LMFDB - Embedded newform 228.2.v.a.23.4

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			23.4
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32091 + 0.505162i) q^{2} +(-1.37188 - 1.05734i) q^{3} +(1.48962 - 1.33455i) q^{4} +(-0.118249 - 0.140923i) q^{5} +(2.34625 + 0.703629i) q^{6} +(1.88835 + 1.09024i) q^{7} +(-1.29350 + 2.51532i) q^{8} +(0.764084 + 2.90106i) q^{9} +O(q^{10})$	\(q+(-1.32091 + 0.505162i) q^{2} +(-1.37188 - 1.05734i) q^{3} +(1.48962 - 1.33455i) q^{4} +(-0.118249 - 0.140923i) q^{5} +(2.34625 + 0.703629i) q^{6} +(1.88835 + 1.09024i) q^{7} +(-1.29350 + 2.51532i) q^{8} +(0.764084 + 2.90106i) q^{9} +(0.227385 + 0.126413i) q^{10} +(-2.97017 - 5.14448i) q^{11} +(-3.45464 + 0.255804i) q^{12} +(0.572936 - 3.24928i) q^{13} +(-3.04509 - 0.486190i) q^{14} +(0.0132193 + 0.318358i) q^{15} +(0.437957 - 3.97595i) 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} +(-1.43783 - 3.49229i) q^{21} +(6.52213 + 5.29500i) q^{22} +(4.68466 + 3.93090i) q^{23} +(4.43406 - 2.08305i) q^{24} +(0.862364 - 4.89071i) q^{25} +(0.884614 + 4.58145i) q^{26} +(2.01917 - 4.78779i) q^{27} +(4.26791 - 0.896050i) q^{28} +(-0.421181 - 1.15719i) q^{29} +(-0.178284 - 0.413845i) q^{30} +(-6.65444 - 3.84194i) q^{31} +(1.42999 + 5.47313i) q^{32} +(-1.36474 + 10.1981i) q^{33} +(0.109644 + 6.76506i) q^{34} +(-0.0696549 - 0.395032i) q^{35} +(5.00981 + 3.30179i) q^{36} -1.63611 q^{37} +(6.14653 - 0.469211i) q^{38} +(-4.22158 + 3.85183i) q^{39} +(0.507423 - 0.115149i) q^{40} +(-1.14765 + 0.202362i) q^{41} +(3.66342 + 3.88668i) q^{42} +(1.51151 + 1.80135i) q^{43} +(-11.2900 - 3.69951i) q^{44} +(0.318476 - 0.450725i) q^{45} +(-8.17377 - 2.82587i) q^{46} +(6.83260 - 2.48686i) q^{47} +(-4.80474 + 4.99144i) q^{48} +(-1.12275 - 1.94467i) q^{49} +(1.33149 + 6.89584i) q^{50} +(-6.99829 + 4.43744i) q^{51} +(-3.48287 - 5.60482i) q^{52} +(-1.42960 + 1.70373i) q^{53} +(-0.248539 + 7.34427i) q^{54} +(-0.373759 + 1.02690i) q^{55} +(-5.18489 + 3.33959i) q^{56} +(4.41789 + 6.12227i) q^{57} +(1.14091 + 1.31578i) q^{58} +(5.82579 + 2.12042i) q^{59} +(0.444556 + 0.456592i) q^{60} +(9.65727 + 8.10341i) q^{61} +(10.7307 + 1.71331i) q^{62} +(-1.72000 + 6.31126i) q^{63} +(-4.65371 - 6.50715i) q^{64} +(-0.525649 + 0.303484i) q^{65} +(-3.34896 - 14.1602i) q^{66} +(3.18066 + 8.73880i) q^{67} +(-3.56228 - 8.88066i) q^{68} +(-2.27050 - 10.3460i) q^{69} +(0.291563 + 0.486616i) q^{70} +(-3.36704 + 2.82528i) q^{71} +(-8.28546 - 1.83061i) q^{72} +(1.20880 + 6.85547i) q^{73} +(2.16115 - 0.826497i) q^{74} +(-6.35418 + 5.79764i) q^{75} +(-7.88201 + 3.72478i) q^{76} -12.9528i q^{77} +(3.63054 - 7.22051i) q^{78} +(6.94773 - 1.22507i) q^{79} +(-0.612093 + 0.408433i) q^{80} +(-7.83235 + 4.43332i) q^{81} +(1.41372 - 0.847052i) q^{82} +(1.86888 - 3.23699i) q^{83} +(-6.80247 - 3.28334i) q^{84} +(-0.827043 + 0.301019i) q^{85} +(-2.90655 - 1.61587i) q^{86} +(-0.645725 + 2.03284i) q^{87} +(16.7820 - 0.816545i) q^{88} +(-1.23073 - 0.217011i) q^{89} +(-0.192990 + 0.756250i) q^{90} +(4.62440 - 5.51115i) q^{91} +(12.2244 - 0.396353i) q^{92} +(5.06684 + 12.3066i) 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} +(2.46543 + 2.00156i) q^{98} +(12.6550 - 12.5475i) 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 $

$2$	−1.32091	+	0.505162i	−0.934027	+	0.357203i
$2$	−1.32091	+	0.505162i	−0.934027	+	0.357203i
$3$	−1.37188	−	1.05734i	−0.792053	−	0.610453i
$3$	−1.37188	−	1.05734i	−0.792053	−	0.610453i
$4$	1.48962	−	1.33455i	0.744812	−	0.667275i
$5$	−0.118249	−	0.140923i	−0.0528825	−	0.0630229i	0.738955	−	0.673755i	$-0.235320\pi$
$5$	−0.118249	−	0.140923i	−0.0528825	−	0.0630229i	−0.791837	+	0.610732i	$0.790875\pi$
$6$	2.34625	+	0.703629i	0.957854	+	0.287256i
$7$	1.88835	+	1.09024i	0.713730	+	0.412072i	0.812440	−	0.583044i	$-0.198139\pi$
$7$	1.88835	+	1.09024i	0.713730	+	0.412072i	−0.0987109	+	0.995116i	$0.531472\pi$
$8$	−1.29350	+	2.51532i	−0.457322	+	0.889301i
$9$	0.764084	+	2.90106i	0.254695	+	0.967021i
$10$	0.227385	+	0.126413i	0.0719056	+	0.0399753i
$11$	−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	$-0.519877\pi$
$12$	−3.45464	+	0.255804i	−0.997270	+	0.0738441i
$13$	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	$-0.0957158\pi$
$14$	−3.04509	−	0.486190i	−0.813836	−	0.129940i
$15$	0.0132193	+	0.318358i	0.00341321	+	0.0821997i
$16$	0.437957	−	3.97595i	0.109489	−	0.993988i
$17$	1.63631	−	4.49572i	0.396863	−	1.09037i	−0.566941	−	0.823759i	$-0.691873\pi$
$17$	1.63631	−	4.49572i	0.396863	−	1.09037i	0.963804	−	0.266613i	$-0.0859047\pi$
$18$	−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
$21$	−1.43783	−	3.49229i	−0.313761	−	0.762081i
$22$	6.52213	+	5.29500i	1.39052	+	1.12890i
$23$	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	$0.502160\pi$
$24$	4.43406	−	2.08305i	0.905099	−	0.425200i
$25$	0.862364	−	4.89071i	0.172473	−	0.978142i
$26$	0.884614	+	4.58145i	0.173487	+	0.898495i
$27$	2.01917	−	4.78779i	0.388589	−	0.921411i
$28$	4.26791	−	0.896050i	0.806559	−	0.169338i
$29$	−0.421181	−	1.15719i	−0.0782113	−	0.214884i	0.894424	−	0.447219i	$-0.147586\pi$
$29$	−0.421181	−	1.15719i	−0.0782113	−	0.214884i	−0.972636	+	0.232335i	$0.925363\pi$
$30$	−0.178284	−	0.413845i	−0.0325500	−	0.0755575i
$31$	−6.65444	−	3.84194i	−1.19517	−	0.690034i	−0.235698	−	0.971826i	$-0.575738\pi$
$31$	−6.65444	−	3.84194i	−1.19517	−	0.690034i	−0.959475	+	0.281793i	$0.909071\pi$
$32$	1.42999	+	5.47313i	0.252790	+	0.967521i
$33$	−1.36474	+	10.1981i	−0.237571	+	1.77525i
$34$	0.109644	+	6.76506i	0.0188037	+	1.16020i
$35$	−0.0696549	−	0.395032i	−0.0117738	−	0.0667727i
$36$	5.00981	+	3.30179i	0.834969	+	0.550298i
$37$	−1.63611			−0.268974			−0.134487	−	0.990915i	$-0.542939\pi$
$37$	−1.63611			−0.268974			−0.134487	+	0.990915i	$0.542939\pi$
$38$	6.14653	−	0.469211i	0.997099	−	0.0761161i
$39$	−4.22158	+	3.85183i	−0.675993	+	0.616786i
$40$	0.507423	−	0.115149i	0.0802306	−	0.0182067i
$41$	−1.14765	+	0.202362i	−0.179233	+	0.0316036i	−0.262544	−	0.964920i	$-0.584562\pi$
$41$	−1.14765	+	0.202362i	−0.179233	+	0.0316036i	0.0833112	+	0.996524i	$0.473450\pi$
$42$	3.66342	+	3.88668i	0.565279	+	0.599727i
$43$	1.51151	+	1.80135i	0.230503	+	0.274703i	0.868882	−	0.495019i	$-0.164839\pi$
$43$	1.51151	+	1.80135i	0.230503	+	0.274703i	−0.638379	+	0.769723i	$0.720395\pi$
$44$	−11.2900	−	3.69951i	−1.70203	−	0.557722i
$45$	0.318476	−	0.450725i	0.0474756	−	0.0671901i
$46$	−8.17377	−	2.82587i	−1.20516	−	0.416651i
$47$	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	$0.210968\pi$
$48$	−4.80474	+	4.99144i	−0.693504	+	0.720453i
$49$	−1.12275	−	1.94467i	−0.160393	−	0.277810i
$50$	1.33149	+	6.89584i	0.188301	+	0.975219i
$51$	−6.99829	+	4.43744i	−0.979957	+	0.621366i
$52$	−3.48287	−	5.60482i	−0.482987	−	0.777249i
$53$	−1.42960	+	1.70373i	−0.196371	+	0.234026i	−0.855240	−	0.518231i	$-0.826591\pi$
$53$	−1.42960	+	1.70373i	−0.196371	+	0.234026i	0.658869	+	0.752257i	$0.271035\pi$
$54$	−0.248539	+	7.34427i	−0.0338218	+	0.999428i
$55$	−0.373759	+	1.02690i	−0.0503977	+	0.138467i
$56$	−5.18489	+	3.33959i	−0.692860	+	0.446271i
$57$	4.41789	+	6.12227i	0.585164	+	0.810915i
$58$	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	$0.478882\pi$
$60$	0.444556	+	0.456592i	0.0573919	+	0.0589457i
$61$	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	$0.423280\pi$
$62$	10.7307	+	1.71331i	1.36281	+	0.217590i
$63$	−1.72000	+	6.31126i	−0.216699	+	0.795144i
$64$	−4.65371	−	6.50715i	−0.581714	−	0.813393i
$65$	−0.525649	+	0.303484i	−0.0651987	+	0.0376425i
$66$	−3.34896	−	14.1602i	−0.412228	−	1.74300i
$67$	3.18066	+	8.73880i	0.388580	+	1.06761i	0.967641	+	0.252330i	$0.0811969\pi$
$67$	3.18066	+	8.73880i	0.388580	+	1.06761i	−0.579061	+	0.815284i	$0.696581\pi$
$68$	−3.56228	−	8.88066i	−0.431989	−	1.07694i
$69$	−2.27050	−	10.3460i	−0.273336	−	1.24551i
$70$	0.291563	+	0.486616i	0.0348485	+	0.0581618i
$71$	−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	$0.361770\pi$
$72$	−8.28546	−	1.83061i	−0.976451	−	0.215739i
$73$	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	$0.810889\pi$
$74$	2.16115	−	0.826497i	0.251229	−	0.0960784i
$75$	−6.35418	+	5.79764i	−0.733717	+	0.669454i
$76$	−7.88201	+	3.72478i	−0.904128	+	0.427261i
$77$		−	12.9528i		−	1.47611i
$78$	3.63054	−	7.22051i	0.411078	−	0.817561i
$79$	6.94773	−	1.22507i	0.781681	−	0.137831i	0.231453	−	0.972846i	$-0.425652\pi$
$79$	6.94773	−	1.22507i	0.781681	−	0.137831i	0.550228	+	0.835015i	$0.314541\pi$
$80$	−0.612093	+	0.408433i	−0.0684340	+	0.0456642i
$81$	−7.83235	+	4.43332i	−0.870261	+	0.492591i
$82$	1.41372	−	0.847052i	0.156120	−	0.0935412i
$83$	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	$0.100903\pi$
$84$	−6.80247	−	3.28334i	−0.742210	−	0.358242i
$85$	−0.827043	+	0.301019i	−0.0897055	+	0.0326501i
$86$	−2.90655	−	1.61587i	−0.313421	−	0.174244i
$87$	−0.645725	+	2.03284i	−0.0692290	+	0.217944i
$88$	16.7820	−	0.816545i	1.78896	−	0.0870440i
$89$	−1.23073	−	0.217011i	−0.130457	−	0.0230031i	0.108038	−	0.994147i	$-0.465543\pi$
$89$	−1.23073	−	0.217011i	−0.130457	−	0.0230031i	−0.238495	+	0.971144i	$0.576654\pi$
$90$	−0.192990	+	0.756250i	−0.0203429	+	0.0797157i
$91$	4.62440	−	5.51115i	0.484769	−	0.577725i
$92$	12.2244	−	0.396353i	1.27448	−	0.0413226i
$93$	5.06684	+	12.3066i	0.525407	+	1.27614i
$94$	−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	$0.805488\pi$
$98$	2.46543	+	2.00156i	0.249046	+	0.202189i
$99$	12.6550	−	12.5475i	1.27188	−	1.26107i
$100$	−5.24230	−	8.43619i	−0.524230	−	0.843619i
$101$	−5.26789	−	0.928871i	−0.524175	−	0.0924261i	−0.0947014	−	0.995506i	$-0.530190\pi$
$101$	−5.26789	−	0.928871i	−0.524175	−	0.0924261i	−0.429473	+	0.903080i	$0.641301\pi$
$102$	7.00251	−	9.39674i	0.693352	−	0.930416i
$103$	4.25613	−	2.45728i	0.419369	−	0.242123i	−0.275438	−	0.961319i	$-0.588823\pi$
$103$	4.25613	−	2.45728i	0.419369	−	0.242123i	0.694807	+	0.719196i	$0.255490\pi$
$104$	7.43191	+	5.64407i	0.728758	+	0.553447i
$105$	−0.322124	+	0.615584i	−0.0314361	+	0.0600748i
$106$	1.02772	−	2.97267i	0.0998210	−	0.288731i
$107$	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	$0.155188\pi$
$108$	−3.38174	−	9.82669i	−0.325408	−	0.945574i
$109$	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	$0.0523025\pi$
$110$	−0.0250444	−	1.54525i	−0.00238789	−	0.147334i
$111$	2.24453	+	1.72991i	0.213042	+	0.164196i
$112$	5.16176	−	7.03051i	0.487740	−	0.664321i
$113$			10.0558i			0.945971i	0.881070	+	0.472986i	$0.156824\pi$
$113$			10.0558i			0.945971i	−0.881070	+	0.472986i	$0.843176\pi$
$114$	−8.92839	−	5.85524i	−0.836220	−	0.548394i
$115$		−	1.12500i		−	0.104907i
$116$	−2.17172	−	1.16168i	−0.201639	−	0.107860i
$117$	9.86415	−	0.820601i	0.911941	−	0.0758646i
$118$	−8.76652	+	0.142082i	−0.807024	+	0.0130797i
$119$	7.99134	−	6.70553i	0.732565	−	0.614695i
$120$	−0.817873	−	0.378545i	−0.0746612	−	0.0345563i
$121$	−12.1438	+	21.0337i	−1.10398	+	1.91215i
$122$	−16.8499	−	5.82542i	−1.52552	−	0.527409i
$123$	1.78840	+	0.935837i	0.161255	+	0.0843816i
$124$	−15.0399	+	3.15763i	−1.35062	+	0.283564i
$125$	−1.58777	+	0.916699i	−0.142014	+	0.0819921i
$126$	−0.916241	−	9.20551i	−0.0816252	−	0.820092i
$127$	5.47645	+	0.965646i	0.485956	+	0.0856872i	0.411258	−	0.911519i	$-0.365090\pi$
$127$	5.47645	+	0.965646i	0.485956	+	0.0856872i	0.0746983	+	0.997206i	$0.476201\pi$
$128$	9.43431	+	6.24450i	0.833883	+	0.551941i
$129$	−0.168975	−	4.06940i	−0.0148775	−	0.358291i
$130$	0.541028	−	0.666413i	0.0474513	−	0.0584483i
$131$	−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
$135$	−0.913476	+	0.281602i	−0.0786195	+	0.0242365i
$136$	9.19163	+	9.93106i	0.788175	+	0.851582i
$137$	7.77091	−	9.26102i	0.663914	−	0.791222i	−0.324028	−	0.946048i	$-0.605037\pi$
$137$	7.77091	−	9.26102i	0.663914	−	0.791222i	0.987942	+	0.154826i	$0.0494816\pi$
$138$	8.22551	+	12.5192i	0.700202	+	1.06570i
$139$	6.01736	+	1.06102i	0.510386	+	0.0899948i	0.422910	−	0.906172i	$-0.361009\pi$
$139$	6.01736	+	1.06102i	0.510386	+	0.0899948i	0.0874760	+	0.996167i	$0.472120\pi$
$140$	−0.630950	−	0.495492i	−0.0533250	−	0.0418767i
$141$	−12.0029	−	3.81268i	−1.01083	−	0.321086i
$142$	3.02035	−	5.43286i	0.253462	−	0.455915i
$143$	−18.4176	+	6.70346i	−1.54016	+	0.560571i
$144$	11.8691	−	1.76742i	0.989094	−	0.147285i
$145$	−0.113270	+	0.196190i	−0.00940659	+	0.0162927i
$146$	−5.05985	−	8.44484i	−0.418756	−	0.698900i
$147$	−0.515886	+	3.85497i	−0.0425496	+	0.317952i
$148$	−2.43718	+	2.18346i	−0.200335	+	0.179480i
$149$	−21.8002	+	3.84397i	−1.78595	+	0.314910i	−0.966195	−	0.257811i	$-0.916999\pi$
$149$	−21.8002	+	3.84397i	−1.78595	+	0.314910i	−0.819750	+	0.572721i	$0.805888\pi$
$150$	5.46457	−	10.8681i	0.446181	−	0.887374i
$151$		−	15.8614i		−	1.29078i	−0.763853	−	0.645391i	$-0.776695\pi$
$151$		−	15.8614i		−	1.29078i	0.763853	−	0.645391i	$-0.223305\pi$
$152$	8.52983	−	8.90180i	0.691861	−	0.722031i
$153$	14.2926	+	1.31193i	1.15549	+	0.106063i
$154$	6.54325	+	17.1095i	0.527270	+	1.37872i
$155$	0.245460	+	1.39207i	0.0197158	+	0.111814i
$156$	−1.14811	+	11.3717i	−0.0919226	+	0.910462i
$157$	−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	$0.441042\pi$
$158$	−8.55849	+	5.12794i	−0.680877	+	0.407957i
$159$	3.76266	−	0.825742i	0.298398	−	0.0654856i
$160$	0.602197	−	0.848710i	0.0476078	−	0.0670964i
$161$	4.56066	+	12.5303i	0.359431	+	0.987528i
$162$	8.10631	−	9.81263i	0.636892	−	0.770953i
$163$	−16.3699	+	9.45115i	−1.28219	+	0.740271i	−0.977248	−	0.212101i	$-0.931969\pi$
$163$	−16.3699	+	9.45115i	−1.28219	+	0.740271i	−0.304939	+	0.952372i	$0.598636\pi$
$164$	−1.43951	+	1.83304i	−0.112407	+	0.143136i
$165$	1.59852	−	1.01358i	0.124445	−	0.0789074i
$166$	−0.833423	+	5.21988i	−0.0646862	+	0.405141i
$167$	−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	$0.764624\pi$
$168$	10.6441	+	0.900667i	0.821209	+	0.0694880i
$169$	1.98642	+	0.722999i	0.152802	+	0.0556153i
$170$	0.940389	−	0.815411i	0.0721246	−	0.0625392i
$171$	0.412500	−	13.0702i	0.0315447	−	0.999502i
$172$	4.65557	+	0.666146i	0.354984	+	0.0507932i
$173$	8.31071	−	22.8335i	0.631852	−	1.73600i	−0.0440736	−	0.999028i	$-0.514034\pi$
$173$	8.31071	−	22.8335i	0.631852	−	1.73600i	0.675925	−	0.736970i	$-0.263744\pi$
$174$	−0.173968	−	3.01140i	−0.0131885	−	0.228294i
$175$	6.96049	−	8.29519i	0.526164	−	0.627058i
$176$	−21.7550	+	9.55619i	−1.63985	+	0.720325i
$177$	−5.75027	−	9.06876i	−0.432217	−	0.681650i
$178$	1.73531	−	0.335065i	0.130067	−	0.0251142i
$179$	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	$0.545867\pi$
$180$	−0.127105	−	1.09643i	−0.00947386	−	0.0817232i
$181$	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	$0.344557\pi$
$182$	−3.32441	+	9.61582i	−0.246422	+	0.712772i
$183$	−4.68055	−	21.3278i	−0.345996	−	1.57660i
$184$	−15.9471	+	6.69883i	−1.17564	+	0.493844i
$185$	0.193467	+	0.230566i	0.0142240	+	0.0169515i
$186$	−12.9097	−	13.6964i	−0.946586	−	1.00427i
$187$	−27.9883	+	4.93509i	−2.04670	+	0.360889i
$188$	6.85916	−	12.8229i	0.500256	−	0.935208i
$189$	9.03274	−	6.83965i	0.657035	−	0.497512i
$190$	−0.792943	−	0.810706i	−0.0575261	−	0.0588148i
$191$	−4.28574			−0.310105			−0.155053	−	0.987906i	$-0.549555\pi$
$191$	−4.28574			−0.310105			−0.155053	+	0.987906i	$0.549555\pi$
$192$	−0.495923	+	13.8475i	−0.0357902	+	0.999359i
$193$	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	$0.735454\pi$
$194$	15.9711	−	0.258848i	1.14666	−	0.0185842i
$195$	1.04201	+	0.139446i	0.0746198	+	0.00998590i
$196$	−4.26774	−	1.39845i	−0.304838	−	0.0998894i
$197$	10.7330	+	6.19668i	0.764692	+	0.441495i	0.830978	−	0.556305i	$-0.187782\pi$
$197$	10.7330	+	6.19668i	0.764692	+	0.441495i	−0.0662856	+	0.997801i	$0.521115\pi$
$198$	−10.3777	+	22.9670i	−0.737510	+	1.63219i
$199$	5.42899	+	14.9160i	0.384851	+	1.05737i	0.969288	+	0.245930i	$0.0790932\pi$
$199$	5.42899	+	14.9160i	0.384851	+	1.05737i	−0.584437	+	0.811439i	$0.698685\pi$
$200$	11.1863	+	8.49526i	0.790988	+	0.600706i
$201$	4.87637	−	15.3516i	0.343952	−	1.08282i
$202$	7.42766	−	1.43418i	0.522608	−	0.100908i
$203$	0.466272	−	2.64436i	0.0327259	−	0.185598i
$204$	−4.50284	+	15.9497i	−0.315262	+	1.11670i
$205$	0.164226	+	0.137802i	0.0114700	+	0.00962450i
$206$	−4.38065	+	5.39588i	−0.305215	+	0.375949i
$207$	−7.82431	+	16.5940i	−0.543827	+	1.15337i
$208$	−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	−0.993913	−	0.110171i	$-0.964860\pi$
$211$	−2.34904	+	6.45394i	−0.161715	+	0.444307i	0.832198	+	0.554479i	$0.187082\pi$
$212$	0.144147	+	4.44580i	0.00990006	+	0.305339i
$213$	7.60644	−	0.315845i	0.521184	−	0.0216414i
$214$	−0.166307	+	1.04161i	−0.0113685	+	0.0712029i
$215$	0.0751179	−	0.426015i	0.00512300	−	0.0290540i
$216$	9.43105	+	11.2719i	0.641702	+	0.766954i
$217$	−8.37728	−	14.5099i	−0.568687	−	0.984995i
$218$	−9.33486	+	16.7911i	−0.632237	+	1.13724i
$219$	5.59020	−	10.6830i	0.377751	−	0.721888i
$220$	0.813681	+	2.02849i	0.0548584	+	0.136761i
$221$	−13.6704	−	7.89259i	−0.919568	−	0.530913i
$222$	−3.83872	−	1.15121i	−0.257638	−	0.0772643i
$223$	7.52455	+	8.96741i	0.503881	+	0.600502i	0.956691	−	0.291105i	$-0.0940229\pi$
$223$	7.52455	+	8.96741i	0.503881	+	0.600502i	−0.452810	+	0.891607i	$0.649578\pi$
$224$	−3.26669	+	11.8942i	−0.218265	+	0.794716i
$225$	14.8472	−	1.23514i	0.989812	−	0.0823428i
$226$	−5.07981	−	13.2829i	−0.337904	−	0.883562i
$227$	0.969889			0.0643738			0.0321869	−	0.999482i	$-0.489753\pi$
$227$	0.969889			0.0643738			0.0321869	+	0.999482i	$0.489753\pi$
$228$	14.7515	+	3.22399i	0.976940	+	0.213514i
$229$	6.77782			0.447891			0.223946	−	0.974602i	$-0.428106\pi$
$229$	6.77782			0.447891			0.223946	+	0.974602i	$0.428106\pi$
$230$	0.568308	+	1.48603i	0.0374731	+	0.0979860i
$231$	−13.6954	+	17.7696i	−0.901094	+	1.16915i
$232$	3.45549	+	0.437413i	0.226864	+	0.0287176i
$233$	4.63498	+	5.52376i	0.303648	+	0.361874i	0.896193	−	0.443663i	$-0.146321\pi$
$233$	4.63498	+	5.52376i	0.303648	+	0.361874i	−0.592546	+	0.805537i	$0.701877\pi$
$234$	−12.6151	+	6.06693i	−0.824678	+	0.396608i
$235$	−1.15840	−	0.668805i	−0.0755659	−	0.0436280i
$236$	11.5080	−	4.61619i	0.749109	−	0.300488i
$237$	−10.8267	−	5.66544i	−0.703272	−	0.368010i
$238$	−7.16849	+	12.8943i	−0.464664	+	0.835816i
$239$	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	$0.774950\pi$
$240$	1.27157	+	0.0868678i	0.0820792	+	0.00560729i
$241$	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	$-0.0964665\pi$
$242$	5.41551	−	33.9183i	0.348122	−	2.18035i
$243$	15.4325	+	2.19946i	0.989996	+	0.141096i
$244$	25.2001	−	0.817068i	1.61327	−	0.0523074i
$245$	−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
$249$	−5.98646	+	2.46472i	−0.379376	+	0.156195i
$250$	1.63422	−	2.01296i	0.103357	−	0.127311i
$251$	−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	$0.839424\pi$
$252$	5.86054	+	11.6968i	0.369179	+	0.736831i
$253$	6.30821	−	35.7756i	0.396593	−	2.24919i
$254$	−7.72172	+	1.49096i	−0.484504	+	0.0935510i
$255$	1.45288	+	0.461501i	0.0909828	+	0.0289003i
$256$	−15.6164	−	3.48259i	−0.976024	−	0.217662i
$257$	5.79901	+	15.9327i	0.361732	+	0.993852i	0.978417	+	0.206641i	$0.0662533\pi$
$257$	5.79901	+	15.9327i	0.361732	+	0.993852i	−0.616684	+	0.787211i	$0.711524\pi$
$258$	2.27891	+	5.28997i	0.141879	+	0.329339i
$259$	−3.08954	−	1.78375i	−0.191975	−	0.110837i
$260$	−0.378005	+	1.15358i	−0.0234429	+	0.0715420i
$261$	3.03525	−	2.10606i	0.187877	−	0.130362i
$262$	3.86095	−	0.0625758i	0.238530	−	0.00386594i
$263$	−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	$-0.266034\pi$
$264$	−23.8861	−	16.6240i	−1.47009	−	1.02313i
$265$	0.409145			0.0251336
$266$	12.1184	+	5.81516i	0.743024	+	0.356550i
$267$	1.45896	+	1.59901i	0.0892866	+	0.0978576i
$268$	16.4003	+	8.77277i	1.00181	+	0.535882i
$269$	13.4723	−	2.37553i	0.821421	−	0.144839i	0.252884	−	0.967496i	$-0.418621\pi$
$269$	13.4723	−	2.37553i	0.821421	−	0.144839i	0.568537	+	0.822658i	$0.307510\pi$
$270$	1.06437	−	0.833425i	0.0647754	−	0.0507207i
$271$	−17.9629	−	21.4073i	−1.09117	−	1.30040i	−0.950629	−	0.310329i	$-0.899561\pi$
$271$	−17.9629	−	21.4073i	−1.09117	−	1.30040i	−0.140539	−	0.990075i	$-0.544884\pi$
$272$	−17.1581	−	8.47481i	−1.04036	−	0.513861i
$273$	−12.1712	+	2.67106i	−0.736637	+	0.161660i
$274$	−5.58640	+	16.1586i	−0.337486	+	0.976175i
$275$	−27.7216	+	10.0898i	−1.67167	+	0.608439i
$276$	−17.1894	−	12.3815i	−1.03468	−	0.745279i
$277$	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	$0.670249\pi$
$278$	−8.48440	+	1.63822i	−0.508860	+	0.0982539i
$279$	6.06117	−	22.2405i	0.362873	−	1.33151i
$280$	1.08373	+	0.335770i	0.0647654	+	0.0200661i
$281$	13.0581	−	15.5621i	0.778984	−	0.928356i	−0.219904	−	0.975522i	$-0.570574\pi$
$281$	13.0581	−	15.5621i	0.778984	−	0.928356i	0.998887	+	0.0471652i	$0.0150187\pi$
$282$	17.7808	−	1.02719i	1.05883	−	0.0611684i
$283$	4.26612	−	11.7211i	0.253595	−	0.696746i	−0.745933	−	0.666021i	$-0.767996\pi$
$283$	4.26612	−	11.7211i	0.253595	−	0.696746i	0.999528	−	0.0307250i	$-0.00978162\pi$
$284$	−1.24515	+	8.70209i	−0.0738858	+	0.516374i
$285$	0.340362	−	1.34654i	0.0201613	−	0.0797619i
$286$	20.9417	−	18.1585i	1.23831	−	1.07374i
$287$	−2.38779	−	0.869085i	−0.140947	−	0.0513005i
$288$	−14.7853	+	8.33044i	−0.871230	+	0.490876i
$289$	−4.51123	−	3.78537i	−0.265367	−	0.222669i
$290$	0.0505127	−	0.316370i	0.00296621	−	0.0185779i
$291$	10.4760	+	16.5217i	0.614113	+	0.968519i
$292$	10.9496	+	8.59886i	0.640778	+	0.503210i
$293$	15.3839	−	8.88190i	0.898737	−	0.518886i	0.0219470	−	0.999759i	$-0.493013\pi$
$293$	15.3839	−	8.88190i	0.898737	−	0.518886i	0.876790	+	0.480873i	$0.159680\pi$
$294$	−1.26594	−	5.35269i	−0.0738312	−	0.312175i
$295$	−0.390077	−	1.07173i	−0.0227111	−	0.0623984i
$296$	2.11630	−	4.11533i	0.123008	−	0.239199i
$297$	−30.6280	+	3.83297i	−1.77722	+	0.222412i
$298$	26.8544	−	16.0902i	1.55563	−	0.932080i
$299$	15.4566	−	12.9696i	0.893879	−	0.750054i
$300$	−1.72810	+	17.1163i	−0.0997719	+	0.988208i
$301$	0.890361	+	5.04949i	0.0513196	+	0.291048i
$302$	8.01256	+	20.9515i	0.461071	+	1.20562i
$303$	6.24476	+	6.84422i	0.358752	+	0.393190i
$304$	−6.77032	+	16.0674i	−0.388305	+	0.921531i
$305$		−	2.31915i		−	0.132794i
$306$	−19.5421	+	5.48716i	−1.11715	+	0.313680i
$307$	20.2500	−	3.57062i	1.15573	−	0.203786i	0.437252	−	0.899339i	$-0.355952\pi$
$307$	20.2500	−	3.57062i	1.15573	−	0.203786i	0.718475	+	0.695553i	$0.244841\pi$
$308$	−17.2861	−	19.2948i	−0.984969	−	1.09942i
$309$	−8.43704	−	1.12908i	−0.479967	−	0.0642309i
$310$	−1.02745	−	1.71481i	−0.0583554	−	0.0973946i
$311$	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	$-0.00767019\pi$
$312$	−4.22797	−	15.6010i	−0.239362	−	0.883231i
$313$	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	$0.290591\pi$
$314$	8.45029	−	15.2000i	0.476877	−	0.857784i
$315$	1.09279	−	0.503911i	0.0615719	−	0.0283922i
$316$	8.71459	−	11.0970i	0.490234	−	0.624254i
$317$	−20.3941	−	3.59602i	−1.14544	−	0.201973i	−0.431458	−	0.902133i	$-0.642001\pi$
$317$	−20.3941	−	3.59602i	−1.14544	−	0.201973i	−0.713986	+	0.700160i	$0.753112\pi$
$318$	−4.55301	+	2.99148i	−0.255320	+	0.167754i
$319$	−4.70214	+	5.60379i	−0.263269	+	0.313752i
$320$	−0.366714	+	1.42528i	−0.0204999	+	0.0796755i
$321$	−1.19458	+	0.491827i	−0.0666749	+	0.0274511i
$322$	−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
$326$	16.8488	−	20.7536i	0.933170	−	1.14943i
$327$	−23.5089	+	0.976170i	−1.30005	+	0.0539823i
$328$	0.975482	−	3.14847i	0.0538620	−	0.173845i
$329$	15.6136	+	2.75310i	0.860807	+	0.151784i
$330$	−1.59949	+	2.14637i	−0.0880489	+	0.118154i
$331$	2.30427	−	1.33037i	0.126654	−	0.0731239i	−0.435334	−	0.900269i	$-0.643370\pi$
$331$	2.30427	−	1.33037i	0.126654	−	0.0731239i	0.561989	+	0.827145i	$0.310036\pi$
$332$	−1.53600	−	7.31602i	−0.0842990	−	0.401519i
$333$	−1.25012	−	4.74645i	−0.0685063	−	0.260104i
$334$	4.58814	+	1.58623i	0.251052	+	0.0867945i
$335$	0.855392	−	1.48158i	0.0467350	−	0.0809475i
$336$	−14.5149	+	4.18728i	−0.791853	+	0.228435i
$337$	−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	$0.493969\pi$
$338$	−2.98912	+	0.0484458i	−0.162587	+	0.00263510i
$339$	10.6324	−	13.7953i	0.577471	−	0.749259i
$340$	−0.830259	+	1.55214i	−0.0450271	+	0.0841764i
$341$			45.6449i			2.47181i
$342$	6.05768	+	17.4730i	0.327562	+	0.944830i
$343$		−	20.1596i		−	1.08852i
$344$	−6.48612	+	1.47190i	−0.349708	+	0.0793593i
$345$	−1.18950	+	1.54336i	−0.0640408	+	0.0830919i
$346$	0.556873	+	34.3593i	0.0299377	+	1.84717i
$347$	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	$0.269543\pi$
$348$	1.75104	+	3.88992i	0.0938657	+	0.208522i
$349$	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	$0.0726985\pi$
$350$	−5.00380	+	14.4734i	−0.267464	+	0.773636i
$351$	−14.4000	−	9.30395i	−0.768617	−	0.496608i
$352$	23.9091	−	23.6127i	1.27436	−	1.25856i
$353$	−31.8933	+	18.4136i	−1.69751	+	0.980058i	−0.749398	+	0.662120i	$0.769657\pi$
$353$	−31.8933	+	18.4136i	−1.69751	+	0.980058i	−0.948112	+	0.317938i	$0.897010\pi$
$354$	12.1768	+	9.07423i	0.647190	+	0.482290i
$355$	0.796297	+	0.140409i	0.0422631	+	0.00745212i
$356$	−2.12294	+	1.31921i	−0.112515	+	0.0699178i
$357$	−18.0531	+	0.749627i	−0.955472	+	0.0396745i
$358$	−23.0698	−	18.7292i	−1.21928	−	0.989871i
$359$	−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
$363$	38.8995	−	16.0155i	2.04169	−	0.840597i
$364$	−0.466279	−	14.3810i	−0.0244397	−	0.753771i
$365$	0.823156	−	0.981000i	0.0430860	−	0.0513479i
$366$	16.9566	+	25.8078i	0.886336	+	1.34900i
$367$	12.8825	+	2.27154i	0.672462	+	0.118573i	0.499445	−	0.866346i	$-0.333537\pi$
$367$	12.8825	+	2.27154i	0.672462	+	0.118573i	0.173017	+	0.984919i	$0.444648\pi$
$368$	17.6807	−	16.9044i	0.921673	−	0.881204i
$369$	−1.46397	−	3.17479i	−0.0762111	−	0.165273i
$370$	−0.372027	−	0.206825i	−0.0193407	−	0.0107523i
$371$	−4.55707	+	1.65864i	−0.236591	+	0.0861122i
$372$	23.9715	+	11.5703i	1.24287	+	0.599893i
$373$	−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	$0.225770\pi$
$374$	34.4771	−	20.6574i	1.78277	−	1.06817i
$375$	3.14748	+	0.421208i	0.162535	+	0.0217511i
$376$	−2.58271	+	20.4030i	−0.133193	+	1.05220i
$377$	−4.00133	+	0.705543i	−0.206079	+	0.0363373i
$378$	−8.47634	+	13.5976i	−0.435976	+	0.699384i
$379$			13.0725i			0.671488i	0.941953	+	0.335744i	$0.108988\pi$
$379$			13.0725i			0.671488i	−0.941953	+	0.335744i	$0.891012\pi$
$380$	1.45695	+	0.670309i	0.0747398	+	0.0343861i
$381$	−6.49200	−	7.11519i	−0.332595	−	0.364522i
$382$	5.66109	−	2.16499i	0.289646	−	0.110771i
$383$	−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	$0.956726\pi$
$384$	−6.34017	−	18.5419i	−0.323545	−	0.946213i
$385$	−1.82535	+	1.53165i	−0.0930285	+	0.0780602i
$386$	−12.3274	−	20.5744i	−0.627450	−	1.04721i
$387$	−4.07091	+	5.76138i	−0.206936	+	0.292867i
$388$	−20.9656	+	8.40988i	−1.06437	+	0.426947i
$389$	5.98431	+	16.4417i	0.303416	+	0.833630i	0.993900	+	0.110282i	$0.0351754\pi$
$389$	5.98431	+	16.4417i	0.303416	+	0.833630i	−0.690484	+	0.723348i	$0.742602\pi$
$390$	−1.44685	+	0.342187i	−0.0732639	+	0.0173273i
$391$	25.3378	−	14.6288i	1.28139	−	0.739809i
$392$	6.34375	−	0.308662i	0.320408	−	0.0155898i
$393$	2.53254	+	3.99407i	0.127750	+	0.201474i
$394$	−17.3076	−	2.76340i	−0.871947	−	0.139218i
$395$	−0.994203	−	0.834235i	−0.0500238	−	0.0419749i
$396$	2.10600	−	35.5798i	0.105830	−	1.78795i
$397$	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
$399$	1.66778	+	16.3776i	0.0834935	+	0.819904i
$400$	−19.0676	−	5.57064i	−0.953378	−	0.278532i
$401$	6.78965	−	18.6544i	0.339059	−	0.931557i	−0.646603	−	0.762827i	$-0.723811\pi$
$401$	6.78965	−	18.6544i	0.339059	−	0.931557i	0.985662	−	0.168731i	$-0.0539668\pi$
$402$	1.31376	+	22.7414i	0.0655246	+	1.13424i
$403$	−16.2961	+	19.4210i	−0.811768	+	0.967428i
$404$	−9.08680	+	5.64659i	−0.452085	+	0.280928i
$405$	1.55092	+	0.579527i	0.0770660	+	0.0287969i
$406$	0.719924	+	3.72851i	0.0357292	+	0.185043i
$407$	4.85951	+	8.41692i	0.240877	+	0.417211i
$408$	−2.10930	−	23.3428i	−0.104426	−	1.15564i
$409$	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	$0.306646\pi$
$410$	−0.286540	−	0.0990637i	−0.0141512	−	0.00489241i
$411$	−20.4527	+	4.48850i	−1.00886	+	0.221401i
$412$	3.06067	−	9.34043i	0.150789	−	0.460170i
$413$	8.68938	+	10.3556i	0.427576	+	0.509566i
$414$	1.95256	−	25.8718i	0.0959633	−	1.27153i
$415$	−0.677161	+	0.119402i	−0.0332405	+	0.00586120i
$416$	18.6030	−	1.51070i	0.912089	−	0.0740683i
$417$	−7.13321	−	7.81796i	−0.349315	−	0.382847i
$418$	−20.6701	−	30.2271i	−1.01101	−	1.47846i
$419$	24.2731			1.18582			0.592910	−	0.805269i	$-0.297979\pi$
$419$	24.2731			1.18582			0.592910	+	0.805269i	$0.297979\pi$
$420$	0.341683	+	1.34688i	0.0166724	+	0.0657209i
$421$	−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	$-0.189058\pi$
$422$	−0.157401	−	9.71174i	−0.00766218	−	0.472760i
$423$	12.4352	+	17.9216i	0.604622	+	0.871380i
$424$	−2.43625	−	5.79970i	−0.118315	−	0.281658i
$425$	−20.5762	−	11.8797i	−0.998091	−	0.576248i
$426$	−9.88789	+	4.25968i	−0.479070	+	0.206382i
$427$	9.40165	+	25.8308i	0.454978	+	1.25004i
$428$	−0.306504	−	1.45989i	−0.0148154	−	0.0705663i
$429$	32.3545	+	10.2773i	1.56209	+	0.496191i
$430$	0.115982	+	0.600675i	0.00559315	+	0.0289671i
$431$	−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	$0.731075\pi$
$432$	−18.1517	−	10.1250i	−0.873325	−	0.487138i
$433$	−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	$0.775660\pi$
$434$	18.3955	+	14.9344i	0.883012	+	0.716875i
$435$	0.362831	−	0.149383i	0.0173964	−	0.00716239i
$436$	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	$-0.586481\pi$
$439$	11.6584	−	32.0313i	0.556426	−	1.52877i	0.824783	−	0.565449i	$-0.191297\pi$
$440$	−2.09952	−	2.26842i	−0.100091	−	0.108142i
$441$	4.78373	−	4.74307i	0.227796	−	0.225861i
$442$	22.0444	+	3.51968i	1.04854	+	0.167414i
$443$	−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	$0.968129\pi$
$444$	5.65216	−	0.418522i	0.268240	−	0.0198622i
$445$	0.114950	+	0.199100i	0.00544917	+	0.00943824i
$446$	−14.4693	−	8.04406i	−0.685140	−	0.380897i
$447$	33.9716	+	17.7767i	1.60680	+	0.840810i
$448$	−1.69349	−	17.3614i	−0.0800098	−	0.820251i
$449$	5.88893	+	3.39998i	0.277916	+	0.160455i	0.632480	−	0.774577i	$-0.282037\pi$
$449$	5.88893	+	3.39998i	0.277916	+	0.160455i	−0.354564	+	0.935032i	$0.615371\pi$
$450$	−18.9879	+	9.13174i	−0.895098	+	0.430474i
$451$	4.44977	+	5.30303i	0.209531	+	0.249710i
$452$	13.4200	+	14.9794i	0.631223	+	0.704571i
$453$	−16.7708	+	21.7598i	−0.787961	+	1.02237i
$454$	−1.28114	+	0.489951i	−0.0601268	+	0.0229945i
$455$	−1.32348			−0.0620457
$456$	−21.1140	+	3.19326i	−0.988756	+	0.149538i
$457$	9.31891			0.435920			0.217960	−	0.975958i	$-0.430060\pi$
$457$	9.31891			0.435920			0.217960	+	0.975958i	$0.430060\pi$
$458$	−8.95292	+	3.42390i	−0.418342	+	0.159988i
$459$	−18.2206	−	16.9119i	−0.850464	−	0.789381i
$460$	−1.50137	−	1.67583i	−0.0700018	−	0.0781360i
$461$	−9.09236	−	10.8358i	−0.423473	−	0.504676i	0.511554	−	0.859251i	$-0.329070\pi$
$461$	−9.09236	−	10.8358i	−0.423473	−	0.504676i	−0.935028	+	0.354575i	$0.884625\pi$
$462$	9.11396	−	30.3905i	0.424020	−	1.41390i
$463$	−21.3119	−	12.3044i	−0.990449	−	0.571836i	−0.0850405	−	0.996377i	$-0.527102\pi$
$463$	−21.3119	−	12.3044i	−0.990449	−	0.571836i	−0.905408	+	0.424541i	$0.860435\pi$
$464$	−4.78537	+	1.16780i	−0.222155	+	0.0542136i
$465$	1.13515	−	2.16928i	0.0526412	−	0.100598i
$466$	−8.91280	−	4.95499i	−0.412878	−	0.229536i
$467$	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	$0.809263\pi$
$468$	13.5987	−	14.3866i	0.628602	−	0.665020i
$469$	−3.52118	+	19.9696i	−0.162593	+	0.922110i
$470$	1.86801	+	0.298252i	0.0861647	+	0.0137573i
$471$	21.2812	−	0.883668i	0.980585	−	0.0407173i
$472$	−12.8692	+	11.9110i	−0.592353	+	0.548248i
$473$	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
$477$	−6.03498	−	2.84557i	−0.276323	−	0.130290i
$478$	−6.19165	−	5.02670i	−0.283200	−	0.229916i
$479$	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	$0.372517\pi$
$480$	−1.72351	+	0.527601i	−0.0786671	+	0.0240816i
$481$	−0.937384	+	5.31617i	−0.0427410	+	0.242396i
$482$	3.82627	+	19.8164i	0.174282	+	0.902611i
$483$	6.99209	−	22.0122i	0.318151	−	1.00159i
$484$	9.98079	+	47.5388i	0.453672	+	2.16085i
$485$	0.710651	+	1.95250i	0.0322690	+	0.0886584i
$486$	−21.4961	+	4.89061i	−0.975082	+	0.221843i
$487$	25.5603	+	14.7572i	1.15825	+	0.668714i	0.950883	−	0.309549i	$-0.100178\pi$
$487$	25.5603	+	14.7572i	1.15825	+	0.668714i	0.207364	+	0.978264i	$0.433512\pi$
$488$	−32.8744	+	13.8094i	−1.48815	+	0.625122i
$489$	32.4504	+	4.34264i	1.46746	+	0.196381i
$490$	−0.00946702	−	0.584120i	−0.000427677	−	0.0263878i
$491$	−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	$0.958944\pi$
$492$	3.91296	−	0.992662i	0.176410	−	0.0447526i
$493$	−5.89156			−0.265343
$494$	1.99697	−	20.2406i	0.0898480	−	0.910670i
$495$	−3.26467	−	0.299665i	−0.146736	−	0.0134689i
$496$	−18.1897	+	24.7751i	−0.816744	+	1.11244i
$497$	−9.43839	+	1.66424i	−0.423370	+	0.0746515i
$498$	6.66251	−	6.27981i	0.298554	−	0.281405i
$499$	−20.1226	−	23.9812i	−0.900810	−	1.07354i	−0.996940	−	0.0781751i	$-0.975091\pi$
$499$	−20.1226	−	23.9812i	−0.900810	−	1.07354i	0.0961293	−	0.995369i	$-0.469354\pi$
$500$	−1.14180	+	3.48449i	−0.0510628	+	0.155831i
$501$	1.27448	+	5.80744i	0.0569398	+	0.259457i
$502$	15.2437	+	5.27012i	0.680362	+	0.235217i
$503$	−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	$0.391947\pi$
$504$	−13.6501	−	12.4900i	−0.608022	−	0.556348i
$505$	0.492022	+	0.852207i	0.0218947	+	0.0379227i
$506$	9.73987	+	50.4431i	0.432990	+	2.24247i
$507$	−1.96067	−	3.09218i	−0.0870766	−	0.137329i
$508$	9.44655	−	5.87014i	0.419123	−	0.260445i
$509$	−6.89445	+	8.21649i	−0.305591	+	0.364189i	−0.896883	−	0.442269i	$-0.854174\pi$
$509$	−6.89445	+	8.21649i	−0.305591	+	0.364189i	0.591292	+	0.806458i	$0.298618\pi$
$510$	−2.15226	+	0.124335i	−0.0953037	+	0.00550566i
$511$	−5.19146	+	14.2634i	−0.229657	+	0.630977i
$512$	22.3872	−	3.28859i	0.989382	−	0.145337i
$513$	−14.3855	+	17.4945i	−0.635134	+	0.772402i
$514$	−15.7086	−	18.1162i	−0.692875	−	0.799072i
$515$	−0.849570	−	0.309218i	−0.0374365	−	0.0136258i
$516$	−5.68253	−	5.83637i	−0.250159	−	0.256932i
$517$	−33.0876	−	27.7638i	−1.45519	−	1.22105i
$518$	4.98210	+	0.795458i	0.218901	+	0.0349504i
$519$	−35.5439	+	22.5375i	−1.56020	+	0.989286i
$520$	−0.0834323	−	1.71473i	−0.00365875	−	0.0751960i
$521$	−11.3664	+	6.56238i	−0.497970	+	0.287503i	−0.727875	−	0.685710i	$-0.759492\pi$
$521$	−11.3664	+	6.56238i	−0.497970	+	0.287503i	0.229905	+	0.973213i	$0.426158\pi$
$522$	−2.94540	+	4.31521i	−0.128917	+	0.188872i
$523$	−6.53155	−	17.9453i	−0.285605	−	0.784693i	−0.996668	−	0.0815648i	$-0.974008\pi$
$523$	−6.53155	−	17.9453i	−0.285605	−	0.784693i	0.711063	−	0.703128i	$-0.248214\pi$
$524$	−5.06837	+	2.03306i	−0.221413	+	0.0888147i
$525$	−18.3197	+	4.02040i	−0.799539	+	0.175465i
$526$	14.4775	+	24.1629i	0.631251	+	1.05355i
$527$	−28.1610	+	23.6299i	−1.22671	+	1.02933i
$528$	39.9493	+	9.89246i	1.73857	+	0.430514i
$529$	2.50019	+	14.1793i	0.108704	+	0.616491i
$530$	−0.540445	+	0.206684i	−0.0234754	+	0.00897779i
$531$	−1.70006	+	18.5212i	−0.0737765	+	0.803751i
$532$	−18.9449	−	1.55959i	−0.821365	−	0.0676168i
$533$			3.84498i			0.166545i
$534$	−2.73491	−	1.37514i	−0.118351	−	0.0595082i
$535$	−0.135125	+	0.0238262i	−0.00584198	+	0.00103010i
$536$	−26.0951	−	3.30324i	−1.12714	−	0.142678i
$537$	4.82730	−	36.0721i	0.208313	−	1.55663i
$538$	−16.5957	+	9.94357i	−0.715493	+	0.428698i
$539$	−6.66954	+	11.5520i	−0.287277	+	0.497579i
$540$	−0.984924	+	1.63856i	−0.0423844	+	0.0705124i
$541$	−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	$0.437112\pi$
$542$	34.5416	+	19.2031i	1.48369	+	0.824843i
$543$	−6.16626	−	1.95869i	−0.264619	−	0.0840553i
$544$	26.9456	+	2.52687i	1.15528	+	0.108339i
$545$	−2.46108	−	0.433955i	−0.105421	−	0.0185886i
$546$	14.7278	−	9.67668i	0.630293	−	0.414124i
$547$	−5.42038	+	6.45975i	−0.231759	+	0.276199i	−0.869373	−	0.494157i	$-0.835477\pi$
$547$	−5.42038	+	6.45975i	−0.231759	+	0.276199i	0.637614	+	0.770356i	$0.279921\pi$
$548$	−0.783542	−	24.1661i	−0.0334713	−	1.03232i
$549$	−16.1296	+	34.2081i	−0.688393	+	1.45996i
$550$	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
$554$	−17.9160	−	14.5452i	−0.761179	−	0.617964i
$555$	−0.0216282	−	0.520867i	−0.000918065	−	0.0221096i
$556$	10.3796	−	6.44994i	0.440193	−	0.273538i
$557$	34.7400	+	6.12560i	1.47198	+	0.259550i	0.851369	−	0.524568i	$-0.175773\pi$
$557$	34.7400	+	6.12560i	1.47198	+	0.259550i	0.620612	+	0.784118i	$0.286884\pi$
$558$	3.22878	+	32.4397i	0.136685	+	1.37328i
$559$	6.71909	−	3.87927i	0.284187	−	0.164076i
$560$	−1.60114	+	0.103937i	−0.0676603	+	0.00439214i
$561$	43.6145	+	22.8227i	1.84140	+	0.963573i
$562$	−9.38731	+	27.1526i	−0.395980	+	1.14537i
$563$	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	$-0.202479\pi$
$564$	−22.9681	+	10.3390i	−0.967130	+	0.435352i
$565$	1.41710	−	1.18909i	0.0596178	−	0.0500253i
$566$	0.285859	+	17.6376i	0.0120155	+	0.741364i
$567$	−19.6236	−	0.167484i	−0.824114	−	0.00703367i
$568$	−2.75123	−	12.1237i	−0.115439	−	0.508700i
$569$		−	38.3107i		−	1.60607i	−0.595933	−	0.803034i	$-0.703217\pi$
$569$		−	38.3107i		−	1.60607i	0.595933	−	0.803034i	$-0.296783\pi$
$570$	0.230630	+	1.95059i	0.00966003	+	0.0817014i
$571$			31.7827i			1.33006i	0.746815	+	0.665032i	$0.231582\pi$
$571$			31.7827i			1.33006i	−0.746815	+	0.665032i	$0.768418\pi$
$572$	−18.4892	+	34.5648i	−0.773072	+	1.44523i
$573$	5.87950	+	4.53146i	0.245620	+	0.189305i
$574$	3.59309	−	0.0582345i	0.149973	−	0.00243066i
$575$	23.2648	−	19.5215i	0.970208	−	0.814101i
$576$	15.3218	−	18.4727i	0.638409	−	0.769697i
$577$	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	$0.0849034\pi$
$578$	7.87117	+	2.72125i	0.327398	+	0.113189i
$579$	13.6195	−	26.0272i	0.566009	−	1.08165i
$580$	0.0930950	+	0.443414i	0.00386556	+	0.0184118i
$581$	7.05820	−	4.07505i	0.292824	−	0.169062i
$582$	−22.1840	−	16.5317i	−0.919556	−	0.685259i
$583$	13.0110	+	2.29419i	0.538860	+	0.0950156i
$584$	−18.8073	−	5.82702i	−0.778252	−	0.241124i
$585$	−1.28207	−	1.29305i	−0.0530069	−	0.0534612i
$586$	−15.8340	+	19.5036i	−0.654097	+	0.805685i
$587$	−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
$591$	−8.17233	−	19.8494i	−0.336165	−	0.816496i
$592$	−0.716544	+	6.50508i	−0.0294498	+	0.267357i
$593$	−3.39597	+	4.04717i	−0.139456	+	0.166197i	−0.831252	−	0.555896i	$-0.812375\pi$
$593$	−3.39597	+	4.04717i	−0.139456	+	0.166197i	0.691796	+	0.722093i	$0.256820\pi$
$594$	38.5207	−	20.5351i	1.58052	−	0.842566i
$595$	−1.88993	−	0.333246i	−0.0774796	−	0.0136617i
$596$	−27.3442	+	34.8196i	−1.12006	+	1.42627i
$597$	8.32334	−	26.2032i	0.340652	−	1.07242i
$598$	−13.8651	+	24.9399i	−0.566985	+	1.01987i
$599$	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	$0.362906\pi$
$600$	−6.36381	−	23.4821i	−0.259801	−	0.958651i
$601$	−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	$0.257519\pi$
$602$	−3.72690	−	6.22016i	−0.151897	−	0.253515i
$603$	−22.9215	+	15.9045i	−0.933437	+	0.647681i
$604$	−21.1678	−	23.6275i	−0.861306	−	0.961389i
$605$	4.40013	−	0.775862i	0.178891	−	0.0315433i
$606$	−11.7062	−	5.88601i	−0.475533	−	0.239103i
$607$		−	17.8562i		−	0.724761i	−0.932030	−	0.362380i	$-0.881964\pi$
$607$		−	17.8562i		−	0.724761i	0.932030	−	0.362380i	$-0.118036\pi$
$608$	0.826357	−	24.6438i	0.0335132	−	0.999438i
$609$	−3.43564	+	3.13473i	−0.139219	+	0.127026i
$610$	1.17155	+	3.06340i	0.0474346	+	0.124033i
$611$	−4.16588	−	23.6259i	−0.168533	−	0.955800i
$612$	23.0415	−	17.1200i	0.931397	−	0.692034i
$613$	−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	$0.942970\pi$
$614$	−24.9447	+	14.9460i	−1.00669	+	0.603171i
$615$	−0.0795947	−	0.362689i	−0.00320957	−	0.0146250i
$616$	32.5805	+	16.7544i	1.31270	+	0.675056i
$617$	−4.11639	−	11.3097i	−0.165720	−	0.455311i	0.828839	−	0.559487i	$-0.189002\pi$
$617$	−4.11639	−	11.3097i	−0.165720	−	0.455311i	−0.994559	+	0.104176i	$0.966780\pi$
$618$	11.7150	−	2.77066i	0.471245	−	0.111452i
$619$	13.8509	−	7.99684i	0.556716	−	0.321420i	−0.195110	−	0.980781i	$-0.562507\pi$
$619$	13.8509	−	7.99684i	0.556716	−	0.321420i	0.751826	+	0.659361i	$0.229173\pi$
$620$	2.22343	+	1.74609i	0.0892951	+	0.0701245i
$621$	28.2795	−	14.4920i	1.13482	−	0.581546i
$622$	−4.09515	+	25.6486i	−0.164200	+	1.02842i
$623$	−2.08746	−	1.75158i	−0.0836322	−	0.0701757i
$624$	13.4658	+	18.4717i	0.539063	+	0.739461i
$625$	−23.0164	−	8.37727i	−0.920655	−	0.335091i
$626$	−11.4904	+	9.96330i	−0.459248	+	0.398214i
$627$	18.3741	−	40.9120i	0.733789	−	1.63387i
$628$	−3.48365	+	24.3466i	−0.139013	+	0.971535i
$629$	−2.67717	+	7.35547i	−0.106746	+	0.293282i
$630$	−1.18893	+	1.21766i	−0.0473680	+	0.0485127i
$631$	−0.877148	+	1.04534i	−0.0349187	+	0.0416145i	−0.783221	−	0.621743i	$-0.786425\pi$
$631$	−0.877148	+	1.04534i	−0.0349187	+	0.0416145i	0.748302	+	0.663358i	$0.230869\pi$
$632$	−5.90544	+	19.0604i	−0.234906	+	0.758183i
$633$	10.0466	−	6.37028i	0.399315	−	0.253196i
$634$	28.7554	−	5.55226i	1.14202	−	0.220508i
$635$	−0.511501	−	0.885946i	−0.0202983	−	0.0351577i
$636$	4.50295	−	6.25149i	0.178554	−	0.247888i
$637$	−6.96204	+	2.53398i	−0.275846	+	0.100400i
$638$	3.38030	−	9.77747i	0.133827	−	0.387094i
$639$	−10.7690	−	7.60925i	−0.426016	−	0.301017i
$640$	−0.235599	−	2.06792i	−0.00931288	−	0.0817417i
$641$	−15.8890	−	18.9358i	−0.627578	−	0.747918i	0.354776	−	0.934951i	$-0.384557\pi$
$641$	−15.8890	−	18.9358i	−0.627578	−	0.747918i	−0.982354	+	0.187033i	$0.940113\pi$
$642$	1.32948	−	1.25312i	0.0524705	−	0.0494565i
$643$	−19.9452	+	3.51687i	−0.786560	+	0.138692i	−0.552481	−	0.833526i	$-0.686319\pi$
$643$	−19.9452	+	3.51687i	−0.786560	+	0.138692i	−0.234079	+	0.972217i	$0.575208\pi$
$644$	23.5160	+	12.5790i	0.926660	+	0.495683i
$645$	−0.553493	+	0.505014i	−0.0217938	+	0.0198849i
$646$	7.94818	−	28.4009i	0.312717	−	1.11742i
$647$	−15.8844			−0.624480			−0.312240	−	0.950003i	$-0.601079\pi$
$647$	−15.8844			−0.624480			−0.312240	+	0.950003i	$0.601079\pi$
$648$	−1.02008	−	25.4354i	−0.0400724	−	0.999197i
$649$	−6.39515	−	36.2687i	−0.251032	−	1.42367i
$650$	23.1694	−	0.375514i	0.908778	−	0.0147289i
$651$	−3.84922	+	28.7633i	−0.150863	+	1.12732i
$652$	−11.7719	+	35.9250i	−0.461024	+	1.40693i
$653$	−0.885563	−	0.511280i	−0.0346548	−	0.0200079i	0.482573	−	0.875856i	$-0.339702\pi$
$653$	−0.885563	−	0.511280i	−0.0346548	−	0.0200079i	−0.517227	+	0.855848i	$0.673036\pi$
$654$	30.5601	−	13.1652i	1.19499	−	0.514801i
$655$	0.171798	+	0.472010i	0.00671269	+	0.0184430i
$656$	0.301959	+	4.65163i	0.0117895	+	0.181616i
$657$	−18.9645	+	8.74498i	−0.739877	+	0.341174i
$658$	−22.0150	+	4.25079i	−0.858234	+	0.165713i
$659$	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	$0.0385825\pi$
$660$	1.02852	−	3.64317i	0.0400352	−	0.141810i
$661$	−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	$0.861363\pi$
$662$	−2.37169	+	2.92134i	−0.0921784	+	0.113541i
$663$	10.4089	+	25.2818i	0.404249	+	0.981864i
$664$	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
$668$	−6.86183	+	0.222482i	−0.265492	+	0.00860811i
$669$	−0.841187	−	20.2581i	−0.0325222	−	0.783225i
$670$	−0.381460	+	2.38915i	−0.0147371	+	0.0923010i
$671$	13.0041	−	73.7502i	0.502020	−	2.84709i
$672$	17.0577	−	12.8634i	0.658014	−	0.496217i
$673$	−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	$0.994856\pi$
$674$	15.8481	−	28.5068i	0.610446	−	1.09804i
$675$	−21.6744	−	14.0040i	−0.834250	−	0.539014i
$676$	3.92390	−	1.57398i	0.150919	−	0.0605378i
$677$	14.7569	+	8.51989i	0.567153	+	0.327446i	0.756012	−	0.654558i	$-0.227145\pi$
$677$	14.7569	+	8.51989i	0.567153	+	0.327446i	−0.188858	+	0.982004i	$0.560479\pi$
$678$	−7.07557	+	23.5935i	−0.271735	+	0.906102i
$679$	−15.8305	−	18.8661i	−0.607520	−	0.724014i
$680$	0.312620	−	2.46965i	0.0119884	−	0.0947068i
$681$	−1.33057	−	1.02550i	−0.0509874	−	0.0392972i
$682$	−23.0580	−	60.2930i	−0.882938	−	2.30874i
$683$	20.9051			0.799913			0.399957	−	0.916534i	$-0.369025\pi$
$683$	20.9051			0.799913			0.399957	+	0.916534i	$0.369025\pi$
$684$	−16.8283	−	20.0202i	−0.643448	−	0.765490i
$685$	−2.22399			−0.0849745
$686$	10.1839	+	26.6291i	0.388822	+	1.01671i
$687$	−9.29833	−	7.16643i	−0.354753	−	0.273416i
$688$	7.82406	−	5.22078i	0.298289	−	0.199041i
$689$	4.71684	+	5.62132i	0.179697	+	0.214155i
$690$	0.791585	−	2.63954i	0.0301351	−	0.100486i
$691$	−20.8238	−	12.0226i	−0.792176	−	0.457363i	0.0485520	−	0.998821i	$-0.484539\pi$
$691$	−20.8238	−	12.0226i	−0.792176	−	0.457363i	−0.840728	+	0.541458i	$0.817873\pi$
$692$	−18.0926	−	45.1044i	−0.687777	−	1.71461i
$693$	37.5769	−	9.89702i	1.42743	−	0.375957i
$694$	−0.662203	+	1.19114i	−0.0251369	+	0.0452150i
$695$	−0.562022	−	0.973451i	−0.0213187	−	0.0369251i
$696$	−4.27801	−	4.25369i	−0.162158	−	0.161236i
$697$	−0.968149	+	5.49065i	−0.0366713	+	0.207973i
$698$	−2.42382	+	15.1808i	−0.0917430	+	0.574603i
$699$	−0.518156	−	12.4786i	−0.0195985	−	0.471986i
$700$	−0.701827	−	21.6458i	−0.0265266	−	0.818136i
$701$	1.70943	−	4.69662i	0.0645643	−	0.177389i	−0.903215	−	0.429188i	$-0.858800\pi$
$701$	1.70943	−	4.69662i	0.0645643	−	0.177389i	0.967780	+	0.251799i	$0.0810221\pi$
$702$	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
$705$	0.882035	+	2.14234i	0.0332194	+	0.0806851i
$706$	32.8264	−	40.4341i	1.23544	−	1.52176i
$707$	−8.93493	−	7.49730i	−0.336033	−	0.281965i
$708$	−20.6685	−	5.83502i	−0.776768	−	0.219294i
$709$	−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	$0.855292\pi$
$710$	−1.12277	+	0.216791i	−0.0421368	+	0.00813602i
$711$	8.86267	+	19.2198i	0.332376	+	0.720798i
$712$	2.13780	−	2.81498i	0.0801176	−	0.105496i
$713$	−16.0715	−	44.1562i	−0.601883	−	1.65366i
$714$	23.4679	−	10.1099i	0.878264	−	0.378355i
$715$	3.12253	+	1.80279i	0.116776	+	0.0674207i
$716$	39.9345	+	13.0857i	1.49242	+	0.489037i
$717$	1.29559	−	9.68131i	0.0483847	−	0.361555i
$718$	31.4419	−	0.509590i	1.17340	−	0.0190177i
$719$	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	$0.899453\pi$
$720$	−1.65258	−	1.46364i	−0.0615881	−	0.0545467i
$721$	10.7161			0.399088
$722$	−26.2634	−	5.67731i	−0.977424	−	0.211288i
$723$	−18.2598	+	16.6605i	−0.679090	+	0.619611i
$724$	3.52375	−	6.58752i	0.130959	−	0.244823i
$725$	−6.02267	+	1.06196i	−0.223676	+	0.0394402i
$726$	−43.2924	+	40.8056i	−1.60673	+	1.51444i
$727$	−3.48854	−	4.15748i	−0.129383	−	0.154192i	0.697464	−	0.716620i	$-0.254312\pi$
$727$	−3.48854	−	4.15748i	−0.129383	−	0.154192i	−0.826846	+	0.562428i	$0.809867\pi$
$728$	7.88066	+	18.7605i	0.292077	+	0.695312i
$729$	−18.8459	−	19.3347i	−0.697997	−	0.716101i
$730$	−0.591755	+	1.71164i	−0.0219018	+	0.0633507i
$731$	10.5717	−	3.84777i	0.391007	−	0.142315i
$732$	−35.4353	−	25.5240i	−1.30973	−	0.943396i
$733$	−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	$-0.351966\pi$
$734$	−18.1642	+	3.50725i	−0.670452	+	0.129455i
$735$	0.604258	−	0.383145i	0.0222884	−	0.0141325i
$736$	−14.8153	+	31.2609i	−0.546098	+	1.15229i
$737$	35.5095	−	42.3186i	1.30801	−	1.55882i
$738$	3.53756	+	3.45408i	0.130219	+	0.127146i
$739$	−2.38377	+	6.54936i	−0.0876885	+	0.240922i	−0.975784	−	0.218737i	$-0.929806\pi$
$739$	−2.38377	+	6.54936i	−0.0876885	+	0.240922i	0.888095	+	0.459659i	$0.152029\pi$
$740$	0.595895	+	0.0852640i	0.0219055	+	0.00313437i
$741$	22.4242	−	10.8473i	0.823772	−	0.398486i
$742$	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	$0.272846\pi$
$744$	−37.5092	−	3.17390i	−1.37515	−	0.116361i
$745$	3.11956	+	2.61762i	0.114292	+	0.0959022i
$746$	1.59003	−	9.95863i	0.0582151	−	0.364611i
$747$	10.8187	+	2.94840i	0.395836	+	0.107876i
$748$	−35.1059	+	44.7031i	−1.28360	+	1.63451i
$749$	1.40844	−	0.813164i	0.0514633	−	0.0297124i
$750$	−4.37033	+	1.03361i	−0.159582	+	0.0377420i
$751$	9.07042	+	24.9208i	0.330984	+	0.909372i	0.987856	+	0.155370i	$0.0496570\pi$
$751$	9.07042	+	24.9208i	0.330984	+	0.909372i	−0.656872	+	0.754002i	$0.728121\pi$
$752$	−6.89526	−	28.2552i	−0.251444	−	1.03036i
$753$	4.23438	+	19.2948i	0.154309	+	0.703141i
$754$	4.92900	−	2.95328i	0.179504	−	0.107552i
$755$	−2.23524	+	1.87559i	−0.0813487	+	0.0682597i
$756$	4.32753	−	22.2431i	0.157391	−	0.808975i
$757$	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	$0.858203\pi$
$758$	−6.60372	−	17.2676i	−0.239858	−	0.627188i
$759$	−46.4809	+	42.4098i	−1.68715	+	1.53938i
$760$	−2.26311	−	0.149427i	−0.0820918	−	0.00542027i
$761$			36.3749i			1.31859i	0.751884	+	0.659295i	$0.229145\pi$
$761$			36.3749i			1.31859i	−0.751884	+	0.659295i	$0.770855\pi$
$762$	12.1697	+	6.11904i	0.440861	+	0.221669i
$763$	29.1709	−	5.14361i	1.05606	−	0.186211i
$764$	−6.38414	+	5.71953i	−0.230970	+	0.206925i
$765$	−1.50521	−	2.16930i	−0.0544209	−	0.0784313i
$766$	1.09740	+	1.83155i	0.0396506	+	0.0661764i
$767$	10.2276	−	17.7148i	0.369299	−	0.639644i
$768$	17.7415	+	21.2894i	0.640190	+	0.768217i
$769$	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	$0.128283\pi$
$770$	1.63740	−	2.94528i	0.0590078	−	0.106140i
$771$	8.89064	−	27.9891i	0.320188	−	1.00800i
$772$	26.6768	+	20.9496i	0.960121	+	0.753993i
$773$	42.7474	+	7.53752i	1.53752	+	0.271106i	0.877290	−	0.479960i	$-0.159349\pi$
$773$	42.7474	+	7.53752i	1.53752	+	0.271106i	0.660227	+	0.751066i	$0.270460\pi$
$774$	2.46689	−	9.66675i	0.0886706	−	0.347464i
$775$	−24.5284	+	29.2318i	−0.881086	+	1.05004i
$776$	23.4454	−	21.6997i	0.841642	−	0.778976i
$777$	2.35245	+	5.71376i	0.0843935	+	0.204980i
$778$	−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
$782$	−26.0791	+	32.1230i	−0.932587	+	1.14872i
$783$	−6.39080	−	0.320026i	−0.228388	−	0.0114368i
$784$	−8.22362	+	3.61234i	−0.293701	+	0.129012i
$785$	2.22787	+	0.392834i	0.0795161	+	0.0140208i
$786$	−5.36291	−	3.99648i	−0.191289	−	0.142550i
$787$	−37.3664	+	21.5735i	−1.33197	+	0.769013i	−0.985601	−	0.169086i	$-0.945918\pi$
$787$	−37.3664	+	21.5735i	−1.33197	+	0.769013i	−0.346368	+	0.938099i	$0.612585\pi$
$788$	24.2579	−	5.09295i	0.864151	−	0.181429i
$789$	−15.9950	+	30.5668i	−0.569438	+	1.08821i
$790$	1.73468	+	0.599719i	0.0617171	+	0.0213370i
$791$	−10.9632	+	18.9889i	−0.389808	+	0.675168i
$792$	15.1917	+	48.0616i	0.539813	+	1.70780i
$793$	31.8633	−	26.7365i	1.13150	−	0.949440i
$794$	−56.0982	+	0.909203i	−1.99085	+	0.0322664i
$795$	−0.561296	−	0.432603i	−0.0199071	−	0.0153429i
$796$	27.9933	+	14.9740i	0.992197	+	0.530740i
$797$			15.1787i			0.537656i	0.963188	+	0.268828i	$0.0866363\pi$
$797$			15.1787i			0.537656i	−0.963188	+	0.268828i	$0.913364\pi$
$798$	−10.4763	−	20.7908i	−0.370857	−	0.735988i
$799$		−	34.7867i		−	1.23067i
$800$	28.0007	−	2.27386i	0.989973	−	0.0803931i
$801$	−0.310819	−	3.73624i	−0.0109823	−	0.132014i
$802$	0.454952	+	28.0707i	0.0160649	+	0.991212i
$803$	31.6775	−	26.5806i	1.11787	−	0.938008i
$804$	−13.2235	−	29.3758i	−0.466356	−	1.03600i
$805$	1.22652	−	2.12440i	0.0432292	−	0.0748753i
$806$	11.7150	−	33.8856i	0.412645	−	1.19357i
$807$	−20.9941	−	10.9858i	−0.739026	−	0.386719i
$808$	9.15043	−	12.0490i	0.321911	−	0.423881i
$809$	−21.0568	+	12.1571i	−0.740317	+	0.427422i	−0.822185	−	0.569221i	$-0.807245\pi$
$809$	−21.0568	+	12.1571i	−0.740317	+	0.427422i	0.0818676	+	0.996643i	$0.473912\pi$
$810$	−2.34139	+	0.0179618i	−0.0822681	+	0.000631115i
$811$	−6.15535	−	1.08535i	−0.216143	−	0.0381119i	0.0645277	−	0.997916i	$-0.479446\pi$
$811$	−6.15535	−	1.08535i	−0.216143	−	0.0381119i	−0.280671	+	0.959804i	$0.590557\pi$
$812$	−2.83446	−	4.56136i	−0.0994700	−	0.160072i
$813$	2.00811	+	48.3610i	0.0704277	+	1.69610i
$814$	−10.6709	−	8.66318i	−0.374015	−	0.303644i
$815$	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
$819$	19.5216	+	9.20471i	0.682141	+	0.321638i
$820$	0.428538	−	0.0138946i	0.0149652	−	0.000485220i
$821$	−13.0197	+	15.5163i	−0.454390	+	0.541521i	−0.943793	−	0.330536i	$-0.892770\pi$
$821$	−13.0197	+	15.5163i	−0.454390	+	0.541521i	0.489403	+	0.872058i	$0.337215\pi$
$822$	24.7489	−	16.2608i	0.863216	−	0.567162i
$823$	47.6559	+	8.40302i	1.66118	+	0.292911i	0.923888	−	0.382664i	$-0.124993\pi$
$823$	47.6559	+	8.40302i	1.66118	+	0.292911i	0.737292	+	0.675574i	$0.236104\pi$
$824$	0.675543	+	13.8840i	0.0235337	+	0.483673i
$825$	48.6988	+	15.4690i	1.69548	+	0.538561i
$826$	−16.7092	−	9.28931i	−0.581386	−	0.323216i
$827$	−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	$0.568874\pi$
$828$	10.4903	+	35.1608i	0.364563	+	1.22192i
$829$	−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	$0.945710\pi$
$830$	0.834154	−	0.499795i	0.0289539	−	0.0173481i
$831$	3.74889	−	28.0136i	0.130048	−	0.971783i
$832$	−23.8098	+	11.3930i	−0.825458	+	0.394983i
$833$	−10.5798	+	1.86551i	−0.366570	+	0.0646362i
$834$	13.3717	+	6.72342i	0.463023	+	0.232813i
$835$			0.631491i			0.0218537i
$836$	42.5730	+	29.4856i	1.47242	+	1.01978i
$837$	−31.8309	+	24.1026i	−1.10024	+	0.833106i
$838$	−32.0627	+	12.2618i	−1.10759	+	0.423578i
$839$	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	$0.817760\pi$
$840$	−1.13173	−	1.60650i	−0.0390482	−	0.0554296i
$841$	21.0536	−	17.6661i	0.725986	−	0.609175i
$842$	12.1466	+	20.2726i	0.418600	+	0.698639i
$843$	−34.3685	+	7.54241i	−1.18371	+	0.259775i
$844$	5.11391	+	12.7489i	0.176028	+	0.438834i
$845$	−0.133005	−	0.365427i	−0.00457550	−	0.0125711i
$846$	−25.4792	−	17.3911i	−0.875993	−	0.597919i
$847$	−45.8635	+	26.4793i	−1.57589	+	0.909841i
$848$	6.14786	+	6.43020i	0.211118	+	0.220814i
$849$	−18.2457	+	11.5691i	−0.626191	+	0.397052i
$850$	33.1805	+	5.29771i	1.13808	+	0.181710i
$851$	−7.66460	−	6.43136i	−0.262739	−	0.220464i
$852$	10.9092	−	10.6217i	0.373744	−	0.363892i
$853$	−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
$855$	−1.89067	+	1.48740i	−0.0646597	+	0.0508681i
$856$	1.14234	+	1.77355i	0.0390445	+	0.0606187i
$857$	6.82116	−	18.7410i	0.233006	−	0.640180i	−0.766992	−	0.641656i	$-0.778248\pi$
$857$	6.82116	−	18.7410i	0.233006	−	0.640180i	0.999999	+	0.00147620i	$0.000469889\pi$
$858$	−47.9291	+	2.76885i	−1.63627	+	0.0945269i
$859$	2.21082	−	2.63475i	0.0754323	−	0.0898967i	−0.727008	−	0.686628i	$-0.759090\pi$
$859$	2.21082	−	2.63475i	0.0754323	−	0.0898967i	0.802441	+	0.596732i	$0.203534\pi$
$860$	−0.456640	−	0.734850i	−0.0155713	−	0.0250582i
$861$	2.35684	+	3.71697i	0.0803208	+	0.126674i
$862$	−9.48237	−	49.1095i	−0.322971	−	1.67268i
$863$	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	$0.818073\pi$
$864$	29.0916	+	4.20465i	0.989716	+	0.143045i
$865$	−4.20051	+	1.52886i	−0.142821	+	0.0519828i
$866$	9.29457	+	3.21335i	0.315842	+	0.109194i
$867$	2.18644	+	9.96295i	0.0742554	+	0.338359i
$868$	−31.8431	−	10.4344i	−1.08083	−	0.354165i
$869$	−26.9383	−	32.1038i	−0.913820	−	1.08905i
$870$	−0.403806	+	0.380611i	−0.0136903	+	0.0129039i
$871$	30.2171	−	5.32810i	1.02387	−	0.180536i
$872$	8.50313	+	37.4703i	0.287952	+	1.26890i
$873$	3.09722	−	33.7423i	0.104825	−	1.14200i
$874$	30.6388	+	21.9633i	1.03637	+	0.742920i
$875$	−3.99769			−0.135147
$876$	−5.92964	−	23.3740i	−0.200344	−	0.789734i
$877$	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	$0.860638\pi$
$878$	0.781192	+	48.1999i	0.0263640	+	1.62667i
$879$	−30.4960	−	4.08108i	−1.02860	−	0.137651i
$880$	3.91920	+	1.93579i	0.132116	+	0.0652553i
$881$	0.798552	+	0.461044i	0.0269039	+	0.0155330i	0.513392	−	0.858154i	$-0.328389\pi$
$881$	0.798552	+	0.461044i	0.0269039	+	0.0155330i	−0.486488	+	0.873687i	$0.661722\pi$
$882$	−3.92287	+	8.68174i	−0.132090	+	0.292329i
$883$	−7.94524	−	21.8294i	−0.267379	−	0.734617i	−0.998621	−	0.0524991i	$-0.983281\pi$
$883$	−7.94524	−	21.8294i	−0.267379	−	0.734617i	0.731242	−	0.682118i	$-0.238941\pi$
$884$	−30.8967	+	6.48679i	−1.03917	+	0.218174i
$885$	−0.598038	+	1.88272i	−0.0201028	+	0.0632869i
$886$	−3.06103	−	15.8532i	−0.102837	−	0.532597i
$887$	−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	$0.941596\pi$
$888$	−7.25459	+	3.40808i	−0.243448	+	0.114368i
$889$	9.28867	+	7.79412i	0.311532	+	0.261406i
$890$	−0.252417	−	0.204925i	−0.00846104	−	0.00686911i
$891$	46.0705	+	27.1257i	1.54342	+	0.908745i
$892$	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
$896$	11.0073	+	22.0775i	0.367728	+	0.737556i
$897$	−34.9178	+	1.44991i	−1.16587	+	0.0484110i
$898$	−9.49630	−	1.51621i	−0.316896	−	0.0505966i
$899$	−1.64312	+	9.31858i	−0.0548010	+	0.310792i
$900$	20.4684	−	21.6542i	0.682279	−	0.721807i
$901$	5.32024	+	9.21493i	0.177243	+	0.306994i
$902$	−8.55664	−	4.75699i	−0.284905	−	0.158390i
$903$	4.11754	−	7.86868i	0.137023	−	0.261853i
$904$	−25.2936	−	13.0072i	−0.841254	−	0.432613i
$905$	−0.595106	−	0.343585i	−0.0197820	−	0.0114211i
$906$	11.1605	−	37.2148i	0.370784	−	1.23638i
$907$	15.4050	+	18.3589i	0.511514	+	0.609598i	0.958552	−	0.284916i	$-0.0919658\pi$
$907$	15.4050	+	18.3589i	0.511514	+	0.609598i	−0.447039	+	0.894515i	$0.647521\pi$
$908$	1.44477	−	1.29436i	0.0479464	−	0.0429550i
$909$	−1.33040	−	15.9922i	−0.0441265	−	0.530429i
$910$	1.74820	−	0.668571i	0.0579523	−	0.0221629i
$911$	−1.44251			−0.0477925			−0.0238962	−	0.999714i	$-0.507607\pi$
$911$	−1.44251			−0.0477925			−0.0238962	+	0.999714i	$0.507607\pi$
$912$	26.2767	−	14.8840i	0.870109	−	0.492859i
$913$	−22.2036			−0.734831
$914$	−12.3095	+	4.70756i	−0.407161	+	0.155712i
$915$	−2.45212	+	3.18159i	−0.0810647	+	0.105180i
$916$	10.0964	−	9.04534i	0.333595	−	0.298866i
$917$	−3.82698	−	4.56082i	−0.126378	−	0.150611i
$918$	32.6111	+	13.1348i	1.07633	+	0.433514i
$919$	10.1682	+	5.87063i	0.335419	+	0.193654i	0.658244	−	0.752804i	$-0.271299\pi$
$919$	10.1682	+	5.87063i	0.335419	+	0.193654i	−0.322826	+	0.946458i	$0.604633\pi$
$920$	2.82975	+	1.45519i	0.0932940	+	0.0479763i
$921$	−31.5558	−	16.5126i	−1.03980	−	0.544108i
$922$	17.4841	+	9.72011i	0.575807	+	0.320115i
$923$	7.25105	+	12.5592i	0.238671	+	0.413390i
$924$	3.31337	+	44.7473i	0.109002	+	1.47208i
$925$	−1.41092	+	8.00172i	−0.0463907	+	0.263095i
$926$	34.3669	+	5.48714i	1.12937	+	0.180319i
$927$	10.3808	+	10.4697i	0.340949	+	0.343871i
$928$	5.73113	−	3.95994i	0.188134	−	0.129992i
$929$	−3.13298	+	8.60779i	−0.102790	+	0.282412i	−0.980417	−	0.196930i	$-0.936903\pi$
$929$	−3.13298	+	8.60779i	−0.102790	+	0.282412i	0.877628	+	0.479343i	$0.159125\pi$
$930$	−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
$933$	−29.4153	+	12.1108i	−0.963015	+	0.396489i
$934$	−3.58498	−	2.91047i	−0.117304	−	0.0952334i
$935$	4.00505	+	3.36063i	0.130979	+	0.109904i
$936$	−10.6952	+	25.8730i	−0.349584	+	0.845685i
$937$	−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	$0.905191\pi$
$938$	−5.43670	−	28.1569i	−0.177515	−	0.919355i
$939$	−17.7524	−	5.63897i	−0.579327	−	0.184021i
$940$	−2.61814	+	0.549679i	−0.0853943	+	0.0179286i
$941$	−7.16383	−	19.6825i	−0.233534	−	0.641630i	0.766466	−	0.642285i	$-0.222014\pi$
$941$	−7.16383	−	19.6825i	−0.233534	−	0.641630i	−1.00000		0.000655452i	$0.999791\pi$
$942$	−27.6642	+	11.9177i	−0.901349	+	0.388299i
$943$	−6.17183	−	3.56330i	−0.200982	−	0.116037i
$944$	10.9821	−	22.2344i	0.357437	−	0.723669i
$945$	−2.03198	−	0.464144i	−0.0661002	−	0.0150986i
$946$	0.320129	+	19.7521i	0.0104083	+	0.642196i
$947$	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	$0.649362\pi$
$948$	−23.6886	+	6.00945i	−0.769369	+	0.195178i
$949$	22.9679			0.745570
$950$	3.00577	−	30.4655i	0.0975202	−	0.988432i
$951$	24.1759	+	26.4966i	0.783957	+	0.859213i
$952$	6.52978	+	28.7744i	0.211631	+	0.932584i
$953$	−5.84883	+	1.03131i	−0.189462	+	0.0334073i	−0.267574	−	0.963537i	$-0.586222\pi$
$953$	−5.84883	+	1.03131i	−0.189462	+	0.0334073i	0.0781118	+	0.996945i	$0.475111\pi$
$954$	9.40916	+	0.710116i	0.304633	+	0.0229908i
$955$	0.506783	+	0.603961i	0.0163991	+	0.0195437i
$956$	10.7179	+	3.51205i	0.346643	+	0.113588i
$957$	12.3758	−	2.71597i	0.400054	−	0.0877948i
$958$	−52.1040	−	18.0136i	−1.68341	−	0.581993i
$959$	24.7709	−	9.01589i	0.799895	−	0.291138i
$960$	2.01008	−	1.56757i	0.0648752	−	0.0505930i
$961$	14.0211	+	24.2852i	0.452293	+	0.783394i
$962$	−1.44732	−	7.49573i	−0.0466635	−	0.241672i
$963$	2.15884	+	0.588344i	0.0695676	+	0.0189591i
$964$	−15.0646	−	24.2428i	−0.485199	−	0.780809i
$965$	2.00548	−	2.39003i	0.0645586	−	0.0769379i
$966$	1.88377	+	32.6083i	0.0606094	+	1.04916i
$967$	19.6928	−	54.1056i	0.633279	−	1.73992i	−0.0385956	−	0.999255i	$-0.512288\pi$
$967$	19.6928	−	54.1056i	0.633279	−	1.73992i	0.671875	−	0.740665i	$-0.265489\pi$
$968$	−37.1985	−	57.7527i	−1.19561	−	1.85624i
$969$	34.7531	−	9.84367i	1.11643	−	0.316224i
$970$	−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	$0.736775\pi$
$972$	25.9239	−	17.3191i	0.831510	−	0.555509i
$973$	10.2061	+	8.56395i	0.327193	+	0.274548i
$974$	−41.2177	−	6.58096i	−1.32070	−	0.210868i
$975$	15.1976	+	23.9682i	0.486714	+	0.767596i
$976$	36.4482	−	34.8479i	1.16668	−	1.11545i
$977$	7.81805	−	4.51375i	0.250122	−	0.144408i	−0.369698	−	0.929152i	$-0.620539\pi$
$977$	7.81805	−	4.51375i	0.250122	−	0.144408i	0.619820	+	0.784744i	$0.287206\pi$
$978$	−45.0580	+	10.6565i	−1.44079	+	0.340756i
$979$	2.53907	+	6.97603i	0.0811490	+	0.222955i
$980$	0.307580	+	0.766789i	0.00982528	+	0.0244942i
$981$	33.2834	+	23.5176i	1.06266	+	0.750859i
$982$	1.46680	+	2.44808i	0.0468075	+	0.0781214i
$983$	−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	$0.354166\pi$
$984$	−4.66723	+	3.28790i	−0.148786	+	0.104814i
$985$	−0.395903	−	2.24528i	−0.0126145	−	0.0715405i
$986$	7.78224	−	2.97619i	0.247837	−	0.0947812i
$987$	−18.5090	−	20.2858i	−0.589148	−	0.645703i
$988$	7.58697	+	27.7449i	0.241374	+	0.882684i
$989$			14.3803i			0.457267i
$990$	4.46373	−	1.25336i	0.141867	−	0.0398343i
$991$	−0.787224	+	0.138809i	−0.0250070	+	0.00440941i	−0.186138	−	0.982524i	$-0.559597\pi$
$991$	−0.787224	+	0.138809i	−0.0250070	+	0.00440941i	0.161131	+	0.986933i	$0.448486\pi$
$992$	11.5116	−	41.9146i	0.365495	−	1.33079i
$993$	−4.56783	−	0.611284i	−0.144956	−	0.0193985i
$994$	11.6266	−	6.96624i	0.368773	−	0.220956i
$995$	1.46005	−	2.52887i	0.0462865	−	0.0801707i
$996$	−5.62828	+	11.6607i	−0.178339	+	0.369484i
$997$	−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	$0.461035\pi$
$998$	38.6945	+	21.5119i	1.22485	+	0.680946i
$999$	−3.30357	+	7.83333i	−0.104520	+	0.247836i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.32091 + 0.505162i) q^{2} +(-1.37188 - 1.05734i) q^{3} +(1.48962 - 1.33455i) q^{4} +(-0.118249 - 0.140923i) q^{5} +(2.34625 + 0.703629i) q^{6} +(1.88835 + 1.09024i) q^{7} +(-1.29350 + 2.51532i) q^{8} +(0.764084 + 2.90106i) q^{9} +O(q^{10})\)	\(q+(-1.32091 + 0.505162i) q^{2} +(-1.37188 - 1.05734i) q^{3} +(1.48962 - 1.33455i) q^{4} +(-0.118249 - 0.140923i) q^{5} +(2.34625 + 0.703629i) q^{6} +(1.88835 + 1.09024i) q^{7} +(-1.29350 + 2.51532i) q^{8} +(0.764084 + 2.90106i) q^{9} +(0.227385 + 0.126413i) q^{10} +(-2.97017 - 5.14448i) q^{11} +(-3.45464 + 0.255804i) q^{12} +(0.572936 - 3.24928i) q^{13} +(-3.04509 - 0.486190i) q^{14} +(0.0132193 + 0.318358i) q^{15} +(0.437957 - 3.97595i) 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} +(-1.43783 - 3.49229i) q^{21} +(6.52213 + 5.29500i) q^{22} +(4.68466 + 3.93090i) q^{23} +(4.43406 - 2.08305i) q^{24} +(0.862364 - 4.89071i) q^{25} +(0.884614 + 4.58145i) q^{26} +(2.01917 - 4.78779i) q^{27} +(4.26791 - 0.896050i) q^{28} +(-0.421181 - 1.15719i) q^{29} +(-0.178284 - 0.413845i) q^{30} +(-6.65444 - 3.84194i) q^{31} +(1.42999 + 5.47313i) q^{32} +(-1.36474 + 10.1981i) q^{33} +(0.109644 + 6.76506i) q^{34} +(-0.0696549 - 0.395032i) q^{35} +(5.00981 + 3.30179i) q^{36} -1.63611 q^{37} +(6.14653 - 0.469211i) q^{38} +(-4.22158 + 3.85183i) q^{39} +(0.507423 - 0.115149i) q^{40} +(-1.14765 + 0.202362i) q^{41} +(3.66342 + 3.88668i) q^{42} +(1.51151 + 1.80135i) q^{43} +(-11.2900 - 3.69951i) q^{44} +(0.318476 - 0.450725i) q^{45} +(-8.17377 - 2.82587i) q^{46} +(6.83260 - 2.48686i) q^{47} +(-4.80474 + 4.99144i) q^{48} +(-1.12275 - 1.94467i) q^{49} +(1.33149 + 6.89584i) q^{50} +(-6.99829 + 4.43744i) q^{51} +(-3.48287 - 5.60482i) q^{52} +(-1.42960 + 1.70373i) q^{53} +(-0.248539 + 7.34427i) q^{54} +(-0.373759 + 1.02690i) q^{55} +(-5.18489 + 3.33959i) q^{56} +(4.41789 + 6.12227i) q^{57} +(1.14091 + 1.31578i) q^{58} +(5.82579 + 2.12042i) q^{59} +(0.444556 + 0.456592i) q^{60} +(9.65727 + 8.10341i) q^{61} +(10.7307 + 1.71331i) q^{62} +(-1.72000 + 6.31126i) q^{63} +(-4.65371 - 6.50715i) q^{64} +(-0.525649 + 0.303484i) q^{65} +(-3.34896 - 14.1602i) q^{66} +(3.18066 + 8.73880i) q^{67} +(-3.56228 - 8.88066i) q^{68} +(-2.27050 - 10.3460i) q^{69} +(0.291563 + 0.486616i) q^{70} +(-3.36704 + 2.82528i) q^{71} +(-8.28546 - 1.83061i) q^{72} +(1.20880 + 6.85547i) q^{73} +(2.16115 - 0.826497i) q^{74} +(-6.35418 + 5.79764i) q^{75} +(-7.88201 + 3.72478i) q^{76} -12.9528i q^{77} +(3.63054 - 7.22051i) q^{78} +(6.94773 - 1.22507i) q^{79} +(-0.612093 + 0.408433i) q^{80} +(-7.83235 + 4.43332i) q^{81} +(1.41372 - 0.847052i) q^{82} +(1.86888 - 3.23699i) q^{83} +(-6.80247 - 3.28334i) q^{84} +(-0.827043 + 0.301019i) q^{85} +(-2.90655 - 1.61587i) q^{86} +(-0.645725 + 2.03284i) q^{87} +(16.7820 - 0.816545i) q^{88} +(-1.23073 - 0.217011i) q^{89} +(-0.192990 + 0.756250i) q^{90} +(4.62440 - 5.51115i) q^{91} +(12.2244 - 0.396353i) q^{92} +(5.06684 + 12.3066i) 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} +(2.46543 + 2.00156i) q^{98} +(12.6550 - 12.5475i) 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

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Database

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