LMFDB - Embedded newform 186.2.p.a.11.2

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			11.2
Character	$\chi$	$=$	186.11
Dual form			186.2.p.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-0.878235 + 1.49288i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.08872 + 1.20592i) q^{5} +(0.373925 - 1.69121i) q^{6} +(0.0316894 + 0.301504i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.45741 - 2.62221i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.878235 + 1.49288i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.08872 + 1.20592i) q^{5} +(0.373925 - 1.69121i) q^{6} +(0.0316894 + 0.301504i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.45741 - 2.62221i) q^{9} +(1.61384 - 1.79235i) q^{10} +(-3.75423 - 1.67149i) q^{11} +(0.166988 + 1.72398i) q^{12} +(0.178771 + 0.841052i) q^{13} +(-0.123308 - 0.276955i) q^{14} +(0.0340837 - 4.17729i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.109838 + 0.0489031i) q^{17} +(2.19638 + 2.04350i) q^{18} +(-7.42953 - 1.57920i) q^{19} +(-0.980985 + 2.20333i) q^{20} +(-0.477942 - 0.217483i) q^{21} +(4.08700 + 0.429561i) q^{22} +(0.787971 + 0.572494i) q^{23} +(-0.691555 - 1.58800i) q^{24} +(0.408492 - 0.707530i) q^{25} +(-0.429921 - 0.744645i) q^{26} +(5.19460 + 0.127175i) q^{27} +(0.202857 + 0.225295i) q^{28} +(1.13592 + 3.49602i) q^{29} +(1.25844 + 3.98338i) q^{30} +(-2.96549 + 4.71231i) q^{31} +1.00000i q^{32} +(5.79244 - 4.13667i) q^{33} +(0.0893503 - 0.0804514i) q^{34} +(-0.429780 - 0.591542i) q^{35} +(-2.72036 - 1.26477i) q^{36} +(-2.14572 - 1.23883i) q^{37} +(7.55390 - 0.793947i) q^{38} +(-1.41260 - 0.471757i) q^{39} +(0.252106 - 2.39863i) q^{40} +(5.77580 + 5.20055i) q^{41} +(0.521755 + 0.0591466i) q^{42} +(-2.37289 + 11.1636i) q^{43} +(-4.01971 + 0.854417i) q^{44} +(6.20628 + 3.71953i) q^{45} +(-0.926316 - 0.300978i) q^{46} +(4.99435 + 1.62276i) q^{47} +(1.14843 + 1.29658i) q^{48} +(6.75713 - 1.43627i) q^{49} +(-0.169861 + 0.799132i) q^{50} +(0.0234570 - 0.206924i) q^{51} +(0.638987 + 0.575346i) q^{52} +(1.15917 - 11.0288i) q^{53} +(-4.97965 + 1.48427i) q^{54} +(9.85721 - 1.03603i) q^{55} +(-0.262549 - 0.151582i) q^{56} +(8.88243 - 9.70452i) q^{57} +(-2.16066 - 2.97389i) q^{58} +(-9.97095 + 8.97788i) q^{59} +(-2.42778 - 3.39954i) q^{60} +3.20415i q^{61} +(1.36416 - 5.39806i) q^{62} +(0.744422 - 0.522510i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.38764 - 1.54114i) q^{65} +(-4.23064 + 5.72417i) q^{66} +(-0.707708 - 1.22579i) q^{67} +(-0.0601164 + 0.104125i) q^{68} +(-1.54669 + 0.673565i) q^{69} +(0.591542 + 0.429780i) q^{70} +(-9.66655 - 1.01600i) q^{71} +(2.97805 + 0.362228i) q^{72} +(-1.27184 + 2.85661i) q^{73} +(2.42353 + 0.515136i) q^{74} +(0.697507 + 1.23121i) q^{75} +(-6.93884 + 3.08937i) q^{76} +(0.384992 - 1.18488i) q^{77} +(1.48924 + 0.0121511i) q^{78} +(-6.12085 - 13.7477i) q^{79} +(0.501450 + 2.35914i) q^{80} +(-4.75193 + 7.64324i) q^{81} +(-7.10017 - 3.16120i) q^{82} +(-2.75278 + 3.05728i) q^{83} +(-0.514496 + 0.104980i) q^{84} +(0.170447 - 0.234601i) q^{85} +(-1.19298 - 11.3504i) q^{86} +(-6.21676 - 1.37452i) q^{87} +(3.55895 - 2.05476i) q^{88} +(-1.33414 + 0.969306i) q^{89} +(-7.05192 - 1.61964i) q^{90} +(-0.247916 + 0.0805526i) q^{91} +0.973986 q^{92} +(-4.43054 - 8.56565i) q^{93} -5.25137 q^{94} +(17.4226 - 5.66094i) q^{95} +(-1.49288 - 0.878235i) q^{96} +(1.75787 - 1.27717i) q^{97} +(-5.98258 + 3.45405i) q^{98} +(1.08844 + 12.2804i) 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
$3$	−0.878235	+	1.49288i	−0.507049	+	0.861917i
$3$	−0.878235	+	1.49288i	−0.507049	+	0.861917i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.08872	+	1.20592i	−0.934103	+	0.539304i	−0.888107	−	0.459637i	$-0.847979\pi$
$5$	−2.08872	+	1.20592i	−0.934103	+	0.539304i	−0.0459959	+	0.998942i	$0.514646\pi$
$6$	0.373925	−	1.69121i	0.152654	−	0.690432i
$7$	0.0316894	+	0.301504i	0.0119775	+	0.113958i	0.998877	−	0.0473778i	$-0.0150865\pi$
$7$	0.0316894	+	0.301504i	0.0119775	+	0.113958i	−0.986900	+	0.161336i	$0.948420\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−1.45741	−	2.62221i	−0.485802	−	0.874069i
$10$	1.61384	−	1.79235i	0.510340	−	0.566790i
$11$	−3.75423	−	1.67149i	−1.13194	−	0.503974i	−0.246695	−	0.969093i	$-0.579345\pi$
$11$	−3.75423	−	1.67149i	−1.13194	−	0.503974i	−0.885248	+	0.465120i	$0.846011\pi$
$12$	0.166988	+	1.72398i	0.0482053	+	0.497671i
$13$	0.178771	+	0.841052i	0.0495822	+	0.233266i	0.995960	−	0.0897955i	$-0.0286213\pi$
$13$	0.178771	+	0.841052i	0.0495822	+	0.233266i	−0.946378	+	0.323061i	$0.895288\pi$
$14$	−0.123308	−	0.276955i	−0.0329555	−	0.0740193i
$15$	0.0340837	−	4.17729i	0.00880036	−	1.07857i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.109838	+	0.0489031i	−0.0266396	+	0.0118607i	−0.420013	−	0.907518i	$-0.637975\pi$
$17$	−0.109838	+	0.0489031i	−0.0266396	+	0.0118607i	0.393374	+	0.919379i	$0.371308\pi$
$18$	2.19638	+	2.04350i	0.517692	+	0.481658i
$19$	−7.42953	−	1.57920i	−1.70445	−	0.362292i	−0.750180	−	0.661234i	$-0.770033\pi$
$19$	−7.42953	−	1.57920i	−1.70445	−	0.362292i	−0.954271	+	0.298942i	$0.903366\pi$
$20$	−0.980985	+	2.20333i	−0.219355	+	0.492679i
$21$	−0.477942	−	0.217483i	−0.104295	−	0.0474587i
$22$	4.08700	+	0.429561i	0.871352	+	0.0915828i
$23$	0.787971	+	0.572494i	0.164303	+	0.119373i	0.666899	−	0.745148i	$-0.267621\pi$
$23$	0.787971	+	0.572494i	0.164303	+	0.119373i	−0.502595	+	0.864522i	$0.667621\pi$
$24$	−0.691555	−	1.58800i	−0.141163	−	0.324150i
$25$	0.408492	−	0.707530i	0.0816985	−	0.141506i
$26$	−0.429921	−	0.744645i	−0.0843144	−	0.146037i
$27$	5.19460	+	0.127175i	0.999700	+	0.0244748i
$28$	0.202857	+	0.225295i	0.0383364	+	0.0425768i
$29$	1.13592	+	3.49602i	0.210936	+	0.649194i	0.999417	+	0.0341352i	$0.0108677\pi$
$29$	1.13592	+	3.49602i	0.210936	+	0.649194i	−0.788481	+	0.615059i	$0.789132\pi$
$30$	1.25844	+	3.98338i	0.229759	+	0.727262i
$31$	−2.96549	+	4.71231i	−0.532617	+	0.846356i
$31$	−2.96549	+	4.71231i	−0.532617	+	0.846356i
$32$			1.00000i			0.176777i
$33$	5.79244	−	4.13667i	1.00833	−	0.720102i
$34$	0.0893503	−	0.0804514i	0.0153235	−	0.0137973i
$35$	−0.429780	−	0.591542i	−0.0726462	−	0.0999889i
$36$	−2.72036	−	1.26477i	−0.453393	−	0.210795i
$37$	−2.14572	−	1.23883i	−0.352755	−	0.203663i	0.313143	−	0.949706i	$-0.398618\pi$
$37$	−2.14572	−	1.23883i	−0.352755	−	0.203663i	−0.665898	+	0.746043i	$0.731951\pi$
$38$	7.55390	−	0.793947i	1.22540	−	0.128795i
$39$	−1.41260	−	0.471757i	−0.226196	−	0.0755415i
$40$	0.252106	−	2.39863i	0.0398615	−	0.379257i
$41$	5.77580	+	5.20055i	0.902028	+	0.812189i	0.982825	−	0.184541i	$-0.0590799\pi$
$41$	5.77580	+	5.20055i	0.902028	+	0.812189i	−0.0807971	+	0.996731i	$0.525747\pi$
$42$	0.521755	+	0.0591466i	0.0805086	+	0.00912651i
$43$	−2.37289	+	11.1636i	−0.361862	+	1.70243i	0.300949	+	0.953640i	$0.402697\pi$
$43$	−2.37289	+	11.1636i	−0.361862	+	1.70243i	−0.662811	+	0.748787i	$0.730637\pi$
$44$	−4.01971	+	0.854417i	−0.605995	+	0.128808i
$45$	6.20628	+	3.71953i	0.925178	+	0.554475i
$46$	−0.926316	−	0.300978i	−0.136578	−	0.0443768i
$47$	4.99435	+	1.62276i	0.728500	+	0.236704i	0.649705	−	0.760187i	$-0.274893\pi$
$47$	4.99435	+	1.62276i	0.728500	+	0.236704i	0.0787956	+	0.996891i	$0.474893\pi$
$48$	1.14843	+	1.29658i	0.165761	+	0.187145i
$49$	6.75713	−	1.43627i	0.965305	−	0.205182i
$50$	−0.169861	+	0.799132i	−0.0240219	+	0.113014i
$51$	0.0234570	−	0.206924i	0.00328464	−	0.0289751i
$52$	0.638987	+	0.575346i	0.0886115	+	0.0797862i
$53$	1.15917	−	11.0288i	0.159224	−	1.51492i	−0.564849	−	0.825195i	$-0.691065\pi$
$53$	1.15917	−	11.0288i	0.159224	−	1.51492i	0.724073	−	0.689723i	$-0.242268\pi$
$54$	−4.97965	+	1.48427i	−0.677645	+	0.201983i
$55$	9.85721	−	1.03603i	1.32915	−	0.139699i
$56$	−0.262549	−	0.151582i	−0.0350845	−	0.0202561i
$57$	8.88243	−	9.70452i	1.17651	−	1.28540i
$58$	−2.16066	−	2.97389i	−0.283708	−	0.390491i
$59$	−9.97095	+	8.97788i	−1.29811	+	1.16882i	−0.323170	+	0.946341i	$0.604749\pi$
$59$	−9.97095	+	8.97788i	−1.29811	+	1.16882i	−0.974937	+	0.222480i	$0.928585\pi$
$60$	−2.42778	−	3.39954i	−0.313425	−	0.438878i
$61$			3.20415i			0.410250i	0.978736	+	0.205125i	$0.0657601\pi$
$61$			3.20415i			0.410250i	−0.978736	+	0.205125i	$0.934240\pi$
$62$	1.36416	−	5.39806i	0.173249	−	0.685554i
$63$	0.744422	−	0.522510i	0.0937884	−	0.0658301i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−1.38764	−	1.54114i	−0.172116	−	0.191154i
$66$	−4.23064	+	5.72417i	−0.520755	+	0.704596i
$67$	−0.707708	−	1.22579i	−0.0864602	−	0.149754i	0.819552	−	0.573004i	$-0.194222\pi$
$67$	−0.707708	−	1.22579i	−0.0864602	−	0.149754i	−0.906013	+	0.423251i	$0.860889\pi$
$68$	−0.0601164	+	0.104125i	−0.00729018	+	0.0126270i
$69$	−1.54669	+	0.673565i	−0.186200	+	0.0810877i
$70$	0.591542	+	0.429780i	0.0707028	+	0.0513686i
$71$	−9.66655	−	1.01600i	−1.14721	−	0.120576i	−0.488214	−	0.872724i	$-0.662351\pi$
$71$	−9.66655	−	1.01600i	−1.14721	−	0.120576i	−0.658995	+	0.752148i	$0.729018\pi$
$72$	2.97805	+	0.362228i	0.350967	+	0.0426890i
$73$	−1.27184	+	2.85661i	−0.148858	+	0.334341i	−0.972549	−	0.232698i	$-0.925244\pi$
$73$	−1.27184	+	2.85661i	−0.148858	+	0.334341i	0.823691	+	0.567039i	$0.191911\pi$
$74$	2.42353	+	0.515136i	0.281729	+	0.0598834i
$75$	0.697507	+	1.23121i	0.0805412	+	0.142168i
$76$	−6.93884	+	3.08937i	−0.795940	+	0.354375i
$77$	0.384992	−	1.18488i	0.0438740	−	0.135030i
$78$	1.48924	+	0.0121511i	0.168623	+	0.00137584i
$79$	−6.12085	−	13.7477i	−0.688650	−	1.54673i	−0.830607	−	0.556859i	$-0.812006\pi$
$79$	−6.12085	−	13.7477i	−0.688650	−	1.54673i	0.141957	−	0.989873i	$-0.454660\pi$
$80$	0.501450	+	2.35914i	0.0560638	+	0.263760i
$81$	−4.75193	+	7.64324i	−0.527993	+	0.849249i
$82$	−7.10017	−	3.16120i	−0.784082	−	0.349096i
$83$	−2.75278	+	3.05728i	−0.302157	+	0.335580i	−0.875034	−	0.484062i	$-0.839161\pi$
$83$	−2.75278	+	3.05728i	−0.302157	+	0.335580i	0.572876	+	0.819642i	$0.305828\pi$
$84$	−0.514496	+	0.104980i	−0.0561361	+	0.0114542i
$85$	0.170447	−	0.234601i	0.0184876	−	0.0254460i
$86$	−1.19298	−	11.3504i	−0.128642	−	1.22395i
$87$	−6.21676	−	1.37452i	−0.666506	−	0.147364i
$88$	3.55895	−	2.05476i	0.379385	−	0.219038i
$89$	−1.33414	+	0.969306i	−0.141418	+	0.102746i	−0.656245	−	0.754548i	$-0.727856\pi$
$89$	−1.33414	+	0.969306i	−0.141418	+	0.102746i	0.514827	+	0.857294i	$0.327856\pi$
$90$	−7.05192	−	1.61964i	−0.743338	−	0.170725i
$91$	−0.247916	+	0.0805526i	−0.0259886	+	0.00844421i
$92$	0.973986			0.101545
$93$	−4.43054	−	8.56565i	−0.459426	−	0.888216i
$94$	−5.25137			−0.541637
$95$	17.4226	−	5.66094i	1.78752	−	0.580800i
$96$	−1.49288	−	0.878235i	−0.152367	−	0.0896345i
$97$	1.75787	−	1.27717i	0.178485	−	0.129677i	−0.494956	−	0.868918i	$-0.664816\pi$
$97$	1.75787	−	1.27717i	0.178485	−	0.129677i	0.673440	+	0.739241i	$0.264816\pi$
$98$	−5.98258	+	3.45405i	−0.604332	+	0.348911i
$99$	1.08844	+	12.2804i	0.109393	+	1.23423i
$100$	−0.0853982	−	0.812509i	−0.00853982	−	0.0812509i
$101$	5.14844	−	7.08622i	0.512289	−	0.705105i	−0.472014	−	0.881591i	$-0.656473\pi$
$101$	5.14844	−	7.08622i	0.512289	−	0.705105i	0.984303	+	0.176486i	$0.0564729\pi$
$102$	0.0416340	+	0.204045i	0.00412238	+	0.0202035i
$103$	−6.05522	+	6.72501i	−0.596639	+	0.662635i	−0.963521	−	0.267633i	$-0.913759\pi$
$103$	−6.05522	+	6.72501i	−0.596639	+	0.662635i	0.366882	+	0.930267i	$0.380425\pi$
$104$	−0.785504	−	0.349729i	−0.0770250	−	0.0342938i
$105$	1.26055	−	0.122099i	0.123017	−	0.0119157i
$106$	2.30564	+	10.8472i	0.223944	+	1.05357i
$107$	−1.66669	−	3.74345i	−0.161125	−	0.361893i	0.814883	−	0.579625i	$-0.196801\pi$
$107$	−1.66669	−	3.74345i	−0.161125	−	0.361893i	−0.976009	+	0.217732i	$0.930134\pi$
$108$	4.27727	−	2.95042i	0.411580	−	0.283904i
$109$	−0.925478	+	2.84833i	−0.0886447	+	0.272820i	−0.985545	−	0.169412i	$-0.945813\pi$
$109$	−0.925478	+	2.84833i	−0.0886447	+	0.272820i	0.896901	+	0.442232i	$0.145813\pi$
$110$	−9.05461	+	4.03137i	−0.863323	+	0.384376i
$111$	3.73389	−	2.11533i	0.354405	−	0.200778i
$112$	0.296540	+	0.0630315i	0.0280204	+	0.00595592i
$113$	−6.04634	+	13.5803i	−0.568792	+	1.27753i	0.368709	+	0.929545i	$0.379800\pi$
$113$	−6.04634	+	13.5803i	−0.568792	+	1.27753i	−0.937501	+	0.347983i	$0.886867\pi$
$114$	−5.44883	+	11.9744i	−0.510330	+	1.12150i
$115$	−2.33623	−	0.245548i	−0.217855	−	0.0228975i
$116$	2.97389	+	2.16066i	0.276119	+	0.200612i
$117$	1.94487	−	1.69453i	0.179803	−	0.156659i
$118$	6.70862	−	11.6197i	0.617578	−	1.06968i
$119$	−0.0182252	−	0.0315669i	−0.00167070	−	0.00289374i
$120$	3.35947	+	2.48293i	0.306676	+	0.226659i
$121$	3.93993	+	4.37573i	0.358175	+	0.397794i
$122$	−0.990138	−	3.04733i	−0.0896429	−	0.275892i
$123$	−12.8363	+	4.05529i	−1.15741	+	0.365653i
$124$	0.370698	+	5.55541i	0.0332897	+	0.498891i
$125$		−	10.0888i		−	0.902367i
$126$	−0.546523	+	0.726976i	−0.0486881	+	0.0647641i
$127$	11.8677	−	10.6857i	1.05308	−	0.948202i	0.0543515	−	0.998522i	$-0.482691\pi$
$127$	11.8677	−	10.6857i	1.05308	−	0.948202i	0.998733	+	0.0503202i	$0.0160242\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−14.5820	−	13.3467i	−1.28387	−	1.17511i
$130$	1.79597	+	1.03690i	0.157517	+	0.0909422i
$131$	14.2025	−	1.49274i	1.24088	−	0.130421i	0.538745	−	0.842469i	$-0.318898\pi$
$131$	14.2025	−	1.49274i	1.24088	−	0.130421i	0.702132	+	0.712047i	$0.252232\pi$
$132$	2.25471	−	6.75135i	0.196247	−	0.587629i
$133$	0.240697	−	2.29008i	0.0208711	−	0.198575i
$134$	1.05186	+	0.947098i	0.0908667	+	0.0818168i
$135$	−11.0034	+	5.99864i	−0.947022	+	0.516281i
$136$	0.0249978	−	0.117605i	0.00214354	−	0.0100846i
$137$	15.3854	−	3.27027i	1.31446	−	0.279398i	0.503246	−	0.864143i	$-0.332139\pi$
$137$	15.3854	−	3.27027i	1.31446	−	0.279398i	0.811217	+	0.584746i	$0.198806\pi$
$138$	1.26285	−	1.11855i	0.107501	−	0.0952175i
$139$	11.8588	+	3.85316i	1.00585	+	0.326821i	0.765202	−	0.643791i	$-0.222639\pi$
$139$	11.8588	+	3.85316i	1.00585	+	0.326821i	0.240650	+	0.970612i	$0.422639\pi$
$140$	−0.695399	−	0.225949i	−0.0587720	−	0.0190962i
$141$	−6.80881	+	6.03082i	−0.573405	+	0.507886i
$142$	9.50739	−	2.02086i	0.797843	−	0.169587i
$143$	0.734663	−	3.45632i	0.0614356	−	0.289032i
$144$	−2.94423	+	0.575769i	−0.245352	+	0.0479808i
$145$	−6.58854	−	5.93235i	−0.547149	−	0.492655i
$146$	0.326855	−	3.10982i	0.0270507	−	0.257370i
$147$	−3.79016	+	11.3490i	−0.312607	+	0.936050i
$148$	−2.46410	+	0.258987i	−0.202547	+	0.0212886i
$149$	−18.2693	−	10.5478i	−1.49668	−	0.864109i	−0.496687	−	0.867930i	$-0.665450\pi$
$149$	−18.2693	−	10.5478i	−1.49668	−	0.864109i	−0.999993	+	0.00382108i	$0.998784\pi$
$150$	−1.04383	−	0.955408i	−0.0852286	−	0.0780087i
$151$	−11.0882	−	15.2616i	−0.902347	−	1.24197i	−0.969713	−	0.244246i	$-0.921460\pi$
$151$	−11.0882	−	15.2616i	−0.902347	−	1.24197i	0.0673664	−	0.997728i	$-0.478540\pi$
$152$	5.64456	−	5.08239i	0.457835	−	0.412236i
$153$	0.288313	+	0.216746i	0.0233087	+	0.0175229i
$154$			1.24586i			0.100394i
$155$	0.511386	−	13.4188i	0.0410755	−	1.07783i
$156$	−1.42011	+	0.448644i	−0.113699	+	0.0359203i
$157$	3.28656	+	10.1150i	0.262296	+	0.807265i	0.992304	+	0.123826i	$0.0395165\pi$
$157$	3.28656	+	10.1150i	0.262296	+	0.807265i	−0.730008	+	0.683439i	$0.760484\pi$
$158$	10.0695	+	11.1834i	0.801089	+	0.889700i
$159$	15.4467	+	11.4164i	1.22500	+	0.905376i
$160$	−1.20592	−	2.08872i	−0.0953365	−	0.165128i
$161$	−0.147639	+	0.255719i	−0.0116356	+	0.0201534i
$162$	2.15747	−	8.73758i	0.169507	−	0.686489i
$163$	8.73131	+	6.34367i	0.683889	+	0.496875i	0.874646	−	0.484763i	$-0.161094\pi$
$163$	8.73131	+	6.34367i	0.683889	+	0.496875i	−0.190756	+	0.981637i	$0.561094\pi$
$164$	7.72952	+	0.812406i	0.603574	+	0.0634382i
$165$	−7.11027	+	15.6256i	−0.553534	+	1.21645i
$166$	1.67330	−	3.75830i	0.129873	−	0.291701i
$167$	18.4855	+	3.92922i	1.43045	+	0.304052i	0.857055	−	0.515224i	$-0.172291\pi$
$167$	18.4855	+	3.92922i	1.43045	+	0.304052i	0.573399	+	0.819277i	$0.305625\pi$
$168$	0.456874	−	0.258830i	0.0352486	−	0.0199691i
$169$	11.2007	−	4.98686i	0.861591	−	0.383605i
$170$	−0.0896095	+	0.275790i	−0.00687273	+	0.0211521i
$171$	6.68687	+	21.7833i	0.511358	+	1.66581i
$172$	4.64207	+	10.4263i	0.353955	+	0.794995i
$173$	4.41924	+	20.7909i	0.335989	+	1.58070i	0.744290	+	0.667856i	$0.232788\pi$
$173$	4.41924	+	20.7909i	0.335989	+	1.58070i	−0.408301	+	0.912847i	$0.633879\pi$
$174$	6.33724	−	0.613837i	0.480425	−	0.0465348i
$175$	0.226268	+	0.100741i	0.0171043	+	0.00761530i
$176$	−2.74980	+	3.05397i	−0.207274	+	0.230201i
$177$	−4.64610	−	22.7702i	−0.349222	−	1.71151i
$178$	0.969306	−	1.33414i	0.0726526	−	0.0999977i
$179$	0.154133	+	1.46648i	0.0115205	+	0.109610i	0.998771	−	0.0495647i	$-0.0157834\pi$
$179$	0.154133	+	1.46648i	0.0115205	+	0.109610i	−0.987250	+	0.159175i	$0.949117\pi$
$180$	7.20727	−	0.638799i	0.537198	−	0.0476133i
$181$	−8.11572	+	4.68561i	−0.603236	+	0.348279i	−0.770314	−	0.637665i	$-0.779900\pi$
$181$	−8.11572	+	4.68561i	−0.603236	+	0.348279i	0.167077	+	0.985944i	$0.446567\pi$
$182$	0.210890	−	0.153220i	0.0156322	−	0.0113574i
$183$	−4.78343	−	2.81400i	−0.353601	−	0.208017i
$184$	−0.926316	+	0.300978i	−0.0682889	+	0.0221884i
$185$	5.97575			0.439346
$186$	6.86063	+	6.77730i	0.503045	+	0.496936i
$187$	0.494098			0.0361321
$188$	4.99435	−	1.62276i	0.364250	−	0.118352i
$189$	0.126270	+	1.57022i	0.00918477	+	0.114217i
$190$	−14.8205	+	10.7677i	−1.07519	+	0.781174i
$191$	−16.8170	+	9.70929i	−1.21683	+	0.702540i	−0.964240	−	0.265032i	$-0.914617\pi$
$191$	−16.8170	+	9.70929i	−1.21683	+	0.702540i	−0.252595	+	0.967572i	$0.581284\pi$
$192$	1.69121	+	0.373925i	0.122052	+	0.0269857i
$193$	2.21070	+	21.0334i	0.159130	+	1.51402i	0.724554	+	0.689218i	$0.242046\pi$
$193$	2.21070	+	21.0334i	0.159130	+	1.51402i	−0.565424	+	0.824800i	$0.691288\pi$
$194$	−1.27717	+	1.75787i	−0.0916953	+	0.126208i
$195$	3.51941	−	0.718113i	0.252031	−	0.0514252i
$196$	4.62242	−	5.13371i	0.330173	−	0.366694i
$197$	−5.08696	−	2.26486i	−0.362431	−	0.161365i	0.217439	−	0.976074i	$-0.430230\pi$
$197$	−5.08696	−	2.26486i	−0.362431	−	0.161365i	−0.579870	+	0.814709i	$0.696897\pi$
$198$	−4.83003	−	11.3430i	−0.343255	−	0.806113i
$199$	−1.18975	−	5.59734i	−0.0843392	−	0.396785i	0.915647	−	0.401983i	$-0.131679\pi$
$199$	−1.18975	−	5.59734i	−0.0843392	−	0.396785i	−0.999986	+	0.00519785i	$0.998345\pi$
$200$	0.332298	+	0.746353i	0.0234970	+	0.0527751i
$201$	2.45149	+	0.0200024i	0.172915	+	0.00141086i
$202$	−2.70670	+	8.33035i	−0.190442	+	0.586122i
$203$	−1.01807	+	0.453273i	−0.0714543	+	0.0318135i
$204$	−0.102650	−	0.181193i	−0.00718691	−	0.0126860i
$205$	−18.3355	−	3.89732i	−1.28060	−	0.272201i
$206$	3.68072	−	8.26703i	0.256448	−	0.575991i
$207$	0.352805	−	2.90058i	0.0245216	−	0.201604i
$208$	0.855131	+	0.0898779i	0.0592927	+	0.00623191i
$209$	25.2526	+	18.3471i	1.74676	+	1.26909i
$210$	−1.16113	+	0.505655i	−0.0801253	+	0.0348935i
$211$	0.145338	−	0.251733i	0.0100055	−	0.0173300i	−0.860979	−	0.508640i	$-0.830148\pi$
$211$	0.145338	−	0.251733i	0.0100055	−	0.0173300i	0.870985	+	0.491310i	$0.163482\pi$
$212$	−5.54476	−	9.60380i	−0.380816	−	0.659592i
$213$	10.0063	−	13.5388i	0.685618	−	0.927660i
$214$	2.74191	+	3.04520i	0.187433	+	0.208166i
$215$	−8.50609	−	26.1790i	−0.580110	−	1.78540i
$216$	−3.15619	+	4.12776i	−0.214752	+	0.280859i
$217$	−1.51476	−	0.744777i	−0.102828	−	0.0505587i
$218$		−	2.99491i		−	0.202841i
$219$	−3.14761	−	4.40749i	−0.212695	−	0.297830i
$220$	7.36569	−	6.63209i	0.496594	−	0.447136i
$221$	−0.0607659	−	0.0836370i	−0.00408755	−	0.00562604i
$222$	−2.89746	+	3.16563i	−0.194465	+	0.212463i
$223$	−18.5103	−	10.6869i	−1.23954	−	0.715648i	−0.270539	−	0.962709i	$-0.587202\pi$
$223$	−18.5103	−	10.6869i	−1.23954	−	0.715648i	−0.969000	+	0.247061i	$0.920535\pi$
$224$	−0.301504	+	0.0316894i	−0.0201451	+	0.00211733i
$225$	−2.45063	−	0.0399933i	−0.163375	−	0.00266622i
$226$	1.55387	−	14.7841i	0.103362	−	0.983421i
$227$	6.92739	+	6.23745i	0.459787	+	0.413994i	0.866202	−	0.499695i	$-0.166554\pi$
$227$	6.92739	+	6.23745i	0.459787	+	0.413994i	−0.406414	+	0.913689i	$0.633221\pi$
$228$	1.48186	−	13.0721i	0.0981386	−	0.865720i
$229$	2.27535	−	10.7047i	0.150359	−	0.707385i	−0.836782	−	0.547536i	$-0.815566\pi$
$229$	2.27535	−	10.7047i	0.150359	−	0.707385i	0.987142	−	0.159849i	$-0.0511007\pi$
$230$	2.29777	−	0.488405i	0.151510	−	0.0322045i
$231$	1.43078	+	1.61536i	0.0941385	+	0.106283i
$232$	−3.49602	−	1.13592i	−0.229525	−	0.0745771i
$233$	−25.8696	−	8.40554i	−1.69477	−	0.550665i	−0.707088	−	0.707125i	$-0.749992\pi$
$233$	−25.8696	−	8.40554i	−1.69477	−	0.550665i	−0.987684	+	0.156460i	$0.949992\pi$
$234$	−1.32604	+	2.21259i	−0.0866861	+	0.144642i
$235$	−12.3887	+	2.63330i	−0.808150	+	0.171778i
$236$	−2.78960	+	13.1240i	−0.181588	+	0.854302i
$237$	25.8992	+	2.93595i	1.68233	+	0.190711i
$238$	0.0270879	+	0.0243900i	0.00175585	+	0.00158097i
$239$	−0.767125	+	7.29871i	−0.0496212	+	0.472114i	0.941290	+	0.337598i	$0.109615\pi$
$239$	−0.767125	+	7.29871i	−0.0496212	+	0.472114i	−0.990911	+	0.134516i	$0.957052\pi$
$240$	−3.96231	−	1.32327i	−0.255766	−	0.0854167i
$241$	6.69809	−	0.703998i	0.431462	−	0.0453485i	0.113691	−	0.993516i	$-0.463732\pi$
$241$	6.69809	−	0.703998i	0.431462	−	0.0453485i	0.317771	+	0.948168i	$0.397066\pi$
$242$	−5.09927	−	2.94406i	−0.327793	−	0.189252i
$243$	−7.23716	−	13.8066i	−0.464264	−	0.885697i
$244$	1.88335	+	2.59221i	0.120569	+	0.165950i
$245$	−12.3817	+	11.1485i	−0.791038	+	0.712254i
$246$	10.9549	−	7.82345i	0.698460	−	0.498805i
$247$		−	6.53093i		−	0.415553i
$248$	−2.06927	−	5.16896i	−0.131399	−	0.328229i
$249$	−2.14657	−	6.79459i	−0.136033	−	0.430590i
$250$	3.11760	+	9.59499i	0.197175	+	0.606841i
$251$	−17.6769	−	19.6322i	−1.11576	−	1.23918i	−0.968215	−	0.250120i	$-0.919530\pi$
$251$	−17.6769	−	19.6322i	−1.11576	−	1.23918i	−0.147544	−	0.989056i	$-0.547137\pi$
$252$	0.295126	−	0.860280i	0.0185912	−	0.0541925i
$253$	−2.00131	−	3.46636i	−0.125821	−	0.217928i
$254$	−7.98476	+	13.8300i	−0.501008	+	0.867772i
$255$	0.200539	+	0.460493i	0.0125582	+	0.0288372i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−14.5275	−	1.52691i	−0.906203	−	0.0952458i	−0.360052	−	0.932932i	$-0.617241\pi$
$257$	−14.5275	−	1.52691i	−0.906203	−	0.0952458i	−0.546151	+	0.837687i	$0.683908\pi$
$258$	17.9926	+	8.18738i	1.12017	+	0.509724i
$259$	0.305517	−	0.686203i	0.0189839	−	0.0426386i
$260$	−2.02848	−	0.431168i	−0.125801	−	0.0267399i
$261$	7.51177	−	8.07374i	0.464967	−	0.499752i
$262$	−13.0461	+	5.80849i	−0.805990	+	0.358850i
$263$	−5.37029	+	16.5281i	−0.331146	+	1.01916i	0.637443	+	0.770497i	$0.279992\pi$
$263$	−5.37029	+	16.5281i	−0.331146	+	1.01916i	−0.968589	+	0.248666i	$0.920008\pi$
$264$	−0.0580748	+	7.11766i	−0.00357426	+	0.438061i
$265$	10.8786	+	24.4338i	0.668270	+	1.50096i
$266$	0.478757	+	2.25237i	0.0293545	+	0.138102i
$267$	−0.275377	−	2.84299i	−0.0168528	−	0.173988i
$268$	−1.29305	−	0.575701i	−0.0789854	−	0.0351666i
$269$	−1.90640	+	2.11727i	−0.116235	+	0.129092i	−0.798454	−	0.602056i	$-0.794348\pi$
$269$	−1.90640	+	2.11727i	−0.116235	+	0.129092i	0.682219	+	0.731148i	$0.261015\pi$
$270$	8.61118	−	9.10529i	0.524060	−	0.554130i
$271$	13.1066	−	18.0397i	0.796171	−	1.09584i	−0.197141	−	0.980375i	$-0.563166\pi$
$271$	13.1066	−	18.0397i	0.796171	−	1.09584i	0.993312	−	0.115460i	$-0.0368342\pi$
$272$	0.0125677	+	0.119574i	0.000762031	+	0.00725024i
$273$	0.0974723	−	0.440853i	0.00589929	−	0.0266817i
$274$	−13.6218	+	7.86456i	−0.822924	+	0.475115i
$275$	−2.71620	+	1.97344i	−0.163793	+	0.119003i
$276$	−0.855388	+	1.45405i	−0.0514883	+	0.0875234i
$277$	8.91469	−	2.89656i	0.535632	−	0.174037i	−0.0286958	−	0.999588i	$-0.509135\pi$
$277$	8.91469	−	2.89656i	0.535632	−	0.174037i	0.564328	+	0.825551i	$0.309135\pi$
$278$	−12.4691			−0.747847
$279$	16.6786	+	0.908367i	0.998520	+	0.0543825i
$280$	0.731186			0.0436967
$281$	−9.28689	+	3.01749i	−0.554010	+	0.180009i	−0.572624	−	0.819818i	$-0.694075\pi$
$281$	−9.28689	+	3.01749i	−0.554010	+	0.180009i	0.0186144	+	0.999827i	$0.494075\pi$
$282$	4.61193	−	7.83968i	0.274637	−	0.466846i
$283$	1.69039	−	1.22814i	0.100484	−	0.0730055i	−0.536409	−	0.843958i	$-0.680220\pi$
$283$	1.69039	−	1.22814i	0.100484	−	0.0730055i	0.636892	+	0.770953i	$0.280220\pi$
$284$	−8.41759	+	4.85990i	−0.499492	+	0.288382i
$285$	−6.84999	+	30.9815i	−0.405758	+	1.83519i
$286$	0.369355	+	3.51418i	0.0218404	+	0.207798i
$287$	−1.38496	+	1.90623i	−0.0817514	+	0.112521i
$288$	2.62221	−	1.45741i	0.154515	−	0.0858785i
$289$	−11.3655	+	12.6227i	−0.668562	+	0.742513i
$290$	8.09928	+	3.60603i	0.475606	+	0.211753i
$291$	0.362840	+	3.74595i	0.0212700	+	0.219591i
$292$	0.650129	+	3.05861i	0.0380459	+	0.178992i
$293$	5.20792	+	11.6972i	0.304250	+	0.683356i	0.999368	−	0.0355389i	$-0.0113148\pi$
$293$	5.20792	+	11.6972i	0.304250	+	0.683356i	−0.695118	+	0.718895i	$0.744648\pi$
$294$	0.0976237	−	11.9648i	0.00569353	−	0.697799i
$295$	9.99987	−	30.7764i	0.582215	−	1.79187i
$296$	2.26346	−	1.00776i	0.131561	−	0.0585748i
$297$	−19.2891	−	9.16016i	−1.11927	−	0.531527i
$298$	20.6346	+	4.38602i	1.19533	+	0.254075i
$299$	−0.340631	+	0.765070i	−0.0196992	+	0.0442451i
$300$	1.28798	+	0.586085i	0.0743617	+	0.0338376i
$301$	−3.44106	−	0.361670i	−0.198339	−	0.0208463i
$302$	15.2616	+	11.0882i	0.878208	+	0.638056i
$303$	6.05737	+	13.9094i	0.347987	+	0.799074i
$304$	−3.79775	+	6.57790i	−0.217816	+	0.377269i
$305$	−3.86396	−	6.69257i	−0.221249	−	0.383215i
$306$	−0.341180	−	0.117045i	−0.0195040	−	0.00669100i
$307$	9.43495	+	10.4786i	0.538481	+	0.598044i	0.949571	−	0.313551i	$-0.101519\pi$
$307$	9.43495	+	10.4786i	0.538481	+	0.598044i	−0.411090	+	0.911595i	$0.634852\pi$
$308$	−0.384992	−	1.18488i	−0.0219370	−	0.0675151i
$309$	−4.72175	−	14.9459i	−0.268611	−	0.850242i
$310$	3.66029	+	12.9201i	0.207890	+	0.733812i
$311$		−	0.677244i		−	0.0384030i	−0.999816	−	0.0192015i	$-0.993888\pi$
$311$		−	0.677244i		−	0.0384030i	0.999816	−	0.0192015i	$-0.00611240\pi$
$312$	1.21196	−	0.865523i	0.0686139	−	0.0490006i
$313$	−13.6214	+	12.2648i	−0.769929	+	0.693247i	−0.957317	−	0.289039i	$-0.906664\pi$
$313$	−13.6214	+	12.2648i	−0.769929	+	0.693247i	0.187389	+	0.982286i	$0.439998\pi$
$314$	−6.25142	−	8.60434i	−0.352788	−	0.485571i
$315$	−0.924781	+	1.98909i	−0.0521055	+	0.112073i
$316$	−13.0325	−	7.52434i	−0.733138	−	0.423277i
$317$	15.7906	−	1.65966i	0.886889	−	0.0932158i	0.349882	−	0.936794i	$-0.386222\pi$
$317$	15.7906	−	1.65966i	0.886889	−	0.0932158i	0.537007	+	0.843578i	$0.319555\pi$
$318$	−18.2185	−	6.08432i	−1.02164	−	0.341192i
$319$	1.57904	−	15.0235i	0.0884091	−	0.841157i
$320$	1.79235	+	1.61384i	0.100195	+	0.0902163i
$321$	7.05229	+	0.799453i	0.393621	+	0.0446211i
$322$	0.0613918	−	0.288826i	0.00342123	−	0.0160956i
$323$	0.893272	−	0.189871i	0.0497030	−	0.0105647i
$324$	0.648189	+	8.97663i	0.0360105	+	0.498702i
$325$	0.668096	+	0.217077i	0.0370593	+	0.0120413i
$326$	−10.2643	−	3.33507i	−0.568486	−	0.184712i
$327$	−3.43944	−	3.88313i	−0.190201	−	0.214738i
$328$	−7.60226	+	1.61591i	−0.419765	+	0.0892237i
$329$	−0.331002	+	1.55724i	−0.0182487	+	0.0858535i
$330$	1.93371	−	17.0580i	0.106447	−	0.939011i
$331$	−3.34709	−	3.01373i	−0.183973	−	0.165650i	0.571998	−	0.820255i	$-0.306168\pi$
$331$	−3.34709	−	3.01373i	−0.183973	−	0.165650i	−0.755971	+	0.654605i	$0.772835\pi$
$332$	−0.430027	+	4.09143i	−0.0236008	+	0.224547i
$333$	−0.121288	+	7.43202i	−0.00664652	+	0.407272i
$334$	−18.7950	+	1.97543i	−1.02842	+	0.108091i
$335$	2.95640	+	1.70688i	0.161525	+	0.0932568i
$336$	−0.354531	+	0.387343i	−0.0193412	+	0.0211313i
$337$	−7.85141	−	10.8065i	−0.427694	−	0.588670i	0.539728	−	0.841839i	$-0.318527\pi$
$337$	−7.85141	−	10.8065i	−0.427694	−	0.588670i	−0.967422	+	0.253169i	$0.918527\pi$
$338$	−9.11146	+	8.20399i	−0.495598	+	0.446238i
$339$	−14.9637	−	20.9532i	−0.812718	−	1.13802i
$340$		−	0.289982i		−	0.0157265i
$341$	19.0097	−	12.7343i	1.02943	−	0.689602i
$342$	−13.0910	−	18.6508i	−0.707880	−	1.00852i
$343$	1.30295	+	4.01008i	0.0703529	+	0.216524i
$344$	−7.63676	−	8.48148i	−0.411747	−	0.457291i
$345$	2.41834	−	3.27207i	0.130199	−	0.176163i
$346$	−10.6277	−	18.4077i	−0.571348	−	0.989604i
$347$	−1.52237	+	2.63683i	−0.0817253	+	0.141552i	−0.903991	−	0.427551i	$-0.859376\pi$
$347$	−1.52237	+	2.63683i	−0.0817253	+	0.141552i	0.822266	+	0.569104i	$0.192710\pi$
$348$	−5.83738	+	2.54211i	−0.312917	+	0.136271i
$349$	2.16241	+	1.57108i	0.115751	+	0.0840981i	0.644155	−	0.764895i	$-0.277209\pi$
$349$	2.16241	+	1.57108i	0.115751	+	0.0840981i	−0.528404	+	0.848993i	$0.677209\pi$
$350$	−0.246324	−	0.0258897i	−0.0131666	−	0.00138386i
$351$	0.821683	+	4.39166i	0.0438582	+	0.234409i
$352$	1.67149	−	3.75423i	0.0890908	−	0.200101i
$353$	−15.9127	−	3.38234i	−0.846946	−	0.180024i	−0.236056	−	0.971740i	$-0.575855\pi$
$353$	−15.9127	−	3.38234i	−0.846946	−	0.180024i	−0.610890	+	0.791716i	$0.709188\pi$
$354$	11.4551	+	20.2200i	0.608830	+	1.07468i
$355$	21.4159	−	9.53497i	1.13664	−	0.506064i
$356$	−0.509595	+	1.56837i	−0.0270085	+	0.0831235i
$357$	0.0631317		0.000515109i	0.00334129		2.72624e-5i
$358$	−0.599757	−	1.34708i	−0.0316981	−	0.0711952i
$359$	7.81891	+	36.7851i	0.412666	+	1.94144i	0.326642	+	0.945148i	$0.394083\pi$
$359$	7.81891	+	36.7851i	0.412666	+	1.94144i	0.0860242	+	0.996293i	$0.472584\pi$
$360$	−6.65713	+	2.83470i	−0.350861	+	0.149402i
$361$	35.3467	+	15.7374i	1.86035	+	0.828282i
$362$	6.27057	−	6.96417i	0.329574	−	0.366029i
$363$	−9.99264	+	2.03893i	−0.524478	+	0.107016i
$364$	−0.153220	+	0.210890i	−0.00803092	+	0.0110536i
$365$	−0.788322	−	7.50039i	−0.0412627	−	0.392588i
$366$	5.41889	+	1.19811i	0.283250	+	0.0626263i
$367$	16.5583	−	9.55992i	0.864334	−	0.499024i	−0.00112720	−	0.999999i	$-0.500359\pi$
$367$	16.5583	−	9.55992i	0.864334	−	0.499024i	0.865461	+	0.500976i	$0.167025\pi$
$368$	0.787971	−	0.572494i	0.0410758	−	0.0298433i
$369$	5.21923	−	22.7246i	0.271702	−	1.18300i
$370$	−5.68327	+	1.84661i	−0.295459	+	0.0960006i
$371$	3.36195			0.174544
$372$	−8.61914	−	4.32555i	−0.446882	−	0.224269i
$373$	5.27595			0.273178			0.136589	−	0.990628i	$-0.456386\pi$
$373$	5.27595			0.273178			0.136589	+	0.990628i	$0.456386\pi$
$374$	−0.469915	+	0.152685i	−0.0242988	+	0.00789514i
$375$	15.0614	+	8.86032i	0.777766	+	0.457545i
$376$	−4.24845	+	3.08668i	−0.219097	+	0.159183i
$377$	−2.73726	+	1.58036i	−0.140976	+	0.0813926i
$378$	−0.605315	−	1.45435i	−0.0311340	−	0.0748037i
$379$	2.12350	+	20.2037i	0.109077	+	1.03779i	0.902960	+	0.429725i	$0.141389\pi$
$379$	2.12350	+	20.2037i	0.109077	+	1.03779i	−0.793883	+	0.608070i	$0.791944\pi$
$380$	10.7677	−	14.8205i	0.552373	−	0.760277i
$381$	5.52990	+	27.1016i	0.283305	+	1.38846i
$382$	12.9936	−	14.4308i	0.664809	−	0.738345i
$383$	−26.1814	−	11.6567i	−1.33781	−	0.595629i	−0.391881	−	0.920016i	$-0.628175\pi$
$383$	−26.1814	−	11.6567i	−1.33781	−	0.595629i	−0.945925	+	0.324387i	$0.894842\pi$
$384$	−1.72398	+	0.166988i	−0.0879766	+	0.00852158i
$385$	0.624738	+	2.93916i	0.0318396	+	0.149793i
$386$	−8.60218	−	19.3208i	−0.437840	−	0.983404i
$387$	32.7314	−	10.0476i	1.66383	−	0.510750i
$388$	0.671447	−	2.06650i	0.0340875	−	0.104911i
$389$	15.9320	−	7.09337i	0.807783	−	0.359648i	0.0390654	−	0.999237i	$-0.487562\pi$
$389$	15.9320	−	7.09337i	0.807783	−	0.359648i	0.768717	+	0.639589i	$0.220895\pi$
$390$	−3.12525	+	1.77053i	−0.158253	+	0.0896540i
$391$	−0.114546	−	0.0243475i	−0.00579284	−	0.00123131i
$392$	−2.80977	+	6.31086i	−0.141915	+	0.318746i
$393$	−10.2446	+	22.5136i	−0.516773	+	1.13566i
$394$	5.53787	+	0.582054i	0.278994	+	0.0293234i
$395$	29.3633	+	21.3337i	1.47743	+	1.07341i
$396$	8.09881	+	9.29529i	0.406981	+	0.467106i
$397$	−2.45723	+	4.25605i	−0.123325	+	0.213605i	−0.921077	−	0.389381i	$-0.872689\pi$
$397$	−2.45723	+	4.25605i	−0.123325	+	0.213605i	0.797752	+	0.602986i	$0.206022\pi$
$398$	2.86119	+	4.95573i	0.143419	+	0.248408i
$399$	3.20743	+	2.37056i	0.160572	+	0.118676i
$400$	−0.546670	−	0.607138i	−0.0273335	−	0.0303569i
$401$	−2.28296	−	7.02623i	−0.114006	−	0.350873i	0.877733	−	0.479150i	$-0.159055\pi$
$401$	−2.28296	−	7.02623i	−0.114006	−	0.350873i	−0.991738	+	0.128278i	$0.959055\pi$
$402$	−2.33769	+	0.738529i	−0.116593	+	0.0368345i
$403$	−4.49344	−	1.65170i	−0.223834	−	0.0822772i
$404$		−	8.75905i		−	0.435779i
$405$	0.708298	−	21.6950i	0.0351956	−	1.07803i
$406$	0.828170	−	0.745688i	0.0411014	−	0.0370079i
$407$	5.98484	+	8.23743i	0.296658	+	0.408314i
$408$	0.153617	+	0.140604i	0.00760519	+	0.00696093i
$409$	−17.3470	−	10.0153i	−0.857753	−	0.495224i	0.00550617	−	0.999985i	$-0.498247\pi$
$409$	−17.3470	−	10.0153i	−0.857753	−	0.495224i	−0.863259	+	0.504761i	$0.831581\pi$
$410$	18.6424	−	1.95939i	0.920682	−	0.0967676i
$411$	−8.62986	+	25.8407i	−0.425680	+	1.27463i
$412$	−0.945919	+	8.99982i	−0.0466021	+	0.443389i
$413$	−3.02284	−	2.72178i	−0.148744	−	0.133930i
$414$	0.560791	+	2.86764i	0.0275614	+	0.140937i
$415$	2.06295	−	9.70543i	0.101266	−	0.476421i
$416$	−0.841052	+	0.178771i	−0.0412360	+	0.00876497i
$417$	−16.1672	+	14.3199i	−0.791709	+	0.701247i
$418$	−29.6862	−	9.64562i	−1.45200	−	0.471783i
$419$	21.3768	+	6.94574i	1.04432	+	0.339321i	0.780438	−	0.625233i	$-0.214996\pi$
$419$	21.3768	+	6.94574i	1.04432	+	0.339321i	0.263885	+	0.964554i	$0.414996\pi$
$420$	0.948040	−	0.839714i	0.0462596	−	0.0409739i
$421$	−16.3119	+	3.46720i	−0.794993	+	0.168981i	−0.587467	−	0.809248i	$-0.699875\pi$
$421$	−16.3119	+	3.46720i	−0.794993	+	0.168981i	−0.207527	+	0.978229i	$0.566541\pi$
$422$	−0.0604350	+	0.284324i	−0.00294193	+	0.0138407i
$423$	−3.02358	−	15.4612i	−0.147011	−	0.751751i
$424$	8.24112	+	7.42034i	0.400224	+	0.360363i
$425$	−0.0102677	+	0.0976902i	−0.000498054	+	0.00473867i
$426$	−5.33282	+	15.9682i	−0.258376	+	0.773663i
$427$	−0.966066	+	0.101538i	−0.0467512	+	0.00491375i
$428$	−3.54873	−	2.04886i	−0.171534	−	0.0990354i
$429$	4.51467	+	4.13223i	0.217971	+	0.199506i
$430$	16.1795	+	22.2692i	0.780247	+	1.07392i
$431$	16.2412	−	14.6236i	0.782309	−	0.704394i	−0.177786	−	0.984069i	$-0.556893\pi$
$431$	16.2412	−	14.6236i	0.782309	−	0.704394i	0.960095	+	0.279675i	$0.0902268\pi$
$432$	1.72617	−	4.90106i	0.0830503	−	0.235802i
$433$		−	1.19640i		−	0.0574954i	−0.999587	−	0.0287477i	$-0.990848\pi$
$433$		−	1.19640i		−	0.0574954i	0.999587	−	0.0287477i	$-0.00915194\pi$
$434$	1.67077	+	0.240239i	0.0801994	+	0.0115319i
$435$	14.6426	−	4.62593i	0.702059	−	0.221797i
$436$	0.925478	+	2.84833i	0.0443223	+	0.136410i
$437$	−4.95017	−	5.49772i	−0.236799	−	0.262992i
$438$	4.35554	+	3.21911i	0.208116	+	0.153815i
$439$	15.0444	+	26.0577i	0.718030	+	1.24366i	0.961779	+	0.273826i	$0.0882891\pi$
$439$	15.0444	+	26.0577i	0.718030	+	1.24366i	−0.243750	+	0.969838i	$0.578378\pi$
$440$	−4.95575	+	8.58362i	−0.236256	+	0.409208i
$441$	−13.6141	−	15.6254i	−0.648290	−	0.744065i
$442$	0.0836370	+	0.0607659i	0.00397821	+	0.00289034i
$443$	1.95090	+	0.205048i	0.0926900	+	0.00974211i	0.150760	−	0.988570i	$-0.451828\pi$
$443$	1.95090	+	0.205048i	0.0926900	+	0.00974211i	−0.0580699	+	0.998313i	$0.518495\pi$
$444$	1.77742	−	3.90606i	0.0843525	−	0.185373i
$445$	1.61772	−	3.63347i	0.0766875	−	0.172243i
$446$	20.9067	+	4.44386i	0.989963	+	0.210423i
$447$	31.7914	−	18.0105i	1.50368	−	0.851868i
$448$	0.276955	−	0.123308i	0.0130849	−	0.00582577i
$449$	0.499839	−	1.53835i	0.0235889	−	0.0725990i	−0.938569	−	0.345091i	$-0.887848\pi$
$449$	0.499839	−	1.53835i	0.0235889	−	0.0725990i	0.962158	+	0.272492i	$0.0878479\pi$
$450$	2.34304	−	0.719250i	0.110452	−	0.0339058i
$451$	−12.9910	−	29.1783i	−0.611722	−	1.37395i
$452$	3.09071	+	14.5407i	0.145375	+	0.683935i
$453$	32.5219	−	3.15013i	1.52801	−	0.148006i
$454$	−8.51582	−	3.79149i	−0.399667	−	0.177943i
$455$	0.420685	−	0.467218i	0.0197220	−	0.0219035i
$456$	2.63016	+	12.8902i	0.123169	+	0.603639i
$457$	−20.5321	+	28.2600i	−0.960452	+	1.32195i	−0.0137275	+	0.999906i	$0.504370\pi$
$457$	−20.5321	+	28.2600i	−0.960452	+	1.32195i	−0.946725	+	0.322044i	$0.895630\pi$
$458$	1.14394	+	10.8839i	0.0534528	+	0.508570i
$459$	−0.576784	+	0.240063i	−0.0269219	+	0.0112052i
$460$	−2.03438	+	1.17455i	−0.0948535	+	0.0547637i
$461$	−16.8982	+	12.2773i	−0.787029	+	0.571810i	−0.907080	−	0.420958i	$-0.861694\pi$
$461$	−16.8982	+	12.2773i	−0.787029	+	0.571810i	0.120052	+	0.992768i	$0.461694\pi$
$462$	−1.85993	−	1.09416i	−0.0865316	−	0.0509049i
$463$	0.681116	−	0.221308i	0.0316541	−	0.0102851i	−0.293147	−	0.956067i	$-0.594703\pi$
$463$	0.681116	−	0.221308i	0.0316541	−	0.0102851i	0.324801	+	0.945782i	$0.394703\pi$
$464$	3.67593			0.170651
$465$	19.5836	+	12.5483i	0.908170	+	0.581915i
$466$	27.2009			1.26006
$467$	−28.7101	+	9.32847i	−1.32854	+	0.431670i	−0.885421	−	0.464791i	$-0.846130\pi$
$467$	−28.7101	+	9.32847i	−1.32854	+	0.431670i	−0.443123	+	0.896461i	$0.646130\pi$
$468$	0.577413	−	2.51407i	0.0266909	−	0.116213i
$469$	0.347153	−	0.252221i	0.0160300	−	0.0116465i
$470$	10.9686	−	6.33274i	0.505945	−	0.292107i
$471$	−17.9869	−	3.97689i	−0.828793	−	0.183245i
$472$	−1.40248	−	13.3437i	−0.0645545	−	0.614195i
$473$	27.5682	−	37.9443i	1.26759	−	1.74468i
$474$	−25.5389	+	5.21104i	−1.17304	+	0.239351i
$475$	−4.15223	+	4.61152i	−0.190518	+	0.211591i
$476$	−0.0332990	−	0.0148257i	−0.00152626	−	0.000679534i
$477$	−30.6091	+	13.0338i	−1.40149	+	0.596777i
$478$	−1.52585	−	7.17854i	−0.0697905	−	0.328339i
$479$	−2.36496	−	5.31180i	−0.108058	−	0.242702i	0.851421	−	0.524483i	$-0.175741\pi$
$479$	−2.36496	−	5.31180i	−0.108058	−	0.242702i	−0.959479	+	0.281781i	$0.909075\pi$
$480$	4.17729	+	0.0340837i	0.190667	+	0.00155570i
$481$	0.658331	−	2.02613i	0.0300173	−	0.0923837i
$482$	−6.15272	+	2.73937i	−0.280249	+	0.124775i
$483$	−0.252096	−	0.444989i	−0.0114708	−	0.0202477i
$484$	5.75946	+	1.22421i	0.261794	+	0.0556459i
$485$	−2.13153	+	4.78749i	−0.0967878	+	0.217389i
$486$	11.1494	+	10.8945i	0.505749	+	0.494184i
$487$	15.1685	+	1.59427i	0.687348	+	0.0722432i	0.441763	−	0.897132i	$-0.354353\pi$
$487$	15.1685	+	1.59427i	0.687348	+	0.0722432i	0.245585	+	0.969375i	$0.421020\pi$
$488$	−2.59221	−	1.88335i	−0.117344	−	0.0852554i
$489$	−17.1385	+	7.46361i	−0.775030	+	0.337516i
$490$	8.33061	−	14.4290i	0.376339	−	0.651838i
$491$	1.82423	+	3.15966i	0.0823264	+	0.142593i	0.904249	−	0.427006i	$-0.140432\pi$
$491$	1.82423	+	3.15966i	0.0823264	+	0.142593i	−0.821922	+	0.569599i	$0.807098\pi$
$492$	−8.00117	+	10.8258i	−0.360720	+	0.488065i
$493$	−0.295734	−	0.328445i	−0.0133192	−	0.0147924i
$494$	2.01817	+	6.21129i	0.0908017	+	0.279459i
$495$	−17.0827	−	24.3377i	−0.767808	−	1.09390i
$496$	3.56529	+	4.27653i	0.160086	+	0.192022i
$497$		−	2.94670i		−	0.132178i
$498$	4.14115	+	5.79872i	0.185569	+	0.259847i
$499$	−15.8472	+	14.2689i	−0.709417	+	0.638762i	−0.942698	−	0.333647i	$-0.891721\pi$
$499$	−15.8472	+	14.2689i	−0.709417	+	0.638762i	0.233281	+	0.972409i	$0.425054\pi$
$500$	−5.93003	−	8.16199i	−0.265199	−	0.365015i
$501$	−22.1005	+	24.1460i	−0.987379	+	1.07876i
$502$	22.8785	+	13.2089i	1.02112	+	0.589541i
$503$	27.7652	−	2.91824i	1.23799	−	0.130118i	0.537181	−	0.843467i	$-0.319489\pi$
$503$	27.7652	−	2.91824i	1.23799	−	0.130118i	0.700809	+	0.713349i	$0.252823\pi$
$504$	−0.0148406	+	0.909374i	−0.000661054	+	0.0405067i
$505$	−2.20821	+	21.0097i	−0.0982641	+	0.934920i
$506$	2.97452	+	2.67827i	0.132234	+	0.119064i
$507$	−2.39202	+	21.1010i	−0.106233	+	0.937127i
$508$	3.32025	−	15.6205i	0.147312	−	0.693049i
$509$	−8.22359	+	1.74798i	−0.364504	+	0.0774778i	−0.386523	−	0.922280i	$-0.626324\pi$
$509$	−8.22359	+	1.74798i	−0.364504	+	0.0774778i	0.0220186	+	0.999758i	$0.492991\pi$
$510$	−0.333024	−	0.375985i	−0.0147465	−	0.0166489i
$511$	−0.901583	−	0.292942i	−0.0398837	−	0.0129590i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−38.3926	−	9.14813i	−1.69507	−	0.403900i
$514$	14.2884	−	3.03708i	0.630232	−	0.133960i
$515$	4.53782	−	21.3488i	0.199960	−	0.940739i
$516$	−19.6420	−	2.22663i	−0.864692	−	0.0980221i
$517$	−16.0375	−	14.4402i	−0.705328	−	0.635080i
$518$	−0.0785158	+	0.747028i	−0.00344978	+	0.0328225i
$519$	−34.9195	−	11.6619i	−1.53280	−	0.511900i
$520$	2.06244	−	0.216771i	0.0904441	−	0.00950605i
$521$	−17.4940	−	10.1001i	−0.766424	−	0.442495i	0.0651734	−	0.997874i	$-0.479240\pi$
$521$	−17.4940	−	10.1001i	−0.766424	−	0.442495i	−0.831598	+	0.555379i	$0.812573\pi$
$522$	−4.64920	+	9.99985i	−0.203490	+	0.437682i
$523$	18.3203	+	25.2157i	0.801089	+	1.10261i	0.992638	+	0.121122i	$0.0386492\pi$
$523$	18.3203	+	25.2157i	0.801089	+	1.10261i	−0.191548	+	0.981483i	$0.561351\pi$
$524$	10.6126	−	9.55567i	0.463615	−	0.417441i
$525$	−0.349111	+	0.249318i	−0.0152365	+	0.0108811i
$526$		−	17.3786i		−	0.757744i
$527$	0.0952769	−	0.662613i	0.00415033	−	0.0288639i
$528$	−2.14424	−	6.78724i	−0.0933162	−	0.295377i
$529$	−6.81424	−	20.9721i	−0.296271	−	0.911830i
$530$	−17.8967	−	19.8763i	−0.777382	−	0.863370i
$531$	38.0736	+	13.0615i	1.65225	+	0.566819i
$532$	−1.15135	−	1.99419i	−0.0499172	−	0.0864591i
$533$	−3.34139	+	5.78745i	−0.144732	+	0.250682i
$534$	1.14043	+	2.61875i	0.0493513	+	0.113324i
$535$	7.99556	+	5.80912i	0.345678	+	0.251150i
$536$	1.40766	+	0.147951i	0.0608017	+	0.00639052i
$537$	−2.32465	−	1.05781i	−0.100316	−	0.0456479i
$538$	1.15882	−	2.60275i	0.0499602	−	0.112213i
$539$	−27.7686	−	5.90239i	−1.19608	−	0.254234i
$540$	−5.37603	+	11.3206i	−0.231347	+	0.487163i
$541$	8.27729	−	3.68529i	0.355868	−	0.158443i	−0.221013	−	0.975271i	$-0.570936\pi$
$541$	8.27729	−	3.68529i	0.355868	−	0.158443i	0.576881	+	0.816828i	$0.304270\pi$
$542$	−6.89056	+	21.2070i	−0.295975	+	0.910917i
$543$	0.132432	−	16.2309i	0.00568321	−	0.696534i
$544$	−0.0489031	−	0.109838i	−0.00209670	−	0.00470927i
$545$	−1.50180	−	7.06540i	−0.0643299	−	0.302649i
$546$	0.0435294	+	0.449397i	0.00186289	+	0.0192324i
$547$	−27.6058	−	12.2909i	−1.18034	−	0.525520i	−0.279699	−	0.960088i	$-0.590235\pi$
$547$	−27.6058	−	12.2909i	−1.18034	−	0.525520i	−0.900639	+	0.434567i	$0.856901\pi$
$548$	10.5248	−	11.6890i	0.449598	−	0.499330i
$549$	8.40195	−	4.66975i	0.358587	−	0.199300i
$550$	1.97344	−	2.71620i	0.0841477	−	0.115819i
$551$	−2.91849	−	27.7676i	−0.124332	−	1.18294i
$552$	0.364197	−	1.64721i	0.0155013	−	0.0701100i
$553$	3.95101	−	2.28112i	0.168014	−	0.0970029i
$554$	−7.58329	+	5.50958i	−0.322183	+	0.234080i
$555$	−5.24811	+	8.92110i	−0.222770	+	0.378680i
$556$	11.8588	−	3.85316i	0.502926	−	0.163411i
$557$	15.6257			0.662083			0.331042	−	0.943616i	$-0.392600\pi$
$557$	15.6257			0.662083			0.331042	+	0.943616i	$0.392600\pi$
$558$	−16.1430	+	4.29006i	−0.683386	+	0.181613i
$559$	−9.81334			−0.415060
$560$	−0.695399	+	0.225949i	−0.0293860	+	0.00954809i
$561$	−0.433935	+	0.737632i	−0.0183207	+	0.0311428i
$562$	7.89990	−	5.73962i	0.333237	−	0.242111i
$563$	−7.97824	+	4.60624i	−0.336243	+	0.194130i	−0.658609	−	0.752485i	$-0.728855\pi$
$563$	−7.97824	+	4.60624i	−0.336243	+	0.194130i	0.322366	+	0.946615i	$0.395522\pi$
$564$	−1.96362	+	8.88115i	−0.0826831	+	0.373964i
$565$	−3.74768	−	35.6568i	−0.157666	−	1.50009i
$566$	−1.22814	+	1.69039i	−0.0516227	+	0.0710526i
$567$	−2.45505	−	1.19052i	−0.103103	−	0.0499971i
$568$	6.50381	−	7.22322i	0.272894	−	0.303079i
$569$	25.6627	+	11.4257i	1.07583	+	0.478992i	0.866667	−	0.498888i	$-0.166258\pi$
$569$	25.6627	+	11.4257i	1.07583	+	0.478992i	0.209168	+	0.977880i	$0.432925\pi$
$570$	−3.05909	−	31.5819i	−0.128131	−	1.32282i
$571$	−0.282296	−	1.32810i	−0.0118137	−	0.0555793i	0.971846	−	0.235617i	$-0.0757112\pi$
$571$	−0.282296	−	1.32810i	−0.0118137	−	0.0555793i	−0.983660	+	0.180038i	$0.942378\pi$
$572$	−1.43722	−	3.22804i	−0.0600931	−	0.134971i
$573$	0.274419	−	33.6329i	0.0114640	−	1.40503i
$574$	0.728115	−	2.24091i	0.0303909	−	0.0935336i
$575$	0.726937	−	0.323653i	0.0303154	−	0.0134973i
$576$	−2.04350	+	2.19638i	−0.0851460	+	0.0915159i
$577$	−31.7388	−	6.74629i	−1.32130	−	0.280852i	−0.507329	−	0.861752i	$-0.669367\pi$
$577$	−31.7388	−	6.74629i	−1.32130	−	0.280852i	−0.813974	+	0.580901i	$0.802700\pi$
$578$	6.90864	−	15.5171i	0.287362	−	0.645425i
$579$	−33.3420	−	15.1720i	−1.38564	−	0.630525i
$580$	−8.81719	−	0.926724i	−0.366114	−	0.0384801i
$581$	−1.00902	−	0.733093i	−0.0418610	−	0.0304138i
$582$	−1.50264	−	3.45049i	−0.0622866	−	0.143027i
$583$	−22.7863	+	39.4670i	−0.943711	+	1.63456i
$584$	−1.56347	−	2.70801i	−0.0646970	−	0.112058i
$585$	−2.01881	+	5.88475i	−0.0834677	+	0.243305i
$586$	−8.56765	−	9.51534i	−0.353926	−	0.393075i
$587$	−5.81480	−	17.8961i	−0.240003	−	0.738652i	−0.996418	−	0.0845608i	$-0.973051\pi$
$587$	−5.81480	−	17.8961i	−0.240003	−	0.738652i	0.756416	−	0.654091i	$-0.226949\pi$
$588$	3.60447	+	11.4093i	0.148646	+	0.470513i
$589$	29.4738	−	30.3272i	1.21445	−	1.24961i
$590$			32.3603i			1.33225i
$591$	7.84872	−	5.60516i	0.322853	−	0.230566i
$592$	−1.84127	+	1.65788i	−0.0756756	+	0.0681386i
$593$	12.2991	+	16.9282i	0.505062	+	0.695159i	0.983077	−	0.183193i	$-0.0586434\pi$
$593$	12.2991	+	16.9282i	0.505062	+	0.695159i	−0.478014	+	0.878352i	$0.658643\pi$
$594$	21.1757	+	2.75116i	0.868850	+	0.112882i
$595$	0.0761345	+	0.0439562i	0.00312121	+	0.00180203i
$596$	−20.9800	+	2.20509i	−0.859375	+	0.0903239i
$597$	9.40106	+	3.13962i	0.384760	+	0.128496i
$598$	0.0875398	−	0.832886i	0.00357977	−	0.0340592i
$599$	−5.17907	−	4.66326i	−0.211611	−	0.190536i	0.556508	−	0.830842i	$-0.312141\pi$
$599$	−5.17907	−	4.66326i	−0.211611	−	0.190536i	−0.768120	+	0.640306i	$0.778807\pi$
$600$	−1.40605	−	0.159391i	−0.0574019	−	0.00650712i
$601$	−8.59495	+	40.4360i	−0.350595	+	1.64942i	0.350654	+	0.936505i	$0.385959\pi$
$601$	−8.59495	+	40.4360i	−0.350595	+	1.64942i	−0.701250	+	0.712916i	$0.747374\pi$
$602$	3.38440	−	0.719377i	0.137938	−	0.0293196i
$603$	−2.18285	+	3.64222i	−0.0888923	+	0.148323i
$604$	−17.9411	−	5.82943i	−0.730014	−	0.237196i
$605$	−13.5062	−	4.38842i	−0.549104	−	0.178415i
$606$	−10.0591	−	11.3568i	−0.408624	−	0.461338i
$607$	−37.2280	+	7.91305i	−1.51104	+	0.321181i	−0.887571	−	0.460671i	$-0.847609\pi$
$607$	−37.2280	+	7.91305i	−1.51104	+	0.321181i	−0.623465	+	0.781851i	$0.714276\pi$
$608$	1.57920	−	7.42953i	0.0640448	−	0.301307i
$609$	0.217419	−	1.91794i	0.00881024	−	0.0777187i
$610$	5.74296	+	5.17098i	0.232526	+	0.209367i
$611$	−0.471982	+	4.49061i	−0.0190943	+	0.181671i
$612$	0.360650	+	0.00588567i	0.0145784	+	0.000237914i
$613$	−27.9110	+	2.93356i	−1.12731	+	0.118485i	−0.649776	−	0.760126i	$-0.725137\pi$
$613$	−27.9110	+	2.93356i	−1.12731	+	0.118485i	−0.477538	+	0.878611i	$0.658471\pi$
$614$	−12.2112	−	7.05016i	−0.492805	−	0.284521i
$615$	21.9211	−	23.9499i	0.883944	−	0.965755i
$616$	0.732299	+	1.00792i	0.0295052	+	0.0406104i
$617$	−13.5388	+	12.1904i	−0.545051	+	0.490767i	−0.895039	−	0.445988i	$-0.852852\pi$
$617$	−13.5388	+	12.1904i	−0.545051	+	0.490767i	0.349988	+	0.936754i	$0.386186\pi$
$618$	9.10918	+	12.7553i	0.366425	+	0.513093i
$619$			9.89872i			0.397863i	0.980013	+	0.198932i	$0.0637472\pi$
$619$			9.89872i			0.397863i	−0.980013	+	0.198932i	$0.936253\pi$
$620$	−7.47367	−	11.1566i	−0.300150	−	0.448062i
$621$	4.02038	+	3.07409i	0.161332	+	0.123359i
$622$	0.209280	+	0.644097i	0.00839136	+	0.0258260i
$623$	−0.334528	−	0.371531i	−0.0134026	−	0.0148851i
$624$	−0.885183	+	1.19768i	−0.0354357	+	0.0479455i
$625$	14.2087	+	24.6102i	0.568349	+	0.984410i
$626$	9.16472	−	15.8738i	0.366296	−	0.634443i
$627$	−49.5677	+	21.5861i	−1.97954	+	0.862066i
$628$	8.60434	+	6.25142i	0.343350	+	0.249459i
$629$	0.296265	+	0.0311387i	0.0118129	+	0.00124158i
$630$	0.264856	−	2.17751i	0.0105521	−	0.0867541i
$631$	−6.38349	+	14.3376i	−0.254123	+	0.570769i	−0.994887	−	0.100996i	$-0.967797\pi$
$631$	−6.38349	+	14.3376i	−0.254123	+	0.570769i	0.740764	+	0.671765i	$0.234464\pi$
$632$	14.7198	+	3.12880i	0.585524	+	0.124457i
$633$	0.248167	+	0.438054i	0.00986376	+	0.0174111i
$634$	−14.5049	+	6.45800i	−0.576063	+	0.256480i
$635$	−11.9021	+	36.6308i	−0.472320	+	1.45365i
$636$	19.2070	+	0.156715i	0.761606	+	0.00621414i
$637$	2.41596	+	5.42633i	0.0957238	+	0.214999i
$638$	3.14077	+	14.7762i	0.124344	+	0.584995i
$639$	11.4239	+	26.8284i	0.451924	+	1.06132i
$640$	−2.20333	−	0.980985i	−0.0870942	−	0.0387768i
$641$	26.0981	−	28.9849i	1.03081	−	1.14483i	0.0414834	−	0.999139i	$-0.486792\pi$
$641$	26.0981	−	28.9849i	1.03081	−	1.14483i	0.989330	−	0.145695i	$-0.0465417\pi$
$642$	−6.95417	+	1.41895i	−0.274459	+	0.0560016i
$643$	10.4949	−	14.4449i	0.413877	−	0.569653i	−0.550282	−	0.834979i	$-0.685480\pi$
$643$	10.4949	−	14.4449i	0.413877	−	0.569653i	0.964159	+	0.265326i	$0.0854797\pi$
$644$	0.0308650	+	0.293661i	0.00121625	+	0.0115719i
$645$	46.5526	+	10.2928i	1.83301	+	0.405277i
$646$	−0.790879	+	0.456614i	−0.0311167	+	0.0179653i
$647$	−2.92824	+	2.12749i	−0.115121	+	0.0836402i	−0.643856	−	0.765147i	$-0.722666\pi$
$647$	−2.92824	+	2.12749i	−0.115121	+	0.0836402i	0.528735	+	0.848787i	$0.322666\pi$
$648$	−3.39040	−	8.33698i	−0.133187	−	0.327507i
$649$	52.4397	−	17.0387i	2.05844	−	0.668827i
$650$	−0.702477			−0.0275534
$651$	2.44218	−	1.60727i	0.0957165	−	0.0629937i
$652$	10.7925			0.422667
$653$	26.0262	−	8.45641i	1.01848	−	0.330925i	0.248255	−	0.968695i	$-0.420143\pi$
$653$	26.0262	−	8.45641i	1.01848	−	0.330925i	0.770227	+	0.637770i	$0.220143\pi$
$654$	4.47105	+	2.63023i	0.174832	+	0.102850i
$655$	−27.8648	+	20.2450i	−1.08877	+	0.791037i
$656$	6.73084	−	3.88605i	0.262795	−	0.151725i
$657$	9.34421	−	0.828201i	0.364552	−	0.0323112i
$658$	−0.166412	−	1.58331i	−0.00648743	−	0.0617238i
$659$	−7.26900	+	10.0049i	−0.283160	+	0.389737i	−0.926777	−	0.375611i	$-0.877433\pi$
$659$	−7.26900	+	10.0049i	−0.283160	+	0.389737i	0.643617	+	0.765348i	$0.277433\pi$
$660$	3.43214	+	16.8207i	0.133596	+	0.654743i
$661$	4.88937	−	5.43019i	0.190174	−	0.211210i	−0.640516	−	0.767945i	$-0.721279\pi$
$661$	4.88937	−	5.43019i	0.190174	−	0.211210i	0.830690	+	0.556735i	$0.187946\pi$
$662$	4.11457	+	1.83192i	0.159917	+	0.0711997i
$663$	0.178227	−	0.0172634i	0.00692177	−	0.000670456i
$664$	−0.855343	−	4.02407i	−0.0331937	−	0.156164i
$665$	2.25891	+	5.07359i	0.0875966	+	0.196745i
$666$	−2.18127	−	7.10575i	−0.0845224	−	0.275342i
$667$	−1.10637	+	3.40507i	−0.0428390	+	0.131845i
$668$	17.2647	−	7.68672i	0.667990	−	0.297408i
$669$	32.2107	−	18.2481i	1.24534	−	0.705511i
$670$	−3.33916	−	0.709760i	−0.129003	−	0.0274204i
$671$	5.35571	−	12.0291i	0.206755	−	0.464379i
$672$	0.217483	−	0.477942i	0.00838959	−	0.0184370i
$673$	24.2281	+	2.54647i	0.933924	+	0.0981594i	0.559252	−	0.828998i	$-0.311089\pi$
$673$	24.2281	+	2.54647i	0.933924	+	0.0981594i	0.374672	+	0.927157i	$0.377755\pi$
$674$	10.8065	+	7.85141i	0.416252	+	0.302425i
$675$	2.21193	−	3.62338i	0.0851373	−	0.139464i
$676$	6.13034	−	10.6181i	0.235782	−	0.408387i
$677$	9.27463	+	16.0641i	0.356453	+	0.617395i	0.987366	−	0.158459i	$-0.0506526\pi$
$677$	9.27463	+	16.0641i	0.356453	+	0.617395i	−0.630912	+	0.775854i	$0.717319\pi$
$678$	20.7062	+	15.3036i	0.795218	+	0.587732i
$679$	0.440777	+	0.489533i	0.0169155	+	0.0187865i
$680$	0.0896095	+	0.275790i	0.00343637	+	0.0105760i
$681$	−15.3957	+	4.86385i	−0.589964	+	0.186383i
$682$	−14.1442	+	17.9854i	−0.541609	+	0.688696i
$683$			10.9042i			0.417238i	0.977997	+	0.208619i	$0.0668969\pi$
$683$			10.9042i			0.417238i	−0.977997	+	0.208619i	$0.933103\pi$
$684$	18.2137	+	13.6926i	0.696418	+	0.523550i
$685$	−28.1920	+	25.3842i	−1.07716	+	0.969882i
$686$	−2.47836	−	3.41118i	−0.0946244	−	0.130239i
$687$	13.9825	+	12.7980i	0.533467	+	0.488276i
$688$	9.88392	+	5.70648i	0.376821	+	0.217558i
$689$	9.48299	−	0.996703i	0.361273	−	0.0379713i
$690$	−1.28885	+	3.85923i	−0.0490656	+	0.146919i
$691$	1.31068	−	12.4703i	0.0498605	−	0.474391i	−0.940892	−	0.338707i	$-0.890010\pi$
$691$	1.31068	−	12.4703i	0.0498605	−	0.474391i	0.990752	−	0.135683i	$-0.0433230\pi$
$692$	15.7958	+	14.2226i	0.600467	+	0.540663i
$693$	−3.66810	+	0.717329i	−0.139340	+	0.0272491i
$694$	0.633039	−	2.97821i	0.0240298	−	0.113051i
$695$	−29.4163	+	6.25264i	−1.11583	+	0.237176i
$696$	4.76613	−	4.22154i	0.180660	−	0.160017i
$697$	−0.888725	−	0.288764i	−0.0336629	−	0.0109377i
$698$	−2.54206	−	0.825967i	−0.0962186	−	0.0312633i
$699$	35.2681	−	31.2383i	1.33396	−	1.18154i
$700$	0.242269	−	0.0514958i	0.00915690	−	0.00194636i
$701$	−0.398322	+	1.87396i	−0.0150444	+	0.0707784i	−0.985029	−	0.172386i	$-0.944852\pi$
$701$	−0.398322	+	1.87396i	−0.0150444	+	0.0707784i	0.969985	+	0.243165i	$0.0781856\pi$
$702$	−2.13856	−	3.92280i	−0.0807149	−	0.148057i
$703$	13.9854	+	12.5925i	0.527468	+	0.474934i
$704$	−0.429561	+	4.08700i	−0.0161897	+	0.154035i
$705$	6.94898	−	20.8075i	0.261714	−	0.783658i
$706$	16.1790	−	1.70049i	0.608906	−	0.0639986i
$707$	2.29968	+	1.32772i	0.0864882	+	0.0499340i
$708$	−17.1427	−	15.6905i	−0.644264	−	0.589687i
$709$	−25.1863	−	34.6660i	−0.945891	−	1.30191i	−0.953328	−	0.301935i	$-0.902367\pi$
$709$	−25.1863	−	34.6660i	−0.945891	−	1.30191i	0.00743720	−	0.999972i	$-0.497633\pi$
$710$	−17.4213	+	15.6862i	−0.653808	+	0.588692i
$711$	−27.1286	+	36.0861i	−1.01740	+	1.35333i
$712$		−	1.64908i		−	0.0618020i
$713$	−5.03449	+	2.01544i	−0.188543	+	0.0754788i
$714$	−0.0602010	+	0.0190189i	−0.00225297	+	0.000711764i
$715$	2.63354	+	8.10521i	0.0984889	+	0.303118i
$716$	0.986672	+	1.09581i	0.0368737	+	0.0409523i
$717$	−10.2224	−	7.55521i	−0.381763	−	0.282154i
$718$	−18.8034	−	32.5685i	−0.701738	−	1.21545i
$719$	20.9330	−	36.2569i	0.780668	−	1.35216i	−0.150886	−	0.988551i	$-0.548213\pi$
$719$	20.9330	−	36.2569i	0.780668	−	1.35216i	0.931553	−	0.363605i	$-0.118454\pi$
$720$	5.45533	−	4.75313i	0.203308	−	0.177139i
$721$	−2.21950	−	1.61256i	−0.0826586	−	0.0600550i
$722$	−38.4798	−	4.04439i	−1.43207	−	0.150517i
$723$	−4.83151	+	10.6177i	−0.179686	+	0.394878i
$724$	−3.81162	+	8.56104i	−0.141658	+	0.318168i
$725$	2.93755	+	0.624396i	0.109098	+	0.0231895i
$726$	8.87350	−	5.02704i	0.329327	−	0.186571i
$727$	1.23330	−	0.549102i	0.0457407	−	0.0203651i	−0.383739	−	0.923442i	$-0.625364\pi$
$727$	1.23330	−	0.549102i	0.0457407	−	0.0203651i	0.429479	+	0.903077i	$0.358697\pi$
$728$	0.0805526	−	0.247916i	0.00298548	−	0.00918836i
$729$	26.9677	+	1.32124i	0.998802	+	0.0489350i
$730$	3.06749	+	6.88969i	0.113533	+	0.254999i
$731$	−0.285299	−	1.34223i	−0.0105522	−	0.0496440i
$732$	−5.52390	+	0.535056i	−0.204169	+	0.0197762i
$733$	15.0626	+	6.70632i	0.556351	+	0.247704i	0.665597	−	0.746311i	$-0.268177\pi$
$733$	15.0626	+	6.70632i	0.556351	+	0.247704i	−0.109246	+	0.994015i	$0.534844\pi$
$734$	−12.7937	+	14.2088i	−0.472223	+	0.524456i
$735$	−5.76943	−	28.2755i	−0.212809	−	1.04296i
$736$	−0.572494	+	0.787971i	−0.0211024	+	0.0290450i
$737$	0.608008	+	5.78481i	0.0223963	+	0.213086i
$738$	2.05851	+	23.2253i	0.0757750	+	0.854933i
$739$	−21.3749	+	12.3408i	−0.786288	+	0.453964i	−0.838654	−	0.544664i	$-0.816657\pi$
$739$	−21.3749	+	12.3408i	−0.786288	+	0.453964i	0.0523659	+	0.998628i	$0.483324\pi$
$740$	4.83448	−	3.51246i	0.177719	−	0.129120i
$741$	9.74993	+	5.73570i	0.358173	+	0.210706i
$742$	−3.19741	+	1.03890i	−0.117381	+	0.0381392i
$743$	37.0361			1.35872			0.679360	−	0.733805i	$-0.262257\pi$
$743$	37.0361			1.35872			0.679360	+	0.733805i	$0.262257\pi$
$744$	9.53396	+	1.45038i	0.349532	+	0.0531734i
$745$	50.8792			1.86407
$746$	−5.01772	+	1.63036i	−0.183712	+	0.0596916i
$747$	12.0287	+	2.76267i	0.440108	+	0.101081i
$748$	0.399734	−	0.290424i	0.0146157	−	0.0106189i
$749$	1.07585	−	0.621143i	0.0393107	−	0.0226961i
$750$	−17.0622	−	3.77244i	−0.623024	−	0.137750i
$751$	−1.81270	−	17.2467i	−0.0661465	−	0.629342i	−0.976501	−	0.215513i	$-0.930858\pi$
$751$	−1.81270	−	17.2467i	−0.0661465	−	0.629342i	0.910354	−	0.413829i	$-0.135809\pi$
$752$	3.08668	−	4.24845i	0.112559	−	0.154925i
$753$	44.8332	−	9.14791i	1.63381	−	0.333368i
$754$	2.11493	−	2.34887i	0.0770213	−	0.0855408i
$755$	41.5645	+	18.5057i	1.51269	+	0.673492i
$756$	1.02511	+	1.19612i	0.0372828	+	0.0435024i
$757$	−9.19145	−	43.2424i	−0.334069	−	1.57167i	−0.749473	−	0.662034i	$-0.769693\pi$
$757$	−9.19145	−	43.2424i	−0.334069	−	1.57167i	0.415404	−	0.909637i	$-0.363640\pi$
$758$	−8.26285	−	18.5587i	−0.300120	−	0.674081i
$759$	6.93249	+	0.0565641i	0.251634	+	0.00205315i
$760$	−5.66094	+	17.4226i	−0.205344	+	0.631983i
$761$	−26.5671	+	11.8284i	−0.963057	+	0.428781i	−0.827175	−	0.561944i	$-0.810054\pi$
$761$	−26.5671	+	11.8284i	−0.963057	+	0.428781i	−0.135882	+	0.990725i	$0.543387\pi$
$762$	−13.6341	−	24.0663i	−0.493911	−	0.871830i
$763$	−0.888110	−	0.188774i	−0.0321518	−	0.00683407i
$764$	−7.89825	+	17.7398i	−0.285749	+	0.641802i
$765$	−0.863582	−	0.105040i	−0.0312229	−	0.00379772i
$766$	28.5021	+	2.99569i	1.02982	+	0.108239i
$767$	−9.33338	−	6.78110i	−0.337009	−	0.244851i
$768$	1.58800	−	0.691555i	0.0573021	−	0.0249543i
$769$	−3.47340	+	6.01611i	−0.125254	+	0.216946i	−0.921832	−	0.387589i	$-0.873308\pi$
$769$	−3.47340	+	6.01611i	−0.125254	+	0.216946i	0.796578	+	0.604536i	$0.206641\pi$
$770$	−1.50241	−	2.60225i	−0.0541431	−	0.0937787i
$771$	15.0381	−	20.3470i	0.541584	−	0.732778i
$772$	14.1516	+	15.7170i	0.509328	+	0.565666i
$773$	15.9073	+	48.9578i	0.572147	+	1.76089i	0.645693	+	0.763597i	$0.276569\pi$
$773$	15.9073	+	48.9578i	0.572147	+	1.76089i	−0.0735457	+	0.997292i	$0.523431\pi$
$774$	−28.0245	+	19.6704i	−1.00732	+	0.707040i
$775$	2.12272	+	4.02311i	0.0762504	+	0.144515i
$776$			2.17285i			0.0780007i
$777$	0.756105	+	1.05875i	0.0271251	+	0.0379824i
$778$	−12.9602	+	11.6694i	−0.464647	+	0.418370i
$779$	−34.6988	−	47.7587i	−1.24321	−	1.71113i
$780$	2.42517	−	2.64963i	0.0868350	−	0.0948718i
$781$	34.5922	+	19.9718i	1.23781	+	0.714648i
$782$	0.116463	−	0.0122408i	0.00416472	−	0.000437730i
$783$	5.45606	+	18.3049i	0.194984	+	0.654162i
$784$	0.722092	−	6.87025i	0.0257890	−	0.245366i
$785$	−19.0626	−	17.1640i	−0.680373	−	0.612611i
$786$	2.78612	−	24.5775i	0.0993778	−	0.876651i
$787$	−2.98928	+	14.0634i	−0.106556	+	0.501307i	0.892209	+	0.451623i	$0.149155\pi$
$787$	−2.98928	+	14.0634i	−0.106556	+	0.501307i	−0.998765	+	0.0496843i	$0.984178\pi$
$788$	−5.44669	+	1.15773i	−0.194030	+	0.0412424i
$789$	−19.9581	−	22.5327i	−0.710527	−	0.802187i
$790$	−34.5186	−	11.2158i	−1.22812	−	0.399040i
$791$	−4.28612	−	1.39265i	−0.152397	−	0.0495168i
$792$	−10.5748	−	6.33767i	−0.375760	−	0.225199i
$793$	−2.69486	+	0.572810i	−0.0956972	+	0.0203411i
$794$	1.02178	−	4.80708i	0.0362615	−	0.170597i
$795$	−46.0309	−	5.21810i	−1.63255	−	0.185067i
$796$	−4.25256	−	3.82902i	−0.150728	−	0.135716i
$797$	−2.91410	+	27.7258i	−0.103223	+	0.982099i	0.813226	+	0.581948i	$0.197709\pi$
$797$	−2.91410	+	27.7258i	−0.103223	+	0.982099i	−0.916449	+	0.400151i	$0.868958\pi$
$798$	−3.78299	−	1.26338i	−0.133916	−	0.0447233i
$799$	−0.627927	+	0.0659978i	−0.0222145	+	0.00233483i
$800$	0.707530	+	0.408492i	0.0250149	+	0.0144424i
$801$	4.48610	+	2.08571i	0.158509	+	0.0736948i
$802$	4.34245	+	5.97686i	0.153337	+	0.211050i
$803$	9.54959	−	8.59849i	0.336998	−	0.303434i
$804$	1.99505	−	1.42477i	0.0703601	−	0.0502477i
$805$		−	0.712165i		−	0.0251005i
$806$	4.78392	+	0.182313i	0.168506	+	0.00642171i
$807$	−1.48657	−	4.70549i	−0.0523298	−	0.165641i
$808$	2.70670	+	8.33035i	0.0952212	+	0.293061i
$809$	1.33535	+	1.48305i	0.0469483	+	0.0521414i	0.766162	−	0.642648i	$-0.222164\pi$
$809$	1.33535	+	1.48305i	0.0469483	+	0.0521414i	−0.719213	+	0.694789i	$0.755498\pi$
$810$	6.03050	+	20.8521i	0.211890	+	0.732667i
$811$	18.8692	+	32.6824i	0.662588	+	1.14764i	0.979933	+	0.199325i	$0.0638751\pi$
$811$	18.8692	+	32.6824i	0.662588	+	1.14764i	−0.317346	+	0.948310i	$0.602792\pi$
$812$	−0.557206	+	0.965110i	−0.0195541	+	0.0338687i
$813$	15.4205	+	35.4098i	0.540821	+	1.24188i
$814$	−8.23743	−	5.98484i	−0.288722	−	0.209769i
$815$	−25.8872	−	2.72086i	−0.906790	−	0.0953074i
$816$	−0.189548	−	0.0862520i	−0.00663550	−	0.00301942i
$817$	35.2589	−	79.1928i	1.23355	−	2.77060i
$818$	19.5929	+	4.16459i	0.685048	+	0.145611i
$819$	0.572539	+	0.532688i	0.0200061	+	0.0186136i
$820$	−17.1245	+	7.62431i	−0.598013	+	0.266253i
$821$	6.83930	−	21.0492i	0.238693	−	0.734622i	−0.757917	−	0.652351i	$-0.773783\pi$
$821$	6.83930	−	21.0492i	0.238693	−	0.734622i	0.996610	−	0.0822708i	$-0.0262172\pi$
$822$	0.222281	−	27.2427i	0.00775292	−	0.950199i
$823$	5.39239	+	12.1115i	0.187967	+	0.422181i	0.982806	−	0.184639i	$-0.0591116\pi$
$823$	5.39239	+	12.1115i	0.187967	+	0.422181i	−0.794839	+	0.606820i	$0.792445\pi$
$824$	−1.88147	−	8.85164i	−0.0655442	−	0.308361i
$825$	−0.560648	−	5.78812i	−0.0195193	−	0.201516i
$826$	3.71597	+	1.65446i	0.129295	+	0.0575659i
$827$	7.11844	−	7.90583i	0.247532	−	0.274913i	−0.606556	−	0.795041i	$-0.707449\pi$
$827$	7.11844	−	7.90583i	0.247532	−	0.274913i	0.854088	+	0.520128i	$0.174116\pi$
$828$	−1.41949	−	2.55399i	−0.0493308	−	0.0887574i
$829$	10.9231	−	15.0344i	0.379376	−	0.522166i	−0.576043	−	0.817419i	$-0.695404\pi$
$829$	10.9231	−	15.0344i	0.379376	−	0.522166i	0.955419	+	0.295253i	$0.0954039\pi$
$830$	1.03716	+	9.86790i	0.0360003	+	0.342520i
$831$	−3.50497	+	15.8525i	−0.121586	+	0.549916i
$832$	0.744645	−	0.429921i	0.0258159	−	0.0149048i
$833$	−0.671952	+	0.488202i	−0.0232818	+	0.0169152i
$834$	10.9508	−	18.6149i	0.379195	−	0.644582i
$835$	−43.3494	+	14.0851i	−1.50017	+	0.487434i
$836$	31.2139			1.07955
$837$	−16.0038	+	24.1014i	−0.553172	+	0.833067i
$838$	−22.4769			−0.776451
$839$	−21.3756	+	6.94537i	−0.737969	+	0.239781i	−0.653796	−	0.756670i	$-0.726825\pi$
$839$	−21.3756	+	6.94537i	−0.737969	+	0.239781i	−0.0841727	+	0.996451i	$0.526825\pi$
$840$	−0.642153	+	1.09158i	−0.0221564	+	0.0376630i
$841$	12.5297	−	9.10335i	0.432058	−	0.313909i
$842$	14.4421	−	8.33816i	0.497708	−	0.287352i
$843$	3.65131	−	16.5143i	0.125758	−	0.568784i
$844$	−0.0303839	−	0.289084i	−0.00104586	−	0.00995068i
$845$	−17.3813	+	23.9233i	−0.597934	+	0.822986i
$846$	7.65338	+	13.7702i	0.263128	+	0.473428i
$847$	−1.19445	+	1.32657i	−0.0410417	+	0.0455814i
$848$	−10.1308	−	4.51051i	−0.347892	−	0.154892i
$849$	0.348912	+	3.60216i	0.0119746	+	0.123626i
$850$	−0.0204228	−	0.0960818i	−0.000700497	−	0.00329558i
$851$	−0.981543	−	2.20458i	−0.0336469	−	0.0755721i
$852$	0.137358	−	16.8346i	0.00470581	−	0.576745i
$853$	10.3901	−	31.9775i	0.355751	−	1.09489i	−0.599821	−	0.800134i	$-0.704762\pi$
$853$	10.3901	−	31.9775i	0.355751	−	1.09489i	0.955573	−	0.294756i	$-0.0952384\pi$
$854$	0.887406	−	0.395099i	0.0303664	−	0.0135200i
$855$	−40.2359	−	37.4353i	−1.37604	−	1.28026i
$856$	4.00818	+	0.851964i	0.136997	+	0.0291195i
$857$	−17.7793	+	39.9329i	−0.607328	+	1.36408i	0.304107	+	0.952638i	$0.401642\pi$
$857$	−17.7793	+	39.9329i	−0.607328	+	1.36408i	−0.911435	+	0.411444i	$0.865025\pi$
$858$	−5.57064	−	2.53487i	−0.190178	−	0.0865390i
$859$	23.2767	+	2.44648i	0.794191	+	0.0834728i	0.492930	−	0.870069i	$-0.335926\pi$
$859$	23.2767	+	2.44648i	0.794191	+	0.0834728i	0.301261	+	0.953542i	$0.402592\pi$
$860$	−22.2692	−	16.1795i	−0.759374	−	0.551718i
$861$	−1.62946	−	3.74170i	−0.0555319	−	0.127517i
$862$	−10.9273	+	18.9267i	−0.372186	+	0.644645i
$863$	7.55736	+	13.0897i	0.257256	+	0.445580i	0.965506	−	0.260382i	$-0.0838484\pi$
$863$	7.55736	+	13.0897i	0.257256	+	0.445580i	−0.708250	+	0.705962i	$0.750515\pi$
$864$	−0.127175	+	5.19460i	−0.00432658	+	0.176724i
$865$	−34.3027	−	38.0971i	−1.16633	−	1.29534i
$866$	0.369708	+	1.13785i	0.0125632	+	0.0386656i
$867$	−8.86264	−	28.0532i	−0.300991	−	0.952735i
$868$	−1.66323	+	0.287814i	−0.0564538	+	0.00976906i
$869$			61.8428i			2.09787i
$870$	−12.4965	+	8.92434i	−0.423669	+	0.302563i
$871$	0.904432	−	0.814354i	0.0306455	−	0.0275933i
$872$	−1.76036	−	2.42293i	−0.0596134	−	0.0820508i
$873$	−5.91093	−	2.74815i	−0.200055	−	0.0930107i
$874$	6.40679	+	3.69896i	0.216713	+	0.125119i
$875$	3.04181	−	0.319707i	0.102832	−	0.0108081i
$876$	−5.13712	−	1.71562i	−0.173567	−	0.0579653i
$877$	−0.854351	+	8.12860i	−0.0288494	+	0.274483i	0.970582	+	0.240770i	$0.0774000\pi$
$877$	−0.854351	+	8.12860i	−0.0288494	+	0.274483i	−0.999432	+	0.0337133i	$0.989267\pi$
$878$	−22.3603	−	20.1333i	−0.754624	−	0.679467i
$879$	−22.0363	−	2.49805i	−0.743266	−	0.0842572i
$880$	2.06072	−	9.69492i	0.0694668	−	0.326816i
$881$	−33.2788	+	7.07362i	−1.12119	+	0.238316i	−0.730973	−	0.682407i	$-0.760933\pi$
$881$	−33.2788	+	7.07362i	−1.12119	+	0.238316i	−0.390217	+	0.920723i	$0.627600\pi$
$882$	17.7763	+	10.6536i	0.598558	+	0.358726i
$883$	53.5571	+	17.4017i	1.80234	+	0.585615i	0.999938	−	0.0111693i	$-0.00355537\pi$
$883$	53.5571	+	17.4017i	1.80234	+	0.585615i	0.802401	+	0.596785i	$0.203555\pi$
$884$	−0.0983212	−	0.0319465i	−0.00330690	−	0.00107448i
$885$	37.1634	+	41.9576i	1.24923	+	1.41039i
$886$	−1.91878	+	0.407849i	−0.0644626	+	0.0137019i
$887$	−7.22918	+	34.0106i	−0.242732	+	1.14196i	0.672833	+	0.739795i	$0.265077\pi$
$887$	−7.22918	+	34.0106i	−0.242732	+	1.14196i	−0.915565	+	0.402170i	$0.868256\pi$
$888$	−0.483386	+	4.26414i	−0.0162214	+	0.143095i
$889$	3.59786	+	3.23953i	0.120668	+	0.108650i
$890$	−0.415744	+	3.95554i	−0.0139358	+	0.132590i
$891$	30.6155	−	20.7517i	1.02566	−	0.695207i
$892$	−21.2567	+	2.23417i	−0.711727	+	0.0748056i
$893$	−34.5430	−	19.9434i	−1.15594	−	0.667381i
$894$	−24.6698	+	26.9531i	−0.825083	+	0.901446i
$895$	−2.09040	−	2.87719i	−0.0698744	−	0.0961738i
$896$	−0.225295	+	0.202857i	−0.00752659	+	0.00677698i
$897$	−0.843007	−	1.18043i	−0.0281472	−	0.0394135i
$898$			1.61751i			0.0539771i
$899$	−19.8429	−	5.01456i	−0.661797	−	0.167245i
$900$	−2.00611	+	1.40809i	−0.0668702	+	0.0469363i
$901$	0.412019	+	1.26807i	0.0137264	+	0.0422454i
$902$	21.3717	+	23.7357i	0.711601	+	0.790313i
$903$	3.56199	−	4.81947i	0.118536	−	0.160382i
$904$	−7.43275	−	12.8739i	−0.247210	−	0.428180i
$905$	11.3010	−	19.5738i	0.375656	−	0.650656i
$906$	−29.9567	+	13.0458i	−0.995246	+	0.433417i
$907$	−3.46106	−	2.51461i	−0.114923	−	0.0834962i	0.528839	−	0.848722i	$-0.322627\pi$
$907$	−3.46106	−	2.51461i	−0.114923	−	0.0834962i	−0.643762	+	0.765226i	$0.722627\pi$
$908$	9.27066	+	0.974386i	0.307658	+	0.0323361i
$909$	−26.0849	−	3.17277i	−0.865182	−	0.105234i
$910$	−0.255717	+	0.574350i	−0.00847694	+	0.0190395i
$911$	35.3490	+	7.51367i	1.17117	+	0.248939i	0.752120	−	0.659026i	$-0.229031\pi$
$911$	35.3490	+	7.51367i	1.17117	+	0.248939i	0.419045	+	0.907965i	$0.362365\pi$
$912$	−6.48473	−	11.4466i	−0.214731	−	0.379033i
$913$	15.4448	−	6.87647i	0.511148	−	0.227578i
$914$	10.7944	−	33.2217i	0.357046	−	1.09888i
$915$	13.3847	+	0.109209i	0.442484	+	0.00361035i
$916$	−4.45125	−	9.99768i	−0.147074	−	0.330333i
$917$	0.900136	+	4.23481i	0.0297251	+	0.139846i
$918$	0.474370	−	0.406549i	0.0156565	−	0.0134181i
$919$	30.2512	+	13.4687i	0.997895	+	0.444292i	0.839662	−	0.543110i	$-0.182753\pi$
$919$	30.2512	+	13.4687i	0.997895	+	0.444292i	0.158234	+	0.987402i	$0.449420\pi$
$920$	1.57185	−	1.74572i	0.0518225	−	0.0575547i
$921$	−23.9294	+	4.88264i	−0.788501	+	0.160888i
$922$	12.2773	−	16.8982i	0.404331	−	0.556513i
$923$	−0.873595	−	8.31170i	−0.0287547	−	0.273583i
$924$	2.10701	+	0.465858i	0.0693155	+	0.0153256i
$925$	−1.75302	+	1.01211i	−0.0576391	+	0.0332779i
$926$	−0.579392	+	0.420953i	−0.0190400	+	0.0138334i
$927$	26.4593	+	6.07698i	0.869037	+	0.199594i
$928$	−3.49602	+	1.13592i	−0.114762	+	0.0372885i
$929$	23.1798			0.760504			0.380252	−	0.924883i	$-0.375837\pi$
$929$	23.1798			0.760504			0.380252	+	0.924883i	$0.375837\pi$
$930$	−22.5028	−	5.88249i	−0.737896	−	0.192894i
$931$	−52.4705			−1.71965
$932$	−25.8696	+	8.40554i	−0.847386	+	0.275333i
$933$	1.01105	+	0.594779i	0.0331002	+	0.0194722i
$934$	24.4222	−	17.7438i	0.799120	−	0.580595i
$935$	−1.03203	+	0.595844i	−0.0337510	+	0.0194862i
$936$	0.227737	+	2.56945i	0.00744382	+	0.0839852i
$937$	0.729566	+	6.94136i	0.0238339	+	0.226764i	0.999955	+	0.00953523i	$0.00303520\pi$
$937$	0.729566	+	6.94136i	0.0238339	+	0.226764i	−0.976121	+	0.217229i	$0.930298\pi$
$938$	−0.252221	+	0.347153i	−0.00823531	+	0.0113349i
$939$	−6.34709	−	31.1066i	−0.207130	−	1.01513i
$940$	−8.47485	+	9.41228i	−0.276419	+	0.306995i
$941$	−27.7977	−	12.3763i	−0.906179	−	0.403457i	−0.0999035	−	0.994997i	$-0.531853\pi$
$941$	−27.7977	−	12.3763i	−0.906179	−	0.403457i	−0.806275	+	0.591540i	$0.798520\pi$
$942$	18.3355	−	1.77601i	0.597402	−	0.0578655i
$943$	1.57387	+	7.40449i	0.0512524	+	0.241123i
$944$	5.45728	+	12.2573i	0.177619	+	0.398940i
$945$	−2.15731	−	3.12748i	−0.0701772	−	0.101737i
$946$	−14.4934	+	44.6062i	−0.471222	+	1.45027i
$947$	−28.2980	+	12.5991i	−0.919560	+	0.409415i	−0.811248	−	0.584702i	$-0.801211\pi$
$947$	−28.2980	+	12.5991i	−0.919560	+	0.409415i	−0.108312	+	0.994117i	$0.534545\pi$
$948$	22.6786	−	12.8479i	0.736567	−	0.417282i
$949$	−2.62992	−	0.559007i	−0.0853709	−	0.0181461i
$950$	2.52397	−	5.66893i	0.0818884	−	0.183924i
$951$	−11.3902	+	25.0311i	−0.369352	+	0.811690i
$952$	0.0362507	+	0.00381010i	0.00117489	+	0.000123486i
$953$	−36.3037	−	26.3762i	−1.17599	−	0.854408i	−0.184278	−	0.982874i	$-0.558995\pi$
$953$	−36.3037	−	26.3762i	−1.17599	−	0.854408i	−0.991714	+	0.128467i	$0.958995\pi$
$954$	25.0833	−	21.8546i	0.812102	−	0.707570i
$955$	23.4173	−	40.5599i	0.757766	−	1.31249i
$956$	3.66946	+	6.35568i	0.118679	+	0.205557i
$957$	21.0416	+	15.5515i	0.680179	+	0.502709i
$958$	3.89065	+	4.32101i	0.125701	+	0.139605i
$959$	1.47355	+	4.53513i	0.0475835	+	0.146447i
$960$	−3.98338	+	1.25844i	−0.128563	+	0.0406160i
$961$	−13.4118	−	27.9486i	−0.432638	−	0.901568i
$962$			2.13040i			0.0686869i
$963$	−7.38706	+	9.82615i	−0.238045	+	0.316643i
$964$	5.00507	−	4.50659i	0.161202	−	0.145147i
$965$	−29.9822	−	41.2669i	−0.965160	−	1.32843i
$966$	0.377267	+	0.345308i	0.0121384	+	0.0111101i
$967$	2.45663	+	1.41834i	0.0789999	+	0.0456106i	0.538980	−	0.842319i	$-0.318810\pi$
$967$	2.45663	+	1.41834i	0.0789999	+	0.0456106i	−0.459980	+	0.887929i	$0.652143\pi$
$968$	−5.85587	+	0.615477i	−0.188215	+	0.0197822i
$969$	−0.501048	+	1.50030i	−0.0160960	+	0.0481967i
$970$	0.547788	−	5.21186i	0.0175884	−	0.167343i
$971$	−17.2278	−	15.5120i	−0.552868	−	0.497805i	0.344681	−	0.938720i	$-0.387987\pi$
$971$	−17.2278	−	15.5120i	−0.552868	−	0.497805i	−0.897549	+	0.440915i	$0.854654\pi$
$972$	−13.9703	−	6.91592i	−0.448098	−	0.221828i
$973$	−0.785947	+	3.69759i	−0.0251963	+	0.118539i
$974$	−14.9187	+	3.17107i	−0.478027	+	0.101608i
$975$	−0.910817	+	0.806744i	−0.0291695	+	0.0258365i
$976$	3.04733	+	0.990138i	0.0975427	+	0.0316935i
$977$	−14.9465	−	4.85641i	−0.478180	−	0.155370i	0.0600026	−	0.998198i	$-0.480889\pi$
$977$	−14.9465	−	4.85641i	−0.478180	−	0.155370i	−0.538183	+	0.842828i	$0.680889\pi$
$978$	13.9933	−	12.3944i	0.447457	−	0.396329i
$979$	6.62884	−	1.40900i	0.211859	−	0.0450319i
$980$	−3.46406	+	16.2971i	−0.110655	+	0.520593i
$981$	8.81770	−	1.72438i	0.281527	−	0.0550551i
$982$	−2.71133	−	2.44130i	−0.0865222	−	0.0779049i
$983$	−0.752504	+	7.15959i	−0.0240011	+	0.228356i	0.975945	+	0.218015i	$0.0699582\pi$
$983$	−0.752504	+	7.15959i	−0.0240011	+	0.228356i	−0.999947	+	0.0103405i	$0.996708\pi$
$984$	4.26420	−	12.7684i	0.135938	−	0.407043i
$985$	13.3565	−	1.40382i	0.425572	−	0.0447295i
$986$	0.382755	+	0.220983i	0.0121894	+	0.00703755i
$987$	−2.03408	−	1.86177i	−0.0647456	−	0.0592608i
$988$	−3.83879	−	5.28364i	−0.122128	−	0.168095i
$989$	−8.26085	+	7.43810i	−0.262680	+	0.236518i
$990$	23.7673	+	17.8677i	0.755376	+	0.567873i
$991$			29.2105i			0.927902i	0.885861	+	0.463951i	$0.153569\pi$
$991$			29.2105i			0.927902i	−0.885861	+	0.463951i	$0.846431\pi$
$992$	−4.71231	−	2.96549i	−0.149616	−	0.0941543i
$993$	7.43869	−	2.35005i	0.236060	−	0.0745766i
$994$	0.910581	+	2.80248i	0.0288819	+	0.0888892i
$995$	9.23500	+	10.2565i	0.292769	+	0.325153i
$996$	−5.73037	−	4.23522i	−0.181574	−	0.134198i
$997$	−4.41284	−	7.64326i	−0.139756	−	0.242064i	0.787648	−	0.616125i	$-0.211298\pi$
$997$	−4.41284	−	7.64326i	−0.139756	−	0.242064i	−0.927404	+	0.374061i	$0.877965\pi$
$998$	10.6622	−	18.4675i	0.337507	−	0.584580i
$999$	−10.9886	−	6.70813i	−0.347665	−	0.212236i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.2	✓	80	1.1	even	1	trivial
186.2.p.a.11.6	yes	80	3.2	odd	2	inner
186.2.p.a.17.2	yes	80	93.17	even	30	inner
186.2.p.a.17.6	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.878235 + 1.49288i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.08872 + 1.20592i) q^{5} +(0.373925 - 1.69121i) q^{6} +(0.0316894 + 0.301504i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.45741 - 2.62221i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-0.878235 + 1.49288i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.08872 + 1.20592i) q^{5} +(0.373925 - 1.69121i) q^{6} +(0.0316894 + 0.301504i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.45741 - 2.62221i) q^{9} +(1.61384 - 1.79235i) q^{10} +(-3.75423 - 1.67149i) q^{11} +(0.166988 + 1.72398i) q^{12} +(0.178771 + 0.841052i) q^{13} +(-0.123308 - 0.276955i) q^{14} +(0.0340837 - 4.17729i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.109838 + 0.0489031i) q^{17} +(2.19638 + 2.04350i) q^{18} +(-7.42953 - 1.57920i) q^{19} +(-0.980985 + 2.20333i) q^{20} +(-0.477942 - 0.217483i) q^{21} +(4.08700 + 0.429561i) q^{22} +(0.787971 + 0.572494i) q^{23} +(-0.691555 - 1.58800i) q^{24} +(0.408492 - 0.707530i) q^{25} +(-0.429921 - 0.744645i) q^{26} +(5.19460 + 0.127175i) q^{27} +(0.202857 + 0.225295i) q^{28} +(1.13592 + 3.49602i) q^{29} +(1.25844 + 3.98338i) q^{30} +(-2.96549 + 4.71231i) q^{31} +1.00000i q^{32} +(5.79244 - 4.13667i) q^{33} +(0.0893503 - 0.0804514i) q^{34} +(-0.429780 - 0.591542i) q^{35} +(-2.72036 - 1.26477i) q^{36} +(-2.14572 - 1.23883i) q^{37} +(7.55390 - 0.793947i) q^{38} +(-1.41260 - 0.471757i) q^{39} +(0.252106 - 2.39863i) q^{40} +(5.77580 + 5.20055i) q^{41} +(0.521755 + 0.0591466i) q^{42} +(-2.37289 + 11.1636i) q^{43} +(-4.01971 + 0.854417i) q^{44} +(6.20628 + 3.71953i) q^{45} +(-0.926316 - 0.300978i) q^{46} +(4.99435 + 1.62276i) q^{47} +(1.14843 + 1.29658i) q^{48} +(6.75713 - 1.43627i) q^{49} +(-0.169861 + 0.799132i) q^{50} +(0.0234570 - 0.206924i) q^{51} +(0.638987 + 0.575346i) q^{52} +(1.15917 - 11.0288i) q^{53} +(-4.97965 + 1.48427i) q^{54} +(9.85721 - 1.03603i) q^{55} +(-0.262549 - 0.151582i) q^{56} +(8.88243 - 9.70452i) q^{57} +(-2.16066 - 2.97389i) q^{58} +(-9.97095 + 8.97788i) q^{59} +(-2.42778 - 3.39954i) q^{60} +3.20415i q^{61} +(1.36416 - 5.39806i) q^{62} +(0.744422 - 0.522510i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.38764 - 1.54114i) q^{65} +(-4.23064 + 5.72417i) q^{66} +(-0.707708 - 1.22579i) q^{67} +(-0.0601164 + 0.104125i) q^{68} +(-1.54669 + 0.673565i) q^{69} +(0.591542 + 0.429780i) q^{70} +(-9.66655 - 1.01600i) q^{71} +(2.97805 + 0.362228i) q^{72} +(-1.27184 + 2.85661i) q^{73} +(2.42353 + 0.515136i) q^{74} +(0.697507 + 1.23121i) q^{75} +(-6.93884 + 3.08937i) q^{76} +(0.384992 - 1.18488i) q^{77} +(1.48924 + 0.0121511i) q^{78} +(-6.12085 - 13.7477i) q^{79} +(0.501450 + 2.35914i) q^{80} +(-4.75193 + 7.64324i) q^{81} +(-7.10017 - 3.16120i) q^{82} +(-2.75278 + 3.05728i) q^{83} +(-0.514496 + 0.104980i) q^{84} +(0.170447 - 0.234601i) q^{85} +(-1.19298 - 11.3504i) q^{86} +(-6.21676 - 1.37452i) q^{87} +(3.55895 - 2.05476i) q^{88} +(-1.33414 + 0.969306i) q^{89} +(-7.05192 - 1.61964i) q^{90} +(-0.247916 + 0.0805526i) q^{91} +0.973986 q^{92} +(-4.43054 - 8.56565i) q^{93} -5.25137 q^{94} +(17.4226 - 5.66094i) q^{95} +(-1.49288 - 0.878235i) q^{96} +(1.75787 - 1.27717i) q^{97} +(-5.98258 + 3.45405i) q^{98} +(1.08844 + 12.2804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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