LMFDB - Embedded newform 186.2.p.a.17.1

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			17.1
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-1.55075 + 0.771484i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.31329 - 0.758228i) q^{5} +(1.71325 - 0.254518i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.80963 - 2.39275i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.55075 + 0.771484i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.31329 - 0.758228i) q^{5} +(1.71325 - 0.254518i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.80963 - 2.39275i) q^{9} +(1.01471 + 1.12695i) q^{10} +(5.28891 - 2.35477i) q^{11} +(-1.70805 - 0.287362i) q^{12} +(0.417276 - 1.96313i) q^{13} +(-0.181081 + 0.406715i) q^{14} +(2.62154 + 0.162637i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.46549 - 1.98816i) q^{17} +(-2.46046 + 1.71644i) q^{18} +(3.78335 - 0.804176i) q^{19} +(-0.616798 - 1.38535i) q^{20} +(0.269421 + 0.722520i) q^{21} +(-5.75772 + 0.605161i) q^{22} +(6.60423 - 4.79825i) q^{23} +(1.53565 + 0.801113i) q^{24} +(-1.35018 - 2.33858i) q^{25} +(-1.00349 + 1.73810i) q^{26} +(-0.960300 + 5.10665i) q^{27} +(0.297900 - 0.330852i) q^{28} +(-0.598955 + 1.84340i) q^{29} +(-2.44297 - 0.964778i) q^{30} +(-5.55810 - 0.327958i) q^{31} -1.00000i q^{32} +(-6.38509 + 7.73197i) q^{33} +(3.63256 + 3.27077i) q^{34} +(-0.396834 + 0.546195i) q^{35} +(2.87044 - 0.872105i) q^{36} +(-2.73153 + 1.57705i) q^{37} +(-3.84669 - 0.404303i) q^{38} +(0.867433 + 3.36623i) q^{39} +(0.158513 + 1.50815i) q^{40} +(0.0381095 - 0.0343139i) q^{41} +(-0.0329632 - 0.770413i) q^{42} +(1.25764 + 5.91671i) q^{43} +(5.66292 + 1.20369i) q^{44} +(-4.19081 + 1.77027i) q^{45} +(-7.76373 + 2.52259i) q^{46} +(-2.69949 + 0.877117i) q^{47} +(-1.21293 - 1.23645i) q^{48} +(6.65316 + 1.41417i) q^{49} +(0.561436 + 2.64135i) q^{50} +(8.45867 - 0.361916i) q^{51} +(1.49148 - 1.34293i) q^{52} +(-0.283448 - 2.69683i) q^{53} +(2.49134 - 4.55996i) q^{54} +(-8.73133 - 0.917700i) q^{55} +(-0.385559 + 0.222603i) q^{56} +(-5.24661 + 4.16587i) q^{57} +(1.13928 - 1.56809i) q^{58} +(4.89938 + 4.41142i) q^{59} +(2.02527 + 1.67248i) q^{60} -4.12882i q^{61} +(5.18472 + 2.02945i) q^{62} +(-0.975216 - 0.912592i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.03650 + 2.26176i) q^{65} +(8.46189 - 5.38044i) q^{66} +(5.67003 - 9.82077i) q^{67} +(-2.44404 - 4.23321i) q^{68} +(-6.53970 + 12.5359i) q^{69} +(0.546195 - 0.396834i) q^{70} +(-9.24128 + 0.971297i) q^{71} +(-2.99945 - 0.0575940i) q^{72} +(-2.32802 - 5.22881i) q^{73} +(3.08517 - 0.655774i) q^{74} +(3.89796 + 2.58490i) q^{75} +(3.53348 + 1.57321i) q^{76} +(-0.796487 - 2.45134i) q^{77} +(0.215246 - 3.46953i) q^{78} +(4.65367 - 10.4523i) q^{79} +(0.315289 - 1.48332i) q^{80} +(-2.45051 - 8.65996i) q^{81} +(-0.0468479 + 0.0208580i) q^{82} +(4.07770 + 4.52874i) q^{83} +(-0.206721 + 0.742893i) q^{84} +(4.35700 + 5.99689i) q^{85} +(0.632282 - 6.01576i) q^{86} +(-0.493322 - 3.32072i) q^{87} +(-5.01380 - 2.89472i) q^{88} +(-12.7668 - 9.27564i) q^{89} +(4.53274 - 0.388591i) q^{90} +(-0.849788 - 0.276113i) q^{91} +8.16327 q^{92} +(8.87221 - 3.77940i) q^{93} +2.83841 q^{94} +(-5.57839 - 1.81253i) q^{95} +(0.771484 + 1.55075i) q^{96} +(-3.13126 - 2.27499i) q^{97} +(-5.89052 - 3.40090i) q^{98} +(3.93656 - 16.9163i) 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
$3$	−1.55075	+	0.771484i	−0.895324	+	0.445416i
$3$	−1.55075	+	0.771484i	−0.895324	+	0.445416i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.31329	−	0.758228i	−0.587321	−	0.339090i	0.176716	−	0.984262i	$-0.443452\pi$
$5$	−1.31329	−	0.758228i	−0.587321	−	0.339090i	−0.764038	+	0.645172i	$0.776786\pi$
$6$	1.71325	−	0.254518i	0.699431	−	0.103907i
$7$	0.0465366	−	0.442766i	0.0175892	−	0.167350i	−0.982201	−	0.187833i	$-0.939854\pi$
$7$	0.0465366	−	0.442766i	0.0175892	−	0.167350i	0.999790	+	0.0204829i	$0.00652035\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	1.80963	−	2.39275i	0.603208	−	0.797584i
$10$	1.01471	+	1.12695i	0.320879	+	0.356372i
$11$	5.28891	−	2.35477i	1.59467	−	0.709991i	0.598807	−	0.800894i	$-0.295642\pi$
$11$	5.28891	−	2.35477i	1.59467	−	0.709991i	0.995860	+	0.0909022i	$0.0289751\pi$
$12$	−1.70805	−	0.287362i	−0.493071	−	0.0829543i
$13$	0.417276	−	1.96313i	0.115731	−	0.544473i	−0.881634	−	0.471934i	$-0.843556\pi$
$13$	0.417276	−	1.96313i	0.115731	−	0.544473i	0.997366	−	0.0725399i	$-0.0231105\pi$
$14$	−0.181081	+	0.406715i	−0.0483960	+	0.108699i
$15$	2.62154	+	0.162637i	0.676879	+	0.0419928i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.46549	−	1.98816i	−1.08304	−	0.482200i	−0.213945	−	0.976846i	$-0.568631\pi$
$17$	−4.46549	−	1.98816i	−1.08304	−	0.482200i	−0.869095	+	0.494645i	$0.835298\pi$
$18$	−2.46046	+	1.71644i	−0.579935	+	0.404568i
$19$	3.78335	−	0.804176i	0.867960	−	0.184491i	0.247652	−	0.968849i	$-0.420341\pi$
$19$	3.78335	−	0.804176i	0.867960	−	0.184491i	0.620308	+	0.784358i	$0.287008\pi$
$20$	−0.616798	−	1.38535i	−0.137920	−	0.309774i
$21$	0.269421	+	0.722520i	0.0587924	+	0.157667i
$22$	−5.75772	+	0.605161i	−1.22755	+	0.129021i
$23$	6.60423	−	4.79825i	1.37708	−	1.00050i	0.379930	−	0.925015i	$-0.375948\pi$
$23$	6.60423	−	4.79825i	1.37708	−	1.00050i	0.997147	−	0.0754892i	$-0.0240518\pi$
$24$	1.53565	+	0.801113i	0.313463	+	0.163526i
$25$	−1.35018	−	2.33858i	−0.270036	−	0.467716i
$26$	−1.00349	+	1.73810i	−0.196801	+	0.340869i
$27$	−0.960300	+	5.10665i	−0.184810	+	0.982774i
$28$	0.297900	−	0.330852i	0.0562979	−	0.0625251i
$29$	−0.598955	+	1.84340i	−0.111223	+	0.342310i	−0.991141	−	0.132817i	$-0.957598\pi$
$29$	−0.598955	+	1.84340i	−0.111223	+	0.342310i	0.879917	+	0.475127i	$0.157598\pi$
$30$	−2.44297	−	0.964778i	−0.446024	−	0.176143i
$31$	−5.55810	−	0.327958i	−0.998264	−	0.0589030i
$31$	−5.55810	−	0.327958i	−0.998264	−	0.0589030i
$32$		−	1.00000i		−	0.176777i
$33$	−6.38509	+	7.73197i	−1.11150	+	1.34596i
$34$	3.63256	+	3.27077i	0.622978	+	0.560932i
$35$	−0.396834	+	0.546195i	−0.0670772	+	0.0923238i
$36$	2.87044	−	0.872105i	0.478407	−	0.145351i
$37$	−2.73153	+	1.57705i	−0.449060	+	0.259265i	−0.707433	−	0.706780i	$-0.750147\pi$
$37$	−2.73153	+	1.57705i	−0.449060	+	0.259265i	0.258373	+	0.966045i	$0.416814\pi$
$38$	−3.84669	−	0.404303i	−0.624015	−	0.0655866i
$39$	0.867433	+	3.36623i	0.138900	+	0.539029i
$40$	0.158513	+	1.50815i	0.0250631	+	0.238459i
$41$	0.0381095	−	0.0343139i	0.00595170	−	0.00535894i	−0.666149	−	0.745818i	$-0.732059\pi$
$41$	0.0381095	−	0.0343139i	0.00595170	−	0.00535894i	0.672101	+	0.740459i	$0.265392\pi$
$42$	−0.0329632	−	0.770413i	−0.00508633	−	0.118877i
$43$	1.25764	+	5.91671i	0.191788	+	0.902290i	0.963788	+	0.266669i	$0.0859229\pi$
$43$	1.25764	+	5.91671i	0.191788	+	0.902290i	−0.772001	+	0.635622i	$0.780744\pi$
$44$	5.66292	+	1.20369i	0.853717	+	0.181463i
$45$	−4.19081	+	1.77027i	−0.624730	+	0.263896i
$46$	−7.76373	+	2.52259i	−1.14470	+	0.371936i
$47$	−2.69949	+	0.877117i	−0.393761	+	0.127941i	−0.499204	−	0.866485i	$-0.666374\pi$
$47$	−2.69949	+	0.877117i	−0.393761	+	0.127941i	0.105443	+	0.994425i	$0.466374\pi$
$48$	−1.21293	−	1.23645i	−0.175072	−	0.178466i
$49$	6.65316	+	1.41417i	0.950451	+	0.202025i
$50$	0.561436	+	2.64135i	0.0793991	+	0.373543i
$51$	8.45867	−	0.361916i	1.18445	−	0.0506784i
$52$	1.49148	−	1.34293i	0.206831	−	0.186232i
$53$	−0.283448	−	2.69683i	−0.0389346	−	0.370438i	−0.996589	−	0.0825195i	$-0.973703\pi$
$53$	−0.283448	−	2.69683i	−0.0389346	−	0.370438i	0.957655	−	0.287919i	$-0.0929633\pi$
$54$	2.49134	−	4.55996i	0.339028	−	0.620532i
$55$	−8.73133	−	0.917700i	−1.17733	−	0.123743i
$56$	−0.385559	+	0.222603i	−0.0515225	+	0.0297465i
$57$	−5.24661	+	4.16587i	−0.694930	+	0.551783i
$58$	1.13928	−	1.56809i	0.149595	−	0.205900i
$59$	4.89938	+	4.41142i	0.637844	+	0.574318i	0.923303	−	0.384074i	$-0.125479\pi$
$59$	4.89938	+	4.41142i	0.637844	+	0.574318i	−0.285458	+	0.958391i	$0.592146\pi$
$60$	2.02527	+	1.67248i	0.261462	+	0.215916i
$61$		−	4.12882i		−	0.528641i	−0.964435	−	0.264320i	$-0.914852\pi$
$61$		−	4.12882i		−	0.528641i	0.964435	−	0.264320i	$-0.0851476\pi$
$62$	5.18472	+	2.02945i	0.658460	+	0.257741i
$63$	−0.975216	−	0.912592i	−0.122866	−	0.114976i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−2.03650	+	2.26176i	−0.252597	+	0.280537i
$66$	8.46189	−	5.38044i	1.04159	−	0.662286i
$67$	5.67003	−	9.82077i	0.692704	−	1.19980i	−0.278245	−	0.960510i	$-0.589753\pi$
$67$	5.67003	−	9.82077i	0.692704	−	1.19980i	0.970949	−	0.239288i	$-0.0769140\pi$
$68$	−2.44404	−	4.23321i	−0.296384	−	0.513352i
$69$	−6.53970	+	12.5359i	−0.787288	+	1.50915i
$70$	0.546195	−	0.396834i	0.0652828	−	0.0474307i
$71$	−9.24128	+	0.971297i	−1.09674	+	0.115272i	−0.635572	−	0.772042i	$-0.719236\pi$
$71$	−9.24128	+	0.971297i	−1.09674	+	0.115272i	−0.461166	+	0.887314i	$0.652569\pi$
$72$	−2.99945	−	0.0575940i	−0.353488	−	0.00678752i
$73$	−2.32802	−	5.22881i	−0.272474	−	0.611986i	0.724538	−	0.689235i	$-0.242053\pi$
$73$	−2.32802	−	5.22881i	−0.272474	−	0.611986i	−0.997012	+	0.0772489i	$0.975386\pi$
$74$	3.08517	−	0.655774i	0.358644	−	0.0762321i
$75$	3.89796	+	2.58490i	0.450098	+	0.298479i
$76$	3.53348	+	1.57321i	0.405318	+	0.180459i
$77$	−0.796487	−	2.45134i	−0.0907681	−	0.279356i
$78$	0.215246	−	3.46953i	0.0243718	−	0.392847i
$79$	4.65367	−	10.4523i	0.523579	−	1.17598i	−0.437378	−	0.899278i	$-0.644093\pi$
$79$	4.65367	−	10.4523i	0.523579	−	1.17598i	0.960957	−	0.276699i	$-0.0892406\pi$
$80$	0.315289	−	1.48332i	0.0352504	−	0.165840i
$81$	−2.45051	−	8.65996i	−0.272279	−	0.962218i
$82$	−0.0468479	+	0.0208580i	−0.00517348	+	0.00230338i
$83$	4.07770	+	4.52874i	0.447586	+	0.497094i	0.924142	−	0.382050i	$-0.124782\pi$
$83$	4.07770	+	4.52874i	0.447586	+	0.497094i	−0.476556	+	0.879144i	$0.658115\pi$
$84$	−0.206721	+	0.742893i	−0.0225551	+	0.0810562i
$85$	4.35700	+	5.99689i	0.472583	+	0.650454i
$86$	0.632282	−	6.01576i	0.0681807	−	0.648696i
$87$	−0.493322	−	3.32072i	−0.0528897	−	0.356019i
$88$	−5.01380	−	2.89472i	−0.534473	−	0.308578i
$89$	−12.7668	−	9.27564i	−1.35328	−	0.983216i	−0.998841	−	0.0481374i	$-0.984671\pi$
$89$	−12.7668	−	9.27564i	−1.35328	−	0.983216i	−0.354440	−	0.935079i	$-0.615329\pi$
$90$	4.53274	−	0.388591i	0.477793	−	0.0409610i
$91$	−0.849788	−	0.276113i	−0.0890820	−	0.0289445i
$92$	8.16327			0.851080
$93$	8.87221	−	3.77940i	0.920005	−	0.391906i
$94$	2.83841			0.292760
$95$	−5.57839	−	1.81253i	−0.572330	−	0.185961i
$96$	0.771484	+	1.55075i	0.0787392	+	0.158272i
$97$	−3.13126	−	2.27499i	−0.317931	−	0.230991i	0.417361	−	0.908741i	$-0.362955\pi$
$97$	−3.13126	−	2.27499i	−0.317931	−	0.230991i	−0.735292	+	0.677750i	$0.762955\pi$
$98$	−5.89052	−	3.40090i	−0.595033	−	0.343542i
$99$	3.93656	−	16.9163i	0.395639	−	1.70015i
$100$	0.282264	−	2.68557i	0.0282264	−	0.268557i
$101$	2.75333	+	3.78963i	0.273966	+	0.377082i	0.923724	−	0.383059i	$-0.125130\pi$
$101$	2.75333	+	3.78963i	0.273966	+	0.377082i	−0.649758	+	0.760142i	$0.725130\pi$
$102$	−8.15651	−	2.26967i	−0.807615	−	0.224731i
$103$	10.0171	+	11.1251i	0.987010	+	1.09619i	0.995360	+	0.0962204i	$0.0306754\pi$
$103$	10.0171	+	11.1251i	0.987010	+	1.09619i	−0.00835015	+	0.999965i	$0.502658\pi$
$104$	−1.83347	+	0.816314i	−0.179787	+	0.0800462i
$105$	0.194008	−	1.15316i	0.0189332	−	0.112537i
$106$	−0.563791	+	2.65243i	−0.0547603	+	0.257627i
$107$	−4.83006	+	10.8485i	−0.466939	+	1.04876i	0.514587	+	0.857438i	$0.327945\pi$
$107$	−4.83006	+	10.8485i	−0.466939	+	1.04876i	−0.981527	+	0.191325i	$0.938722\pi$
$108$	−3.77851	+	3.56691i	−0.363587	+	0.343226i
$109$	5.33158	+	16.4089i	0.510673	+	1.57169i	0.791020	+	0.611791i	$0.209551\pi$
$109$	5.33158	+	16.4089i	0.510673	+	1.57169i	−0.280347	+	0.959899i	$0.590449\pi$
$110$	8.02040	+	3.57091i	0.764715	+	0.340473i
$111$	3.01924	−	4.55293i	0.286573	−	0.432145i
$112$	0.435476	−	0.0925634i	0.0411487	−	0.00874642i
$113$	5.08748	+	11.4267i	0.478590	+	1.07493i	0.978008	+	0.208569i	$0.0668806\pi$
$113$	5.08748	+	11.4267i	0.478590	+	1.07493i	−0.499418	+	0.866361i	$0.666453\pi$
$114$	6.27715	−	2.34068i	0.587909	−	0.219225i
$115$	−12.3114	+	1.29398i	−1.14805	+	0.120665i
$116$	−1.56809	+	1.13928i	−0.145593	+	0.105780i
$117$	−3.94216	−	4.55096i	−0.364453	−	0.420736i
$118$	−3.29638	−	5.70950i	−0.303456	−	0.525602i
$119$	−1.08810	+	1.88465i	−0.0997460	+	0.172765i
$120$	−1.40933	−	2.21647i	−0.128653	−	0.202335i
$121$	15.0672	−	16.7338i	1.36974	−	1.52125i
$122$	−1.27587	+	3.92674i	−0.115512	+	0.355510i
$123$	−0.0326255	+	0.0826130i	−0.00294174	+	0.00744897i
$124$	−4.30383	−	3.53229i	−0.386495	−	0.317209i
$125$			11.6773i			1.04445i
$126$	0.645479	+	1.16928i	0.0575038	+	0.104168i
$127$	−5.94008	−	5.34847i	−0.527097	−	0.474600i	0.362091	−	0.932143i	$-0.382063\pi$
$127$	−5.94008	−	5.34847i	−0.527097	−	0.474600i	−0.889188	+	0.457543i	$0.848730\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−6.51492	−	8.20507i	−0.573607	−	0.722416i
$130$	2.63575	−	1.52175i	0.231171	−	0.133467i
$131$	16.9294	+	1.77935i	1.47913	+	0.155463i	0.809450	−	0.587189i	$-0.199766\pi$
$131$	16.9294	+	1.77935i	1.47913	+	0.155463i	0.669678	+	0.742652i	$0.266432\pi$
$132$	−9.71038	+	2.50223i	−0.845180	+	0.217791i
$133$	−0.179998	−	1.71256i	−0.0156078	−	0.148498i
$134$	−8.42730	+	7.58797i	−0.728008	+	0.655501i
$135$	5.13316	−	5.97838i	0.441792	−	0.514537i
$136$	1.01629	+	4.78127i	0.0871462	+	0.409990i
$137$	0.422413	+	0.0897868i	0.0360892	+	0.00767100i	0.225921	−	0.974146i	$-0.427461\pi$
$137$	0.422413	+	0.0897868i	0.0360892	+	0.00767100i	−0.189832	+	0.981817i	$0.560794\pi$
$138$	10.0934	−	9.90149i	0.859211	−	0.842871i
$139$	3.15138	−	1.02395i	0.267297	−	0.0868500i	−0.172302	−	0.985044i	$-0.555121\pi$
$139$	3.15138	−	1.02395i	0.267297	−	0.0868500i	0.439599	+	0.898194i	$0.355121\pi$
$140$	−0.642091	+	0.208628i	−0.0542666	+	0.0176323i
$141$	3.50954	−	3.44280i	0.295557	−	0.289936i
$142$	9.08912	+	1.93195i	0.762742	+	0.162126i
$143$	−2.41579	−	11.3654i	−0.202018	−	0.950422i
$144$	2.83485	+	0.981655i	0.236237	+	0.0818046i
$145$	2.18432	−	1.96677i	0.181398	−	0.163331i
$146$	0.598284	+	5.69229i	0.0495143	+	0.471097i
$147$	−11.4084	+	2.93978i	−0.940946	+	0.242469i
$148$	−3.13682	−	0.329693i	−0.257845	−	0.0271006i
$149$	5.67147	−	3.27443i	0.464625	−	0.268251i	−0.249362	−	0.968410i	$-0.580221\pi$
$149$	5.67147	−	3.27443i	0.464625	−	0.268251i	0.713987	+	0.700159i	$0.246888\pi$
$150$	−2.90840	−	3.66292i	−0.237470	−	0.299077i
$151$	−13.3881	+	18.4272i	−1.08951	+	1.49958i	−0.240912	+	0.970547i	$0.577446\pi$
$151$	−13.3881	+	18.4272i	−1.08951	+	1.49958i	−0.848599	+	0.529036i	$0.822554\pi$
$152$	−2.87439	−	2.58811i	−0.233144	−	0.209924i
$153$	−12.8380	+	7.08697i	−1.03789	+	0.572947i
$154$			2.57749i			0.207700i
$155$	7.05073	+	4.64501i	0.566328	+	0.373096i
$156$	−1.27685	+	3.23320i	−0.102230	+	0.258863i
$157$	−5.20192	+	16.0099i	−0.415159	+	1.27773i	0.496950	+	0.867779i	$0.334453\pi$
$157$	−5.20192	+	16.0099i	−0.415159	+	1.27773i	−0.912109	+	0.409948i	$0.865547\pi$
$158$	−7.65585	+	8.50268i	−0.609066	+	0.676437i
$159$	2.52012	+	3.96342i	0.199858	+	0.314320i
$160$	−0.758228	+	1.31329i	−0.0599432	+	0.103825i
$161$	−1.81717	−	3.14742i	−0.143213	−	0.248052i
$162$	−0.345501	+	8.99337i	−0.0271451	+	0.706586i
$163$	3.39436	−	2.46615i	0.265867	−	0.193164i	−0.446863	−	0.894603i	$-0.647459\pi$
$163$	3.39436	−	2.46615i	0.265867	−	0.193164i	0.712729	+	0.701439i	$0.247459\pi$
$164$	0.0510004	−	0.00536036i	0.00398247	−	0.000418574i
$165$	14.2481	−	5.31296i	1.10921	−	0.413613i
$166$	−2.47866	−	5.56717i	−0.192382	−	0.432096i
$167$	−6.04365	+	1.28462i	−0.467671	+	0.0994066i	−0.435719	−	0.900083i	$-0.643506\pi$
$167$	−6.04365	+	1.28462i	−0.467671	+	0.0994066i	−0.0319524	+	0.999489i	$0.510172\pi$
$168$	0.426170	−	0.642653i	0.0328797	−	0.0495817i
$169$	8.19634	+	3.64925i	0.630488	+	0.280711i
$170$	−2.29061	−	7.04977i	−0.175682	−	0.540693i
$171$	4.92226	−	10.5079i	0.376414	−	0.803557i
$172$	−2.46031	+	5.52594i	−0.187597	+	0.421349i
$173$	1.29890	−	6.11083i	0.0987534	−	0.464598i	−0.900786	−	0.434262i	$-0.857009\pi$
$173$	1.29890	−	6.11083i	0.0987534	−	0.464598i	0.999540	−	0.0303356i	$-0.00965760\pi$
$174$	−0.556982	+	3.31064i	−0.0422247	+	0.250979i
$175$	−1.09828	+	0.488985i	−0.0830220	+	0.0369638i
$176$	3.87389	+	4.30239i	0.292005	+	0.324305i
$177$	−11.0010	−	3.06120i	−0.826888	−	0.230094i
$178$	9.27564	+	12.7668i	0.695239	+	0.956914i
$179$	−2.21712	+	21.0945i	−0.165715	+	1.57667i	0.523442	+	0.852061i	$0.324648\pi$
$179$	−2.21712	+	21.0945i	−0.165715	+	1.57667i	−0.689157	+	0.724612i	$0.742019\pi$
$180$	−4.43098	−	1.03112i	−0.330265	−	0.0768554i
$181$	−9.22668	−	5.32703i	−0.685814	−	0.395955i	0.116228	−	0.993223i	$-0.462920\pi$
$181$	−9.22668	−	5.32703i	−0.685814	−	0.395955i	−0.802042	+	0.597268i	$0.796253\pi$
$182$	0.722873	+	0.525198i	0.0535829	+	0.0389303i
$183$	3.18531	+	6.40274i	0.235465	+	0.473304i
$184$	−7.76373	−	2.52259i	−0.572350	−	0.185968i
$185$	4.78305			0.351657
$186$	−9.60587	+	0.852761i	−0.704337	+	0.0625275i
$187$	−28.2992			−2.06945
$188$	−2.69949	−	0.877117i	−0.196880	−	0.0639703i
$189$	2.21636	+	0.662835i	0.161217	+	0.0482141i
$190$	4.74526	+	3.44763i	0.344257	+	0.250118i
$191$	−8.14907	−	4.70487i	−0.589646	−	0.340432i	0.175311	−	0.984513i	$-0.443907\pi$
$191$	−8.14907	−	4.70487i	−0.589646	−	0.340432i	−0.764958	+	0.644081i	$0.777240\pi$
$192$	−0.254518	−	1.71325i	−0.0183682	−	0.123643i
$193$	−0.877734	+	8.35108i	−0.0631807	+	0.601124i	0.916427	+	0.400203i	$0.131060\pi$
$193$	−0.877734	+	8.35108i	−0.0631807	+	0.601124i	−0.979607	+	0.200921i	$0.935606\pi$
$194$	2.27499	+	3.13126i	0.163335	+	0.224811i
$195$	1.41318	−	5.07855i	0.101200	−	0.363683i
$196$	4.55129	+	5.05472i	0.325092	+	0.361051i
$197$	−4.28977	+	1.90993i	−0.305633	+	0.136077i	−0.553822	−	0.832635i	$-0.686831\pi$
$197$	−4.28977	+	1.90993i	−0.305633	+	0.136077i	0.248189	+	0.968712i	$0.420165\pi$
$198$	−8.97131	+	14.8719i	−0.637564	+	1.05690i
$199$	−4.11535	+	19.3612i	−0.291729	+	1.37248i	0.551164	+	0.834397i	$0.314184\pi$
$199$	−4.11535	+	19.3612i	−0.291729	+	1.37248i	−0.842893	+	0.538081i	$0.819150\pi$
$200$	−1.09834	+	2.46690i	−0.0776640	+	0.174436i
$201$	−1.21620	+	19.6039i	−0.0857842	+	1.38275i
$202$	−1.44751	−	4.45498i	−0.101846	−	0.313451i
$203$	0.788320	+	0.350983i	0.0553292	+	0.0246342i
$204$	7.05594	+	4.67909i	0.494015	+	0.327602i
$205$	−0.0760666	+	0.0161685i	−0.00531272	+	0.00112925i
$206$	−6.08895	−	13.6760i	−0.424237	−	0.952853i
$207$	0.470156	−	24.4853i	0.0326781	−	1.70185i
$208$	1.99599	−	0.209787i	0.138397	−	0.0145461i
$209$	18.1162	−	13.1622i	1.25312	−	0.910446i
$210$	−0.540859	+	1.03677i	−0.0373228	+	0.0715439i
$211$	−2.58650	−	4.47996i	−0.178062	−	0.308413i	0.763155	−	0.646216i	$-0.223650\pi$
$211$	−2.58650	−	4.47996i	−0.178062	−	0.308413i	−0.941217	+	0.337803i	$0.890316\pi$
$212$	1.35584	−	2.34839i	0.0931197	−	0.161288i
$213$	13.5815	−	8.63573i	0.930591	−	0.591711i
$214$	7.94603	−	8.82496i	0.543179	−	0.603262i
$215$	2.83458	−	8.72394i	0.193317	−	0.594967i
$216$	4.69581	−	2.22471i	0.319510	−	0.151372i
$217$	−0.403864	+	2.44568i	−0.0274161	+	0.166023i
$218$		−	17.2534i		−	1.16855i
$219$	7.64410	+	6.31253i	0.516541	+	0.426561i
$220$	−6.52438	−	5.87458i	−0.439874	−	0.396064i
$221$	−5.76636	+	7.93671i	−0.387887	+	0.533881i
$222$	−4.27840	+	3.39710i	−0.287147	+	0.227998i
$223$	1.74777	−	1.00908i	0.117039	−	0.0675727i	−0.440338	−	0.897832i	$-0.645141\pi$
$223$	1.74777	−	1.00908i	0.117039	−	0.0675727i	0.557377	+	0.830260i	$0.311808\pi$
$224$	−0.442766	−	0.0465366i	−0.0295836	−	0.00310936i
$225$	−8.03896	−	1.00131i	−0.535931	−	0.0667540i
$226$	−1.30745	−	12.4395i	−0.0869701	−	0.827465i
$227$	21.2323	−	19.1177i	1.40924	−	1.26888i	0.491971	−	0.870611i	$-0.336277\pi$
$227$	21.2323	−	19.1177i	1.40924	−	1.26888i	0.917267	−	0.398272i	$-0.130390\pi$
$228$	−6.69323	+	0.286379i	−0.443270	+	0.0189659i
$229$	−4.60625	−	21.6707i	−0.304389	−	1.43204i	−0.818595	−	0.574372i	$-0.805246\pi$
$229$	−4.60625	−	21.6707i	−0.304389	−	1.43204i	0.514205	−	0.857667i	$-0.328087\pi$
$230$	12.1087	+	2.57379i	0.798426	+	0.169711i
$231$	3.12631	+	3.18692i	0.205696	+	0.209684i
$232$	1.84340	−	0.598955i	0.121025	−	0.0393233i
$233$	8.14229	−	2.64559i	0.533419	−	0.173318i	−0.0299075	−	0.999553i	$-0.509521\pi$
$233$	8.14229	−	2.64559i	0.533419	−	0.173318i	0.563327	+	0.826234i	$0.309521\pi$
$234$	2.34289	+	5.54642i	0.153160	+	0.362581i
$235$	4.21027	+	0.894920i	0.274648	+	0.0583781i
$236$	1.37071	+	6.44869i	0.0892258	+	0.419774i
$237$	0.847132	+	19.7991i	0.0550271	+	1.28609i
$238$	1.61723	−	1.45616i	0.104830	−	0.0943890i
$239$	−2.47825	−	23.5790i	−0.160305	−	1.52520i	−0.718522	−	0.695504i	$-0.755181\pi$
$239$	−2.47825	−	23.5790i	−0.160305	−	1.52520i	0.558217	−	0.829695i	$-0.311485\pi$
$240$	0.655423	+	2.54349i	0.0423074	+	0.164182i
$241$	13.2675	+	1.39447i	0.854635	+	0.0898258i	0.521705	−	0.853126i	$-0.325296\pi$
$241$	13.2675	+	1.39447i	0.854635	+	0.0898258i	0.332930	+	0.942952i	$0.391963\pi$
$242$	−19.5008	+	11.2588i	−1.25356	+	0.723741i
$243$	10.4811	+	11.5389i	0.672366	+	0.740219i
$244$	2.42686	−	3.34028i	0.155364	−	0.213840i
$245$	−7.66526	−	6.90183i	−0.489715	−	0.440942i
$246$	0.0565575	−	0.0684878i	0.00360597	−	0.00436663i
$247$		−	7.76276i		−	0.493933i
$248$	3.00164	+	4.68936i	0.190605	+	0.297775i
$249$	−9.81733	−	3.87705i	−0.622148	−	0.245698i
$250$	3.60847	−	11.1057i	0.228220	−	0.702388i
$251$	−12.2127	+	13.5636i	−0.770859	+	0.856126i	−0.992905	−	0.118910i	$-0.962060\pi$
$251$	−12.2127	+	13.5636i	−0.770859	+	0.856126i	0.222046	+	0.975036i	$0.428727\pi$
$252$	−0.252558	−	1.31152i	−0.0159097	−	0.0826180i
$253$	23.6304	−	40.9290i	1.48563	−	2.57318i
$254$	3.99658	+	6.92228i	0.250768	+	0.434343i
$255$	−11.3831	−	5.93830i	−0.712838	−	0.371871i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.50364	+	0.158039i	−0.0937943	+	0.00985818i	−0.151309	−	0.988486i	$-0.548349\pi$
$257$	−1.50364	+	0.158039i	−0.0937943	+	0.00985818i	0.0575150	+	0.998345i	$0.481682\pi$
$258$	3.66055	+	9.81671i	0.227896	+	0.611162i
$259$	0.571148	+	1.28282i	0.0354894	+	0.0797105i
$260$	−2.97700	+	0.632780i	−0.184625	+	0.0392434i
$261$	3.32690	+	4.76901i	0.205930	+	0.295194i
$262$	−15.5510	−	6.92373i	−0.960741	−	0.427750i
$263$	4.83712	+	14.8871i	0.298269	+	0.917979i	0.982104	+	0.188341i	$0.0603111\pi$
$263$	4.83712	+	14.8871i	0.298269	+	0.917979i	−0.683834	+	0.729637i	$0.739689\pi$
$264$	10.0084	+	0.620907i	0.615971	+	0.0382142i
$265$	−1.67256	+	3.75664i	−0.102745	+	0.230769i
$266$	−0.358024	+	1.68437i	−0.0219518	+	0.103275i
$267$	26.9541	+	4.53476i	1.64956	+	0.277523i
$268$	10.3597	−	4.61241i	0.632816	−	0.281748i
$269$	−8.96818	−	9.96017i	−0.546800	−	0.607282i	0.404882	−	0.914369i	$-0.367313\pi$
$269$	−8.96818	−	9.96017i	−0.546800	−	0.607282i	−0.951682	+	0.307087i	$0.900646\pi$
$270$	−6.72934	+	4.09954i	−0.409535	+	0.249490i
$271$	18.9726	+	26.1135i	1.15250	+	1.58628i	0.735738	+	0.677266i	$0.236835\pi$
$271$	18.9726	+	26.1135i	1.15250	+	1.58628i	0.416763	+	0.909015i	$0.363165\pi$
$272$	0.510944	−	4.86131i	0.0309805	−	0.294760i
$273$	1.53082	−	0.227417i	0.0926496	−	0.0137639i
$274$	−0.373993	−	0.215925i	−0.0225938	−	0.0130445i
$275$	−12.6478	−	9.18917i	−0.762692	−	0.554128i
$276$	−12.6592	+	6.29783i	−0.761992	+	0.379085i
$277$	−27.9823	−	9.09198i	−1.68129	−	0.546284i	−0.696129	−	0.717916i	$-0.745096\pi$
$277$	−27.9823	−	9.09198i	−1.68129	−	0.546284i	−0.985161	+	0.171632i	$0.945096\pi$
$278$	−3.31356			−0.198734
$279$	−10.8428	+	12.7057i	−0.649141	+	0.760668i
$280$	0.675134			0.0403470
$281$	2.52970	+	0.821948i	0.150909	+	0.0490333i	0.383497	−	0.923542i	$-0.374720\pi$
$281$	2.52970	+	0.821948i	0.150909	+	0.0490333i	−0.232588	+	0.972575i	$0.574720\pi$
$282$	−4.40165	+	2.18979i	−0.262115	+	0.130400i
$283$	13.2056	+	9.59441i	0.784990	+	0.570328i	0.906472	−	0.422265i	$-0.138765\pi$
$283$	13.2056	+	9.59441i	0.784990	+	0.570328i	−0.121483	+	0.992594i	$0.538765\pi$
$284$	−8.04726	−	4.64609i	−0.477517	−	0.275695i
$285$	10.0490	−	1.49287i	0.595251	−	0.0884297i
$286$	−1.21455	+	11.5557i	−0.0718177	+	0.683300i
$287$	−0.0134196	−	0.0184705i	−0.000792132	−	0.00109028i
$288$	−2.39275	−	1.80963i	−0.140994	−	0.106633i
$289$	4.61257	+	5.12278i	0.271328	+	0.301340i
$290$	−2.68517	+	1.19552i	−0.157679	+	0.0702031i
$291$	6.61091	+	1.11222i	0.387539	+	0.0651995i
$292$	1.19001	−	5.59857i	0.0696402	−	0.327631i
$293$	0.444331	−	0.997984i	0.0259581	−	0.0583029i	−0.900101	−	0.435681i	$-0.856508\pi$
$293$	0.444331	−	0.997984i	0.0259581	−	0.0583029i	0.926059	+	0.377378i	$0.123174\pi$
$294$	11.7584	+	0.729481i	0.685766	+	0.0425442i
$295$	−3.08944	−	9.50832i	−0.179874	−	0.553596i
$296$	2.88141	+	1.28289i	0.167479	+	0.0745663i
$297$	6.94606	+	29.2699i	0.403051	+	1.69841i
$298$	−6.40574	+	1.36158i	−0.371075	+	0.0788744i
$299$	−6.66379	−	14.9671i	−0.385377	−	0.865571i
$300$	1.63415	+	4.38239i	0.0943478	+	0.253018i
$301$	2.67825	−	0.281495i	0.154372	−	0.0162251i
$302$	18.4272	−	13.3881i	1.06037	−	0.770401i
$303$	−7.19335	−	3.75260i	−0.413247	−	0.215581i
$304$	1.93394	+	3.34968i	0.110919	+	0.192117i
$305$	−3.13058	+	5.42233i	−0.179257	+	0.310482i
$306$	14.3997	−	2.77294i	0.823176	−	0.158518i
$307$	−9.38507	+	10.4232i	−0.535634	+	0.594882i	−0.948841	−	0.315755i	$-0.897742\pi$
$307$	−9.38507	+	10.4232i	−0.535634	+	0.594882i	0.413206	+	0.910637i	$0.364409\pi$
$308$	0.796487	−	2.45134i	0.0453841	−	0.139678i
$309$	−24.1167	−	9.52416i	−1.37195	−	0.541810i
$310$	−5.27025	−	6.59646i	−0.299330	−	0.374654i
$311$		−	8.81000i		−	0.499569i	−0.968301	−	0.249785i	$-0.919640\pi$
$311$		−	8.81000i		−	0.499569i	0.968301	−	0.249785i	$-0.0803598\pi$
$312$	2.21348	−	2.68039i	0.125313	−	0.151747i
$313$	8.09230	+	7.28634i	0.457404	+	0.411849i	0.865358	−	0.501154i	$-0.167091\pi$
$313$	8.09230	+	7.28634i	0.457404	+	0.411849i	−0.407954	+	0.913002i	$0.633758\pi$
$314$	9.89464	−	13.6188i	0.558387	−	0.768554i
$315$	0.588788	+	1.93793i	0.0331744	+	0.109190i
$316$	9.90861	−	5.72074i	0.557403	−	0.321817i
$317$	24.4835	+	2.57332i	1.37513	+	0.144532i	0.763089	−	0.646294i	$-0.223682\pi$
$317$	24.4835	+	2.57332i	1.37513	+	0.144532i	0.612041	+	0.790826i	$0.290349\pi$
$318$	−1.17201	−	4.54820i	−0.0657230	−	0.255050i
$319$	1.17296	+	11.1600i	0.0656731	+	0.624838i
$320$	1.12695	−	1.01471i	0.0629982	−	0.0567239i
$321$	−0.879241	−	20.5496i	−0.0490744	−	1.14696i
$322$	0.755620	+	3.55491i	0.0421091	+	0.198108i
$323$	−18.4933	−	3.93088i	−1.02900	−	0.218720i
$324$	3.10769	−	8.44643i	0.172650	−	0.469246i
$325$	−5.15433	+	1.67474i	−0.285911	+	0.0928980i
$326$	−3.99031	+	1.29653i	−0.221003	+	0.0718082i
$327$	−20.9271	−	21.3328i	−1.15727	−	1.17971i
$328$	−0.0501607	−	0.0106620i	−0.00276966	−	0.000588710i
$329$	0.262733	+	1.23606i	0.0144849	+	0.0681462i
$330$	−15.1925	+	0.650032i	−0.836320	+	0.0357831i
$331$	13.7730	−	12.4013i	0.757033	−	0.681635i	−0.197313	−	0.980341i	$-0.563221\pi$
$331$	13.7730	−	12.4013i	0.757033	−	0.681635i	0.954345	+	0.298705i	$0.0965548\pi$
$332$	0.636999	+	6.06064i	0.0349599	+	0.332621i
$333$	−1.16956	+	9.38973i	−0.0640914	+	0.514554i
$334$	6.14482	+	0.645846i	0.336229	+	0.0353391i
$335$	−14.8928	+	8.59835i	−0.813679	+	0.469778i
$336$	−0.603902	+	0.479505i	−0.0329456	+	0.0261592i
$337$	−4.86237	+	6.69248i	−0.264870	+	0.364563i	−0.920650	−	0.390390i	$-0.872340\pi$
$337$	−4.86237	+	6.69248i	−0.264870	+	0.364563i	0.655779	+	0.754953i	$0.272340\pi$
$338$	−6.66751	−	6.00345i	−0.362664	−	0.326545i
$339$	−16.7049	−	13.7949i	−0.907284	−	0.749239i
$340$			7.41257i			0.402003i
$341$	−30.1685	+	11.3535i	−1.63372	+	0.614828i
$342$	−7.92846	+	8.47252i	−0.428722	+	0.458142i
$343$	1.89880	−	5.84389i	0.102525	−	0.315540i
$344$	4.04750	−	4.49521i	0.218227	−	0.242365i
$345$	18.0936	−	11.5047i	0.974127	−	0.619393i
$346$	−3.12368	+	5.41037i	−0.167930	+	0.290863i
$347$	6.56431	+	11.3697i	0.352391	+	0.610359i	0.986668	−	0.162747i	$-0.0520355\pi$
$347$	6.56431	+	11.3697i	0.352391	+	0.610359i	−0.634277	+	0.773106i	$0.718702\pi$
$348$	1.55277	−	2.97649i	0.0832370	−	0.159556i
$349$	−16.3305	+	11.8648i	−0.874152	+	0.635109i	−0.931698	−	0.363234i	$-0.881673\pi$
$349$	−16.3305	+	11.8648i	−0.874152	+	0.635109i	0.0575457	+	0.998343i	$0.481673\pi$
$350$	1.19563	−	0.125666i	0.0639090	−	0.00671711i
$351$	9.62428	+	4.01607i	0.513706	+	0.214362i
$352$	−2.35477	−	5.28891i	−0.125510	−	0.281900i
$353$	33.7575	−	7.17537i	1.79673	−	0.381907i	0.816120	−	0.577882i	$-0.196121\pi$
$353$	33.7575	−	7.17537i	1.79673	−	0.381907i	0.980609	+	0.195976i	$0.0627874\pi$
$354$	9.51663	+	6.31088i	0.505803	+	0.335419i
$355$	12.8729	+	5.73140i	0.683225	+	0.304191i
$356$	−4.87649	−	15.0083i	−0.258454	−	0.795439i
$357$	0.233394	−	3.76206i	0.0123525	−	0.199109i
$358$	8.62715	−	19.3769i	0.455959	−	1.02410i
$359$	5.73074	−	26.9610i	0.302457	−	1.42295i	−0.520022	−	0.854153i	$-0.674076\pi$
$359$	5.73074	−	26.9610i	0.302457	−	1.42295i	0.822479	−	0.568796i	$-0.192590\pi$
$360$	3.89547	+	2.34990i	0.205310	+	0.123851i
$361$	−3.69031	+	1.64303i	−0.194227	+	0.0864754i
$362$	7.12895	+	7.91750i	0.374689	+	0.416135i
$363$	−10.4555	+	37.5739i	−0.548772	+	1.97212i
$364$	−0.525198	−	0.722873i	−0.0275278	−	0.0378888i
$365$	−0.907271	+	8.63211i	−0.0474887	+	0.451825i
$366$	−1.05086	−	7.07369i	−0.0549292	−	0.369748i
$367$	−31.6580	−	18.2778i	−1.65254	−	0.954092i	−0.976025	−	0.217659i	$-0.930158\pi$
$367$	−31.6580	−	18.2778i	−1.65254	−	0.954092i	−0.676511	−	0.736433i	$-0.736509\pi$
$368$	6.60423	+	4.79825i	0.344269	+	0.250126i
$369$	−0.0131408	−	0.153282i	−0.000684083	−	0.00797953i
$370$	−4.54895	−	1.47804i	−0.236489	−	0.0768398i
$371$	−1.20726			−0.0626777
$372$	9.39925	+	2.15735i	0.487328	+	0.111854i
$373$	15.7886			0.817502			0.408751	−	0.912646i	$-0.365964\pi$
$373$	15.7886			0.817502			0.408751	+	0.912646i	$0.365964\pi$
$374$	26.9142	+	8.74495i	1.39170	+	0.452190i
$375$	−9.00882	−	18.1085i	−0.465213	−	0.935117i
$376$	2.29632	+	1.66838i	0.118424	+	0.0860399i
$377$	3.36889	+	1.94503i	0.173507	+	0.100174i
$378$	−1.90306	−	1.31529i	−0.0978827	−	0.0676510i
$379$	−2.85044	+	27.1201i	−0.146417	+	1.39307i	0.636662	+	0.771143i	$0.280315\pi$
$379$	−2.85044	+	27.1201i	−0.146417	+	1.39307i	−0.783079	+	0.621922i	$0.786352\pi$
$380$	−3.44763	−	4.74526i	−0.176860	−	0.243427i
$381$	13.3378	+	3.71144i	0.683317	+	0.190143i
$382$	6.29634	+	6.99280i	0.322149	+	0.357783i
$383$	3.77097	−	1.67894i	0.192687	−	0.0857900i	−0.308125	−	0.951346i	$-0.599701\pi$
$383$	3.77097	−	1.67894i	0.192687	−	0.0857900i	0.500812	+	0.865556i	$0.333035\pi$
$384$	−0.287362	+	1.70805i	−0.0146644	+	0.0871634i
$385$	−0.812653	+	3.82323i	−0.0414166	+	0.194850i
$386$	3.41540	−	7.67112i	0.173839	−	0.390449i
$387$	16.4331	+	7.69782i	0.835340	+	0.391302i
$388$	−1.19604	−	3.68102i	−0.0607195	−	0.186875i
$389$	14.1418	+	6.29632i	0.717016	+	0.319236i	0.732616	−	0.680642i	$-0.238299\pi$
$389$	14.1418	+	6.29632i	0.717016	+	0.319236i	−0.0156002	+	0.999878i	$0.504966\pi$
$390$	−2.91337	+	4.39329i	−0.147524	+	0.222463i
$391$	−39.0308	+	8.29625i	−1.97387	+	0.419560i
$392$	−2.76654	−	6.21375i	−0.139731	−	0.313842i
$393$	−27.6259	+	10.3014i	−1.39354	+	0.519638i
$394$	4.67001	−	0.490838i	0.235272	−	0.0247281i
$395$	−14.0369	+	10.1984i	−0.706271	+	0.513136i
$396$	13.1279	−	11.3717i	0.659702	−	0.571451i
$397$	−5.35373	−	9.27293i	−0.268696	−	0.465395i	0.699829	−	0.714310i	$-0.253259\pi$
$397$	−5.35373	−	9.27293i	−0.268696	−	0.465395i	−0.968525	+	0.248915i	$0.919926\pi$
$398$	9.89686	−	17.1419i	0.496085	−	0.859244i
$399$	1.60035	+	2.51689i	0.0801175	+	0.126002i
$400$	1.80689	−	2.00676i	0.0903447	−	0.100338i
$401$	−6.30852	+	19.4156i	−0.315033	+	0.969571i	0.660708	+	0.750643i	$0.270256\pi$
$401$	−6.30852	+	19.4156i	−0.315033	+	0.969571i	−0.975741	+	0.218928i	$0.929744\pi$
$402$	7.21460	−	18.2685i	0.359832	−	0.911152i
$403$	−2.96308	+	10.7744i	−0.147602	+	0.536711i
$404$			4.68424i			0.233050i
$405$	−3.34800	+	13.2311i	−0.166363	+	0.657458i
$406$	−0.641277	−	0.577409i	−0.0318261	−	0.0286563i
$407$	−10.7332	+	14.7730i	−0.532026	+	0.732271i
$408$	−5.26468	−	6.63048i	−0.260640	−	0.328258i
$409$	20.1660	−	11.6429i	0.997146	−	0.575702i	0.0897434	−	0.995965i	$-0.471395\pi$
$409$	20.1660	−	11.6429i	0.997146	−	0.575702i	0.907403	+	0.420262i	$0.138062\pi$
$410$	0.0773399	+	0.00812876i	0.00381955	+	0.000401451i
$411$	−0.724325	+	0.186649i	−0.0357283	+	0.00920670i
$412$	1.56482	+	14.8882i	0.0770930	+	0.733491i
$413$	2.18123	−	1.96399i	0.107331	−	0.0966415i
$414$	−8.01352	+	23.1416i	−0.393843	+	1.13735i
$415$	−1.92138	−	9.03938i	−0.0943168	−	0.443726i
$416$	−1.96313	−	0.417276i	−0.0962502	−	0.0204586i
$417$	−4.09704	+	4.01912i	−0.200633	+	0.196817i
$418$	−21.2968	+	6.91976i	−1.04166	+	0.338456i
$419$	−26.4966	+	8.60926i	−1.29444	+	0.420590i	−0.873645	−	0.486565i	$-0.838250\pi$
$419$	−26.4966	+	8.60926i	−1.29444	+	0.420590i	−0.420798	+	0.907154i	$0.638250\pi$
$420$	0.834767	−	0.818892i	0.0407324	−	0.0399578i
$421$	3.78824	+	0.805216i	0.184628	+	0.0392438i	0.299297	−	0.954160i	$-0.403248\pi$
$421$	3.78824	+	0.805216i	0.184628	+	0.0392438i	−0.114670	+	0.993404i	$0.536581\pi$
$422$	1.07553	+	5.05996i	0.0523559	+	0.246315i
$423$	−2.78634	+	8.04646i	−0.135477	+	0.391232i
$424$	−2.01518	+	1.81447i	−0.0978656	+	0.0881186i
$425$	1.37973	+	13.1273i	0.0669269	+	0.636767i
$426$	−15.5854	+	4.01614i	−0.755115	+	0.194583i
$427$	−1.82810	−	0.192141i	−0.0884680	−	0.00929836i
$428$	−10.2842	+	5.93757i	−0.497105	+	0.287004i
$429$	12.5145	+	15.7611i	0.604205	+	0.760953i
$430$	−5.39169	+	7.42102i	−0.260010	+	0.357873i
$431$	−7.13571	−	6.42502i	−0.343715	−	0.309482i	0.479135	−	0.877741i	$-0.340951\pi$
$431$	−7.13571	−	6.42502i	−0.343715	−	0.309482i	−0.822850	+	0.568259i	$0.807617\pi$
$432$	−5.15346	+	0.664740i	−0.247946	+	0.0319823i
$433$		−	6.69986i		−	0.321975i	−0.986956	−	0.160987i	$-0.948532\pi$
$433$		−	6.69986i		−	0.321975i	0.986956	−	0.160987i	$-0.0514679\pi$
$434$	1.13985	−	2.20118i	0.0547147	−	0.105660i
$435$	−1.86999	+	4.73512i	−0.0896592	+	0.227032i
$436$	−5.33158	+	16.4089i	−0.255336	+	0.785845i
$437$	21.1275	−	23.4644i	1.01066	−	1.12246i
$438$	−5.31929	−	8.36573i	−0.254166	−	0.399730i
$439$	−2.48466	+	4.30355i	−0.118586	+	0.205397i	−0.919208	−	0.393773i	$-0.871170\pi$
$439$	−2.48466	+	4.30355i	−0.118586	+	0.205397i	0.800621	+	0.599171i	$0.204503\pi$
$440$	4.38971	+	7.60320i	0.209271	+	0.362469i
$441$	15.4235	−	13.3602i	0.734452	−	0.636201i
$442$	7.93671	−	5.76636i	0.377511	−	0.274278i
$443$	−7.46121	+	0.784204i	−0.354493	+	0.0372587i	−0.280101	−	0.959970i	$-0.590368\pi$
$443$	−7.46121	+	0.784204i	−0.354493	+	0.0372587i	−0.0743913	+	0.997229i	$0.523701\pi$
$444$	5.11876	−	1.90873i	0.242926	−	0.0905846i
$445$	9.73349	+	21.8618i	0.461412	+	1.03635i
$446$	−1.97405	+	0.419597i	−0.0934739	+	0.0198685i
$447$	−6.26884	+	9.45325i	−0.296506	+	0.447123i
$448$	0.406715	+	0.181081i	0.0192155	+	0.00855529i
$449$	−9.33448	−	28.7286i	−0.440521	−	1.35579i	−0.887321	−	0.461152i	$-0.847436\pi$
$449$	−9.33448	−	28.7286i	−0.440521	−	1.35579i	0.446800	−	0.894634i	$-0.352564\pi$
$450$	7.33608	+	3.43648i	0.345826	+	0.161997i
$451$	0.120756	−	0.271223i	0.00568618	−	0.0127714i
$452$	−2.60057	+	12.2347i	−0.122320	+	0.575472i
$453$	6.54532	−	38.9046i	0.307526	−	1.82790i
$454$	−26.1008	+	11.6208i	−1.22497	+	0.545393i
$455$	0.906661	+	1.00695i	0.0425049	+	0.0472065i
$456$	6.45414	+	1.79596i	0.302243	+	0.0841035i
$457$	16.3963	+	22.5675i	0.766985	+	1.05566i	0.996601	+	0.0823829i	$0.0262531\pi$
$457$	16.3963	+	22.5675i	0.766985	+	1.05566i	−0.229616	+	0.973281i	$0.573747\pi$
$458$	−2.31581	+	22.0335i	−0.108211	+	1.02956i
$459$	14.4411	−	20.8944i	0.674051	−	0.975268i
$460$	−10.7207	−	6.18962i	−0.499857	−	0.288593i
$461$	1.15666	+	0.840360i	0.0538708	+	0.0391395i	0.614395	−	0.788999i	$-0.289400\pi$
$461$	1.15666	+	0.840360i	0.0538708	+	0.0391395i	−0.560524	+	0.828138i	$0.689400\pi$
$462$	−1.98849	−	3.99703i	−0.0925129	−	0.185958i
$463$	5.56056	+	1.80673i	0.258421	+	0.0839660i	0.435362	−	0.900255i	$-0.356620\pi$
$463$	5.56056	+	1.80673i	0.258421	+	0.0839660i	−0.176941	+	0.984221i	$0.556620\pi$
$464$	−1.93826			−0.0899815
$465$	−14.5174	−	1.76371i	−0.673230	−	0.0817901i
$466$	−8.56131			−0.396595
$467$	9.20360	+	2.99043i	0.425892	+	0.138381i	0.514117	−	0.857720i	$-0.328120\pi$
$467$	9.20360	+	2.99043i	0.425892	+	0.138381i	−0.0882255	+	0.996101i	$0.528120\pi$
$468$	−0.514288	−	5.99895i	−0.0237730	−	0.277302i
$469$	−4.08444	−	2.96752i	−0.188602	−	0.137027i
$470$	−3.72766	−	2.15216i	−0.171944	−	0.0992719i
$471$	−4.28450	−	28.8404i	−0.197419	−	1.32890i
$472$	0.689131	−	6.55664i	0.0317198	−	0.301794i
$473$	20.5841	+	28.3315i	0.946456	+	1.30268i
$474$	5.31259	−	19.0919i	0.244015	−	0.876918i
$475$	−6.98884	−	7.76189i	−0.320670	−	0.356140i
$476$	−1.98806	+	0.885141i	−0.0911225	+	0.0405704i
$477$	−6.96578	−	4.20203i	−0.318941	−	0.192398i
$478$	−4.92935	+	23.1908i	−0.225463	+	1.06072i
$479$	−4.07232	+	9.14657i	−0.186069	+	0.417917i	−0.982361	−	0.186995i	$-0.940125\pi$
$479$	−4.07232	+	9.14657i	−0.186069	+	0.417917i	0.796292	+	0.604912i	$0.206792\pi$
$480$	0.162637	−	2.62154i	0.00742335	−	0.119656i
$481$	1.95615	+	6.02040i	0.0891926	+	0.274507i
$482$	−12.1872	−	5.42610i	−0.555113	−	0.247152i
$483$	5.24615	+	3.47894i	0.238708	+	0.158297i
$484$	22.0255	−	4.68166i	1.00116	−	0.212803i
$485$	2.38729	+	5.36194i	0.108401	+	0.243473i
$486$	−6.40245	−	14.2130i	−0.290421	−	0.644714i
$487$	30.1876	−	3.17284i	1.36793	−	0.143775i	0.608080	−	0.793875i	$-0.291940\pi$
$487$	30.1876	−	3.17284i	1.36793	−	0.143775i	0.759848	+	0.650100i	$0.225273\pi$
$488$	−3.34028	+	2.42686i	−0.151207	+	0.109859i
$489$	−3.36120	+	6.44306i	−0.151999	+	0.291365i
$490$	5.15731	+	8.93272i	0.232984	+	0.403539i
$491$	−4.73158	+	8.19534i	−0.213533	+	0.369851i	−0.952818	−	0.303543i	$-0.901831\pi$
$491$	−4.73158	+	8.19534i	−0.213533	+	0.369851i	0.739284	+	0.673393i	$0.235164\pi$
$492$	−0.0749533	+	0.0476586i	−0.00337916	+	0.00214861i
$493$	6.33960	−	7.04084i	0.285521	−	0.317103i
$494$	−2.39883	+	7.38283i	−0.107928	+	0.332169i
$495$	−17.9963	+	19.2312i	−0.808872	+	0.864378i
$496$	−1.40564	−	5.38741i	−0.0631151	−	0.241902i
$497$			4.13693i			0.185567i
$498$	8.13876	+	6.72102i	0.364707	+	0.301176i
$499$	−21.3394	−	19.2141i	−0.955282	−	0.860140i	0.0349753	−	0.999388i	$-0.488865\pi$
$499$	−21.3394	−	19.2141i	−0.955282	−	0.860140i	−0.990258	+	0.139248i	$0.955531\pi$
$500$	−6.86372	+	9.44710i	−0.306955	+	0.422487i
$501$	8.38110	−	6.65469i	0.374440	−	0.297310i
$502$	15.8064	−	9.12580i	0.705472	−	0.407304i
$503$	15.5895	+	1.63852i	0.695102	+	0.0730581i	0.445489	−	0.895288i	$-0.353030\pi$
$503$	15.5895	+	1.63852i	0.695102	+	0.0730581i	0.249613	+	0.968346i	$0.419697\pi$
$504$	−0.165085	+	1.32537i	−0.00735346	+	0.0590369i
$505$	−0.742512	−	7.06453i	−0.0330414	−	0.314367i
$506$	−35.1216	+	31.6236i	−1.56134	+	1.40584i
$507$	−15.5258	+	0.664292i	−0.689524	+	0.0295022i
$508$	−1.66187	−	7.81850i	−0.0737337	−	0.346890i
$509$	−28.2421	−	6.00304i	−1.25181	−	0.266080i	−0.466130	−	0.884716i	$-0.654352\pi$
$509$	−28.2421	−	6.00304i	−1.25181	−	0.266080i	−0.785678	+	0.618636i	$0.787686\pi$
$510$	8.99094	+	9.16524i	0.398125	+	0.405843i
$511$	−2.42348	+	0.787436i	−0.107208	+	0.0348341i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	0.473488	+	20.0925i	0.0209050	+	0.887105i
$514$	1.47888	+	0.314346i	0.0652306	+	0.0138652i
$515$	−4.71996	−	22.2057i	−0.207986	−	0.978498i
$516$	−0.447863	−	10.4674i	−0.0197161	−	0.460802i
$517$	−12.2119	+	10.9957i	−0.537081	+	0.483590i
$518$	−0.146781	−	1.39653i	−0.00644919	−	0.0613599i
$519$	2.70015	+	10.4784i	0.118523	+	0.459952i
$520$	3.02683	+	0.318133i	0.132735	+	0.0139510i
$521$	−11.1483	+	6.43646i	−0.488415	+	0.281987i	−0.723917	−	0.689887i	$-0.757660\pi$
$521$	−11.1483	+	6.43646i	−0.488415	+	0.281987i	0.235502	+	0.971874i	$0.424327\pi$
$522$	−1.69037	−	5.56366i	−0.0739853	−	0.243515i
$523$	18.9299	−	26.0547i	0.827745	−	1.13929i	−0.160594	−	0.987021i	$-0.551341\pi$
$523$	18.9299	−	26.0547i	0.827745	−	1.13929i	0.988339	−	0.152272i	$-0.0486591\pi$
$524$	12.6503	+	11.3904i	0.552630	+	0.497591i
$525$	1.32591	−	1.60559i	0.0578673	−	0.0700739i
$526$		−	15.6532i		−	0.682513i
$527$	24.1676	+	12.5149i	1.05276	+	0.545158i
$528$	−9.32664	−	3.68327i	−0.405890	−	0.160294i
$529$	13.4852	−	41.5032i	0.586313	−	1.80449i
$530$	2.75157	−	3.05593i	0.119520	−	0.132741i
$531$	19.4215	−	3.73997i	0.842819	−	0.162301i
$532$	0.860999	−	1.49129i	0.0373290	−	0.0646558i
$533$	−0.0514605	−	0.0891321i	−0.00222900	−	0.00386074i
$534$	−24.2336	−	12.6421i	−1.04869	−	0.547077i
$535$	14.5689	−	10.5849i	0.629868	−	0.457626i
$536$	−11.2779	+	1.18536i	−0.487132	+	0.0511997i
$537$	−12.8358	−	34.4226i	−0.553908	−	1.48544i
$538$	5.45138	+	12.2440i	0.235026	+	0.527877i
$539$	38.5180	−	8.18726i	1.65909	−	0.352650i
$540$	7.66681	−	1.81942i	0.329927	−	0.0782952i
$541$	−13.0901	−	5.82810i	−0.562788	−	0.250569i	0.105566	−	0.994412i	$-0.466334\pi$
$541$	−13.0901	−	5.82810i	−0.562788	−	0.250569i	−0.668355	+	0.743843i	$0.733001\pi$
$542$	−9.97446	−	30.6982i	−0.428440	−	1.31860i
$543$	18.4179	+	1.14263i	0.790390	+	0.0490349i
$544$	−1.98816	+	4.46549i	−0.0852418	+	0.191456i
$545$	5.43980	−	25.5922i	0.233015	−	1.09625i
$546$	−1.52617	−	0.256764i	−0.0653142	−	0.0109885i
$547$	31.1143	−	13.8530i	1.33035	−	0.592310i	0.386379	−	0.922340i	$-0.373726\pi$
$547$	31.1143	−	13.8530i	1.33035	−	0.592310i	0.943970	+	0.330030i	$0.107059\pi$
$548$	0.288964	+	0.320927i	0.0123439	+	0.0137093i
$549$	−9.87923	−	7.47161i	−0.421635	−	0.318880i
$550$	9.18917	+	12.6478i	0.391828	+	0.539304i
$551$	−0.783644	+	7.45588i	−0.0333844	+	0.317631i
$552$	13.9857	−	2.07770i	0.595272	−	0.0884327i
$553$	−4.41137	−	2.54690i	−0.187590	−	0.108305i
$554$	23.8031	+	17.2940i	1.01130	+	0.734751i
$555$	−7.41730	+	3.69005i	−0.314847	+	0.156634i
$556$	3.15138	+	1.02395i	0.133648	+	0.0434250i
$557$	39.4877			1.67315			0.836574	−	0.547854i	$-0.184555\pi$
$557$	39.4877			1.67315			0.836574	+	0.547854i	$0.184555\pi$
$558$	14.2384	−	8.73319i	0.602759	−	0.369706i
$559$	12.1400			0.513469
$560$	−0.642091	−	0.208628i	−0.0271333	−	0.00881614i
$561$	43.8849	−	21.8324i	1.85282	−	0.921765i
$562$	−2.15189	−	1.56344i	−0.0907719	−	0.0659496i
$563$	29.9644	+	17.2999i	1.26285	+	0.729106i	0.973625	−	0.228156i	$-0.0732696\pi$
$563$	29.9644	+	17.2999i	1.26285	+	0.729106i	0.289224	+	0.957262i	$0.406603\pi$
$564$	4.86290	−	0.722426i	0.204765	−	0.0304196i
$565$	1.98269	−	18.8640i	0.0834122	−	0.793614i
$566$	−9.59441	−	13.2056i	−0.403283	−	0.555071i
$567$	−3.94838	+	0.681999i	−0.165816	+	0.0286413i
$568$	6.21768	+	6.90544i	0.260888	+	0.289746i
$569$	−17.2623	+	7.68568i	−0.723675	+	0.322201i	−0.735309	−	0.677732i	$-0.762963\pi$
$569$	−17.2623	+	7.68568i	−0.723675	+	0.322201i	0.0116348	+	0.999932i	$0.496296\pi$
$570$	−10.0185	−	1.68551i	−0.419628	−	0.0705983i
$571$	−0.562858	+	2.64804i	−0.0235549	+	0.110817i	−0.988354	−	0.152169i	$-0.951374\pi$
$571$	−0.562858	+	2.64804i	−0.0235549	+	0.110817i	0.964800	+	0.262986i	$0.0847074\pi$
$572$	4.72600	−	10.6148i	0.197604	−	0.443825i
$573$	16.2669	+	1.00918i	0.679558	+	0.0421590i
$574$	0.00705508	+	0.0217133i	0.000294474	+	0.000906296i
$575$	−20.1380	−	8.96601i	−0.839812	−	0.373908i
$576$	1.71644	+	2.46046i	0.0715182	+	0.102519i
$577$	−11.3752	+	2.41787i	−0.473554	+	0.100657i	−0.438505	−	0.898729i	$-0.644492\pi$
$577$	−11.3752	+	2.41787i	−0.473554	+	0.100657i	−0.0350489	+	0.999386i	$0.511159\pi$
$578$	−2.80379	−	6.29741i	−0.116622	−	0.261938i
$579$	−5.08158	−	13.6276i	−0.211183	−	0.566342i
$580$	2.92319	−	0.307239i	0.121379	−	0.0127574i
$581$	2.19494	−	1.59472i	0.0910614	−	0.0661600i
$582$	−5.94366	−	3.10067i	−0.246372	−	0.128527i
$583$	−7.84956	−	13.5958i	−0.325096	−	0.563082i
$584$	−2.86182	+	4.95682i	−0.118423	+	0.205115i
$585$	1.72653	+	8.96579i	0.0713834	+	0.370690i
$586$	−0.730978	+	0.811834i	−0.0301964	+	0.0335365i
$587$	6.04469	−	18.6037i	0.249491	−	0.767855i	−0.745374	−	0.666646i	$-0.767729\pi$
$587$	6.04469	−	18.6037i	0.249491	−	0.767855i	0.994865	−	0.101208i	$-0.0322709\pi$
$588$	−10.9575	−	4.32734i	−0.451881	−	0.178456i
$589$	−21.2920	+	3.22891i	−0.877321	+	0.133045i
$590$			9.99763i			0.411596i
$591$	5.17886	−	6.27130i	0.213030	−	0.257967i
$592$	−2.34395	−	2.11050i	−0.0963358	−	0.0867411i
$593$	−19.6516	+	27.0480i	−0.806993	+	1.11073i	0.184788	+	0.982778i	$0.440840\pi$
$593$	−19.6516	+	27.0480i	−0.806993	+	1.11073i	−0.991780	+	0.127952i	$0.959160\pi$
$594$	2.43880	−	29.9838i	0.100065	−	1.23025i
$595$	2.85798	−	1.65006i	0.117166	−	0.0676457i
$596$	6.51298	+	0.684541i	0.266782	+	0.0280399i
$597$	−8.55498	−	33.1992i	−0.350132	−	1.35875i
$598$	1.71255	+	16.2938i	0.0700313	+	0.666303i
$599$	2.19117	−	1.97294i	0.0895287	−	0.0806120i	−0.623151	−	0.782101i	$-0.714148\pi$
$599$	2.19117	−	1.97294i	0.0895287	−	0.0806120i	0.712680	+	0.701489i	$0.247481\pi$
$600$	−0.199936	−	4.67289i	−0.00816234	−	0.190770i
$601$	4.59804	+	21.6321i	0.187558	+	0.882390i	0.966774	+	0.255635i	$0.0822844\pi$
$601$	4.59804	+	21.6321i	0.187558	+	0.882390i	−0.779216	+	0.626756i	$0.784382\pi$
$602$	−2.63415	−	0.559906i	−0.107360	−	0.0228201i
$603$	−13.2380	−	31.3389i	−0.539095	−	1.27622i
$604$	−21.6625	+	7.03856i	−0.881433	+	0.286395i
$605$	−32.4756	+	10.5520i	−1.32032	+	0.428998i
$606$	5.68166	+	5.79180i	0.230802	+	0.235276i
$607$	4.58018	+	0.973547i	0.185904	+	0.0395151i	0.299923	−	0.953964i	$-0.403039\pi$
$607$	4.58018	+	0.973547i	0.185904	+	0.0395151i	−0.114019	+	0.993479i	$0.536372\pi$
$608$	−0.804176	−	3.78335i	−0.0326137	−	0.153435i
$609$	−1.49326	+	0.0638912i	−0.0605100	+	0.00258900i
$610$	4.65295	−	4.18954i	0.188393	−	0.169629i
$611$	0.595462	+	5.66544i	0.0240898	+	0.229199i
$612$	−14.5518	−	1.81253i	−0.588222	−	0.0732673i
$613$	−8.74491	−	0.919127i	−0.353204	−	0.0371232i	−0.0737346	−	0.997278i	$-0.523492\pi$
$613$	−8.74491	−	0.919127i	−0.353204	−	0.0371232i	−0.279469	+	0.960155i	$0.590158\pi$
$614$	12.1467	−	7.01288i	0.490200	−	0.283017i
$615$	0.105486	−	0.0837573i	0.00425362	−	0.00337742i
$616$	−1.51501	+	2.08523i	−0.0610414	+	0.0840163i
$617$	−14.0825	−	12.6799i	−0.566939	−	0.510474i	0.335069	−	0.942194i	$-0.391240\pi$
$617$	−14.0825	−	12.6799i	−0.566939	−	0.510474i	−0.902008	+	0.431719i	$0.857907\pi$
$618$	19.9932	+	16.5105i	0.804246	+	0.664149i
$619$		−	7.72738i		−	0.310590i	−0.987868	−	0.155295i	$-0.950367\pi$
$619$		−	7.72738i		−	0.310590i	0.987868	−	0.155295i	$-0.0496328\pi$
$620$	2.97389	+	7.90220i	0.119434	+	0.317360i
$621$	18.1609	+	38.3332i	0.728773	+	1.53826i
$622$	−2.72244	+	8.37881i	−0.109160	+	0.335959i
$623$	−4.70107	+	5.22106i	−0.188344	+	0.209178i
$624$	−2.93343	+	1.86520i	−0.117431	+	0.0746678i
$625$	2.10313	−	3.64273i	0.0841252	−	0.145709i
$626$	−5.44464	−	9.43038i	−0.217611	−	0.376914i
$627$	−17.9392	+	34.3875i	−0.716421	+	1.37330i
$628$	−13.6188	+	9.89464i	−0.543450	+	0.394839i
$629$	15.3330	−	1.61157i	0.611368	−	0.0642574i
$630$	0.0388837	−	2.02503i	0.00154916	−	0.0806791i
$631$	−1.62998	−	3.66100i	−0.0648886	−	0.145742i	0.878190	−	0.478312i	$-0.158751\pi$
$631$	−1.62998	−	3.66100i	−0.0648886	−	0.145742i	−0.943079	+	0.332569i	$0.892084\pi$
$632$	−11.1915	+	2.37882i	−0.445172	+	0.0946243i
$633$	7.46722	+	4.95183i	0.296795	+	0.196817i
$634$	−22.4900	−	10.0132i	−0.893192	−	0.397675i
$635$	3.74568	+	11.5280i	0.148643	+	0.457476i
$636$	−0.290824	+	4.68777i	−0.0115319	+	0.185882i
$637$	5.55240	−	12.4709i	0.219994	−	0.494115i
$638$	2.33307	−	10.9762i	0.0923670	−	0.434552i
$639$	−14.3992	+	23.8698i	−0.569623	+	0.944273i
$640$	−1.38535	+	0.616798i	−0.0547608	+	0.0243811i
$641$	−4.15635	−	4.61610i	−0.164166	−	0.182325i	0.655449	−	0.755239i	$-0.272479\pi$
$641$	−4.15635	−	4.61610i	−0.164166	−	0.182325i	−0.819615	+	0.572914i	$0.805813\pi$
$642$	−5.51396	+	19.8155i	−0.217618	+	0.782055i
$643$	−20.7930	−	28.6191i	−0.819996	−	1.12863i	−0.989704	−	0.143133i	$-0.954282\pi$
$643$	−20.7930	−	28.6191i	−0.819996	−	1.12863i	0.169708	−	0.985494i	$-0.445718\pi$
$644$	0.379891	−	3.61442i	0.0149698	−	0.142428i
$645$	2.33466	+	15.7154i	0.0919273	+	0.618795i
$646$	16.3735	+	9.45325i	0.644207	+	0.371933i
$647$	8.66503	+	6.29551i	0.340657	+	0.247502i	0.744939	−	0.667132i	$-0.232478\pi$
$647$	8.66503	+	6.29551i	0.340657	+	0.247502i	−0.404282	+	0.914634i	$0.632478\pi$
$648$	−5.56568	+	7.07271i	−0.218641	+	0.277842i
$649$	36.3003	+	11.7947i	1.42491	+	0.462981i
$650$	5.41958			0.212573
$651$	−1.26051	−	4.10420i	−0.0494033	−	0.160856i
$652$	4.19566			0.164315
$653$	−35.6623	−	11.5874i	−1.39557	−	0.453450i	−0.487818	−	0.872946i	$-0.662207\pi$
$653$	−35.6623	−	11.5874i	−1.39557	−	0.453450i	−0.907757	+	0.419496i	$0.862207\pi$
$654$	13.3107	+	26.7556i	0.520489	+	1.04623i
$655$	−20.8840	−	15.1731i	−0.816007	−	0.592864i
$656$	0.0444110	+	0.0256407i	0.00173396	+	0.00100110i
$657$	−16.7241	−	3.89182i	−0.652468	−	0.151834i
$658$	0.132090	−	1.25675i	0.00514941	−	0.0489933i
$659$	25.5163	+	35.1202i	0.993975	+	1.36809i	0.928950	+	0.370205i	$0.120713\pi$
$659$	25.5163	+	35.1202i	0.993975	+	1.36809i	0.0650248	+	0.997884i	$0.479287\pi$
$660$	14.6498	+	4.07653i	0.570243	+	0.158679i
$661$	2.38791	+	2.65204i	0.0928788	+	0.103152i	0.787792	−	0.615941i	$-0.211224\pi$
$661$	2.38791	+	2.65204i	0.0928788	+	0.103152i	−0.694914	+	0.719093i	$0.744557\pi$
$662$	−16.9311	+	7.53821i	−0.658046	+	0.292981i
$663$	2.81911	−	16.7565i	0.109485	−	0.650767i
$664$	1.26702	−	5.96086i	0.0491699	−	0.231326i
$665$	−1.06213	+	2.38557i	−0.0411875	+	0.0925086i
$666$	4.01390	−	8.56875i	0.155536	−	0.332032i
$667$	4.88944	+	15.0481i	0.189320	+	0.582666i
$668$	−5.64449	−	2.51309i	−0.218392	−	0.0972343i
$669$	−1.93186	+	2.91320i	−0.0746901	+	0.112631i
$670$	16.8209	−	3.57539i	0.649848	−	0.138129i
$671$	−9.72243	−	21.8369i	−0.375330	−	0.843006i
$672$	0.722520	−	0.269421i	0.0278718	−	0.0103931i
$673$	−31.4236	+	3.30275i	−1.21129	+	0.127312i	−0.688555	−	0.725184i	$-0.741755\pi$
$673$	−31.4236	+	3.30275i	−1.21129	+	0.127312i	−0.522734	+	0.852496i	$0.675088\pi$
$674$	6.69248	−	4.86237i	0.257785	−	0.187292i
$675$	13.2389	−	4.64915i	0.509565	−	0.178946i
$676$	4.48601	+	7.76999i	0.172539	+	0.298846i
$677$	0.517745	−	0.896760i	0.0198985	−	0.0344653i	−0.855905	−	0.517134i	$-0.826999\pi$
$677$	0.517745	−	0.896760i	0.0198985	−	0.0344653i	0.875803	+	0.482668i	$0.160332\pi$
$678$	11.6244	+	18.2819i	0.446433	+	0.702111i
$679$	−1.15301	+	1.28055i	−0.0442484	+	0.0491429i
$680$	2.29061	−	7.04977i	0.0878409	−	0.270346i
$681$	−18.1770	+	46.0270i	−0.696543	+	1.76376i
$682$	32.2004	−	1.47525i	1.23302	−	0.0564903i
$683$		−	3.29130i		−	0.125938i	−0.998015	−	0.0629691i	$-0.979943\pi$
$683$		−	3.29130i		−	0.125938i	0.998015	−	0.0629691i	$-0.0200570\pi$
$684$	10.1586	−	5.60782i	0.388422	−	0.214420i
$685$	−0.486672	−	0.438202i	−0.0185948	−	0.0167428i
$686$	−3.61172	+	4.97111i	−0.137896	+	0.189798i
$687$	23.8617	+	30.0521i	0.910381	+	1.14656i
$688$	−5.23850	+	3.02445i	−0.199716	+	0.115306i
$689$	−5.41250	−	0.568877i	−0.206200	−	0.0216725i
$690$	−20.7632	+	5.35040i	−0.790442	+	0.203686i
$691$	−2.53028	−	24.0740i	−0.0962565	−	0.915820i	−0.930960	−	0.365121i	$-0.881028\pi$
$691$	−2.53028	−	24.0740i	−0.0962565	−	0.915820i	0.834704	−	0.550699i	$-0.185639\pi$
$692$	4.64269	−	4.18029i	0.176488	−	0.158911i
$693$	−7.30678	−	2.53020i	−0.277561	−	0.0961145i
$694$	−2.72959	−	12.8417i	−0.103614	−	0.487465i
$695$	−4.91506	−	1.04473i	−0.186439	−	0.0396288i
$696$	−2.39655	+	2.35098i	−0.0908411	+	0.0891136i
$697$	−0.238399	+	0.0774606i	−0.00903001	+	0.00293403i
$698$	19.1977	−	6.23770i	0.726642	−	0.236100i
$699$	−10.5856	+	10.3843i	−0.400384	+	0.392770i
$700$	−1.17594	−	0.249954i	−0.0444465	−	0.00944739i
$701$	7.98943	+	37.5873i	0.301757	+	1.41965i	0.823870	+	0.566778i	$0.191810\pi$
$701$	7.98943	+	37.5873i	0.301757	+	1.41965i	−0.522114	+	0.852876i	$0.674856\pi$
$702$	−7.91220	−	6.79358i	−0.298627	−	0.256407i
$703$	−9.06611	+	8.16316i	−0.341935	+	0.307879i
$704$	0.605161	+	5.75772i	0.0228078	+	0.217002i
$705$	−7.21947	+	1.86036i	−0.271901	+	0.0700652i
$706$	−34.3226	−	3.60745i	−1.29175	−	0.135768i
$707$	1.80605	−	1.04272i	0.0679235	−	0.0392157i
$708$	−7.10069	−	8.94280i	−0.266860	−	0.336091i
$709$	−16.5675	+	22.8032i	−0.622206	+	0.856393i	−0.997511	−	0.0705082i	$-0.977538\pi$
$709$	−16.5675	+	22.8032i	−0.622206	+	0.856393i	0.375305	+	0.926901i	$0.377538\pi$
$710$	−10.4718	−	9.42885i	−0.392999	−	0.353858i
$711$	−16.5884	−	30.0498i	−0.622113	−	1.12696i
$712$			15.7807i			0.591405i
$713$	−38.2806	+	24.5032i	−1.43362	+	0.917653i
$714$	−1.38451	+	3.50581i	−0.0518140	+	0.131202i
$715$	−5.44493	+	16.7578i	−0.203629	+	0.626705i
$716$	−14.1927	+	15.7626i	−0.530406	+	0.589075i
$717$	22.0340	+	34.6531i	0.822873	+	1.29414i
$718$	−13.7817	+	23.8706i	−0.514328	+	0.890841i
$719$	10.0625	+	17.4288i	0.375268	+	0.649984i	0.990367	−	0.138466i	$-0.0442173\pi$
$719$	10.0625	+	17.4288i	0.375268	+	0.649984i	−0.615099	+	0.788450i	$0.710884\pi$
$720$	−2.97866	−	3.43866i	−0.111008	−	0.128151i
$721$	5.39197	−	3.91749i	0.200807	−	0.145895i
$722$	4.01742	−	0.422248i	0.149513	−	0.0157144i
$723$	−21.6503	+	8.07319i	−0.805185	+	0.300245i
$724$	−4.33339	−	9.73296i	−0.161049	−	0.361723i
$725$	5.11963	−	1.08821i	0.190138	−	0.0404151i
$726$	21.5548	−	32.5040i	0.799972	−	1.20634i
$727$	40.3783	+	17.9776i	1.49755	+	0.666751i	0.981788	−	0.189981i	$-0.0608428\pi$
$727$	40.3783	+	17.9776i	1.49755	+	0.666751i	0.515761	+	0.856733i	$0.327509\pi$
$728$	0.276113	+	0.849788i	0.0102334	+	0.0314952i
$729$	−25.1556	−	9.80783i	−0.931691	−	0.363253i
$730$	3.53033	−	7.92926i	0.130664	−	0.293475i
$731$	6.14743	−	28.9214i	0.227371	−	1.06970i
$732$	−1.18646	+	7.05221i	−0.0438530	+	0.260657i
$733$	−25.6166	+	11.4052i	−0.946170	+	0.421262i	−0.821035	−	0.570878i	$-0.806603\pi$
$733$	−25.6166	+	11.4052i	−0.946170	+	0.421262i	−0.125135	+	0.992140i	$0.539936\pi$
$734$	24.4604	+	27.1661i	0.902851	+	1.00272i
$735$	17.2115	+	4.78936i	0.634856	+	0.176658i
$736$	−4.79825	−	6.60423i	−0.176866	−	0.243435i
$737$	6.86255	−	65.2928i	0.252785	−	2.40509i
$738$	−0.0348691	+	0.149840i	−0.00128355	+	0.00551570i
$739$	35.9604	+	20.7617i	1.32282	+	0.763733i	0.984178	−	0.177181i	$-0.0566978\pi$
$739$	35.9604	+	20.7617i	1.32282	+	0.763733i	0.338646	+	0.940914i	$0.390031\pi$
$740$	3.86957	+	2.81141i	0.142248	+	0.103349i
$741$	5.98885	+	12.0381i	0.220006	+	0.442230i
$742$	1.14817	+	0.373063i	0.0421506	+	0.0136956i
$743$	0.914304			0.0335425			0.0167713	−	0.999859i	$-0.494661\pi$
$743$	0.914304			0.0335425			0.0167713	+	0.999859i	$0.494661\pi$
$744$	−8.27256	−	4.95629i	−0.303287	−	0.181706i
$745$	−9.93105			−0.363845
$746$	−15.0158	−	4.87894i	−0.549769	−	0.178631i
$747$	18.2153	−	1.56159i	0.666462	−	0.0571355i
$748$	−22.8946	−	16.6339i	−0.837108	−	0.608195i
$749$	4.57857	+	2.64344i	0.167297	+	0.0965892i
$750$	2.97207	+	20.0060i	0.108525	+	0.730518i
$751$	1.35910	−	12.9310i	0.0495942	−	0.471857i	−0.941335	−	0.337473i	$-0.890428\pi$
$751$	1.35910	−	12.9310i	0.0495942	−	0.471857i	0.990929	−	0.134384i	$-0.0429056\pi$
$752$	−1.66838	−	2.29632i	−0.0608394	−	0.0837383i
$753$	8.47472	−	30.4556i	0.308836	−	1.10986i
$754$	−2.60296	−	2.89088i	−0.0947941	−	0.105280i
$755$	31.5545	−	14.0490i	1.14839	−	0.511295i
$756$	1.40347	+	1.83899i	0.0510437	+	0.0668834i
$757$	2.08803	−	9.82343i	0.0758909	−	0.357039i	−0.923774	−	0.382939i	$-0.874912\pi$
$757$	2.08803	−	9.82343i	0.0758909	−	0.357039i	0.999665	+	0.0259004i	$0.00824528\pi$
$758$	11.0915	−	24.9119i	0.402861	−	0.904841i
$759$	−5.06863	+	81.7009i	−0.183980	+	2.96555i
$760$	1.81253	+	5.57839i	0.0657473	+	0.202349i
$761$	7.26212	+	3.23330i	0.263252	+	0.117207i	0.534118	−	0.845410i	$-0.320644\pi$
$761$	7.26212	+	3.23330i	0.263252	+	0.117207i	−0.270867	+	0.962617i	$0.587310\pi$
$762$	−11.5381	−	7.65140i	−0.417982	−	0.277181i
$763$	7.51343	−	1.59703i	0.272005	−	0.0578163i
$764$	−3.82729	−	8.59622i	−0.138466	−	0.311000i
$765$	22.2336	+	0.426920i	0.803858	+	0.0154353i
$766$	−4.10523	+	0.431477i	−0.148328	+	0.0155899i
$767$	10.7046	−	7.77732i	0.386519	−	0.280823i
$768$	0.801113	−	1.53565i	0.0289077	−	0.0554130i
$769$	−3.53908	−	6.12986i	−0.127622	−	0.221049i	0.795133	−	0.606436i	$-0.207401\pi$
$769$	−3.53908	−	6.12986i	−0.127622	−	0.221049i	−0.922755	+	0.385387i	$0.874068\pi$
$770$	1.95432	−	3.38499i	0.0704289	−	0.121986i
$771$	2.20984	−	1.40511i	0.0795853	−	0.0506038i
$772$	−5.61874	+	6.24025i	−0.202223	+	0.224591i
$773$	0.733266	−	2.25676i	0.0263738	−	0.0811701i	−0.937003	−	0.349321i	$-0.886412\pi$
$773$	0.733266	−	2.25676i	0.0263738	−	0.0811701i	0.963377	+	0.268150i	$0.0864124\pi$
$774$	−13.2500	−	12.3992i	−0.476262	−	0.445679i
$775$	6.73747	+	13.4409i	0.242017	+	0.482810i
$776$			3.87045i			0.138941i
$777$	−1.87538	−	1.54870i	−0.0672789	−	0.0555591i
$778$	−11.5039	−	10.3582i	−0.412436	−	0.371359i
$779$	0.116587	−	0.160468i	0.00417717	−	0.00574938i
$780$	4.12839	−	3.27799i	0.147820	−	0.117371i
$781$	−46.5891	+	26.8982i	−1.66709	+	0.962494i
$782$	39.6842	+	4.17098i	1.41910	+	0.149154i
$783$	−8.83839	−	4.82887i	−0.315858	−	0.172570i
$784$	0.710981	+	6.76453i	0.0253922	+	0.241590i
$785$	18.9708	−	17.0814i	0.677096	−	0.609660i
$786$	29.4571	−	1.26036i	1.05070	−	0.0449557i
$787$	6.46072	+	30.3953i	0.230300	+	1.08348i	0.929578	+	0.368626i	$0.120172\pi$
$787$	6.46072	+	30.3953i	0.230300	+	1.08348i	−0.699278	+	0.714850i	$0.746495\pi$
$788$	−4.59312	−	0.976298i	−0.163623	−	0.0347792i
$789$	−18.9863	−	19.3544i	−0.675930	−	0.689034i
$790$	16.5013	−	5.36160i	0.587090	−	0.190757i
$791$	5.29610	−	1.72081i	0.188308	−	0.0611848i
$792$	−15.9994	+	6.75841i	−0.568515	+	0.240150i
$793$	−8.10539	−	1.72285i	−0.287831	−	0.0611803i
$794$	2.22621	+	10.4735i	0.0790051	+	0.371690i
$795$	−0.304466	−	7.11595i	−0.0107983	−	0.252377i
$796$	−14.7096	+	13.2446i	−0.521368	+	0.469442i
$797$	−0.857016	−	8.15396i	−0.0303571	−	0.288828i	−0.999159	−	0.0409936i	$-0.986948\pi$
$797$	−0.857016	−	8.15396i	−0.0303571	−	0.288828i	0.968802	−	0.247835i	$-0.0797190\pi$
$798$	−0.744259	−	2.88824i	−0.0263465	−	0.102242i
$799$	13.7984	+	1.45027i	0.488152	+	0.0513068i
$800$	−2.33858	+	1.35018i	−0.0826813	+	0.0477361i
$801$	−45.2975	+	13.7624i	−1.60051	+	0.486270i
$802$	11.9995	−	16.5159i	0.423718	−	0.583198i
$803$	−24.6253	−	22.1727i	−0.869009	−	0.782459i
$804$	−12.5068	+	15.1450i	−0.441080	+	0.534122i
$805$			5.51131i			0.194248i
$806$	6.14753	−	9.33142i	0.216538	−	0.328685i
$807$	21.5915	+	8.52689i	0.760056	+	0.300161i
$808$	1.44751	−	4.45498i	0.0509232	−	0.156725i
$809$	−24.5966	+	27.3173i	−0.864772	+	0.960426i	−0.999536	−	0.0304513i	$-0.990306\pi$
$809$	−24.5966	+	27.3173i	−0.864772	+	0.960426i	0.134765	+	0.990878i	$0.456972\pi$
$810$	7.27277	−	11.5489i	0.255539	−	0.405788i
$811$	−5.94022	+	10.2888i	−0.208589	+	0.361288i	−0.951270	−	0.308358i	$-0.900221\pi$
$811$	−5.94022	+	10.2888i	−0.208589	+	0.361288i	0.742681	+	0.669645i	$0.233554\pi$
$812$	0.431462	+	0.747314i	0.0151413	+	0.0262256i
$813$	−49.5678	−	25.8584i	−1.73842	−	0.906892i
$814$	14.7730	−	10.7332i	0.517793	−	0.376199i
$815$	−6.32768	+	0.665066i	−0.221649	+	0.0232962i
$816$	2.95808	+	7.93284i	0.103553	+	0.277705i
$817$	9.51616	+	21.3736i	0.332928	+	0.747769i
$818$	−22.7769	+	4.84137i	−0.796375	+	0.169275i
$819$	−2.19847	+	1.53367i	−0.0768207	+	0.0535908i
$820$	−0.0710427	−	0.0316303i	−0.00248092	−	0.00110458i
$821$	−8.24535	−	25.3766i	−0.287765	−	0.885649i	−0.985556	−	0.169348i	$-0.945834\pi$
$821$	−8.24535	−	25.3766i	−0.287765	−	0.885649i	0.697792	−	0.716301i	$-0.254166\pi$
$822$	0.746552	+	0.0463152i	0.0260390	+	0.00161543i
$823$	−1.59308	+	3.57811i	−0.0555313	+	0.124725i	−0.939180	−	0.343425i	$-0.888413\pi$
$823$	−1.59308	+	3.57811i	−0.0555313	+	0.124725i	0.883649	+	0.468150i	$0.155079\pi$
$824$	3.11249	−	14.6431i	0.108429	−	0.510117i
$825$	26.7028	+	4.49249i	0.929673	+	0.156408i
$826$	−2.68138	+	1.19383i	−0.0932970	+	0.0415385i
$827$	6.97434	+	7.74579i	0.242522	+	0.269347i	0.852101	−	0.523378i	$-0.175328\pi$
$827$	6.97434	+	7.74579i	0.242522	+	0.269347i	−0.609579	+	0.792725i	$0.708662\pi$
$828$	14.7725	−	19.5327i	0.513379	−	0.678807i
$829$	−20.4338	−	28.1247i	−0.709694	−	0.976811i	−0.999804	−	0.0198170i	$-0.993692\pi$
$829$	−20.4338	−	28.1247i	−0.709694	−	0.976811i	0.290109	−	0.956994i	$-0.406308\pi$
$830$	−0.965982	+	9.19070i	−0.0335297	+	0.319014i
$831$	50.4077	−	7.48850i	1.74862	−	0.259773i
$832$	1.73810	+	1.00349i	0.0602578	+	0.0347898i
$833$	−26.8980	−	19.5425i	−0.931960	−	0.677109i
$834$	5.13849	−	2.55636i	0.177931	−	0.0885195i
$835$	8.91109	+	2.89539i	0.308381	+	0.100199i
$836$	22.3928			0.774471
$837$	7.01221	−	28.0683i	0.242377	−	0.970182i
$838$	27.8602			0.962413
$839$	−23.5469	−	7.65086i	−0.812930	−	0.264137i	−0.127092	−	0.991891i	$-0.540564\pi$
$839$	−23.5469	−	7.65086i	−0.812930	−	0.264137i	−0.685838	+	0.727754i	$0.740564\pi$
$840$	−1.04696	+	0.520855i	−0.0361236	+	0.0179712i
$841$	20.4221	+	14.8375i	0.704212	+	0.511640i
$842$	−3.35401	−	1.93644i	−0.115587	−	0.0667340i
$843$	−4.55703	+	0.676987i	−0.156953	+	0.0233167i
$844$	0.540726	−	5.14467i	0.0186126	−	0.177087i
$845$	−7.99721	−	11.0072i	−0.275112	−	0.378660i
$846$	5.13646	−	6.79161i	0.176595	−	0.233500i
$847$	−6.70799	−	7.44997i	−0.230489	−	0.255984i
$848$	2.47725	−	1.10294i	0.0850691	−	0.0378752i
$849$	−27.8804	−	4.69060i	−0.956853	−	0.160981i
$850$	2.74435	−	12.9111i	0.0941304	−	0.442849i
$851$	−10.4726	+	23.5217i	−0.358995	+	0.806315i
$852$	16.0636	+	0.996571i	0.550331	+	0.0341419i
$853$	4.53923	+	13.9703i	0.155420	+	0.478335i	0.998203	−	0.0599189i	$-0.0190842\pi$
$853$	4.53923	+	13.9703i	0.155420	+	0.478335i	−0.842783	+	0.538254i	$0.819084\pi$
$854$	1.67925	+	0.747651i	0.0574628	+	0.0255841i
$855$	−14.4317	+	10.0677i	−0.493554	+	0.344308i
$856$	11.6156	−	2.46898i	0.397015	−	0.0843881i
$857$	11.7054	+	26.2907i	0.399848	+	0.898073i	0.995494	+	0.0948259i	$0.0302294\pi$
$857$	11.7054	+	26.2907i	0.399848	+	0.898073i	−0.595646	+	0.803247i	$0.703104\pi$
$858$	−7.03154	−	18.8569i	−0.240053	−	0.643763i
$859$	18.4609	−	1.94032i	0.629878	−	0.0662028i	0.215790	−	0.976440i	$-0.430767\pi$
$859$	18.4609	−	1.94032i	0.629878	−	0.0662028i	0.414088	+	0.910237i	$0.364101\pi$
$860$	7.42102	−	5.39169i	0.253055	−	0.183855i
$861$	0.0350600	+	0.0182900i	0.00119484	+	0.000623321i
$862$	4.80102	+	8.31562i	0.163523	+	0.283231i
$863$	10.6573	−	18.4590i	0.362780	−	0.628353i	−0.625637	−	0.780114i	$-0.715161\pi$
$863$	10.6573	−	18.4590i	0.362780	−	0.628353i	0.988417	+	0.151761i	$0.0484944\pi$
$864$	5.10665	+	0.960300i	0.173732	+	0.0326701i
$865$	−6.33923	+	7.04043i	−0.215540	+	0.239382i
$866$	−2.07037	+	6.37195i	−0.0703541	+	0.216528i
$867$	−11.1051	−	4.38560i	−0.377148	−	0.148943i
$868$	−1.76427	+	1.74121i	−0.0598831	+	0.0591005i
$869$		−	66.2397i		−	2.24703i
$870$	3.24170	−	3.92551i	0.109904	−	0.133087i
$871$	−16.9135	−	15.2289i	−0.573091	−	0.516013i
$872$	10.1413	−	13.9583i	0.343427	−	0.472686i
$873$	−11.1099	+	3.37544i	−0.376013	+	0.114241i
$874$	−27.3443	+	15.7873i	−0.924936	+	0.534012i
$875$	5.17030	+	0.543420i	0.174788	+	0.0183710i
$876$	2.47380	+	9.60003i	0.0835819	+	0.324355i
$877$	−0.458228	−	4.35975i	−0.0154733	−	0.147218i	0.984057	−	0.177851i	$-0.0569145\pi$
$877$	−0.458228	−	4.35975i	−0.0154733	−	0.147218i	−0.999531	+	0.0306326i	$0.990248\pi$
$878$	3.69292	−	3.32512i	0.124630	−	0.112217i
$879$	0.0808840	+	1.89041i	0.00272815	+	0.0637621i
$880$	−1.82534	−	8.58757i	−0.0615324	−	0.289487i
$881$	−5.04761	−	1.07290i	−0.170058	−	0.0361470i	0.122095	−	0.992518i	$-0.461039\pi$
$881$	−5.04761	−	1.07290i	−0.170058	−	0.0361470i	−0.292154	+	0.956371i	$0.594372\pi$
$882$	−18.7971	+	7.94021i	−0.632933	+	0.267361i
$883$	3.13892	−	1.01990i	0.105633	−	0.0343223i	−0.255724	−	0.966750i	$-0.582314\pi$
$883$	3.13892	−	1.01990i	0.105633	−	0.0343223i	0.361357	+	0.932428i	$0.382314\pi$
$884$	−9.33016	+	3.03155i	−0.313807	+	0.101962i
$885$	12.1264	+	12.3615i	0.407626	+	0.415528i
$886$	7.33836	+	1.55982i	0.246537	+	0.0524031i
$887$	6.31757	+	29.7218i	0.212123	+	0.997961i	0.947365	+	0.320156i	$0.103735\pi$
$887$	6.31757	+	29.7218i	0.212123	+	0.997961i	−0.735242	+	0.677805i	$0.762931\pi$
$888$	−5.45806	+	0.233531i	−0.183161	+	0.00783678i
$889$	−2.64455	+	2.38117i	−0.0886955	+	0.0798618i
$890$	−2.50144	−	23.7996i	−0.0838484	−	0.797764i
$891$	−33.3528	−	40.0314i	−1.11736	−	1.34110i
$892$	2.00709	+	0.210954i	0.0672025	+	0.00706327i
$893$	−9.50776	+	5.48931i	−0.318165	+	0.183693i
$894$	8.88324	−	7.05340i	0.297100	−	0.235901i
$895$	18.9061	−	26.0220i	0.631962	−	0.869821i
$896$	−0.330852	−	0.297900i	−0.0110530	−	0.00995216i
$897$	21.8807	+	18.0692i	0.730577	+	0.603313i
$898$			30.2070i			1.00802i
$899$	3.93361	−	10.0493i	0.131193	−	0.335164i
$900$	−5.91510	−	5.53526i	−0.197170	−	0.184509i
$901$	−4.09601	+	12.6062i	−0.136458	+	0.419974i
$902$	−0.198658	+	0.220632i	−0.00661460	+	0.00734625i
$903$	−3.93611	+	2.50275i	−0.130986	+	0.0832864i
$904$	6.25402	−	10.8323i	0.208006	−	0.360276i
$905$	8.07820	+	13.9919i	0.268529	+	0.465105i
$906$	−18.2472	+	34.9779i	−0.606221	+	1.16206i
$907$	−8.63900	+	6.27660i	−0.286853	+	0.208411i	−0.721901	−	0.691996i	$-0.756731\pi$
$907$	−8.63900	+	6.27660i	−0.286853	+	0.208411i	0.435048	+	0.900407i	$0.356731\pi$
$908$	28.4144	−	2.98647i	0.942965	−	0.0991096i
$909$	14.0501	+	0.269784i	0.466013	+	0.00894818i
$910$	−0.551122	−	1.23784i	−0.0182695	−	0.0410340i
$911$	−42.2028	+	8.97048i	−1.39824	+	0.297205i	−0.844532	−	0.535505i	$-0.820121\pi$
$911$	−42.2028	+	8.97048i	−1.39824	+	0.297205i	−0.553709	+	0.832710i	$0.686788\pi$
$912$	−5.58327	−	3.70250i	−0.184880	−	0.122602i
$913$	32.2308	+	14.3501i	1.06668	+	0.474918i
$914$	−8.62003	−	26.5297i	−0.285125	−	0.877525i
$915$	0.671500	−	10.8239i	0.0221991	−	0.357826i
$916$	9.01118	−	20.2394i	0.297738	−	0.668730i
$917$	1.57567	−	7.41296i	0.0520333	−	0.244797i
$918$	−20.1910	+	15.4093i	−0.666402	+	0.508581i
$919$	37.2111	−	16.5675i	1.22748	−	0.546510i	0.312466	−	0.949929i	$-0.398845\pi$
$919$	37.2111	−	16.5675i	1.22748	−	0.546510i	0.915015	+	0.403419i	$0.132178\pi$
$920$	8.28333	+	9.19957i	0.273093	+	0.303301i
$921$	6.51255	−	23.4041i	0.214596	−	0.771192i
$922$	−0.840360	−	1.15666i	−0.0276758	−	0.0380924i
$923$	−1.94938	+	18.5471i	−0.0641646	+	0.610485i
$924$	0.656016	+	4.41587i	0.0215814	+	0.145272i
$925$	7.37611	+	4.25860i	0.242525	+	0.140022i
$926$	−4.73009	−	3.43661i	−0.155440	−	0.112934i
$927$	44.7466	−	3.83611i	1.46967	−	0.125995i
$928$	1.84340	+	0.598955i	0.0605124	+	0.0196617i
$929$	−24.0138			−0.787867			−0.393934	−	0.919139i	$-0.628886\pi$
$929$	−24.0138			−0.787867			−0.393934	+	0.919139i	$0.628886\pi$
$930$	13.2619	+	6.16352i	0.434874	+	0.202110i
$931$	26.3085			0.862226
$932$	8.14229	+	2.64559i	0.266710	+	0.0866592i
$933$	6.79677	+	13.6621i	0.222516	+	0.447276i
$934$	−7.82905	−	5.68814i	−0.256174	−	0.186122i
$935$	37.1651	+	21.4573i	1.21543	+	0.701728i
$936$	−1.36466	+	5.86426i	−0.0446053	+	0.191679i
$937$	5.74496	−	54.6596i	0.187680	−	1.78565i	−0.344265	−	0.938872i	$-0.611872\pi$
$937$	5.74496	−	54.6596i	0.187680	−	1.78565i	0.531945	−	0.846779i	$-0.321461\pi$
$938$	2.96752	+	4.08444i	0.0968930	+	0.133362i
$939$	−18.1704	−	5.05619i	−0.592969	−	0.165002i
$940$	2.88016	+	3.19874i	0.0939403	+	0.104331i
$941$	−8.38482	+	3.73316i	−0.273337	+	0.121698i	−0.538828	−	0.842416i	$-0.681133\pi$
$941$	−8.38482	+	3.73316i	−0.273337	+	0.121698i	0.265491	+	0.964113i	$0.414466\pi$
$942$	−4.83739	+	28.7529i	−0.157611	+	0.936819i
$943$	0.0870368	−	0.409476i	0.00283431	−	0.0133344i
$944$	−2.68152	+	6.02279i	−0.0872760	+	0.196025i
$945$	−2.40814	−	2.55100i	−0.0783370	−	0.0829841i
$946$	−10.8217	−	33.3057i	−0.351843	−	1.08286i
$947$	−26.1412	−	11.6388i	−0.849473	−	0.378210i	−0.0646339	−	0.997909i	$-0.520588\pi$
$947$	−26.1412	−	11.6388i	−0.849473	−	0.378210i	−0.784839	+	0.619699i	$0.787255\pi$
$948$	−10.9523	+	16.5158i	−0.355714	+	0.536407i
$949$	−11.2362	+	2.38834i	−0.364744	+	0.0775287i
$950$	4.24822	+	9.54166i	0.137831	+	0.309572i
$951$	−39.9530	+	14.8981i	−1.29556	+	0.483103i
$952$	2.16428	−	0.227475i	0.0701447	−	0.00737251i
$953$	30.8526	−	22.4157i	0.999414	−	0.726116i	0.0374512	−	0.999298i	$-0.488076\pi$
$953$	30.8526	−	22.4157i	0.999414	−	0.726116i	0.961962	+	0.273182i	$0.0880761\pi$
$954$	5.32635	+	6.14892i	0.172447	+	0.199078i
$955$	7.13473	+	12.3577i	0.230874	+	0.399886i
$956$	11.8544	−	20.5325i	0.383400	−	0.664068i
$957$	−10.4287	−	16.4013i	−0.337112	−	0.530180i
$958$	6.69945	−	7.44049i	0.216449	−	0.240391i
$959$	0.0594122	−	0.182852i	0.00191852	−	0.00590460i
$960$	−0.964778	+	2.44297i	−0.0311381	+	0.0788467i
$961$	30.7849	+	3.64565i	0.993061	+	0.117602i
$962$		−	6.33022i		−	0.204095i
$963$	17.2171	+	31.1888i	0.554814	+	1.00505i
$964$	9.91399	+	8.92659i	0.319308	+	0.287506i
$965$	7.48474	−	10.3019i	0.240942	−	0.331629i
$966$	−3.91433	−	4.92982i	−0.125942	−	0.158614i
$967$	−14.2132	+	8.20597i	−0.457065	+	0.263886i	−0.710809	−	0.703385i	$-0.751671\pi$
$967$	−14.2132	+	8.20597i	−0.457065	+	0.263886i	0.253745	+	0.967271i	$0.418338\pi$
$968$	−22.3942	−	2.35372i	−0.719776	−	0.0756516i
$969$	31.7111	−	8.17152i	1.01871	−	0.262507i
$970$	−0.613516	−	5.83722i	−0.0196988	−	0.187422i
$971$	−14.0545	+	12.6547i	−0.451030	+	0.406110i	−0.863092	−	0.505046i	$-0.831475\pi$
$971$	−14.0545	+	12.6547i	−0.451030	+	0.406110i	0.412062	+	0.911156i	$0.364809\pi$
$972$	1.69704	+	15.4958i	0.0544327	+	0.497028i
$973$	−0.306714	−	1.44298i	−0.00983281	−	0.0462597i
$974$	−29.6905	−	6.31092i	−0.951346	−	0.202215i
$975$	6.70101	−	6.57358i	0.214604	−	0.210523i
$976$	3.92674	−	1.27587i	0.125692	−	0.0408397i
$977$	−15.4533	+	5.02108i	−0.494394	+	0.160638i	−0.545593	−	0.838050i	$-0.683696\pi$
$977$	−15.4533	+	5.02108i	−0.494394	+	0.160638i	0.0511990	+	0.998688i	$0.483696\pi$
$978$	5.18770	−	5.08905i	0.165884	−	0.162730i
$979$	−89.3647	−	18.9950i	−2.85611	−	0.607084i
$980$	−2.14453	−	10.0892i	−0.0685045	−	0.322288i
$981$	48.9106	+	16.9369i	1.56160	+	0.540752i
$982$	7.03250	−	6.33210i	0.224416	−	0.202065i
$983$	−1.30725	−	12.4377i	−0.0416949	−	0.396701i	−0.995389	−	0.0959218i	$-0.969420\pi$
$983$	−1.30725	−	12.4377i	−0.0416949	−	0.396701i	0.953694	−	0.300779i	$-0.0972466\pi$
$984$	0.0860121	−	0.0221642i	0.00274197	−	0.000706568i
$985$	7.08187	+	0.744334i	0.225647	+	0.0237165i
$986$	−8.20506	+	4.73719i	−0.261302	+	0.150863i
$987$	−1.36103	−	1.71412i	−0.0433222	−	0.0545611i
$988$	4.56284	−	6.28021i	0.145163	−	0.199800i
$989$	36.6956	+	33.0409i	1.16685	+	1.05064i
$990$	23.0582	−	12.7288i	0.732839	−	0.404548i
$991$		−	47.4390i		−	1.50695i	−0.657477	−	0.753474i	$-0.728377\pi$
$991$		−	47.4390i		−	1.50695i	0.657477	−	0.753474i	$-0.271623\pi$
$992$	−0.327958	+	5.55810i	−0.0104127	+	0.176470i
$993$	−11.7910	+	29.8569i	−0.374178	+	0.947479i
$994$	1.27838	−	3.93445i	0.0405478	−	0.124793i
$995$	20.0848	−	22.3065i	0.636732	−	0.707163i
$996$	−5.66351	−	8.90708i	−0.179455	−	0.282232i
$997$	−23.2503	+	40.2707i	−0.736344	+	1.27538i	0.217787	+	0.975996i	$0.430116\pi$
$997$	−23.2503	+	40.2707i	−0.736344	+	1.27538i	−0.954131	+	0.299389i	$0.903217\pi$
$998$	14.3575	+	24.8679i	0.454478	+	0.787180i
$999$	−5.43034	−	15.4634i	−0.171808	−	0.489240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.17.1	yes	80
3.2	odd	2	inner	186.2.p.a.17.9	yes	80
31.11	odd	30	inner	186.2.p.a.11.9	yes	80
93.11	even	30	inner	186.2.p.a.11.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.1	✓	80	93.11	even	30	inner
186.2.p.a.11.9	yes	80	31.11	odd	30	inner
186.2.p.a.17.1	yes	80	1.1	even	1	trivial
186.2.p.a.17.9	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.55075 + 0.771484i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.31329 - 0.758228i) q^{5} +(1.71325 - 0.254518i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.80963 - 2.39275i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-1.55075 + 0.771484i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.31329 - 0.758228i) q^{5} +(1.71325 - 0.254518i) q^{6} +(0.0465366 - 0.442766i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(1.80963 - 2.39275i) q^{9} +(1.01471 + 1.12695i) q^{10} +(5.28891 - 2.35477i) q^{11} +(-1.70805 - 0.287362i) q^{12} +(0.417276 - 1.96313i) q^{13} +(-0.181081 + 0.406715i) q^{14} +(2.62154 + 0.162637i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.46549 - 1.98816i) q^{17} +(-2.46046 + 1.71644i) q^{18} +(3.78335 - 0.804176i) q^{19} +(-0.616798 - 1.38535i) q^{20} +(0.269421 + 0.722520i) q^{21} +(-5.75772 + 0.605161i) q^{22} +(6.60423 - 4.79825i) q^{23} +(1.53565 + 0.801113i) q^{24} +(-1.35018 - 2.33858i) q^{25} +(-1.00349 + 1.73810i) q^{26} +(-0.960300 + 5.10665i) q^{27} +(0.297900 - 0.330852i) q^{28} +(-0.598955 + 1.84340i) q^{29} +(-2.44297 - 0.964778i) q^{30} +(-5.55810 - 0.327958i) q^{31} -1.00000i q^{32} +(-6.38509 + 7.73197i) q^{33} +(3.63256 + 3.27077i) q^{34} +(-0.396834 + 0.546195i) q^{35} +(2.87044 - 0.872105i) q^{36} +(-2.73153 + 1.57705i) q^{37} +(-3.84669 - 0.404303i) q^{38} +(0.867433 + 3.36623i) q^{39} +(0.158513 + 1.50815i) q^{40} +(0.0381095 - 0.0343139i) q^{41} +(-0.0329632 - 0.770413i) q^{42} +(1.25764 + 5.91671i) q^{43} +(5.66292 + 1.20369i) q^{44} +(-4.19081 + 1.77027i) q^{45} +(-7.76373 + 2.52259i) q^{46} +(-2.69949 + 0.877117i) q^{47} +(-1.21293 - 1.23645i) q^{48} +(6.65316 + 1.41417i) q^{49} +(0.561436 + 2.64135i) q^{50} +(8.45867 - 0.361916i) q^{51} +(1.49148 - 1.34293i) q^{52} +(-0.283448 - 2.69683i) q^{53} +(2.49134 - 4.55996i) q^{54} +(-8.73133 - 0.917700i) q^{55} +(-0.385559 + 0.222603i) q^{56} +(-5.24661 + 4.16587i) q^{57} +(1.13928 - 1.56809i) q^{58} +(4.89938 + 4.41142i) q^{59} +(2.02527 + 1.67248i) q^{60} -4.12882i q^{61} +(5.18472 + 2.02945i) q^{62} +(-0.975216 - 0.912592i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.03650 + 2.26176i) q^{65} +(8.46189 - 5.38044i) q^{66} +(5.67003 - 9.82077i) q^{67} +(-2.44404 - 4.23321i) q^{68} +(-6.53970 + 12.5359i) q^{69} +(0.546195 - 0.396834i) q^{70} +(-9.24128 + 0.971297i) q^{71} +(-2.99945 - 0.0575940i) q^{72} +(-2.32802 - 5.22881i) q^{73} +(3.08517 - 0.655774i) q^{74} +(3.89796 + 2.58490i) q^{75} +(3.53348 + 1.57321i) q^{76} +(-0.796487 - 2.45134i) q^{77} +(0.215246 - 3.46953i) q^{78} +(4.65367 - 10.4523i) q^{79} +(0.315289 - 1.48332i) q^{80} +(-2.45051 - 8.65996i) q^{81} +(-0.0468479 + 0.0208580i) q^{82} +(4.07770 + 4.52874i) q^{83} +(-0.206721 + 0.742893i) q^{84} +(4.35700 + 5.99689i) q^{85} +(0.632282 - 6.01576i) q^{86} +(-0.493322 - 3.32072i) q^{87} +(-5.01380 - 2.89472i) q^{88} +(-12.7668 - 9.27564i) q^{89} +(4.53274 - 0.388591i) q^{90} +(-0.849788 - 0.276113i) q^{91} +8.16327 q^{92} +(8.87221 - 3.77940i) q^{93} +2.83841 q^{94} +(-5.57839 - 1.81253i) q^{95} +(0.771484 + 1.55075i) q^{96} +(-3.13126 - 2.27499i) q^{97} +(-5.89052 - 3.40090i) q^{98} +(3.93656 - 16.9163i) 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

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