LMFDB - Embedded newform 228.2.v.a.23.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (of order $18$, degree $6$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.12
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687167 - 1.23604i) q^{2} +(0.927511 - 1.46278i) q^{3} +(-1.05560 + 1.69873i) q^{4} +(0.118249 + 0.140923i) q^{5} +(-2.44541 - 0.141271i) q^{6} +(-1.88835 - 1.09024i) q^{7} +(2.82509 + 0.137458i) q^{8} +(-1.27945 - 2.71349i) q^{9} +O(q^{10})$	\(q+(-0.687167 - 1.23604i) q^{2} +(0.927511 - 1.46278i) q^{3} +(-1.05560 + 1.69873i) q^{4} +(0.118249 + 0.140923i) q^{5} +(-2.44541 - 0.141271i) q^{6} +(-1.88835 - 1.09024i) q^{7} +(2.82509 + 0.137458i) q^{8} +(-1.27945 - 2.71349i) q^{9} +(0.0929307 - 0.242998i) q^{10} +(-2.97017 - 5.14448i) q^{11} +(1.50579 + 3.11971i) q^{12} +(0.572936 - 3.24928i) q^{13} +(-0.0499714 + 3.08326i) q^{14} +(0.315817 - 0.0422638i) q^{15} +(-1.77140 - 3.58638i) q^{16} +(-1.63631 + 4.49572i) q^{17} +(-2.47480 + 3.44607i) q^{18} +(4.17803 + 1.24260i) q^{19} +(-0.364215 + 0.0521140i) q^{20} +(-3.34625 + 1.75103i) q^{21} +(-4.31780 + 7.20637i) q^{22} +(4.68466 + 3.93090i) q^{23} +(2.82137 - 4.00498i) q^{24} +(0.862364 - 4.89071i) q^{25} +(-4.40995 + 1.52462i) q^{26} +(-5.15593 - 0.645244i) q^{27} +(3.84538 - 2.05695i) q^{28} +(0.421181 + 1.15719i) q^{29} +(-0.269259 - 0.361321i) q^{30} +(6.65444 + 3.84194i) q^{31} +(-3.21567 + 4.65397i) q^{32} +(-10.2801 - 0.426865i) q^{33} +(6.68132 - 1.06676i) q^{34} +(-0.0696549 - 0.395032i) q^{35} +(5.96009 + 0.690930i) q^{36} -1.63611 q^{37} +(-1.33509 - 6.01810i) q^{38} +(-4.22158 - 3.85183i) q^{39} +(0.314692 + 0.414375i) q^{40} +(1.14765 - 0.202362i) q^{41} +(4.46378 + 2.93285i) q^{42} +(-1.51151 - 1.80135i) q^{43} +(11.8744 + 0.385007i) q^{44} +(0.231101 - 0.501170i) q^{45} +(1.63962 - 8.49163i) q^{46} +(6.83260 - 2.48686i) q^{47} +(-6.88908 - 0.735242i) q^{48} +(-1.12275 - 1.94467i) q^{49} +(-6.63772 + 2.29481i) q^{50} +(5.05855 + 6.56339i) q^{51} +(4.91488 + 4.40322i) q^{52} +(1.42960 - 1.70373i) q^{53} +(2.74544 + 6.81635i) q^{54} +(0.373759 - 1.02690i) q^{55} +(-5.18489 - 3.33959i) q^{56} +(5.69282 - 4.95901i) q^{57} +(1.14091 - 1.31578i) q^{58} +(5.82579 + 2.12042i) q^{59} +(-0.261583 + 0.581103i) q^{60} +(9.65727 + 8.10341i) q^{61} +(0.176097 - 10.8652i) q^{62} +(-0.542311 + 6.51892i) q^{63} +(7.96221 + 0.776659i) q^{64} +(0.525649 - 0.303484i) q^{65} +(6.53652 + 13.0000i) q^{66} +(-3.18066 - 8.73880i) q^{67} +(-5.90974 - 7.52535i) q^{68} +(10.0951 - 3.20667i) q^{69} +(-0.440412 + 0.357549i) q^{70} +(-3.36704 + 2.82528i) q^{71} +(-3.24155 - 7.84170i) q^{72} +(1.20880 + 6.85547i) q^{73} +(1.12428 + 2.02230i) q^{74} +(-6.35418 - 5.79764i) q^{75} +(-6.52120 + 5.78567i) q^{76} +12.9528i q^{77} +(-1.86009 + 7.86490i) q^{78} +(-6.94773 + 1.22507i) q^{79} +(0.295939 - 0.673717i) q^{80} +(-5.72604 + 6.94352i) q^{81} +(-1.03876 - 1.27949i) q^{82} +(1.86888 - 3.23699i) q^{83} +(0.557775 - 7.53278i) q^{84} +(-0.827043 + 0.301019i) q^{85} +(-1.18788 + 3.10612i) q^{86} +(2.08336 + 0.457208i) q^{87} +(-7.68383 - 14.9419i) q^{88} +(1.23073 + 0.217011i) q^{89} +(-0.778273 + 0.0587368i) q^{90} +(-4.62440 + 5.51115i) q^{91} +(-11.6227 + 3.80853i) q^{92} +(11.7920 - 6.17053i) q^{93} +(-7.76901 - 6.73650i) q^{94} +(0.318935 + 0.735718i) q^{95} +(3.82516 + 9.02043i) q^{96} +(-10.6136 - 3.86302i) q^{97} +(-1.63217 + 2.72408i) q^{98} +(-10.1593 + 14.6416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−0.687167	−	1.23604i	−0.485900	−	0.874014i
$2$	−0.687167	−	1.23604i	−0.485900	−	0.874014i
$3$	0.927511	−	1.46278i	0.535499	−	0.844536i
$3$	0.927511	−	1.46278i	0.535499	−	0.844536i
$4$	−1.05560	+	1.69873i	−0.527802	+	0.849367i
$5$	0.118249	+	0.140923i	0.0528825	+	0.0630229i	0.791837	−	0.610732i	$-0.209125\pi$
$5$	0.118249	+	0.140923i	0.0528825	+	0.0630229i	−0.738955	+	0.673755i	$0.764680\pi$
$6$	−2.44541	−	0.141271i	−0.998335	−	0.0576735i
$7$	−1.88835	−	1.09024i	−0.713730	−	0.412072i	0.0987109	−	0.995116i	$-0.468528\pi$
$7$	−1.88835	−	1.09024i	−0.713730	−	0.412072i	−0.812440	+	0.583044i	$0.801861\pi$
$8$	2.82509	+	0.137458i	0.998818	+	0.0485986i
$9$	−1.27945	−	2.71349i	−0.426482	−	0.904496i
$10$	0.0929307	−	0.242998i	0.0293873	−	0.0768428i
$11$	−2.97017	−	5.14448i	−0.895540	−	1.55112i	−0.833135	−	0.553069i	$-0.813456\pi$
$11$	−2.97017	−	5.14448i	−0.895540	−	1.55112i	−0.0624045	−	0.998051i	$-0.519877\pi$
$12$	1.50579	+	3.11971i	0.434684	+	0.900583i
$13$	0.572936	−	3.24928i	0.158904	−	0.901189i	−0.796226	−	0.605000i	$-0.793173\pi$
$13$	0.572936	−	3.24928i	0.158904	−	0.901189i	0.955129	−	0.296189i	$-0.0957158\pi$
$14$	−0.0499714	+	3.08326i	−0.0133554	+	0.824036i
$15$	0.315817	−	0.0422638i	0.0815436	−	0.0109125i
$16$	−1.77140	−	3.58638i	−0.442850	−	0.896596i
$17$	−1.63631	+	4.49572i	−0.396863	+	1.09037i	0.566941	+	0.823759i	$0.308127\pi$
$17$	−1.63631	+	4.49572i	−0.396863	+	1.09037i	−0.963804	+	0.266613i	$0.914095\pi$
$18$	−2.47480	+	3.44607i	−0.583315	+	0.812246i
$19$	4.17803	+	1.24260i	0.958506	+	0.285072i
$19$	4.17803	+	1.24260i	0.958506	+	0.285072i
$20$	−0.364215	+	0.0521140i	−0.0814410	+	0.0116531i
$21$	−3.34625	+	1.75103i	−0.730211	+	0.382106i
$22$	−4.31780	+	7.20637i	−0.920558	+	1.53640i
$23$	4.68466	+	3.93090i	0.976820	+	0.819649i	0.983607	−	0.180328i	$-0.0577159\pi$
$23$	4.68466	+	3.93090i	0.976820	+	0.819649i	−0.00678675	+	0.999977i	$0.502160\pi$
$24$	2.82137	−	4.00498i	0.575909	−	0.817514i
$25$	0.862364	−	4.89071i	0.172473	−	0.978142i
$26$	−4.40995	+	1.52462i	−0.864863	+	0.299004i
$27$	−5.15593	−	0.645244i	−0.992260	−	0.124177i
$28$	3.84538	−	2.05695i	0.726708	−	0.388726i
$29$	0.421181	+	1.15719i	0.0782113	+	0.214884i	0.972636	−	0.232335i	$-0.0746366\pi$
$29$	0.421181	+	1.15719i	0.0782113	+	0.214884i	−0.894424	+	0.447219i	$0.852414\pi$
$30$	−0.269259	−	0.361321i	−0.0491597	−	0.0659679i
$31$	6.65444	+	3.84194i	1.19517	+	0.690034i	0.959475	−	0.281793i	$-0.0909291\pi$
$31$	6.65444	+	3.84194i	1.19517	+	0.690034i	0.235698	+	0.971826i	$0.424262\pi$
$32$	−3.21567	+	4.65397i	−0.568456	+	0.822713i
$33$	−10.2801	−	0.426865i	−1.78954	−	0.0743077i
$34$	6.68132	−	1.06676i	1.14584	−	0.182948i
$35$	−0.0696549	−	0.395032i	−0.0117738	−	0.0667727i
$36$	5.96009	+	0.690930i	0.993348	+	0.115155i
$37$	−1.63611			−0.268974			−0.134487	−	0.990915i	$-0.542939\pi$
$37$	−1.63611			−0.268974			−0.134487	+	0.990915i	$0.542939\pi$
$38$	−1.33509	−	6.01810i	−0.216581	−	0.976265i
$39$	−4.22158	−	3.85183i	−0.675993	−	0.616786i
$40$	0.314692	+	0.414375i	0.0497571	+	0.0655184i
$41$	1.14765	−	0.202362i	0.179233	−	0.0316036i	−0.0833112	−	0.996524i	$-0.526550\pi$
$41$	1.14765	−	0.202362i	0.179233	−	0.0316036i	0.262544	+	0.964920i	$0.415438\pi$
$42$	4.46378	+	2.93285i	0.688776	+	0.452549i
$43$	−1.51151	−	1.80135i	−0.230503	−	0.274703i	0.638379	−	0.769723i	$-0.279605\pi$
$43$	−1.51151	−	1.80135i	−0.230503	−	0.274703i	−0.868882	+	0.495019i	$0.835161\pi$
$44$	11.8744	+	0.385007i	1.79014	+	0.0580420i
$45$	0.231101	−	0.501170i	0.0344505	−	0.0747101i
$46$	1.63962	−	8.49163i	0.241748	−	1.25202i
$47$	6.83260	−	2.48686i	0.996637	−	0.362746i	0.208350	−	0.978054i	$-0.433191\pi$
$47$	6.83260	−	2.48686i	0.996637	−	0.362746i	0.788287	+	0.615308i	$0.210968\pi$
$48$	−6.88908	−	0.735242i	−0.994353	−	0.106123i
$49$	−1.12275	−	1.94467i	−0.160393	−	0.277810i
$50$	−6.63772	+	2.29481i	−0.938715	+	0.324536i
$51$	5.05855	+	6.56339i	0.708339	+	0.919058i
$52$	4.91488	+	4.40322i	0.681571	+	0.610617i
$53$	1.42960	−	1.70373i	0.196371	−	0.234026i	−0.658869	−	0.752257i	$-0.728965\pi$
$53$	1.42960	−	1.70373i	0.196371	−	0.234026i	0.855240	+	0.518231i	$0.173409\pi$
$54$	2.74544	+	6.81635i	0.373607	+	0.927587i
$55$	0.373759	−	1.02690i	0.0503977	−	0.138467i
$56$	−5.18489	−	3.33959i	−0.692860	−	0.446271i
$57$	5.69282	−	4.95901i	0.754033	−	0.656837i
$58$	1.14091	−	1.31578i	0.149809	−	0.172770i
$59$	5.82579	+	2.12042i	0.758454	+	0.276055i	0.692159	−	0.721745i	$-0.256660\pi$
$59$	5.82579	+	2.12042i	0.758454	+	0.276055i	0.0662951	+	0.997800i	$0.478882\pi$
$60$	−0.261583	+	0.581103i	−0.0337702	+	0.0750201i
$61$	9.65727	+	8.10341i	1.23649	+	1.03754i	0.997790	+	0.0664414i	$0.0211646\pi$
$61$	9.65727	+	8.10341i	1.23649	+	1.03754i	0.238697	+	0.971094i	$0.423280\pi$
$62$	0.176097	−	10.8652i	0.0223643	−	1.37989i
$63$	−0.542311	+	6.51892i	−0.0683247	+	0.821307i
$64$	7.96221	+	0.776659i	0.995276	+	0.0970824i
$65$	0.525649	−	0.303484i	0.0651987	−	0.0376425i
$66$	6.53652	+	13.0000i	0.804591	+	1.60019i
$67$	−3.18066	−	8.73880i	−0.388580	−	1.06761i	−0.967641	−	0.252330i	$-0.918803\pi$
$67$	−3.18066	−	8.73880i	−0.388580	−	1.06761i	0.579061	−	0.815284i	$-0.303419\pi$
$68$	−5.90974	−	7.52535i	−0.716662	−	0.912583i
$69$	10.0951	−	3.20667i	1.21531	−	0.386038i
$70$	−0.440412	+	0.357549i	−0.0526393	+	0.0427353i
$71$	−3.36704	+	2.82528i	−0.399594	+	0.335300i	−0.820337	−	0.571881i	$-0.806214\pi$
$71$	−3.36704	+	2.82528i	−0.399594	+	0.335300i	0.420742	+	0.907180i	$0.361770\pi$
$72$	−3.24155	−	7.84170i	−0.382021	−	0.924154i
$73$	1.20880	+	6.85547i	0.141480	+	0.802372i	0.970126	+	0.242600i	$0.0780002\pi$
$73$	1.20880	+	6.85547i	0.141480	+	0.802372i	−0.828647	+	0.559772i	$0.810889\pi$
$74$	1.12428	+	2.02230i	0.130695	+	0.235087i
$75$	−6.35418	−	5.79764i	−0.733717	−	0.669454i
$76$	−6.52120	+	5.78567i	−0.748033	+	0.663662i
$77$			12.9528i			1.47611i
$78$	−1.86009	+	7.86490i	−0.210614	+	0.890524i
$79$	−6.94773	+	1.22507i	−0.781681	+	0.137831i	−0.550228	−	0.835015i	$-0.685459\pi$
$79$	−6.94773	+	1.22507i	−0.781681	+	0.137831i	−0.231453	+	0.972846i	$0.574348\pi$
$80$	0.295939	−	0.673717i	0.0330870	−	0.0753239i
$81$	−5.72604	+	6.94352i	−0.636226	+	0.771502i
$82$	−1.03876	−	1.27949i	−0.114711	−	0.141296i
$83$	1.86888	−	3.23699i	0.205136	−	0.355306i	−0.745040	−	0.667020i	$-0.767570\pi$
$83$	1.86888	−	3.23699i	0.205136	−	0.355306i	0.950176	+	0.311714i	$0.100903\pi$
$84$	0.557775	−	7.53278i	0.0608582	−	0.821894i
$85$	−0.827043	+	0.301019i	−0.0897055	+	0.0326501i
$86$	−1.18788	+	3.10612i	−0.128093	+	0.334942i
$87$	2.08336	+	0.457208i	0.223359	+	0.0490178i
$88$	−7.68383	−	14.9419i	−0.819099	−	1.59281i
$89$	1.23073	+	0.217011i	0.130457	+	0.0230031i	0.238495	−	0.971144i	$-0.423346\pi$
$89$	1.23073	+	0.217011i	0.130457	+	0.0230031i	−0.108038	+	0.994147i	$0.534457\pi$
$90$	−0.778273	+	0.0587368i	−0.0820372	+	0.00619140i
$91$	−4.62440	+	5.51115i	−0.484769	+	0.577725i
$92$	−11.6227	+	3.80853i	−1.21175	+	0.397067i
$93$	11.7920	−	6.17053i	1.22277	−	0.639855i
$94$	−7.76901	−	6.73650i	−0.801312	−	0.694817i
$95$	0.318935	+	0.735718i	0.0327221	+	0.0754831i
$96$	3.82516	+	9.02043i	0.390403	+	0.920644i
$97$	−10.6136	−	3.86302i	−1.07764	−	0.392231i	−0.258614	−	0.965981i	$-0.583266\pi$
$97$	−10.6136	−	3.86302i	−1.07764	−	0.392231i	−0.819031	+	0.573750i	$0.805488\pi$
$98$	−1.63217	+	2.72408i	−0.164874	+	0.275174i
$99$	−10.1593	+	14.6416i	−1.02105	+	1.47154i
$100$	7.39771	+	6.62758i	0.739771	+	0.662758i
$101$	5.26789	+	0.928871i	0.524175	+	0.0924261i	0.429473	−	0.903080i	$-0.358699\pi$
$101$	5.26789	+	0.928871i	0.524175	+	0.0924261i	0.0947014	+	0.995506i	$0.469810\pi$
$102$	4.63656	−	10.7627i	0.459088	−	1.06567i
$103$	−4.25613	+	2.45728i	−0.419369	+	0.242123i	−0.694807	−	0.719196i	$-0.744510\pi$
$103$	−4.25613	+	2.45728i	−0.419369	+	0.242123i	0.275438	+	0.961319i	$0.411177\pi$
$104$	2.06523	−	9.10074i	0.202513	−	0.892401i
$105$	−0.642451	−	0.264507i	−0.0626968	−	0.0258133i
$106$	−3.08826	−	0.596301i	−0.299959	−	0.0579179i
$107$	0.372929	−	0.645932i	0.0360524	−	0.0624446i	−0.847436	−	0.530897i	$-0.821855\pi$
$107$	0.372929	−	0.645932i	0.0360524	−	0.0624446i	0.883489	+	0.468453i	$0.155188\pi$
$108$	6.53872	−	8.07744i	0.629189	−	0.777252i
$109$	10.4064	−	8.73199i	0.996751	−	0.836373i	0.0102196	−	0.999948i	$-0.496747\pi$
$109$	10.4064	−	8.73199i	0.996751	−	0.836373i	0.986531	+	0.163575i	$0.0523025\pi$
$110$	−1.52612	+	0.243666i	−0.145510	+	0.0232326i
$111$	−1.51751	+	2.39326i	−0.144035	+	0.227158i
$112$	−0.564991	+	8.70360i	−0.0533866	+	0.822413i
$113$		−	10.0558i		−	0.945971i	−0.881070	−	0.472986i	$-0.843176\pi$
$113$		−	10.0558i		−	0.945971i	0.881070	−	0.472986i	$-0.156824\pi$
$114$	−10.0415	−	3.62891i	−0.940469	−	0.339878i
$115$			1.12500i			0.104907i
$116$	−2.41035	−	0.506054i	−0.223795	−	0.0469860i
$117$	−9.54993	+	2.60262i	−0.882891	+	0.240613i
$118$	−1.38237	−	8.65801i	−0.127257	−	0.797034i
$119$	7.99134	−	6.70553i	0.732565	−	0.614695i
$120$	0.898019	−	0.0759874i	0.0819775	−	0.00693667i
$121$	−12.1438	+	21.0337i	−1.10398	+	1.91215i
$122$	3.38001	−	17.5052i	0.306012	−	1.58485i
$123$	0.768449	−	1.86645i	0.0692887	−	0.168292i
$124$	−13.5509	+	7.24856i	−1.21691	+	0.650940i
$125$	1.58777	−	0.916699i	0.142014	−	0.0819921i
$126$	8.43032	−	3.80927i	0.751033	−	0.339356i
$127$	−5.47645	−	0.965646i	−0.485956	−	0.0856872i	−0.0746983	−	0.997206i	$-0.523799\pi$
$127$	−5.47645	−	0.965646i	−0.485956	−	0.0856872i	−0.411258	+	0.911519i	$0.634910\pi$
$128$	−4.51138	−	10.3753i	−0.398754	−	0.917058i
$129$	−4.03692	+	0.540236i	−0.355431	+	0.0475651i
$130$	−0.736327	−	0.441181i	−0.0645802	−	0.0386941i
$131$	−2.56580	−	0.933874i	−0.224175	−	0.0815929i	0.227491	−	0.973780i	$-0.426948\pi$
$131$	−2.56580	−	0.933874i	−0.224175	−	0.0815929i	−0.451666	+	0.892187i	$0.649170\pi$
$132$	11.5769	−	17.0126i	1.00764	−	1.48076i
$133$	−6.53485	−	6.90152i	−0.566644	−	0.598438i
$134$	−8.61588	+	9.93645i	−0.744299	+	0.858378i
$135$	−0.518753	−	0.802891i	−0.0446471	−	0.0691019i
$136$	−5.24068	+	12.4759i	−0.449385	+	1.06980i
$137$	−7.77091	+	9.26102i	−0.663914	+	0.791222i	−0.987942	−	0.154826i	$-0.950518\pi$
$137$	−7.77091	+	9.26102i	−0.663914	+	0.791222i	0.324028	+	0.946048i	$0.394963\pi$
$138$	−10.9006	−	10.2745i	−0.927922	−	0.874621i
$139$	−6.01736	−	1.06102i	−0.510386	−	0.0899948i	−0.0874760	−	0.996167i	$-0.527880\pi$
$139$	−6.01736	−	1.06102i	−0.510386	−	0.0899948i	−0.422910	+	0.906172i	$0.638991\pi$
$140$	0.744583	+	0.298673i	0.0629288	+	0.0252424i
$141$	2.69958	−	12.3012i	0.227346	−	1.03595i
$142$	5.80589	+	2.22037i	0.487220	+	0.186329i
$143$	−18.4176	+	6.70346i	−1.54016	+	0.560571i
$144$	−7.46520	+	9.39526i	−0.622100	+	0.782938i
$145$	−0.113270	+	0.196190i	−0.00940659	+	0.0162927i
$146$	7.64300	−	6.20498i	0.632540	−	0.513528i
$147$	−3.88599	−	0.161359i	−0.320511	−	0.0133087i
$148$	1.72708	−	2.77931i	0.141965	−	0.228458i
$149$	21.8002	−	3.84397i	1.78595	−	0.314910i	0.819750	−	0.572721i	$-0.194112\pi$
$149$	21.8002	−	3.84397i	1.78595	−	0.314910i	0.966195	+	0.257811i	$0.0830011\pi$
$150$	−2.79975	+	11.8380i	−0.228599	+	0.966567i
$151$			15.8614i			1.29078i	0.763853	+	0.645391i	$0.223305\pi$
$151$			15.8614i			1.29078i	−0.763853	+	0.645391i	$0.776695\pi$
$152$	11.6325	+	4.08476i	0.943519	+	0.331318i
$153$	14.2926	−	1.31193i	1.15549	−	0.106063i
$154$	16.0102	−	8.90072i	1.29014	−	0.717241i
$155$	0.245460	+	1.39207i	0.0197158	+	0.111814i
$156$	10.9995	−	3.10534i	0.880668	−	0.248626i
$157$	−9.42027	+	7.90454i	−0.751819	+	0.630851i	−0.935983	−	0.352044i	$-0.885487\pi$
$157$	−9.42027	+	7.90454i	−0.751819	+	0.630851i	0.184164	+	0.982896i	$0.441042\pi$
$158$	6.28849	+	7.74587i	0.500286	+	0.616228i
$159$	−1.16621	−	3.67143i	−0.0924868	−	0.291163i
$160$	−1.03610	+	0.0971624i	−0.0819111	+	0.00768136i
$161$	−4.56066	−	12.5303i	−0.359431	−	0.987528i
$162$	12.5172	+	2.30627i	0.983447	+	0.181198i
$163$	16.3699	−	9.45115i	1.28219	−	0.740271i	0.304939	−	0.952372i	$-0.401364\pi$
$163$	16.3699	−	9.45115i	1.28219	−	0.740271i	0.977248	+	0.212101i	$0.0680306\pi$
$164$	−0.867706	+	2.16317i	−0.0677565	+	0.168915i
$165$	−1.15545	−	1.49918i	−0.0899520	−	0.116711i
$166$	−5.28530	−	0.0856606i	−0.410219	−	0.00664855i
$167$	−2.62961	−	2.20651i	−0.203486	−	0.170745i	0.535350	−	0.844630i	$-0.320180\pi$
$167$	−2.62961	−	2.20651i	−0.203486	−	0.170745i	−0.738836	+	0.673885i	$0.764624\pi$
$168$	−9.69412	+	4.48684i	−0.747918	+	0.346167i
$169$	1.98642	+	0.722999i	0.152802	+	0.0556153i
$170$	0.940389	+	0.815411i	0.0721246	+	0.0625392i
$171$	−1.97378	−	12.9269i	−0.150939	−	0.988543i
$172$	4.65557	−	0.666146i	0.354984	−	0.0507932i
$173$	−8.31071	+	22.8335i	−0.631852	+	1.73600i	0.0440736	+	0.999028i	$0.485966\pi$
$173$	−8.31071	+	22.8335i	−0.631852	+	1.73600i	−0.675925	+	0.736970i	$0.736256\pi$
$174$	−0.866485	−	2.88930i	−0.0656881	−	0.219037i
$175$	−6.96049	+	8.29519i	−0.526164	+	0.627058i
$176$	−13.1887	+	19.7651i	−0.994138	+	1.48985i
$177$	8.50519	−	6.55514i	0.639289	−	0.492714i
$178$	−0.577482	−	1.67036i	−0.0432841	−	0.125199i
$179$	10.5059	+	18.1968i	0.785251	+	1.36009i	0.928849	+	0.370459i	$0.120800\pi$
$179$	10.5059	+	18.1968i	0.785251	+	1.36009i	−0.143598	+	0.989636i	$0.545867\pi$
$180$	0.607405	+	0.921617i	0.0452733	+	0.0686933i
$181$	3.51011	−	1.27757i	0.260904	−	0.0949614i	−0.208256	−	0.978074i	$-0.566779\pi$
$181$	3.51011	−	1.27757i	0.260904	−	0.0949614i	0.469160	+	0.883113i	$0.344557\pi$
$182$	9.98975	+	1.92888i	0.740489	+	0.142978i
$183$	20.8107	−	6.61045i	1.53837	−	0.488658i
$184$	12.6942	+	11.7491i	0.935832	+	0.866153i
$185$	−0.193467	−	0.230566i	−0.0142240	−	0.0169515i
$186$	−15.7301	−	10.3352i	−1.15339	−	0.757815i
$187$	27.9883	−	4.93509i	2.04670	−	0.360889i
$188$	−2.98800	+	14.2319i	−0.217922	+	1.03797i
$189$	9.03274	+	6.83965i	0.657035	+	0.497512i
$190$	0.690218	−	0.899779i	0.0500737	−	0.0652768i
$191$	−4.28574			−0.310105			−0.155053	−	0.987906i	$-0.549555\pi$
$191$	−4.28574			−0.310105			−0.155053	+	0.987906i	$0.549555\pi$
$192$	8.52112	−	10.9266i	0.614959	−	0.788559i
$193$	2.94504	+	16.7022i	0.211989	+	1.20225i	0.886056	+	0.463578i	$0.153435\pi$
$193$	2.94504	+	16.7022i	0.211989	+	1.20225i	−0.674068	+	0.738670i	$0.735454\pi$
$194$	2.51843	+	15.7734i	0.180813	+	1.13246i
$195$	0.0436159	−	1.05039i	0.00312340	−	0.0752202i
$196$	4.48866	+	0.145537i	0.320618	+	0.0103955i
$197$	−10.7330	−	6.19668i	−0.764692	−	0.441495i	0.0662856	−	0.997801i	$-0.478885\pi$
$197$	−10.7330	−	6.19668i	−0.764692	−	0.441495i	−0.830978	+	0.556305i	$0.812218\pi$
$198$	25.0788	+	2.49614i	1.78227	+	0.177393i
$199$	−5.42899	−	14.9160i	−0.384851	−	1.05737i	−0.969288	−	0.245930i	$-0.920907\pi$
$199$	−5.42899	−	14.9160i	−0.384851	−	1.05737i	0.584437	−	0.811439i	$-0.301315\pi$
$200$	3.10852	−	13.6981i	0.219805	−	0.968604i
$201$	−15.7330	−	3.45273i	−1.10972	−	0.243537i
$202$	−2.47179	−	7.14963i	−0.173915	−	0.503046i
$203$	0.466272	−	2.64436i	0.0327259	−	0.185598i
$204$	−16.4893	+	1.66480i	−1.15448	+	0.116559i
$205$	0.164226	+	0.137802i	0.0114700	+	0.00962450i
$206$	5.96197	+	3.57220i	0.415390	+	0.248887i
$207$	4.67268	−	17.7412i	0.324773	−	1.23310i
$208$	−12.6681	+	3.70101i	−0.878373	+	0.256619i
$209$	−6.01691	−	25.1845i	−0.416199	−	1.74205i
$210$	0.114528	+	0.975857i	0.00790321	+	0.0673405i
$211$	2.34904	−	6.45394i	0.161715	−	0.444307i	−0.832198	−	0.554479i	$-0.812918\pi$
$211$	2.34904	−	6.45394i	0.161715	−	0.444307i	0.993913	+	0.110171i	$0.0351399\pi$
$212$	1.38510	+	4.22699i	0.0951290	+	0.290311i
$213$	1.00980	+	7.54572i	0.0691901	+	0.517024i
$214$	−1.05466	−	0.0170933i	−0.0720953	−	0.00116847i
$215$	0.0751179	−	0.426015i	0.00512300	−	0.0290540i
$216$	−14.4773	−	2.53159i	−0.985053	−	0.172253i
$217$	−8.37728	−	14.5099i	−0.568687	−	0.984995i
$218$	−17.9440	−	6.86240i	−1.21532	−	0.464780i
$219$	11.1492	+	4.59031i	0.753394	+	0.310185i
$220$	1.34988	+	1.71891i	0.0910090	+	0.115889i
$221$	13.6704	+	7.89259i	0.919568	+	0.530913i
$222$	4.00095	+	0.231134i	0.268526	+	0.0155127i
$223$	−7.52455	−	8.96741i	−0.503881	−	0.600502i	0.452810	−	0.891607i	$-0.350422\pi$
$223$	−7.52455	−	8.96741i	−0.503881	−	0.600502i	−0.956691	+	0.291105i	$0.905977\pi$
$224$	11.1463	−	5.28247i	0.744741	−	0.352950i
$225$	−14.3742	+	3.91738i	−0.958282	+	0.261159i
$226$	−12.4294	+	6.91002i	−0.826792	+	0.459648i
$227$	0.969889			0.0643738			0.0321869	−	0.999482i	$-0.489753\pi$
$227$	0.969889			0.0643738			0.0321869	+	0.999482i	$0.489753\pi$
$228$	2.41468	+	14.9053i	0.159916	+	0.987131i
$229$	6.77782			0.447891			0.223946	−	0.974602i	$-0.428106\pi$
$229$	6.77782			0.447891			0.223946	+	0.974602i	$0.428106\pi$
$230$	1.39055	−	0.773064i	0.0916903	−	0.0509744i
$231$	18.9471	+	12.0139i	1.24663	+	0.790454i
$232$	1.03081	+	3.32704i	0.0676759	+	0.218431i
$233$	−4.63498	−	5.52376i	−0.303648	−	0.361874i	0.592546	−	0.805537i	$-0.298123\pi$
$233$	−4.63498	−	5.52376i	−0.303648	−	0.361874i	−0.896193	+	0.443663i	$0.853679\pi$
$234$	9.77935	+	10.0157i	0.639296	+	0.654746i
$235$	1.15840	+	0.668805i	0.0755659	+	0.0436280i
$236$	−9.75175	+	7.65816i	−0.634785	+	0.498504i
$237$	−4.65209	+	11.2993i	−0.302186	+	0.733966i
$238$	−13.7797	−	5.26982i	−0.893205	−	0.341592i
$239$	2.81967	+	4.88381i	0.182389	+	0.315907i	0.942694	−	0.333660i	$-0.108284\pi$
$239$	2.81967	+	4.88381i	0.182389	+	0.315907i	−0.760304	+	0.649567i	$0.774950\pi$
$240$	−0.711012	−	1.05777i	−0.0458957	−	0.0682790i
$241$	2.47815	−	14.0543i	0.159632	−	0.905317i	−0.794796	−	0.606876i	$-0.792422\pi$
$241$	2.47815	−	14.0543i	0.159632	−	0.905317i	0.954428	−	0.298441i	$-0.0964665\pi$
$242$	34.3434	+	0.556615i	2.20768	+	0.0357805i
$243$	4.84587	+	14.8161i	0.310863	+	0.950455i
$244$	−23.9598	+	7.85115i	−1.53387	+	0.502618i
$245$	0.141285	−	0.388177i	0.00902636	−	0.0247997i
$246$	−2.83507	+	0.332729i	−0.180757	+	0.0212140i
$247$	6.43131	−	12.8637i	0.409214	−	0.818496i
$248$	18.2713	+	11.7685i	1.16023	+	0.747302i
$249$	−3.00160	−	5.73611i	−0.190219	−	0.363511i
$250$	−2.22414	−	1.33263i	−0.140667	−	0.0842827i
$251$	−8.73670	−	7.33096i	−0.551456	−	0.462726i	0.323978	−	0.946065i	$-0.394980\pi$
$251$	−8.73670	−	7.33096i	−0.551456	−	0.462726i	−0.875434	+	0.483338i	$0.839424\pi$
$252$	−10.5015	−	7.80264i	−0.661529	−	0.491520i
$253$	6.30821	−	35.7756i	0.396593	−	2.24919i
$254$	2.56965	+	7.43269i	0.161234	+	0.466368i
$255$	−0.326768	+	1.48898i	−0.0204630	+	0.0932436i
$256$	−9.72428	+	12.7058i	−0.607767	+	0.794115i
$257$	−5.79901	−	15.9327i	−0.361732	−	0.993852i	−0.978417	−	0.206641i	$-0.933747\pi$
$257$	−5.79901	−	15.9327i	−0.361732	−	0.993852i	0.616684	−	0.787211i	$-0.288476\pi$
$258$	3.44179	+	4.61858i	0.214277	+	0.287540i
$259$	3.08954	+	1.78375i	0.191975	+	0.110837i
$260$	−0.0393390	+	1.21330i	−0.00243970	+	0.0752455i
$261$	2.60113	−	2.62342i	0.161006	−	0.162386i
$262$	0.608822	+	3.81316i	0.0376132	+	0.235578i
$263$	−3.45871	−	19.6153i	−0.213273	−	1.20953i	−0.883878	−	0.467717i	$-0.845077\pi$
$263$	−3.45871	−	19.6153i	−0.213273	−	1.20953i	0.670606	−	0.741814i	$-0.266034\pi$
$264$	−28.9835	−	2.61901i	−1.78381	−	0.161189i
$265$	0.409145			0.0251336
$266$	−4.04005	+	12.8199i	−0.247711	+	0.786036i
$267$	1.45896	−	1.59901i	0.0892866	−	0.0978576i
$268$	18.2024	+	3.82161i	1.11189	+	0.233442i
$269$	−13.4723	+	2.37553i	−0.821421	+	0.144839i	−0.568537	−	0.822658i	$-0.692490\pi$
$269$	−13.4723	+	2.37553i	−0.821421	+	0.144839i	−0.252884	+	0.967496i	$0.581379\pi$
$270$	−0.635938	+	1.19292i	−0.0387020	+	0.0725988i
$271$	17.9629	+	21.4073i	1.09117	+	1.30040i	0.950629	+	0.310329i	$0.100439\pi$
$271$	17.9629	+	21.4073i	1.09117	+	1.30040i	0.140539	+	0.990075i	$0.455116\pi$
$272$	19.0219	−	2.09529i	1.15337	−	0.127046i
$273$	3.77241	+	11.8761i	0.228316	+	0.718776i
$274$	16.7869	+	3.24132i	1.01414	+	0.195815i
$275$	−27.7216	+	10.0898i	−1.67167	+	0.608439i
$276$	−5.20915	+	20.5339i	−0.313554	+	1.23600i
$277$	8.15894	+	14.1317i	0.490223	+	0.849091i	0.999937	−	0.0112531i	$-0.00358204\pi$
$277$	8.15894	+	14.1317i	0.490223	+	0.849091i	−0.509714	+	0.860344i	$0.670249\pi$
$278$	2.82346	+	8.16681i	0.169340	+	0.489813i
$279$	1.91107	−	22.9723i	0.114413	−	1.37532i
$280$	−0.142481	−	1.12557i	−0.00851485	−	0.0672659i
$281$	−13.0581	+	15.5621i	−0.778984	+	0.928356i	−0.998887	−	0.0471652i	$-0.984981\pi$
$281$	−13.0581	+	15.5621i	−0.778984	+	0.928356i	0.219904	+	0.975522i	$0.429426\pi$
$282$	−17.0598	+	5.11616i	−1.01590	+	0.304663i
$283$	−4.26612	+	11.7211i	−0.253595	+	0.696746i	0.745933	+	0.666021i	$0.232004\pi$
$283$	−4.26612	+	11.7211i	−0.253595	+	0.696746i	−0.999528	+	0.0307250i	$0.990218\pi$
$284$	−1.24515	−	8.70209i	−0.0738858	−	0.516374i
$285$	1.37201	+	0.215855i	0.0812708	+	0.0127862i
$286$	20.9417	+	18.1585i	1.23831	+	1.07374i
$287$	−2.38779	−	0.869085i	−0.140947	−	0.0513005i
$288$	16.7428	+	2.77119i	0.986577	+	0.163294i
$289$	−4.51123	−	3.78537i	−0.265367	−	0.222669i
$290$	0.320335	+	0.00519177i	0.0188107	+	0.000304871i
$291$	−15.4950	+	11.9423i	−0.908331	+	0.700071i
$292$	−12.9216	−	5.18322i	−0.756182	−	0.303325i
$293$	−15.3839	+	8.88190i	−0.898737	+	0.518886i	−0.876790	−	0.480873i	$-0.840320\pi$
$293$	−15.3839	+	8.88190i	−0.898737	+	0.518886i	−0.0219470	+	0.999759i	$0.506987\pi$
$294$	2.47087	+	4.91413i	0.144104	+	0.286598i
$295$	0.390077	+	1.07173i	0.0227111	+	0.0623984i
$296$	−4.62214	−	0.224895i	−0.268656	−	0.0130718i
$297$	11.9945	+	28.4411i	0.695994	+	1.65032i
$298$	−19.7317	−	24.3046i	−1.14303	−	1.40793i
$299$	15.4566	−	12.9696i	0.893879	−	0.750054i
$300$	16.5561	−	4.67405i	0.955869	−	0.269857i
$301$	0.890361	+	5.04949i	0.0513196	+	0.291048i
$302$	19.6054	−	10.8994i	1.12816	−	0.627191i
$303$	6.24476	−	6.84422i	0.358752	−	0.393190i
$304$	−2.94452	−	17.1852i	−0.168880	−	0.985637i
$305$			2.31915i			0.132794i
$306$	−11.4430	−	16.7648i	−0.654154	−	0.958381i
$307$	−20.2500	+	3.57062i	−1.15573	+	0.203786i	−0.718475	−	0.695553i	$-0.755159\pi$
$307$	−20.2500	+	3.57062i	−1.15573	+	0.203786i	−0.437252	+	0.899339i	$0.644048\pi$
$308$	−22.0034	−	13.6730i	−1.25376	−	0.779092i
$309$	−0.353154	+	8.50493i	−0.0200902	+	0.483828i
$310$	1.55199	−	1.25998i	0.0881470	−	0.0715623i
$311$	9.18302	−	15.9055i	0.520721	−	0.901915i	−0.478989	−	0.877821i	$-0.658996\pi$
$311$	9.18302	−	15.9055i	0.520721	−	0.901915i	0.999710	−	0.0240943i	$-0.00767019\pi$
$312$	−11.3969	−	11.4620i	−0.645220	−	0.648909i
$313$	10.1054	−	3.67808i	0.571193	−	0.207897i	−0.0402445	−	0.999190i	$-0.512814\pi$
$313$	10.1054	−	3.67808i	0.571193	−	0.207897i	0.611438	+	0.791293i	$0.290591\pi$
$314$	16.2436	+	6.21212i	0.916682	+	0.350570i
$315$	−0.982796	+	0.694430i	−0.0553743	+	0.0391267i
$316$	5.25298	−	13.0956i	0.295503	−	0.736682i
$317$	20.3941	+	3.59602i	1.14544	+	0.201973i	0.713986	−	0.700160i	$-0.246888\pi$
$317$	20.3941	+	3.59602i	1.14544	+	0.201973i	0.431458	+	0.902133i	$0.357999\pi$
$318$	−3.73666	+	3.96437i	−0.209541	+	0.222311i
$319$	4.70214	−	5.60379i	0.263269	−	0.313752i
$320$	0.832072	+	1.21390i	0.0465143	+	0.0678591i
$321$	−0.598960	−	1.14462i	−0.0334307	−	0.0638866i
$322$	−12.3541	+	14.2476i	−0.688466	+	0.793988i
$323$	−12.4229	+	16.7500i	−0.691231	+	0.931993i
$324$	−5.75078	−	17.0566i	−0.319488	−	0.947590i
$325$	−15.3972	−	5.60413i	−0.854084	−	0.310861i
$326$	−22.9308	−	13.7393i	−1.27002	−	0.760952i
$327$	−3.12094	−	23.3213i	−0.172588	−	1.28967i
$328$	3.27003	−	0.413936i	0.180557	−	0.0228558i
$329$	−15.6136	−	2.75310i	−0.860807	−	0.151784i
$330$	−1.05907	+	2.45838i	−0.0582997	+	0.135329i
$331$	−2.30427	+	1.33037i	−0.126654	+	0.0731239i	−0.561989	−	0.827145i	$-0.689964\pi$
$331$	−2.30427	+	1.33037i	−0.126654	+	0.0731239i	0.435334	+	0.900269i	$0.356630\pi$
$332$	3.52600	+	6.59172i	0.193514	+	0.361767i
$333$	2.09331	+	4.43955i	0.114713	+	0.243286i
$334$	−0.920356	+	4.76656i	−0.0503596	+	0.260814i
$335$	0.855392	−	1.48158i	0.0467350	−	0.0809475i
$336$	12.2074	+	8.89914i	0.665969	+	0.485488i
$337$	−17.6673	+	14.8246i	−0.962397	+	0.807547i	−0.981341	−	0.192274i	$-0.938414\pi$
$337$	−17.6673	+	14.8246i	−0.962397	+	0.807547i	0.0189445	+	0.999821i	$0.493969\pi$
$338$	−0.471346	−	2.95213i	−0.0256379	−	0.160574i
$339$	−14.7094	−	9.32688i	−0.798907	−	0.506567i
$340$	0.361678	−	1.72268i	0.0196148	−	0.0934257i
$341$		−	45.6449i		−	2.47181i
$342$	−14.6219	+	11.3226i	−0.790660	+	0.612256i
$343$			20.1596i			1.08852i
$344$	−4.02254	−	5.29673i	−0.216881	−	0.285581i
$345$	1.64563	+	1.04345i	0.0885978	+	0.0561776i
$346$	33.9340	−	5.41802i	1.82430	−	0.291275i
$347$	0.738215	−	0.619436i	0.0396295	−	0.0332531i	−0.622758	−	0.782415i	$-0.713988\pi$
$347$	0.738215	−	0.619436i	0.0396295	−	0.0332531i	0.662387	+	0.749162i	$0.269543\pi$
$348$	−2.97587	+	3.05644i	−0.159524	+	0.163842i
$349$	5.43522	−	9.41407i	0.290940	−	0.503924i	−0.683092	−	0.730332i	$-0.739365\pi$
$349$	5.43522	−	9.41407i	0.290940	−	0.503924i	0.974032	+	0.226409i	$0.0726985\pi$
$350$	15.0362	+	2.90329i	0.803721	+	0.155187i
$351$	−5.05060	+	16.3834i	−0.269581	+	0.874481i
$352$	33.4934	+	2.71991i	1.78520	+	0.144972i
$353$	31.8933	−	18.4136i	1.69751	−	0.980058i	0.749398	−	0.662120i	$-0.230343\pi$
$353$	31.8933	−	18.4136i	1.69751	−	0.980058i	0.948112	−	0.317938i	$-0.102990\pi$
$354$	−13.9469	−	6.00830i	−0.741270	−	0.319338i
$355$	−0.796297	−	0.140409i	−0.0422631	−	0.00745212i
$356$	−1.66781	+	1.86161i	−0.0883936	+	0.0986650i
$357$	−2.39665	−	17.9090i	−0.126844	−	0.947845i
$358$	15.2727	−	25.4901i	0.807189	−	1.34719i
$359$	−20.8947	−	7.60506i	−1.10278	−	0.401380i	−0.274441	−	0.961604i	$-0.588493\pi$
$359$	−20.8947	−	7.60506i	−1.10278	−	0.401380i	−0.828341	+	0.560224i	$0.810715\pi$
$360$	0.721770	−	1.38408i	0.0380406	−	0.0729476i
$361$	15.9119	+	10.3833i	0.837467	+	0.546487i
$362$	−3.99117	−	3.46074i	−0.209771	−	0.181892i
$363$	19.5041	+	37.2727i	1.02370	+	1.95631i
$364$	−4.48044	−	13.6732i	−0.234839	−	0.716672i
$365$	−0.823156	+	0.981000i	−0.0430860	+	0.0513479i
$366$	−22.4712	−	21.1805i	−1.17459	−	1.10712i
$367$	−12.8825	−	2.27154i	−0.672462	−	0.118573i	−0.173017	−	0.984919i	$-0.555352\pi$
$367$	−12.8825	−	2.27154i	−0.672462	−	0.118573i	−0.499445	+	0.866346i	$0.666463\pi$
$368$	5.79929	−	23.7642i	0.302309	−	1.23879i
$369$	−2.01746	−	2.85523i	−0.105025	−	0.148637i
$370$	−0.152044	+	0.397571i	−0.00790442	+	0.0206687i
$371$	−4.55707	+	1.65864i	−0.236591	+	0.0861122i
$372$	−1.96557	+	26.5451i	−0.101910	+	1.37630i
$373$	−3.56550	+	6.17564i	−0.184615	+	0.319762i	−0.943447	−	0.331524i	$-0.892437\pi$
$373$	−3.56550	+	6.17564i	−0.184615	+	0.319762i	0.758832	+	0.651287i	$0.225770\pi$
$374$	−25.3326	−	31.2035i	−1.30992	−	1.61349i
$375$	0.131746	−	3.17281i	0.00680332	−	0.163843i
$376$	19.6445	−	6.08641i	1.01309	−	0.313883i
$377$	4.00133	−	0.705543i	0.206079	−	0.0363373i
$378$	2.24711	−	15.8648i	0.115579	−	0.815999i
$379$		−	13.0725i		−	0.671488i	−0.941953	−	0.335744i	$-0.891012\pi$
$379$		−	13.0725i		−	0.671488i	0.941953	−	0.335744i	$-0.108988\pi$
$380$	−1.58646	−	0.234841i	−0.0813837	−	0.0120471i
$381$	−6.49200	+	7.11519i	−0.332595	+	0.364522i
$382$	2.94502	+	5.29736i	0.150680	+	0.271036i
$383$	−0.262170	−	1.48684i	−0.0133962	−	0.0759739i	0.977377	−	0.211506i	$-0.0678368\pi$
$383$	−0.262170	−	1.48684i	−0.0133962	−	0.0759739i	−0.990773	+	0.135532i	$0.956726\pi$
$384$	−19.3612	−	3.02408i	−0.988021	−	0.154322i
$385$	−1.82535	+	1.53165i	−0.0930285	+	0.0780602i
$386$	18.6208	−	15.1174i	0.947776	−	0.769453i
$387$	−2.95404	+	6.40620i	−0.150162	+	0.325645i
$388$	17.7660	−	13.9518i	0.901931	−	0.708296i
$389$	−5.98431	−	16.4417i	−0.303416	−	0.833630i	−0.993900	−	0.110282i	$-0.964825\pi$
$389$	−5.98431	−	16.4417i	−0.303416	−	0.833630i	0.690484	−	0.723348i	$-0.257398\pi$
$390$	−1.32830	+	0.667884i	−0.0672612	+	0.0338196i
$391$	−25.3378	+	14.6288i	−1.28139	+	0.739809i
$392$	−2.90457	−	5.64818i	−0.146703	−	0.285276i
$393$	−3.74586	+	2.88702i	−0.188954	+	0.145631i
$394$	−0.284027	+	17.5246i	−0.0143090	+	0.882875i
$395$	−0.994203	−	0.834235i	−0.0500238	−	0.0419749i
$396$	−14.1480	−	32.7137i	−0.710963	−	1.64393i
$397$	37.2801	+	13.5688i	1.87103	+	0.681001i	0.967723	+	0.252015i	$0.0810931\pi$
$397$	37.2801	+	13.5688i	1.87103	+	0.681001i	0.903311	+	0.428986i	$0.141129\pi$
$398$	−14.7062	+	16.9603i	−0.737156	+	0.850141i
$399$	−16.1566	+	3.15781i	−0.808839	+	0.158088i
$400$	−19.0676	+	5.57064i	−0.953378	+	0.278532i
$401$	−6.78965	+	18.6544i	−0.339059	+	0.931557i	0.646603	+	0.762827i	$0.276189\pi$
$401$	−6.78965	+	18.6544i	−0.339059	+	0.931557i	−0.985662	+	0.168731i	$0.946033\pi$
$402$	6.54350	+	21.8193i	0.326360	+	1.08825i
$403$	16.2961	−	19.4210i	0.811768	−	0.967428i
$404$	−7.13871	+	7.96823i	−0.355164	+	0.396434i
$405$	−1.65560	+	0.0141303i	−0.0822675	+	0.000702139i
$406$	−3.58895	+	1.24078i	−0.178117	+	0.0615791i
$407$	4.85951	+	8.41692i	0.240877	+	0.417211i
$408$	13.3886	+	19.2375i	0.662837	+	0.952396i
$409$	9.71138	−	3.53465i	0.480197	−	0.174777i	−0.0905691	−	0.995890i	$-0.528869\pi$
$409$	9.71138	−	3.53465i	0.480197	−	0.174777i	0.570766	+	0.821113i	$0.306646\pi$
$410$	0.0574785	−	0.297683i	0.00283866	−	0.0147015i
$411$	6.33921	+	19.9568i	0.312690	+	0.984398i
$412$	0.318524	−	9.82395i	0.0156925	−	0.483991i
$413$	−8.68938	−	10.3556i	−0.427576	−	0.509566i
$414$	−25.1397	+	6.41550i	−1.23555	+	0.315305i
$415$	0.677161	−	0.119402i	0.0332405	−	0.00586120i
$416$	13.2797	+	13.1151i	0.651090	+	0.643019i
$417$	−7.13321	+	7.81796i	−0.349315	+	0.382847i
$418$	−26.9946	+	24.7431i	−1.32035	+	1.21023i
$419$	24.2731			1.18582			0.592910	−	0.805269i	$-0.297979\pi$
$419$	24.2731			1.18582			0.592910	+	0.805269i	$0.297979\pi$
$420$	1.12750	−	0.812139i	0.0550164	−	0.0396283i
$421$	−2.90184	−	16.4572i	−0.141427	−	0.802073i	−0.970167	−	0.242439i	$-0.922053\pi$
$421$	−2.90184	−	16.4572i	−0.141427	−	0.802073i	0.828740	−	0.559634i	$-0.189058\pi$
$422$	−9.59153	+	1.53142i	−0.466908	+	0.0745481i
$423$	−15.4900	−	15.3584i	−0.753150	−	0.746750i
$424$	4.27294	−	4.61669i	0.207512	−	0.224206i
$425$	20.5762	+	11.8797i	0.998091	+	0.576248i
$426$	8.63294	−	6.43332i	0.418267	−	0.311695i
$427$	−9.40165	−	25.8308i	−0.454978	−	1.25004i
$428$	0.703602	+	1.31536i	0.0340099	+	0.0635801i
$429$	−7.27685	+	33.1584i	−0.351330	+	1.60090i
$430$	−0.578191	+	0.199894i	−0.0278828	+	0.00963976i
$431$	−6.14143	+	34.8298i	−0.295822	+	1.67769i	0.368020	+	0.929818i	$0.380036\pi$
$431$	−6.14143	+	34.8298i	−0.295822	+	1.67769i	−0.663842	+	0.747873i	$0.731075\pi$
$432$	6.81913	+	19.6341i	0.328086	+	0.944648i
$433$	−5.32703	−	4.46991i	−0.256001	−	0.214810i	0.505750	−	0.862680i	$-0.331216\pi$
$433$	−5.32703	−	4.46991i	−0.256001	−	0.214810i	−0.761751	+	0.647870i	$0.775660\pi$
$434$	−12.1782	+	20.3254i	−0.584574	+	0.975650i
$435$	0.181923	+	0.347658i	0.00872254	+	0.0166689i
$436$	3.84832	+	26.8952i	0.184301	+	1.28805i
$437$	14.6881	+	22.2446i	0.702628	+	1.06410i
$438$	−1.98755	−	16.9352i	−0.0949688	−	0.809196i
$439$	−11.6584	+	32.0313i	−0.556426	+	1.52877i	0.268357	+	0.963320i	$0.413519\pi$
$439$	−11.6584	+	32.0313i	−0.556426	+	1.52877i	−0.824783	+	0.565449i	$0.808703\pi$
$440$	1.19706	−	2.84969i	0.0570674	−	0.135854i
$441$	−3.84033	+	5.53468i	−0.182873	+	0.263556i
$442$	0.361759	−	22.3207i	0.0172071	−	1.06169i
$443$	−1.98253	+	11.2435i	−0.0941928	+	0.534194i	0.900799	+	0.434237i	$0.142982\pi$
$443$	−1.98253	+	11.2435i	−0.0941928	+	0.534194i	−0.994992	+	0.0999575i	$0.968129\pi$
$444$	−2.46363	−	5.10418i	−0.116919	−	0.242233i
$445$	0.114950	+	0.199100i	0.00544917	+	0.00943824i
$446$	−5.91348	+	15.4628i	−0.280012	+	0.732183i
$447$	14.5971	−	35.4543i	0.690419	−	1.67693i
$448$	−14.1887	−	10.1473i	−0.670353	−	0.479416i
$449$	−5.88893	−	3.39998i	−0.277916	−	0.160455i	0.354564	−	0.935032i	$-0.384629\pi$
$449$	−5.88893	−	3.39998i	−0.277916	−	0.160455i	−0.632480	+	0.774577i	$0.717963\pi$
$450$	14.7195	+	15.0753i	0.693886	+	0.710655i
$451$	−4.44977	−	5.30303i	−0.209531	−	0.249710i
$452$	17.0822	+	10.6150i	0.803477	+	0.499285i
$453$	23.2017	+	14.7116i	1.09011	+	0.691212i
$454$	−0.666475	−	1.19882i	−0.0312792	−	0.0562636i
$455$	−1.32348			−0.0620457
$456$	16.7644	−	13.2271i	0.785063	−	0.619416i
$457$	9.31891			0.435920			0.217960	−	0.975958i	$-0.430060\pi$
$457$	9.31891			0.435920			0.217960	+	0.975958i	$0.430060\pi$
$458$	−4.65749	−	8.37768i	−0.217630	−	0.391463i
$459$	11.3375	−	22.1238i	0.529191	−	1.03265i
$460$	−1.91108	−	1.18756i	−0.0891046	−	0.0553701i
$461$	9.09236	+	10.8358i	0.423473	+	0.504676i	0.935028	−	0.354575i	$-0.115375\pi$
$461$	9.09236	+	10.8358i	0.423473	+	0.504676i	−0.511554	+	0.859251i	$0.670930\pi$
$462$	1.82985	−	31.6749i	0.0851322	−	1.47365i
$463$	21.3119	+	12.3044i	0.990449	+	0.571836i	0.905408	−	0.424541i	$-0.139565\pi$
$463$	21.3119	+	12.3044i	0.990449	+	0.571836i	0.0850405	+	0.996377i	$0.472898\pi$
$464$	3.40403	−	3.56035i	0.158028	−	0.165285i
$465$	2.26396	+	0.932109i	0.104989	+	0.0432255i
$466$	−3.64260	+	9.52478i	−0.168740	+	0.441227i
$467$	1.63259	+	2.82773i	0.0755474	+	0.130852i	0.901324	−	0.433145i	$-0.142596\pi$
$467$	1.63259	+	2.82773i	0.0755474	+	0.130852i	−0.825777	+	0.563997i	$0.809263\pi$
$468$	5.65977	−	18.9701i	0.261623	−	0.876895i
$469$	−3.52118	+	19.9696i	−0.162593	+	0.922110i
$470$	0.0306548	−	1.89142i	0.00141400	−	0.0872446i
$471$	2.82520	+	21.1113i	0.130178	+	0.972759i
$472$	16.1669	+	6.79115i	0.744142	+	0.312588i
$473$	−4.77757	+	13.1263i	−0.219673	+	0.603546i
$474$	17.1631	−	2.01430i	0.788329	−	0.0925198i
$475$	9.68019	−	19.3620i	0.444158	−	0.888388i
$476$	2.95523	+	20.6535i	0.135453	+	0.946654i
$477$	−6.45216	−	1.69938i	−0.295424	−	0.0778090i
$478$	4.09902	−	6.84122i	0.187485	−	0.312910i
$479$	29.8626	+	25.0577i	1.36446	+	1.14491i	0.974578	+	0.224048i	$0.0719272\pi$
$479$	29.8626	+	25.0577i	1.36446	+	1.14491i	0.389878	+	0.920867i	$0.372517\pi$
$480$	−0.818870	+	1.60571i	−0.0373761	+	0.0732902i
$481$	−0.937384	+	5.31617i	−0.0427410	+	0.242396i
$482$	−19.0746	+	6.59454i	−0.868825	+	0.300373i
$483$	−22.5592	−	4.95077i	−1.02648	−	0.225268i
$484$	−22.9116	−	42.8324i	−1.04144	−	1.94693i
$485$	−0.710651	−	1.95250i	−0.0322690	−	0.0886584i
$486$	14.9834	−	16.1709i	0.679663	−	0.733525i
$487$	−25.5603	−	14.7572i	−1.15825	−	0.668714i	−0.207364	−	0.978264i	$-0.566488\pi$
$487$	−25.5603	−	14.7572i	−1.15825	−	0.668714i	−0.950883	+	0.309549i	$0.899822\pi$
$488$	26.1687	+	24.2203i	1.18460	+	1.09640i
$489$	1.35829	−	32.7115i	0.0614242	−	1.47927i
$490$	−0.576889	+	0.0921081i	−0.0260612	+	0.00416102i
$491$	−0.350421	−	1.98734i	−0.0158143	−	0.0896872i	0.975879	−	0.218312i	$-0.0700549\pi$
$491$	−0.350421	−	1.98734i	−0.0158143	−	0.0896872i	−0.991693	+	0.128624i	$0.958944\pi$
$492$	2.35943	+	3.27563i	0.106371	+	0.147677i
$493$	−5.89156			−0.265343
$494$	−20.3194	+	0.890111i	−0.914214	+	0.0400480i
$495$	−3.26467	+	0.299665i	−0.146736	+	0.0134689i
$496$	1.99100	−	30.6710i	0.0893984	−	1.37717i
$497$	9.43839	−	1.66424i	0.423370	−	0.0746515i
$498$	−5.02747	+	7.65177i	−0.225287	+	0.342884i
$499$	20.1226	+	23.9812i	0.900810	+	1.07354i	0.996940	+	0.0781751i	$0.0249093\pi$
$499$	20.1226	+	23.9812i	0.900810	+	1.07354i	−0.0961293	+	0.995369i	$0.530646\pi$
$500$	−0.118827	+	3.66487i	−0.00531410	+	0.163898i
$501$	−5.66663	+	1.79998i	−0.253166	+	0.0804174i
$502$	−3.05781	+	15.8365i	−0.136477	+	0.706819i
$503$	−0.404915	+	0.147377i	−0.0180543	+	0.00657122i	−0.351031	−	0.936364i	$-0.614169\pi$
$503$	−0.404915	+	0.147377i	−0.0180543	+	0.00657122i	0.332977	+	0.942935i	$0.391947\pi$
$504$	−2.42815	+	18.3420i	−0.108158	+	0.817016i
$505$	0.492022	+	0.852207i	0.0218947	+	0.0379227i
$506$	−48.5550	+	16.7866i	−2.15853	+	0.746255i
$507$	2.90002	−	2.23511i	0.128794	−	0.0992647i
$508$	7.42134	−	8.28370i	0.329269	−	0.367530i
$509$	6.89445	−	8.21649i	0.305591	−	0.364189i	−0.591292	−	0.806458i	$-0.701382\pi$
$509$	6.89445	−	8.21649i	0.305591	−	0.364189i	0.896883	+	0.442269i	$0.145826\pi$
$510$	2.06499	−	0.619279i	0.0914392	−	0.0274221i
$511$	5.19146	−	14.2634i	0.229657	−	0.630977i
$512$	22.3872	+	3.28859i	0.989382	+	0.145337i
$513$	−20.7399	−	9.10263i	−0.915688	−	0.401891i
$514$	−15.7086	+	18.1162i	−0.692875	+	0.799072i
$515$	−0.849570	−	0.309218i	−0.0374365	−	0.0136258i
$516$	3.34367	−	7.42793i	0.147197	−	0.326997i
$517$	−33.0876	−	27.7638i	−1.45519	−	1.22105i
$518$	0.0817585	−	5.04454i	0.00359226	−	0.221644i
$519$	25.6921	+	33.3351i	1.12776	+	1.46325i
$520$	1.52672	−	0.785112i	0.0669511	−	0.0344295i
$521$	11.3664	−	6.56238i	0.497970	−	0.287503i	−0.229905	−	0.973213i	$-0.573842\pi$
$521$	11.3664	−	6.56238i	0.497970	−	0.287503i	0.727875	+	0.685710i	$0.240508\pi$
$522$	−5.03008	−	1.41238i	−0.220160	−	0.0618181i
$523$	6.53155	+	17.9453i	0.285605	+	0.784693i	0.996668	+	0.0815648i	$0.0259917\pi$
$523$	6.53155	+	17.9453i	0.285605	+	0.784693i	−0.711063	+	0.703128i	$0.751786\pi$
$524$	4.29487	−	3.37281i	0.187622	−	0.147342i
$525$	5.67810	+	17.8756i	0.247813	+	0.780153i
$526$	−21.8686	+	17.7541i	−0.953518	+	0.774115i
$527$	−28.1610	+	23.6299i	−1.22671	+	1.02933i
$528$	16.6793	+	37.6246i	0.725873	+	1.63740i
$529$	2.50019	+	14.1793i	0.108704	+	0.616491i
$530$	−0.281151	−	0.505721i	−0.0122124	−	0.0219671i
$531$	−1.70006	−	18.5212i	−0.0737765	−	0.803751i
$532$	18.6221	−	3.81571i	0.807369	−	0.165432i
$533$		−	3.84498i		−	0.166545i
$534$	−2.97899	−	0.704547i	−0.128913	−	0.0304887i
$535$	0.135125	−	0.0238262i	0.00584198	−	0.00103010i
$536$	−7.78443	−	25.1251i	−0.336236	−	1.08524i
$537$	36.3623	+	1.50989i	1.56915	+	0.0651565i
$538$	12.1940	+	15.0200i	0.525720	+	0.647557i
$539$	−6.66954	+	11.5520i	−0.287277	+	0.497579i
$540$	1.91150	−	0.0336886i	0.0822577	−	0.00144973i
$541$	−6.59715	+	2.40117i	−0.283633	+	0.103234i	−0.479919	−	0.877313i	$-0.659334\pi$
$541$	−6.59715	+	2.40117i	−0.283633	+	0.103234i	0.196286	+	0.980547i	$0.437112\pi$
$542$	14.1169	−	36.9133i	0.606373	−	1.58556i
$543$	1.38685	−	6.31948i	0.0595156	−	0.271195i
$544$	−15.6611	−	22.0721i	−0.671464	−	0.946333i
$545$	2.46108	+	0.433955i	0.105421	+	0.0185886i
$546$	12.0871	−	12.8237i	0.517282	−	0.548805i
$547$	5.42038	−	6.45975i	0.231759	−	0.276199i	−0.637614	−	0.770356i	$-0.720079\pi$
$547$	5.42038	−	6.45975i	0.231759	−	0.276199i	0.869373	+	0.494157i	$0.164523\pi$
$548$	−7.52900	−	22.9767i	−0.321623	−	0.981516i
$549$	9.63256	−	36.5728i	0.411108	−	1.56089i
$550$	31.5208	+	27.3316i	1.34405	+	1.16542i
$551$	0.321786	+	5.35812i	0.0137086	+	0.228263i
$552$	28.9603	−	7.67148i	1.23263	−	0.326520i
$553$	14.4554	+	5.26133i	0.614705	+	0.223734i
$554$	11.8608	−	19.7956i	0.503918	−	0.841035i
$555$	−0.516710	+	0.0691480i	−0.0219331	+	0.00293517i
$556$	8.15434	−	9.10188i	0.345821	−	0.386006i
$557$	−34.7400	−	6.12560i	−1.47198	−	0.259550i	−0.620612	−	0.784118i	$-0.713116\pi$
$557$	−34.7400	−	6.12560i	−1.47198	−	0.259550i	−0.851369	+	0.524568i	$0.824227\pi$
$558$	−29.7080	+	13.4236i	−1.25764	+	0.568268i
$559$	−6.71909	+	3.87927i	−0.284187	+	0.164076i
$560$	−1.29335	+	0.949570i	−0.0546540	+	0.0401266i
$561$	18.7405	−	45.5180i	0.791224	−	1.92177i
$562$	28.2085	+	5.44668i	1.18991	+	0.229754i
$563$	21.7508	−	37.6734i	0.916686	−	1.58775i	0.112271	−	0.993678i	$-0.464188\pi$
$563$	21.7508	−	37.6734i	0.916686	−	1.58775i	0.804415	−	0.594068i	$-0.202479\pi$
$564$	18.0468	+	17.5710i	0.759905	+	0.739875i
$565$	1.41710	−	1.18909i	0.0596178	−	0.0500253i
$566$	17.4193	−	2.78122i	0.732188	−	0.116904i
$567$	18.3829	−	6.86905i	0.772008	−	0.288473i
$568$	−9.90054	+	7.51884i	−0.415417	+	0.315484i
$569$			38.3107i			1.60607i	0.595933	+	0.803034i	$0.296783\pi$
$569$			38.3107i			1.60607i	−0.595933	+	0.803034i	$0.703217\pi$
$570$	−0.675993	−	1.84419i	−0.0283142	−	0.0772447i
$571$		−	31.7827i		−	1.33006i	−0.746815	−	0.665032i	$-0.768418\pi$
$571$		−	31.7827i		−	1.33006i	0.746815	−	0.665032i	$-0.231582\pi$
$572$	8.05429	−	38.3628i	0.336767	−	1.60403i
$573$	−3.97507	+	6.26909i	−0.166061	+	0.261895i
$574$	0.566584	+	3.54862i	0.0236488	+	0.148117i
$575$	23.2648	−	19.5215i	0.970208	−	0.814101i
$576$	−8.07976	−	22.5991i	−0.336657	−	0.941627i
$577$	6.10252	−	10.5699i	0.254051	−	0.440030i	−0.710586	−	0.703610i	$-0.751570\pi$
$577$	6.10252	−	10.5699i	0.254051	−	0.440030i	0.964637	+	0.263580i	$0.0849034\pi$
$578$	−1.57892	+	8.17726i	−0.0656742	+	0.340129i
$579$	27.1631	+	11.1835i	1.12886	+	0.464770i
$580$	−0.213706	−	0.399515i	−0.00887366	−	0.0165890i
$581$	−7.05820	+	4.07505i	−0.292824	+	0.169062i
$582$	25.4088	+	10.9461i	1.05323	+	0.453729i
$583$	−13.0110	−	2.29419i	−0.538860	−	0.0950156i
$584$	2.47264	+	19.5334i	0.102319	+	0.808300i
$585$	−1.49604	−	1.03805i	−0.0618536	−	0.0429181i
$586$	21.5497	+	12.9118i	0.890211	+	0.533382i
$587$	−20.4481	−	7.44250i	−0.843984	−	0.307185i	−0.116399	−	0.993203i	$-0.537135\pi$
$587$	−20.4481	−	7.44250i	−0.843984	−	0.307185i	−0.727585	+	0.686018i	$0.759357\pi$
$588$	4.37617	−	6.43093i	0.180470	−	0.265207i
$589$	23.0285	+	24.3206i	0.948871	+	1.00211i
$590$	1.05665	−	1.21861i	0.0435017	−	0.0501692i
$591$	−19.0193	+	9.95247i	−0.782351	+	0.409390i
$592$	2.89820	+	5.86770i	0.119115	+	0.241161i
$593$	3.39597	−	4.04717i	0.139456	−	0.166197i	−0.691796	−	0.722093i	$-0.743180\pi$
$593$	3.39597	−	4.04717i	0.139456	−	0.166197i	0.831252	+	0.555896i	$0.187625\pi$
$594$	26.9122	−	34.3696i	1.10422	−	1.41020i
$595$	1.88993	+	0.333246i	0.0774796	+	0.0136617i
$596$	−16.4825	+	41.0906i	−0.675151	+	1.68313i
$597$	−26.8543	−	5.89337i	−1.09907	−	0.241199i
$598$	−26.6523	−	10.1927i	−1.08989	−	0.416812i
$599$	3.75042	−	1.36504i	0.153238	−	0.0557741i	−0.264262	−	0.964451i	$-0.585128\pi$
$599$	3.75042	−	1.36504i	0.153238	−	0.0557741i	0.417500	+	0.908677i	$0.362906\pi$
$600$	−17.1542	−	17.2522i	−0.700316	−	0.704320i
$601$	−6.90255	+	11.9556i	−0.281561	+	0.487678i	−0.971769	−	0.235933i	$-0.924186\pi$
$601$	−6.90255	+	11.9556i	−0.281561	+	0.487678i	0.690208	+	0.723611i	$0.257519\pi$
$602$	5.62956	−	4.57037i	0.229444	−	0.186274i
$603$	−19.6431	+	19.8115i	−0.799931	+	0.806787i
$604$	−26.9443	−	16.7433i	−1.09635	−	0.681277i
$605$	−4.40013	+	0.775862i	−0.178891	+	0.0315433i
$606$	−12.7509	−	3.01567i	−0.517972	−	0.122503i
$607$			17.8562i			0.724761i	0.932030	+	0.362380i	$0.118036\pi$
$607$			17.8562i			0.724761i	−0.932030	+	0.362380i	$0.881964\pi$
$608$	−19.2182	+	15.4486i	−0.779402	+	0.626524i
$609$	−3.43564	−	3.13473i	−0.139219	−	0.127026i
$610$	2.86657	−	1.59365i	0.116064	−	0.0645248i
$611$	−4.16588	−	23.6259i	−0.168533	−	0.955800i
$612$	−12.8588	+	25.6643i	−0.519785	+	1.03742i
$613$	−32.9382	+	27.6385i	−1.33036	+	1.11631i	−0.346370	+	0.938098i	$0.612586\pi$
$613$	−32.9382	+	27.6385i	−1.33036	+	1.11631i	−0.983993	+	0.178209i	$0.942970\pi$
$614$	18.3285	+	22.5762i	0.739680	+	0.911103i
$615$	0.353895	−	0.112413i	0.0142704	−	0.00453295i
$616$	−1.78046	+	36.5927i	−0.0717368	+	1.47436i
$617$	4.11639	+	11.3097i	0.165720	+	0.455311i	0.994559	−	0.104176i	$-0.0332204\pi$
$617$	4.11639	+	11.3097i	0.165720	+	0.455311i	−0.828839	+	0.559487i	$0.810998\pi$
$618$	10.7551	−	5.40779i	0.432635	−	0.217533i
$619$	−13.8509	+	7.99684i	−0.556716	+	0.321420i	−0.751826	−	0.659361i	$-0.770827\pi$
$619$	−13.8509	+	7.99684i	−0.556716	+	0.321420i	0.195110	+	0.980781i	$0.437493\pi$
$620$	−2.62387	−	1.05251i	−0.105377	−	0.0422696i
$621$	−21.6174	−	23.2902i	−0.867477	−	0.934604i
$622$	−25.9701	−	0.420906i	−1.04131	−	0.0168768i
$623$	−2.08746	−	1.75158i	−0.0836322	−	0.0701757i
$624$	−6.33601	+	21.9633i	−0.253643	+	0.879236i
$625$	−23.0164	−	8.37727i	−0.920655	−	0.335091i
$626$	−11.4904	−	9.96330i	−0.459248	−	0.398214i
$627$	−42.4202	−	14.5575i	−1.69410	−	0.581372i
$628$	−3.48365	−	24.3466i	−0.139013	−	0.971535i
$629$	2.67717	−	7.35547i	0.106746	−	0.293282i
$630$	1.53369	+	0.737589i	0.0611037	+	0.0293862i
$631$	0.877148	−	1.04534i	0.0349187	−	0.0416145i	−0.748302	−	0.663358i	$-0.769131\pi$
$631$	0.877148	−	1.04534i	0.0349187	−	0.0416145i	0.783221	+	0.621743i	$0.213575\pi$
$632$	−19.7963	+	2.50592i	−0.787456	+	0.0996800i
$633$	−7.26192	−	9.42223i	−0.288636	−	0.374500i
$634$	−9.56928	−	27.6790i	−0.380045	−	1.09927i
$635$	−0.511501	−	0.885946i	−0.0202983	−	0.0351577i
$636$	7.46784	+	1.89448i	0.296119	+	0.0751211i
$637$	−6.96204	+	2.53398i	−0.275846	+	0.100400i
$638$	−10.1577	−	1.96131i	−0.402147	−	0.0776489i
$639$	11.9743	+	5.52163i	0.473697	+	0.218432i
$640$	0.928661	−	1.86263i	0.0367086	−	0.0736269i
$641$	15.8890	+	18.9358i	0.627578	+	0.747918i	0.982354	−	0.187033i	$-0.0598872\pi$
$641$	15.8890	+	18.9358i	0.627578	+	0.747918i	−0.354776	+	0.934951i	$0.615443\pi$
$642$	−1.00322	+	1.52689i	−0.0395938	+	0.0602614i
$643$	19.9452	−	3.51687i	0.786560	−	0.138692i	0.234079	−	0.972217i	$-0.424792\pi$
$643$	19.9452	−	3.51687i	0.786560	−	0.138692i	0.552481	+	0.833526i	$0.313681\pi$
$644$	26.1000	+	5.47970i	1.02848	+	0.215930i
$645$	−0.553493	−	0.505014i	−0.0217938	−	0.0198849i
$646$	29.2403	+	3.84526i	1.15044	+	0.151290i
$647$	−15.8844			−0.624480			−0.312240	−	0.950003i	$-0.601079\pi$
$647$	−15.8844			−0.624480			−0.312240	+	0.950003i	$0.601079\pi$
$648$	−17.1310	+	18.8290i	−0.672969	+	0.739671i
$649$	−6.39515	−	36.2687i	−0.251032	−	1.42367i
$650$	3.65351	+	22.8826i	0.143303	+	0.897529i
$651$	−28.9948	−	1.20396i	−1.13639	−	0.0471870i
$652$	−1.22510	+	37.7847i	−0.0479787	+	1.47976i
$653$	0.885563	+	0.511280i	0.0346548	+	0.0200079i	0.517227	−	0.855848i	$-0.326964\pi$
$653$	0.885563	+	0.511280i	0.0346548	+	0.0200079i	−0.482573	+	0.875856i	$0.660298\pi$
$654$	−26.6815	+	19.8832i	−1.04333	+	0.777495i
$655$	−0.171798	−	0.472010i	−0.00671269	−	0.0184430i
$656$	−2.75870	−	3.75745i	−0.107709	−	0.146704i
$657$	17.0556	−	12.0513i	0.665404	−	0.470165i
$658$	7.32621	+	21.1910i	0.285605	+	0.826109i
$659$	0.475168	−	2.69481i	0.0185099	−	0.104975i	−0.974153	−	0.225889i	$-0.927471\pi$
$659$	0.475168	−	2.69481i	0.0185099	−	0.104975i	0.992663	+	0.120914i	$0.0385825\pi$
$660$	3.76642	−	0.380267i	0.146608	−	0.0148019i
$661$	−16.6751	−	13.9921i	−0.648586	−	0.544228i	0.258055	−	0.966130i	$-0.416918\pi$
$661$	−16.6751	−	13.9921i	−0.648586	−	0.544228i	−0.906642	+	0.421902i	$0.861363\pi$
$662$	3.22782	+	1.93399i	0.125453	+	0.0751668i
$663$	24.2245	−	12.6763i	0.940803	−	0.492305i
$664$	5.72469	−	8.88789i	0.222161	−	0.344917i
$665$	0.199848	−	1.73701i	0.00774977	−	0.0673584i
$666$	4.04903	−	5.63813i	0.156897	−	0.218473i
$667$	−2.57569	+	7.07664i	−0.0997310	+	0.274009i
$668$	6.52411	−	2.13782i	0.252425	−	0.0827147i
$669$	−20.0964	+	2.68938i	−0.776973	+	0.103977i
$670$	−2.41910	−	0.0392071i	−0.0934578	−	0.00151470i
$671$	13.0041	−	73.7502i	0.502020	−	2.84709i
$672$	2.61120	−	21.2041i	0.100729	−	0.817965i
$673$	−12.6064	−	21.8349i	−0.485940	−	0.841673i	0.513929	−	0.857832i	$-0.328189\pi$
$673$	−12.6064	−	21.8349i	−0.485940	−	0.841673i	−0.999869	+	0.0161597i	$0.994856\pi$
$674$	30.4642	+	11.6505i	1.17344	+	0.448761i
$675$	−7.60200	+	24.6597i	−0.292601	+	0.949154i
$676$	−3.32506	+	2.61121i	−0.127887	+	0.100431i
$677$	−14.7569	−	8.51989i	−0.567153	−	0.327446i	0.188858	−	0.982004i	$-0.439521\pi$
$677$	−14.7569	−	8.51989i	−0.567153	−	0.327446i	−0.756012	+	0.654558i	$0.772855\pi$
$678$	−1.42059	+	24.5906i	−0.0545575	+	0.944397i
$679$	15.8305	+	18.8661i	0.607520	+	0.724014i
$680$	−2.37785	+	0.736721i	−0.0911862	+	0.0282520i
$681$	0.899583	−	1.41873i	0.0344721	−	0.0543660i
$682$	−56.4191	+	31.3657i	−2.16040	+	1.20105i
$683$	20.9051			0.799913			0.399957	−	0.916534i	$-0.369025\pi$
$683$	20.9051			0.799913			0.399957	+	0.916534i	$0.369025\pi$
$684$	24.0429	+	10.2927i	0.919302	+	0.393553i
$685$	−2.22399			−0.0849745
$686$	24.9182	−	13.8530i	0.951381	−	0.528911i
$687$	6.28651	−	9.91446i	0.239845	−	0.378260i
$688$	−3.78284	+	8.61177i	−0.144219	+	0.328321i
$689$	−4.71684	−	5.62132i	−0.179697	−	0.214155i
$690$	0.158930	−	2.75110i	0.00605035	−	0.104732i
$691$	20.8238	+	12.0226i	0.792176	+	0.457363i	0.840728	−	0.541458i	$-0.182127\pi$
$691$	20.8238	+	12.0226i	0.792176	+	0.457363i	−0.0485520	+	0.998821i	$0.515461\pi$
$692$	−30.0152	−	38.2208i	−1.14101	−	1.45294i
$693$	35.1472	−	16.5724i	1.33513	−	0.629533i
$694$	−1.27293	−	0.486810i	−0.0483196	−	0.0184790i
$695$	−0.562022	−	0.973451i	−0.0213187	−	0.0369251i
$696$	5.82281	+	1.57802i	0.220713	+	0.0598148i
$697$	−0.968149	+	5.49065i	−0.0366713	+	0.207973i
$698$	−15.3711	−	0.249125i	−0.581804	−	0.00942950i
$699$	−12.3790	+	1.65661i	−0.468218	+	0.0626587i
$700$	−6.74381	−	20.5805i	−0.254892	−	0.777869i
$701$	−1.70943	+	4.69662i	−0.0645643	+	0.177389i	−0.967780	−	0.251799i	$-0.918978\pi$
$701$	−1.70943	+	4.69662i	−0.0645643	+	0.177389i	0.903215	+	0.429188i	$0.141200\pi$
$702$	23.7212	−	5.01537i	0.895299	−	0.189293i
$703$	−6.83570	−	2.03303i	−0.257813	−	0.0766771i
$704$	−19.6536	−	43.2683i	−0.740723	−	1.63073i
$705$	2.05275	−	1.07417i	0.0773109	−	0.0404554i
$706$	−44.6760	−	26.7683i	−1.68140	−	1.00744i
$707$	−8.93493	−	7.49730i	−0.336033	−	0.281965i
$708$	2.15734	+	21.3677i	0.0810776	+	0.803047i
$709$	−5.44172	+	30.8615i	−0.204368	+	1.15903i	0.694063	+	0.719915i	$0.255819\pi$
$709$	−5.44172	+	30.8615i	−0.204368	+	1.15903i	−0.898431	+	0.439115i	$0.855292\pi$
$710$	0.373638	+	1.08074i	0.0140224	+	0.0405595i
$711$	12.2135	+	17.2852i	0.458041	+	0.648245i
$712$	3.44709	+	0.782248i	0.129185	+	0.0293160i
$713$	16.0715	+	44.1562i	0.601883	+	1.65366i
$714$	−20.4894	+	15.2688i	−0.766797	+	0.571422i
$715$	−3.12253	−	1.80279i	−0.116776	−	0.0674207i
$716$	−42.0017	−	1.36183i	−1.56968	−	0.0508940i
$717$	9.75921	+	0.405236i	0.364464	+	0.0151338i
$718$	4.95798	+	31.0527i	0.185030	+	1.15888i
$719$	1.31189	+	7.44009i	0.0489252	+	0.277469i	0.999449	−	0.0331821i	$-0.0105641\pi$
$719$	1.31189	+	7.44009i	0.0489252	+	0.277469i	−0.950524	+	0.310651i	$0.899453\pi$
$720$	−2.20676	+	0.0589568i	−0.0822412	+	0.00219719i
$721$	10.7161			0.399088
$722$	1.90004	−	26.8028i	0.0707121	−	0.997497i
$723$	−18.2598	−	16.6605i	−0.679090	−	0.619611i
$724$	−1.53502	+	7.31136i	−0.0570487	+	0.271724i
$725$	6.02267	−	1.06196i	0.223676	−	0.0394402i
$726$	32.6681	−	49.7205i	1.21243	−	1.84530i
$727$	3.48854	+	4.15748i	0.129383	+	0.154192i	0.826846	−	0.562428i	$-0.190133\pi$
$727$	3.48854	+	4.15748i	0.129383	+	0.154192i	−0.697464	+	0.716620i	$0.745688\pi$
$728$	−13.8219	+	14.9338i	−0.512273	+	0.553483i
$729$	26.1673	+	6.65368i	0.969160	+	0.246432i
$730$	1.77820	+	0.343346i	0.0658143	+	0.0127078i
$731$	10.5717	−	3.84777i	0.391007	−	0.142315i
$732$	−10.7385	+	42.3299i	−0.396906	+	1.56456i
$733$	−14.8855	−	25.7824i	−0.549808	−	0.952295i	−0.998287	−	0.0585020i	$-0.981368\pi$
$733$	−14.8855	−	25.7824i	−0.549808	−	0.952295i	0.448479	−	0.893793i	$-0.351966\pi$
$734$	6.04472	+	17.4843i	0.223115	+	0.645356i
$735$	−0.436774	−	0.566707i	−0.0161106	−	0.0209033i
$736$	−33.3586	+	9.16179i	−1.22962	+	0.337708i
$737$	−35.5095	+	42.3186i	−1.30801	+	1.55882i
$738$	−2.14285	+	4.45569i	−0.0788794	+	0.164016i
$739$	2.38377	−	6.54936i	0.0876885	−	0.240922i	−0.888095	−	0.459659i	$-0.847971\pi$
$739$	2.38377	−	6.54936i	0.0876885	−	0.240922i	0.975784	+	0.218737i	$0.0701937\pi$
$740$	0.595895	−	0.0852640i	0.0219055	−	0.00313437i
$741$	−12.8516	−	21.3388i	−0.472115	−	0.783900i
$742$	5.18162	+	4.49297i	0.190223	+	0.164942i
$743$	44.7565	+	16.2900i	1.64196	+	0.597624i	0.987380	−	0.158371i	$-0.0506241\pi$
$743$	44.7565	+	16.2900i	1.64196	+	0.597624i	0.654578	+	0.755994i	$0.272846\pi$
$744$	34.1616	−	15.8114i	1.25242	−	0.579673i
$745$	3.11956	+	2.61762i	0.114292	+	0.0959022i
$746$	10.0834	+	0.163426i	0.369181	+	0.00598344i
$747$	−11.1747	−	0.929624i	−0.408860	−	0.0340132i
$748$	−21.1611	+	52.7541i	−0.773727	+	1.92888i
$749$	−1.40844	+	0.813164i	−0.0514633	+	0.0297124i
$750$	−4.01225	+	2.01740i	−0.146507	+	0.0736651i
$751$	−9.07042	−	24.9208i	−0.330984	−	0.909372i	−0.987856	−	0.155370i	$-0.950343\pi$
$751$	−9.07042	−	24.9208i	−0.330984	−	0.909372i	0.656872	−	0.754002i	$-0.271879\pi$
$752$	−21.0221	−	20.0991i	−0.766598	−	0.732938i
$753$	−18.8270	+	5.98031i	−0.686093	+	0.217935i
$754$	−3.62166	−	4.46099i	−0.131893	−	0.162460i
$755$	−2.23524	+	1.87559i	−0.0813487	+	0.0682597i
$756$	−21.1538	+	8.12427i	−0.769355	+	0.295477i
$757$	2.55734	+	14.5034i	0.0929481	+	0.527135i	0.995357	+	0.0962538i	$0.0306861\pi$
$757$	2.55734	+	14.5034i	0.0929481	+	0.527135i	−0.902409	+	0.430881i	$0.858203\pi$
$758$	−16.1582	+	8.98298i	−0.586890	+	0.326276i
$759$	−46.4809	−	42.4098i	−1.68715	−	1.53938i
$760$	0.799889	+	2.12231i	0.0290150	+	0.0769842i
$761$		−	36.3749i		−	1.31859i	−0.751884	−	0.659295i	$-0.770855\pi$
$761$		−	36.3749i		−	1.31859i	0.751884	−	0.659295i	$-0.229145\pi$
$762$	13.2558	+	3.13506i	0.480206	+	0.113571i
$763$	−29.1709	+	5.14361i	−1.05606	+	0.186211i
$764$	4.52404	−	7.28033i	0.163674	−	0.263393i
$765$	1.87497	+	1.85904i	0.0677897	+	0.0672136i
$766$	−1.65764	+	1.34576i	−0.0598930	+	0.0486242i
$767$	10.2276	−	17.7148i	0.369299	−	0.639644i
$768$	9.56646	+	26.0093i	0.345200	+	0.938529i
$769$	38.0595	−	13.8525i	1.37246	−	0.499534i	0.452576	−	0.891726i	$-0.350505\pi$
$769$	38.0595	−	13.8525i	1.37246	−	0.499534i	0.919884	+	0.392192i	$0.128283\pi$
$770$	3.14751	+	1.20371i	0.113428	+	0.0433788i
$771$	−28.6846	−	6.29504i	−1.03305	−	0.226710i
$772$	−31.4813	−	12.6280i	−1.13304	−	0.454492i
$773$	−42.7474	−	7.53752i	−1.53752	−	0.271106i	−0.660227	−	0.751066i	$-0.729540\pi$
$773$	−42.7474	−	7.53752i	−1.53752	−	0.271106i	−0.877290	+	0.479960i	$0.840651\pi$
$774$	9.94826	−	0.750801i	0.357583	−	0.0269870i
$775$	24.5284	−	29.2318i	0.881086	−	1.05004i
$776$	−29.4532	−	12.3723i	−1.05731	−	0.444139i
$777$	5.47481	−	2.86487i	0.196408	−	0.102777i
$778$	−16.2105	+	18.6951i	−0.581174	+	0.670251i
$779$	5.04638	+	0.580600i	0.180805	+	0.0208021i
$780$	1.73830	+	1.18289i	0.0622410	+	0.0423543i
$781$	24.5353	+	8.93012i	0.877943	+	0.319545i
$782$	35.4931	+	21.2662i	1.26923	+	0.760477i
$783$	−1.42491	−	6.23814i	−0.0509223	−	0.222933i
$784$	−4.98547	+	7.47141i	−0.178053	+	0.266836i
$785$	−2.22787	−	0.392834i	−0.0795161	−	0.0140208i
$786$	6.14250	+	2.64618i	0.219096	+	0.0943861i
$787$	37.3664	−	21.5735i	1.33197	−	0.769013i	0.346368	−	0.938099i	$-0.387415\pi$
$787$	37.3664	−	21.5735i	1.33197	−	0.769013i	0.985601	+	0.169086i	$0.0540816\pi$
$788$	21.8563	−	11.6912i	0.778598	−	0.416483i
$789$	−31.9008	−	13.1341i	−1.13570	−	0.467586i
$790$	−0.347967	+	1.80214i	−0.0123801	+	0.0641171i
$791$	−10.9632	+	18.9889i	−0.389808	+	0.675168i
$792$	−30.7136	+	39.9673i	−1.09136	+	1.42018i
$793$	31.8633	−	26.7365i	1.13150	−	0.949440i
$794$	−8.84597	−	55.4039i	−0.313932	−	1.96621i
$795$	0.379486	−	0.598489i	0.0134590	−	0.0212262i
$796$	31.0692	+	6.52300i	1.10122	+	0.231202i
$797$		−	15.1787i		−	0.537656i	−0.963188	−	0.268828i	$-0.913364\pi$
$797$		−	15.1787i		−	0.537656i	0.963188	−	0.268828i	$-0.0866363\pi$
$798$	15.0054	+	17.8003i	0.531186	+	0.630122i
$799$			34.7867i			1.23067i
$800$	19.9881	+	19.7404i	0.706687	+	0.697927i
$801$	−0.985796	−	3.61723i	−0.0348314	−	0.127808i
$802$	27.7233	−	4.42639i	0.978943	−	0.156301i
$803$	31.6775	−	26.5806i	1.11787	−	0.938008i
$804$	22.4731	−	23.0815i	0.792566	−	0.814023i
$805$	1.22652	−	2.12440i	0.0432292	−	0.0748753i
$806$	−35.2033	−	6.79727i	−1.23998	−	0.239424i
$807$	−9.02084	+	21.9104i	−0.317549	+	0.771281i
$808$	14.7546	+	3.34825i	0.519063	+	0.117791i
$809$	21.0568	−	12.1571i	0.740317	−	0.427422i	−0.0818676	−	0.996643i	$-0.526088\pi$
$809$	21.0568	−	12.1571i	0.740317	−	0.427422i	0.822185	+	0.569221i	$0.192755\pi$
$810$	1.15514	+	2.03668i	0.0405875	+	0.0715618i
$811$	6.15535	+	1.08535i	0.216143	+	0.0381119i	0.280671	−	0.959804i	$-0.409443\pi$
$811$	6.15535	+	1.08535i	0.216143	+	0.0381119i	−0.0645277	+	0.997916i	$0.520554\pi$
$812$	3.99987	+	3.58347i	0.140368	+	0.125755i
$813$	47.9750	−	6.42020i	1.68256	−	0.225166i
$814$	7.06438	−	11.7904i	0.247606	−	0.413253i
$815$	3.26760	+	1.18931i	0.114459	+	0.0416597i
$816$	14.5781	−	29.7683i	0.510336	−	1.04210i
$817$	−4.07678	−	9.40430i	−0.142629	−	0.329015i
$818$	−11.0423	−	9.57479i	−0.386086	−	0.334775i
$819$	20.8711	+	5.49705i	0.729295	+	0.192082i
$820$	−0.407446	+	0.133512i	−0.0142286	+	0.00466244i
$821$	13.0197	−	15.5163i	0.454390	−	0.541521i	−0.489403	−	0.872058i	$-0.662785\pi$
$821$	13.0197	−	15.5163i	0.454390	−	0.541521i	0.943793	+	0.330536i	$0.107230\pi$
$822$	20.3114	−	21.5492i	0.708442	−	0.751615i
$823$	−47.6559	−	8.40302i	−1.66118	−	0.292911i	−0.737292	−	0.675574i	$-0.763896\pi$
$823$	−47.6559	−	8.40302i	−1.66118	−	0.292911i	−0.923888	+	0.382664i	$0.875007\pi$
$824$	−12.3617	+	6.35698i	−0.430640	+	0.221456i
$825$	−10.9529	+	49.9089i	−0.381330	+	1.73761i
$826$	−6.82891	+	17.8565i	−0.237608	+	0.621306i
$827$	−28.9574	+	10.5396i	−1.00695	+	0.366499i	−0.792260	−	0.610183i	$-0.791096\pi$
$827$	−28.9574	+	10.5396i	−1.00695	+	0.366499i	−0.214688	+	0.976683i	$0.568874\pi$
$828$	25.2050	+	26.6653i	0.875935	+	0.926682i
$829$	−18.4195	+	31.9035i	−0.639736	+	1.10806i	0.345754	+	0.938325i	$0.387623\pi$
$829$	−18.4195	+	31.9035i	−0.639736	+	1.10806i	−0.985490	+	0.169731i	$0.945710\pi$
$830$	−0.612908	−	0.754951i	−0.0212744	−	0.0262047i
$831$	28.2390	+	1.17258i	0.979602	+	0.0406764i
$832$	7.08542	−	25.4265i	0.245643	−	0.881505i
$833$	10.5798	−	1.86551i	0.366570	−	0.0646362i
$834$	14.5650	+	3.44471i	0.504346	+	0.119281i
$835$		−	0.631491i		−	0.0218537i
$836$	49.1334	+	16.3638i	1.69931	+	0.565953i
$837$	−31.8309	−	24.1026i	−1.10024	−	0.833106i
$838$	−16.6797	−	30.0026i	−0.576190	−	1.03642i
$839$	3.89877	+	22.1110i	0.134601	+	0.763358i	0.975137	+	0.221603i	$0.0711289\pi$
$839$	3.89877	+	22.1110i	0.134601	+	0.763358i	−0.840536	+	0.541755i	$0.817760\pi$
$840$	−1.77862	−	0.835565i	−0.0613682	−	0.0288297i
$841$	21.0536	−	17.6661i	0.725986	−	0.609175i
$842$	−18.3477	+	14.8956i	−0.632304	+	0.513337i
$843$	10.6523	+	33.5352i	0.366886	+	1.15501i
$844$	8.48387	+	10.8032i	0.292027	+	0.371862i
$845$	0.133005	+	0.365427i	0.00457550	+	0.0125711i
$846$	−8.33939	+	29.7001i	−0.286714	+	1.02111i
$847$	45.8635	−	26.4793i	1.57589	−	0.909841i
$848$	−8.64264	−	2.10911i	−0.296790	−	0.0724270i
$849$	13.1885	+	17.1118i	0.452627	+	0.587277i
$850$	0.544507	−	33.5963i	0.0186764	−	1.15234i
$851$	−7.66460	−	6.43136i	−0.262739	−	0.220464i
$852$	−13.8841	−	6.24992i	−0.475662	−	0.214119i
$853$	−35.4174	−	12.8909i	−1.21267	−	0.441375i	−0.345040	−	0.938588i	$-0.612134\pi$
$853$	−35.4174	−	12.8909i	−1.21267	−	0.441375i	−0.867628	+	0.497213i	$0.834357\pi$
$854$	−25.4675	+	29.3709i	−0.871480	+	1.00505i
$855$	1.58830	−	1.80674i	0.0543188	−	0.0617892i
$856$	1.14234	−	1.77355i	0.0390445	−	0.0606187i
$857$	−6.82116	+	18.7410i	−0.233006	+	0.640180i	−0.999999	−	0.00147620i	$-0.999530\pi$
$857$	−6.82116	+	18.7410i	−0.233006	+	0.640180i	0.766992	+	0.641656i	$0.221752\pi$
$858$	45.9856	−	13.7909i	1.56992	−	0.470812i
$859$	−2.21082	+	2.63475i	−0.0754323	+	0.0898967i	−0.802441	−	0.596732i	$-0.796466\pi$
$859$	−2.21082	+	2.63475i	−0.0754323	+	0.0898967i	0.727008	+	0.686628i	$0.240910\pi$
$860$	0.644391	+	0.577308i	0.0219736	+	0.0196860i
$861$	−3.48598	+	2.68673i	−0.118802	+	0.0915634i
$862$	47.2713	−	16.3428i	1.61007	−	0.556638i
$863$	1.40781	+	2.43839i	0.0479223	+	0.0830038i	0.888992	−	0.457924i	$-0.151407\pi$
$863$	1.40781	+	2.43839i	0.0479223	+	0.0830038i	−0.841069	+	0.540927i	$0.818073\pi$
$864$	19.5828	−	21.9207i	0.666219	−	0.745756i
$865$	−4.20051	+	1.52886i	−0.142821	+	0.0519828i
$866$	−1.86444	+	9.65601i	−0.0633563	+	0.328125i
$867$	−9.72139	+	3.08796i	−0.330156	+	0.104873i
$868$	33.4915	+	1.08590i	1.13678	+	0.0368579i
$869$	26.9383	+	32.1038i	0.913820	+	1.08905i
$870$	0.304709	−	0.463764i	0.0103306	−	0.0157231i
$871$	−30.2171	+	5.32810i	−1.02387	+	0.180536i
$872$	30.5992	−	23.2382i	1.03622	−	0.786944i
$873$	3.09722	+	33.7423i	0.104825	+	1.14200i
$874$	17.4021	−	33.4409i	0.588634	−	1.13116i
$875$	−3.99769			−0.135147
$876$	−19.5669	+	14.0940i	−0.661104	+	0.476193i
$877$	2.67669	+	15.1802i	0.0903853	+	0.512601i	0.996064	+	0.0886360i	$0.0282508\pi$
$877$	2.67669	+	15.1802i	0.0903853	+	0.512601i	−0.905679	+	0.423965i	$0.860638\pi$
$878$	47.6033	−	7.60050i	1.60653	−	0.256505i
$879$	−1.27648	+	30.7413i	−0.0430548	+	1.03688i
$880$	−4.34492	+	0.478599i	−0.146467	+	0.0161336i
$881$	−0.798552	−	0.461044i	−0.0269039	−	0.0155330i	0.486488	−	0.873687i	$-0.338278\pi$
$881$	−0.798552	−	0.461044i	−0.0269039	−	0.0155330i	−0.513392	+	0.858154i	$0.671611\pi$
$882$	9.48004	+	0.943566i	0.319210	+	0.0317715i
$883$	7.94524	+	21.8294i	0.267379	+	0.734617i	0.998621	+	0.0524991i	$0.0167187\pi$
$883$	7.94524	+	21.8294i	0.267379	+	0.734617i	−0.731242	+	0.682118i	$0.761059\pi$
$884$	−27.8379	+	14.8909i	−0.936290	+	0.500834i
$885$	1.92950	+	0.423443i	0.0648595	+	0.0142339i
$886$	15.2598	−	5.27566i	0.512661	−	0.177239i
$887$	−3.62448	+	20.5555i	−0.121698	+	0.690185i	0.861516	+	0.507731i	$0.169515\pi$
$887$	−3.62448	+	20.5555i	−0.121698	+	0.690185i	−0.983214	+	0.182455i	$0.941596\pi$
$888$	−4.61606	+	6.55257i	−0.154905	+	0.219890i
$889$	9.28867	+	7.79412i	0.311532	+	0.261406i
$890$	0.167106	−	0.278899i	0.00560141	−	0.00934870i
$891$	52.7281	+	8.83407i	1.76646	+	0.295953i
$892$	23.1762	−	3.31618i	0.775996	−	0.111034i
$893$	31.6370	−	1.89999i	1.05869	−	0.0635807i
$894$	−53.8536	+	6.32036i	−1.80114	+	0.211385i
$895$	−1.32204	+	3.63229i	−0.0441911	+	0.121414i
$896$	−2.79252	+	24.5107i	−0.0932917	+	0.818847i
$897$	−4.63553	−	34.6391i	−0.154776	−	1.15657i
$898$	−0.155839	+	9.61532i	−0.00520041	+	0.320867i
$899$	−1.64312	+	9.31858i	−0.0548010	+	0.310792i
$900$	8.51890	−	28.5532i	0.283963	−	0.951774i
$901$	5.32024	+	9.21493i	0.177243	+	0.306994i
$902$	−3.49704	+	9.14416i	−0.116439	+	0.304467i
$903$	8.21211	+	3.38106i	0.273282	+	0.112515i
$904$	1.38225	−	28.4085i	0.0459729	−	0.944854i
$905$	0.595106	+	0.343585i	0.0197820	+	0.0114211i
$906$	2.24075	−	38.7876i	0.0744438	−	1.28863i
$907$	−15.4050	−	18.3589i	−0.511514	−	0.609598i	0.447039	−	0.894515i	$-0.352479\pi$
$907$	−15.4050	−	18.3589i	−0.511514	−	0.609598i	−0.958552	+	0.284916i	$0.908034\pi$
$908$	−1.02382	+	1.64758i	−0.0339766	+	0.0546770i
$909$	−4.21950	−	15.4828i	−0.139952	−	0.513532i
$910$	0.909451	+	1.63588i	0.0301480	+	0.0542288i
$911$	−1.44251			−0.0477925			−0.0238962	−	0.999714i	$-0.507607\pi$
$911$	−1.44251			−0.0477925			−0.0238962	+	0.999714i	$0.507607\pi$
$912$	−27.8692	−	11.6322i	−0.922841	−	0.385182i
$913$	−22.2036			−0.734831
$914$	−6.40365	−	11.5186i	−0.211814	−	0.381001i
$915$	3.39241	+	2.15104i	0.112150	+	0.0711112i
$916$	−7.15470	+	11.5137i	−0.236398	+	0.380424i
$917$	3.82698	+	4.56082i	0.126378	+	0.150611i
$918$	−35.1368	+	1.18907i	−1.15969	+	0.0392452i
$919$	−10.1682	−	5.87063i	−0.335419	−	0.193654i	0.322826	−	0.946458i	$-0.395367\pi$
$919$	−10.1682	−	5.87063i	−0.335419	−	0.193654i	−0.658244	+	0.752804i	$0.728701\pi$
$920$	−0.154640	+	3.17823i	−0.00509834	+	0.104783i
$921$	−13.5591	+	32.9330i	−0.446786	+	1.08518i
$922$	7.14561	−	18.6846i	0.235328	−	0.615344i
$923$	7.25105	+	12.5592i	0.238671	+	0.413390i
$924$	−40.4090	+	19.5042i	−1.32936	+	0.641640i
$925$	−1.41092	+	8.00172i	−0.0463907	+	0.263095i
$926$	0.563977	−	34.7977i	0.0185334	−	1.14352i
$927$	12.1133	+	8.40500i	0.397852	+	0.276056i
$928$	−6.73989	−	1.76097i	−0.221248	−	0.0578066i
$929$	3.13298	−	8.60779i	0.102790	−	0.282412i	−0.877628	−	0.479343i	$-0.840875\pi$
$929$	3.13298	−	8.60779i	0.102790	−	0.282412i	0.980417	+	0.196930i	$0.0630973\pi$
$930$	−0.403592	−	3.43887i	−0.0132343	−	0.112765i
$931$	−2.27445	−	9.52002i	−0.0745422	−	0.312006i
$932$	14.2761	−	2.04271i	0.467630	−	0.0669111i
$933$	−14.7488	−	28.1852i	−0.482854	−	0.922742i
$934$	2.37334	−	3.96108i	0.0776579	−	0.129610i
$935$	4.00505	+	3.36063i	0.130979	+	0.109904i
$936$	−27.3371	+	6.03993i	−0.893542	+	0.197421i
$937$	−4.83717	+	27.4329i	−0.158023	+	0.896195i	0.797946	+	0.602729i	$0.205920\pi$
$937$	−4.83717	+	27.4329i	−0.158023	+	0.896195i	−0.955969	+	0.293466i	$0.905191\pi$
$938$	27.1029	−	9.37012i	0.884942	−	0.305945i
$939$	3.99269	−	18.1935i	0.130297	−	0.593722i
$940$	−2.35894	+	1.26183i	−0.0769401	+	0.0411563i
$941$	7.16383	+	19.6825i	0.233534	+	0.641630i	1.00000		0.000655452i	$-0.000208637\pi$
$941$	7.16383	+	19.6825i	0.233534	+	0.641630i	−0.766466	+	0.642285i	$0.777986\pi$
$942$	24.1531	−	17.9991i	0.786951	−	0.586441i
$943$	6.17183	+	3.56330i	0.200982	+	0.116037i
$944$	−2.71519	−	24.6496i	−0.0883721	−	0.802277i
$945$	0.104243	+	2.08171i	0.00339104	+	0.0677179i
$946$	19.5076	−	3.11465i	0.634247	−	0.101266i
$947$	8.54827	+	48.4796i	0.277781	+	1.57538i	0.729986	+	0.683462i	$0.239527\pi$
$947$	8.54827	+	48.4796i	0.277781	+	1.57538i	−0.452205	+	0.891914i	$0.649362\pi$
$948$	−14.2837	−	19.8302i	−0.463913	−	0.644056i
$949$	22.9679			0.745570
$950$	−30.5841	+	1.33977i	−0.992280	+	0.0434677i
$951$	24.1759	−	26.4966i	0.783957	−	0.859213i
$952$	23.4979	−	17.8452i	0.761572	−	0.578367i
$953$	5.84883	−	1.03131i	0.189462	−	0.0334073i	−0.0781118	−	0.996945i	$-0.524889\pi$
$953$	5.84883	−	1.03131i	0.189462	−	0.0334073i	0.267574	+	0.963537i	$0.413778\pi$
$954$	2.33321	+	9.14290i	0.0755405	+	0.296012i
$955$	−0.506783	−	0.603961i	−0.0163991	−	0.0195437i
$956$	−11.2728	−	0.365499i	−0.364587	−	0.0118211i
$957$	−3.83582	−	12.0758i	−0.123995	−	0.390354i
$958$	10.4518	−	54.1302i	0.337682	−	1.74887i
$959$	24.7709	−	9.01589i	0.799895	−	0.291138i
$960$	2.54743	−	0.0912313i	0.0822178	−	0.00294448i
$961$	14.0211	+	24.2852i	0.452293	+	0.783394i
$962$	7.21515	−	2.49445i	0.232626	−	0.0804242i
$963$	−2.22987	−	0.185504i	−0.0718566	−	0.00597777i
$964$	21.2586	+	19.0455i	0.684693	+	0.613414i
$965$	−2.00548	+	2.39003i	−0.0645586	+	0.0769379i
$966$	9.38254	+	31.2861i	0.301878	+	1.00661i
$967$	−19.6928	+	54.1056i	−0.633279	+	1.73992i	0.0385956	+	0.999255i	$0.487712\pi$
$967$	−19.6928	+	54.1056i	−0.633279	+	1.73992i	−0.671875	+	0.740665i	$0.734511\pi$
$968$	−37.1985	+	57.7527i	−1.19561	+	1.85624i
$969$	12.9791	+	33.7078i	0.416949	+	1.08285i
$970$	−1.92504	+	2.22009i	−0.0618092	+	0.0712827i
$971$	−22.5240	−	8.19808i	−0.722831	−	0.263089i	−0.0457037	−	0.998955i	$-0.514553\pi$
$971$	−22.5240	−	8.19808i	−0.722831	−	0.263089i	−0.677127	+	0.735866i	$0.736775\pi$
$972$	−30.2840	−	7.40810i	−0.971359	−	0.237615i
$973$	10.2061	+	8.56395i	0.327193	+	0.274548i
$974$	−0.676402	+	41.7343i	−0.0216733	+	1.33725i
$975$	−22.4787	+	17.3248i	−0.719895	+	0.554839i
$976$	11.9550	−	48.9891i	0.382671	−	1.56810i
$977$	−7.81805	+	4.51375i	−0.250122	+	0.144408i	−0.619820	−	0.784744i	$-0.712794\pi$
$977$	−7.81805	+	4.51375i	−0.250122	+	0.144408i	0.369698	+	0.929152i	$0.379461\pi$
$978$	−41.3662	+	20.7994i	−1.32275	+	0.665091i
$979$	−2.53907	−	6.97603i	−0.0811490	−	0.222955i
$980$	0.510269	+	0.649766i	0.0162999	+	0.0207560i
$981$	−37.0086	−	17.0655i	−1.18159	−	0.544859i
$982$	−2.21564	+	1.79877i	−0.0707038	+	0.0574010i
$983$	−11.4173	+	9.58024i	−0.364155	+	0.305562i	−0.806444	−	0.591310i	$-0.798611\pi$
$983$	−11.4173	+	9.58024i	−0.364155	+	0.305562i	0.442289	+	0.896872i	$0.354166\pi$
$984$	2.42749	−	5.16726i	0.0773856	−	0.164726i
$985$	−0.395903	−	2.24528i	−0.0126145	−	0.0715405i
$986$	4.04848	+	7.28222i	0.128930	+	0.231913i
$987$	−18.5090	+	20.2858i	−0.589148	+	0.645703i
$988$	15.0631	+	24.5040i	0.479219	+	0.779577i
$989$		−	14.3803i		−	0.457267i
$990$	2.61377	+	3.82936i	0.0830712	+	0.121705i
$991$	0.787224	−	0.138809i	0.0250070	−	0.00440941i	−0.161131	−	0.986933i	$-0.551514\pi$
$991$	0.787224	−	0.138809i	0.0250070	−	0.00440941i	0.186138	+	0.982524i	$0.440403\pi$
$992$	−39.2788	+	18.6151i	−1.24710	+	0.591031i
$993$	−0.191198	+	4.60458i	−0.00606748	+	0.146122i
$994$	−8.54283	−	10.5226i	−0.270962	−	0.333758i
$995$	1.46005	−	2.52887i	0.0462865	−	0.0801707i
$996$	12.9126	+	0.956132i	0.409152	+	0.0302962i
$997$	−13.3352	+	4.85363i	−0.422331	+	0.153716i	−0.544438	−	0.838801i	$-0.683257\pi$
$997$	−13.3352	+	4.85363i	−0.422331	+	0.153716i	0.122107	+	0.992517i	$0.461035\pi$
$998$	15.8142	−	41.3514i	0.500589	−	1.30896i
$999$	8.43565	+	1.05569i	0.266892	+	0.0334005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.12	yes	216
3.2	odd	2	inner	228.2.v.a.23.25	yes	216
4.3	odd	2	inner	228.2.v.a.23.33	yes	216
12.11	even	2	inner	228.2.v.a.23.4	✓	216
19.5	even	9	inner	228.2.v.a.119.4	yes	216
57.5	odd	18	inner	228.2.v.a.119.33	yes	216
76.43	odd	18	inner	228.2.v.a.119.25	yes	216
228.119	even	18	inner	228.2.v.a.119.12	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.4	✓	216	12.11	even	2	inner
228.2.v.a.23.12	yes	216	1.1	even	1	trivial
228.2.v.a.23.25	yes	216	3.2	odd	2	inner
228.2.v.a.23.33	yes	216	4.3	odd	2	inner
228.2.v.a.119.4	yes	216	19.5	even	9	inner
228.2.v.a.119.12	yes	216	228.119	even	18	inner
228.2.v.a.119.25	yes	216	76.43	odd	18	inner
228.2.v.a.119.33	yes	216	57.5	odd	18	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687167 - 1.23604i) q^{2} +(0.927511 - 1.46278i) q^{3} +(-1.05560 + 1.69873i) q^{4} +(0.118249 + 0.140923i) q^{5} +(-2.44541 - 0.141271i) q^{6} +(-1.88835 - 1.09024i) q^{7} +(2.82509 + 0.137458i) q^{8} +(-1.27945 - 2.71349i) q^{9} +O(q^{10})\)	\(q+(-0.687167 - 1.23604i) q^{2} +(0.927511 - 1.46278i) q^{3} +(-1.05560 + 1.69873i) q^{4} +(0.118249 + 0.140923i) q^{5} +(-2.44541 - 0.141271i) q^{6} +(-1.88835 - 1.09024i) q^{7} +(2.82509 + 0.137458i) q^{8} +(-1.27945 - 2.71349i) q^{9} +(0.0929307 - 0.242998i) q^{10} +(-2.97017 - 5.14448i) q^{11} +(1.50579 + 3.11971i) q^{12} +(0.572936 - 3.24928i) q^{13} +(-0.0499714 + 3.08326i) q^{14} +(0.315817 - 0.0422638i) q^{15} +(-1.77140 - 3.58638i) q^{16} +(-1.63631 + 4.49572i) q^{17} +(-2.47480 + 3.44607i) q^{18} +(4.17803 + 1.24260i) q^{19} +(-0.364215 + 0.0521140i) q^{20} +(-3.34625 + 1.75103i) q^{21} +(-4.31780 + 7.20637i) q^{22} +(4.68466 + 3.93090i) q^{23} +(2.82137 - 4.00498i) q^{24} +(0.862364 - 4.89071i) q^{25} +(-4.40995 + 1.52462i) q^{26} +(-5.15593 - 0.645244i) q^{27} +(3.84538 - 2.05695i) q^{28} +(0.421181 + 1.15719i) q^{29} +(-0.269259 - 0.361321i) q^{30} +(6.65444 + 3.84194i) q^{31} +(-3.21567 + 4.65397i) q^{32} +(-10.2801 - 0.426865i) q^{33} +(6.68132 - 1.06676i) q^{34} +(-0.0696549 - 0.395032i) q^{35} +(5.96009 + 0.690930i) q^{36} -1.63611 q^{37} +(-1.33509 - 6.01810i) q^{38} +(-4.22158 - 3.85183i) q^{39} +(0.314692 + 0.414375i) q^{40} +(1.14765 - 0.202362i) q^{41} +(4.46378 + 2.93285i) q^{42} +(-1.51151 - 1.80135i) q^{43} +(11.8744 + 0.385007i) q^{44} +(0.231101 - 0.501170i) q^{45} +(1.63962 - 8.49163i) q^{46} +(6.83260 - 2.48686i) q^{47} +(-6.88908 - 0.735242i) q^{48} +(-1.12275 - 1.94467i) q^{49} +(-6.63772 + 2.29481i) q^{50} +(5.05855 + 6.56339i) q^{51} +(4.91488 + 4.40322i) q^{52} +(1.42960 - 1.70373i) q^{53} +(2.74544 + 6.81635i) q^{54} +(0.373759 - 1.02690i) q^{55} +(-5.18489 - 3.33959i) q^{56} +(5.69282 - 4.95901i) q^{57} +(1.14091 - 1.31578i) q^{58} +(5.82579 + 2.12042i) q^{59} +(-0.261583 + 0.581103i) q^{60} +(9.65727 + 8.10341i) q^{61} +(0.176097 - 10.8652i) q^{62} +(-0.542311 + 6.51892i) q^{63} +(7.96221 + 0.776659i) q^{64} +(0.525649 - 0.303484i) q^{65} +(6.53652 + 13.0000i) q^{66} +(-3.18066 - 8.73880i) q^{67} +(-5.90974 - 7.52535i) q^{68} +(10.0951 - 3.20667i) q^{69} +(-0.440412 + 0.357549i) q^{70} +(-3.36704 + 2.82528i) q^{71} +(-3.24155 - 7.84170i) q^{72} +(1.20880 + 6.85547i) q^{73} +(1.12428 + 2.02230i) q^{74} +(-6.35418 - 5.79764i) q^{75} +(-6.52120 + 5.78567i) q^{76} +12.9528i q^{77} +(-1.86009 + 7.86490i) q^{78} +(-6.94773 + 1.22507i) q^{79} +(0.295939 - 0.673717i) q^{80} +(-5.72604 + 6.94352i) q^{81} +(-1.03876 - 1.27949i) q^{82} +(1.86888 - 3.23699i) q^{83} +(0.557775 - 7.53278i) q^{84} +(-0.827043 + 0.301019i) q^{85} +(-1.18788 + 3.10612i) q^{86} +(2.08336 + 0.457208i) q^{87} +(-7.68383 - 14.9419i) q^{88} +(1.23073 + 0.217011i) q^{89} +(-0.778273 + 0.0587368i) q^{90} +(-4.62440 + 5.51115i) q^{91} +(-11.6227 + 3.80853i) q^{92} +(11.7920 - 6.17053i) q^{93} +(-7.76901 - 6.73650i) q^{94} +(0.318935 + 0.735718i) q^{95} +(3.82516 + 9.02043i) q^{96} +(-10.6136 - 3.86302i) q^{97} +(-1.63217 + 2.72408i) q^{98} +(-10.1593 + 14.6416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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