LMFDB - Embedded newform 186.2.p.a.11.1

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			11.1
Character	$\chi$	$=$	186.11
Dual form			186.2.p.a.17.1

$q$-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 $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{23}{30}\right)$

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	−0.764038	−	0.645172i	$-0.776786\pi$
$5$	−1.31329	+	0.758228i	−0.587321	+	0.339090i	0.176716	+	0.984262i	$0.443452\pi$
$6$	1.71325	+	0.254518i	0.699431	+	0.103907i
$7$	0.0465366	+	0.442766i	0.0175892	+	0.167350i	0.999790	−	0.0204829i	$-0.00652035\pi$
$7$	0.0465366	+	0.442766i	0.0175892	+	0.167350i	−0.982201	+	0.187833i	$0.939854\pi$
$8$	−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	0.995860	−	0.0909022i	$-0.0289751\pi$
$11$	5.28891	+	2.35477i	1.59467	+	0.709991i	0.598807	+	0.800894i	$0.295642\pi$
$12$	−1.70805	+	0.287362i	−0.493071	+	0.0829543i
$13$	0.417276	+	1.96313i	0.115731	+	0.544473i	0.997366	+	0.0725399i	$0.0231105\pi$
$13$	0.417276	+	1.96313i	0.115731	+	0.544473i	−0.881634	+	0.471934i	$0.843556\pi$
$14$	−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	−0.869095	−	0.494645i	$-0.835298\pi$
$17$	−4.46549	+	1.98816i	−1.08304	+	0.482200i	−0.213945	+	0.976846i	$0.568631\pi$
$18$	−2.46046	−	1.71644i	−0.579935	−	0.404568i
$19$	3.78335	+	0.804176i	0.867960	+	0.184491i	0.620308	−	0.784358i	$-0.287008\pi$
$19$	3.78335	+	0.804176i	0.867960	+	0.184491i	0.247652	+	0.968849i	$0.420341\pi$
$20$	−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	0.997147	+	0.0754892i	$0.0240518\pi$
$23$	6.60423	+	4.79825i	1.37708	+	1.00050i	0.379930	+	0.925015i	$0.375948\pi$
$24$	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	0.879917	−	0.475127i	$-0.157598\pi$
$29$	−0.598955	−	1.84340i	−0.111223	−	0.342310i	−0.991141	+	0.132817i	$0.957598\pi$
$30$	−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	0.258373	−	0.966045i	$-0.416814\pi$
$37$	−2.73153	−	1.57705i	−0.449060	−	0.259265i	−0.707433	+	0.706780i	$0.750147\pi$
$38$	−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	0.672101	−	0.740459i	$-0.265392\pi$
$41$	0.0381095	+	0.0343139i	0.00595170	+	0.00535894i	−0.666149	+	0.745818i	$0.732059\pi$
$42$	−0.0329632	+	0.770413i	−0.00508633	+	0.118877i
$43$	1.25764	−	5.91671i	0.191788	−	0.902290i	−0.772001	−	0.635622i	$-0.780744\pi$
$43$	1.25764	−	5.91671i	0.191788	−	0.902290i	0.963788	−	0.266669i	$-0.0859229\pi$
$44$	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	0.105443	−	0.994425i	$-0.466374\pi$
$47$	−2.69949	−	0.877117i	−0.393761	−	0.127941i	−0.499204	+	0.866485i	$0.666374\pi$
$48$	−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	0.957655	+	0.287919i	$0.0929633\pi$
$53$	−0.283448	+	2.69683i	−0.0389346	+	0.370438i	−0.996589	+	0.0825195i	$0.973703\pi$
$54$	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	−0.285458	−	0.958391i	$-0.592146\pi$
$59$	4.89938	−	4.41142i	0.637844	−	0.574318i	0.923303	+	0.384074i	$0.125479\pi$
$60$	2.02527	−	1.67248i	0.261462	−	0.215916i
$61$			4.12882i			0.528641i	0.964435	+	0.264320i	$0.0851476\pi$
$61$			4.12882i			0.528641i	−0.964435	+	0.264320i	$0.914852\pi$
$62$	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	0.970949	+	0.239288i	$0.0769140\pi$
$67$	5.67003	+	9.82077i	0.692704	+	1.19980i	−0.278245	+	0.960510i	$0.589753\pi$
$68$	−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	−0.461166	−	0.887314i	$-0.652569\pi$
$71$	−9.24128	−	0.971297i	−1.09674	−	0.115272i	−0.635572	+	0.772042i	$0.719236\pi$
$72$	−2.99945	+	0.0575940i	−0.353488	+	0.00678752i
$73$	−2.32802	+	5.22881i	−0.272474	+	0.611986i	−0.997012	−	0.0772489i	$-0.975386\pi$
$73$	−2.32802	+	5.22881i	−0.272474	+	0.611986i	0.724538	+	0.689235i	$0.242053\pi$
$74$	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	0.960957	+	0.276699i	$0.0892406\pi$
$79$	4.65367	+	10.4523i	0.523579	+	1.17598i	−0.437378	+	0.899278i	$0.644093\pi$
$80$	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	−0.476556	−	0.879144i	$-0.658115\pi$
$83$	4.07770	−	4.52874i	0.447586	−	0.497094i	0.924142	+	0.382050i	$0.124782\pi$
$84$	−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	−0.354440	+	0.935079i	$0.615329\pi$
$89$	−12.7668	+	9.27564i	−1.35328	+	0.983216i	−0.998841	+	0.0481374i	$0.984671\pi$
$90$	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	−0.735292	−	0.677750i	$-0.762955\pi$
$97$	−3.13126	+	2.27499i	−0.317931	+	0.230991i	0.417361	+	0.908741i	$0.362955\pi$
$98$	−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	−0.649758	−	0.760142i	$-0.725130\pi$
$101$	2.75333	−	3.78963i	0.273966	−	0.377082i	0.923724	+	0.383059i	$0.125130\pi$
$102$	−8.15651	+	2.26967i	−0.807615	+	0.224731i
$103$	10.0171	−	11.1251i	0.987010	−	1.09619i	−0.00835015	−	0.999965i	$-0.502658\pi$
$103$	10.0171	−	11.1251i	0.987010	−	1.09619i	0.995360	−	0.0962204i	$-0.0306754\pi$
$104$	−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	−0.981527	−	0.191325i	$-0.938722\pi$
$107$	−4.83006	−	10.8485i	−0.466939	−	1.04876i	0.514587	−	0.857438i	$-0.327945\pi$
$108$	−3.77851	−	3.56691i	−0.363587	−	0.343226i
$109$	5.33158	−	16.4089i	0.510673	−	1.57169i	−0.280347	−	0.959899i	$-0.590449\pi$
$109$	5.33158	−	16.4089i	0.510673	−	1.57169i	0.791020	−	0.611791i	$-0.209551\pi$
$110$	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	−0.499418	−	0.866361i	$-0.666453\pi$
$113$	5.08748	−	11.4267i	0.478590	−	1.07493i	0.978008	−	0.208569i	$-0.0668806\pi$
$114$	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	−0.889188	−	0.457543i	$-0.848730\pi$
$127$	−5.94008	+	5.34847i	−0.527097	+	0.474600i	0.362091	+	0.932143i	$0.382063\pi$
$128$	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	0.669678	−	0.742652i	$-0.266432\pi$
$131$	16.9294	−	1.77935i	1.47913	−	0.155463i	0.809450	+	0.587189i	$0.199766\pi$
$132$	−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	−0.189832	−	0.981817i	$-0.560794\pi$
$137$	0.422413	−	0.0897868i	0.0360892	−	0.00767100i	0.225921	+	0.974146i	$0.427461\pi$
$138$	10.0934	+	9.90149i	0.859211	+	0.842871i
$139$	3.15138	+	1.02395i	0.267297	+	0.0868500i	0.439599	−	0.898194i	$-0.355121\pi$
$139$	3.15138	+	1.02395i	0.267297	+	0.0868500i	−0.172302	+	0.985044i	$0.555121\pi$
$140$	−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	0.713987	−	0.700159i	$-0.246888\pi$
$149$	5.67147	+	3.27443i	0.464625	+	0.268251i	−0.249362	+	0.968410i	$0.580221\pi$
$150$	−2.90840	+	3.66292i	−0.237470	+	0.299077i
$151$	−13.3881	−	18.4272i	−1.08951	−	1.49958i	−0.848599	−	0.529036i	$-0.822554\pi$
$151$	−13.3881	−	18.4272i	−1.08951	−	1.49958i	−0.240912	−	0.970547i	$-0.577446\pi$
$152$	−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	−0.912109	−	0.409948i	$-0.865547\pi$
$157$	−5.20192	−	16.0099i	−0.415159	−	1.27773i	0.496950	−	0.867779i	$-0.334453\pi$
$158$	−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	0.712729	−	0.701439i	$-0.247459\pi$
$163$	3.39436	+	2.46615i	0.265867	+	0.193164i	−0.446863	+	0.894603i	$0.647459\pi$
$164$	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	−0.0319524	−	0.999489i	$-0.510172\pi$
$167$	−6.04365	−	1.28462i	−0.467671	−	0.0994066i	−0.435719	+	0.900083i	$0.643506\pi$
$168$	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	0.999540	+	0.0303356i	$0.00965760\pi$
$173$	1.29890	+	6.11083i	0.0987534	+	0.464598i	−0.900786	+	0.434262i	$0.857009\pi$
$174$	−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	−0.689157	−	0.724612i	$-0.742019\pi$
$179$	−2.21712	−	21.0945i	−0.165715	−	1.57667i	0.523442	−	0.852061i	$-0.324648\pi$
$180$	−4.43098	+	1.03112i	−0.330265	+	0.0768554i
$181$	−9.22668	+	5.32703i	−0.685814	+	0.395955i	−0.802042	−	0.597268i	$-0.796253\pi$
$181$	−9.22668	+	5.32703i	−0.685814	+	0.395955i	0.116228	+	0.993223i	$0.462920\pi$
$182$	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	−0.764958	−	0.644081i	$-0.777240\pi$
$191$	−8.14907	+	4.70487i	−0.589646	+	0.340432i	0.175311	+	0.984513i	$0.443907\pi$
$192$	−0.254518	+	1.71325i	−0.0183682	+	0.123643i
$193$	−0.877734	−	8.35108i	−0.0631807	−	0.601124i	−0.979607	−	0.200921i	$-0.935606\pi$
$193$	−0.877734	−	8.35108i	−0.0631807	−	0.601124i	0.916427	−	0.400203i	$-0.131060\pi$
$194$	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	0.248189	−	0.968712i	$-0.420165\pi$
$197$	−4.28977	−	1.90993i	−0.305633	−	0.136077i	−0.553822	+	0.832635i	$0.686831\pi$
$198$	−8.97131	−	14.8719i	−0.637564	−	1.05690i
$199$	−4.11535	−	19.3612i	−0.291729	−	1.37248i	−0.842893	−	0.538081i	$-0.819150\pi$
$199$	−4.11535	−	19.3612i	−0.291729	−	1.37248i	0.551164	−	0.834397i	$-0.314184\pi$
$200$	−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	−0.941217	−	0.337803i	$-0.890316\pi$
$211$	−2.58650	+	4.47996i	−0.178062	+	0.308413i	0.763155	+	0.646216i	$0.223650\pi$
$212$	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	0.557377	−	0.830260i	$-0.311808\pi$
$223$	1.74777	+	1.00908i	0.117039	+	0.0675727i	−0.440338	+	0.897832i	$0.645141\pi$
$224$	−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	0.917267	+	0.398272i	$0.130390\pi$
$227$	21.2323	+	19.1177i	1.40924	+	1.26888i	0.491971	+	0.870611i	$0.336277\pi$
$228$	−6.69323	−	0.286379i	−0.443270	−	0.0189659i
$229$	−4.60625	+	21.6707i	−0.304389	+	1.43204i	0.514205	+	0.857667i	$0.328087\pi$
$229$	−4.60625	+	21.6707i	−0.304389	+	1.43204i	−0.818595	+	0.574372i	$0.805246\pi$
$230$	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	0.563327	−	0.826234i	$-0.309521\pi$
$233$	8.14229	+	2.64559i	0.533419	+	0.173318i	−0.0299075	+	0.999553i	$0.509521\pi$
$234$	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	0.558217	+	0.829695i	$0.311485\pi$
$239$	−2.47825	+	23.5790i	−0.160305	+	1.52520i	−0.718522	+	0.695504i	$0.755181\pi$
$240$	0.655423	−	2.54349i	0.0423074	−	0.164182i
$241$	13.2675	−	1.39447i	0.854635	−	0.0898258i	0.332930	−	0.942952i	$-0.391963\pi$
$241$	13.2675	−	1.39447i	0.854635	−	0.0898258i	0.521705	+	0.853126i	$0.325296\pi$
$242$	−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	0.222046	−	0.975036i	$-0.428727\pi$
$251$	−12.2127	−	13.5636i	−0.770859	−	0.856126i	−0.992905	+	0.118910i	$0.962060\pi$
$252$	−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	0.0575150	−	0.998345i	$-0.481682\pi$
$257$	−1.50364	−	0.158039i	−0.0937943	−	0.00985818i	−0.151309	+	0.988486i	$0.548349\pi$
$258$	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	−0.683834	−	0.729637i	$-0.739689\pi$
$263$	4.83712	−	14.8871i	0.298269	−	0.917979i	0.982104	−	0.188341i	$-0.0603111\pi$
$264$	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	−0.951682	−	0.307087i	$-0.900646\pi$
$269$	−8.96818	+	9.96017i	−0.546800	+	0.607282i	0.404882	+	0.914369i	$0.367313\pi$
$270$	−6.72934	−	4.09954i	−0.409535	−	0.249490i
$271$	18.9726	−	26.1135i	1.15250	−	1.58628i	0.416763	−	0.909015i	$-0.363165\pi$
$271$	18.9726	−	26.1135i	1.15250	−	1.58628i	0.735738	−	0.677266i	$-0.236835\pi$
$272$	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	−0.985161	−	0.171632i	$-0.945096\pi$
$277$	−27.9823	+	9.09198i	−1.68129	+	0.546284i	−0.696129	+	0.717916i	$0.745096\pi$
$278$	−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	−0.232588	−	0.972575i	$-0.574720\pi$
$281$	2.52970	−	0.821948i	0.150909	−	0.0490333i	0.383497	+	0.923542i	$0.374720\pi$
$282$	−4.40165	−	2.18979i	−0.262115	−	0.130400i
$283$	13.2056	−	9.59441i	0.784990	−	0.570328i	−0.121483	−	0.992594i	$-0.538765\pi$
$283$	13.2056	−	9.59441i	0.784990	−	0.570328i	0.906472	+	0.422265i	$0.138765\pi$
$284$	−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	0.926059	−	0.377378i	$-0.123174\pi$
$293$	0.444331	+	0.997984i	0.0259581	+	0.0583029i	−0.900101	+	0.435681i	$0.856508\pi$
$294$	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	0.413206	−	0.910637i	$-0.364409\pi$
$307$	−9.38507	−	10.4232i	−0.535634	−	0.594882i	−0.948841	+	0.315755i	$0.897742\pi$
$308$	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	$0.0803598\pi$
$311$			8.81000i			0.499569i	−0.968301	+	0.249785i	$0.919640\pi$
$312$	2.21348	+	2.68039i	0.125313	+	0.151747i
$313$	8.09230	−	7.28634i	0.457404	−	0.411849i	−0.407954	−	0.913002i	$-0.633758\pi$
$313$	8.09230	−	7.28634i	0.457404	−	0.411849i	0.865358	+	0.501154i	$0.167091\pi$
$314$	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	0.612041	−	0.790826i	$-0.290349\pi$
$317$	24.4835	−	2.57332i	1.37513	−	0.144532i	0.763089	+	0.646294i	$0.223682\pi$
$318$	−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	0.954345	−	0.298705i	$-0.0965548\pi$
$331$	13.7730	+	12.4013i	0.757033	+	0.681635i	−0.197313	+	0.980341i	$0.563221\pi$
$332$	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	0.655779	−	0.754953i	$-0.272340\pi$
$337$	−4.86237	−	6.69248i	−0.264870	−	0.364563i	−0.920650	+	0.390390i	$0.872340\pi$
$338$	−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	−0.634277	−	0.773106i	$-0.718702\pi$
$347$	6.56431	−	11.3697i	0.352391	−	0.610359i	0.986668	+	0.162747i	$0.0520355\pi$
$348$	1.55277	+	2.97649i	0.0832370	+	0.159556i
$349$	−16.3305	−	11.8648i	−0.874152	−	0.635109i	0.0575457	−	0.998343i	$-0.481673\pi$
$349$	−16.3305	−	11.8648i	−0.874152	−	0.635109i	−0.931698	+	0.363234i	$0.881673\pi$
$350$	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	0.980609	−	0.195976i	$-0.0627874\pi$
$353$	33.7575	+	7.17537i	1.79673	+	0.381907i	0.816120	+	0.577882i	$0.196121\pi$
$354$	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	0.822479	+	0.568796i	$0.192590\pi$
$359$	5.73074	+	26.9610i	0.302457	+	1.42295i	−0.520022	+	0.854153i	$0.674076\pi$
$360$	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	−0.676511	+	0.736433i	$0.736509\pi$
$367$	−31.6580	+	18.2778i	−1.65254	+	0.954092i	−0.976025	+	0.217659i	$0.930158\pi$
$368$	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	−0.783079	−	0.621922i	$-0.786352\pi$
$379$	−2.85044	−	27.1201i	−0.146417	−	1.39307i	0.636662	−	0.771143i	$-0.280315\pi$
$380$	−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	0.500812	−	0.865556i	$-0.333035\pi$
$383$	3.77097	+	1.67894i	0.192687	+	0.0857900i	−0.308125	+	0.951346i	$0.599701\pi$
$384$	−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	−0.0156002	−	0.999878i	$-0.504966\pi$
$389$	14.1418	−	6.29632i	0.717016	−	0.319236i	0.732616	+	0.680642i	$0.238299\pi$
$390$	−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	−0.968525	−	0.248915i	$-0.919926\pi$
$397$	−5.35373	+	9.27293i	−0.268696	+	0.465395i	0.699829	+	0.714310i	$0.253259\pi$
$398$	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	−0.975741	−	0.218928i	$-0.929744\pi$
$401$	−6.30852	−	19.4156i	−0.315033	−	0.969571i	0.660708	−	0.750643i	$-0.270256\pi$
$402$	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	0.907403	−	0.420262i	$-0.138062\pi$
$409$	20.1660	+	11.6429i	0.997146	+	0.575702i	0.0897434	+	0.995965i	$0.471395\pi$
$410$	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	−0.420798	−	0.907154i	$-0.638250\pi$
$419$	−26.4966	−	8.60926i	−1.29444	−	0.420590i	−0.873645	+	0.486565i	$0.838250\pi$
$420$	0.834767	+	0.818892i	0.0407324	+	0.0399578i
$421$	3.78824	−	0.805216i	0.184628	−	0.0392438i	−0.114670	−	0.993404i	$-0.536581\pi$
$421$	3.78824	−	0.805216i	0.184628	−	0.0392438i	0.299297	+	0.954160i	$0.403248\pi$
$422$	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	−0.822850	−	0.568259i	$-0.807617\pi$
$431$	−7.13571	+	6.42502i	−0.343715	+	0.309482i	0.479135	+	0.877741i	$0.340951\pi$
$432$	−5.15346	−	0.664740i	−0.247946	−	0.0319823i
$433$			6.69986i			0.321975i	0.986956	+	0.160987i	$0.0514679\pi$
$433$			6.69986i			0.321975i	−0.986956	+	0.160987i	$0.948532\pi$
$434$	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	0.800621	−	0.599171i	$-0.204503\pi$
$439$	−2.48466	−	4.30355i	−0.118586	−	0.205397i	−0.919208	+	0.393773i	$0.871170\pi$
$440$	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	−0.0743913	−	0.997229i	$-0.523701\pi$
$443$	−7.46121	−	0.784204i	−0.354493	−	0.0372587i	−0.280101	+	0.959970i	$0.590368\pi$
$444$	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	0.446800	+	0.894634i	$0.352564\pi$
$449$	−9.33448	+	28.7286i	−0.440521	+	1.35579i	−0.887321	+	0.461152i	$0.847436\pi$
$450$	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	−0.229616	−	0.973281i	$-0.573747\pi$
$457$	16.3963	−	22.5675i	0.766985	−	1.05566i	0.996601	−	0.0823829i	$-0.0262531\pi$
$458$	−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	−0.560524	−	0.828138i	$-0.689400\pi$
$461$	1.15666	−	0.840360i	0.0538708	−	0.0391395i	0.614395	+	0.788999i	$0.289400\pi$
$462$	−1.98849	+	3.99703i	−0.0925129	+	0.185958i
$463$	5.56056	−	1.80673i	0.258421	−	0.0839660i	−0.176941	−	0.984221i	$-0.556620\pi$
$463$	5.56056	−	1.80673i	0.258421	−	0.0839660i	0.435362	+	0.900255i	$0.356620\pi$
$464$	−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	−0.0882255	−	0.996101i	$-0.528120\pi$
$467$	9.20360	−	2.99043i	0.425892	−	0.138381i	0.514117	+	0.857720i	$0.328120\pi$
$468$	−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	0.796292	−	0.604912i	$-0.206792\pi$
$479$	−4.07232	−	9.14657i	−0.186069	−	0.417917i	−0.982361	+	0.186995i	$0.940125\pi$
$480$	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	0.759848	−	0.650100i	$-0.225273\pi$
$487$	30.1876	+	3.17284i	1.36793	+	0.143775i	0.608080	+	0.793875i	$0.291940\pi$
$488$	−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	0.739284	−	0.673393i	$-0.235164\pi$
$491$	−4.73158	−	8.19534i	−0.213533	−	0.369851i	−0.952818	+	0.303543i	$0.901831\pi$
$492$	−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	−0.990258	−	0.139248i	$-0.955531\pi$
$499$	−21.3394	+	19.2141i	−0.955282	+	0.860140i	0.0349753	+	0.999388i	$0.488865\pi$
$500$	−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	0.249613	−	0.968346i	$-0.419697\pi$
$503$	15.5895	−	1.63852i	0.695102	−	0.0730581i	0.445489	+	0.895288i	$0.353030\pi$
$504$	−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	−0.785678	−	0.618636i	$-0.787686\pi$
$509$	−28.2421	+	6.00304i	−1.25181	+	0.266080i	−0.466130	+	0.884716i	$0.654352\pi$
$510$	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	0.235502	−	0.971874i	$-0.424327\pi$
$521$	−11.1483	−	6.43646i	−0.488415	−	0.281987i	−0.723917	+	0.689887i	$0.757660\pi$
$522$	−1.69037	+	5.56366i	−0.0739853	+	0.243515i
$523$	18.9299	+	26.0547i	0.827745	+	1.13929i	0.988339	+	0.152272i	$0.0486591\pi$
$523$	18.9299	+	26.0547i	0.827745	+	1.13929i	−0.160594	+	0.987021i	$0.551341\pi$
$524$	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	−0.668355	−	0.743843i	$-0.733001\pi$
$541$	−13.0901	+	5.82810i	−0.562788	+	0.250569i	0.105566	+	0.994412i	$0.466334\pi$
$542$	−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	0.943970	−	0.330030i	$-0.107059\pi$
$547$	31.1143	+	13.8530i	1.33035	+	0.592310i	0.386379	+	0.922340i	$0.373726\pi$
$548$	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	0.289224	−	0.957262i	$-0.406603\pi$
$563$	29.9644	−	17.2999i	1.26285	−	0.729106i	0.973625	+	0.228156i	$0.0732696\pi$
$564$	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	0.0116348	−	0.999932i	$-0.496296\pi$
$569$	−17.2623	−	7.68568i	−0.723675	−	0.322201i	−0.735309	+	0.677732i	$0.762963\pi$
$570$	−10.0185	+	1.68551i	−0.419628	+	0.0705983i
$571$	−0.562858	−	2.64804i	−0.0235549	−	0.110817i	0.964800	−	0.262986i	$-0.0847074\pi$
$571$	−0.562858	−	2.64804i	−0.0235549	−	0.110817i	−0.988354	+	0.152169i	$0.951374\pi$
$572$	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	−0.0350489	−	0.999386i	$-0.511159\pi$
$577$	−11.3752	−	2.41787i	−0.473554	−	0.100657i	−0.438505	+	0.898729i	$0.644492\pi$
$578$	−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	0.994865	+	0.101208i	$0.0322709\pi$
$587$	6.04469	+	18.6037i	0.249491	+	0.767855i	−0.745374	+	0.666646i	$0.767729\pi$
$588$	−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	−0.991780	−	0.127952i	$-0.959160\pi$
$593$	−19.6516	−	27.0480i	−0.806993	−	1.11073i	0.184788	−	0.982778i	$-0.440840\pi$
$594$	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	0.712680	−	0.701489i	$-0.247481\pi$
$599$	2.19117	+	1.97294i	0.0895287	+	0.0806120i	−0.623151	+	0.782101i	$0.714148\pi$
$600$	−0.199936	+	4.67289i	−0.00816234	+	0.190770i
$601$	4.59804	−	21.6321i	0.187558	−	0.882390i	−0.779216	−	0.626756i	$-0.784382\pi$
$601$	4.59804	−	21.6321i	0.187558	−	0.882390i	0.966774	−	0.255635i	$-0.0822844\pi$
$602$	−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	−0.114019	−	0.993479i	$-0.536372\pi$
$607$	4.58018	−	0.973547i	0.185904	−	0.0395151i	0.299923	+	0.953964i	$0.403039\pi$
$608$	−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	−0.279469	−	0.960155i	$-0.590158\pi$
$613$	−8.74491	+	0.919127i	−0.353204	+	0.0371232i	−0.0737346	+	0.997278i	$0.523492\pi$
$614$	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	−0.902008	−	0.431719i	$-0.857907\pi$
$617$	−14.0825	+	12.6799i	−0.566939	+	0.510474i	0.335069	+	0.942194i	$0.391240\pi$
$618$	19.9932	−	16.5105i	0.804246	−	0.664149i
$619$			7.72738i			0.310590i	0.987868	+	0.155295i	$0.0496328\pi$
$619$			7.72738i			0.310590i	−0.987868	+	0.155295i	$0.950367\pi$
$620$	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	−0.943079	−	0.332569i	$-0.892084\pi$
$631$	−1.62998	+	3.66100i	−0.0648886	+	0.145742i	0.878190	+	0.478312i	$0.158751\pi$
$632$	−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	−0.819615	−	0.572914i	$-0.805813\pi$
$641$	−4.15635	+	4.61610i	−0.164166	+	0.182325i	0.655449	+	0.755239i	$0.272479\pi$
$642$	−5.51396	−	19.8155i	−0.217618	−	0.782055i
$643$	−20.7930	+	28.6191i	−0.819996	+	1.12863i	0.169708	+	0.985494i	$0.445718\pi$
$643$	−20.7930	+	28.6191i	−0.819996	+	1.12863i	−0.989704	+	0.143133i	$0.954282\pi$
$644$	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	−0.404282	−	0.914634i	$-0.632478\pi$
$647$	8.66503	−	6.29551i	0.340657	−	0.247502i	0.744939	+	0.667132i	$0.232478\pi$
$648$	−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	−0.907757	−	0.419496i	$-0.862207\pi$
$653$	−35.6623	+	11.5874i	−1.39557	+	0.453450i	−0.487818	+	0.872946i	$0.662207\pi$
$654$	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	0.0650248	−	0.997884i	$-0.479287\pi$
$659$	25.5163	−	35.1202i	0.993975	−	1.36809i	0.928950	−	0.370205i	$-0.120713\pi$
$660$	14.6498	−	4.07653i	0.570243	−	0.158679i
$661$	2.38791	−	2.65204i	0.0928788	−	0.103152i	−0.694914	−	0.719093i	$-0.744557\pi$
$661$	2.38791	−	2.65204i	0.0928788	−	0.103152i	0.787792	+	0.615941i	$0.211224\pi$
$662$	−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	−0.522734	−	0.852496i	$-0.675088\pi$
$673$	−31.4236	−	3.30275i	−1.21129	−	0.127312i	−0.688555	+	0.725184i	$0.741755\pi$
$674$	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	0.875803	−	0.482668i	$-0.160332\pi$
$677$	0.517745	+	0.896760i	0.0198985	+	0.0344653i	−0.855905	+	0.517134i	$0.826999\pi$
$678$	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	$0.0200570\pi$
$683$			3.29130i			0.125938i	−0.998015	+	0.0629691i	$0.979943\pi$
$684$	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	0.834704	+	0.550699i	$0.185639\pi$
$691$	−2.53028	+	24.0740i	−0.0962565	+	0.915820i	−0.930960	+	0.365121i	$0.881028\pi$
$692$	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	−0.522114	−	0.852876i	$-0.674856\pi$
$701$	7.98943	−	37.5873i	0.301757	−	1.41965i	0.823870	−	0.566778i	$-0.191810\pi$
$702$	−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	0.375305	−	0.926901i	$-0.377538\pi$
$709$	−16.5675	−	22.8032i	−0.622206	−	0.856393i	−0.997511	+	0.0705082i	$0.977538\pi$
$710$	−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	−0.615099	−	0.788450i	$-0.710884\pi$
$719$	10.0625	−	17.4288i	0.375268	−	0.649984i	0.990367	+	0.138466i	$0.0442173\pi$
$720$	−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	0.515761	−	0.856733i	$-0.327509\pi$
$727$	40.3783	−	17.9776i	1.49755	−	0.666751i	0.981788	+	0.189981i	$0.0608428\pi$
$728$	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	−0.125135	−	0.992140i	$-0.539936\pi$
$733$	−25.6166	−	11.4052i	−0.946170	−	0.421262i	−0.821035	+	0.570878i	$0.806603\pi$
$734$	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	0.338646	−	0.940914i	$-0.390031\pi$
$739$	35.9604	−	20.7617i	1.32282	−	0.763733i	0.984178	+	0.177181i	$0.0566978\pi$
$740$	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	0.990929	+	0.134384i	$0.0429056\pi$
$751$	1.35910	+	12.9310i	0.0495942	+	0.471857i	−0.941335	+	0.337473i	$0.890428\pi$
$752$	−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	0.999665	−	0.0259004i	$-0.00824528\pi$
$757$	2.08803	+	9.82343i	0.0758909	+	0.357039i	−0.923774	+	0.382939i	$0.874912\pi$
$758$	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	−0.270867	−	0.962617i	$-0.587310\pi$
$761$	7.26212	−	3.23330i	0.263252	−	0.117207i	0.534118	+	0.845410i	$0.320644\pi$
$762$	−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	−0.922755	−	0.385387i	$-0.874068\pi$
$769$	−3.53908	+	6.12986i	−0.127622	+	0.221049i	0.795133	+	0.606436i	$0.207401\pi$
$770$	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	0.963377	−	0.268150i	$-0.0864124\pi$
$773$	0.733266	+	2.25676i	0.0263738	+	0.0811701i	−0.937003	+	0.349321i	$0.886412\pi$
$774$	−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	−0.699278	−	0.714850i	$-0.746495\pi$
$787$	6.46072	−	30.3953i	0.230300	−	1.08348i	0.929578	−	0.368626i	$-0.120172\pi$
$788$	−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	0.968802	+	0.247835i	$0.0797190\pi$
$797$	−0.857016	+	8.15396i	−0.0303571	+	0.288828i	−0.999159	+	0.0409936i	$0.986948\pi$
$798$	−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	0.134765	−	0.990878i	$-0.456972\pi$
$809$	−24.5966	−	27.3173i	−0.864772	−	0.960426i	−0.999536	+	0.0304513i	$0.990306\pi$
$810$	7.27277	+	11.5489i	0.255539	+	0.405788i
$811$	−5.94022	−	10.2888i	−0.208589	−	0.361288i	0.742681	−	0.669645i	$-0.233554\pi$
$811$	−5.94022	−	10.2888i	−0.208589	−	0.361288i	−0.951270	+	0.308358i	$0.900221\pi$
$812$	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	0.697792	+	0.716301i	$0.254166\pi$
$821$	−8.24535	+	25.3766i	−0.287765	+	0.885649i	−0.985556	+	0.169348i	$0.945834\pi$
$822$	0.746552	−	0.0463152i	0.0260390	−	0.00161543i
$823$	−1.59308	−	3.57811i	−0.0555313	−	0.124725i	0.883649	−	0.468150i	$-0.155079\pi$
$823$	−1.59308	−	3.57811i	−0.0555313	−	0.124725i	−0.939180	+	0.343425i	$0.888413\pi$
$824$	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	−0.609579	−	0.792725i	$-0.708662\pi$
$827$	6.97434	−	7.74579i	0.242522	−	0.269347i	0.852101	+	0.523378i	$0.175328\pi$
$828$	14.7725	+	19.5327i	0.513379	+	0.678807i
$829$	−20.4338	+	28.1247i	−0.709694	+	0.976811i	0.290109	+	0.956994i	$0.406308\pi$
$829$	−20.4338	+	28.1247i	−0.709694	+	0.976811i	−0.999804	+	0.0198170i	$0.993692\pi$
$830$	−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	−0.685838	−	0.727754i	$-0.740564\pi$
$839$	−23.5469	+	7.65086i	−0.812930	+	0.264137i	−0.127092	+	0.991891i	$0.540564\pi$
$840$	−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	−0.842783	−	0.538254i	$-0.819084\pi$
$853$	4.53923	−	13.9703i	0.155420	−	0.478335i	0.998203	+	0.0599189i	$0.0190842\pi$
$854$	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	−0.595646	−	0.803247i	$-0.703104\pi$
$857$	11.7054	−	26.2907i	0.399848	−	0.898073i	0.995494	−	0.0948259i	$-0.0302294\pi$
$858$	−7.03154	+	18.8569i	−0.240053	+	0.643763i
$859$	18.4609	+	1.94032i	0.629878	+	0.0662028i	0.414088	−	0.910237i	$-0.364101\pi$
$859$	18.4609	+	1.94032i	0.629878	+	0.0662028i	0.215790	+	0.976440i	$0.430767\pi$
$860$	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	0.988417	−	0.151761i	$-0.0484944\pi$
$863$	10.6573	+	18.4590i	0.362780	+	0.628353i	−0.625637	+	0.780114i	$0.715161\pi$
$864$	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	−0.999531	−	0.0306326i	$-0.990248\pi$
$877$	−0.458228	+	4.35975i	−0.0154733	+	0.147218i	0.984057	+	0.177851i	$0.0569145\pi$
$878$	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	−0.292154	−	0.956371i	$-0.594372\pi$
$881$	−5.04761	+	1.07290i	−0.170058	+	0.0361470i	0.122095	+	0.992518i	$0.461039\pi$
$882$	−18.7971	−	7.94021i	−0.632933	−	0.267361i
$883$	3.13892	+	1.01990i	0.105633	+	0.0343223i	0.361357	−	0.932428i	$-0.382314\pi$
$883$	3.13892	+	1.01990i	0.105633	+	0.0343223i	−0.255724	+	0.966750i	$0.582314\pi$
$884$	−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	−0.735242	−	0.677805i	$-0.762931\pi$
$887$	6.31757	−	29.7218i	0.212123	−	0.997961i	0.947365	−	0.320156i	$-0.103735\pi$
$888$	−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	0.435048	−	0.900407i	$-0.356731\pi$
$907$	−8.63900	−	6.27660i	−0.286853	−	0.208411i	−0.721901	+	0.691996i	$0.756731\pi$
$908$	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	−0.553709	−	0.832710i	$-0.686788\pi$
$911$	−42.2028	−	8.97048i	−1.39824	−	0.297205i	−0.844532	+	0.535505i	$0.820121\pi$
$912$	−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	0.915015	−	0.403419i	$-0.132178\pi$
$919$	37.2111	+	16.5675i	1.22748	+	0.546510i	0.312466	+	0.949929i	$0.398845\pi$
$920$	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	0.531945	+	0.846779i	$0.321461\pi$
$937$	5.74496	+	54.6596i	0.187680	+	1.78565i	−0.344265	+	0.938872i	$0.611872\pi$
$938$	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	0.265491	−	0.964113i	$-0.414466\pi$
$941$	−8.38482	−	3.73316i	−0.273337	−	0.121698i	−0.538828	+	0.842416i	$0.681133\pi$
$942$	−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	−0.784839	−	0.619699i	$-0.787255\pi$
$947$	−26.1412	+	11.6388i	−0.849473	+	0.378210i	−0.0646339	+	0.997909i	$0.520588\pi$
$948$	−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	0.961962	−	0.273182i	$-0.0880761\pi$
$953$	30.8526	+	22.4157i	0.999414	+	0.726116i	0.0374512	+	0.999298i	$0.488076\pi$
$954$	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	0.253745	−	0.967271i	$-0.418338\pi$
$967$	−14.2132	−	8.20597i	−0.457065	−	0.263886i	−0.710809	+	0.703385i	$0.751671\pi$
$968$	−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	0.412062	−	0.911156i	$-0.364809\pi$
$971$	−14.0545	−	12.6547i	−0.451030	−	0.406110i	−0.863092	+	0.505046i	$0.831475\pi$
$972$	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	0.0511990	−	0.998688i	$-0.483696\pi$
$977$	−15.4533	−	5.02108i	−0.494394	−	0.160638i	−0.545593	+	0.838050i	$0.683696\pi$
$978$	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	0.953694	+	0.300779i	$0.0972466\pi$
$983$	−1.30725	+	12.4377i	−0.0416949	+	0.396701i	−0.995389	+	0.0959218i	$0.969420\pi$
$984$	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	$0.271623\pi$
$991$			47.4390i			1.50695i	−0.657477	+	0.753474i	$0.728377\pi$
$992$	−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	−0.954131	−	0.299389i	$-0.903217\pi$
$997$	−23.2503	−	40.2707i	−0.736344	−	1.27538i	0.217787	−	0.975996i	$-0.430116\pi$
$998$	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.11.1	✓	80
3.2	odd	2	inner	186.2.p.a.11.9	yes	80
31.17	odd	30	inner	186.2.p.a.17.9	yes	80
93.17	even	30	inner	186.2.p.a.17.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.1	✓	80	1.1	even	1	trivial
186.2.p.a.11.9	yes	80	3.2	odd	2	inner
186.2.p.a.17.1	yes	80	93.17	even	30	inner
186.2.p.a.17.9	yes	80	31.17	odd	30	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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more