LMFDB - Embedded newform 186.2.p.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("186.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.143963 + 1.72606i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.52111 - 0.878214i) q^{5} +(-0.670298 + 1.59709i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.95855 - 0.496976i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.143963 + 1.72606i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.52111 - 0.878214i) q^{5} +(-0.670298 + 1.59709i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.95855 - 0.496976i) q^{9} +(-1.17528 - 1.30528i) q^{10} +(3.79438 - 1.68937i) q^{11} +(-1.13102 + 1.31179i) q^{12} +(1.03437 - 4.86633i) q^{13} +(-2.04567 + 4.59464i) q^{14} +(1.73483 - 2.49910i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.59577 + 1.60094i) q^{17} +(-2.66017 - 1.38689i) q^{18} +(2.69057 - 0.571899i) q^{19} +(-0.714403 - 1.60458i) q^{20} +(-8.55790 - 1.62752i) q^{21} +(4.13071 - 0.434155i) q^{22} +(-4.16079 + 3.02299i) q^{23} +(-1.48103 + 0.898083i) q^{24} +(-0.957481 - 1.65841i) q^{25} +(2.48752 - 4.30852i) q^{26} +(1.28373 - 5.03508i) q^{27} +(-3.36537 + 3.73762i) q^{28} +(-0.603399 + 1.85707i) q^{29} +(2.42218 - 1.84069i) q^{30} +(0.331085 - 5.55791i) q^{31} +1.00000i q^{32} +(2.36969 + 6.79252i) q^{33} +(2.92506 + 2.63373i) q^{34} +(5.19243 - 7.14677i) q^{35} +(-2.10140 - 2.14105i) q^{36} +(0.116641 - 0.0673425i) q^{37} +(2.73561 + 0.287524i) q^{38} +(8.25066 + 2.48595i) q^{39} +(-0.183597 - 1.74681i) q^{40} +(5.89201 - 5.30519i) q^{41} +(-7.63612 - 4.19240i) q^{42} +(-0.0835168 - 0.392915i) q^{43} +(4.06270 + 0.863553i) q^{44} +(4.06383 + 3.35419i) q^{45} +(-4.89131 + 1.58928i) q^{46} +(3.92867 - 1.27650i) q^{47} +(-1.68607 + 0.396465i) q^{48} +(-17.8957 - 3.80385i) q^{49} +(-0.398143 - 1.87312i) q^{50} +(-3.28097 + 5.97602i) q^{51} +(3.69718 - 3.32896i) q^{52} +(0.662698 + 6.30515i) q^{53} +(2.77682 - 4.39195i) q^{54} +(-7.25529 - 0.762562i) q^{55} +(-4.35564 + 2.51473i) q^{56} +(0.599788 + 4.72641i) q^{57} +(-1.14773 + 1.57972i) q^{58} +(-7.26288 - 6.53952i) q^{59} +(2.87244 - 1.00210i) q^{60} +3.59736i q^{61} +(2.03237 - 5.18358i) q^{62} +(4.04120 - 14.5371i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-5.84707 + 6.49383i) q^{65} +(0.154709 + 7.19234i) q^{66} +(-2.82129 + 4.88662i) q^{67} +(1.96803 + 3.40872i) q^{68} +(-4.61886 - 7.61697i) q^{69} +(7.14677 - 5.19243i) q^{70} +(-4.82420 + 0.507044i) q^{71} +(-1.33693 - 2.68563i) q^{72} +(2.62863 + 5.90400i) q^{73} +(0.131742 - 0.0280026i) q^{74} +(3.00035 - 1.41392i) q^{75} +(2.51287 + 1.11880i) q^{76} +(6.45527 + 19.8673i) q^{77} +(7.07864 + 4.91388i) q^{78} +(-3.25109 + 7.30206i) q^{79} +(0.365182 - 1.71805i) q^{80} +(8.50603 + 2.94065i) q^{81} +(7.24302 - 3.22480i) q^{82} +(4.50537 + 5.00373i) q^{83} +(-5.96686 - 6.34690i) q^{84} +(-4.06359 - 5.59305i) q^{85} +(0.0419884 - 0.399493i) q^{86} +(-3.11854 - 1.30885i) q^{87} +(3.59700 + 2.07673i) q^{88} +(-10.1413 - 7.36810i) q^{89} +(2.82843 + 4.44582i) q^{90} +(23.7972 + 7.73217i) q^{91} -5.14302 q^{92} +(9.54561 + 1.37160i) q^{93} +4.13084 q^{94} +(-4.59491 - 1.49298i) q^{95} +(-1.72606 - 0.143963i) q^{96} +(-10.1882 - 7.40220i) q^{97} +(-15.8444 - 9.14776i) q^{98} +(-12.0654 + 3.11236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.143963	+	1.72606i	−0.0831169	+	0.996540i
$3$	−0.143963	+	1.72606i	−0.0831169	+	0.996540i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.52111	−	0.878214i	−0.680262	−	0.392749i	0.119692	−	0.992811i	$-0.461809\pi$
$5$	−1.52111	−	0.878214i	−0.680262	−	0.392749i	−0.799954	+	0.600062i	$0.795143\pi$
$6$	−0.670298	+	1.59709i	−0.273648	+	0.652010i
$7$	−0.525722	+	5.00191i	−0.198704	+	1.89055i	0.209733	+	0.977759i	$0.432741\pi$
$7$	−0.525722	+	5.00191i	−0.198704	+	1.89055i	−0.408437	+	0.912786i	$0.633926\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−2.95855	−	0.496976i	−0.986183	−	0.165659i
$10$	−1.17528	−	1.30528i	−0.371656	−	0.412766i
$11$	3.79438	−	1.68937i	1.14405	−	0.509363i	0.254893	−	0.966969i	$-0.417960\pi$
$11$	3.79438	−	1.68937i	1.14405	−	0.509363i	0.889155	+	0.457607i	$0.151293\pi$
$12$	−1.13102	+	1.31179i	−0.326497	+	0.378681i
$13$	1.03437	−	4.86633i	0.286883	−	1.34968i	−0.564630	−	0.825344i	$-0.690981\pi$
$13$	1.03437	−	4.86633i	0.286883	−	1.34968i	0.851513	−	0.524334i	$-0.175686\pi$
$14$	−2.04567	+	4.59464i	−0.546728	+	1.22797i
$15$	1.73483	−	2.49910i	0.447931	−	0.645264i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.59577	+	1.60094i	0.872101	+	0.388284i	0.793463	−	0.608619i	$-0.208276\pi$
$17$	3.59577	+	1.60094i	0.872101	+	0.388284i	0.0786384	+	0.996903i	$0.474943\pi$
$18$	−2.66017	−	1.38689i	−0.627009	−	0.326894i
$19$	2.69057	−	0.571899i	0.617259	−	0.131203i	0.111339	−	0.993783i	$-0.464486\pi$
$19$	2.69057	−	0.571899i	0.617259	−	0.131203i	0.505921	+	0.862580i	$0.331153\pi$
$20$	−0.714403	−	1.60458i	−0.159745	−	0.358794i
$21$	−8.55790	−	1.62752i	−1.86749	−	0.355153i
$22$	4.13071	−	0.434155i	0.880670	−	0.0925622i
$23$	−4.16079	+	3.02299i	−0.867586	+	0.630338i	−0.929938	−	0.367716i	$-0.880140\pi$
$23$	−4.16079	+	3.02299i	−0.867586	+	0.630338i	0.0623524	+	0.998054i	$0.480140\pi$
$24$	−1.48103	+	0.898083i	−0.302314	+	0.183320i
$25$	−0.957481	−	1.65841i	−0.191496	−	0.331681i
$26$	2.48752	−	4.30852i	0.487844	−	0.844970i
$27$	1.28373	−	5.03508i	0.247054	−	0.969002i
$28$	−3.36537	+	3.73762i	−0.635995	+	0.706344i
$29$	−0.603399	+	1.85707i	−0.112048	+	0.344849i	−0.991320	−	0.131471i	$-0.958030\pi$
$29$	−0.603399	+	1.85707i	−0.112048	+	0.344849i	0.879272	+	0.476321i	$0.158030\pi$
$30$	2.42218	−	1.84069i	0.442228	−	0.336062i
$31$	0.331085	−	5.55791i	0.0594646	−	0.998230i
$31$	0.331085	−	5.55791i	0.0594646	−	0.998230i
$32$			1.00000i			0.176777i
$33$	2.36969	+	6.79252i	0.412511	+	1.18243i
$34$	2.92506	+	2.63373i	0.501643	+	0.451682i
$35$	5.19243	−	7.14677i	0.877681	−	1.20802i
$36$	−2.10140	−	2.14105i	−0.350234	−	0.356842i
$37$	0.116641	−	0.0673425i	0.0191756	−	0.0110710i	−0.490382	−	0.871508i	$-0.663143\pi$
$37$	0.116641	−	0.0673425i	0.0191756	−	0.0110710i	0.509557	+	0.860437i	$0.329809\pi$
$38$	2.73561	+	0.287524i	0.443775	+	0.0466426i
$39$	8.25066	+	2.48595i	1.32116	+	0.398071i
$40$	−0.183597	−	1.74681i	−0.0290292	−	0.276194i
$41$	5.89201	−	5.30519i	0.920177	−	0.828531i	−0.0653828	−	0.997860i	$-0.520827\pi$
$41$	5.89201	−	5.30519i	0.920177	−	0.828531i	0.985560	+	0.169329i	$0.0541602\pi$
$42$	−7.63612	−	4.19240i	−1.17828	−	0.646901i
$43$	−0.0835168	−	0.392915i	−0.0127362	−	0.0599190i	0.971321	−	0.237774i	$-0.0764177\pi$
$43$	−0.0835168	−	0.392915i	−0.0127362	−	0.0599190i	−0.984057	+	0.177855i	$0.943084\pi$
$44$	4.06270	+	0.863553i	0.612475	+	0.130186i
$45$	4.06383	+	3.35419i	0.605800	+	0.500014i
$46$	−4.89131	+	1.58928i	−0.721184	+	0.234327i
$47$	3.92867	−	1.27650i	0.573055	−	0.186197i	−0.00813196	−	0.999967i	$-0.502589\pi$
$47$	3.92867	−	1.27650i	0.573055	−	0.186197i	0.581187	+	0.813770i	$0.302589\pi$
$48$	−1.68607	+	0.396465i	−0.243363	+	0.0572247i
$49$	−17.8957	−	3.80385i	−2.55653	−	0.543407i
$50$	−0.398143	−	1.87312i	−0.0563059	−	0.264899i
$51$	−3.28097	+	5.97602i	−0.459427	+	0.836811i
$52$	3.69718	−	3.32896i	0.512707	−	0.461643i
$53$	0.662698	+	6.30515i	0.0910286	+	0.866079i	0.940808	+	0.338941i	$0.110069\pi$
$53$	0.662698	+	6.30515i	0.0910286	+	0.866079i	−0.849779	+	0.527139i	$0.823265\pi$
$54$	2.77682	−	4.39195i	0.377878	−	0.597669i
$55$	−7.25529	−	0.762562i	−0.978303	−	0.102824i
$56$	−4.35564	+	2.51473i	−0.582047	+	0.336045i
$57$	0.599788	+	4.72641i	0.0794439	+	0.626029i
$58$	−1.14773	+	1.57972i	−0.150705	+	0.207427i
$59$	−7.26288	−	6.53952i	−0.945546	−	0.851373i	0.0434893	−	0.999054i	$-0.486153\pi$
$59$	−7.26288	−	6.53952i	−0.945546	−	0.851373i	−0.989035	+	0.147681i	$0.952819\pi$
$60$	2.87244	−	1.00210i	0.370830	−	0.129371i
$61$			3.59736i			0.460595i	0.973120	+	0.230297i	$0.0739699\pi$
$61$			3.59736i			0.460595i	−0.973120	+	0.230297i	$0.926030\pi$
$62$	2.03237	−	5.18358i	0.258111	−	0.658315i
$63$	4.04120	−	14.5371i	0.509144	−	1.83151i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−5.84707	+	6.49383i	−0.725240	+	0.805461i
$66$	0.154709	+	7.19234i	0.0190433	+	0.885316i
$67$	−2.82129	+	4.88662i	−0.344676	+	0.596996i	−0.985295	−	0.170863i	$-0.945345\pi$
$67$	−2.82129	+	4.88662i	−0.344676	+	0.596996i	0.640619	+	0.767859i	$0.278678\pi$
$68$	1.96803	+	3.40872i	0.238658	+	0.413368i
$69$	−4.61886	−	7.61697i	−0.556046	−	0.916975i
$70$	7.14677	−	5.19243i	0.854202	−	0.620614i
$71$	−4.82420	+	0.507044i	−0.572527	+	0.0601750i	−0.386368	−	0.922345i	$-0.626271\pi$
$71$	−4.82420	+	0.507044i	−0.572527	+	0.0601750i	−0.186159	+	0.982520i	$0.559604\pi$
$72$	−1.33693	−	2.68563i	−0.157559	−	0.316505i
$73$	2.62863	+	5.90400i	0.307658	+	0.691010i	0.999519	−	0.0310202i	$-0.00987562\pi$
$73$	2.62863	+	5.90400i	0.307658	+	0.691010i	−0.691861	+	0.722031i	$0.743209\pi$
$74$	0.131742	−	0.0280026i	0.0153147	−	0.00325523i
$75$	3.00035	−	1.41392i	0.346450	−	0.163265i
$76$	2.51287	+	1.11880i	0.288246	+	0.128335i
$77$	6.45527	+	19.8673i	0.735646	+	2.26409i
$78$	7.07864	+	4.91388i	0.801498	+	0.556387i
$79$	−3.25109	+	7.30206i	−0.365776	+	0.821546i	0.633096	+	0.774073i	$0.281784\pi$
$79$	−3.25109	+	7.30206i	−0.365776	+	0.821546i	−0.998872	+	0.0474735i	$0.984883\pi$
$80$	0.365182	−	1.71805i	0.0408286	−	0.192083i
$81$	8.50603	+	2.94065i	0.945114	+	0.326739i
$82$	7.24302	−	3.22480i	0.799858	−	0.356120i
$83$	4.50537	+	5.00373i	0.494529	+	0.549230i	0.937808	−	0.347153i	$-0.112852\pi$
$83$	4.50537	+	5.00373i	0.494529	+	0.549230i	−0.443279	+	0.896384i	$0.646185\pi$
$84$	−5.96686	−	6.34690i	−0.651038	−	0.692503i
$85$	−4.06359	−	5.59305i	−0.440758	−	0.606652i
$86$	0.0419884	−	0.399493i	0.00452772	−	0.0430784i
$87$	−3.11854	−	1.30885i	−0.334343	−	0.140323i
$88$	3.59700	+	2.07673i	0.383442	+	0.221380i
$89$	−10.1413	−	7.36810i	−1.07498	−	0.781017i	−0.0981772	−	0.995169i	$-0.531301\pi$
$89$	−10.1413	−	7.36810i	−1.07498	−	0.781017i	−0.976800	+	0.214152i	$0.931301\pi$
$90$	2.82843	+	4.44582i	0.298143	+	0.468631i
$91$	23.7972	+	7.73217i	2.49462	+	0.810552i
$92$	−5.14302			−0.536197
$93$	9.54561	+	1.37160i	0.989834	+	0.142229i
$94$	4.13084			0.426064
$95$	−4.59491	−	1.49298i	−0.471428	−	0.153176i
$96$	−1.72606	−	0.143963i	−0.176165	−	0.0146931i
$97$	−10.1882	−	7.40220i	−1.03446	−	0.751579i	−0.0652635	−	0.997868i	$-0.520789\pi$
$97$	−10.1882	−	7.40220i	−1.03446	−	0.751579i	−0.969196	+	0.246289i	$0.920789\pi$
$98$	−15.8444	−	9.14776i	−1.60052	−	0.924063i
$99$	−12.0654	+	3.11236i	−1.21262	+	0.312804i
$100$	0.200168	−	1.90447i	0.0200168	−	0.190447i
$101$	−8.68120	−	11.9487i	−0.863812	−	1.18894i	−0.980647	−	0.195784i	$-0.937275\pi$
$101$	−8.68120	−	11.9487i	−0.863812	−	1.18894i	0.116835	−	0.993151i	$-0.462725\pi$
$102$	−4.96708	+	4.66966i	−0.491814	+	0.462365i
$103$	4.18427	+	4.64710i	0.412288	+	0.457893i	0.913143	−	0.407639i	$-0.133648\pi$
$103$	4.18427	+	4.64710i	0.412288	+	0.457893i	−0.500855	+	0.865531i	$0.666981\pi$
$104$	4.54493	−	2.02353i	0.445667	−	0.198424i
$105$	11.5882	+	9.99130i	1.13089	+	0.975051i
$106$	−1.31814	+	6.20134i	−0.128029	+	0.602328i
$107$	3.41484	−	7.66985i	0.330125	−	0.741472i	−0.669875	−	0.742474i	$-0.733652\pi$
$107$	3.41484	−	7.66985i	0.330125	−	0.741472i	0.999999	+	0.00100171i	$0.000318853\pi$
$108$	3.99811	−	3.31891i	0.384718	−	0.319362i
$109$	0.400274	+	1.23192i	0.0383393	+	0.117996i	0.968394	−	0.249424i	$-0.0802412\pi$
$109$	0.400274	+	1.23192i	0.0383393	+	0.117996i	−0.930055	+	0.367420i	$0.880241\pi$
$110$	−6.66455	−	2.96725i	−0.635440	−	0.282916i
$111$	0.0994451	+	0.211023i	0.00943891	+	0.0200294i
$112$	−4.91956	+	1.04568i	−0.464855	+	0.0988079i
$113$	−0.293125	−	0.658370i	−0.0275749	−	0.0619342i	0.899233	−	0.437470i	$-0.144125\pi$
$113$	−0.293125	−	0.658370i	−0.0275749	−	0.0619342i	−0.926808	+	0.375536i	$0.877459\pi$
$114$	−0.890110	+	4.68043i	−0.0833664	+	0.438363i
$115$	8.98387	−	0.944242i	0.837750	−	0.0880510i
$116$	−1.57972	+	1.14773i	−0.146673	+	0.106564i
$117$	−5.47869	+	13.8832i	−0.506505	+	1.28350i
$118$	−4.88658	−	8.46381i	−0.449846	−	0.779157i
$119$	−9.89812	+	17.1441i	−0.907360	+	1.57159i
$120$	3.04152	−	0.0654237i	0.277651	−	0.00597234i
$121$	4.18290	−	4.64558i	0.380264	−	0.422326i
$122$	−1.11165	+	3.42129i	−0.100644	+	0.309749i
$123$	8.30883	+	10.9337i	0.749182	+	0.985858i
$124$	3.53471	−	4.30184i	0.317426	−	0.386316i
$125$			12.1456i			1.08634i
$126$	8.33563	−	12.5768i	0.742597	−	1.12043i
$127$	−12.5992	−	11.3444i	−1.11800	−	1.00665i	−0.999907	−	0.0136489i	$-0.995655\pi$
$127$	−12.5992	−	11.3444i	−1.11800	−	1.00665i	−0.118093	−	0.993003i	$-0.537678\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	0.690218	−	0.0875896i	0.0607703	−	0.00771183i
$130$	−7.56760	+	4.36916i	−0.663723	+	0.383200i
$131$	16.2620	+	1.70920i	1.42082	+	0.149334i	0.783559	−	0.621317i	$-0.213402\pi$
$131$	16.2620	+	1.70920i	1.42082	+	0.149334i	0.637257	+	0.770651i	$0.280069\pi$
$132$	−2.07542	+	6.88813i	−0.180642	+	0.599535i
$133$	1.44609	+	13.7587i	0.125392	+	1.19303i
$134$	−4.19326	+	3.77563i	−0.362242	+	0.326165i
$135$	−6.37457	+	6.53153i	−0.548636	+	0.562144i
$136$	0.818352	+	3.85004i	0.0701731	+	0.330138i
$137$	4.61161	+	0.980228i	0.393996	+	0.0837465i	0.400650	−	0.916231i	$-0.368784\pi$
$137$	4.61161	+	0.980228i	0.393996	+	0.0837465i	−0.00665328	+	0.999978i	$0.502118\pi$
$138$	−2.03903	−	8.67147i	−0.173573	−	0.738165i
$139$	4.71268	−	1.53124i	0.399725	−	0.129878i	−0.102254	−	0.994758i	$-0.532606\pi$
$139$	4.71268	−	1.53124i	0.399725	−	0.129878i	0.501979	+	0.864880i	$0.332606\pi$
$140$	8.40153	−	2.72982i	0.710059	−	0.230712i
$141$	1.63773	+	6.96487i	0.137922	+	0.586548i
$142$	−4.74477	−	1.00853i	−0.398172	−	0.0846341i
$143$	−4.29622	−	20.2121i	−0.359268	−	1.69022i
$144$	−0.441590	−	2.96732i	−0.0367992	−	0.247277i
$145$	2.54874	−	2.29490i	0.211661	−	0.190581i
$146$	0.675539	+	6.42732i	0.0559080	+	0.531929i
$147$	9.14198	−	30.3414i	0.754018	−	2.50252i
$148$	0.133947	+	0.0140784i	0.0110104	+	0.00115724i
$149$	−1.43841	+	0.830464i	−0.117839	+	0.0680342i	−0.557761	−	0.830002i	$-0.688339\pi$
$149$	−1.43841	+	0.830464i	−0.117839	+	0.0680342i	0.439922	+	0.898036i	$0.355006\pi$
$150$	3.29042	−	0.417559i	0.268662	−	0.0340936i
$151$	−0.614655	+	0.846000i	−0.0500199	+	0.0688465i	−0.833294	−	0.552830i	$-0.813548\pi$
$151$	−0.614655	+	0.846000i	−0.0500199	+	0.0688465i	0.783274	+	0.621676i	$0.213548\pi$
$152$	2.04415	+	1.84056i	0.165803	+	0.149289i
$153$	−9.84262	−	6.52346i	−0.795729	−	0.527391i
$154$			20.8897i			1.68334i
$155$	−5.38465	+	8.16344i	−0.432506	+	0.655703i
$156$	5.21372	+	6.86079i	0.417431	+	0.549303i
$157$	4.06134	−	12.4995i	0.324131	−	0.997571i	−0.647701	−	0.761895i	$-0.724269\pi$
$157$	4.06134	−	12.4995i	0.324131	−	0.997571i	0.971832	−	0.235677i	$-0.0757306\pi$
$158$	−5.34843	+	5.94003i	−0.425498	+	0.472564i
$159$	−10.9785	+	0.236149i	−0.870649	+	0.0187278i
$160$	0.878214	−	1.52111i	0.0694289	−	0.120254i
$161$	−12.9333	−	22.4012i	−1.01929	−	1.76546i
$162$	7.18100	+	5.42524i	0.564193	+	0.426247i
$163$	−2.57892	+	1.87370i	−0.201997	+	0.146759i	−0.684185	−	0.729308i	$-0.739842\pi$
$163$	−2.57892	+	1.87370i	−0.201997	+	0.146759i	0.482189	+	0.876067i	$0.339842\pi$
$164$	7.88504	−	0.828751i	0.615718	−	0.0647146i
$165$	2.36072	−	12.4133i	0.183782	−	0.966372i
$166$	2.73863	+	6.15106i	0.212559	+	0.477415i
$167$	4.12869	−	0.877580i	0.319488	−	0.0679092i	−0.0453765	−	0.998970i	$-0.514449\pi$
$167$	4.12869	−	0.877580i	0.319488	−	0.0679092i	0.364864	+	0.931061i	$0.381115\pi$
$168$	−3.71352	−	7.88012i	−0.286504	−	0.607964i
$169$	−10.7352	−	4.77961i	−0.825783	−	0.367662i
$170$	−2.13636	−	6.57503i	−0.163851	−	0.504282i
$171$	−8.24441	+	0.354842i	−0.630466	+	0.0271354i
$172$	0.163383	−	0.366965i	0.0124579	−	0.0279808i
$173$	−1.94882	+	9.16849i	−0.148166	+	0.697067i	0.839863	+	0.542799i	$0.182635\pi$
$173$	−1.94882	+	9.16849i	−0.148166	+	0.697067i	−0.988029	+	0.154268i	$0.950698\pi$
$174$	−2.56145	−	2.20847i	−0.194183	−	0.167424i
$175$	8.79857	−	3.91738i	0.665109	−	0.296126i
$176$	2.77921	+	3.08662i	0.209491	+	0.232663i
$177$	12.3332	−	11.5947i	0.927018	−	0.871511i
$178$	−7.36810	−	10.1413i	−0.552262	−	0.760124i
$179$	0.776953	−	7.39222i	0.0580722	−	0.552520i	−0.926346	−	0.376675i	$-0.877067\pi$
$179$	0.776953	−	7.39222i	0.0580722	−	0.552520i	0.984418	−	0.175845i	$-0.0562659\pi$
$180$	1.31616	+	5.10226i	0.0981010	+	0.380300i
$181$	−5.67062	−	3.27393i	−0.421494	−	0.243350i	0.274222	−	0.961666i	$-0.411580\pi$
$181$	−5.67062	−	3.27393i	−0.421494	−	0.243350i	−0.695716	+	0.718317i	$0.744913\pi$
$182$	20.2431	+	14.7075i	1.50052	+	1.09019i
$183$	−6.20925	−	0.517885i	−0.459001	−	0.0382832i
$184$	−4.89131	−	1.58928i	−0.360592	−	0.117163i
$185$	−0.236564			−0.0173926
$186$	8.65457	+	4.25423i	0.634584	+	0.311935i
$187$	16.3483			1.19550
$188$	3.92867	+	1.27650i	0.286527	+	0.0930984i
$189$	24.5101	+	9.06815i	1.78285	+	0.659611i
$190$	−3.90866	−	2.83981i	−0.283564	−	0.206021i
$191$	−8.38122	−	4.83890i	−0.606444	−	0.350130i	0.165129	−	0.986272i	$-0.447196\pi$
$191$	−8.38122	−	4.83890i	−0.606444	−	0.350130i	−0.771572	+	0.636142i	$0.780529\pi$
$192$	−1.59709	−	0.670298i	−0.115260	−	0.0483746i
$193$	2.06578	−	19.6546i	0.148698	−	1.41477i	−0.624708	−	0.780858i	$-0.714782\pi$
$193$	2.06578	−	19.6546i	0.148698	−	1.41477i	0.773406	−	0.633911i	$-0.218551\pi$
$194$	−7.40220	−	10.1882i	−0.531447	−	0.731474i
$195$	−10.3670	−	11.0273i	−0.742394	−	0.789678i
$196$	−12.2421	−	13.5962i	−0.874435	−	0.971158i
$197$	5.61294	−	2.49904i	0.399905	−	0.178049i	−0.196922	−	0.980419i	$-0.563095\pi$
$197$	5.61294	−	2.49904i	0.399905	−	0.178049i	0.596827	+	0.802370i	$0.296428\pi$
$198$	−12.4367	−	0.768393i	−0.883836	−	0.0546073i
$199$	−0.514312	+	2.41965i	−0.0364586	+	0.171524i	−0.992610	−	0.121349i	$-0.961278\pi$
$199$	−0.514312	+	2.41965i	−0.0364586	+	0.171524i	0.956151	+	0.292873i	$0.0946113\pi$
$200$	0.778885	−	1.74940i	0.0550755	−	0.123702i
$201$	−8.02843	−	5.57321i	−0.566282	−	0.393104i
$202$	−4.56398	−	14.0465i	−0.321120	−	0.988307i
$203$	−8.97168	−	3.99445i	−0.629688	−	0.280355i
$204$	−6.16698	+	2.90620i	−0.431775	+	0.203475i
$205$	−13.6215	+	2.89534i	−0.951366	+	0.202219i
$206$	2.54344	+	5.71267i	0.177210	+	0.398020i
$207$	13.8123	−	6.87586i	0.960019	−	0.477906i
$208$	4.94780	−	0.520034i	0.343068	−	0.0360579i
$209$	9.24290	−	6.71536i	0.639344	−	0.464511i
$210$	7.93357	+	13.0832i	0.547468	+	0.902830i
$211$	12.9600	+	22.4473i	0.892201	+	1.54534i	0.837230	+	0.546850i	$0.184173\pi$
$211$	12.9600	+	22.4473i	0.892201	+	1.54534i	0.0549711	+	0.998488i	$0.482493\pi$
$212$	−3.16994	+	5.49050i	−0.217713	+	0.377089i
$213$	−0.180682	−	8.39984i	−0.0123801	−	0.575548i
$214$	5.61782	−	6.23922i	0.384026	−	0.426504i
$215$	−0.218026	+	0.671014i	−0.0148692	+	0.0457627i
$216$	4.82802	−	1.92099i	0.328505	−	0.130707i
$217$	27.6261	+	4.57798i	1.87538	+	0.310773i
$218$			1.29531i			0.0877297i
$219$	−10.5691	+	3.68721i	−0.714191	+	0.249158i
$220$	−5.42143	−	4.88148i	−0.365513	−	0.329109i
$221$	11.5101	−	15.8422i	0.774250	−	1.06566i
$222$	0.0293682	+	0.231425i	0.00197106	+	0.0155322i
$223$	−14.0224	+	8.09584i	−0.939010	+	0.542138i	−0.889650	−	0.456643i	$-0.849052\pi$
$223$	−14.0224	+	8.09584i	−0.939010	+	0.542138i	−0.0493601	+	0.998781i	$0.515718\pi$
$224$	−5.00191	−	0.525722i	−0.334204	−	0.0351263i
$225$	2.00857	+	5.38232i	0.133905	+	0.358821i
$226$	−0.0753311	−	0.716728i	−0.00501095	−	0.0476760i
$227$	0.519770	−	0.468003i	0.0344984	−	0.0310625i	−0.651701	−	0.758476i	$-0.725944\pi$
$227$	0.519770	−	0.468003i	0.0344984	−	0.0310625i	0.686200	+	0.727413i	$0.259278\pi$
$228$	−2.29288	+	4.17630i	−0.151850	+	0.276582i
$229$	2.51786	+	11.8456i	0.166385	+	0.782780i	0.979622	+	0.200848i	$0.0643696\pi$
$229$	2.51786	+	11.8456i	0.166385	+	0.782780i	−0.813238	+	0.581932i	$0.802297\pi$
$230$	8.83595	+	1.87814i	0.582625	+	0.123841i
$231$	−35.2214	+	8.28202i	−2.31740	+	0.544917i
$232$	−1.85707	+	0.603399i	−0.121923	+	0.0396151i
$233$	−0.597184	+	0.194037i	−0.0391228	+	0.0127118i	−0.328513	−	0.944499i	$-0.606547\pi$
$233$	−0.597184	+	0.194037i	−0.0391228	+	0.0127118i	0.289390	+	0.957211i	$0.406547\pi$
$234$	−9.50069	+	11.5107i	−0.621080	+	0.752480i
$235$	−7.09698	−	1.50851i	−0.462956	−	0.0984043i
$236$	−2.03195	−	9.55960i	−0.132269	−	0.622277i
$237$	−12.1357	−	6.66279i	−0.788302	−	0.432795i
$238$	−14.7115	+	13.2463i	−0.953604	+	0.858629i
$239$	1.83778	+	17.4853i	0.118876	+	1.13103i	0.877526	+	0.479530i	$0.159193\pi$
$239$	1.83778	+	17.4853i	0.118876	+	1.13103i	−0.758650	+	0.651499i	$0.774141\pi$
$240$	2.91287	+	0.877659i	0.188025	+	0.0566527i
$241$	11.7058	+	1.23033i	0.754039	+	0.0792527i	0.473746	−	0.880662i	$-0.342902\pi$
$241$	11.7058	+	1.23033i	0.754039	+	0.0792527i	0.280293	+	0.959914i	$0.409568\pi$
$242$	5.41374	−	3.12562i	0.348008	−	0.200923i
$243$	−6.30029	+	14.2586i	−0.404164	+	0.914687i
$244$	−2.11447	+	2.91032i	−0.135365	+	0.186314i
$245$	23.8808	+	21.5023i	1.52569	+	1.37373i
$246$	4.52347	+	12.9661i	0.288406	+	0.826690i
$247$		−	13.6848i		−	0.870741i
$248$	4.69105	−	2.99901i	0.297882	−	0.190437i
$249$	−9.28532	+	7.05619i	−0.588433	+	0.447168i
$250$	−3.75321	+	11.5512i	−0.237374	+	0.730561i
$251$	9.12018	−	10.1290i	0.575661	−	0.639336i	−0.383047	−	0.923729i	$-0.625125\pi$
$251$	9.12018	−	10.1290i	0.575661	−	0.639336i	0.958708	+	0.284393i	$0.0917920\pi$
$252$	11.8141	−	9.38543i	0.744219	−	0.591226i
$253$	−10.6807	+	18.4995i	−0.671489	+	1.16305i
$254$	−8.47696	−	14.6825i	−0.531892	−	0.921263i
$255$	10.2389	−	6.20880i	0.641187	−	0.388810i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−17.8707	+	1.87829i	−1.11474	+	0.117164i	−0.643942	−	0.765074i	$-0.722702\pi$
$257$	−17.8707	+	1.87829i	−1.11474	+	0.117164i	−0.470803	+	0.882239i	$0.656036\pi$
$258$	0.683503	+	0.129986i	0.0425530	+	0.00809260i
$259$	0.275521	+	0.618830i	0.0171200	+	0.0384522i
$260$	−8.54736	+	1.81680i	−0.530085	+	0.112673i
$261$	2.70810	−	5.19436i	0.167627	−	0.321523i
$262$	14.9379	+	6.65078i	0.922866	+	0.410886i
$263$	4.55490	+	14.0185i	0.280867	+	0.864420i	0.987607	+	0.156947i	$0.0501651\pi$
$263$	4.55490	+	14.0185i	0.280867	+	0.864420i	−0.706740	+	0.707474i	$0.749835\pi$
$264$	−4.10239	+	5.90966i	−0.252485	+	0.363715i
$265$	4.52924	−	10.1728i	0.278229	−	0.624912i
$266$	−2.87634	+	13.5321i	−0.176360	+	0.829708i
$267$	14.1777	−	16.4438i	0.867663	−	1.00634i
$268$	−5.15476	+	2.29505i	−0.314877	+	0.140192i
$269$	−19.3565	−	21.4975i	−1.18018	−	1.31073i	−0.940467	−	0.339885i	$-0.889612\pi$
$269$	−19.3565	−	21.4975i	−1.18018	−	1.31073i	−0.239718	−	0.970843i	$-0.577055\pi$
$270$	−8.08093	+	4.24200i	−0.491790	+	0.258160i
$271$	−5.49471	−	7.56282i	−0.333780	−	0.459409i	0.608832	−	0.793299i	$-0.291638\pi$
$271$	−5.49471	−	7.56282i	−0.333780	−	0.459409i	−0.942612	+	0.333891i	$0.891638\pi$
$272$	−0.411430	+	3.91449i	−0.0249466	+	0.237351i
$273$	−16.7721	+	39.9622i	−1.01509	+	2.41862i
$274$	4.08299	+	2.35732i	0.246663	+	0.142411i
$275$	−6.43470	−	4.67508i	−0.388027	−	0.281918i
$276$	0.740403	−	8.87716i	0.0445671	−	0.534342i
$277$	9.90037	+	3.21682i	0.594855	+	0.193280i	0.590945	−	0.806712i	$-0.298755\pi$
$277$	9.90037	+	3.21682i	0.594855	+	0.193280i	0.00391077	+	0.999992i	$0.498755\pi$
$278$	4.95521			0.297194
$279$	−3.74168	+	16.2788i	−0.224008	+	0.974587i
$280$	8.83389			0.527926
$281$	3.62125	+	1.17662i	0.216026	+	0.0701910i	0.415030	−	0.909808i	$-0.363771\pi$
$281$	3.62125	+	1.17662i	0.216026	+	0.0701910i	−0.199005	+	0.979999i	$0.563771\pi$
$282$	−0.594687	+	7.13008i	−0.0354131	+	0.424590i
$283$	0.532489	+	0.386876i	0.0316532	+	0.0229974i	0.603499	−	0.797363i	$-0.293773\pi$
$283$	0.532489	+	0.386876i	0.0316532	+	0.0229974i	−0.571846	+	0.820361i	$0.693773\pi$
$284$	−4.20089	−	2.42539i	−0.249277	−	0.143920i
$285$	3.23846	−	7.71614i	0.191830	−	0.457065i
$286$	2.15994	−	20.5505i	0.127720	−	1.21518i
$287$	23.4385	+	32.2604i	1.38353	+	1.90427i
$288$	0.496976	−	2.95855i	0.0292846	−	0.174334i
$289$	−1.00869	−	1.12027i	−0.0593350	−	0.0658981i
$290$	3.13316	−	1.39497i	0.183985	−	0.0819156i
$291$	14.2433	−	16.5199i	0.834960	−	0.968412i
$292$	−1.34368	+	6.32150i	−0.0786327	+	0.369938i
$293$	5.61426	−	12.6098i	0.327989	−	0.736674i	−0.672004	−	0.740548i	$-0.734566\pi$
$293$	5.61426	−	12.6098i	0.327989	−	0.736674i	0.999992	+	0.00387313i	$0.00123286\pi$
$294$	18.0706	−	26.0314i	1.05390	−	1.51818i
$295$	5.30454	+	16.3257i	0.308842	+	0.950519i
$296$	0.123041	+	0.0547813i	0.00715160	+	0.00318410i
$297$	−3.63514	−	21.2737i	−0.210932	−	1.23442i
$298$	−1.62463	+	0.345326i	−0.0941124	+	0.0200042i
$299$	10.4071	+	23.3747i	0.601858	+	1.35179i
$300$	3.25841	+	0.619674i	0.188124	+	0.0357769i
$301$	2.00924	−	0.211179i	0.115810	−	0.0121722i
$302$	−0.846000	+	0.614655i	−0.0486819	+	0.0353694i
$303$	21.8738	−	13.2641i	1.25662	−	0.762002i
$304$	1.37534	+	2.38216i	0.0788812	+	0.136626i
$305$	3.15925	−	5.47198i	0.180898	−	0.313325i
$306$	−7.34503	−	9.24572i	−0.419887	−	0.528543i
$307$	−21.9309	+	24.3568i	−1.25166	+	1.39011i	−0.362848	+	0.931848i	$0.618196\pi$
$307$	−21.9309	+	24.3568i	−1.25166	+	1.39011i	−0.888816	+	0.458265i	$0.848471\pi$
$308$	−6.45527	+	19.8673i	−0.367823	+	1.13204i
$309$	−8.62355	+	6.55328i	−0.490576	+	0.372803i
$310$	−7.64375	+	6.09994i	−0.434136	+	0.346453i
$311$			16.7668i			0.950761i	0.879780	+	0.475380i	$0.157690\pi$
$311$			16.7668i			0.950761i	−0.879780	+	0.475380i	$0.842310\pi$
$312$	2.83844	+	8.13613i	0.160695	+	0.460618i
$313$	7.62463	+	6.86525i	0.430970	+	0.388047i	0.855868	−	0.517194i	$-0.173024\pi$
$313$	7.62463	+	6.86525i	0.430970	+	0.388047i	−0.424898	+	0.905241i	$0.639690\pi$
$314$	7.72514	−	10.6327i	0.435955	−	0.600040i
$315$	−18.9138	+	18.5636i	−1.06567	+	1.04594i
$316$	−6.92223	+	3.99655i	−0.389406	+	0.224824i
$317$	−18.1983	−	1.91272i	−1.02212	−	0.107429i	−0.421388	−	0.906880i	$-0.638457\pi$
$317$	−18.1983	−	1.91272i	−1.02212	−	0.107429i	−0.600731	+	0.799451i	$0.705124\pi$
$318$	−10.5141	−	3.16794i	−0.589602	−	0.177649i
$319$	0.847748	+	8.06578i	0.0474648	+	0.451597i
$320$	1.30528	−	1.17528i	0.0729674	−	0.0657001i
$321$	12.7470	+	6.99838i	0.711468	+	0.390611i
$322$	−5.37798	−	25.3014i	−0.299703	−	1.40999i
$323$	10.5902	+	2.25102i	0.589257	+	0.125250i
$324$	5.15305	+	7.37876i	0.286281	+	0.409931i
$325$	−9.06074	+	2.94401i	−0.502600	+	0.163305i
$326$	−3.03170	+	0.985060i	−0.167911	+	0.0545575i
$327$	−2.18398	+	0.513546i	−0.120774	+	0.0283991i
$328$	7.75522	+	1.64842i	0.428210	+	0.0910189i
$329$	4.31956	+	20.3219i	0.238145	+	1.12038i
$330$	6.08109	−	11.0762i	0.334753	−	0.609726i
$331$	−20.6416	+	18.5857i	−1.13456	+	1.02156i	−0.135035	+	0.990841i	$0.543115\pi$
$331$	−20.6416	+	18.5857i	−1.13456	+	1.02156i	−0.999528	+	0.0307241i	$0.990219\pi$
$332$	0.703809	+	6.69629i	0.0386265	+	0.367507i
$333$	−0.378555	+	0.141269i	−0.0207447	+	0.00774147i
$334$	4.19781	+	0.441207i	0.229694	+	0.0241418i
$335$	8.58300	−	4.95540i	0.468940	−	0.270742i
$336$	−1.09668	−	8.64198i	−0.0598287	−	0.471459i
$337$	9.98456	−	13.7426i	0.543894	−	0.748605i	−0.445274	−	0.895394i	$-0.646894\pi$
$337$	9.98456	−	13.7426i	0.543894	−	0.748605i	0.989168	+	0.146789i	$0.0468938\pi$
$338$	−8.73278	−	7.86303i	−0.475001	−	0.427692i
$339$	1.17858	−	0.411170i	0.0640119	−	0.0223317i
$340$		−	6.91340i		−	0.374932i
$341$	−8.13308	−	21.6481i	−0.440431	−	1.17231i
$342$	−7.95055	−	2.21019i	−0.429917	−	0.119513i
$343$	17.5554	−	54.0299i	0.947901	−	2.91734i
$344$	0.268785	−	0.298516i	0.0144919	−	0.0160949i
$345$	0.336476	+	15.6426i	0.0181152	+	0.842169i
$346$	−4.68666	+	8.11753i	−0.251956	+	0.436401i
$347$	5.71673	+	9.90167i	0.306890	+	0.531550i	0.977680	−	0.210098i	$-0.0673782\pi$
$347$	5.71673	+	9.90167i	0.306890	+	0.531550i	−0.670790	+	0.741647i	$0.734045\pi$
$348$	−1.75363	−	2.89191i	−0.0940045	−	0.155023i
$349$	11.2259	−	8.15607i	0.600907	−	0.436584i	−0.245294	−	0.969449i	$-0.578884\pi$
$349$	11.2259	−	8.15607i	0.600907	−	0.436584i	0.846201	+	0.532864i	$0.178884\pi$
$350$	9.57847	−	1.00674i	0.511991	−	0.0538124i
$351$	−23.1745	−	11.4552i	−1.23696	−	0.611433i
$352$	1.68937	+	3.79438i	0.0900435	+	0.202241i
$353$	28.3539	−	6.02680i	1.50913	−	0.320774i	0.622263	−	0.782808i	$-0.286214\pi$
$353$	28.3539	−	6.02680i	1.50913	−	0.320774i	0.886862	+	0.462034i	$0.152880\pi$
$354$	15.3125	−	7.21605i	0.813850	−	0.383529i
$355$	7.78344	+	3.46541i	0.413102	+	0.183925i
$356$	−3.87364	−	11.9218i	−0.205302	−	0.631856i
$357$	−28.1667	−	19.5528i	−1.49074	−	1.03485i
$358$	3.02325	−	6.79033i	0.159784	−	0.358880i
$359$	3.72095	−	17.5057i	0.196384	−	0.923916i	−0.763995	−	0.645222i	$-0.776765\pi$
$359$	3.72095	−	17.5057i	0.196384	−	0.923916i	0.960380	−	0.278694i	$-0.0899017\pi$
$360$	−0.324940	+	5.25925i	−0.0171258	+	0.277187i
$361$	−10.4453	+	4.65053i	−0.549750	+	0.244765i
$362$	−4.38138	−	4.86601i	−0.230280	−	0.255752i
$363$	7.41636	+	7.88872i	0.389258	+	0.414050i
$364$	14.7075	+	20.2431i	0.770881	+	1.06103i
$365$	1.18654	−	11.2891i	0.0621061	−	0.590900i
$366$	−5.74531	−	2.41130i	−0.300312	−	0.126041i
$367$	16.2659	+	9.39111i	0.849072	+	0.490212i	0.860338	−	0.509724i	$-0.170253\pi$
$367$	16.2659	+	9.39111i	0.849072	+	0.490212i	−0.0112654	+	0.999937i	$0.503586\pi$
$368$	−4.16079	−	3.02299i	−0.216896	−	0.157584i
$369$	−20.0683	+	12.7675i	−1.04472	+	0.664648i
$370$	−0.224986	−	0.0731024i	−0.0116965	−	0.00380041i
$371$	−31.8862			−1.65545
$372$	6.91635	+	6.72042i	0.358596	+	0.348438i
$373$	−12.4063			−0.642374			−0.321187	−	0.947016i	$-0.604082\pi$
$373$	−12.4063			−0.642374			−0.321187	+	0.947016i	$0.604082\pi$
$374$	15.5481	+	5.05189i	0.803974	+	0.261227i
$375$	−20.9641	−	1.74852i	−1.08258	−	0.0902930i
$376$	3.34192	+	2.42805i	0.172347	+	0.125217i
$377$	8.41298	+	4.85724i	0.433291	+	0.250160i
$378$	20.5083	+	16.1984i	1.05483	+	0.833155i
$379$	−0.482573	+	4.59138i	−0.0247881	+	0.235843i	0.975112	+	0.221713i	$0.0711647\pi$
$379$	−0.482573	+	4.59138i	−0.0247881	+	0.235843i	−0.999900	+	0.0141305i	$0.995502\pi$
$380$	−2.83981	−	3.90866i	−0.145679	−	0.200510i
$381$	21.3949	−	20.1138i	1.09609	−	1.03046i
$382$	−6.47571	−	7.19201i	−0.331326	−	0.367975i
$383$	−22.9985	+	10.2396i	−1.17517	+	0.523218i	−0.899024	−	0.437899i	$-0.855723\pi$
$383$	−22.9985	+	10.2396i	−1.17517	+	0.523218i	−0.276143	+	0.961117i	$0.589056\pi$
$384$	−1.31179	−	1.13102i	−0.0669420	−	0.0577171i
$385$	7.62854	−	35.8894i	0.388786	−	1.82910i
$386$	8.03828	−	18.0543i	0.409138	−	0.918938i
$387$	0.0518191	+	1.20397i	0.00263411	+	0.0612010i
$388$	−3.89157	−	11.9770i	−0.197564	−	0.608040i
$389$	−14.9970	−	6.67708i	−0.760376	−	0.338541i	−0.0103474	−	0.999946i	$-0.503294\pi$
$389$	−14.9970	−	6.67708i	−0.760376	−	0.338541i	−0.750029	+	0.661405i	$0.769960\pi$
$390$	−6.45196	−	13.6911i	−0.326708	−	0.693276i
$391$	−19.8009	+	4.20880i	−1.00137	+	0.212848i
$392$	−7.44146	−	16.7138i	−0.375850	−	0.844174i
$393$	−5.29130	+	27.8231i	−0.266911	+	1.40349i
$394$	6.11047	−	0.642236i	0.307841	−	0.0323554i
$395$	11.3580	−	8.25210i	0.571485	−	0.415208i
$396$	−11.5905	−	4.57393i	−0.582446	−	0.229849i
$397$	−8.76406	−	15.1798i	−0.439856	−	0.761852i	0.557822	−	0.829960i	$-0.311637\pi$
$397$	−8.76406	−	15.1798i	−0.439856	−	0.761852i	−0.997678	+	0.0681082i	$0.978304\pi$
$398$	−1.23685	+	2.14229i	−0.0619978	+	0.107383i
$399$	−23.9564	+	0.515308i	−1.19932	+	0.0257976i
$400$	1.28136	−	1.42309i	0.0640680	−	0.0711547i
$401$	−9.69603	+	29.8413i	−0.484197	+	1.49020i	0.348945	+	0.937143i	$0.386540\pi$
$401$	−9.69603	+	29.8413i	−0.484197	+	1.49020i	−0.833141	+	0.553060i	$0.813460\pi$
$402$	−5.91328	−	7.78136i	−0.294928	−	0.388099i
$403$	−26.7042	−	7.36011i	−1.33023	−	0.366633i
$404$		−	14.7693i		−	0.734802i
$405$	−10.3561	−	11.9432i	−0.514598	−	0.593461i
$406$	−7.29822	−	6.57135i	−0.362205	−	0.326131i
$407$	0.328812	−	0.452571i	0.0162986	−	0.0224331i
$408$	−6.76321	+	0.858260i	−0.334829	+	0.0424902i
$409$	−15.7954	+	9.11946i	−0.781031	+	0.450929i	−0.836796	−	0.547515i	$-0.815574\pi$
$409$	−15.7954	+	9.11946i	−0.781031	+	0.450929i	0.0557645	+	0.998444i	$0.482240\pi$
$410$	−13.8495	−	1.45564i	−0.683978	−	0.0718890i
$411$	−2.35583	+	7.81879i	−0.116204	+	0.385672i
$412$	0.653647	+	6.21904i	0.0322029	+	0.306390i
$413$	36.5284	−	32.8903i	1.79744	−	1.61843i
$414$	15.2610	−	2.27111i	0.750038	−	0.111619i
$415$	−2.45883	−	11.5679i	−0.120699	−	0.567846i
$416$	4.86633	+	1.03437i	0.238592	+	0.0507142i
$417$	1.96456	+	8.35480i	0.0962051	+	0.409137i
$418$	10.8657	−	3.53047i	0.531458	−	0.172681i
$419$	24.4868	−	7.95626i	1.19626	−	0.388689i	0.357877	−	0.933769i	$-0.383501\pi$
$419$	24.4868	−	7.95626i	1.19626	−	0.388689i	0.838384	+	0.545080i	$0.183501\pi$
$420$	3.50232	+	14.8945i	0.170896	+	0.726778i
$421$	30.0398	+	6.38516i	1.46405	+	0.311193i	0.869927	−	0.493181i	$-0.164166\pi$
$421$	30.0398	+	6.38516i	1.46405	+	0.311193i	0.594123	+	0.804374i	$0.297499\pi$
$422$	5.38906	+	25.3535i	0.262335	+	1.23419i
$423$	−12.2575	+	1.82414i	−0.595982	+	0.0886927i
$424$	−4.71145	+	4.24221i	−0.228808	+	0.206020i
$425$	−0.787872	−	7.49611i	−0.0382174	−	0.363615i
$426$	2.42385	−	8.04456i	0.117436	−	0.389760i
$427$	−17.9937	−	1.89121i	−0.870775	−	0.0915221i
$428$	7.27089	−	4.19785i	0.351452	−	0.202911i
$429$	35.5058	−	4.50573i	1.71424	−	0.217539i
$430$	−0.414709	+	0.570798i	−0.0199991	+	0.0275263i
$431$	−24.9909	−	22.5019i	−1.20377	−	1.08388i	−0.994361	−	0.106053i	$-0.966179\pi$
$431$	−24.9909	−	22.5019i	−1.20377	−	1.08388i	−0.209411	−	0.977828i	$-0.567155\pi$
$432$	5.18534	−	0.335027i	0.249480	−	0.0161190i
$433$		−	10.4643i		−	0.502884i	−0.967872	−	0.251442i	$-0.919095\pi$
$433$		−	10.4643i		−	0.502884i	0.967872	−	0.251442i	$-0.0809048\pi$
$434$	24.8593	+	12.8909i	1.19329	+	0.618781i
$435$	3.59420	+	4.72965i	0.172329	+	0.226769i
$436$	−0.400274	+	1.23192i	−0.0191696	+	0.0589981i
$437$	−9.46607	+	10.5131i	−0.452823	+	0.502911i
$438$	−11.1912	+	0.240725i	−0.534735	+	0.0115023i
$439$	−6.43053	+	11.1380i	−0.306912	+	0.531588i	−0.977685	−	0.210075i	$-0.932629\pi$
$439$	−6.43053	+	11.1380i	−0.306912	+	0.531588i	0.670773	+	0.741663i	$0.265963\pi$
$440$	−3.64763	−	6.31788i	−0.173894	−	0.301193i
$441$	51.0549	+	20.1476i	2.43119	+	0.959410i
$442$	15.8422	−	11.5101i	0.753538	−	0.547477i
$443$	16.5868	−	1.74334i	0.788062	−	0.0828286i	0.298057	−	0.954548i	$-0.403662\pi$
$443$	16.5868	−	1.74334i	0.788062	−	0.0828286i	0.490005	+	0.871720i	$0.336995\pi$
$444$	−0.0435835	+	0.229174i	−0.00206838	+	0.0108761i
$445$	8.95530	+	20.1139i	0.424522	+	0.953492i
$446$	−15.8379	+	3.36644i	−0.749944	+	0.159406i
$447$	−1.22635	−	2.60233i	−0.0580044	−	0.123086i
$448$	−4.59464	−	2.04567i	−0.217077	−	0.0966487i
$449$	11.0954	+	34.1480i	0.523622	+	1.61154i	0.767024	+	0.641618i	$0.221737\pi$
$449$	11.0954	+	34.1480i	0.523622	+	1.61154i	−0.243402	+	0.969925i	$0.578263\pi$
$450$	0.247033	+	5.73957i	0.0116452	+	0.270566i
$451$	13.3941	−	30.0836i	0.630703	−	1.41658i
$452$	0.149837	−	0.704927i	0.00704773	−	0.0331570i
$453$	−1.37176	−	1.18272i	−0.0644508	−	0.0555692i
$454$	0.638952	−	0.284480i	0.0299875	−	0.0133513i
$455$	−29.4076	−	32.6605i	−1.37865	−	1.53115i
$456$	−3.47120	+	3.26335i	−0.162554	+	0.152821i
$457$	18.1903	+	25.0369i	0.850908	+	1.17117i	0.983662	+	0.180026i	$0.0576181\pi$
$457$	18.1903	+	25.0369i	0.850908	+	1.17117i	−0.132754	+	0.991149i	$0.542382\pi$
$458$	−1.26587	+	12.0439i	−0.0591500	+	0.562775i
$459$	12.6768	−	16.0498i	0.591704	−	0.749140i
$460$	7.82311	+	4.51668i	0.364754	+	0.210591i
$461$	27.5867	+	20.0429i	1.28484	+	0.933492i	0.999688	−	0.0249900i	$-0.00795539\pi$
$461$	27.5867	+	20.0429i	1.28484	+	0.933492i	0.285154	+	0.958482i	$0.407955\pi$
$462$	−36.0568	−	3.00733i	−1.67751	−	0.139914i
$463$	14.7965	+	4.80769i	0.687654	+	0.223432i	0.631943	−	0.775015i	$-0.282258\pi$
$463$	14.7965	+	4.80769i	0.687654	+	0.223432i	0.0557106	+	0.998447i	$0.482258\pi$
$464$	−1.95264			−0.0906490
$465$	−13.3154	−	10.4694i	−0.617486	−	0.485509i
$466$	−0.627917			−0.0290877
$467$	2.65198	+	0.861682i	0.122719	+	0.0398739i	0.369733	−	0.929138i	$-0.379449\pi$
$467$	2.65198	+	0.861682i	0.122719	+	0.0398739i	−0.247014	+	0.969012i	$0.579449\pi$
$468$	−12.5927	+	8.01148i	−0.582098	+	0.370331i
$469$	−22.9593	−	16.6809i	−1.06016	−	0.770251i
$470$	−6.28347	−	3.62777i	−0.289835	−	0.167336i
$471$	20.9902	+	8.80958i	0.967179	+	0.405924i
$472$	1.02157	−	9.71962i	0.0470217	−	0.447382i
$473$	−0.980672	−	1.34978i	−0.0450913	−	0.0620629i
$474$	−9.48287	−	10.0868i	−0.435562	−	0.463304i
$475$	−3.52461	−	3.91448i	−0.161720	−	0.179609i
$476$	−18.0848	+	8.05186i	−0.828914	+	0.369056i
$477$	1.17288	−	18.9835i	0.0537026	−	0.869193i
$478$	−3.65542	+	17.1974i	−0.167195	+	0.786590i
$479$	−17.4966	+	39.2979i	−0.799438	+	1.79557i	−0.230752	+	0.973013i	$0.574119\pi$
$479$	−17.4966	+	39.2979i	−0.799438	+	1.79557i	−0.568686	+	0.822555i	$0.692548\pi$
$480$	2.49910	+	1.73483i	0.114068	+	0.0791838i
$481$	−0.207061	−	0.637269i	−0.00944118	−	0.0290570i
$482$	10.7527	+	4.78742i	0.489773	+	0.218061i
$483$	40.5277	−	19.0987i	1.84407	−	0.869023i
$484$	6.11464	−	1.29971i	0.277938	−	0.0590776i
$485$	8.99675	+	20.2070i	0.408521	+	0.917554i
$486$	−10.3981	+	11.6138i	−0.471666	+	0.526812i
$487$	24.5501	−	2.58032i	1.11247	−	0.116925i	0.469584	−	0.882888i	$-0.344404\pi$
$487$	24.5501	−	2.58032i	1.11247	−	0.116925i	0.642885	+	0.765962i	$0.277737\pi$
$488$	−2.91032	+	2.11447i	−0.131744	+	0.0957178i
$489$	−2.86284	−	4.72111i	−0.129462	−	0.213496i
$490$	16.0674	+	27.8295i	0.725850	+	1.25721i
$491$	−6.06911	+	10.5120i	−0.273895	+	0.474400i	−0.969856	−	0.243680i	$-0.921645\pi$
$491$	−6.06911	+	10.5120i	−0.273895	+	0.474400i	0.695961	+	0.718080i	$0.254979\pi$
$492$	0.295321	+	13.7293i	0.0133141	+	0.618967i
$493$	−5.14273	+	5.71158i	−0.231617	+	0.257237i
$494$	4.22883	−	13.0150i	0.190264	−	0.585572i
$495$	21.0862	+	5.86178i	0.947753	+	0.263467i
$496$	5.38820	−	1.40261i	0.241937	−	0.0629790i
$497$		−	24.3968i		−	1.09435i
$498$	−11.0113	+	3.84151i	−0.493430	+	0.172142i
$499$	23.9683	+	21.5812i	1.07297	+	0.966107i	0.999513	−	0.0311914i	$-0.00993016\pi$
$499$	23.9683	+	21.5812i	1.07297	+	0.966107i	0.0734570	+	0.997298i	$0.476597\pi$
$500$	−7.13902	+	9.82602i	−0.319267	+	0.439433i
$501$	0.920377	+	7.25270i	0.0411194	+	0.324027i
$502$	11.8038	−	6.81495i	0.526831	−	0.304166i
$503$	−41.8990	−	4.40377i	−1.86819	−	0.196354i	−0.898212	−	0.439563i	$-0.855133\pi$
$503$	−41.8990	−	4.40377i	−1.86819	−	0.196354i	−0.969974	+	0.243209i	$0.921800\pi$
$504$	14.1361	−	5.27531i	0.629674	−	0.234981i
$505$	2.71160	+	25.7992i	0.120665	+	1.14805i
$506$	−15.8746	+	14.2935i	−0.705711	+	0.635425i
$507$	9.79534	−	17.8414i	0.435026	−	0.792366i
$508$	−3.52492	−	16.5834i	−0.156393	−	0.735771i
$509$	−3.33307	−	0.708465i	−0.147736	−	0.0314022i	0.133450	−	0.991056i	$-0.457394\pi$
$509$	−3.33307	−	0.708465i	−0.147736	−	0.0314022i	−0.281186	+	0.959653i	$0.590728\pi$
$510$	11.6564	−	2.74092i	0.516156	−	0.121370i
$511$	−30.9132	+	10.0443i	−1.36752	+	0.444334i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	0.574409	−	14.2814i	0.0253608	−	0.630540i
$514$	−17.5765	−	3.73600i	−0.775266	−	0.164788i
$515$	−2.28359	−	10.7434i	−0.100627	−	0.473413i
$516$	0.609882	+	0.334838i	0.0268486	+	0.0147404i
$517$	12.7504	−	11.4805i	0.560760	−	0.504911i
$518$	0.0708069	+	0.673683i	0.00311108	+	0.0295999i
$519$	−15.5448	−	4.68370i	−0.682340	−	0.205592i
$520$	−8.69044	−	0.913403i	−0.381101	−	0.0400554i
$521$	−4.50543	+	2.60121i	−0.197387	+	0.113961i	−0.595436	−	0.803403i	$-0.703021\pi$
$521$	−4.50543	+	2.60121i	−0.197387	+	0.113961i	0.398049	+	0.917364i	$0.369687\pi$
$522$	4.18070	−	4.10328i	0.182984	−	0.179596i
$523$	−1.49823	+	2.06213i	−0.0655129	+	0.0901707i	−0.840516	−	0.541786i	$-0.817748\pi$
$523$	−1.49823	+	2.06213i	−0.0655129	+	0.0901707i	0.775003	+	0.631957i	$0.217748\pi$
$524$	12.1516	+	10.9413i	0.530844	+	0.477974i
$525$	5.49495	+	15.7508i	0.239819	+	0.687421i
$526$			14.7400i			0.642693i
$527$	10.0884	−	19.4549i	0.439457	−	0.847469i
$528$	−5.72779	+	4.35272i	−0.249270	+	0.189428i
$529$	1.06633	−	3.28181i	0.0463620	−	0.142688i
$530$	7.45114	−	8.27533i	0.323657	−	0.359457i
$531$	18.2376	+	22.9570i	0.791444	+	0.996248i
$532$	−6.91722	+	11.9810i	−0.299900	+	0.519442i
$533$	−19.7223	−	34.1600i	−0.854267	−	1.47963i
$534$	18.5652	−	11.2578i	0.803396	−	0.487172i
$535$	−11.9301	+	8.66774i	−0.515784	+	0.374739i
$536$	−5.61168	+	0.589811i	−0.242388	+	0.0254760i
$537$	12.6475	+	2.40527i	0.545782	+	0.103795i
$538$	−11.7660	−	26.4269i	−0.507268	−	1.13934i
$539$	−74.3292	+	15.7992i	−3.20158	+	0.680518i
$540$	−8.99627	+	1.53724i	−0.387138	+	0.0661522i
$541$	6.92965	+	3.08528i	0.297929	+	0.132647i	0.550257	−	0.834995i	$-0.314530\pi$
$541$	6.92965	+	3.08528i	0.297929	+	0.132647i	−0.252328	+	0.967642i	$0.581196\pi$
$542$	−2.88874	−	8.89063i	−0.124082	−	0.381885i
$543$	6.46736	−	9.31649i	0.277541	−	0.399809i
$544$	−1.60094	+	3.59577i	−0.0686396	+	0.154167i
$545$	0.473025	−	2.22541i	0.0202622	−	0.0953259i
$546$	−28.3002	+	32.8234i	−1.21114	+	1.40471i
$547$	−16.0002	+	7.12375i	−0.684120	+	0.304590i	−0.719208	−	0.694795i	$-0.755495\pi$
$547$	−16.0002	+	7.12375i	−0.684120	+	0.304590i	0.0350887	+	0.999384i	$0.488829\pi$
$548$	3.15471	+	3.50366i	0.134762	+	0.149669i
$549$	1.78780	−	10.6430i	0.0763014	−	0.454231i
$550$	−4.67508	−	6.43470i	−0.199346	−	0.274376i
$551$	−0.561431	+	5.34166i	−0.0239178	+	0.227562i
$552$	3.44736	−	8.21388i	0.146729	−	0.349606i
$553$	−34.8151	−	20.1005i	−1.48049	−	0.854761i
$554$	8.42176	+	6.11876i	0.357806	+	0.259961i
$555$	0.0340564	−	0.408324i	0.00144562	−	0.0173324i
$556$	4.71268	+	1.53124i	0.199862	+	0.0649392i
$557$	−20.4242			−0.865401			−0.432700	−	0.901538i	$-0.642439\pi$
$557$	−20.4242			−0.865401			−0.432700	+	0.901538i	$0.642439\pi$
$558$	−8.58898	+	14.3258i	−0.363600	+	0.606461i
$559$	−1.99844			−0.0845252
$560$	8.40153	+	2.72982i	0.355029	+	0.115356i
$561$	−2.35354	+	28.2180i	−0.0993665	+	1.19137i
$562$	3.08042	+	2.23806i	0.129940	+	0.0944067i
$563$	10.4932	+	6.05824i	0.442235	+	0.255324i	0.704545	−	0.709659i	$-0.251151\pi$
$563$	10.4932	+	6.05824i	0.442235	+	0.255324i	−0.262310	+	0.964984i	$0.584484\pi$
$564$	−2.76890	+	6.59734i	−0.116592	+	0.277798i
$565$	−0.132314	+	1.25888i	−0.00556648	+	0.0529615i
$566$	0.386876	+	0.532489i	0.0162616	+	0.0223822i
$567$	−19.1807	+	41.0005i	−0.805514	+	1.72186i
$568$	−3.24580	−	3.60483i	−0.136191	−	0.151255i
$569$	−18.0767	+	8.04828i	−0.757816	+	0.337402i	−0.749009	−	0.662560i	$-0.769470\pi$
$569$	−18.0767	+	8.04828i	−0.757816	+	0.337402i	−0.00880727	+	0.999961i	$0.502803\pi$
$570$	5.46437	−	6.33775i	0.228877	−	0.265459i
$571$	3.62896	−	17.0729i	0.151867	−	0.714478i	−0.834645	−	0.550789i	$-0.814327\pi$
$571$	3.62896	−	17.0729i	0.151867	−	0.714478i	0.986512	−	0.163690i	$-0.0523396\pi$
$572$	8.40467	−	18.8772i	0.351417	−	0.789296i
$573$	9.55880	−	13.7698i	0.399325	−	0.575244i
$574$	12.3224	+	37.9243i	0.514325	+	1.58293i
$575$	8.99723	+	4.00583i	0.375211	+	0.167054i
$576$	1.38689	−	2.66017i	0.0577872	−	0.110841i
$577$	−22.0402	+	4.68479i	−0.917546	+	0.195030i	−0.642398	−	0.766371i	$-0.722060\pi$
$577$	−22.0402	+	4.68479i	−0.917546	+	0.195030i	−0.275148	+	0.961402i	$0.588727\pi$
$578$	−0.613143	−	1.37714i	−0.0255034	−	0.0572816i
$579$	33.6276	+	6.39519i	1.39751	+	0.265775i
$580$	3.41088	−	0.358498i	0.141629	−	0.0148858i
$581$	−27.3968	+	19.9049i	−1.13661	+	0.825795i
$582$	18.6511	−	11.3099i	0.773115	−	0.468810i
$583$	13.1662	+	22.8046i	0.545290	+	0.944469i
$584$	−3.23136	+	5.59689i	−0.133715	+	0.231601i
$585$	20.5261	−	16.3065i	0.848651	−	0.674190i
$586$	9.23613	−	10.2578i	0.381541	−	0.423744i
$587$	9.37400	−	28.8502i	0.386906	−	1.19077i	−0.548182	−	0.836359i	$-0.684680\pi$
$587$	9.37400	−	28.8502i	0.386906	−	1.19077i	0.935088	−	0.354416i	$-0.115320\pi$
$588$	25.2303	−	19.1732i	1.04048	−	0.790689i
$589$	−2.28775	−	15.1433i	−0.0942653	−	0.623969i
$590$			17.1659i			0.706707i
$591$	3.50543	+	10.0480i	0.144194	+	0.413320i
$592$	0.100090	+	0.0901219i	0.00411369	+	0.00370399i
$593$	−18.5909	+	25.5882i	−0.763436	+	1.05078i	0.233484	+	0.972361i	$0.424987\pi$
$593$	−18.5909	+	25.5882i	−0.763436	+	1.05078i	−0.996920	+	0.0784190i	$0.975013\pi$
$594$	3.11671	−	21.3558i	0.127880	−	0.876239i
$595$	30.1123	−	17.3853i	1.23448	−	0.712729i
$596$	−1.65183	−	0.173614i	−0.0676615	−	0.00711151i
$597$	−4.10241	−	1.23607i	−0.167900	−	0.0505890i
$598$	2.67455	+	25.4466i	0.109370	+	1.04059i
$599$	26.5065	−	23.8665i	1.08302	−	0.975160i	0.0832527	−	0.996528i	$-0.473469\pi$
$599$	26.5065	−	23.8665i	1.08302	−	0.975160i	0.999772	+	0.0213689i	$0.00680246\pi$
$600$	2.90744	+	1.59625i	0.118696	+	0.0651666i
$601$	−3.46814	−	16.3163i	−0.141468	−	0.665555i	−0.990534	−	0.137268i	$-0.956168\pi$
$601$	−3.46814	−	16.3163i	−0.141468	−	0.665555i	0.849066	−	0.528287i	$-0.177166\pi$
$602$	1.97615	+	0.420045i	0.0805420	+	0.0171197i
$603$	10.7755	−	13.0552i	0.438811	−	0.531649i
$604$	−0.994533	+	0.323143i	−0.0404670	+	0.0131485i
$605$	−10.4425	+	3.39296i	−0.424547	+	0.137944i
$606$	24.9021	−	5.85552i	1.01158	−	0.237864i
$607$	−3.30567	−	0.702643i	−0.134173	−	0.0285194i	0.140336	−	0.990104i	$-0.455182\pi$
$607$	−3.30567	−	0.702643i	−0.134173	−	0.0285194i	−0.274509	+	0.961585i	$0.588515\pi$
$608$	0.571899	+	2.69057i	0.0231936	+	0.109117i
$609$	8.18624	−	14.9106i	0.331723	−	0.604207i
$610$	4.69556	−	4.22790i	0.190118	−	0.171183i
$611$	−2.14818	−	20.4386i	−0.0869061	−	0.826856i
$612$	−4.12845	−	11.0629i	−0.166883	−	0.447193i
$613$	37.8104	+	3.97403i	1.52715	+	0.160510i	0.830547	−	0.556949i	$-0.188028\pi$
$613$	37.8104	+	3.97403i	1.52715	+	0.160510i	0.696601	+	0.717459i	$0.254695\pi$
$614$	−28.3842	+	16.3876i	−1.14549	+	0.661351i
$615$	−3.03653	−	23.9283i	−0.122445	−	0.964881i
$616$	−12.2787	+	16.9001i	−0.494721	+	0.680925i
$617$	−0.254194	−	0.228877i	−0.0102335	−	0.00921425i	0.663998	−	0.747734i	$-0.268858\pi$
$617$	−0.254194	−	0.228877i	−0.0102335	−	0.00921425i	−0.674231	+	0.738520i	$0.735525\pi$
$618$	−10.2266	+	3.56772i	−0.411372	+	0.143515i
$619$		−	35.3995i		−	1.42282i	−0.702775	−	0.711412i	$-0.748056\pi$
$619$		−	35.3995i		−	1.42282i	0.702775	−	0.711412i	$-0.251944\pi$
$620$	−9.15462	+	3.43934i	−0.367658	+	0.138127i
$621$	9.87969	+	24.8306i	0.396458	+	0.996419i
$622$	−5.18124	+	15.9462i	−0.207749	+	0.639385i
$623$	42.1861	−	46.8524i	1.69015	−	1.87710i
$624$	0.185311	+	8.61504i	0.00741839	+	0.344878i
$625$	5.87906	−	10.1828i	0.235162	−	0.407313i
$626$	5.12998	+	8.88538i	0.205035	+	0.355131i
$627$	10.2605	+	16.9205i	0.409763	+	0.675741i
$628$	10.6327	−	7.72514i	0.424292	−	0.308266i
$629$	0.527223	−	0.0554134i	0.0210218	−	0.00220948i
$630$	−23.7246	+	11.8103i	−0.945210	+	0.470533i
$631$	11.0349	+	24.7849i	0.439294	+	0.986670i	0.988533	+	0.151005i	$0.0482508\pi$
$631$	11.0349	+	24.7849i	0.439294	+	0.986670i	−0.549239	+	0.835665i	$0.685082\pi$
$632$	−7.81844	+	1.66186i	−0.311001	+	0.0661052i
$633$	−40.6111	+	19.1381i	−1.61415	+	0.760671i
$634$	−16.7166	−	7.44269i	−0.663899	−	0.295587i
$635$	9.20201	+	28.3209i	0.365171	+	1.12388i
$636$	−9.02057	−	6.26193i	−0.357689	−	0.248302i
$637$	−37.0216	+	83.1519i	−1.46685	+	3.29460i
$638$	−1.68621	+	7.93298i	−0.0667576	+	0.314070i
$639$	14.5246	+	0.897395i	0.574585	+	0.0355004i
$640$	1.60458	−	0.714403i	0.0634265	−	0.0282393i
$641$	−23.5475	−	26.1522i	−0.930071	−	1.03295i	−0.999375	−	0.0353531i	$-0.988744\pi$
$641$	−23.5475	−	26.1522i	−0.930071	−	1.03295i	0.0693037	−	0.997596i	$-0.477922\pi$
$642$	9.96050	+	10.5949i	0.393109	+	0.418147i
$643$	−6.14520	−	8.45814i	−0.242343	−	0.333556i	0.670468	−	0.741938i	$-0.266093\pi$
$643$	−6.14520	−	8.45814i	−0.242343	−	0.333556i	−0.912811	+	0.408382i	$0.866093\pi$
$644$	2.70380	−	25.7250i	0.106545	−	1.01371i
$645$	−1.12682	−	0.472925i	−0.0443685	−	0.0186214i
$646$	9.37631	+	5.41341i	0.368906	+	0.212988i
$647$	29.3878	+	21.3515i	1.15535	+	0.839414i	0.989184	−	0.146683i	$-0.0468598\pi$
$647$	29.3878	+	21.3515i	1.15535	+	0.839414i	0.166170	+	0.986097i	$0.446860\pi$
$648$	2.62068	+	8.61000i	0.102950	+	0.338233i
$649$	−38.6057	−	12.5438i	−1.51541	−	0.492386i
$650$	−9.52703			−0.373681
$651$	−11.8790	+	47.0252i	−0.465574	+	1.84306i
$652$	−3.18772			−0.124841
$653$	17.1285	+	5.56539i	0.670290	+	0.217791i	0.624340	−	0.781153i	$-0.285368\pi$
$653$	17.1285	+	5.56539i	0.670290	+	0.217791i	0.0459510	+	0.998944i	$0.485368\pi$
$654$	−2.23578	−	0.186477i	−0.0874261	−	0.00729182i
$655$	−23.2352	−	16.8814i	−0.907876	−	0.659610i
$656$	6.86626	+	3.96424i	0.268082	+	0.154777i
$657$	−4.84278	−	18.7736i	−0.188935	−	0.732429i
$658$	−2.17168	+	20.6621i	−0.0846608	+	0.805493i
$659$	−22.6931	−	31.2343i	−0.883997	−	1.21672i	−0.975298	−	0.220894i	$-0.929102\pi$
$659$	−22.6931	−	31.2343i	−0.883997	−	1.21672i	0.0913008	−	0.995823i	$-0.470898\pi$
$660$	9.20620	−	8.65495i	0.358351	−	0.336894i
$661$	7.77409	+	8.63400i	0.302377	+	0.335824i	0.875115	−	0.483915i	$-0.160785\pi$
$661$	7.77409	+	8.63400i	0.302377	+	0.335824i	−0.572738	+	0.819738i	$0.694119\pi$
$662$	−25.3746	+	11.2975i	−0.986212	+	0.439090i
$663$	25.6876	+	22.1477i	0.997623	+	0.860145i
$664$	−1.39991	+	6.58604i	−0.0543269	+	0.255588i
$665$	9.88338	−	22.1984i	0.383261	−	0.860818i
$666$	−0.403681	+	0.0173746i	−0.0156423	+	0.000673251i
$667$	−3.10329	−	9.55096i	−0.120160	−	0.369814i
$668$	3.85601	+	1.71681i	0.149194	+	0.0664252i
$669$	−11.9552	−	25.3690i	−0.462214	−	0.980822i
$670$	9.69422	−	2.06057i	0.374521	−	0.0796068i
$671$	6.07725	+	13.6497i	0.234610	+	0.526942i
$672$	1.62752	−	8.55790i	0.0627828	−	0.330128i
$673$	1.03021	−	0.108280i	0.0397118	−	0.00417388i	−0.0846517	−	0.996411i	$-0.526978\pi$
$673$	1.03021	−	0.108280i	0.0397118	−	0.00417388i	0.124364	+	0.992237i	$0.460311\pi$
$674$	13.7426	−	9.98456i	0.529344	−	0.384591i
$675$	−9.57935	+	2.69205i	−0.368709	+	0.103617i
$676$	−5.87556	−	10.1768i	−0.225983	−	0.391414i
$677$	−10.5730	+	18.3129i	−0.406352	+	0.703823i	−0.994478	−	0.104947i	$-0.966533\pi$
$677$	−10.5730	+	18.3129i	−0.406352	+	0.703823i	0.588126	+	0.808770i	$0.299866\pi$
$678$	1.24796	−	0.0268438i	0.0479275	−	0.00103093i
$679$	42.3813	−	47.0692i	1.62645	−	1.80635i
$680$	2.13636	−	6.57503i	0.0819255	−	0.252141i
$681$	0.732973	+	0.964529i	0.0280876	+	0.0369608i
$682$	−1.04538	−	23.1019i	−0.0400297	−	0.884616i
$683$			29.6799i			1.13567i	0.823142	+	0.567835i	$0.192219\pi$
$683$			29.6799i			1.13567i	−0.823142	+	0.567835i	$0.807781\pi$
$684$	−6.87844	−	4.55887i	−0.263004	−	0.174313i
$685$	−6.15392	−	5.54101i	−0.235129	−	0.211711i
$686$	33.3923	−	45.9606i	1.27492	−	1.75478i
$687$	−20.8087	+	2.64065i	−0.793900	+	0.100747i
$688$	0.347877	−	0.200847i	0.0132627	−	0.00765721i
$689$	31.3684	+	3.29696i	1.19504	+	0.125604i
$690$	−4.51382	+	14.9810i	−0.171838	+	0.570316i
$691$	−4.38106	−	41.6830i	−0.166663	−	1.58570i	−0.683719	−	0.729745i	$-0.739639\pi$
$691$	−4.38106	−	41.6830i	−0.166663	−	1.58570i	0.517056	−	0.855952i	$-0.327028\pi$
$692$	−6.96573	+	6.27197i	−0.264797	+	0.238425i
$693$	−9.22468	−	61.9864i	−0.350417	−	2.35467i
$694$	2.37715	+	11.1836i	0.0902354	+	0.424524i
$695$	−8.51327	−	1.80955i	−0.322927	−	0.0686402i
$696$	−0.774152	−	3.29228i	−0.0293442	−	0.124793i
$697$	29.6795	−	9.64347i	1.12419	−	0.365272i
$698$	13.1968	−	4.28790i	0.499506	−	0.162299i
$699$	−0.248947	−	1.05871i	−0.00941603	−	0.0400440i
$700$	9.42077	+	2.00245i	0.356072	+	0.0756853i
$701$	1.08350	+	5.09748i	0.0409234	+	0.192529i	0.993861	−	0.110638i	$-0.0352893\pi$
$701$	1.08350	+	5.09748i	0.0409234	+	0.192529i	−0.952937	+	0.303167i	$0.901956\pi$
$702$	−18.5004	−	18.0559i	−0.698254	−	0.681474i
$703$	0.275317	−	0.247896i	0.0103838	−	0.00934959i
$704$	0.434155	+	4.13071i	0.0163628	+	0.155682i
$705$	3.62547	−	12.0326i	0.136543	−	0.453175i
$706$	28.8285	+	3.03000i	1.08498	+	0.114036i
$707$	64.3300	−	37.1409i	2.41938	−	1.39683i
$708$	16.7929	−	2.13105i	0.631117	−	0.0800896i
$709$	−6.99628	+	9.62955i	−0.262751	+	0.361645i	−0.919926	−	0.392093i	$-0.871751\pi$
$709$	−6.99628	+	9.62955i	−0.262751	+	0.361645i	0.657175	+	0.753738i	$0.271751\pi$
$710$	6.33162	+	5.70101i	0.237621	+	0.213955i
$711$	13.2475	−	19.9878i	0.496818	−	0.749601i
$712$		−	12.5354i		−	0.469782i
$713$	15.4240	+	24.1262i	0.577632	+	0.903533i
$714$	−20.7459	−	27.2998i	−0.776397	−	1.02167i
$715$	−11.2155	+	34.5179i	−0.419437	+	1.29090i
$716$	4.97361	−	5.52375i	0.185872	−	0.206432i
$717$	−30.4452	+	0.654881i	−1.13700	+	0.0244570i
$718$	8.94840	−	15.4991i	0.333951	−	0.578421i
$719$	12.7348	+	22.0573i	0.474928	+	0.822600i	0.999588	−	0.0287124i	$-0.00914071\pi$
$719$	12.7348	+	22.0573i	0.474928	+	0.822600i	−0.524660	+	0.851312i	$0.675807\pi$
$720$	−1.93424	+	4.90144i	−0.0720847	+	0.182666i
$721$	−25.4442	+	18.4863i	−0.947590	+	0.688465i
$722$	−11.3711	+	1.19515i	−0.423189	+	0.0444790i
$723$	−3.80883	+	20.0278i	−0.141652	+	0.744843i
$724$	−2.66326	−	5.98177i	−0.0989792	−	0.222311i
$725$	3.65752	−	0.777429i	0.135837	−	0.0288730i
$726$	4.61563	+	9.79440i	0.171302	+	0.363504i
$727$	−14.2499	−	6.34446i	−0.528499	−	0.235303i	0.125100	−	0.992144i	$-0.460075\pi$
$727$	−14.2499	−	6.34446i	−0.528499	−	0.235303i	−0.653599	+	0.756841i	$0.726742\pi$
$728$	7.73217	+	23.7972i	0.286573	+	0.881982i
$729$	−23.7041	−	12.9274i	−0.877929	−	0.478791i
$730$	4.61700	−	10.3699i	0.170883	−	0.383809i
$731$	0.328727	−	1.54654i	0.0121584	−	0.0572007i
$732$	−4.71898	−	4.06868i	−0.174419	−	0.150383i
$733$	−24.0416	+	10.7040i	−0.887997	+	0.395362i	−0.799466	−	0.600712i	$-0.794884\pi$
$733$	−24.0416	+	10.7040i	−0.887997	+	0.395362i	−0.0885311	+	0.996073i	$0.528217\pi$
$734$	12.5678	+	13.9579i	0.463885	+	0.515196i
$735$	−40.5522	+	38.1240i	−1.49579	+	1.40623i
$736$	−3.02299	−	4.16079i	−0.111429	−	0.153369i
$737$	−2.44976	+	23.3079i	−0.0902380	+	0.858557i
$738$	−23.0315	+	5.94113i	−0.847801	+	0.218696i
$739$	−10.0189	−	5.78440i	−0.368551	−	0.212783i	0.304275	−	0.952584i	$-0.401586\pi$
$739$	−10.0189	−	5.78440i	−0.368551	−	0.212783i	−0.672825	+	0.739802i	$0.734919\pi$
$740$	−0.191385	−	0.139049i	−0.00703544	−	0.00511155i
$741$	23.6207	+	1.97010i	0.867728	+	0.0723733i
$742$	−30.3256	−	9.85338i	−1.11329	−	0.361729i
$743$	−19.1118			−0.701145			−0.350572	−	0.936536i	$-0.614013\pi$
$743$	−19.1118			−0.701145			−0.350572	+	0.936536i	$0.614013\pi$
$744$	4.50112	+	8.52877i	0.165019	+	0.312680i
$745$	2.91730			0.106882
$746$	−11.7991	−	3.83376i	−0.431995	−	0.140364i
$747$	−10.8426	−	17.0428i	−0.396712	−	0.623565i
$748$	13.2260	+	9.60926i	0.483591	+	0.351349i
$749$	36.5687	+	21.1129i	1.33619	+	0.771450i
$750$	−19.3977	−	8.14119i	−0.708303	−	0.297274i
$751$	2.26921	−	21.5901i	0.0828047	−	0.787834i	−0.871781	−	0.489897i	$-0.837035\pi$
$751$	2.26921	−	21.5901i	0.0828047	−	0.787834i	0.954585	−	0.297938i	$-0.0962988\pi$
$752$	2.42805	+	3.34192i	0.0885419	+	0.121867i
$753$	16.1703	+	17.2002i	0.589277	+	0.626809i
$754$	6.50025	+	7.21926i	0.236725	+	0.262910i
$755$	1.67793	−	0.747062i	0.0610661	−	0.0271884i
$756$	14.4990	+	21.7430i	0.527324	+	0.790785i
$757$	0.264939	−	1.24644i	0.00962939	−	0.0453027i	−0.973071	−	0.230507i	$-0.925961\pi$
$757$	0.264939	−	1.24644i	0.00962939	−	0.0453027i	0.982700	+	0.185205i	$0.0592948\pi$
$758$	−1.87777	+	4.21754i	−0.0682036	+	0.153188i
$759$	−30.3935	−	21.0987i	−1.10322	−	0.765834i
$760$	−1.49298	−	4.59491i	−0.0541559	−	0.166675i
$761$	5.92691	+	2.63883i	0.214850	+	0.0956575i	0.511340	−	0.859379i	$-0.329149\pi$
$761$	5.92691	+	2.63883i	0.214850	+	0.0956575i	−0.296490	+	0.955036i	$0.595816\pi$
$762$	26.5632	−	12.5180i	0.962285	−	0.453479i
$763$	−6.37237	+	1.35449i	−0.230695	+	0.0490358i
$764$	−3.93632	−	8.84111i	−0.142411	−	0.319860i
$765$	9.24273	+	18.5668i	0.334171	+	0.671285i
$766$	−25.0371	+	2.63150i	−0.904625	+	0.0950800i
$767$	−39.3360	+	28.5793i	−1.42034	+	1.03194i
$768$	−0.898083	−	1.48103i	−0.0324068	−	0.0534420i
$769$	−22.8211	−	39.5273i	−0.822950	−	1.42539i	−0.903476	−	0.428639i	$-0.858993\pi$
$769$	−22.8211	−	39.5273i	−0.822950	−	1.42539i	0.0805257	−	0.996753i	$-0.474340\pi$
$770$	18.3456	−	31.7755i	0.661130	−	1.14511i
$771$	−0.669318	−	31.1163i	−0.0241049	−	1.12063i
$772$	13.2239	−	14.6867i	0.475940	−	0.528585i
$773$	10.2933	−	31.6796i	0.370225	−	1.13943i	−0.576420	−	0.817154i	$-0.695551\pi$
$773$	10.2933	−	31.6796i	0.370225	−	1.13943i	0.946644	−	0.322280i	$-0.104449\pi$
$774$	−0.322763	+	1.16105i	−0.0116015	+	0.0417332i
$775$	−9.53428	+	4.77252i	−0.342481	+	0.171434i
$776$		−	12.5934i		−	0.452076i
$777$	−1.10780	+	0.386476i	−0.0397421	+	0.0138648i
$778$	−12.1996	−	10.9846i	−0.437378	−	0.393817i
$779$	12.8188	−	17.6436i	0.459282	−	0.632148i
$780$	−1.90540	−	15.0148i	−0.0682241	−	0.537616i
$781$	−17.4482	+	10.0737i	−0.624347	+	0.360467i
$782$	−20.1323	−	2.11599i	−0.719931	−	0.0756678i
$783$	8.57590	+	5.42213i	0.306478	+	0.193771i
$784$	−1.91240	−	18.1953i	−0.0683001	−	0.649832i
$785$	−17.1550	+	15.4464i	−0.612289	+	0.551307i
$786$	−13.6301	+	24.8262i	−0.486170	+	0.885521i
$787$	11.5782	+	54.4714i	0.412720	+	1.94169i	0.325645	+	0.945492i	$0.394419\pi$
$787$	11.5782	+	54.4714i	0.412720	+	1.94169i	0.0870753	+	0.996202i	$0.472248\pi$
$788$	6.00986	+	1.27744i	0.214092	+	0.0455067i
$789$	−24.8525	+	5.84387i	−0.884774	+	0.208047i
$790$	13.3522	−	4.33839i	0.475049	−	0.154353i
$791$	3.44721	−	1.12007i	0.122569	−	0.0398250i
$792$	−9.60983	−	7.93173i	−0.341470	−	0.281842i
$793$	17.5059	+	3.72100i	0.621654	+	0.132137i
$794$	−3.64430	−	17.1451i	−0.129331	−	0.608456i
$795$	16.9068	+	9.28223i	0.599624	+	0.329207i
$796$	−1.83832	+	1.65523i	−0.0651575	+	0.0586681i
$797$	−0.991228	−	9.43090i	−0.0351111	−	0.334060i	−0.997951	−	0.0639862i	$-0.979619\pi$
$797$	−0.991228	−	9.43090i	−0.0351111	−	0.334060i	0.962840	−	0.270074i	$-0.0870480\pi$
$798$	−22.9432	−	6.91286i	−0.812179	−	0.244712i
$799$	16.1702	+	1.69955i	0.572059	+	0.0601259i
$800$	1.65841	−	0.957481i	0.0586335	−	0.0338521i
$801$	26.3418	+	26.8389i	0.930743	+	0.948305i
$802$	−18.4429	+	25.3845i	−0.651243	+	0.896359i
$803$	19.9480	+	17.9613i	0.703950	+	0.633839i
$804$	−3.21929	−	9.22781i	−0.113536	−	0.325440i
$805$			45.4329i			1.60130i
$806$	−23.1228	−	15.2519i	−0.814465	−	0.537226i
$807$	39.8926	−	30.3155i	1.40429	−	1.06716i
$808$	4.56398	−	14.0465i	0.160560	−	0.494153i
$809$	12.4087	−	13.7812i	0.436265	−	0.484522i	−0.484416	−	0.874838i	$-0.660968\pi$
$809$	12.4087	−	13.7812i	0.436265	−	0.484522i	0.920681	+	0.390316i	$0.127634\pi$
$810$	−6.15859	−	14.5588i	−0.216391	−	0.511546i
$811$	14.0012	−	24.2508i	0.491649	−	0.851561i	−0.508305	−	0.861177i	$-0.669728\pi$
$811$	14.0012	−	24.2508i	0.491649	−	0.851561i	0.999954	+	0.00961643i	$0.00306105\pi$
$812$	−4.91036	−	8.50500i	−0.172320	−	0.298467i
$813$	13.8449	−	8.39542i	0.485562	−	0.294440i
$814$	0.452571	−	0.328812i	0.0158626	−	0.0115249i
$815$	5.56833	−	0.585255i	0.195050	−	0.0205006i
$816$	−6.69741	−	1.27369i	−0.234456	−	0.0445881i
$817$	−0.449416	−	1.00940i	−0.0157231	−	0.0353146i
$818$	−17.8404	+	3.79209i	−0.623774	+	0.132587i
$819$	−66.5624	−	34.7026i	−2.32588	−	1.21261i
$820$	−12.7218	−	5.66413i	−0.444266	−	0.197800i
$821$	−15.8746	−	48.8570i	−0.554028	−	1.70512i	−0.698498	−	0.715612i	$-0.746148\pi$
$821$	−15.8746	−	48.8570i	−0.554028	−	1.70512i	0.144470	−	0.989509i	$-0.453852\pi$
$822$	−4.65666	+	6.70812i	−0.162420	+	0.233972i
$823$	4.89364	−	10.9913i	0.170581	−	0.383132i	−0.807944	−	0.589260i	$-0.799419\pi$
$823$	4.89364	−	10.9913i	0.170581	−	0.383132i	0.978525	+	0.206127i	$0.0660861\pi$
$824$	−1.30013	+	6.11664i	−0.0452923	+	0.213083i
$825$	8.99581	−	10.4336i	0.313194	−	0.363252i
$826$	44.9042	−	19.9926i	1.56242	−	0.695633i
$827$	34.4731	+	38.2863i	1.19875	+	1.33134i	0.929745	+	0.368204i	$0.120027\pi$
$827$	34.4731	+	38.2863i	1.19875	+	1.33134i	0.269002	+	0.963140i	$0.413306\pi$
$828$	15.2159	+	2.55596i	0.528789	+	0.0888257i
$829$	−11.0611	−	15.2243i	−0.384167	−	0.528760i	0.572516	−	0.819894i	$-0.305968\pi$
$829$	−11.0611	−	15.2243i	−0.384167	−	0.528760i	−0.956682	+	0.291134i	$0.905968\pi$
$830$	1.23619	−	11.7616i	0.0429087	−	0.408249i
$831$	−6.97771	+	16.6255i	−0.242054	+	0.576732i
$832$	4.30852	+	2.48752i	0.149371	+	0.0862394i
$833$	−58.2591	−	42.3277i	−2.01856	−	1.46657i
$834$	−0.713365	+	8.55298i	−0.0247018	+	0.296165i
$835$	−7.05090	−	2.29098i	−0.244006	−	0.0792825i
$836$	11.4248			0.395137
$837$	−27.5595	−	8.80189i	−0.952596	−	0.304238i
$838$	25.7470			0.889415
$839$	34.3792	+	11.1705i	1.18690	+	0.385648i	0.834927	−	0.550361i	$-0.185510\pi$
$839$	34.3792	+	11.1705i	1.18690	+	0.385648i	0.351975	+	0.936009i	$0.385510\pi$
$840$	−1.27175	+	15.2478i	−0.0438796	+	0.526099i
$841$	20.3769	+	14.8047i	0.702651	+	0.510506i
$842$	26.5964	+	15.3555i	0.916573	+	0.529184i
$843$	−2.55223	+	6.08110i	−0.0879035	+	0.209444i
$844$	−2.70937	+	25.7780i	−0.0932604	+	0.887314i
$845$	12.1319	+	16.6981i	0.417349	+	0.574432i
$846$	−12.2213	−	2.05293i	−0.420177	−	0.0705812i
$847$	21.0377	+	23.3648i	0.722866	+	0.802824i
$848$	−5.79177	+	2.57866i	−0.198890	+	0.0885517i
$849$	−0.744428	+	0.863410i	−0.0255487	+	0.0296322i
$850$	1.56711	−	7.37269i	0.0537515	−	0.252881i
$851$	−0.281742	+	0.632802i	−0.00965798	+	0.0216922i
$852$	4.79113	−	6.90182i	0.164141	−	0.236452i
$853$	−0.124823	−	0.384167i	−0.00427387	−	0.0131536i	0.948897	−	0.315586i	$-0.102201\pi$
$853$	−0.124823	−	0.384167i	−0.00427387	−	0.0131536i	−0.953171	+	0.302433i	$0.902201\pi$
$854$	−16.5286	−	7.35900i	−0.565597	−	0.251820i
$855$	12.8523	+	6.70060i	0.439539	+	0.229156i
$856$	8.21223	−	1.74556i	0.280688	−	0.0596621i
$857$	−2.45165	−	5.50649i	−0.0837467	−	0.188098i	0.866818	−	0.498625i	$-0.166161\pi$
$857$	−2.45165	−	5.50649i	−0.0837467	−	0.188098i	−0.950565	+	0.310526i	$0.899495\pi$
$858$	35.1604	+	6.68669i	1.20035	+	0.228280i
$859$	−16.1411	+	1.69650i	−0.550726	+	0.0578837i	−0.375805	−	0.926699i	$-0.622634\pi$
$859$	−16.1411	+	1.69650i	−0.550726	+	0.0578837i	−0.174921	+	0.984582i	$0.555967\pi$
$860$	−0.570798	+	0.414709i	−0.0194641	+	0.0141415i
$861$	−59.0575	+	35.8119i	−2.01267	+	1.22047i
$862$	−16.8143	−	29.1232i	−0.572698	−	0.991942i
$863$	4.32367	−	7.48881i	0.147179	−	0.254922i	−0.783005	−	0.622016i	$-0.786314\pi$
$863$	4.32367	−	7.48881i	0.147179	−	0.254922i	0.930184	+	0.367094i	$0.119647\pi$
$864$	5.03508	+	1.28373i	0.171297	+	0.0436734i
$865$	11.0163	−	12.2348i	0.374564	−	0.415996i
$866$	3.23366	−	9.95218i	0.109884	−	0.338189i
$867$	2.07886	−	1.57979i	0.0706019	−	0.0536524i
$868$	19.6591	+	19.9419i	0.667275	+	0.676872i
$869$			33.1991i			1.12620i
$870$	1.95674	+	5.60883i	0.0663398	+	0.190157i
$871$	20.8617	+	18.7839i	0.706871	+	0.636469i
$872$	−0.761366	+	1.04793i	−0.0257831	+	0.0354874i
$873$	26.4637	+	26.9631i	0.895662	+	0.912562i
$874$	−12.2515	+	7.07341i	−0.414413	+	0.239262i
$875$	−60.7514	−	6.38523i	−2.05377	−	0.215860i
$876$	−10.7178	−	3.22932i	−0.362122	−	0.109109i
$877$	0.978434	+	9.30918i	0.0330394	+	0.314349i	0.998543	+	0.0539595i	$0.0171842\pi$
$877$	0.978434	+	9.30918i	0.0330394	+	0.314349i	−0.965504	+	0.260389i	$0.916149\pi$
$878$	−9.55763	+	8.60573i	−0.322554	+	0.290429i
$879$	20.9571	+	11.5059i	0.706864	+	0.388084i
$880$	−1.51677	−	7.13584i	−0.0511303	−	0.240549i
$881$	27.4880	+	5.84276i	0.926095	+	0.196848i	0.646187	−	0.763179i	$-0.276363\pi$
$881$	27.4880	+	5.84276i	0.926095	+	0.196848i	0.279908	+	0.960027i	$0.409696\pi$
$882$	42.3302	+	34.9384i	1.42533	+	1.17644i
$883$	3.14980	−	1.02343i	0.105999	−	0.0344412i	−0.255537	−	0.966799i	$-0.582252\pi$
$883$	3.14980	−	1.02343i	0.105999	−	0.0344412i	0.361536	+	0.932358i	$0.382252\pi$
$884$	18.6237	−	6.05119i	0.626381	−	0.203524i
$885$	−28.9427	+	6.80565i	−0.972900	+	0.228769i
$886$	16.3137	+	3.46758i	0.548069	+	0.116496i
$887$	−6.92772	−	32.5924i	−0.232610	−	1.09434i	−0.927092	−	0.374834i	$-0.877700\pi$
$887$	−6.92772	−	32.5924i	−0.232610	−	1.09434i	0.694482	−	0.719510i	$-0.255634\pi$
$888$	−0.112269	+	0.204489i	−0.00376750	+	0.00686221i
$889$	63.3673	−	57.0562i	2.12527	−	1.91360i
$890$	2.30145	+	21.8968i	0.0771448	+	0.733984i
$891$	37.2429	−	3.21184i	1.24768	−	0.107601i
$892$	−16.1030	−	1.69249i	−0.539168	−	0.0566688i
$893$	9.84033	−	5.68132i	0.329294	−	0.190118i
$894$	−0.362167	−	2.85392i	−0.0121127	−	0.0954495i
$895$	−7.67378	+	10.5621i	−0.256506	+	0.353050i
$896$	−3.73762	−	3.36537i	−0.124865	−	0.112429i
$897$	−41.8443	+	14.5982i	−1.39714	+	0.487418i
$898$			35.9053i			1.19818i
$899$	10.1217	+	3.96848i	0.337576	+	0.132356i
$900$	−1.53868	+	5.53499i	−0.0512894	+	0.184500i
$901$	−7.71125	+	23.7328i	−0.256899	+	0.790654i
$902$	22.0349	−	24.4722i	0.733681	−	0.814836i
$903$	0.0752525	+	3.49846i	0.00250425	+	0.116421i
$904$	0.360338	−	0.624123i	0.0119847	−	0.0207580i
$905$	5.75043	+	9.96003i	0.191151	+	0.331083i
$906$	−0.939138	−	1.54873i	−0.0312008	−	0.0514532i
$907$	6.78734	−	4.93129i	0.225370	−	0.163741i	−0.469371	−	0.883001i	$-0.655519\pi$
$907$	6.78734	−	4.93129i	0.225370	−	0.163741i	0.694741	+	0.719260i	$0.255519\pi$
$908$	0.695589	−	0.0731093i	0.0230839	−	0.00242622i
$909$	19.7456	+	39.6650i	0.654920	+	1.31561i
$910$	−17.8757	−	40.1494i	−0.592573	−	1.33094i
$911$	36.9801	−	7.86037i	1.22521	−	0.260426i	0.450517	−	0.892768i	$-0.351240\pi$
$911$	36.9801	−	7.86037i	1.22521	−	0.260426i	0.774689	+	0.632342i	$0.217906\pi$
$912$	−4.30974	+	2.03097i	−0.142710	+	0.0672523i
$913$	25.5482	+	11.3748i	0.845522	+	0.376451i
$914$	9.56323	+	29.4326i	0.316324	+	0.973544i
$915$	8.99014	+	6.24081i	0.297205	+	0.206315i
$916$	−4.92568	+	11.0633i	−0.162749	+	0.365540i
$917$	−17.0986	+	80.4425i	−0.564645	+	2.65644i
$918$	17.0161	−	11.3469i	0.561613	−	0.374504i
$919$	39.4530	−	17.5656i	1.30144	−	0.579436i	0.365239	−	0.930914i	$-0.380987\pi$
$919$	39.4530	−	17.5656i	1.30144	−	0.579436i	0.936196	+	0.351477i	$0.114321\pi$
$920$	6.04449	+	6.71309i	0.199281	+	0.221324i
$921$	−38.8839	−	41.3605i	−1.28127	−	1.36287i
$922$	20.0429	+	27.5867i	0.660078	+	0.908520i
$923$	−2.52257	+	24.0006i	−0.0830313	+	0.789990i
$924$	−33.3627	−	14.0023i	−1.09755	−	0.460642i
$925$	−0.223362	−	0.128958i	−0.00734411	−	0.00424012i
$926$	12.5867	+	9.14477i	0.413624	+	0.300516i
$927$	−10.0699	−	15.8282i	−0.330738	−	0.519865i
$928$	−1.85707	−	0.603399i	−0.0609613	−	0.0198075i
$929$	−27.0438			−0.887277			−0.443639	−	0.896206i	$-0.646313\pi$
$929$	−27.0438			−0.887277			−0.443639	+	0.896206i	$0.646313\pi$
$930$	−9.42844	−	14.0717i	−0.309171	−	0.461430i
$931$	−50.3251			−1.64934
$932$	−0.597184	−	0.194037i	−0.0195614	−	0.00635589i
$933$	−28.9405	−	2.41380i	−0.947471	−	0.0790243i
$934$	2.25591	+	1.63902i	0.0738157	+	0.0536302i
$935$	−24.8675	−	14.3573i	−0.813255	−	0.469533i
$936$	−14.4521	+	3.72801i	−0.472380	+	0.121854i
$937$	−3.16386	+	30.1021i	−0.103359	+	0.983393i	0.812791	+	0.582556i	$0.197947\pi$
$937$	−3.16386	+	30.1021i	−0.103359	+	0.983393i	−0.916149	+	0.400837i	$0.868719\pi$
$938$	−16.6809	−	22.9593i	−0.544650	−	0.749646i
$939$	−12.9475	+	12.1722i	−0.422525	+	0.397225i
$940$	−4.85490	−	5.39191i	−0.158349	−	0.175865i
$941$	30.1356	−	13.4173i	0.982394	−	0.437390i	0.148258	−	0.988949i	$-0.452633\pi$
$941$	30.1356	−	13.4173i	0.982394	−	0.437390i	0.834136	+	0.551559i	$0.185967\pi$
$942$	17.2406	+	14.8647i	0.561729	+	0.484320i
$943$	−8.47788	+	39.8853i	−0.276078	+	1.29884i
$944$	3.97510	−	8.92823i	0.129379	−	0.290589i
$945$	−29.3189	−	35.3188i	−0.953743	−	1.14892i
$946$	−0.515570	−	1.58676i	−0.0167626	−	0.0515900i
$947$	−47.3634	−	21.0875i	−1.53910	−	0.685253i	−0.550367	−	0.834923i	$-0.685512\pi$
$947$	−47.3634	−	21.0875i	−1.53910	−	0.685253i	−0.988736	+	0.149670i	$0.952179\pi$
$948$	−5.90174	−	12.5235i	−0.191679	−	0.406745i
$949$	31.4498	−	6.68486i	1.02090	−	0.217000i
$950$	−2.14246	−	4.81205i	−0.0695107	−	0.156124i
$951$	5.92134	−	31.1360i	0.192013	−	1.00965i
$952$	−19.6878	+	2.06927i	−0.638085	+	0.0670655i
$953$	−13.2562	+	9.63121i	−0.429411	+	0.311986i	−0.781413	−	0.624014i	$-0.785501\pi$
$953$	−13.2562	+	9.63121i	−0.429411	+	0.311986i	0.352002	+	0.935999i	$0.385501\pi$
$954$	6.98169	−	17.6919i	0.226040	−	0.572796i
$955$	8.49918	+	14.7210i	0.275027	+	0.476361i
$956$	−8.79079	+	15.2261i	−0.284315	+	0.492447i
$957$	−14.0440	+	0.302090i	−0.453980	+	0.00976519i
$958$	−28.7839	+	31.9678i	−0.929967	+	1.03283i
$959$	−7.32744	+	22.5515i	−0.236615	+	0.728227i
$960$	1.84069	+	2.42218i	0.0594080	+	0.0781757i
$961$	−30.7808	−	3.68028i	−0.992928	−	0.118719i
$962$		−	0.670064i		−	0.0216037i
$963$	−13.9147	+	20.9945i	−0.448395	+	0.676540i
$964$	8.74705	+	7.87588i	0.281723	+	0.253665i
$965$	−20.4032	+	28.0826i	−0.656803	+	0.904012i
$966$	44.4459	−	5.64025i	1.43002	−	0.181472i
$967$	−23.1861	+	13.3865i	−0.745616	+	0.430481i	−0.824107	−	0.566433i	$-0.808323\pi$
$967$	−23.1861	+	13.3865i	−0.745616	+	0.430481i	0.0784920	+	0.996915i	$0.474989\pi$
$968$	6.21700	+	0.653433i	0.199822	+	0.0210021i
$969$	−5.41000	+	17.9553i	−0.173794	+	0.576807i
$970$	2.31210	+	21.9982i	0.0742371	+	0.706319i
$971$	8.42920	−	7.58968i	0.270506	−	0.243565i	−0.522702	−	0.852515i	$-0.675076\pi$
$971$	8.42920	−	7.58968i	0.270506	−	0.243565i	0.793208	+	0.608951i	$0.208409\pi$
$972$	−13.4780	+	7.83220i	−0.432307	+	0.251218i
$973$	5.18158	+	24.3774i	0.166114	+	0.781505i
$974$	24.1459	+	5.13236i	0.773683	+	0.164451i
$975$	−3.77713	−	16.0632i	−0.120965	−	0.514434i
$976$	−3.42129	+	1.11165i	−0.109513	+	0.0355829i
$977$	−11.7627	+	3.82194i	−0.376322	+	0.122275i	−0.491070	−	0.871120i	$-0.663394\pi$
$977$	−11.7627	+	3.82194i	−0.376322	+	0.122275i	0.114748	+	0.993395i	$0.463394\pi$
$978$	−1.26382	−	5.37471i	−0.0404125	−	0.171864i
$979$	−50.9274	−	10.8249i	−1.62765	−	0.345967i
$980$	6.68119	+	31.4325i	0.213423	+	1.00408i
$981$	−0.571997	−	3.84361i	−0.0182625	−	0.122717i
$982$	−9.02045	+	8.12205i	−0.287854	+	0.259185i
$983$	3.04641	+	28.9846i	0.0971653	+	0.924466i	0.929159	+	0.369681i	$0.120533\pi$
$983$	3.04641	+	28.9846i	0.0971653	+	0.924466i	−0.831994	+	0.554785i	$0.812800\pi$
$984$	−3.96173	+	13.1486i	−0.126295	+	0.419163i
$985$	−10.7326	−	1.12804i	−0.341969	−	0.0359424i
$986$	−6.65601	+	3.84285i	−0.211970	+	0.122381i
$987$	−35.6987	+	4.53021i	−1.13630	+	0.144198i
$988$	8.04371	−	11.0712i	0.255904	−	0.352222i
$989$	1.53528	+	1.38237i	0.0488190	+	0.0439568i
$990$	18.2427	+	12.0909i	0.579792	+	0.384273i
$991$		−	18.4294i		−	0.585430i	−0.956200	−	0.292715i	$-0.905441\pi$
$991$		−	18.4294i		−	0.585430i	0.956200	−	0.292715i	$-0.0945588\pi$
$992$	5.55791	+	0.331085i	0.176464	+	0.0105120i
$993$	−29.1085	−	38.3042i	−0.923729	−	1.21555i
$994$	7.53902	−	23.2027i	0.239123	−	0.735946i
$995$	2.90729	−	3.22887i	0.0921673	−	0.102362i
$996$	−11.6595	+	0.250798i	−0.369446	+	0.00794685i
$997$	29.1761	−	50.5344i	0.924015	−	1.60044i	0.130877	−	0.991399i	$-0.458221\pi$
$997$	29.1761	−	50.5344i	0.924015	−	1.60044i	0.793138	−	0.609042i	$-0.208446\pi$
$998$	16.1263	+	27.9316i	0.510469	+	0.884158i
$999$	−0.189340	−	0.673745i	−0.00599045	−	0.0213163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.17.7	yes	80
3.2	odd	2	inner	186.2.p.a.17.4	yes	80
31.11	odd	30	inner	186.2.p.a.11.4	✓	80
93.11	even	30	inner	186.2.p.a.11.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.4	✓	80	31.11	odd	30	inner
186.2.p.a.11.7	yes	80	93.11	even	30	inner
186.2.p.a.17.4	yes	80	3.2	odd	2	inner
186.2.p.a.17.7	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.143963 + 1.72606i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.52111 - 0.878214i) q^{5} +(-0.670298 + 1.59709i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.95855 - 0.496976i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.143963 + 1.72606i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.52111 - 0.878214i) q^{5} +(-0.670298 + 1.59709i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.95855 - 0.496976i) q^{9} +(-1.17528 - 1.30528i) q^{10} +(3.79438 - 1.68937i) q^{11} +(-1.13102 + 1.31179i) q^{12} +(1.03437 - 4.86633i) q^{13} +(-2.04567 + 4.59464i) q^{14} +(1.73483 - 2.49910i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.59577 + 1.60094i) q^{17} +(-2.66017 - 1.38689i) q^{18} +(2.69057 - 0.571899i) q^{19} +(-0.714403 - 1.60458i) q^{20} +(-8.55790 - 1.62752i) q^{21} +(4.13071 - 0.434155i) q^{22} +(-4.16079 + 3.02299i) q^{23} +(-1.48103 + 0.898083i) q^{24} +(-0.957481 - 1.65841i) q^{25} +(2.48752 - 4.30852i) q^{26} +(1.28373 - 5.03508i) q^{27} +(-3.36537 + 3.73762i) q^{28} +(-0.603399 + 1.85707i) q^{29} +(2.42218 - 1.84069i) q^{30} +(0.331085 - 5.55791i) q^{31} +1.00000i q^{32} +(2.36969 + 6.79252i) q^{33} +(2.92506 + 2.63373i) q^{34} +(5.19243 - 7.14677i) q^{35} +(-2.10140 - 2.14105i) q^{36} +(0.116641 - 0.0673425i) q^{37} +(2.73561 + 0.287524i) q^{38} +(8.25066 + 2.48595i) q^{39} +(-0.183597 - 1.74681i) q^{40} +(5.89201 - 5.30519i) q^{41} +(-7.63612 - 4.19240i) q^{42} +(-0.0835168 - 0.392915i) q^{43} +(4.06270 + 0.863553i) q^{44} +(4.06383 + 3.35419i) q^{45} +(-4.89131 + 1.58928i) q^{46} +(3.92867 - 1.27650i) q^{47} +(-1.68607 + 0.396465i) q^{48} +(-17.8957 - 3.80385i) q^{49} +(-0.398143 - 1.87312i) q^{50} +(-3.28097 + 5.97602i) q^{51} +(3.69718 - 3.32896i) q^{52} +(0.662698 + 6.30515i) q^{53} +(2.77682 - 4.39195i) q^{54} +(-7.25529 - 0.762562i) q^{55} +(-4.35564 + 2.51473i) q^{56} +(0.599788 + 4.72641i) q^{57} +(-1.14773 + 1.57972i) q^{58} +(-7.26288 - 6.53952i) q^{59} +(2.87244 - 1.00210i) q^{60} +3.59736i q^{61} +(2.03237 - 5.18358i) q^{62} +(4.04120 - 14.5371i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-5.84707 + 6.49383i) q^{65} +(0.154709 + 7.19234i) q^{66} +(-2.82129 + 4.88662i) q^{67} +(1.96803 + 3.40872i) q^{68} +(-4.61886 - 7.61697i) q^{69} +(7.14677 - 5.19243i) q^{70} +(-4.82420 + 0.507044i) q^{71} +(-1.33693 - 2.68563i) q^{72} +(2.62863 + 5.90400i) q^{73} +(0.131742 - 0.0280026i) q^{74} +(3.00035 - 1.41392i) q^{75} +(2.51287 + 1.11880i) q^{76} +(6.45527 + 19.8673i) q^{77} +(7.07864 + 4.91388i) q^{78} +(-3.25109 + 7.30206i) q^{79} +(0.365182 - 1.71805i) q^{80} +(8.50603 + 2.94065i) q^{81} +(7.24302 - 3.22480i) q^{82} +(4.50537 + 5.00373i) q^{83} +(-5.96686 - 6.34690i) q^{84} +(-4.06359 - 5.59305i) q^{85} +(0.0419884 - 0.399493i) q^{86} +(-3.11854 - 1.30885i) q^{87} +(3.59700 + 2.07673i) q^{88} +(-10.1413 - 7.36810i) q^{89} +(2.82843 + 4.44582i) q^{90} +(23.7972 + 7.73217i) q^{91} -5.14302 q^{92} +(9.54561 + 1.37160i) q^{93} +4.13084 q^{94} +(-4.59491 - 1.49298i) q^{95} +(-1.72606 - 0.143963i) q^{96} +(-10.1882 - 7.40220i) q^{97} +(-15.8444 - 9.14776i) q^{98} +(-12.0654 + 3.11236i) 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