LMFDB - Embedded newform 186.2.p.a.17.4

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			17.4
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(1.70155 - 0.323596i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.52111 + 0.878214i) q^{5} +(-1.71827 - 0.218051i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.79057 - 1.10123i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.70155 - 0.323596i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.52111 + 0.878214i) q^{5} +(-1.71827 - 0.218051i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.79057 - 1.10123i) q^{9} +(-1.17528 - 1.30528i) q^{10} +(-3.79438 + 1.68937i) q^{11} +(1.56679 + 0.738353i) q^{12} +(1.03437 - 4.86633i) q^{13} +(2.04567 - 4.59464i) q^{14} +(2.87244 + 1.00210i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-3.59577 - 1.60094i) q^{17} +(-2.99429 + 0.185001i) q^{18} +(2.69057 - 0.571899i) q^{19} +(0.714403 + 1.60458i) q^{20} +(0.724055 + 8.68115i) q^{21} +(4.13071 - 0.434155i) q^{22} +(4.16079 - 3.02299i) q^{23} +(-1.26194 - 1.18638i) q^{24} +(-0.957481 - 1.65841i) q^{25} +(-2.48752 + 4.30852i) q^{26} +(4.39195 - 2.77682i) 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} +(-5.90966 + 4.10239i) q^{33} +(2.92506 + 2.63373i) q^{34} +(-5.19243 + 7.14677i) q^{35} +(2.90491 + 0.749341i) q^{36} +(0.116641 - 0.0673425i) q^{37} +(-2.73561 - 0.287524i) q^{38} +(0.185311 - 8.61504i) q^{39} +(-0.183597 - 1.74681i) q^{40} +(-5.89201 + 5.30519i) q^{41} +(1.99400 - 8.48001i) q^{42} +(-0.0835168 - 0.392915i) q^{43} +(-4.06270 - 0.863553i) q^{44} +(5.21189 + 0.775621i) q^{45} +(-4.89131 + 1.58928i) q^{46} +(-3.92867 + 1.27650i) q^{47} +(0.833567 + 1.51828i) q^{48} +(-17.8957 - 3.80385i) q^{49} +(0.398143 + 1.87312i) q^{50} +(-6.63645 - 1.56051i) q^{51} +(3.69718 - 3.32896i) q^{52} +(-0.662698 - 6.30515i) q^{53} +(-5.03508 + 1.28373i) q^{54} +(-7.25529 - 0.762562i) q^{55} +(4.35564 - 2.51473i) q^{56} +(4.39309 - 1.84377i) q^{57} +(-1.14773 + 1.57972i) q^{58} +(7.26288 + 6.53952i) q^{59} +(1.73483 + 2.49910i) 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} +(6.88813 - 2.07542i) q^{66} +(-2.82129 + 4.88662i) q^{67} +(-1.96803 - 3.40872i) q^{68} +(6.10159 - 6.49020i) q^{69} +(7.14677 - 5.19243i) q^{70} +(4.82420 - 0.507044i) q^{71} +(-2.53117 - 1.61033i) q^{72} +(2.62863 + 5.90400i) q^{73} +(-0.131742 + 0.0280026i) q^{74} +(-2.16586 - 2.51203i) q^{75} +(2.51287 + 1.11880i) q^{76} +(-6.45527 - 19.8673i) q^{77} +(-2.83844 + 8.13613i) q^{78} +(-3.25109 + 7.30206i) q^{79} +(-0.365182 + 1.71805i) q^{80} +(6.57457 - 6.14614i) q^{81} +(7.24302 - 3.22480i) q^{82} +(-4.50537 - 5.00373i) q^{83} +(-4.51688 + 7.44878i) q^{84} +(-4.06359 - 5.59305i) q^{85} +(-0.0419884 + 0.399493i) q^{86} +(0.425774 - 3.35516i) q^{87} +(3.59700 + 2.07673i) q^{88} +(10.1413 + 7.36810i) q^{89} +(-4.71712 - 2.34822i) q^{90} +(23.7972 + 7.73217i) q^{91} +5.14302 q^{92} +(-1.23516 - 9.56422i) q^{93} +4.13084 q^{94} +(4.59491 + 1.49298i) q^{95} +(-0.323596 - 1.70155i) q^{96} +(-10.1882 - 7.40220i) q^{97} +(15.8444 + 9.14776i) q^{98} +(-8.72809 + 8.89278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.70155	−	0.323596i	0.982393	−	0.186828i
$3$	1.70155	−	0.323596i	0.982393	−	0.186828i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	1.52111	+	0.878214i	0.680262	+	0.392749i	0.799954	−	0.600062i	$-0.204857\pi$
$5$	1.52111	+	0.878214i	0.680262	+	0.392749i	−0.119692	+	0.992811i	$0.538191\pi$
$6$	−1.71827	−	0.218051i	−0.701481	−	0.0890189i
$7$	−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
$9$	2.79057	−	1.10123i	0.930190	−	0.367078i
$10$	−1.17528	−	1.30528i	−0.371656	−	0.412766i
$11$	−3.79438	+	1.68937i	−1.14405	+	0.509363i	−0.889155	−	0.457607i	$-0.848707\pi$
$11$	−3.79438	+	1.68937i	−1.14405	+	0.509363i	−0.254893	+	0.966969i	$0.582040\pi$
$12$	1.56679	+	0.738353i	0.452294	+	0.213144i
$13$	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
$15$	2.87244	+	1.00210i	0.741661	+	0.258742i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−3.59577	−	1.60094i	−0.872101	−	0.388284i	−0.0786384	−	0.996903i	$-0.525057\pi$
$17$	−3.59577	−	1.60094i	−0.872101	−	0.388284i	−0.793463	+	0.608619i	$0.791724\pi$
$18$	−2.99429	+	0.185001i	−0.705761	+	0.0436050i
$19$	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
$21$	0.724055	+	8.68115i	0.158002	+	1.89438i
$22$	4.13071	−	0.434155i	0.880670	−	0.0925622i
$23$	4.16079	−	3.02299i	0.867586	−	0.630338i	−0.0623524	−	0.998054i	$-0.519860\pi$
$23$	4.16079	−	3.02299i	0.867586	−	0.630338i	0.929938	+	0.367716i	$0.119860\pi$
$24$	−1.26194	−	1.18638i	−0.257593	−	0.242169i
$25$	−0.957481	−	1.65841i	−0.191496	−	0.331681i
$26$	−2.48752	+	4.30852i	−0.487844	+	0.844970i
$27$	4.39195	−	2.77682i	0.845232	−	0.534400i
$28$	−3.36537	+	3.73762i	−0.635995	+	0.706344i
$29$	0.603399	−	1.85707i	0.112048	−	0.344849i	−0.879272	−	0.476321i	$-0.841970\pi$
$29$	0.603399	−	1.85707i	0.112048	−	0.344849i	0.991320	+	0.131471i	$0.0419702\pi$
$30$	−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
$33$	−5.90966	+	4.10239i	−1.02874	+	0.714135i
$34$	2.92506	+	2.63373i	0.501643	+	0.451682i
$35$	−5.19243	+	7.14677i	−0.877681	+	1.20802i
$36$	2.90491	+	0.749341i	0.484151	+	0.124890i
$37$	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
$39$	0.185311	−	8.61504i	0.0296736	−	1.37951i
$40$	−0.183597	−	1.74681i	−0.0290292	−	0.276194i
$41$	−5.89201	+	5.30519i	−0.920177	+	0.828531i	−0.985560	−	0.169329i	$-0.945840\pi$
$41$	−5.89201	+	5.30519i	−0.920177	+	0.828531i	0.0653828	+	0.997860i	$0.479173\pi$
$42$	1.99400	−	8.48001i	0.307682	−	1.30849i
$43$	−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
$45$	5.21189	+	0.775621i	0.776942	+	0.115623i
$46$	−4.89131	+	1.58928i	−0.721184	+	0.234327i
$47$	−3.92867	+	1.27650i	−0.573055	+	0.186197i	−0.581187	−	0.813770i	$-0.697411\pi$
$47$	−3.92867	+	1.27650i	−0.573055	+	0.186197i	0.00813196	+	0.999967i	$0.497411\pi$
$48$	0.833567	+	1.51828i	0.120315	+	0.219144i
$49$	−17.8957	−	3.80385i	−2.55653	−	0.543407i
$50$	0.398143	+	1.87312i	0.0563059	+	0.264899i
$51$	−6.63645	−	1.56051i	−0.929288	−	0.218515i
$52$	3.69718	−	3.32896i	0.512707	−	0.461643i
$53$	−0.662698	−	6.30515i	−0.0910286	−	0.866079i	−0.940808	−	0.338941i	$-0.889931\pi$
$53$	−0.662698	−	6.30515i	−0.0910286	−	0.866079i	0.849779	−	0.527139i	$-0.176735\pi$
$54$	−5.03508	+	1.28373i	−0.685188	+	0.174693i
$55$	−7.25529	−	0.762562i	−0.978303	−	0.102824i
$56$	4.35564	−	2.51473i	0.582047	−	0.336045i
$57$	4.39309	−	1.84377i	0.581879	−	0.244214i
$58$	−1.14773	+	1.57972i	−0.150705	+	0.207427i
$59$	7.26288	+	6.53952i	0.945546	+	0.851373i	0.989035	−	0.147681i	$-0.0471808\pi$
$59$	7.26288	+	6.53952i	0.945546	+	0.851373i	−0.0434893	+	0.999054i	$0.513847\pi$
$60$	1.73483	+	2.49910i	0.223966	+	0.322632i
$61$			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
$66$	6.88813	−	2.07542i	0.847871	−	0.255466i
$67$	−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
$69$	6.10159	−	6.49020i	0.734545	−	0.781329i
$70$	7.14677	−	5.19243i	0.854202	−	0.620614i
$71$	4.82420	−	0.507044i	0.572527	−	0.0601750i	0.186159	−	0.982520i	$-0.440396\pi$
$71$	4.82420	−	0.507044i	0.572527	−	0.0601750i	0.386368	+	0.922345i	$0.373729\pi$
$72$	−2.53117	−	1.61033i	−0.298302	−	0.189779i
$73$	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
$75$	−2.16586	−	2.51203i	−0.250092	−	0.290064i
$76$	2.51287	+	1.11880i	0.288246	+	0.128335i
$77$	−6.45527	−	19.8673i	−0.735646	−	2.26409i
$78$	−2.83844	+	8.13613i	−0.321390	+	0.921235i
$79$	−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
$81$	6.57457	−	6.14614i	0.730508	−	0.682904i
$82$	7.24302	−	3.22480i	0.799858	−	0.356120i
$83$	−4.50537	−	5.00373i	−0.494529	−	0.549230i	0.443279	−	0.896384i	$-0.353815\pi$
$83$	−4.50537	−	5.00373i	−0.494529	−	0.549230i	−0.937808	+	0.347153i	$0.887148\pi$
$84$	−4.51688	+	7.44878i	−0.492832	+	0.812729i
$85$	−4.06359	−	5.59305i	−0.440758	−	0.606652i
$86$	−0.0419884	+	0.399493i	−0.00452772	+	0.0430784i
$87$	0.425774	−	3.35516i	0.0456478	−	0.359711i
$88$	3.59700	+	2.07673i	0.383442	+	0.221380i
$89$	10.1413	+	7.36810i	1.07498	+	0.781017i	0.976800	−	0.214152i	$-0.0686988\pi$
$89$	10.1413	+	7.36810i	1.07498	+	0.781017i	0.0981772	+	0.995169i	$0.468699\pi$
$90$	−4.71712	−	2.34822i	−0.497228	−	0.247524i
$91$	23.7972	+	7.73217i	2.49462	+	0.810552i
$92$	5.14302			0.536197
$93$	−1.23516	−	9.56422i	−0.128080	−	0.991764i
$94$	4.13084			0.426064
$95$	4.59491	+	1.49298i	0.471428	+	0.153176i
$96$	−0.323596	−	1.70155i	−0.0330269	−	0.173664i
$97$	−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
$99$	−8.72809	+	8.89278i	−0.877206	+	0.893758i
$100$	0.200168	−	1.90447i	0.0200168	−	0.190447i
$101$	8.68120	+	11.9487i	0.863812	+	1.18894i	0.980647	+	0.195784i	$0.0627251\pi$
$101$	8.68120	+	11.9487i	0.863812	+	1.18894i	−0.116835	+	0.993151i	$0.537275\pi$
$102$	5.82941	+	3.53490i	0.577198	+	0.350008i
$103$	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
$105$	−6.52253	+	13.8409i	−0.636534	+	1.35073i
$106$	−1.31814	+	6.20134i	−0.128029	+	0.602328i
$107$	−3.41484	+	7.66985i	−0.330125	+	0.741472i	−0.999999	−	0.00100171i	$-0.999681\pi$
$107$	−3.41484	+	7.66985i	−0.330125	+	0.741472i	0.669875	+	0.742474i	$0.266348\pi$
$108$	5.18534	+	0.335027i	0.498960	+	0.0322379i
$109$	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
$111$	0.176679	−	0.152331i	0.0167696	−	0.0144587i
$112$	−4.91956	+	1.04568i	−0.464855	+	0.0988079i
$113$	0.293125	+	0.658370i	0.0275749	+	0.0619342i	0.926808	−	0.375536i	$-0.122541\pi$
$113$	0.293125	+	0.658370i	0.0275749	+	0.0619342i	−0.899233	+	0.437470i	$0.855875\pi$
$114$	−4.74783	+	0.395995i	−0.444675	+	0.0370884i
$115$	8.98387	−	0.944242i	0.837750	−	0.0880510i
$116$	1.57972	−	1.14773i	0.146673	−	0.106564i
$117$	−2.47248	−	14.7189i	−0.228581	−	1.36077i
$118$	−4.88658	−	8.46381i	−0.449846	−	0.779157i
$119$	9.89812	−	17.1441i	0.907360	−	1.57159i
$120$	−0.877659	−	2.91287i	−0.0801190	−	0.265908i
$121$	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
$126$	0.648808	−	15.0744i	0.0578005	−	1.34294i
$127$	−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
$129$	−0.269254	−	0.641541i	−0.0237065	−	0.0564845i
$130$	−7.56760	+	4.36916i	−0.663723	+	0.383200i
$131$	−16.2620	−	1.70920i	−1.42082	−	0.149334i	−0.637257	−	0.770651i	$-0.719931\pi$
$131$	−16.2620	−	1.70920i	−1.42082	−	0.149334i	−0.783559	+	0.621317i	$0.786598\pi$
$132$	−7.19234	−	0.154709i	−0.626013	−	0.0134657i
$133$	1.44609	+	13.7587i	0.125392	+	1.19303i
$134$	4.19326	−	3.77563i	0.362242	−	0.326165i
$135$	9.11929	−	0.366785i	0.784864	−	0.0315678i
$136$	0.818352	+	3.85004i	0.0701731	+	0.330138i
$137$	−4.61161	−	0.980228i	−0.393996	−	0.0837465i	0.00665328	−	0.999978i	$-0.497882\pi$
$137$	−4.61161	−	0.980228i	−0.393996	−	0.0837465i	−0.400650	+	0.916231i	$0.631216\pi$
$138$	−7.80854	+	4.28706i	−0.664707	+	0.364939i
$139$	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
$141$	−6.27177	+	3.44334i	−0.528178	+	0.289981i
$142$	−4.74477	−	1.00853i	−0.398172	−	0.0846341i
$143$	4.29622	+	20.2121i	0.359268	+	1.69022i
$144$	1.90967	+	2.31369i	0.159139	+	0.192808i
$145$	2.54874	−	2.29490i	0.211661	−	0.190581i
$146$	−0.675539	−	6.42732i	−0.0559080	−	0.531929i
$147$	−31.6814	−	0.681474i	−2.61304	−	0.0562070i
$148$	0.133947	+	0.0140784i	0.0110104	+	0.00115724i
$149$	1.43841	−	0.830464i	0.117839	−	0.0680342i	−0.439922	−	0.898036i	$-0.644994\pi$
$149$	1.43841	−	0.830464i	0.117839	−	0.0680342i	0.557761	+	0.830002i	$0.311661\pi$
$150$	1.28359	+	3.05837i	0.104805	+	0.249715i
$151$	−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
$153$	−11.7972	−	0.507757i	−0.953751	−	0.0410497i
$154$			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
$159$	−3.16794	−	10.5141i	−0.251234	−	0.833823i
$160$	0.878214	−	1.52111i	0.0694289	−	0.120254i
$161$	12.9333	+	22.4012i	1.01929	+	1.76546i
$162$	−8.15205	+	3.81367i	−0.640486	+	0.299630i
$163$	−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
$165$	−12.5920	+	1.05024i	−0.980288	+	0.0817614i
$166$	2.73863	+	6.15106i	0.212559	+	0.477415i
$167$	−4.12869	+	0.877580i	−0.319488	+	0.0679092i	−0.364864	−	0.931061i	$-0.618885\pi$
$167$	−4.12869	+	0.877580i	−0.319488	+	0.0679092i	0.0453765	+	0.998970i	$0.485551\pi$
$168$	6.59761	−	5.68842i	0.509016	−	0.438871i
$169$	−10.7352	−	4.77961i	−0.825783	−	0.367662i
$170$	2.13636	+	6.57503i	0.163851	+	0.504282i
$171$	6.87844	−	4.55887i	0.526007	−	0.348625i
$172$	0.163383	−	0.366965i	0.0124579	−	0.0279808i
$173$	1.94882	−	9.16849i	0.148166	−	0.697067i	−0.839863	−	0.542799i	$-0.817365\pi$
$173$	1.94882	−	9.16849i	0.148166	−	0.697067i	0.988029	−	0.154268i	$-0.0493020\pi$
$174$	−1.44174	+	3.05938i	−0.109298	+	0.231931i
$175$	8.79857	−	3.91738i	0.665109	−	0.296126i
$176$	−2.77921	−	3.08662i	−0.209491	−	0.232663i
$177$	14.4743	+	8.77711i	1.08796	+	0.659728i
$178$	−7.36810	−	10.1413i	−0.552262	−	0.760124i
$179$	−0.776953	+	7.39222i	−0.0580722	+	0.552520i	0.926346	+	0.376675i	$0.122933\pi$
$179$	−0.776953	+	7.39222i	−0.0580722	+	0.552520i	−0.984418	+	0.175845i	$0.943734\pi$
$180$	3.76061	+	3.69096i	0.280299	+	0.275108i
$181$	−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
$183$	1.16409	+	6.12110i	0.0860521	+	0.452485i
$184$	−4.89131	−	1.58928i	−0.360592	−	0.117163i
$185$	0.236564			0.0173926
$186$	−1.78080	+	9.47780i	−0.130575	+	0.694946i
$187$	16.3483			1.19550
$188$	−3.92867	−	1.27650i	−0.286527	−	0.0930984i
$189$	11.5805	+	23.4280i	0.842356	+	1.70414i
$190$	−3.90866	−	2.83981i	−0.283564	−	0.206021i
$191$	8.38122	+	4.83890i	0.606444	+	0.350130i	0.771572	−	0.636142i	$-0.219471\pi$
$191$	8.38122	+	4.83890i	0.606444	+	0.350130i	−0.165129	+	0.986272i	$0.552804\pi$
$192$	−0.218051	+	1.71827i	−0.0157365	+	0.124005i
$193$	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
$195$	7.84773	−	12.9417i	0.561988	−	0.926774i
$196$	−12.2421	−	13.5962i	−0.874435	−	0.971158i
$197$	−5.61294	+	2.49904i	−0.399905	+	0.178049i	−0.596827	−	0.802370i	$-0.703572\pi$
$197$	−5.61294	+	2.49904i	−0.399905	+	0.178049i	0.196922	+	0.980419i	$0.436905\pi$
$198$	11.0489	−	5.76041i	0.785213	−	0.409375i
$199$	−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
$201$	−3.21929	+	9.22781i	−0.227071	+	0.650880i
$202$	−4.56398	−	14.0465i	−0.321120	−	0.988307i
$203$	8.97168	+	3.99445i	0.629688	+	0.280355i
$204$	−4.45175	−	5.16328i	−0.311685	−	0.361502i
$205$	−13.6215	+	2.89534i	−0.951366	+	0.202219i
$206$	−2.54344	−	5.71267i	−0.177210	−	0.398020i
$207$	8.28197	−	13.0179i	0.575637	−	0.904805i
$208$	4.94780	−	0.520034i	0.343068	−	0.0360579i
$209$	−9.24290	+	6.71536i	−0.639344	+	0.464511i
$210$	10.4804	−	11.1479i	0.723214	−	0.769276i
$211$	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
$213$	8.04456	−	2.42385i	0.551204	−	0.166080i
$214$	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
$219$	6.38326	+	9.19535i	0.431341	+	0.621364i
$220$	−5.42143	−	4.88148i	−0.365513	−	0.329109i
$221$	−11.5101	+	15.8422i	−0.774250	+	1.06566i
$222$	−0.215104	+	0.0902790i	−0.0144369	+	0.00605913i
$223$	−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
$225$	−4.49821	−	3.57349i	−0.299881	−	0.238233i
$226$	−0.0753311	−	0.716728i	−0.00501095	−	0.0476760i
$227$	−0.519770	+	0.468003i	−0.0344984	+	0.0310625i	−0.686200	−	0.727413i	$-0.740722\pi$
$227$	−0.519770	+	0.468003i	−0.0344984	+	0.0310625i	0.651701	+	0.758476i	$0.274056\pi$
$228$	4.63783	+	1.09055i	0.307148	+	0.0722233i
$229$	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
$231$	−17.4130	−	31.7163i	−1.14569	−	2.08678i
$232$	−1.85707	+	0.603399i	−0.121923	+	0.0396151i
$233$	0.597184	−	0.194037i	0.0391228	−	0.0127118i	−0.289390	−	0.957211i	$-0.593453\pi$
$233$	0.597184	−	0.194037i	0.0391228	−	0.0127118i	0.328513	+	0.944499i	$0.393453\pi$
$234$	−2.19693	+	14.7626i	−0.143618	+	0.965059i
$235$	−7.09698	−	1.50851i	−0.462956	−	0.0984043i
$236$	2.03195	+	9.55960i	0.132269	+	0.622277i
$237$	−3.16898	+	13.4769i	−0.205848	+	0.875418i
$238$	−14.7115	+	13.2463i	−0.953604	+	0.858629i
$239$	−1.83778	−	17.4853i	−0.118876	−	1.13103i	−0.877526	−	0.479530i	$-0.840807\pi$
$239$	−1.83778	−	17.4853i	−0.118876	−	1.13103i	0.758650	−	0.651499i	$-0.225859\pi$
$240$	−0.0654237	+	3.04152i	−0.00422308	+	0.196329i
$241$	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
$243$	9.19813	−	12.5855i	0.590060	−	0.807359i
$244$	−2.11447	+	2.91032i	−0.135365	+	0.186314i
$245$	−23.8808	−	21.5023i	−1.52569	−	1.37373i
$246$	11.2809	−	7.83099i	0.719241	−	0.499286i
$247$		−	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	−0.958708	−	0.284393i	$-0.908208\pi$
$251$	−9.12018	+	10.1290i	−0.575661	+	0.639336i	0.383047	+	0.923729i	$0.374875\pi$
$252$	−5.27531	+	14.1361i	−0.332313	+	0.890494i
$253$	−10.6807	+	18.4995i	−0.671489	+	1.16305i
$254$	8.47696	+	14.6825i	0.531892	+	0.921263i
$255$	−8.72431	−	8.20192i	−0.546338	−	0.513624i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	17.8707	−	1.87829i	1.11474	−	0.117164i	0.470803	−	0.882239i	$-0.343964\pi$
$257$	17.8707	−	1.87829i	1.11474	−	0.117164i	0.643942	+	0.765074i	$0.277298\pi$
$258$	0.0578288	+	0.693346i	0.00360027	+	0.0431658i
$259$	0.275521	+	0.618830i	0.0171200	+	0.0384522i
$260$	8.54736	−	1.81680i	0.530085	−	0.112673i
$261$	−0.361239	−	5.84677i	−0.0223601	−	0.361906i
$262$	14.9379	+	6.65078i	0.922866	+	0.410886i
$263$	−4.55490	−	14.0185i	−0.280867	−	0.864420i	−0.987607	−	0.156947i	$-0.949835\pi$
$263$	−4.55490	−	14.0185i	−0.280867	−	0.864420i	0.706740	−	0.707474i	$-0.250165\pi$
$264$	6.79252	+	2.36969i	0.418051	+	0.145845i
$265$	4.52924	−	10.1728i	0.278229	−	0.624912i
$266$	2.87634	−	13.5321i	0.176360	−	0.829708i
$267$	19.6403	+	9.25552i	1.20197	+	0.566429i
$268$	−5.15476	+	2.29505i	−0.314877	+	0.140192i
$269$	19.3565	+	21.4975i	1.18018	+	1.31073i	0.940467	+	0.339885i	$0.110388\pi$
$269$	19.3565	+	21.4975i	1.18018	+	1.31073i	0.239718	+	0.970843i	$0.422945\pi$
$270$	−8.78631	−	2.46918i	−0.534718	−	0.150270i
$271$	−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
$273$	42.9943	+	5.45603i	2.60213	+	0.330214i
$274$	4.08299	+	2.35732i	0.246663	+	0.142411i
$275$	6.43470	+	4.67508i	0.388027	+	0.281918i
$276$	8.75113	−	1.66426i	0.526756	−	0.100177i
$277$	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
$279$	−5.19664	−	15.8743i	−0.311115	−	0.950372i
$280$	8.83389			0.527926
$281$	−3.62125	−	1.17662i	−0.216026	−	0.0701910i	0.199005	−	0.979999i	$-0.436229\pi$
$281$	−3.62125	−	1.17662i	−0.216026	−	0.0701910i	−0.415030	+	0.909808i	$0.636229\pi$
$282$	7.02886	−	1.33673i	0.418562	−	0.0796008i
$283$	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
$285$	8.30160	+	1.05348i	0.491745	+	0.0624030i
$286$	2.15994	−	20.5505i	0.127720	−	1.21518i
$287$	−23.4385	−	32.2604i	−1.38353	−	1.90427i
$288$	−1.10123	−	2.79057i	−0.0648908	−	0.164436i
$289$	−1.00869	−	1.12027i	−0.0593350	−	0.0658981i
$290$	−3.13316	+	1.39497i	−0.183985	+	0.0819156i
$291$	−19.7312	−	9.29836i	−1.15666	−	0.545079i
$292$	−1.34368	+	6.32150i	−0.0786327	+	0.369938i
$293$	−5.61426	+	12.6098i	−0.327989	+	0.736674i	−0.999992	−	0.00387313i	$-0.998767\pi$
$293$	−5.61426	+	12.6098i	−0.327989	+	0.736674i	0.672004	+	0.740548i	$0.265434\pi$
$294$	29.9202	+	10.4382i	1.74498	+	0.608769i
$295$	5.30454	+	16.3257i	0.308842	+	0.950519i
$296$	−0.123041	−	0.0547813i	−0.00715160	−	0.00318410i
$297$	−11.9736	+	17.9559i	−0.694782	+	1.04191i
$298$	−1.62463	+	0.345326i	−0.0941124	+	0.0200042i
$299$	−10.4071	−	23.3747i	−0.601858	−	1.35179i
$300$	−0.275683	−	3.30533i	−0.0159166	−	0.190834i
$301$	2.00924	−	0.211179i	0.115810	−	0.0121722i
$302$	0.846000	−	0.614655i	0.0486819	−	0.0353694i
$303$	18.6381	+	17.5221i	1.07073	+	1.00662i
$304$	1.37534	+	2.38216i	0.0788812	+	0.136626i
$305$	−3.15925	+	5.47198i	−0.180898	+	0.313325i
$306$	11.0629	+	4.12845i	0.632426	+	0.236008i
$307$	−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	$-0.842310\pi$
$311$		−	16.7668i		−	0.950761i	0.879780	−	0.475380i	$-0.157690\pi$
$312$	−7.07864	+	4.91388i	−0.400749	+	0.278193i
$313$	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
$315$	−6.61959	+	25.6616i	−0.372972	+	1.44587i
$316$	−6.92223	+	3.99655i	−0.389406	+	0.224824i
$317$	18.1983	+	1.91272i	1.02212	+	0.107429i	0.600731	−	0.799451i	$-0.294876\pi$
$317$	18.1983	+	1.91272i	1.02212	+	0.107429i	0.421388	+	0.906880i	$0.361543\pi$
$318$	−0.236149	+	10.9785i	−0.0132426	+	0.615642i
$319$	0.847748	+	8.06578i	0.0474648	+	0.451597i
$320$	−1.30528	+	1.17528i	−0.0729674	+	0.0657001i
$321$	−3.32860	+	14.1557i	−0.185784	+	0.790094i
$322$	−5.37798	−	25.3014i	−0.299703	−	1.40999i
$323$	−10.5902	−	2.25102i	−0.589257	−	0.125250i
$324$	8.93155	−	1.10789i	0.496197	−	0.0615495i
$325$	−9.06074	+	2.94401i	−0.502600	+	0.163305i
$326$	3.03170	−	0.985060i	0.167911	−	0.0545575i
$327$	1.07973	+	1.96664i	0.0597092	+	0.108756i
$328$	7.75522	+	1.64842i	0.428210	+	0.0910189i
$329$	−4.31956	−	20.3219i	−0.238145	−	1.12038i
$330$	12.3003	+	2.89231i	0.677108	+	0.159216i
$331$	−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
$333$	0.251334	−	0.316372i	0.0137730	−	0.0173371i
$334$	4.19781	+	0.441207i	0.229694	+	0.0241418i
$335$	−8.58300	+	4.95540i	−0.468940	+	0.270742i
$336$	−8.03251	+	3.37124i	−0.438210	+	0.183916i
$337$	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
$339$	0.711814	+	1.02540i	0.0386604	+	0.0556920i
$340$		−	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
$345$	14.9810	−	4.51382i	0.806549	−	0.243016i
$346$	−4.68666	+	8.11753i	−0.251956	+	0.436401i
$347$	−5.71673	−	9.90167i	−0.306890	−	0.531550i	0.670790	−	0.741647i	$-0.265955\pi$
$347$	−5.71673	−	9.90167i	−0.306890	−	0.531550i	−0.977680	+	0.210098i	$0.932622\pi$
$348$	2.31657	−	2.46412i	0.124181	−	0.132091i
$349$	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
$351$	−8.97004	−	24.2450i	−0.478786	−	1.29410i
$352$	1.68937	+	3.79438i	0.0900435	+	0.202241i
$353$	−28.3539	+	6.02680i	−1.50913	+	0.320774i	−0.886862	−	0.462034i	$-0.847120\pi$
$353$	−28.3539	+	6.02680i	−1.50913	+	0.320774i	−0.622263	+	0.782808i	$0.713786\pi$
$354$	−11.0536	−	12.8203i	−0.587494	−	0.681394i
$355$	7.78344	+	3.46541i	0.413102	+	0.183925i
$356$	3.87364	+	11.9218i	0.205302	+	0.631856i
$357$	11.2944	−	32.3745i	0.597765	−	1.71344i
$358$	3.02325	−	6.79033i	0.159784	−	0.358880i
$359$	−3.72095	+	17.5057i	−0.196384	+	0.923916i	0.763995	+	0.645222i	$0.223235\pi$
$359$	−3.72095	+	17.5057i	−0.196384	+	0.923916i	−0.960380	+	0.278694i	$0.910098\pi$
$360$	−2.43598	−	4.67240i	−0.128387	−	0.246257i
$361$	−10.4453	+	4.65053i	−0.549750	+	0.244765i
$362$	4.38138	+	4.86601i	0.230280	+	0.255752i
$363$	5.61414	−	9.25828i	0.294666	−	0.485934i
$364$	14.7075	+	20.2431i	0.770881	+	1.06103i
$365$	−1.18654	+	11.2891i	−0.0621061	+	0.590900i
$366$	0.784407	−	6.18124i	0.0410016	−	0.323098i
$367$	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
$369$	−10.5998	+	21.2930i	−0.551804	+	1.10847i
$370$	−0.224986	−	0.0731024i	−0.0116965	−	0.00380041i
$371$	31.8862			1.65545
$372$	4.62244	−	8.46363i	0.239663	−	0.438819i
$373$	−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
$375$	−3.93028	−	20.6664i	−0.202959	−	1.06721i
$376$	3.34192	+	2.42805i	0.172347	+	0.125217i
$377$	−8.41298	−	4.85724i	−0.433291	−	0.250160i
$378$	−3.77405	−	25.8599i	−0.194116	−	1.33009i
$379$	−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
$381$	−25.1092	−	15.2260i	−1.28639	−	0.780053i
$382$	−6.47571	−	7.19201i	−0.331326	−	0.367975i
$383$	22.9985	−	10.2396i	1.17517	−	0.523218i	0.276143	−	0.961117i	$-0.410944\pi$
$383$	22.9985	−	10.2396i	1.17517	−	0.523218i	0.899024	+	0.437899i	$0.144277\pi$
$384$	0.738353	−	1.56679i	0.0376789	−	0.0799550i
$385$	7.62854	−	35.8894i	0.388786	−	1.82910i
$386$	−8.03828	+	18.0543i	−0.409138	+	0.918938i
$387$	−0.665751	−	1.00449i	−0.0338420	−	0.0510609i
$388$	−3.89157	−	11.9770i	−0.197564	−	0.608040i
$389$	14.9970	+	6.67708i	0.760376	+	0.338541i	0.750029	−	0.661405i	$-0.230040\pi$
$389$	14.9970	+	6.67708i	0.760376	+	0.338541i	0.0103474	+	0.999946i	$0.496706\pi$
$390$	−11.4628	+	9.88320i	−0.580443	+	0.500455i
$391$	−19.8009	+	4.20880i	−1.00137	+	0.212848i
$392$	7.44146	+	16.7138i	0.375850	+	0.844174i
$393$	−28.2237	+	2.35401i	−1.42370	+	0.118744i
$394$	6.11047	−	0.642236i	0.307841	−	0.0323554i
$395$	−11.3580	+	8.25210i	−0.571485	+	0.415208i
$396$	−12.2882	+	2.06417i	−0.617506	+	0.103728i
$397$	−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
$399$	6.91286	+	22.9432i	0.346076	+	1.14859i
$400$	1.28136	−	1.42309i	0.0640680	−	0.0711547i
$401$	9.69603	−	29.8413i	0.484197	−	1.49020i	−0.348945	−	0.937143i	$-0.613460\pi$
$401$	9.69603	−	29.8413i	0.484197	−	1.49020i	0.833141	−	0.553060i	$-0.186540\pi$
$402$	5.91328	−	7.78136i	0.294928	−	0.388099i
$403$	−26.7042	−	7.36011i	−1.33023	−	0.366633i
$404$			14.7693i			0.734802i
$405$	15.3983	−	3.57507i	0.765147	−	0.177647i
$406$	−7.29822	−	6.57135i	−0.362205	−	0.326131i
$407$	−0.328812	+	0.452571i	−0.0162986	+	0.0224331i
$408$	2.63833	+	6.28624i	0.130617	+	0.311215i
$409$	−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
$411$	−8.16410	−	0.175611i	−0.402705	−	0.00866227i
$412$	0.653647	+	6.21904i	0.0322029	+	0.306390i
$413$	−36.5284	+	32.8903i	−1.79744	+	1.61843i
$414$	−11.8994	+	9.82147i	−0.584822	+	0.482699i
$415$	−2.45883	−	11.5679i	−0.120699	−	0.567846i
$416$	−4.86633	−	1.03437i	−0.238592	−	0.0507142i
$417$	7.52338	−	4.13050i	0.368422	−	0.202271i
$418$	10.8657	−	3.53047i	0.531458	−	0.172681i
$419$	−24.4868	+	7.95626i	−1.19626	+	0.388689i	−0.838384	−	0.545080i	$-0.816499\pi$
$419$	−24.4868	+	7.95626i	−1.19626	+	0.388689i	−0.357877	+	0.933769i	$0.616499\pi$
$420$	−13.4123	+	7.36364i	−0.654453	+	0.359309i
$421$	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
$423$	−9.55750	+	7.88854i	−0.464702	+	0.383554i
$424$	−4.71145	+	4.24221i	−0.228808	+	0.206020i
$425$	0.787872	+	7.49611i	0.0382174	+	0.363615i
$426$	−8.39984	−	0.180682i	−0.406974	−	0.00875408i
$427$	−17.9937	−	1.89121i	−0.870775	−	0.0915221i
$428$	−7.27089	+	4.19785i	−0.351452	+	0.202911i
$429$	13.8508	+	33.0018i	0.668724	+	1.59334i
$430$	−0.414709	+	0.570798i	−0.0199991	+	0.0275263i
$431$	24.9909	+	22.5019i	1.20377	+	1.08388i	0.994361	+	0.106053i	$0.0338213\pi$
$431$	24.9909	+	22.5019i	1.20377	+	1.08388i	0.209411	+	0.977828i	$0.432845\pi$
$432$	3.99811	+	3.31891i	0.192359	+	0.159681i
$433$		−	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
$438$	−3.22932	−	10.7178i	−0.154303	−	0.512118i
$439$	−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
$441$	−54.1282	+	9.09242i	−2.57753	+	0.432973i
$442$	15.8422	−	11.5101i	0.753538	−	0.547477i
$443$	−16.5868	+	1.74334i	−0.788062	+	0.0828286i	−0.490005	−	0.871720i	$-0.663005\pi$
$443$	−16.5868	+	1.74334i	−0.788062	+	0.0828286i	−0.298057	+	0.954548i	$0.596338\pi$
$444$	0.232474	−	0.0193896i	0.0110327	−	0.000920190i
$445$	8.95530	+	20.1139i	0.424522	+	0.953492i
$446$	15.8379	−	3.36644i	0.749944	−	0.159406i
$447$	2.17879	−	1.87854i	0.103053	−	0.0888520i
$448$	−4.59464	−	2.04567i	−0.217077	−	0.0966487i
$449$	−11.0954	−	34.1480i	−0.523622	−	1.61154i	−0.767024	−	0.641618i	$-0.778263\pi$
$449$	−11.0954	−	34.1480i	−0.523622	−	1.61154i	0.243402	−	0.969925i	$-0.421737\pi$
$450$	3.17378	+	4.78861i	0.149614	+	0.225737i
$451$	13.3941	−	30.0836i	0.630703	−	1.41658i
$452$	−0.149837	+	0.704927i	−0.00704773	+	0.0331570i
$453$	−0.772107	+	1.63842i	−0.0362767	+	0.0769795i
$454$	0.638952	−	0.284480i	0.0299875	−	0.0133513i
$455$	29.4076	+	32.6605i	1.37865	+	1.53115i
$456$	−4.07384	−	2.47034i	−0.190775	−	0.115684i
$457$	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
$459$	−20.2380	+	2.95357i	−0.944627	+	0.137861i
$460$	7.82311	+	4.51668i	0.364754	+	0.210591i
$461$	−27.5867	−	20.0429i	−1.28484	−	0.933492i	−0.285154	−	0.958482i	$-0.592045\pi$
$461$	−27.5867	−	20.0429i	−1.28484	−	0.933492i	−0.999688	+	0.0249900i	$0.992045\pi$
$462$	6.75982	+	35.5449i	0.314495	+	1.65370i
$463$	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
$465$	6.52062	−	15.6330i	0.302386	−	0.724962i
$466$	−0.627917			−0.0290877
$467$	−2.65198	−	0.861682i	−0.122719	−	0.0398739i	0.247014	−	0.969012i	$-0.420551\pi$
$467$	−2.65198	−	0.861682i	−0.122719	−	0.0398739i	−0.369733	+	0.929138i	$0.620551\pi$
$468$	6.65129	−	13.3611i	0.307456	−	0.617619i
$469$	−22.9593	−	16.6809i	−1.06016	−	0.770251i
$470$	6.28347	+	3.62777i	0.289835	+	0.167336i
$471$	2.86580	−	22.5829i	0.132049	−	1.04056i
$472$	1.02157	−	9.71962i	0.0470217	−	0.447382i
$473$	0.980672	+	1.34978i	0.0450913	+	0.0620629i
$474$	7.17847	−	11.8380i	0.329718	−	0.543738i
$475$	−3.52461	−	3.91448i	−0.161720	−	0.179609i
$476$	18.0848	−	8.05186i	0.828914	−	0.369056i
$477$	−8.79275	−	16.8652i	−0.402592	−	0.772204i
$478$	−3.65542	+	17.1974i	−0.167195	+	0.786590i
$479$	17.4966	−	39.2979i	0.799438	−	1.79557i	0.230752	−	0.973013i	$-0.425881\pi$
$479$	17.4966	−	39.2979i	0.799438	−	1.79557i	0.568686	−	0.822555i	$-0.307452\pi$
$480$	1.00210	−	2.87244i	0.0457395	−	0.131108i
$481$	−0.207061	−	0.637269i	−0.00944118	−	0.0290570i
$482$	−10.7527	−	4.78742i	−0.489773	−	0.218061i
$483$	29.2557	+	33.9316i	1.33118	+	1.54394i
$484$	6.11464	−	1.29971i	0.277938	−	0.0590776i
$485$	−8.99675	−	20.2070i	−0.408521	−	0.917554i
$486$	−12.6371	+	9.12713i	−0.573229	+	0.414015i
$487$	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
$489$	−3.78185	+	4.02272i	−0.171021	+	0.181914i
$490$	16.0674	+	27.8295i	0.725850	+	1.25721i
$491$	6.06911	−	10.5120i	0.273895	−	0.474400i	−0.695961	−	0.718080i	$-0.745021\pi$
$491$	6.06911	−	10.5120i	0.273895	−	0.474400i	0.969856	+	0.243680i	$0.0783546\pi$
$492$	−13.1486	+	3.96173i	−0.592787	+	0.178609i
$493$	−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
$498$	6.65039	+	9.58015i	0.298011	+	0.429297i
$499$	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
$501$	−6.74121	+	2.82928i	−0.301175	+	0.126403i
$502$	11.8038	−	6.81495i	0.526831	−	0.304166i
$503$	41.8990	+	4.40377i	1.86819	+	0.196354i	0.969974	−	0.243209i	$-0.0781999\pi$
$503$	41.8990	+	4.40377i	1.86819	+	0.196354i	0.898212	+	0.439563i	$0.144867\pi$
$504$	9.38543	−	11.8141i	0.418060	−	0.526243i
$505$	2.71160	+	25.7992i	0.120665	+	1.14805i
$506$	15.8746	−	14.2935i	0.705711	−	0.635425i
$507$	−19.8131	−	4.65890i	−0.879933	−	0.206909i
$508$	−3.52492	−	16.5834i	−0.156393	−	0.735771i
$509$	3.33307	+	0.708465i	0.147736	+	0.0314022i	0.281186	−	0.959653i	$-0.409272\pi$
$509$	3.33307	+	0.708465i	0.147736	+	0.0314022i	−0.133450	+	0.991056i	$0.542606\pi$
$510$	5.76278	+	10.4965i	0.255180	+	0.464791i
$511$	−30.9132	+	10.0443i	−1.36752	+	0.444334i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	10.2288	−	9.98300i	0.451613	−	0.440760i
$514$	−17.5765	−	3.73600i	−0.775266	−	0.164788i
$515$	2.28359	+	10.7434i	0.100627	+	0.473413i
$516$	0.159257	−	0.677281i	0.00701091	−	0.0298156i
$517$	12.7504	−	11.4805i	0.560760	−	0.504911i
$518$	−0.0708069	−	0.673683i	−0.00311108	−	0.0295999i
$519$	0.349139	−	16.2313i	0.0153255	−	0.712475i
$520$	−8.69044	−	0.913403i	−0.381101	−	0.0400554i
$521$	4.50543	−	2.60121i	0.197387	−	0.113961i	−0.398049	−	0.917364i	$-0.630313\pi$
$521$	4.50543	−	2.60121i	0.197387	−	0.113961i	0.595436	+	0.803403i	$0.296979\pi$
$522$	−1.46319	+	5.67223i	−0.0640422	+	0.248267i
$523$	−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
$525$	13.7036	−	9.51281i	0.598074	−	0.415173i
$526$			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
$531$	27.4691	+	10.2509i	1.19206	+	0.444851i
$532$	−6.91722	+	11.9810i	−0.299900	+	0.519442i
$533$	19.7223	+	34.1600i	0.854267	+	1.47963i
$534$	−15.8189	−	14.8717i	−0.684551	−	0.643562i
$535$	−11.9301	+	8.66774i	−0.515784	+	0.374739i
$536$	5.61168	−	0.589811i	0.242388	−	0.0254760i
$537$	1.07007	+	12.8297i	0.0461767	+	0.553641i
$538$	−11.7660	−	26.4269i	−0.507268	−	1.13934i
$539$	74.3292	−	15.7992i	3.20158	−	0.680518i
$540$	7.59325	+	5.06345i	0.326762	+	0.217896i
$541$	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
$543$	−10.7083	−	3.73578i	−0.459537	−	0.160318i
$544$	−1.60094	+	3.59577i	−0.0686396	+	0.154167i
$545$	−0.473025	+	2.22541i	−0.0202622	+	0.0953259i
$546$	−39.2040	−	18.4750i	−1.67778	−	0.790655i
$547$	−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
$549$	3.96153	+	10.0387i	0.169074	+	0.428441i
$550$	−4.67508	−	6.43470i	−0.199346	−	0.274376i
$551$	0.561431	−	5.34166i	0.0239178	−	0.227562i
$552$	−8.83711	−	1.12144i	−0.376132	−	0.0477317i
$553$	−34.8151	−	20.1005i	−1.48049	−	0.854761i
$554$	−8.42176	−	6.11876i	−0.357806	−	0.259961i
$555$	0.402527	−	0.0765513i	0.0170863	−	0.00324942i
$556$	4.71268	+	1.53124i	0.199862	+	0.0649392i
$557$	20.4242			0.865401			0.432700	−	0.901538i	$-0.357561\pi$
$557$	20.4242			0.865401			0.432700	+	0.901538i	$0.357561\pi$
$558$	0.0368521	+	16.7033i	0.00156008	+	0.707105i
$559$	−1.99844			−0.0845252
$560$	−8.40153	−	2.72982i	−0.355029	−	0.115356i
$561$	27.8174	−	5.29023i	1.17445	−	0.223354i
$562$	3.08042	+	2.23806i	0.129940	+	0.0944067i
$563$	−10.4932	−	6.05824i	−0.442235	−	0.255324i	0.262310	−	0.964984i	$-0.415516\pi$
$563$	−10.4932	−	6.05824i	−0.442235	−	0.255324i	−0.704545	+	0.709659i	$0.748849\pi$
$564$	−7.09791	−	0.900734i	−0.298876	−	0.0379278i
$565$	−0.132314	+	1.25888i	−0.00556648	+	0.0529615i
$566$	−0.386876	−	0.532489i	−0.0162616	−	0.0223822i
$567$	27.2860	+	36.1166i	1.14591	+	1.51675i
$568$	−3.24580	−	3.60483i	−0.136191	−	0.151255i
$569$	18.0767	−	8.04828i	0.757816	−	0.337402i	0.00880727	−	0.999961i	$-0.497197\pi$
$569$	18.0767	−	8.04828i	0.757816	−	0.337402i	0.749009	+	0.662560i	$0.230530\pi$
$570$	−7.56975	−	3.56726i	−0.317062	−	0.149416i
$571$	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
$573$	15.8269	+	5.52152i	0.661180	+	0.230665i
$574$	12.3224	+	37.9243i	0.514325	+	1.58293i
$575$	−8.99723	−	4.00583i	−0.375211	−	0.167054i
$576$	0.185001	+	2.99429i	0.00770835	+	0.124762i
$577$	−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
$579$	−2.84511	−	34.1118i	−0.118239	−	1.41764i
$580$	3.41088	−	0.358498i	0.141629	−	0.0148858i
$581$	27.3968	−	19.9049i	1.13661	−	0.825795i
$582$	15.8921	+	14.9405i	0.658749	+	0.619305i
$583$	13.1662	+	22.8046i	0.545290	+	0.944469i
$584$	3.23136	−	5.59689i	0.133715	−	0.231601i
$585$	9.16545	−	24.5605i	0.378945	−	1.01545i
$586$	9.23613	−	10.2578i	0.381541	−	0.423744i
$587$	−9.37400	+	28.8502i	−0.386906	+	1.19077i	0.548182	+	0.836359i	$0.315320\pi$
$587$	−9.37400	+	28.8502i	−0.386906	+	1.19077i	−0.935088	+	0.354416i	$0.884680\pi$
$588$	−25.2303	−	19.1732i	−1.04048	−	0.790689i
$589$	−2.28775	−	15.1433i	−0.0942653	−	0.623969i
$590$		−	17.1659i		−	0.706707i
$591$	−8.74203	+	6.06858i	−0.359599	+	0.249628i
$592$	0.100090	+	0.0901219i	0.00411369	+	0.00370399i
$593$	18.5909	−	25.5882i	0.763436	−	1.05078i	−0.233484	−	0.972361i	$-0.575013\pi$
$593$	18.5909	−	25.5882i	0.763436	−	1.05078i	0.996920	−	0.0784190i	$-0.0249872\pi$
$594$	16.9363	−	13.3770i	0.694905	−	0.548867i
$595$	30.1123	−	17.3853i	1.23448	−	0.712729i
$596$	1.65183	+	0.173614i	0.0676615	+	0.00711151i
$597$	−0.0921408	+	4.28359i	−0.00377107	+	0.175316i
$598$	2.67455	+	25.4466i	0.109370	+	1.04059i
$599$	−26.5065	+	23.8665i	−1.08302	+	0.975160i	−0.999772	−	0.0213689i	$-0.993198\pi$
$599$	−26.5065	+	23.8665i	−1.08302	+	0.975160i	−0.0832527	+	0.996528i	$0.526531\pi$
$600$	−0.759214	+	3.22875i	−0.0309948	+	0.131813i
$601$	−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
$603$	−2.49171	+	16.7434i	−0.101470	+	0.681843i
$604$	−0.994533	+	0.323143i	−0.0404670	+	0.0131485i
$605$	10.4425	−	3.39296i	0.424547	−	0.137944i
$606$	−12.3112	−	22.4240i	−0.500110	−	0.910911i
$607$	−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
$609$	16.5584	+	3.89357i	0.670980	+	0.157775i
$610$	4.69556	−	4.22790i	0.190118	−	0.171183i
$611$	2.14818	+	20.4386i	0.0869061	+	0.826856i
$612$	−9.24572	−	7.34503i	−0.373736	−	0.296905i
$613$	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
$615$	−22.2408	+	9.33443i	−0.896834	+	0.376400i
$616$	−12.2787	+	16.9001i	−0.494721	+	0.680925i
$617$	0.254194	+	0.228877i	0.0102335	+	0.00921425i	0.674231	−	0.738520i	$-0.264475\pi$
$617$	0.254194	+	0.228877i	0.0102335	+	0.00921425i	−0.663998	+	0.747734i	$0.731142\pi$
$618$	−6.17640	−	8.89736i	−0.248451	−	0.357904i
$619$		−	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
$624$	8.25066	−	2.48595i	0.330291	−	0.0995178i
$625$	5.87906	−	10.1828i	0.235162	−	0.407313i
$626$	−5.12998	−	8.88538i	−0.205035	−	0.355131i
$627$	−13.5542	+	14.4175i	−0.541303	+	0.575780i
$628$	10.6327	−	7.72514i	0.424292	−	0.308266i
$629$	−0.527223	+	0.0554134i	−0.0210218	+	0.00220948i
$630$	14.2255	−	22.3601i	0.566757	−	0.890848i
$631$	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
$633$	29.3160	+	34.0016i	1.16521	+	1.35144i
$634$	−16.7166	−	7.44269i	−0.663899	−	0.295587i
$635$	−9.20201	−	28.3209i	−0.365171	−	1.12388i
$636$	3.61712	−	10.3682i	0.143428	−	0.411124i
$637$	−37.0216	+	83.1519i	−1.46685	+	3.29460i
$638$	1.68621	−	7.93298i	0.0667576	−	0.314070i
$639$	12.9039	−	6.72751i	0.510470	−	0.266136i
$640$	1.60458	−	0.714403i	0.0634265	−	0.0282393i
$641$	23.5475	+	26.1522i	0.930071	+	1.03295i	0.999375	+	0.0353531i	$0.0112556\pi$
$641$	23.5475	+	26.1522i	0.930071	+	1.03295i	−0.0693037	+	0.997596i	$0.522078\pi$
$642$	7.54003	−	12.4343i	0.297581	−	0.490742i
$643$	−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
$645$	0.153845	−	1.21232i	0.00605763	−	0.0477350i
$646$	9.37631	+	5.41341i	0.368906	+	0.212988i
$647$	−29.3878	−	21.3515i	−1.15535	−	0.839414i	−0.166170	−	0.986097i	$-0.553140\pi$
$647$	−29.3878	−	21.3515i	−1.15535	−	0.839414i	−0.989184	+	0.146683i	$0.953140\pi$
$648$	−8.83677	−	1.70633i	−0.347141	−	0.0670311i
$649$	−38.6057	−	12.5438i	−1.51541	−	0.492386i
$650$	9.52703			0.373681
$651$	48.4888	−	1.15004i	1.90042	−	0.0450735i
$652$	−3.18772			−0.124841
$653$	−17.1285	−	5.56539i	−0.670290	−	0.217791i	−0.0459510	−	0.998944i	$-0.514632\pi$
$653$	−17.1285	−	5.56539i	−0.670290	−	0.217791i	−0.624340	+	0.781153i	$0.714632\pi$
$654$	−0.419158	−	2.20404i	−0.0163904	−	0.0861850i
$655$	−23.2352	−	16.8814i	−0.907876	−	0.659610i
$656$	−6.86626	−	3.96424i	−0.268082	−	0.154777i
$657$	13.8370	+	13.5808i	0.539835	+	0.529837i
$658$	−2.17168	+	20.6621i	−0.0846608	+	0.805493i
$659$	22.6931	+	31.2343i	0.883997	+	1.21672i	0.975298	+	0.220894i	$0.0708975\pi$
$659$	22.6931	+	31.2343i	0.883997	+	1.21672i	−0.0913008	+	0.995823i	$0.529102\pi$
$660$	−10.8045	−	6.55174i	−0.420564	−	0.255026i
$661$	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
$663$	−14.4585	+	30.6810i	−0.561521	+	1.19155i
$664$	−1.39991	+	6.58604i	−0.0543269	+	0.255588i
$665$	−9.88338	+	22.1984i	−0.383261	+	0.860818i
$666$	−0.336798	+	0.223222i	−0.0130506	+	0.00864966i
$667$	−3.10329	−	9.55096i	−0.120160	−	0.369814i
$668$	−3.85601	−	1.71681i	−0.149194	−	0.0664252i
$669$	−21.2401	+	18.3131i	−0.821190	+	0.708026i
$670$	9.69422	−	2.06057i	0.374521	−	0.0796068i
$671$	−6.07725	−	13.6497i	−0.234610	−	0.526942i
$672$	8.68115	−	0.724055i	0.334882	−	0.0279310i
$673$	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
$675$	−8.81031	−	4.62488i	−0.339109	−	0.178012i
$676$	−5.87556	−	10.1768i	−0.225983	−	0.391414i
$677$	10.5730	−	18.3129i	0.406352	−	0.703823i	−0.588126	−	0.808770i	$-0.700134\pi$
$677$	10.5730	−	18.3129i	0.406352	−	0.703823i	0.994478	+	0.104947i	$0.0334673\pi$
$678$	−0.360110	−	1.19517i	−0.0138300	−	0.0459004i
$679$	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	$-0.807781\pi$
$683$		−	29.6799i		−	1.13567i	0.823142	−	0.567835i	$-0.192219\pi$
$684$	8.24441	+	0.354842i	0.315233	+	0.0135677i
$685$	−6.15392	−	5.54101i	−0.235129	−	0.211711i
$686$	−33.3923	+	45.9606i	−1.27492	+	1.75478i
$687$	8.11747	+	19.3412i	0.309701	+	0.737911i
$688$	0.347877	−	0.200847i	0.0132627	−	0.00765721i
$689$	−31.3684	−	3.29696i	−1.19504	−	0.125604i
$690$	−15.6426	−	0.336476i	−0.595504	−	0.0128094i
$691$	−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
$693$	−39.8924	−	48.3323i	−1.51539	−	1.83599i
$694$	2.37715	+	11.1836i	0.0902354	+	0.424524i
$695$	8.51327	+	1.80955i	0.322927	+	0.0686402i
$696$	−2.96465	+	1.62766i	−0.112375	+	0.0616961i
$697$	29.6795	−	9.64347i	1.12419	−	0.365272i
$698$	−13.1968	+	4.28790i	−0.499506	+	0.162299i
$699$	0.953352	−	0.523411i	0.0360591	−	0.0197972i
$700$	9.42077	+	2.00245i	0.356072	+	0.0756853i
$701$	−1.08350	−	5.09748i	−0.0409234	−	0.192529i	0.952937	−	0.303167i	$-0.0980440\pi$
$701$	−1.08350	−	5.09748i	−0.0409234	−	0.192529i	−0.993861	+	0.110638i	$0.964711\pi$
$702$	1.03891	+	25.8302i	0.0392112	+	0.974899i
$703$	0.275317	−	0.247896i	0.0103838	−	0.00934959i
$704$	−0.434155	−	4.13071i	−0.0163628	−	0.155682i
$705$	−12.5640	−	0.270255i	−0.473189	−	0.0101784i
$706$	28.8285	+	3.03000i	1.08498	+	0.114036i
$707$	−64.3300	+	37.1409i	−2.41938	+	1.39683i
$708$	6.55093	+	15.6086i	0.246199	+	0.586608i
$709$	−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
$711$	−1.03112	+	23.9571i	−0.0386701	+	0.898463i
$712$		−	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
$717$	−8.78524	−	29.1574i	−0.328091	−	1.08890i
$718$	8.94840	−	15.4991i	0.333951	−	0.578421i
$719$	−12.7348	−	22.0573i	−0.474928	−	0.822600i	0.524660	−	0.851312i	$-0.324193\pi$
$719$	−12.7348	−	22.0573i	−0.474928	−	0.822600i	−0.999588	+	0.0287124i	$0.990859\pi$
$720$	0.872902	+	5.19648i	0.0325311	+	0.193661i
$721$	−25.4442	+	18.4863i	−0.947590	+	0.688465i
$722$	11.3711	−	1.19515i	0.423189	−	0.0444790i
$723$	20.3162	−	1.69449i	0.755569	−	0.0630186i
$724$	−2.66326	−	5.98177i	−0.0989792	−	0.222311i
$725$	−3.65752	+	0.777429i	−0.135837	+	0.0288730i
$726$	−8.20033	+	7.07028i	−0.304343	+	0.262403i
$727$	−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
$729$	11.5785	−	24.3914i	0.428833	−	0.903384i
$730$	4.61700	−	10.3699i	0.170883	−	0.383809i
$731$	−0.328727	+	1.54654i	−0.0121584	+	0.0572007i
$732$	−2.65612	+	5.63631i	−0.0981731	+	0.208324i
$733$	−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
$735$	−47.5925	−	28.8597i	−1.75548	−	1.06450i
$736$	−3.02299	−	4.16079i	−0.111429	−	0.153369i
$737$	2.44976	−	23.3079i	0.0902380	−	0.858557i
$738$	16.6609	−	16.9753i	0.613297	−	0.624869i
$739$	−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
$741$	−4.42834	−	23.2854i	−0.162679	−	0.855410i
$742$	−30.3256	−	9.85338i	−1.11329	−	0.361729i
$743$	19.1118			0.701145			0.350572	−	0.936536i	$-0.385987\pi$
$743$	19.1118			0.701145			0.350572	+	0.936536i	$0.385987\pi$
$744$	−7.01161	+	6.62098i	−0.257058	+	0.242737i
$745$	2.91730			0.106882
$746$	11.7991	+	3.83376i	0.431995	+	0.140364i
$747$	−18.0828	−	9.00179i	−0.661616	−	0.329358i
$748$	13.2260	+	9.60926i	0.483591	+	0.351349i
$749$	−36.5687	−	21.1129i	−1.33619	−	0.771450i
$750$	−2.64836	+	20.8695i	−0.0967046	+	0.762046i
$751$	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
$753$	−12.2408	+	20.1863i	−0.446079	+	0.735629i
$754$	6.50025	+	7.21926i	0.236725	+	0.262910i
$755$	−1.67793	+	0.747062i	−0.0610661	+	0.0271884i
$756$	−4.40182	+	25.7605i	−0.160093	+	0.936900i
$757$	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
$759$	−12.1874	+	34.9341i	−0.442374	+	1.26803i
$760$	−1.49298	−	4.59491i	−0.0541559	−	0.166675i
$761$	−5.92691	−	2.63883i	−0.214850	−	0.0956575i	0.296490	−	0.955036i	$-0.404184\pi$
$761$	−5.92691	−	2.63883i	−0.214850	−	0.0956575i	−0.511340	+	0.859379i	$0.670851\pi$
$762$	19.1752	+	22.2400i	0.694645	+	0.805670i
$763$	−6.37237	+	1.35449i	−0.230695	+	0.0490358i
$764$	3.93632	+	8.84111i	0.142411	+	0.319860i
$765$	−17.4990	−	11.1329i	−0.632678	−	0.402509i
$766$	−25.0371	+	2.63150i	−0.904625	+	0.0950800i
$767$	39.3360	−	28.5793i	1.42034	−	1.03194i
$768$	−1.18638	+	1.26194i	−0.0428098	+	0.0455364i
$769$	−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
$771$	29.8002	−	8.97891i	1.07323	−	0.323367i
$772$	13.2239	−	14.6867i	0.475940	−	0.528585i
$773$	−10.2933	+	31.6796i	−0.370225	+	1.13943i	0.576420	+	0.817154i	$0.304449\pi$
$773$	−10.2933	+	31.6796i	−0.370225	+	1.13943i	−0.946644	+	0.322280i	$0.895551\pi$
$774$	0.322763	+	1.16105i	0.0116015	+	0.0417332i
$775$	−9.53428	+	4.77252i	−0.342481	+	0.171434i
$776$			12.5934i			0.452076i
$777$	0.669064	+	0.963815i	0.0240025	+	0.0345767i
$778$	−12.1996	−	10.9846i	−0.437378	−	0.393817i
$779$	−12.8188	+	17.6436i	−0.459282	+	0.632148i
$780$	13.9559	−	5.85727i	0.499701	−	0.209724i
$781$	−17.4482	+	10.0737i	−0.624347	+	0.360467i
$782$	20.1323	+	2.11599i	0.719931	+	0.0756678i
$783$	−2.50666	−	9.83169i	−0.0895807	−	0.351356i
$784$	−1.91240	−	18.1953i	−0.0683001	−	0.649832i
$785$	17.1550	−	15.4464i	0.612289	−	0.551307i
$786$	27.5698	+	6.48281i	0.983382	+	0.231234i
$787$	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
$789$	−12.2868	−	22.3794i	−0.437420	−	0.796726i
$790$	13.3522	−	4.33839i	0.475049	−	0.154353i
$791$	−3.44721	+	1.12007i	−0.122569	+	0.0398250i
$792$	12.3247	+	1.83413i	0.437938	+	0.0651729i
$793$	17.5059	+	3.72100i	0.621654	+	0.132137i
$794$	3.64430	+	17.1451i	0.129331	+	0.608456i
$795$	4.41485	−	18.7753i	0.156579	−	0.665890i
$796$	−1.83832	+	1.65523i	−0.0651575	+	0.0586681i
$797$	0.991228	+	9.43090i	0.0351111	+	0.334060i	0.997951	+	0.0639862i	$0.0203814\pi$
$797$	0.991228	+	9.43090i	0.0351111	+	0.334060i	−0.962840	+	0.270074i	$0.912952\pi$
$798$	0.515308	−	23.9564i	0.0182417	−	0.848048i
$799$	16.1702	+	1.69955i	0.572059	+	0.0601259i
$800$	−1.65841	+	0.957481i	−0.0586335	+	0.0338521i
$801$	36.4141	+	9.39325i	1.28663	+	0.331894i
$802$	−18.4429	+	25.3845i	−0.651243	+	0.896359i
$803$	−19.9480	−	17.9613i	−0.703950	−	0.633839i
$804$	−8.02843	+	5.57321i	−0.283141	+	0.196552i
$805$			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	−0.920681	−	0.390316i	$-0.872366\pi$
$809$	−12.4087	+	13.7812i	−0.436265	+	0.484522i	0.484416	+	0.874838i	$0.339032\pi$
$810$	−15.7494	−	1.35823i	−0.553377	−	0.0477235i
$811$	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
$813$	−11.7968	−	11.0905i	−0.413733	−	0.388960i
$814$	0.452571	−	0.328812i	0.0158626	−	0.0115249i
$815$	−5.56833	+	0.585255i	−0.195050	+	0.0205006i
$816$	−0.566645	−	6.79386i	−0.0198365	−	0.237833i
$817$	−0.449416	−	1.00940i	−0.0157231	−	0.0353146i
$818$	17.8404	−	3.79209i	0.623774	−	0.132587i
$819$	74.9226	−	4.62905i	2.61801	−	0.161752i
$820$	−12.7218	−	5.66413i	−0.444266	−	0.197800i
$821$	15.8746	+	48.8570i	0.554028	+	1.70512i	0.698498	+	0.715612i	$0.253852\pi$
$821$	15.8746	+	48.8570i	0.554028	+	1.70512i	−0.144470	+	0.989509i	$0.546148\pi$
$822$	7.71025	+	2.68986i	0.268926	+	0.0938197i
$823$	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
$825$	12.4618	+	5.87266i	0.433865	+	0.204460i
$826$	44.9042	−	19.9926i	1.56242	−	0.695633i
$827$	−34.4731	−	38.2863i	−1.19875	−	1.33134i	−0.929745	−	0.368204i	$-0.879973\pi$
$827$	−34.4731	−	38.2863i	−1.19875	−	1.33134i	−0.269002	−	0.963140i	$-0.586694\pi$
$828$	14.3520	−	5.66367i	0.498766	−	0.196826i
$829$	−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
$831$	17.8870	+	2.26988i	0.620492	+	0.0787412i
$832$	4.30852	+	2.48752i	0.149371	+	0.0862394i
$833$	58.2591	+	42.3277i	2.01856	+	1.46657i
$834$	−8.43155	+	1.60349i	−0.291961	+	0.0555242i
$835$	−7.05090	−	2.29098i	−0.244006	−	0.0792825i
$836$	−11.4248			−0.395137
$837$	−13.9792	−	25.3294i	−0.483193	−	0.875514i
$838$	25.7470			0.889415
$839$	−34.3792	−	11.1705i	−1.18690	−	0.385648i	−0.351975	−	0.936009i	$-0.614490\pi$
$839$	−34.3792	−	11.1705i	−1.18690	−	0.385648i	−0.834927	+	0.550361i	$0.814490\pi$
$840$	15.0313	−	2.85861i	0.518631	−	0.0986315i
$841$	20.3769	+	14.8047i	0.702651	+	0.510506i
$842$	−26.5964	−	15.3555i	−0.916573	−	0.529184i
$843$	−6.54250	−	0.830252i	−0.225336	−	0.0285954i
$844$	−2.70937	+	25.7780i	−0.0932604	+	0.887314i
$845$	−12.1319	−	16.6981i	−0.417349	−	0.574432i
$846$	11.5274	−	4.54902i	0.396321	−	0.156399i
$847$	21.0377	+	23.3648i	0.722866	+	0.802824i
$848$	5.79177	−	2.57866i	0.198890	−	0.0885517i
$849$	1.03125	+	0.485978i	0.0353924	+	0.0166787i
$850$	1.56711	−	7.37269i	0.0537515	−	0.252881i
$851$	0.281742	−	0.632802i	0.00965798	−	0.0216922i
$852$	7.93289	+	2.76753i	0.271776	+	0.0948141i
$853$	−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
$855$	14.4665	−	0.893806i	0.494745	−	0.0305675i
$856$	8.21223	−	1.74556i	0.280688	−	0.0596621i
$857$	2.45165	+	5.50649i	0.0837467	+	0.188098i	0.950565	−	0.310526i	$-0.100505\pi$
$857$	2.45165	+	5.50649i	0.0837467	+	0.188098i	−0.866818	+	0.498625i	$0.833839\pi$
$858$	−2.97480	−	35.6667i	−0.101558	−	1.21764i
$859$	−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
$861$	−50.3212	−	47.3081i	−1.71494	−	1.61226i
$862$	−16.8143	−	29.1232i	−0.572698	−	0.991942i
$863$	−4.32367	+	7.48881i	−0.147179	+	0.254922i	−0.930184	−	0.367094i	$-0.880353\pi$
$863$	−4.32367	+	7.48881i	−0.147179	+	0.254922i	0.783005	+	0.622016i	$0.213686\pi$
$864$	−2.77682	−	4.39195i	−0.0944695	−	0.149417i
$865$	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
$870$	−4.87983	+	3.38750i	−0.165442	+	0.114847i
$871$	20.8617	+	18.7839i	0.706871	+	0.636469i
$872$	0.761366	−	1.04793i	0.0257831	−	0.0354874i
$873$	−36.5826	−	9.43672i	−1.23813	−	0.319385i
$874$	−12.2515	+	7.07341i	−0.414413	+	0.239262i
$875$	60.7514	+	6.38523i	2.05377	+	0.215860i
$876$	−0.240725	+	11.1912i	−0.00813333	+	0.378115i
$877$	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
$879$	−5.47247	+	23.2731i	−0.184582	+	0.784981i
$880$	−1.51677	−	7.13584i	−0.0511303	−	0.240549i
$881$	−27.4880	−	5.84276i	−0.926095	−	0.196848i	−0.279908	−	0.960027i	$-0.590304\pi$
$881$	−27.4880	−	5.84276i	−0.926095	−	0.196848i	−0.646187	+	0.763179i	$0.723637\pi$
$882$	54.2887	+	8.07912i	1.82799	+	0.272038i
$883$	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
$885$	14.3089	+	26.0625i	0.480988	+	0.876082i
$886$	16.3137	+	3.46758i	0.548069	+	0.116496i
$887$	6.92772	+	32.5924i	0.232610	+	1.09434i	0.927092	+	0.374834i	$0.122300\pi$
$887$	6.92772	+	32.5924i	0.232610	+	1.09434i	−0.694482	+	0.719510i	$0.744366\pi$
$888$	−0.227088	−	0.0533978i	−0.00762056	−	0.00179191i
$889$	63.3673	−	57.0562i	2.12527	−	1.91360i
$890$	−2.30145	−	21.8968i	−0.0771448	−	0.733984i
$891$	−14.5633	+	34.4276i	−0.487890	+	1.15337i
$892$	−16.1030	−	1.69249i	−0.539168	−	0.0566688i
$893$	−9.84033	+	5.68132i	−0.329294	+	0.190118i
$894$	−2.65265	+	1.11332i	−0.0887180	+	0.0372349i
$895$	−7.67378	+	10.5621i	−0.256506	+	0.353050i
$896$	3.73762	+	3.36537i	0.124865	+	0.112429i
$897$	−25.2722	−	36.4056i	−0.843814	−	1.21555i
$898$			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
$903$	3.35049	−	1.00951i	0.111497	−	0.0335945i
$904$	0.360338	−	0.624123i	0.0119847	−	0.0207580i
$905$	−5.75043	−	9.96003i	−0.191151	−	0.331083i
$906$	1.24062	−	1.31963i	0.0412167	−	0.0438418i
$907$	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
$909$	37.3838	+	23.7835i	1.23994	+	0.788850i
$910$	−17.8757	−	40.1494i	−0.592573	−	1.33094i
$911$	−36.9801	+	7.86037i	−1.22521	+	0.260426i	−0.774689	−	0.632342i	$-0.782094\pi$
$911$	−36.9801	+	7.86037i	−1.22521	+	0.260426i	−0.450517	+	0.892768i	$0.648760\pi$
$912$	3.11107	+	3.60832i	0.103018	+	0.119483i
$913$	25.5482	+	11.3748i	0.845522	+	0.376451i
$914$	−9.56323	−	29.4326i	−0.316324	−	0.973544i
$915$	−3.60492	+	10.3332i	−0.119175	+	0.341605i
$916$	−4.92568	+	11.0633i	−0.162749	+	0.365540i
$917$	17.0986	−	80.4425i	0.564645	−	2.65644i
$918$	20.1601	+	3.44486i	0.665384	+	0.113697i
$919$	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
$921$	−29.4349	+	48.5411i	−0.969913	+	1.59948i
$922$	20.0429	+	27.5867i	0.660078	+	0.908520i
$923$	2.52257	−	24.0006i	0.0830313	−	0.789990i
$924$	4.55501	−	35.8941i	0.149849	−	1.18083i
$925$	−0.223362	−	0.128958i	−0.00734411	−	0.00424012i
$926$	−12.5867	−	9.14477i	−0.413624	−	0.300516i
$927$	16.7940	+	8.36022i	0.551589	+	0.274586i
$928$	−1.85707	−	0.603399i	−0.0609613	−	0.0198075i
$929$	27.0438			0.887277			0.443639	−	0.896206i	$-0.353687\pi$
$929$	27.0438			0.887277			0.443639	+	0.896206i	$0.353687\pi$
$930$	−11.0323	+	12.8529i	−0.361764	+	0.421462i
$931$	−50.3251			−1.64934
$932$	0.597184	+	0.194037i	0.0195614	+	0.00635589i
$933$	−5.42569	−	28.5297i	−0.177629	−	0.934020i
$934$	2.25591	+	1.63902i	0.0738157	+	0.0536302i
$935$	24.8675	+	14.3573i	0.813255	+	0.469533i
$936$	−10.4546	+	10.6518i	−0.341719	+	0.348166i
$937$	−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
$939$	15.1953	+	9.21429i	0.495880	+	0.300697i
$940$	−4.85490	−	5.39191i	−0.158349	−	0.175865i
$941$	−30.1356	+	13.4173i	−0.982394	+	0.437390i	−0.834136	−	0.551559i	$-0.814033\pi$
$941$	−30.1356	+	13.4173i	−0.982394	+	0.437390i	−0.148258	+	0.988949i	$0.547367\pi$
$942$	−9.70402	+	20.5920i	−0.316174	+	0.670924i
$943$	−8.47788	+	39.8853i	−0.276078	+	1.29884i
$944$	−3.97510	+	8.92823i	−0.129379	+	0.290589i
$945$	−2.95959	+	45.8067i	−0.0962754	+	1.49009i
$946$	−0.515570	−	1.58676i	−0.0167626	−	0.0515900i
$947$	47.3634	+	21.0875i	1.53910	+	0.685253i	0.988736	−	0.149670i	$-0.0478211\pi$
$947$	47.3634	+	21.0875i	1.53910	+	0.685253i	0.550367	+	0.834923i	$0.314488\pi$
$948$	−10.4853	+	9.04036i	−0.340546	+	0.293617i
$949$	31.4498	−	6.68486i	1.02090	−	0.217000i
$950$	2.14246	+	4.81205i	0.0695107	+	0.156124i
$951$	31.5844	−	2.63431i	1.02419	−	0.0854233i
$952$	−19.6878	+	2.06927i	−0.638085	+	0.0670655i
$953$	13.2562	−	9.63121i	0.429411	−	0.311986i	−0.352002	−	0.935999i	$-0.614499\pi$
$953$	13.2562	−	9.63121i	0.429411	−	0.311986i	0.781413	+	0.624014i	$0.214499\pi$
$954$	3.15077	+	18.7569i	0.102010	+	0.607276i
$955$	8.49918	+	14.7210i	0.275027	+	0.476361i
$956$	8.79079	−	15.2261i	0.284315	−	0.492447i
$957$	4.05254	+	13.4500i	0.131000	+	0.434778i
$958$	−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
$963$	−1.08306	+	25.1638i	−0.0349010	+	0.810892i
$964$	8.74705	+	7.87588i	0.281723	+	0.253665i
$965$	20.4032	−	28.0826i	0.656803	−	0.904012i
$966$	−17.3384	−	41.3114i	−0.557853	−	1.32917i
$967$	−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
$969$	−18.7483	−	0.403279i	−0.602282	−	0.0129552i
$970$	2.31210	+	21.9982i	0.0742371	+	0.706319i
$971$	−8.42920	+	7.58968i	−0.270506	+	0.243565i	−0.793208	−	0.608951i	$-0.791591\pi$
$971$	−8.42920	+	7.58968i	−0.270506	+	0.243565i	0.522702	+	0.852515i	$0.324924\pi$
$972$	14.8390	−	4.77535i	0.475961	−	0.153169i
$973$	5.18158	+	24.3774i	0.166114	+	0.781505i
$974$	−24.1459	−	5.13236i	−0.773683	−	0.164451i
$975$	−14.4647	+	7.94142i	−0.463240	+	0.254329i
$976$	−3.42129	+	1.11165i	−0.109513	+	0.0355829i
$977$	11.7627	−	3.82194i	0.376322	−	0.122275i	−0.114748	−	0.993395i	$-0.536606\pi$
$977$	11.7627	−	3.82194i	0.376322	−	0.122275i	0.491070	+	0.871120i	$0.336606\pi$
$978$	4.83985	−	2.65718i	0.154761	−	0.0849673i
$979$	−50.9274	−	10.8249i	−1.62765	−	0.345967i
$980$	−6.68119	−	31.4325i	−0.213423	−	1.00408i
$981$	2.47362	+	2.99695i	0.0789765	+	0.0956854i
$982$	−9.02045	+	8.12205i	−0.287854	+	0.259185i
$983$	−3.04641	−	28.9846i	−0.0971653	−	0.924466i	−0.929159	−	0.369681i	$-0.879467\pi$
$983$	−3.04641	−	28.9846i	−0.0971653	−	0.924466i	0.831994	−	0.554785i	$-0.187200\pi$
$984$	13.7293	+	0.295321i	0.437676	+	0.00941449i
$985$	−10.7326	−	1.12804i	−0.341969	−	0.0359424i
$986$	6.65601	−	3.84285i	0.211970	−	0.122381i
$987$	−13.9261	−	33.1811i	−0.443272	−	1.05617i
$988$	8.04371	−	11.0712i	0.255904	−	0.352222i
$989$	−1.53528	−	1.38237i	−0.0488190	−	0.0439568i
$990$	21.8655	+	0.941099i	0.694932	+	0.0299101i
$991$		−	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
$996$	−3.36446	−	11.1664i	−0.106607	−	0.353819i
$997$	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
$999$	0.325282	−	0.619656i	0.0102915	−	0.0196050i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.70155 - 0.323596i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.52111 + 0.878214i) q^{5} +(-1.71827 - 0.218051i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.79057 - 1.10123i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.70155 - 0.323596i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.52111 + 0.878214i) q^{5} +(-1.71827 - 0.218051i) q^{6} +(-0.525722 + 5.00191i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(2.79057 - 1.10123i) q^{9} +(-1.17528 - 1.30528i) q^{10} +(-3.79438 + 1.68937i) q^{11} +(1.56679 + 0.738353i) q^{12} +(1.03437 - 4.86633i) q^{13} +(2.04567 - 4.59464i) q^{14} +(2.87244 + 1.00210i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-3.59577 - 1.60094i) q^{17} +(-2.99429 + 0.185001i) q^{18} +(2.69057 - 0.571899i) q^{19} +(0.714403 + 1.60458i) q^{20} +(0.724055 + 8.68115i) q^{21} +(4.13071 - 0.434155i) q^{22} +(4.16079 - 3.02299i) q^{23} +(-1.26194 - 1.18638i) q^{24} +(-0.957481 - 1.65841i) q^{25} +(-2.48752 + 4.30852i) q^{26} +(4.39195 - 2.77682i) 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} +(-5.90966 + 4.10239i) q^{33} +(2.92506 + 2.63373i) q^{34} +(-5.19243 + 7.14677i) q^{35} +(2.90491 + 0.749341i) q^{36} +(0.116641 - 0.0673425i) q^{37} +(-2.73561 - 0.287524i) q^{38} +(0.185311 - 8.61504i) q^{39} +(-0.183597 - 1.74681i) q^{40} +(-5.89201 + 5.30519i) q^{41} +(1.99400 - 8.48001i) q^{42} +(-0.0835168 - 0.392915i) q^{43} +(-4.06270 - 0.863553i) q^{44} +(5.21189 + 0.775621i) q^{45} +(-4.89131 + 1.58928i) q^{46} +(-3.92867 + 1.27650i) q^{47} +(0.833567 + 1.51828i) q^{48} +(-17.8957 - 3.80385i) q^{49} +(0.398143 + 1.87312i) q^{50} +(-6.63645 - 1.56051i) q^{51} +(3.69718 - 3.32896i) q^{52} +(-0.662698 - 6.30515i) q^{53} +(-5.03508 + 1.28373i) q^{54} +(-7.25529 - 0.762562i) q^{55} +(4.35564 - 2.51473i) q^{56} +(4.39309 - 1.84377i) q^{57} +(-1.14773 + 1.57972i) q^{58} +(7.26288 + 6.53952i) q^{59} +(1.73483 + 2.49910i) 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} +(6.88813 - 2.07542i) q^{66} +(-2.82129 + 4.88662i) q^{67} +(-1.96803 - 3.40872i) q^{68} +(6.10159 - 6.49020i) q^{69} +(7.14677 - 5.19243i) q^{70} +(4.82420 - 0.507044i) q^{71} +(-2.53117 - 1.61033i) q^{72} +(2.62863 + 5.90400i) q^{73} +(-0.131742 + 0.0280026i) q^{74} +(-2.16586 - 2.51203i) q^{75} +(2.51287 + 1.11880i) q^{76} +(-6.45527 - 19.8673i) q^{77} +(-2.83844 + 8.13613i) q^{78} +(-3.25109 + 7.30206i) q^{79} +(-0.365182 + 1.71805i) q^{80} +(6.57457 - 6.14614i) q^{81} +(7.24302 - 3.22480i) q^{82} +(-4.50537 - 5.00373i) q^{83} +(-4.51688 + 7.44878i) q^{84} +(-4.06359 - 5.59305i) q^{85} +(-0.0419884 + 0.399493i) q^{86} +(0.425774 - 3.35516i) q^{87} +(3.59700 + 2.07673i) q^{88} +(10.1413 + 7.36810i) q^{89} +(-4.71712 - 2.34822i) q^{90} +(23.7972 + 7.73217i) q^{91} +5.14302 q^{92} +(-1.23516 - 9.56422i) q^{93} +4.13084 q^{94} +(4.59491 + 1.49298i) q^{95} +(-0.323596 - 1.70155i) q^{96} +(-10.1882 - 7.40220i) q^{97} +(15.8444 + 9.14776i) q^{98} +(-8.72809 + 8.89278i) 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

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Database

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