61256i	−0.0826586	+	0.0600550i
$722$	38.4798	−	4.04439i	1.43207	−	0.150517i
$723$	−10.0546	−	5.91490i	−0.373933	−	0.219978i
$724$	−3.81162	−	8.56104i	−0.141658	−	0.318168i
$725$	−2.93755	+	0.624396i	−0.109098	+	0.0231895i
$726$	−10.1510	+	0.983248i	−0.376740	+	0.0364918i
$727$	1.23330	+	0.549102i	0.0457407	+	0.0203651i	0.429479	−	0.903077i	$-0.358697\pi$
$727$	1.23330	+	0.549102i	0.0457407	+	0.0203651i	−0.383739	+	0.923442i	$0.625364\pi$
$728$	−0.0805526	−	0.247916i	−0.00298548	−	0.00918836i
$729$	−22.5939	+	14.7823i	−0.836811	+	0.547492i
$730$	3.06749	−	6.88969i	0.113533	−	0.254999i
$731$	0.285299	−	1.34223i	0.0105522	−	0.0496440i
$732$	−4.82871	+	2.73557i	−0.178474	+	0.101110i
$733$	15.0626	−	6.70632i	0.556351	−	0.247704i	−0.109246	−	0.994015i	$-0.534844\pi$
$733$	15.0626	−	6.70632i	0.556351	−	0.247704i	0.665597	+	0.746311i	$0.268177\pi$
$734$	12.7937	+	14.2088i	0.472223	+	0.524456i
$735$	−11.5222	−	26.4581i	−0.425001	−	0.975921i
$736$	−0.572494	−	0.787971i	−0.0211024	−	0.0290450i
$737$	−0.608008	+	5.78481i	−0.0223963	+	0.213086i
$738$	−21.1429	−	9.82990i	−0.778281	−	0.361844i
$739$	−21.3749	−	12.3408i	−0.786288	−	0.453964i	0.0523659	−	0.998628i	$-0.483324\pi$
$739$	−21.3749	−	12.3408i	−0.786288	−	0.453964i	−0.838654	+	0.544664i	$0.816657\pi$
$740$	−4.83448	−	3.51246i	−0.177719	−	0.129120i
$741$	4.68513	−	10.2961i	0.172113	−	0.378235i
$742$	−3.19741	−	1.03890i	−0.117381	−	0.0381392i
$743$	−37.0361			−1.35872			−0.679360	−	0.733805i	$-0.737743\pi$
$743$	−37.0361			−1.35872			−0.679360	+	0.733805i	$0.737743\pi$
$744$	−6.97030	+	6.66445i	−0.255544	+	0.244331i
$745$	50.8792			1.86407
$746$	5.01772	+	1.63036i	0.183712	+	0.0596916i
$747$	−1.49019	+	12.2516i	−0.0545234	+	0.448263i
$748$	0.399734	+	0.290424i	0.0146157	+	0.0106189i
$749$	−1.07585	−	0.621143i	−0.0393107	−	0.0226961i
$750$	−11.7981	+	12.8901i	−0.430807	+	0.470679i
$751$	−1.81270	+	17.2467i	−0.0661465	+	0.629342i	0.910354	+	0.413829i	$0.135809\pi$
$751$	−1.81270	+	17.2467i	−0.0661465	+	0.629342i	−0.976501	+	0.215513i	$0.930858\pi$
$752$	−3.08668	−	4.24845i	−0.112559	−	0.154925i
$753$	−41.9515	+	18.2693i	−1.52880	+	0.665772i
$754$	2.11493	+	2.34887i	0.0770213	+	0.0855408i
$755$	−41.5645	+	18.5057i	−1.51269	+	0.673492i
$756$	−1.42299	−	0.675758i	−0.0517536	−	0.0245771i
$757$	−9.19145	+	43.2424i	−0.334069	+	1.57167i	0.415404	+	0.909637i	$0.363640\pi$
$757$	−9.19145	+	43.2424i	−0.334069	+	1.57167i	−0.749473	+	0.662034i	$0.769693\pi$
$758$	8.26285	−	18.5587i	0.300120	−	0.674081i
$759$	5.64175	−	4.02906i	0.204783	−	0.146246i
$760$	−5.66094	−	17.4226i	−0.205344	−	0.631983i
$761$	26.5671	+	11.8284i	0.963057	+	0.428781i	0.827175	−	0.561944i	$-0.189946\pi$
$761$	26.5671	+	11.8284i	0.963057	+	0.428781i	0.135882	+	0.990725i	$0.456613\pi$
$762$	−2.66672	−	27.5312i	−0.0966051	−	0.997349i
$763$	−0.888110	+	0.188774i	−0.0321518	+	0.00683407i
$764$	7.89825	+	17.7398i	0.285749	+	0.641802i
$765$	−0.194733	+	0.847872i	−0.00704059	+	0.0306549i
$766$	28.5021	−	2.99569i	1.02982	−	0.108239i
$767$	9.33338	−	6.78110i	0.337009	−	0.244851i
$768$	1.69708	−	0.346279i	0.0612382	−	0.0124953i
$769$	−3.47340	−	6.01611i	−0.125254	−	0.216946i	0.796578	−	0.604536i	$-0.206641\pi$
$769$	−3.47340	−	6.01611i	−0.125254	−	0.216946i	−0.921832	+	0.387589i	$0.873308\pi$
$770$	1.50241	−	2.60225i	0.0541431	−	0.0937787i
$771$	−23.9981	−	8.01452i	−0.864272	−	0.288636i
$772$	14.1516	−	15.7170i	0.509328	−	0.565666i
$773$	−15.9073	+	48.9578i	−0.572147	+	1.76089i	0.0735457	+	0.997292i	$0.476569\pi$
$773$	−15.9073	+	48.9578i	−0.572147	+	1.76089i	−0.645693	+	0.763597i	$0.723431\pi$
$774$	28.0245	−	19.6704i	1.00732	−	0.707040i
$775$	2.12272	−	4.02311i	0.0762504	−	0.144515i
$776$			2.17285i			0.0780007i
$777$	0.0106150	−	1.30097i	0.000380811	−	0.0466722i
$778$	−12.9602	−	11.6694i	−0.464647	−	0.418370i
$779$	34.6988	−	47.7587i	1.24321	−	1.71113i
$780$	−3.50723	−	0.775446i	−0.125579	−	0.0277654i
$781$	34.5922	−	19.9718i	1.23781	−	0.714648i
$782$	−0.116463	−	0.0122408i	−0.00416472	−	0.000437730i
$783$	19.0950	+	0.467486i	0.682398	+	0.0167066i
$784$	0.722092	+	6.87025i	0.0257890	+	0.245366i
$785$	19.0626	−	17.1640i	0.680373	−	0.612611i
$786$	16.4004	+	18.5161i	0.584982	+	0.660446i
$787$	−2.98928	−	14.0634i	−0.106556	−	0.501307i	−0.998765	−	0.0496843i	$-0.984178\pi$
$787$	−2.98928	−	14.0634i	−0.106556	−	0.501307i	0.892209	−	0.451623i	$-0.149155\pi$
$788$	5.44669	+	1.15773i	0.194030	+	0.0412424i
$789$	3.39052	−	29.9091i	0.120706	−	1.06479i
$790$	−34.5186	+	11.2158i	−1.22812	+	0.399040i
$791$	4.28612	−	1.39265i	0.152397	−	0.0495168i
$792$	2.36613	+	12.0994i	0.0840769	+	0.429932i
$793$	−2.69486	−	0.572810i	−0.0956972	−	0.0203411i
$794$	−1.02178	−	4.80708i	−0.0362615	−	0.170597i
$795$	−34.6785	+	30.7160i	−1.22992	+	1.08939i
$796$	−4.25256	+	3.82902i	−0.150728	+	0.135716i
$797$	2.91410	+	27.7258i	0.103223	+	0.982099i	0.916449	+	0.400151i	$0.131042\pi$
$797$	2.91410	+	27.7258i	0.103223	+	0.982099i	−0.813226	+	0.581948i	$0.802291\pi$
$798$	2.37056	−	3.20743i	0.0839169	−	0.113542i
$799$	−0.627927	−	0.0659978i	−0.0222145	−	0.00233483i
$800$	−0.707530	+	0.408492i	−0.0250149	+	0.0144424i
$801$	0.436775	+	4.92793i	0.0154327	+	0.174120i
$802$	4.34245	−	5.97686i	0.153337	−	0.211050i
$803$	−9.54959	−	8.59849i	−0.336998	−	0.303434i
$804$	2.45149	+	0.0200024i	0.0864574	+	0.000705429i
$805$			0.712165i			0.0251005i
$806$	−4.78392	+	0.182313i	−0.168506	+	0.00642171i
$807$	−1.48657	−	4.70549i	−0.0523298	−	0.165641i
$808$	2.70670	−	8.33035i	0.0952212	−	0.293061i
$809$	−1.33535	+	1.48305i	−0.0469483	+	0.0521414i	−0.766162	−	0.642648i	$-0.777836\pi$
$809$	−1.33535	+	1.48305i	−0.0469483	+	0.0521414i	0.719213	+	0.694789i	$0.244502\pi$
$810$	−17.9680	+	12.1790i	−0.631330	+	0.427926i
$811$	18.8692	−	32.6824i	0.662588	−	1.14764i	−0.317346	−	0.948310i	$-0.602792\pi$
$811$	18.8692	−	32.6824i	0.662588	−	1.14764i	0.979933	−	0.199325i	$-0.0638751\pi$
$812$	0.557206	+	0.965110i	0.0195541	+	0.0338687i
$813$	−7.72143	−	37.8421i	−0.270802	−	1.32718i
$814$	−8.23743	+	5.98484i	−0.288722	+	0.209769i
$815$	25.8872	−	2.72086i	0.906790	−	0.0953074i
$816$	0.105593	−	0.179494i	0.00369648	−	0.00628353i
$817$	35.2589	+	79.1928i	1.23355	+	2.77060i
$818$	−19.5929	+	4.16459i	−0.685048	+	0.145611i
$819$	−0.306377	−	0.719507i	−0.0107057	−	0.0251416i
$820$	−17.1245	−	7.62431i	−0.598013	−	0.266253i
$821$	−6.83930	−	21.0492i	−0.238693	−	0.734622i	−0.996610	−	0.0822708i	$-0.973783\pi$
$821$	−6.83930	−	21.0492i	−0.238693	−	0.734622i	0.757917	−	0.652351i	$-0.226217\pi$
$822$	15.8330	+	22.1705i	0.552241	+	0.773284i
$823$	5.39239	−	12.1115i	0.187967	−	0.422181i	−0.794839	−	0.606820i	$-0.792445\pi$
$823$	5.39239	−	12.1115i	0.187967	−	0.422181i	0.982806	+	0.184639i	$0.0591116\pi$
$824$	1.88147	−	8.85164i	0.0655442	−	0.308361i
$825$	−2.86642	−	5.05967i	−0.0997959	−	0.176155i
$826$	3.71597	−	1.65446i	0.129295	−	0.0575659i
$827$	−7.11844	−	7.90583i	−0.247532	−	0.274913i	0.606556	−	0.795041i	$-0.292551\pi$
$827$	−7.11844	−	7.90583i	−0.247532	−	0.274913i	−0.854088	+	0.520128i	$0.825884\pi$
$828$	−1.91948	−	2.20305i	−0.0667065	−	0.0765613i
$829$	10.9231	+	15.0344i	0.379376	+	0.522166i	0.955419	−	0.295253i	$-0.0954039\pi$
$829$	10.9231	+	15.0344i	0.379376	+	0.522166i	−0.576043	+	0.817419i	$0.695404\pi$
$830$	−1.03716	+	9.86790i	−0.0360003	+	0.342520i
$831$	−11.9762	−	10.9616i	−0.415448	−	0.380254i
$832$	0.744645	+	0.429921i	0.0258159	+	0.0149048i
$833$	0.671952	+	0.488202i	0.0232818	+	0.0169152i
$834$	−19.6576	−	8.94502i	−0.680688	−	0.309741i
$835$	−43.3494	−	14.0851i	−1.50017	−	0.487434i
$836$	−31.2139			−1.07955
$837$	−19.0641	+	21.7614i	−0.658952	+	0.752185i
$838$	−22.4769			−0.776451
$839$	21.3756	+	6.94537i	0.737969	+	0.239781i	0.653796	−	0.756670i	$-0.273175\pi$
$839$	21.3756	+	6.94537i	0.737969	+	0.239781i	0.0841727	+	0.996451i	$0.473175\pi$
$840$	−1.15272	−	0.524535i	−0.0397726	−	0.0180982i
$841$	12.5297	+	9.10335i	0.432058	+	0.313909i
$842$	−14.4421	−	8.33816i	−0.497708	−	0.287352i
$843$	−12.4762	−	11.4193i	−0.429702	−	0.393301i
$844$	−0.0303839	+	0.289084i	−0.00104586	+	0.00995068i
$845$	17.3813	+	23.9233i	0.597934	+	0.822986i
$846$	−10.3491	−	11.8780i	−0.355810	−	0.408375i
$847$	−1.19445	−	1.32657i	−0.0410417	−	0.0455814i
$848$	10.1308	−	4.51051i	0.347892	−	0.154892i
$849$	−1.78388	−	3.14882i	−0.0612225	−	0.108067i
$850$	−0.0204228	+	0.0960818i	−0.000700497	+	0.00329558i
$851$	0.981543	−	2.20458i	0.0336469	−	0.0755721i
$852$	−9.78402	−	13.7002i	−0.335195	−	0.469362i
$853$	10.3901	+	31.9775i	0.355751	+	1.09489i	0.955573	+	0.294756i	$0.0952384\pi$
$853$	10.3901	+	31.9775i	0.355751	+	1.09489i	−0.599821	+	0.800134i	$0.704762\pi$
$854$	−0.887406	−	0.395099i	−0.0303664	−	0.0135200i
$855$	−21.5310	−	50.5643i	−0.736345	−	1.72926i
$856$	4.00818	−	0.851964i	0.136997	−	0.0291195i
$857$	17.7793	+	39.9329i	0.607328	+	1.36408i	0.911435	+	0.411444i	$0.134975\pi$
$857$	17.7793	+	39.9329i	0.607328	+	1.36408i	−0.304107	+	0.952638i	$0.598358\pi$
$858$	−3.10327	+	5.27516i	−0.105944	+	0.180091i
$859$	23.2767	−	2.44648i	0.794191	−	0.0834728i	0.301261	−	0.953542i	$-0.402592\pi$
$859$	23.2767	−	2.44648i	0.794191	−	0.0834728i	0.492930	+	0.870069i	$0.335926\pi$
$860$	22.2692	−	16.1795i	0.759374	−	0.551718i
$861$	−0.815912	−	3.99872i	−0.0278062	−	0.136276i
$862$	−10.9273	−	18.9267i	−0.372186	−	0.644645i
$863$	−7.55736	+	13.0897i	−0.257256	+	0.445580i	−0.965506	−	0.260382i	$-0.916152\pi$
$863$	−7.55736	+	13.0897i	−0.257256	+	0.445580i	0.708250	+	0.705962i	$0.249485\pi$
$864$	4.97965	−	1.48427i	0.169411	−	0.0504958i
$865$	−34.3027	+	38.0971i	−1.16633	+	1.29534i
$866$	−0.369708	+	1.13785i	−0.0125632	+	0.0386656i
$867$	8.86264	+	28.0532i	0.300991	+	0.952735i
$868$	−1.66323	−	0.287814i	−0.0564538	−	0.00976906i
$869$			61.8428i			2.09787i
$870$	15.3554	+	0.125289i	0.520598	+	0.00424770i
$871$	0.904432	+	0.814354i	0.0306455	+	0.0275933i
$872$	1.76036	−	2.42293i	0.0596134	−	0.0820508i
$873$	0.575499	+	6.49309i	0.0194777	+	0.219758i
$874$	6.40679	−	3.69896i	0.216713	−	0.125119i
$875$	−3.04181	−	0.319707i	−0.102832	−	0.0108081i
$876$	−3.21911	+	4.35554i	−0.108763	+	0.147160i
$877$	−0.854351	−	8.12860i	−0.0288494	−	0.274483i	−0.999432	−	0.0337133i	$-0.989267\pi$
$877$	−0.854351	−	8.12860i	−0.0288494	−	0.274483i	0.970582	−	0.240770i	$-0.0774000\pi$
$878$	22.3603	−	20.1333i	0.754624	−	0.679467i
$879$	16.6016	−	14.7046i	0.559957	−	0.495975i
$880$	2.06072	+	9.69492i	0.0694668	+	0.326816i
$881$	33.2788	+	7.07362i	1.12119	+	0.238316i	0.730973	−	0.682407i	$-0.239067\pi$
$881$	33.2788	+	7.07362i	1.12119	+	0.238316i	0.390217	+	0.920723i	$0.372400\pi$
$882$	3.97747	+	20.3390i	0.133928	+	0.684850i
$883$	53.5571	−	17.4017i	1.80234	−	0.585615i	0.802401	−	0.596785i	$-0.203555\pi$
$883$	53.5571	−	17.4017i	1.80234	−	0.585615i	0.999938	+	0.0111693i	$0.00355537\pi$
$884$	0.0983212	−	0.0319465i	0.00330690	−	0.00107448i
$885$	6.31339	−	55.6929i	0.212222	−	1.87210i
$886$	−1.91878	−	0.407849i	−0.0644626	−	0.0137019i
$887$	7.22918	+	34.0106i	0.242732	+	1.14196i	0.915565	+	0.402170i	$0.131744\pi$
$887$	7.22918	+	34.0106i	0.242732	+	1.14196i	−0.672833	+	0.739795i	$0.734923\pi$
$888$	2.84542	+	3.21249i	0.0954862	+	0.107804i
$889$	3.59786	−	3.23953i	0.120668	−	0.108650i
$890$	0.415744	+	3.95554i	0.0139358	+	0.132590i
$891$	10.2753	+	35.5297i	0.344236	+	1.19029i
$892$	−21.2567	−	2.23417i	−0.711727	−	0.0748056i
$893$	34.5430	−	19.9434i	1.15594	−	0.667381i
$894$	−35.6770	−	7.88816i	−1.19322	−	0.263819i
$895$	−2.09040	+	2.87719i	−0.0698744	+	0.0961738i
$896$	0.225295	+	0.202857i	0.00752659	+	0.00677698i
$897$	0.0118350	−	1.45050i	0.000395159	−	0.0484307i
$898$		−	1.61751i		−	0.0539771i
$899$	19.8429	−	5.01456i	0.661797	−	0.167245i
$900$	−2.00611	+	1.40809i	−0.0668702	+	0.0469363i
$901$	0.412019	−	1.26807i	0.0137264	−	0.0422454i
$902$	−21.3717	+	23.7357i	−0.711601	+	0.790313i
$903$	5.68430	+	1.89835i	0.189162	+	0.0631733i
$904$	−7.43275	+	12.8739i	−0.247210	+	0.428180i
$905$	−11.3010	−	19.5738i	−0.375656	−	0.650656i
$906$	32.0145	−	6.53234i	1.06361	−	0.217023i
$907$	−3.46106	+	2.51461i	−0.114923	+	0.0834962i	−0.643762	−	0.765226i	$-0.722627\pi$
$907$	−3.46106	+	2.51461i	−0.114923	+	0.0834962i	0.528839	+	0.848722i	$0.322627\pi$
$908$	−9.27066	+	0.974386i	−0.307658	+	0.0323361i
$909$	5.88201	−	25.6104i	0.195094	−	0.849442i
$910$	−0.255717	−	0.574350i	−0.00847694	−	0.0190395i
$911$	−35.3490	+	7.51367i	−1.17117	+	0.248939i	−0.752120	−	0.659026i	$-0.770969\pi$
$911$	−35.3490	+	7.51367i	−1.17117	+	0.248939i	−0.419045	+	0.907965i	$0.637635\pi$
$912$	1.26836	+	13.0945i	0.0419996	+	0.433603i
$913$	15.4448	+	6.87647i	0.511148	+	0.227578i
$914$	−10.7944	−	33.2217i	−0.357046	−	1.09888i
$915$	−10.8926	+	7.77897i	−0.360099	+	0.257165i
$916$	−4.45125	+	9.99768i	−0.147074	+	0.330333i
$917$	−0.900136	+	4.23481i	−0.0297251	+	0.139846i
$918$	0.268000	−	0.564345i	0.00884533	−	0.0186262i
$919$	30.2512	−	13.4687i	0.997895	−	0.444292i	0.158234	−	0.987402i	$-0.449420\pi$
$919$	30.2512	−	13.4687i	0.997895	−	0.444292i	0.839662	+	0.543110i	$0.182753\pi$
$920$	−1.57185	−	1.74572i	−0.0518225	−	0.0575547i
$921$	−22.3913	+	9.75114i	−0.737820	+	0.321311i
$922$	12.2773	+	16.8982i	0.404331	+	0.556513i
$923$	0.873595	−	8.31170i	0.0287547	−	0.273583i
$924$	−1.45695	+	1.59179i	−0.0479301	+	0.0523662i
$925$	−1.75302	−	1.01211i	−0.0576391	−	0.0332779i
$926$	0.579392	+	0.420953i	0.0190400	+	0.0138334i
$927$	3.27794	−	26.9495i	0.107662	−	0.885139i
$928$	−3.49602	−	1.13592i	−0.114762	−	0.0372885i
$929$	−23.1798			−0.760504			−0.380252	−	0.924883i	$-0.624163\pi$
$929$	−23.1798			−0.760504			−0.380252	+	0.924883i	$0.624163\pi$
$930$	−15.0390	+	17.7428i	−0.493149	+	0.581810i
$931$	−52.4705			−1.71965
$932$	25.8696	+	8.40554i	0.847386	+	0.275333i
$933$	−0.485838	+	1.06768i	−0.0159056	+	0.0349543i
$934$	24.4222	+	17.7438i	0.799120	+	0.580595i
$935$	1.03203	+	0.595844i	0.0337510	+	0.0194862i
$936$	2.33908	+	1.08750i	0.0764552	+	0.0355460i
$937$	0.729566	−	6.94136i	0.0238339	−	0.226764i	−0.976121	−	0.217229i	$-0.930298\pi$
$937$	0.729566	−	6.94136i	0.0238339	−	0.226764i	0.999955	−	0.00953523i	$-0.00303520\pi$
$938$	0.252221	+	0.347153i	0.00823531	+	0.0113349i
$939$	12.6758	+	29.1072i	0.413660	+	0.949877i
$940$	−8.47485	−	9.41228i	−0.276419	−	0.306995i
$941$	27.7977	−	12.3763i	0.906179	−	0.403457i	0.0999035	−	0.994997i	$-0.468147\pi$
$941$	27.7977	−	12.3763i	0.906179	−	0.403457i	0.806275	+	0.591540i	$0.201480\pi$
$942$	−16.0279	+	9.08018i	−0.522218	+	0.295848i
$943$	1.57387	−	7.40449i	0.0512524	−	0.241123i
$944$	−5.45728	+	12.2573i	−0.177619	+	0.398940i
$945$	−3.58358	−	1.26215i	−0.116574	−	0.0410578i
$946$	−14.4934	−	44.6062i	−0.471222	−	1.45027i
$947$	28.2980	+	12.5991i	0.919560	+	0.409415i	0.811248	−	0.584702i	$-0.198789\pi$
$947$	28.2980	+	12.5991i	0.919560	+	0.409415i	0.108312	+	0.994117i	$0.465455\pi$
$948$	25.9437	−	2.51295i	0.842611	−	0.0816169i
$949$	−2.62992	+	0.559007i	−0.0853709	+	0.0181461i
$950$	−2.52397	−	5.66893i	−0.0818884	−	0.183924i
$951$	23.7034	+	13.9443i	0.768636	+	0.452174i
$952$	0.0362507	−	0.00381010i	0.00117489	−	0.000123486i
$953$	36.3037	−	26.3762i	1.17599	−	0.854408i	0.184278	−	0.982874i	$-0.441005\pi$
$953$	36.3037	−	26.3762i	1.17599	−	0.854408i	0.991714	+	0.128467i	$0.0410055\pi$
$954$	29.0790	−	16.1619i	0.941468	−	0.523262i
$955$	23.4173	+	40.5599i	0.757766	+	1.31249i
$956$	−3.66946	+	6.35568i	−0.118679	+	0.205557i
$957$	8.28815	−	24.8175i	0.267918	−	0.802235i
$958$	3.89065	−	4.32101i	0.125701	−	0.139605i
$959$	−1.47355	+	4.53513i	−0.0475835	+	0.146447i
$960$	3.98338	−	1.25844i	0.128563	−	0.0406160i
$961$	−13.4118	+	27.9486i	−0.432638	+	0.901568i
$962$			2.13040i			0.0686869i
$963$	11.7519	−	3.60752i	0.378700	−	0.116251i
$964$	5.00507	+	4.50659i	0.161202	+	0.145147i
$965$	29.9822	−	41.2669i	0.965160	−	1.32843i
$966$	0.110412	−	0.499377i	0.00355244	−	0.0160672i
$967$	2.45663	−	1.41834i	0.0789999	−	0.0456106i	−0.459980	−	0.887929i	$-0.652143\pi$
$967$	2.45663	−	1.41834i	0.0789999	−	0.0456106i	0.538980	+	0.842319i	$0.318810\pi$
$968$	5.85587	+	0.615477i	0.188215	+	0.0197822i
$969$	1.27204	+	0.940144i	0.0408639	+	0.0302018i
$970$	0.547788	+	5.21186i	0.0175884	+	0.167343i
$971$	17.2278	−	15.5120i	0.552868	−	0.497805i	−0.344681	−	0.938720i	$-0.612013\pi$
$971$	17.2278	−	15.5120i	0.552868	−	0.497805i	0.897549	+	0.440915i	$0.145346\pi$
$972$	14.4875	−	5.75432i	0.464687	−	0.184570i
$973$	−0.785947	−	3.69759i	−0.0251963	−	0.118539i
$974$	14.9187	+	3.17107i	0.478027	+	0.101608i
$975$	−1.20898	−	0.137051i	−0.0387184	−	0.00438915i
$976$	3.04733	−	0.990138i	0.0975427	−	0.0316935i
$977$	14.9465	−	4.85641i	0.478180	−	0.155370i	−0.0600026	−	0.998198i	$-0.519111\pi$
$977$	14.9465	−	4.85641i	0.478180	−	0.155370i	0.538183	+	0.842828i	$0.319111\pi$
$978$	−18.5742	−	2.10558i	−0.593937	−	0.0673291i
$979$	6.62884	+	1.40900i	0.211859	+	0.0450319i
$980$	3.46406	+	16.2971i	0.110655	+	0.520593i
$981$	4.61873	−	7.70666i	0.147465	−	0.246055i
$982$	−2.71133	+	2.44130i	−0.0865222	+	0.0779049i
$983$	0.752504	+	7.15959i	0.0240011	+	0.228356i	0.999947	+	0.0103405i	$0.00329153\pi$
$983$	0.752504	+	7.15959i	0.0240011	+	0.228356i	−0.975945	+	0.218015i	$0.930042\pi$
$984$	10.8258	+	8.00117i	0.345114	+	0.255068i
$985$	13.3565	+	1.40382i	0.425572	+	0.0447295i
$986$	−0.382755	+	0.220983i	−0.0121894	+	0.00703755i
$987$	0.595299	−	2.69245i	0.0189486	−	0.0857017i
$988$	−3.83879	+	5.28364i	−0.122128	+	0.168095i
$989$	8.26085	+	7.43810i	0.262680	+	0.236518i
$990$	8.72581	+	28.4254i	0.277324	+	0.903418i
$991$		−	29.2105i		−	0.927902i	−0.885861	−	0.463951i	$-0.846431\pi$
$991$		−	29.2105i		−	0.927902i	0.885861	−	0.463951i	$-0.153569\pi$
$992$	4.71231	−	2.96549i	0.149616	−	0.0941543i
$993$	7.43869	−	2.35005i	0.236060	−	0.0745766i
$994$	0.910581	−	2.80248i	0.0288819	−	0.0888892i
$995$	−9.23500	+	10.2565i	−0.292769	+	0.325153i
$996$	2.25715	−	6.75866i	0.0715206	−	0.214156i
$997$	−4.41284	+	7.64326i	−0.139756	+	0.242064i	−0.927404	−	0.374061i	$-0.877965\pi$
$997$	−4.41284	+	7.64326i	−0.139756	+	0.242064i	0.787648	+	0.616125i	$0.211298\pi$
$998$	−10.6622	−	18.4675i	−0.337507	−	0.584580i
$999$	9.35380	+	8.84620i	0.295941	+	0.279881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.17.6	yes	80
3.2	odd	2	inner	186.2.p.a.17.2	yes	80
31.11	odd	30	inner	186.2.p.a.11.2	✓	80
93.11	even	30	inner	186.2.p.a.11.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.2	✓	80	31.11	odd	30	inner
186.2.p.a.11.6	yes	80	93.11	even	30	inner
186.2.p.a.17.2	yes	80	3.2	odd	2	inner
186.2.p.a.17.6	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-1.57651 - 0.717375i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.08872 + 1.20592i) q^{5} +(-1.27767 - 1.16943i) q^{6} +(0.0316894 - 0.301504i) q^{7} +(0.587785 + 0.809017i) q^{8} +(1.97075 + 2.26189i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-1.57651 - 0.717375i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.08872 + 1.20592i) q^{5} +(-1.27767 - 1.16943i) q^{6} +(0.0316894 - 0.301504i) q^{7} +(0.587785 + 0.809017i) q^{8} +(1.97075 + 2.26189i) q^{9} +(1.61384 + 1.79235i) q^{10} +(3.75423 - 1.67149i) q^{11} +(-0.853758 - 1.50702i) q^{12} +(0.178771 - 0.841052i) q^{13} +(0.123308 - 0.276955i) q^{14} +(-2.42778 - 3.39954i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.109838 + 0.0489031i) q^{17} +(1.17533 + 2.76018i) q^{18} +(-7.42953 + 1.57920i) q^{19} +(0.980985 + 2.20333i) q^{20} +(-0.266250 + 0.452590i) q^{21} +(4.08700 - 0.429561i) q^{22} +(-0.787971 + 0.572494i) q^{23} +(-0.346279 - 1.69708i) q^{24} +(0.408492 + 0.707530i) q^{25} +(0.429921 - 0.744645i) q^{26} +(-1.48427 - 4.97965i) q^{27} +(0.202857 - 0.225295i) q^{28} +(-1.13592 + 3.49602i) q^{29} +(-1.25844 - 3.98338i) q^{30} +(-2.96549 - 4.71231i) q^{31} +1.00000i q^{32} +(-7.11766 - 0.0580748i) q^{33} +(0.0893503 + 0.0804514i) q^{34} +(0.429780 - 0.591542i) q^{35} +(0.264859 + 2.98829i) q^{36} +(-2.14572 + 1.23883i) q^{37} +(-7.55390 - 0.793947i) q^{38} +(-0.885183 + 1.19768i) q^{39} +(0.252106 + 2.39863i) q^{40} +(-5.77580 + 5.20055i) q^{41} +(-0.393077 + 0.348163i) q^{42} +(-2.37289 - 11.1636i) q^{43} +(4.01971 + 0.854417i) q^{44} +(1.38867 + 7.10102i) q^{45} +(-0.926316 + 0.300978i) q^{46} +(-4.99435 + 1.62276i) q^{47} +(0.195097 - 1.72103i) q^{48} +(6.75713 + 1.43627i) q^{49} +(0.169861 + 0.799132i) q^{50} +(-0.138079 - 0.155891i) q^{51} +(0.638987 - 0.575346i) q^{52} +(-1.15917 - 11.0288i) q^{53} +(0.127175 - 5.19460i) q^{54} +(9.85721 + 1.03603i) q^{55} +(0.262549 - 0.151582i) q^{56} +(12.8456 + 2.84015i) q^{57} +(-2.16066 + 2.97389i) q^{58} +(9.97095 + 8.97788i) q^{59} +(0.0340837 - 4.17729i) q^{60} -3.20415i q^{61} +(-1.36416 - 5.39806i) q^{62} +(0.744422 - 0.522510i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.38764 - 1.54114i) q^{65} +(-6.75135 - 2.25471i) q^{66} +(-0.707708 + 1.22579i) q^{67} +(0.0601164 + 0.104125i) q^{68} +(1.65293 - 0.337270i) q^{69} +(0.591542 - 0.429780i) q^{70} +(9.66655 - 1.01600i) q^{71} +(-0.671535 + 2.92387i) q^{72} +(-1.27184 - 2.85661i) q^{73} +(-2.42353 + 0.515136i) q^{74} +(-0.136427 - 1.40847i) q^{75} +(-6.93884 - 3.08937i) q^{76} +(-0.384992 - 1.18488i) q^{77} +(-1.21196 + 0.865523i) q^{78} +(-6.12085 + 13.7477i) q^{79} +(-0.501450 + 2.35914i) q^{80} +(-1.23232 + 8.91523i) q^{81} +(-7.10017 + 3.16120i) q^{82} +(2.75278 + 3.05728i) q^{83} +(-0.481427 + 0.209655i) q^{84} +(0.170447 + 0.234601i) q^{85} +(1.19298 - 11.3504i) q^{86} +(4.29875 - 4.69661i) q^{87} +(3.55895 + 2.05476i) q^{88} +(1.33414 + 0.969306i) q^{89} +(-0.873636 + 7.18259i) q^{90} +(-0.247916 - 0.0805526i) q^{91} -0.973986 q^{92} +(1.29461 + 9.55636i) q^{93} -5.25137 q^{94} +(-17.4226 - 5.66094i) q^{95} +(0.717375 - 1.57651i) q^{96} +(1.75787 + 1.27717i) q^{97} +(5.98258 + 3.45405i) q^{98} +(11.1794 + 5.19758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

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