LMFDB - Embedded newform 945.2.do.a.758.122

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(2,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9, 12]))

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

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

chi := DirichletCharacter("945.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.do (of order $36$, degree $12$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$1680$
Relative dimension:	$140$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			758.122
Character	$\chi$	$=$	945.758
Dual form			945.2.do.a.662.122

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.192271 + 2.19767i) q^{2} +(-1.70674 + 0.295033i) q^{3} +(-2.82316 + 0.497800i) q^{4} +(1.08549 + 1.95492i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(2.64048 + 0.166853i) q^{7} +(-0.494869 - 1.84688i) q^{8} +(2.82591 - 1.00709i) q^{9} +O(q^{10})$	\(q+(0.192271 + 2.19767i) q^{2} +(-1.70674 + 0.295033i) q^{3} +(-2.82316 + 0.497800i) q^{4} +(1.08549 + 1.95492i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(2.64048 + 0.166853i) q^{7} +(-0.494869 - 1.84688i) q^{8} +(2.82591 - 1.00709i) q^{9} +(-4.08756 + 2.76141i) q^{10} +(-4.18808 - 0.738472i) q^{11} +(4.67153 - 1.68254i) q^{12} +(-0.0731741 + 0.104503i) q^{13} +(0.141002 + 5.83499i) q^{14} +(-2.42941 - 3.01629i) q^{15} +(-1.42399 + 0.518289i) q^{16} +(-1.83962 + 0.492925i) q^{17} +(2.75659 + 6.01678i) q^{18} +(-2.22549 + 1.28489i) q^{19} +(-4.03766 - 4.97871i) q^{20} +(-4.55584 + 0.494256i) q^{21} +(0.817670 - 9.34601i) q^{22} +(-0.462525 + 5.28668i) q^{23} +(1.38950 + 3.00613i) q^{24} +(-2.64344 + 4.24408i) q^{25} +(-0.243733 - 0.140719i) q^{26} +(-4.52597 + 2.55257i) q^{27} +(-7.53758 + 0.843380i) q^{28} +(-0.465271 + 2.63868i) q^{29} +(6.16169 - 5.91898i) q^{30} +(-0.0315243 - 0.178783i) q^{31} +(-3.02893 - 6.49557i) q^{32} +(7.36584 + 0.0247558i) q^{33} +(-1.43699 - 3.94810i) q^{34} +(2.54003 + 5.34306i) q^{35} +(-7.47668 + 4.24991i) q^{36} +(0.606980 - 0.606980i) q^{37} +(-3.25166 - 4.64385i) q^{38} +(0.0940571 - 0.199949i) q^{39} +(3.07333 - 2.97219i) q^{40} +(-10.1168 + 1.78386i) q^{41} +(-1.96217 - 9.91720i) q^{42} +(-1.07069 - 12.2381i) q^{43} +12.1913 q^{44} +(5.03627 + 4.43125i) q^{45} -11.7073 q^{46} +(-3.19029 + 2.23386i) q^{47} +(2.27746 - 1.30471i) q^{48} +(6.94432 + 0.881145i) q^{49} +(-9.83534 - 4.99339i) q^{50} +(2.99432 - 1.38404i) q^{51} +(0.154561 - 0.331456i) q^{52} +(10.6064 + 2.84198i) q^{53} +(-6.47992 - 9.45579i) q^{54} +(-3.10245 - 8.98898i) q^{55} +(-0.998538 - 4.95922i) q^{56} +(3.41925 - 2.84956i) q^{57} +(-5.88840 - 0.515169i) q^{58} +(3.88857 + 1.41532i) q^{59} +(8.36012 + 7.30611i) q^{60} +(0.393991 - 2.23444i) q^{61} +(0.386845 - 0.103655i) q^{62} +(7.62981 - 2.18769i) q^{63} +(11.0680 - 6.39013i) q^{64} +(-0.283726 - 0.0296126i) q^{65} +(1.36183 + 16.1924i) q^{66} +(1.17970 - 13.4841i) q^{67} +(4.94817 - 2.30737i) q^{68} +(-0.770337 - 9.15944i) q^{69} +(-11.2539 + 6.60945i) q^{70} +(3.39061 - 1.95757i) q^{71} +(-3.25842 - 4.72073i) q^{72} +(4.68183 + 4.68183i) q^{73} +(1.45065 + 1.21724i) q^{74} +(3.25951 - 8.02344i) q^{75} +(5.64331 - 4.73530i) q^{76} +(-10.9354 - 2.64872i) q^{77} +(0.457506 + 0.168262i) q^{78} +(-8.13529 + 9.69526i) q^{79} +(-2.55893 - 2.22119i) q^{80} +(6.97155 - 5.69188i) q^{81} +(-5.86550 - 21.8903i) q^{82} +(1.70228 + 2.43111i) q^{83} +(12.6158 - 3.66326i) q^{84} +(-2.96051 - 3.06125i) q^{85} +(26.6894 - 4.70605i) q^{86} +(0.0155972 - 4.64081i) q^{87} +(0.708686 + 8.10032i) q^{88} +(8.23114 + 14.2567i) q^{89} +(-8.77010 + 11.9200i) q^{90} +(-0.210652 + 0.263731i) q^{91} +(-1.32593 - 15.1554i) q^{92} +(0.106551 + 0.295836i) q^{93} +(-5.52269 - 6.58168i) q^{94} +(-4.92760 - 2.95593i) q^{95} +(7.08601 + 10.1926i) q^{96} +(-5.77479 + 0.505228i) q^{97} +(-0.601272 + 15.4307i) q^{98} +(-12.5789 + 2.13091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8}+O(q^{10}) $ 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8	$ 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8} + 6 q^{10} + 12 q^{11} - 6 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 18 q^{17} - 6 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} + 42 q^{23} - 6 q^{25} - 24 q^{27} - 24 q^{28} + 30 q^{30} - 12 q^{31} + 90 q^{32} - 6 q^{33} - 18 q^{35} - 84 q^{36} - 12 q^{37} - 30 q^{38} - 54 q^{40} - 72 q^{41} - 108 q^{42} - 24 q^{43} - 6 q^{45} - 24 q^{46} - 6 q^{47} - 96 q^{48} - 72 q^{50} - 12 q^{51} - 30 q^{52} - 90 q^{53} - 48 q^{55} - 72 q^{56} - 24 q^{57} - 6 q^{58} + 186 q^{60} + 24 q^{61} - 36 q^{62} - 54 q^{63} + 138 q^{65} - 12 q^{66} - 6 q^{67} + 114 q^{68} - 12 q^{70} - 72 q^{71} + 18 q^{72} - 12 q^{73} - 150 q^{75} - 156 q^{77} - 84 q^{78} + 12 q^{81} - 12 q^{82} - 24 q^{83} - 24 q^{85} - 120 q^{86} - 102 q^{87} - 6 q^{88} + 30 q^{90} - 12 q^{91} + 108 q^{92} + 138 q^{93} - 66 q^{95} - 444 q^{96} - 24 q^{97} - 360 q^{98}+O(q^{100}) $ 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8 + 6 * q^10 + 12 * q^11 - 6 * q^12 - 24 * q^13 - 24 * q^15 - 12 * q^16 - 18 * q^17 - 6 * q^18 - 24 * q^20 - 24 * q^21 - 24 * q^22 + 42 * q^23 - 6 * q^25 - 24 * q^27 - 24 * q^28 + 30 * q^30 - 12 * q^31 + 90 * q^32 - 6 * q^33 - 18 * q^35 - 84 * q^36 - 12 * q^37 - 30 * q^38 - 54 * q^40 - 72 * q^41 - 108 * q^42 - 24 * q^43 - 6 * q^45 - 24 * q^46 - 6 * q^47 - 96 * q^48 - 72 * q^50 - 12 * q^51 - 30 * q^52 - 90 * q^53 - 48 * q^55 - 72 * q^56 - 24 * q^57 - 6 * q^58 + 186 * q^60 + 24 * q^61 - 36 * q^62 - 54 * q^63 + 138 * q^65 - 12 * q^66 - 6 * q^67 + 114 * q^68 - 12 * q^70 - 72 * q^71 + 18 * q^72 - 12 * q^73 - 150 * q^75 - 156 * q^77 - 84 * q^78 + 12 * q^81 - 12 * q^82 - 24 * q^83 - 24 * q^85 - 120 * q^86 - 102 * q^87 - 6 * q^88 + 30 * q^90 - 12 * q^91 + 108 * q^92 + 138 * q^93 - 66 * q^95 - 444 * q^96 - 24 * q^97 - 360 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.192271	+	2.19767i	0.135956	+	1.55399i	0.691425	+	0.722449i	$0.256983\pi$
$2$	0.192271	+	2.19767i	0.135956	+	1.55399i	−0.555468	+	0.831538i	$0.687461\pi$
$3$	−1.70674	+	0.295033i	−0.985386	+	0.170337i
$3$	−1.70674	+	0.295033i	−0.985386	+	0.170337i
$4$	−2.82316	+	0.497800i	−1.41158	+	0.248900i
$5$	1.08549	+	1.95492i	0.485444	+	0.874268i
$5$	1.08549	+	1.95492i	0.485444	+	0.874268i
$6$	−0.976541	−	3.69412i	−0.398671	−	1.50812i
$7$	2.64048	+	0.166853i	0.998009	+	0.0630644i
$7$	2.64048	+	0.166853i	0.998009	+	0.0630644i
$8$	−0.494869	−	1.84688i	−0.174963	−	0.652970i
$9$	2.82591	−	1.00709i	0.941970	−	0.335696i
$10$	−4.08756	+	2.76141i	−1.29260	+	0.873236i
$11$	−4.18808	−	0.738472i	−1.26275	−	0.222658i	−0.498112	−	0.867112i	$-0.665973\pi$
$11$	−4.18808	−	0.738472i	−1.26275	−	0.222658i	−0.764643	+	0.644455i	$0.777084\pi$
$12$	4.67153	−	1.68254i	1.34856	−	0.485708i
$13$	−0.0731741	+	0.104503i	−0.0202948	+	0.0289840i	−0.829171	−	0.558995i	$-0.811187\pi$
$13$	−0.0731741	+	0.104503i	−0.0202948	+	0.0289840i	0.808876	+	0.587979i	$0.200076\pi$
$14$	0.141002	+	5.83499i	0.0376843	+	1.55947i
$15$	−2.42941	−	3.01629i	−0.627270	−	0.778802i
$16$	−1.42399	+	0.518289i	−0.355997	+	0.129572i
$17$	−1.83962	+	0.492925i	−0.446173	+	0.119552i	−0.474908	−	0.880035i	$-0.657519\pi$
$17$	−1.83962	+	0.492925i	−0.446173	+	0.119552i	0.0287350	+	0.999587i	$0.490852\pi$
$18$	2.75659	+	6.01678i	0.649734	+	1.41817i
$19$	−2.22549	+	1.28489i	−0.510563	+	0.294774i	−0.733065	−	0.680159i	$-0.761911\pi$
$19$	−2.22549	+	1.28489i	−0.510563	+	0.294774i	0.222502	+	0.974932i	$0.428578\pi$
$20$	−4.03766	−	4.97871i	−0.902849	−	1.11327i
$21$	−4.55584	+	0.494256i	−0.994167	+	0.107856i
$22$	0.817670	−	9.34601i	0.174328	−	1.99258i
$23$	−0.462525	+	5.28668i	−0.0964431	+	1.10235i	0.781604	+	0.623775i	$0.214402\pi$
$23$	−0.462525	+	5.28668i	−0.0964431	+	1.10235i	−0.878047	+	0.478574i	$0.841154\pi$
$24$	1.38950	+	3.00613i	0.283631	+	0.613624i
$25$	−2.64344	+	4.24408i	−0.528688	+	0.848816i
$26$	−0.243733	−	0.140719i	−0.0478000	−	0.0275974i
$27$	−4.52597	+	2.55257i	−0.871023	+	0.491243i
$28$	−7.53758	+	0.843380i	−1.42447	+	0.159384i
$29$	−0.465271	+	2.63868i	−0.0863986	+	0.489991i	0.910647	+	0.413184i	$0.135583\pi$
$29$	−0.465271	+	2.63868i	−0.0863986	+	0.489991i	−0.997046	+	0.0768065i	$0.975528\pi$
$30$	6.16169	−	5.91898i	1.12497	−	1.08065i
$31$	−0.0315243	−	0.178783i	−0.00566193	−	0.0321104i	0.981846	−	0.189680i	$-0.0607452\pi$
$31$	−0.0315243	−	0.178783i	−0.00566193	−	0.0321104i	−0.987508	+	0.157570i	$0.949634\pi$
$32$	−3.02893	−	6.49557i	−0.535445	−	1.14827i
$33$	7.36584	+	0.0247558i	1.28223	+	0.00430943i
$34$	−1.43699	−	3.94810i	−0.246442	−	0.677093i
$35$	2.54003	+	5.34306i	0.429343	+	0.903142i
$36$	−7.47668	+	4.24991i	−1.24611	+	0.708319i
$37$	0.606980	−	0.606980i	0.0997869	−	0.0997869i	−0.655451	−	0.755238i	$-0.727521\pi$
$37$	0.606980	−	0.606980i	0.0997869	−	0.0997869i	0.755238	+	0.655451i	$0.227521\pi$
$38$	−3.25166	−	4.64385i	−0.527488	−	0.753331i
$39$	0.0940571	−	0.199949i	0.0150612	−	0.0320174i
$40$	3.07333	−	2.97219i	0.485935	−	0.469945i
$41$	−10.1168	+	1.78386i	−1.57997	+	0.278592i	−0.893671	−	0.448723i	$-0.851879\pi$
$41$	−10.1168	+	1.78386i	−1.57997	+	0.278592i	−0.686304	+	0.727315i	$0.740768\pi$
$42$	−1.96217	−	9.91720i	−0.302769	−	1.53026i
$43$	−1.07069	−	12.2381i	−0.163279	−	1.86629i	−0.430418	−	0.902630i	$-0.641634\pi$
$43$	−1.07069	−	12.2381i	−0.163279	−	1.86629i	0.267139	−	0.963658i	$-0.413922\pi$
$44$	12.1913			1.83790
$45$	5.03627	+	4.43125i	0.750762	+	0.660572i
$46$	−11.7073			−1.72615
$47$	−3.19029	+	2.23386i	−0.465351	+	0.325842i	−0.782627	−	0.622491i	$-0.786121\pi$
$47$	−3.19029	+	2.23386i	−0.465351	+	0.325842i	0.317276	+	0.948333i	$0.397232\pi$
$48$	2.27746	−	1.30471i	0.328723	−	0.188318i
$49$	6.94432	+	0.881145i	0.992046	+	0.125878i
$50$	−9.83534	−	4.99339i	−1.39093	−	0.706172i
$51$	2.99432	−	1.38404i	0.419289	−	0.193805i
$52$	0.154561	−	0.331456i	0.0214337	−	0.0459647i
$53$	10.6064	+	2.84198i	1.45690	+	0.390375i	0.898418	−	0.439141i	$-0.144717\pi$
$53$	10.6064	+	2.84198i	1.45690	+	0.390375i	0.558483	+	0.829516i	$0.311384\pi$
$54$	−6.47992	−	9.45579i	−0.881806	−	1.28677i
$55$	−3.10245	−	8.98898i	−0.418335	−	1.21207i
$56$	−0.998538	−	4.95922i	−0.133435	−	0.662704i
$57$	3.41925	−	2.84956i	0.452890	−	0.377434i
$58$	−5.88840	−	0.515169i	−0.773185	−	0.0676450i
$59$	3.88857	+	1.41532i	0.506249	+	0.184259i	0.582502	−	0.812829i	$-0.302074\pi$
$59$	3.88857	+	1.41532i	0.506249	+	0.184259i	−0.0762537	+	0.997088i	$0.524296\pi$
$60$	8.36012	+	7.30611i	1.07929	+	0.943214i
$61$	0.393991	−	2.23444i	0.0504454	−	0.286090i	−0.949141	−	0.314852i	$-0.898045\pi$
$61$	0.393991	−	2.23444i	0.0504454	−	0.286090i	0.999586	+	0.0287615i	$0.00915633\pi$
$62$	0.386845	−	0.103655i	0.0491294	−	0.0131642i
$63$	7.62981	−	2.18769i	0.961266	−	0.275623i
$64$	11.0680	−	6.39013i	1.38350	−	0.798766i
$65$	−0.283726	−	0.0296126i	−0.0351918	−	0.00367299i
$66$	1.36183	+	16.1924i	0.167630	+	1.99315i
$67$	1.17970	−	13.4841i	0.144124	−	1.64734i	−0.488269	−	0.872693i	$-0.662372\pi$
$67$	1.17970	−	13.4841i	0.144124	−	1.64734i	0.632393	−	0.774648i	$-0.282073\pi$
$68$	4.94817	−	2.30737i	0.600053	−	0.279810i
$69$	−0.770337	−	9.15944i	−0.0927377	−	1.10267i
$70$	−11.2539	+	6.60945i	−1.34510	+	0.789980i
$71$	3.39061	−	1.95757i	0.402391	−	0.232321i	−0.285124	−	0.958491i	$-0.592035\pi$
$71$	3.39061	−	1.95757i	0.402391	−	0.232321i	0.687515	+	0.726170i	$0.258701\pi$
$72$	−3.25842	−	4.72073i	−0.384009	−	0.556344i
$73$	4.68183	+	4.68183i	0.547967	+	0.547967i	0.925852	−	0.377886i	$-0.123349\pi$
$73$	4.68183	+	4.68183i	0.547967	+	0.547967i	−0.377886	+	0.925852i	$0.623349\pi$
$74$	1.45065	+	1.21724i	0.168634	+	0.141501i
$75$	3.25951	−	8.02344i	0.376376	−	0.926467i
$76$	5.64331	−	4.73530i	0.647332	−	0.543176i
$77$	−10.9354	−	2.64872i	−1.24620	−	0.301850i
$78$	0.457506	+	0.168262i	0.0518023	+	0.0190519i
$79$	−8.13529	+	9.69526i	−0.915292	+	1.09080i	0.0802774	+	0.996773i	$0.474419\pi$
$79$	−8.13529	+	9.69526i	−0.915292	+	1.09080i	−0.995569	+	0.0940299i	$0.970025\pi$
$80$	−2.55893	−	2.22119i	−0.286098	−	0.248336i
$81$	6.97155	−	5.69188i	0.774616	−	0.632432i
$82$	−5.86550	−	21.8903i	−0.647736	−	2.41738i
$83$	1.70228	+	2.43111i	0.186850	+	0.266849i	0.901638	−	0.432492i	$-0.142366\pi$
$83$	1.70228	+	2.43111i	0.186850	+	0.266849i	−0.714788	+	0.699341i	$0.753477\pi$
$84$	12.6158	−	3.66326i	1.37650	−	0.399695i
$85$	−2.96051	−	3.06125i	−0.321112	−	0.332039i
$86$	26.6894	−	4.70605i	2.87799	−	0.507467i
$87$	0.0155972	−	4.64081i	0.00167220	−	0.497547i
$88$	0.708686	+	8.10032i	0.0755462	+	0.863497i
$89$	8.23114	+	14.2567i	0.872499	+	1.51121i	0.859403	+	0.511298i	$0.170835\pi$
$89$	8.23114	+	14.2567i	0.872499	+	1.51121i	0.0130953	+	0.999914i	$0.495832\pi$
$90$	−8.77010	+	11.9200i	−0.924450	+	1.25648i
$91$	−0.210652	+	0.263731i	−0.0220823	+	0.0276465i
$92$	−1.32593	−	15.1554i	−0.138237	−	1.58006i
$93$	0.106551	+	0.295836i	0.0110488	+	0.0306767i
$94$	−5.52269	−	6.58168i	−0.569622	−	0.678849i
$95$	−4.92760	−	2.95593i	−0.505561	−	0.303272i
$96$	7.08601	+	10.1926i	0.723213	+	1.04028i
$97$	−5.77479	+	0.505228i	−0.586341	+	0.0512982i	−0.376467	−	0.926430i	$-0.622861\pi$
$97$	−5.77479	+	0.505228i	−0.586341	+	0.0512982i	−0.209874	+	0.977728i	$0.567305\pi$
$98$	−0.601272	+	15.4307i	−0.0607377	+	1.55874i
$99$	−12.5789	+	2.13091i	−1.26422	+	0.214165i
$100$	5.35015	−	13.2976i	0.535015	−	1.32976i
$101$	−6.53154	+	7.78399i	−0.649913	+	0.774536i	−0.985901	−	0.167331i	$-0.946485\pi$
$101$	−6.53154	+	7.78399i	−0.649913	+	0.774536i	0.335988	+	0.941866i	$0.390930\pi$
$102$	3.61739	+	6.31441i	0.358175	+	0.625220i
$103$	−2.41279	+	3.44582i	−0.237739	+	0.339527i	−0.920237	−	0.391360i	$-0.872005\pi$
$103$	−2.41279	+	3.44582i	−0.237739	+	0.339527i	0.682498	+	0.730887i	$0.260893\pi$
$104$	0.229217	+	0.0834280i	0.0224765	+	0.00818079i
$105$	−5.91154	−	8.36981i	−0.576907	−	0.816810i
$106$	−4.20642	+	23.8558i	−0.408563	+	2.31708i
$107$	−3.95536	+	1.05984i	−0.382379	+	0.102458i	−0.444888	−	0.895586i	$-0.646756\pi$
$107$	−3.95536	+	1.05984i	−0.382379	+	0.102458i	0.0625089	+	0.998044i	$0.480090\pi$
$108$	11.5069	−	9.45935i	1.10725	−	0.910227i
$109$	2.74723	−	1.58611i	0.263137	−	0.151922i	−0.362628	−	0.931934i	$-0.618120\pi$
$109$	2.74723	−	1.58611i	0.263137	−	0.151922i	0.625765	+	0.780012i	$0.284787\pi$
$110$	19.1583	−	8.54648i	1.82667	−	0.814875i
$111$	−0.856877	+	1.21504i	−0.0813312	+	0.115326i
$112$	−3.84650	+	1.13094i	−0.363460	+	0.106864i
$113$	0.240874	−	2.75320i	0.0226595	−	0.259000i	−0.976412	−	0.215916i	$-0.930726\pi$
$113$	0.240874	−	2.75320i	0.0226595	−	0.259000i	0.999071	−	0.0430836i	$-0.0137182\pi$
$114$	6.91981	+	6.96648i	0.648100	+	0.652471i
$115$	−10.8371	+	4.83442i	−1.01057	+	0.450812i
$116$		−	7.68104i		−	0.713167i
$117$	−0.101539	+	0.369010i	−0.00938731	+	0.0341150i
$118$	−2.36275	+	8.81791i	−0.217509	+	0.811755i
$119$	−4.93973	+	0.994614i	−0.452825	+	0.0911761i
$120$	−4.36847	+	5.97948i	−0.398785	+	0.545850i
$121$	6.65809	+	2.42335i	0.605281	+	0.220304i
$122$	4.98630	+	0.436245i	0.451439	+	0.0394958i
$123$	16.7404	−	6.02937i	1.50943	−	0.543650i
$124$	0.177997	+	0.489041i	0.0159846	+	0.0439172i
$125$	−11.1663	−	0.560822i	−0.998741	−	0.0501615i
$126$	6.27481	+	16.3472i	0.559004	+	1.45632i
$127$	1.92064	+	7.16793i	0.170429	+	0.636051i	0.997285	+	0.0736371i	$0.0234607\pi$
$127$	1.92064	+	7.16793i	0.170429	+	0.636051i	−0.826856	+	0.562414i	$0.809873\pi$
$128$	7.94972	+	11.3534i	0.702663	+	1.00351i
$129$	5.43803	+	20.5713i	0.478791	+	1.81120i
$130$	0.0105264	−	0.629228i	0.000923227	−	0.0551870i
$131$	−5.06210	−	6.03277i	−0.442277	−	0.527086i	0.498145	−	0.867094i	$-0.334015\pi$
$131$	−5.06210	−	6.03277i	−0.442277	−	0.527086i	−0.940423	+	0.340008i	$0.889570\pi$
$132$	−20.8073	+	3.59682i	−1.81104	+	0.313063i
$133$	−6.09076	+	3.02140i	−0.528136	+	0.261988i
$134$	29.8603			2.57954
$135$	−9.90296	−	6.07713i	−0.852311	−	0.523036i
$136$	1.82074	+	3.15362i	0.156127	+	0.270420i
$137$	14.4328	+	6.73011i	1.23308	+	0.574992i	0.926299	−	0.376789i	$-0.122972\pi$
$137$	14.4328	+	6.73011i	1.23308	+	0.574992i	0.306776	+	0.951782i	$0.400750\pi$
$138$	19.9813	−	3.45404i	1.70092	−	0.294028i
$139$	−7.80023	+	21.4310i	−0.661607	+	1.81775i	−0.0921223	+	0.995748i	$0.529365\pi$
$139$	−7.80023	+	21.4310i	−0.661607	+	1.81775i	−0.569485	+	0.822002i	$0.692857\pi$
$140$	−9.83068	−	13.8199i	−0.830844	−	1.16799i
$141$	4.78592	−	4.75386i	0.403047	−	0.400347i
$142$	4.95400	+	7.07505i	0.415731	+	0.593725i
$143$	0.383632	−	0.383632i	0.0320809	−	0.0320809i
$144$	−3.50210	+	2.89872i	−0.291842	+	0.241560i
$145$	−5.66346	+	1.95468i	−0.470325	+	0.162328i
$146$	−9.38893	+	11.1893i	−0.777033	+	0.926032i
$147$	−12.1121	+	0.544920i	−0.998989	+	0.0449443i
$148$	−1.41145	+	2.01576i	−0.116020	+	0.165694i
$149$	−1.52867	−	0.556392i	−0.125234	−	0.0455814i	0.278643	−	0.960395i	$-0.410115\pi$
$149$	−1.52867	−	0.556392i	−0.125234	−	0.0455814i	−0.403877	+	0.914813i	$0.632338\pi$
$150$	18.2596	+	5.62065i	1.49089	+	0.458925i
$151$	−0.258696	+	1.46714i	−0.0210524	+	0.119394i	−0.993523	−	0.113632i	$-0.963752\pi$
$151$	−0.258696	+	1.46714i	−0.0210524	+	0.119394i	0.972471	+	0.233026i	$0.0748627\pi$
$152$	3.47436	+	3.47436i	0.281808	+	0.281808i
$153$	−4.70218	+	3.24562i	−0.380149	+	0.262393i
$154$	3.71845	−	24.5416i	0.299641	−	1.97762i
$155$	0.315288	−	0.255694i	0.0253245	−	0.0205379i
$156$	−0.166004	+	0.611310i	−0.0132910	+	0.0489440i
$157$	8.05037	−	3.75395i	0.642490	−	0.299598i	−0.0739342	−	0.997263i	$-0.523555\pi$
$157$	8.05037	−	3.75395i	0.642490	−	0.299598i	0.716424	+	0.697665i	$0.245778\pi$
$158$	−22.8712	−	16.0146i	−1.81953	−	1.27405i
$159$	−18.9408	−	1.72127i	−1.50210	−	0.136506i
$160$	9.41047	−	12.9722i	0.743963	−	1.02554i
$161$	−2.10339	+	13.8822i	−0.165770	+	1.09407i
$162$	13.8493	+	14.2268i	1.08810	+	1.11776i
$163$	−0.167712	+	0.0449382i	−0.0131362	+	0.00351983i	−0.265381	−	0.964144i	$-0.585498\pi$
$163$	−0.167712	+	0.0449382i	−0.0131362	+	0.00351983i	0.252245	+	0.967663i	$0.418831\pi$
$164$	27.6733	−	10.0723i	2.16092	−	0.786511i
$165$	7.94712	+	14.4265i	0.618683	+	1.12310i
$166$	−5.01548	+	4.20849i	−0.389277	+	0.326642i
$167$	−22.8982	−	2.00334i	−1.77192	−	0.155023i	−0.846109	−	0.533011i	$-0.821061\pi$
$167$	−22.8982	−	2.00334i	−1.77192	−	0.155023i	−0.925811	+	0.377988i	$0.876616\pi$
$168$	3.16738	+	8.16949i	0.244368	+	0.630290i
$169$	4.44070	+	12.2007i	0.341592	+	0.938516i
$170$	6.15839	−	7.09481i	0.472327	−	0.544147i
$171$	−4.99505	+	5.87225i	−0.381981	+	0.449062i
$172$	9.11485	+	34.0171i	0.695001	+	2.59378i
$173$	−2.78531	+	5.97312i	−0.211763	+	0.454128i	−0.983285	−	0.182076i	$-0.941718\pi$
$173$	−2.78531	+	5.97312i	−0.211763	+	0.454128i	0.771521	+	0.636204i	$0.219496\pi$
$174$	10.2020	−	0.858016i	0.773408	−	0.0650460i
$175$	−7.68810	+	10.7654i	−0.581165	+	0.813785i
$176$	6.34652	−	1.11906i	0.478387	−	0.0843526i
$177$	−7.05434	−	1.26833i	−0.530236	−	0.0953336i
$178$	−29.7490	+	20.8305i	−2.22978	+	1.56131i
$179$	5.03410	−	8.71932i	0.376266	−	0.651713i	−0.614249	−	0.789112i	$-0.710541\pi$
$179$	5.03410	−	8.71932i	0.376266	−	0.651713i	0.990516	+	0.137399i	$0.0438744\pi$
$180$	−16.4241	−	10.0031i	−1.22418	−	0.745587i
$181$	1.31310	−	2.27436i	0.0976020	−	0.169052i	−0.813090	−	0.582139i	$-0.802216\pi$
$181$	1.31310	−	2.27436i	0.0976020	−	0.169052i	0.910692	+	0.413087i	$0.135549\pi$
$182$	−0.620094	−	0.412235i	−0.0459645	−	0.0305569i
$183$	−0.0132078	+	3.92984i	−0.000976345	+	0.290502i
$184$	9.99274	−	1.76199i	0.736674	−	0.129896i
$185$	1.84547	+	0.527730i	0.135681	+	0.0387995i
$186$	−0.629662	+	0.291044i	−0.0461690	+	0.0213404i
$187$	8.06849	−	0.705902i	0.590027	−	0.0516206i
$188$	7.89468	−	7.89468i	0.575779	−	0.575779i
$189$	−12.3766	+	5.98486i	−0.900269	+	0.435335i
$190$	5.54873	−	11.3976i	0.402547	−	0.826866i
$191$	5.27702	−	6.28891i	0.381832	−	0.455049i	−0.540560	−	0.841306i	$-0.681788\pi$
$191$	5.27702	−	6.28891i	0.381832	−	0.455049i	0.922391	+	0.386256i	$0.126232\pi$
$192$	−17.0049	+	14.1717i	−1.22722	+	1.02276i
$193$	6.24909	−	8.92462i	0.449819	−	0.642409i	−0.528641	−	0.848846i	$-0.677298\pi$
$193$	6.24909	−	8.92462i	0.449819	−	0.642409i	0.978460	+	0.206437i	$0.0661869\pi$
$194$	−2.22065	−	12.5939i	−0.159433	−	0.904191i
$195$	0.492982	−	0.0331675i	0.0353032	−	0.00237517i
$196$	−20.0436	+	0.969266i	−1.43168	+	0.0692333i
$197$	21.3104	−	5.71010i	1.51830	−	0.406828i	0.599119	−	0.800660i	$-0.295518\pi$
$197$	21.3104	−	5.71010i	1.51830	−	0.406828i	0.919182	+	0.393832i	$0.128851\pi$
$198$	−7.10159	−	27.2345i	−0.504688	−	1.93547i
$199$	−3.52436	−	2.03479i	−0.249835	−	0.144242i	0.369854	−	0.929090i	$-0.379408\pi$
$199$	−3.52436	−	2.03479i	−0.249835	−	0.144242i	−0.619689	+	0.784848i	$0.712741\pi$
$200$	9.14645	+	2.78184i	0.646752	+	0.196706i
$201$	1.96480	+	23.3618i	0.138586	+	1.64782i
$202$	−18.3624	−	12.8575i	−1.29198	−	0.904652i
$203$	−1.66881	+	6.88977i	−0.117128	+	0.483567i
$204$	−7.76448	+	5.39795i	−0.543622	+	0.377932i
$205$	−14.4689	−	17.8411i	−1.01055	−	1.24608i
$206$	−8.03668	−	4.63998i	−0.559942	−	0.323283i
$207$	4.01710	+	15.4055i	0.279208	+	1.07076i
$208$	0.0500360	−	0.186737i	0.00346937	−	0.0129479i
$209$	10.2694	−	3.73776i	0.710349	−	0.258546i
$210$	17.2574	−	14.6009i	1.19088	−	1.00756i
$211$	7.13070	−	5.98336i	0.490897	−	0.411912i	−0.363450	−	0.931614i	$-0.618401\pi$
$211$	7.13070	−	5.98336i	0.490897	−	0.411912i	0.854348	+	0.519702i	$0.173957\pi$
$212$	−31.3583	−	2.74350i	−2.15370	−	0.188424i
$213$	−5.20933	+	4.34140i	−0.356938	+	0.297468i
$214$	−3.08967	−	8.48879i	−0.211205	−	0.580282i
$215$	22.7622	−	15.3774i	1.55237	−	1.04873i
$216$	6.95405	+	7.09571i	0.473163	+	0.482802i
$217$	−0.0534090	−	0.477334i	−0.00362564	−	0.0324036i
$218$	4.01396	+	5.73254i	0.271860	+	0.388256i
$219$	−9.37195	−	6.60936i	−0.633298	−	0.446619i
$220$	13.2334	+	23.8330i	0.892199	+	1.60682i
$221$	0.0831002	−	0.228316i	0.00558992	−	0.0153582i
$222$	−2.83500	−	1.64952i	−0.190273	−	0.110708i
$223$	13.9381	+	6.49943i	0.933362	+	0.435234i	0.828964	−	0.559302i	$-0.188931\pi$
$223$	13.9381	+	6.49943i	0.933362	+	0.435234i	0.104398	+	0.994536i	$0.466708\pi$
$224$	−6.91405	−	17.6568i	−0.461965	−	1.17975i
$225$	−3.19596	+	14.6556i	−0.213064	+	0.977038i
$226$	6.09694			0.405563
$227$	20.9572	−	14.6744i	1.39098	−	0.973974i	0.392449	−	0.919774i	$-0.371628\pi$
$227$	20.9572	−	14.6744i	1.39098	−	0.973974i	0.998530	−	0.0541997i	$-0.0172608\pi$
$228$	−8.23458	+	9.74688i	−0.545348	+	0.645503i
$229$	1.14999	−	3.15958i	0.0759937	−	0.208791i	−0.895879	−	0.444298i	$-0.853453\pi$
$229$	1.14999	−	3.15958i	0.0759937	−	0.208791i	0.971873	+	0.235508i	$0.0756752\pi$
$230$	−12.7081	−	22.8869i	−0.837949	−	1.50912i
$231$	19.4453	+	1.29438i	1.27940	+	0.0851638i
$232$	5.10357	−	0.446504i	0.335066	−	0.0293144i
$233$	13.6426	−	13.6426i	0.893759	−	0.893759i	−0.101116	−	0.994875i	$-0.532241\pi$
$233$	13.6426	−	13.6426i	0.893759	−	0.893759i	0.994875	+	0.101116i	$0.0322412\pi$
$234$	−0.830485	−	0.152200i	−0.0542905	−	0.00994961i
$235$	−7.83004	−	3.81193i	−0.510775	−	0.248663i
$236$	−11.6826	−	2.05996i	−0.760473	−	0.134092i
$237$	11.0244	−	18.9475i	0.716111	−	1.23077i
$238$	−3.13560	−	10.6647i	−0.203251	−	0.691287i
$239$	26.0992	+	9.49934i	1.68822	+	0.614461i	0.994399	−	0.105688i	$-0.0337046\pi$
$239$	26.0992	+	9.49934i	1.68822	+	0.614461i	0.693819	+	0.720149i	$0.255927\pi$
$240$	5.02275	+	3.03602i	0.324217	+	0.195974i
$241$	−14.4196	+	5.24830i	−0.928848	+	0.338073i	−0.761753	−	0.647868i	$-0.775661\pi$
$241$	−14.4196	+	5.24830i	−0.928848	+	0.338073i	−0.167095	+	0.985941i	$0.553439\pi$
$242$	−4.04556	+	15.0982i	−0.260058	+	0.970550i
$243$	−10.2193	+	11.7714i	−0.655569	+	0.755135i
$244$			6.50431i			0.416396i
$245$	5.81540	+	14.5321i	0.371532	+	0.928420i
$246$	16.4692	+	35.6306i	1.05004	+	2.27172i
$247$	0.0285731	−	0.326592i	0.00181806	−	0.0207806i
$248$	−0.314590	+	0.146696i	−0.0199765	+	0.00931519i
$249$	−3.62261	−	3.64705i	−0.229574	−	0.231122i
$250$	−0.914448	−	24.6476i	−0.0578348	−	1.55885i
$251$	−12.5196	−	7.22819i	−0.790230	−	0.456240i	0.0498135	−	0.998759i	$-0.484137\pi$
$251$	−12.5196	−	7.22819i	−0.790230	−	0.456240i	−0.840044	+	0.542519i	$0.817471\pi$
$252$	−20.4512	+	9.97432i	−1.28830	+	0.628323i
$253$	5.84116	−	21.7995i	0.367231	−	1.37052i
$254$	−15.3835	+	5.59912i	−0.965244	+	0.351320i
$255$	5.95599	+	4.35130i	0.372978	+	0.272489i
$256$	−3.84197	+	3.22379i	−0.240123	+	0.201487i
$257$	8.84196	+	18.9616i	0.551546	+	1.18280i	0.962536	+	0.271155i	$0.0874056\pi$
$257$	8.84196	+	18.9616i	0.551546	+	1.18280i	−0.410989	+	0.911640i	$0.634817\pi$
$258$	−44.1633	+	15.9062i	−2.74949	+	0.990279i
$259$	1.70400	−	1.50145i	0.105881	−	0.0932953i
$260$	0.815745	−	0.0576374i	0.0505903	−	0.00357452i
$261$	1.34257	+	7.92525i	0.0831031	+	0.490560i
$262$	12.2847	−	12.2847i	0.758954	−	0.758954i
$263$	−30.6639	+	2.68274i	−1.89082	+	0.165425i	−0.972882	−	0.231303i	$-0.925701\pi$
$263$	−30.6639	+	2.68274i	−1.89082	+	0.165425i	−0.917936	+	0.396728i	$0.870146\pi$
$264$	−3.59940	−	13.6160i	−0.221528	−	0.838010i
$265$	5.95726	+	23.8196i	0.365952	+	1.46323i
$266$	−7.81111	−	12.8046i	−0.478930	−	0.785097i
$267$	−18.2546	−	21.9041i	−1.11716	−	1.34051i
$268$	3.38187	+	38.6550i	0.206581	+	2.36123i
$269$	9.42540	+	16.3253i	0.574677	+	0.995369i	0.996077	+	0.0884943i	$0.0282055\pi$
$269$	9.42540	+	16.3253i	0.574677	+	0.995369i	−0.421400	+	0.906875i	$0.638461\pi$
$270$	11.4515	−	22.9319i	0.696914	−	1.39559i
$271$	−8.64270	+	14.9696i	−0.525007	+	0.909339i	0.474569	+	0.880218i	$0.342604\pi$
$271$	−8.64270	+	14.9696i	−0.525007	+	0.909339i	−0.999576	+	0.0291203i	$0.990729\pi$
$272$	2.36412	−	1.65537i	0.143346	−	0.100372i
$273$	0.281718	−	0.512268i	0.0170504	−	0.0310039i
$274$	−12.0156	+	33.0125i	−0.725886	+	1.99436i
$275$	14.2051	−	15.8225i	0.856599	−	0.954131i
$276$	6.73436	+	25.4751i	0.405361	+	1.53342i
$277$	−16.5664	+	1.44937i	−0.995378	+	0.0870843i	−0.573189	−	0.819423i	$-0.694294\pi$
$277$	−16.5664	+	1.44937i	−0.995378	+	0.0870843i	−0.422189	+	0.906508i	$0.638738\pi$
$278$	−48.5979	−	13.0218i	−2.91471	−	0.780994i
$279$	−0.269135	−	0.473478i	−0.0161127	−	0.0283464i
$280$	8.61099	−	7.33523i	0.514605	−	0.438364i
$281$	−10.1467	+	12.0923i	−0.605298	+	0.721367i	−0.978468	−	0.206396i	$-0.933826\pi$
$281$	−10.1467	+	12.0923i	−0.605298	+	0.721367i	0.373170	+	0.927763i	$0.378271\pi$
$282$	11.3676	+	9.60384i	0.676931	+	0.571900i
$283$	−7.66872	−	0.670926i	−0.455858	−	0.0398824i	−0.143085	−	0.989710i	$-0.545702\pi$
$283$	−7.66872	−	0.670926i	−0.455858	−	0.0398824i	−0.312773	+	0.949828i	$0.601258\pi$
$284$	−8.59776	+	7.21438i	−0.510183	+	0.428095i
$285$	9.28222	+	3.59120i	0.549831	+	0.212724i
$286$	0.916858	+	0.769335i	0.0542149	+	0.0454917i
$287$	−27.0108	+	3.02224i	−1.59440	+	0.178397i
$288$	−15.1011	−	15.3055i	−0.889842	−	0.901885i
$289$	−11.5812	+	6.68641i	−0.681247	+	0.393318i
$290$	−5.38467	−	12.0706i	−0.316199	−	0.708809i
$291$	9.70699	−	2.56605i	0.569034	−	0.150424i
$292$	−15.5482	−	10.8870i	−0.909888	−	0.637111i
$293$	−26.5984	+	12.4030i	−1.55389	+	0.724593i	−0.994542	−	0.104337i	$-0.966728\pi$
$293$	−26.5984	+	12.4030i	−1.55389	+	0.724593i	−0.559353	+	0.828930i	$0.688950\pi$
$294$	−3.52636	−	26.5136i	−0.205662	−	1.54631i
$295$	1.45414	+	9.13816i	0.0846634	+	0.532044i
$296$	−1.42139	−	0.820642i	−0.0826168	−	0.0476988i
$297$	20.8401	−	7.34809i	1.20927	−	0.426379i
$298$	0.928845	−	3.46650i	0.0538065	−	0.200809i
$299$	−0.518632	−	0.435184i	−0.0299932	−	0.0251673i
$300$	−5.20807	+	24.2741i	−0.300688	+	1.40146i
$301$	−0.785190	−	32.4931i	−0.0452576	−	1.87287i
$302$	−3.27402	−	0.286440i	−0.188399	−	0.0164828i
$303$	8.85110	−	15.2122i	0.508482	−	0.873921i
$304$	2.50313	−	2.98311i	0.143564	−	0.171093i
$305$	4.79582	−	1.65523i	0.274608	−	0.0947781i
$306$	−8.03689	−	9.70980i	−0.459438	−	0.555072i
$307$	27.3222	+	7.32095i	1.55936	+	0.417829i	0.932460	−	0.361273i	$-0.117658\pi$
$307$	27.3222	+	7.32095i	1.55936	+	0.417829i	0.626898	+	0.779102i	$0.284324\pi$
$308$	32.1908	+	2.03415i	1.83424	+	0.115906i
$309$	3.10137	−	6.59297i	0.176431	−	0.375061i
$310$	0.622552	+	0.643736i	0.0353586	+	0.0365617i
$311$	17.5739	+	20.9437i	0.996524	+	1.18761i	0.982224	+	0.187713i	$0.0601075\pi$
$311$	17.5739	+	20.9437i	0.996524	+	1.18761i	0.0142999	+	0.999898i	$0.495448\pi$
$312$	−0.415827	−	0.0747633i	−0.0235416	−	0.00423264i
$313$	17.7697	+	8.28614i	1.00440	+	0.468360i	0.854005	−	0.520265i	$-0.174167\pi$
$313$	17.7697	+	8.28614i	1.00440	+	0.468360i	0.150397	+	0.988626i	$0.451945\pi$
$314$	9.79779	+	16.9703i	0.552921	+	0.957688i
$315$	12.5588	+	12.5410i	0.707609	+	0.706604i
$316$	18.1410	−	31.4211i	1.02051	−	1.76757i
$317$	−6.64443	+	4.65248i	−0.373188	+	0.261309i	−0.745091	−	0.666962i	$-0.767594\pi$
$317$	−6.64443	+	4.65248i	−0.373188	+	0.261309i	0.371903	+	0.928271i	$0.378705\pi$
$318$	0.141012	−	41.9566i	0.00790753	−	2.35281i
$319$	3.89719	−	10.7074i	0.218201	−	0.599501i
$320$	24.5064	+	14.7007i	1.36995	+	0.821796i
$321$	6.43808	−	2.97582i	0.359338	−	0.166094i
$322$	−30.9130	−	1.95340i	−1.72271	−	0.108859i
$323$	3.46070	−	3.46070i	0.192559	−	0.192559i
$324$	−16.8484	+	19.5395i	−0.936022	+	1.08553i
$325$	−0.250090	−	0.586805i	−0.0138725	−	0.0325501i
$326$	−0.131005	−	0.359934i	−0.00725571	−	0.0199349i
$327$	−4.22085	+	3.51760i	−0.233413	+	0.194524i
$328$	8.30105	+	17.8017i	0.458349	+	0.982932i
$329$	−8.79663	+	5.36617i	−0.484974	+	0.295847i
$330$	−30.1767	+	20.2389i	−1.66117	+	1.11412i
$331$	2.11914	−	12.0182i	0.116478	−	0.660581i	−0.869529	−	0.493881i	$-0.835578\pi$
$331$	2.11914	−	12.0182i	0.116478	−	0.660581i	0.986008	−	0.166700i	$-0.0533111\pi$
$332$	−6.01604	−	6.01604i	−0.330173	−	0.330173i
$333$	1.10399	−	2.32655i	0.0604982	−	0.127494i
$334$		−	50.7079i		−	2.77461i
$335$	27.6408	−	12.3305i	1.51018	−	0.673689i
$336$	6.23130	−	3.06506i	0.339945	−	0.167213i
$337$	25.3535	+	17.7527i	1.38109	+	0.967051i	0.999080	+	0.0428932i	$0.0136575\pi$
$337$	25.3535	+	17.7527i	1.38109	+	0.967051i	0.382012	+	0.924157i	$0.375231\pi$
$338$	−25.9593	+	12.1050i	−1.41200	+	0.658426i
$339$	0.401177	+	4.77006i	0.0217889	+	0.259074i
$340$	9.88189	+	7.16866i	0.535921	+	0.388775i
$341$			0.772039i			0.0418083i
$342$	−13.8657	−	9.84839i	−0.749769	−	0.532540i
$343$	18.1894	+	3.48533i	0.982133	+	0.188190i
$344$	−22.0724	+	8.03368i	−1.19006	+	0.433147i
$345$	17.0698	−	11.4484i	0.919007	−	0.616361i
$346$	−13.6625	−	4.97274i	−0.734499	−	0.267336i
$347$	−17.7052	+	25.2856i	−0.950463	+	1.35740i	−0.0165648	+	0.999863i	$0.505273\pi$
$347$	−17.7052	+	25.2856i	−0.950463	+	1.35740i	−0.933898	+	0.357539i	$0.883616\pi$
$348$	2.26616	+	13.1095i	0.121479	+	0.702744i
$349$	−22.8884	−	4.03584i	−1.22519	−	0.216033i	−0.476630	−	0.879104i	$-0.658142\pi$
$349$	−22.8884	−	4.03584i	−1.22519	−	0.216033i	−0.748557	+	0.663071i	$0.769253\pi$
$350$	−25.1369	−	14.8260i	−1.34362	−	0.792484i
$351$	0.0644308	−	0.659761i	0.00343906	−	0.0352155i
$352$	7.88864	+	29.4408i	0.420466	+	1.56920i
$353$	6.17217	−	13.2363i	0.328512	−	0.704495i	−0.670798	−	0.741640i	$-0.734048\pi$
$353$	6.17217	−	13.2363i	0.328512	−	0.704495i	0.999310	+	0.0371444i	$0.0118262\pi$
$354$	1.43102	−	15.7470i	0.0760581	−	0.836941i
$355$	7.50735	+	4.50346i	0.398449	+	0.239019i
$356$	−30.3348	−	36.1517i	−1.60774	−	1.91603i
$357$	8.13739	−	3.15493i	0.430676	−	0.166977i
$358$	20.1301	+	9.38681i	1.06391	+	0.496109i
$359$	11.5318	+	19.9736i	0.608623	+	1.05417i	0.991468	+	0.130353i	$0.0416111\pi$
$359$	11.5318	+	19.9736i	0.608623	+	1.05417i	−0.382845	+	0.923813i	$0.625056\pi$
$360$	5.69169	−	11.4943i	0.299978	−	0.605800i
$361$	−6.19813	+	10.7355i	−0.326217	+	0.565025i
$362$	5.25075	+	2.44847i	0.275973	+	0.128689i
$363$	−12.0786	−	2.17166i	−0.633961	−	0.113983i
$364$	0.463419	−	0.849417i	0.0242898	−	0.0445215i
$365$	−4.07055	+	14.2347i	−0.213062	+	0.745077i
$366$	−8.63902	+	0.726568i	−0.451569	+	0.0379783i
$367$	−5.11471	−	7.30456i	−0.266986	−	0.381295i	0.663165	−	0.748473i	$-0.269213\pi$
$367$	−5.11471	−	7.30456i	−0.266986	−	0.381295i	−0.930151	+	0.367178i	$0.880324\pi$
$368$	−2.08140	−	7.76789i	−0.108500	−	0.404929i
$369$	−26.7926	+	15.2295i	−1.39477	+	0.792817i
$370$	−0.804946	+	4.15719i	−0.0418471	+	0.216122i
$371$	27.5318	+	9.27390i	1.42938	+	0.481477i
$372$	−0.448077	−	0.782151i	−0.0232317	−	0.0405526i
$373$	1.47694	−	2.10929i	0.0764731	−	0.109215i	−0.779093	−	0.626908i	$-0.784320\pi$
$373$	1.47694	−	2.10929i	0.0764731	−	0.109215i	0.855566	+	0.517693i	$0.173209\pi$
$374$	3.10268	+	17.5961i	0.160436	+	0.909875i
$375$	19.2234	−	2.33724i	0.992690	−	0.120695i
$376$	5.70444	+	4.78660i	0.294184	+	0.246850i
$377$	−0.241706	−	0.241706i	−0.0124485	−	0.0124485i
$378$	−15.5324	−	26.0491i	−0.798901	−	1.33982i
$379$		−	9.42082i		−	0.483915i	−0.970287	−	0.241957i	$-0.922211\pi$
$379$		−	9.42082i		−	0.483915i	0.970287	−	0.241957i	$-0.0777894\pi$
$380$	15.3829	+	5.89212i	0.789125	+	0.302260i
$381$	−5.39281	−	11.6671i	−0.276282	−	0.597725i
$382$	14.8355	+	10.3880i	0.759053	+	0.531494i
$383$	−2.41542	−	1.69129i	−0.123422	−	0.0864211i	0.510235	−	0.860035i	$-0.329558\pi$
$383$	−2.41542	−	1.69129i	−0.123422	−	0.0864211i	−0.633658	+	0.773614i	$0.718447\pi$
$384$	−16.9177	−	17.0318i	−0.863328	−	0.869151i
$385$	−6.69214	−	24.2529i	−0.341063	−	1.23604i
$386$	20.8149	+	12.0175i	1.05945	+	0.611674i
$387$	−15.3505	−	33.5054i	−0.780310	−	1.70318i
$388$	16.0517	−	4.30103i	0.814900	−	0.218352i
$389$	−1.28986	+	7.31519i	−0.0653987	+	0.370895i	0.934490	+	0.355989i	$0.115856\pi$
$389$	−1.28986	+	7.31519i	−0.0653987	+	0.370895i	−0.999889	+	0.0149057i	$0.995255\pi$
$390$	0.167677	+	1.07703i	0.00849067	+	0.0545377i
$391$	−1.75507	−	9.95347i	−0.0887575	−	0.503369i
$392$	−1.80916	−	13.2614i	−0.0913766	−	0.669800i
$393$	10.4195	+	8.80288i	0.525596	+	0.444046i
$394$	16.6463	+	45.7352i	0.838627	+	2.30411i
$395$	−27.7842	−	5.37978i	−1.39798	−	0.270686i
$396$	34.4514	−	12.2777i	1.73125	−	0.616976i
$397$	21.0579	+	5.64243i	1.05686	+	0.283186i	0.745085	−	0.666969i	$-0.232409\pi$
$397$	21.0579	+	5.64243i	1.05686	+	0.283186i	0.311778	+	0.950155i	$0.399075\pi$
$398$	3.79416	−	8.13661i	0.190184	−	0.407851i
$399$	9.50393	−	6.95371i	0.475791	−	0.348121i
$400$	1.56456	−	7.41359i	0.0782281	−	0.370679i
$401$	2.46029	+	2.93206i	0.122861	+	0.146420i	0.823969	−	0.566635i	$-0.191755\pi$
$401$	2.46029	+	2.93206i	0.122861	+	0.146420i	−0.701108	+	0.713055i	$0.747311\pi$
$402$	−50.9638	+	8.80978i	−2.54184	+	0.439392i
$403$	0.0209902	+	0.00978791i	0.00104560	+	0.000487570i
$404$	14.5647	−	25.2269i	0.724623	−	1.25508i
$405$	18.6947	+	7.45037i	0.928947	+	0.370212i
$406$	−15.4623	−	2.34279i	−0.767380	−	0.116271i
$407$	−2.99032	+	2.09385i	−0.148225	+	0.103788i
$408$	−4.03795	−	4.84522i	−0.199908	−	0.239874i
$409$	22.6384	−	3.99177i	1.11940	−	0.197380i	0.416822	−	0.908988i	$-0.363144\pi$
$409$	22.6384	−	3.99177i	1.11940	−	0.197380i	0.702576	+	0.711608i	$0.252033\pi$
$410$	36.4270	−	35.2282i	1.79900	−	1.73980i
$411$	−26.6186	−	7.22840i	−1.31300	−	0.356551i
$412$	5.09637	−	10.9292i	0.251080	−	0.538443i
$413$	10.0316	+	4.38596i	0.493621	+	0.215819i
$414$	−33.0838	+	11.7903i	−1.62598	+	0.579461i
$415$	−2.90483	+	5.96678i	−0.142593	+	0.292897i
$416$	0.900449	+	0.158774i	0.0441482	+	0.00778451i
$417$	6.99011	−	38.8784i	0.342307	−	1.90388i
$418$	10.1889	+	21.8501i	0.498353	+	1.06872i
$419$	−5.17645	−	29.3571i	−0.252886	−	1.43419i	−0.801442	−	0.598073i	$-0.795933\pi$
$419$	−5.17645	−	29.3571i	−0.252886	−	1.43419i	0.548556	−	0.836114i	$-0.315178\pi$
$420$	20.8557	+	20.6866i	1.01766	+	1.00940i
$421$	−13.7480	−	11.5360i	−0.670038	−	0.562229i	0.243039	−	0.970017i	$-0.421856\pi$
$421$	−13.7480	−	11.5360i	−0.670038	−	0.562229i	−0.913077	+	0.407788i	$0.866300\pi$
$422$	14.5205	+	14.5205i	0.706846	+	0.706846i
$423$	−6.76577	+	9.52560i	−0.328963	+	0.463150i
$424$		−	20.9951i		−	1.01961i
$425$	2.77091	−	9.11051i	0.134409	−	0.441925i
$426$	−10.5426	−	10.6137i	−0.510789	−	0.514234i
$427$	1.41315	−	5.83426i	0.0683871	−	0.282339i
$428$	10.6390	−	4.96106i	0.514257	−	0.239802i
$429$	−0.541576	+	0.767944i	−0.0261475	+	0.0370767i
$430$	38.1709	+	47.0672i	1.84076	+	2.26978i
$431$	−15.4453	+	8.91734i	−0.743973	+	0.429533i	−0.823512	−	0.567299i	$-0.807989\pi$
$431$	−15.4453	+	8.91734i	−0.743973	+	0.429533i	0.0795389	+	0.996832i	$0.474655\pi$
$432$	5.12195	−	5.98059i	0.246430	−	0.287741i
$433$	24.2832	+	24.2832i	1.16698	+	1.16698i	0.982915	+	0.184060i	$0.0589241\pi$
$433$	24.2832	+	24.2832i	1.16698	+	1.16698i	0.184060	+	0.982915i	$0.441076\pi$
$434$	1.03875	−	0.209153i	0.0498618	−	0.0100397i
$435$	9.08935	−	5.00704i	0.435801	−	0.240069i
$436$	−6.96631	+	5.84543i	−0.333626	+	0.279945i
$437$	−5.76345	−	12.3598i	−0.275703	−	0.591247i
$438$	12.7232	−	21.8672i	0.607939	−	1.04486i
$439$	1.45622	+	0.256770i	0.0695014	+	0.0122550i	0.208291	−	0.978067i	$-0.433210\pi$
$439$	1.45622	+	0.256770i	0.0695014	+	0.0122550i	−0.138789	+	0.990322i	$0.544321\pi$
$440$	−15.0662	+	10.1782i	−0.718254	+	0.485227i
$441$	20.5114	−	4.50351i	0.976734	−	0.214453i
$442$	0.517740	+	0.138728i	0.0246264	+	0.00659862i
$443$	−0.0875963	+	0.187851i	−0.00416182	+	0.00892506i	−0.908378	−	0.418151i	$-0.862678\pi$
$443$	−0.0875963	+	0.187851i	−0.00416182	+	0.00892506i	0.904216	+	0.427076i	$0.140456\pi$
$444$	1.81426	−	3.85680i	0.0861009	−	0.183035i
$445$	−18.9360	+	31.5667i	−0.897654	+	1.49641i
$446$	−11.6037	+	31.8809i	−0.549451	+	1.50960i
$447$	2.77320	+	0.498606i	0.131168	+	0.0235832i
$448$	30.2912	−	15.0263i	1.43112	−	0.709926i
$449$	7.92140	+	13.7203i	0.373834	+	0.647499i	0.990152	−	0.139998i	$-0.0447097\pi$
$449$	7.92140	+	13.7203i	0.373834	+	0.647499i	−0.616318	+	0.787497i	$0.711376\pi$
$450$	−32.8226	−	4.20581i	−1.54727	−	0.198264i
$451$	43.6872			2.05715
$452$	0.690517	+	7.89265i	0.0324792	+	0.371239i
$453$	0.00867225	−	2.58034i	0.000407458	−	0.121235i
$454$	36.2789	+	43.2355i	1.70265	+	2.02914i
$455$	−0.744232	−	0.125532i	−0.0348901	−	0.00588503i
$456$	−6.95487	−	4.90477i	−0.325692	−	0.229687i
$457$	41.9950	−	3.67409i	1.96445	−	0.171867i	0.967677	−	0.252194i	$-0.0811523\pi$
$457$	41.9950	−	3.67409i	1.96445	−	0.171867i	0.996768	+	0.0803278i	$0.0255967\pi$
$458$	7.16482	+	1.91981i	0.334790	+	0.0897067i
$459$	7.06783	−	6.92672i	0.329898	−	0.323312i
$460$	28.1884	−	19.0431i	1.31429	−	0.887888i
$461$	−32.6444	−	5.75608i	−1.52040	−	0.268087i	−0.649809	−	0.760097i	$-0.725151\pi$
$461$	−32.6444	−	5.75608i	−1.52040	−	0.268087i	−0.870590	+	0.492010i	$0.836262\pi$
$462$	0.894145	+	42.9831i	0.0415994	+	1.99975i
$463$	−12.7455	−	27.3328i	−0.592333	−	1.27026i	−0.942698	−	0.333648i	$-0.891720\pi$
$463$	−12.7455	−	27.3328i	−0.592333	−	1.27026i	0.350365	−	0.936613i	$-0.386057\pi$
$464$	−0.705060	−	3.99859i	−0.0327316	−	0.185630i
$465$	−0.462676	+	0.529424i	−0.0214561	+	0.0245514i
$466$	32.6051	+	27.3589i	1.51040	+	1.26738i
$467$	−0.184351	+	0.688006i	−0.00853073	+	0.0318371i	−0.970060	−	0.242865i	$-0.921913\pi$
$467$	−0.184351	+	0.688006i	−0.00853073	+	0.0318371i	0.961529	+	0.274702i	$0.0885794\pi$
$468$	0.102969	−	1.09232i	0.00475974	−	0.0504926i
$469$	5.36484	−	35.4076i	0.247725	−	1.63497i
$470$	6.87187	−	17.9408i	0.316976	−	0.827545i
$471$	−12.6323	+	8.78214i	−0.582068	+	0.404660i
$472$	0.689595	−	7.88211i	0.0317412	−	0.362803i
$473$	−4.55332	+	52.0447i	−0.209362	+	2.39302i
$474$	43.7599	+	20.5849i	2.00996	+	0.945496i
$475$	0.429780	−	12.8417i	0.0197196	−	0.589217i
$476$	13.4506	−	5.26696i	0.616505	−	0.241410i
$477$	32.8349	−	2.65041i	1.50340	−	0.121354i
$478$	−15.8583	+	59.1839i	−0.725341	+	2.70701i
$479$	−23.8128	−	19.9814i	−1.08804	−	0.912971i	−0.0914736	−	0.995807i	$-0.529158\pi$
$479$	−23.8128	−	19.9814i	−1.08804	−	0.912971i	−0.996563	+	0.0828362i	$0.973602\pi$
$480$	−12.2340	+	24.9165i	−0.558402	+	1.13728i
$481$	0.0190163	+	0.107847i	0.000867068	+	0.00491739i
$482$	−14.3065	−	30.6804i	−0.651643	−	1.39745i
$483$	−0.505784	−	24.3139i	−0.0230140	−	1.10632i
$484$	−20.0032	−	3.52711i	−0.909237	−	0.160323i
$485$	−7.25613	−	10.7408i	−0.329484	−	0.487716i
$486$	−27.8345	−	20.1954i	−1.26260	−	0.916080i
$487$	7.12957	+	1.91036i	0.323072	+	0.0865668i	0.416710	−	0.909040i	$-0.363183\pi$
$487$	7.12957	+	1.91036i	0.323072	+	0.0865668i	−0.0936384	+	0.995606i	$0.529850\pi$
$488$	−4.32170	+	0.378100i	−0.195634	+	0.0171158i
$489$	0.272982	−	0.126178i	0.0123447	−	0.00570598i
$490$	−30.8185	+	15.5744i	−1.39224	+	0.703580i
$491$	14.5682	+	17.3617i	0.657453	+	0.783522i	0.987018	−	0.160611i	$-0.0513464\pi$
$491$	14.5682	+	17.3617i	0.657453	+	0.783522i	−0.329565	+	0.944133i	$0.606902\pi$
$492$	−44.2594	+	25.3552i	−1.99537	+	1.14310i
$493$	−0.444750	−	5.08351i	−0.0200305	−	0.228950i
$494$	0.723235			0.0325399
$495$	−17.8200	−	22.2776i	−0.800947	−	1.00130i
$496$	0.137552	+	0.238246i	0.00617625	+	0.0106976i
$497$	9.27948	−	4.60320i	0.416241	−	0.206482i
$498$	7.31847	−	8.66252i	0.327949	−	0.388177i
$499$	4.78722	−	13.1528i	0.214305	−	0.588799i	−0.785232	−	0.619201i	$-0.787457\pi$
$499$	4.78722	−	13.1528i	0.214305	−	0.588799i	0.999538	+	0.0304022i	$0.00967881\pi$
$500$	31.8034	−	3.97527i	1.42229	−	0.177780i
$501$	39.6724	−	3.33657i	1.77243	−	0.149067i
$502$	13.4780	−	28.9037i	0.601553	−	1.29004i
$503$	8.90651	+	2.38649i	0.397122	+	0.106408i	0.451852	−	0.892093i	$-0.350763\pi$
$503$	8.90651	+	2.38649i	0.397122	+	0.106408i	−0.0547308	+	0.998501i	$0.517430\pi$
$504$	−7.81615	−	13.0087i	−0.348159	−	0.579454i
$505$	−22.3070	−	4.31924i	−0.992648	−	0.192204i
$506$	49.0312	+	8.64552i	2.17970	+	0.384340i
$507$	−11.1787	−	19.5133i	−0.496464	−	0.866615i
$508$	−8.99048	−	19.2801i	−0.398888	−	0.855418i
$509$	−18.9535	+	15.9039i	−0.840100	+	0.704928i	−0.957586	−	0.288147i	$-0.906961\pi$
$509$	−18.9535	+	15.9039i	−0.840100	+	0.704928i	0.117486	+	0.993075i	$0.462517\pi$
$510$	−8.41756	+	13.9259i	−0.372736	+	0.616650i
$511$	11.5811	+	13.1435i	0.512319	+	0.581433i
$512$	11.7774	+	11.7774i	0.520490	+	0.520490i
$513$	6.79273	−	11.4961i	0.299906	−	0.507565i
$514$	−39.9714	+	23.0775i	−1.76306	+	1.01790i
$515$	−9.35536	−	0.976424i	−0.412246	−	0.0430264i
$516$	−25.5928	−	55.3691i	−1.12666	−	2.43749i
$517$	15.0108	−	6.99967i	0.660176	−	0.307845i
$518$	3.62731	+	3.45614i	0.159375	+	0.151854i
$519$	2.99153	−	11.0163i	0.131314	−	0.483563i
$520$	0.0857163	+	0.538661i	0.00375891	+	0.0236218i
$521$		−	36.8697i		−	1.61529i	−0.589668	−	0.807646i	$-0.700741\pi$
$521$		−	36.8697i		−	1.61529i	0.589668	−	0.807646i	$-0.299259\pi$
$522$	−17.1589	+	4.47432i	−0.751026	+	0.195836i
$523$	17.0612	+	17.0612i	0.746034	+	0.746034i	0.973732	−	0.227698i	$-0.0731198\pi$
$523$	17.0612	+	17.0612i	0.746034	+	0.746034i	−0.227698	+	0.973732i	$0.573120\pi$
$524$	17.2942	+	14.5116i	0.755502	+	0.633942i
$525$	9.94543	−	20.6419i	0.434054	−	0.900887i
$526$	−11.7916	−	66.8733i	−0.514137	−	2.91581i
$527$	0.146119	+	0.313354i	0.00636506	+	0.0136499i
$528$	−10.5017	+	3.78238i	−0.457028	+	0.164607i
$529$	−5.08450	−	0.896534i	−0.221065	−	0.0389797i
$530$	−51.2022	+	17.6719i	−2.22408	+	0.767618i
$531$	12.4141	+	0.0834458i	0.538726	+	0.00362124i
$532$	15.6912	−	11.5619i	0.680298	−	0.501271i
$533$	0.553866	−	1.18777i	0.0239906	−	0.0514480i
$534$	44.6281	−	44.3291i	1.93125	−	1.91831i
$535$	−6.36538	−	6.58198i	−0.275200	−	0.284564i
$536$	−25.4872	+	4.49408i	−1.10088	+	0.194115i
$537$	−6.01941	+	16.3668i	−0.259757	+	0.706281i
$538$	−34.0653	+	23.8528i	−1.46866	+	1.02837i
$539$	−28.4327	−	8.81850i	−1.22468	−	0.379840i
$540$	30.9828	+	12.2270i	1.33329	+	0.526168i
$541$	−17.1878	+	29.7702i	−0.738962	+	1.27992i	0.214001	+	0.976834i	$0.431351\pi$
$541$	−17.1878	+	29.7702i	−0.738962	+	1.27992i	−0.952963	+	0.303087i	$0.901983\pi$
$542$	−34.5600	−	16.1156i	−1.48448	−	0.692223i
$543$	−1.57011	+	4.26914i	−0.0673798	+	0.183206i
$544$	8.77391	+	10.4563i	0.376178	+	0.448312i
$545$	6.08281	+	3.64891i	0.260559	+	0.156302i
$546$	1.17996	+	0.520629i	0.0504977	+	0.0222809i
$547$	−13.6459	+	29.2636i	−0.583455	+	1.25122i	0.364020	+	0.931391i	$0.381404\pi$
$547$	−13.6459	+	29.2636i	−0.583455	+	1.25122i	−0.947475	+	0.319831i	$0.896374\pi$
$548$	−44.0963	−	11.8156i	−1.88370	−	0.504736i
$549$	−1.13689	−	6.71110i	−0.0485213	−	0.286423i
$550$	37.5038	+	28.1759i	1.59917	+	1.20142i
$551$	−2.35495	−	6.47018i	−0.100324	−	0.275639i
$552$	−16.5351	+	5.95544i	−0.703783	+	0.253480i
$553$	−23.0988	+	24.2428i	−0.982261	+	1.03091i
$554$	−6.37048	−	36.1288i	−0.270656	−	1.53496i
$555$	−3.30543	−	0.356223i	−0.140308	−	0.0151208i
$556$	11.3530	−	64.3860i	0.481474	−	2.73058i
$557$	27.5720	−	7.38790i	1.16826	−	0.313036i	0.378002	−	0.925805i	$-0.376611\pi$
$557$	27.5720	−	7.38790i	1.16826	−	0.313036i	0.790262	+	0.612769i	$0.209944\pi$
$558$	0.988800	−	0.682506i	0.0418593	−	0.0288928i
$559$	1.35727	+	0.783619i	0.0574063	+	0.0331435i
$560$	−6.38621	−	6.29198i	−0.269867	−	0.265885i
$561$	−13.5625	+	3.58526i	−0.572611	+	0.151370i
$562$	−28.5258	−	19.9740i	−1.20329	−	0.842551i
$563$	9.95365	+	6.96962i	0.419496	+	0.293735i	0.764203	−	0.644976i	$-0.223133\pi$
$563$	9.95365	+	6.96962i	0.419496	+	0.293735i	−0.344706	+	0.938711i	$0.612022\pi$
$564$	−11.1450	+	15.8033i	−0.469288	+	0.665441i
$565$	5.64376	−	2.51768i	0.237435	−	0.105919i
$566$		−	16.9823i		−	0.713820i
$567$	19.3580	−	13.8661i	0.812958	−	0.582322i
$568$	−5.29330	−	5.29330i	−0.222102	−	0.222102i
$569$	−6.95868	−	5.83903i	−0.291723	−	0.244785i	0.485166	−	0.874422i	$-0.338759\pi$
$569$	−6.95868	−	5.83903i	−0.291723	−	0.244785i	−0.776889	+	0.629637i	$0.783204\pi$
$570$	−6.10757	+	21.0897i	−0.255818	+	0.883351i
$571$	−5.48737	−	31.1204i	−0.229639	−	1.30235i	−0.853614	−	0.520905i	$-0.825594\pi$
$571$	−5.48737	−	31.1204i	−0.229639	−	1.30235i	0.623975	−	0.781444i	$-0.285517\pi$
$572$	−0.892084	+	1.27403i	−0.0372999	+	0.0532698i
$573$	−7.15105	+	12.2904i	−0.298740	+	0.513439i
$574$	−11.8353	−	58.7798i	−0.493996	−	2.45342i
$575$	−21.2145	−	15.9380i	−0.884704	−	0.664661i
$576$	24.8418	−	29.2044i	1.03508	−	1.21685i
$577$	−8.07602	−	30.1401i	−0.336209	−	1.25475i	−0.902552	−	0.430580i	$-0.858309\pi$
$577$	−8.07602	−	30.1401i	−0.336209	−	1.25475i	0.566343	−	0.824170i	$-0.308358\pi$
$578$	−16.9213	−	24.1660i	−0.703831	−	1.00518i
$579$	−8.03250	+	17.0757i	−0.333819	+	0.709641i
$580$	15.0158	−	8.33766i	0.623498	−	0.346203i
$581$	4.08922	+	6.70335i	0.169649	+	0.278102i
$582$	7.50569	+	20.8394i	0.311121	+	0.863820i
$583$	−42.3218	−	19.7350i	−1.75279	−	0.817339i
$584$	6.32987	−	10.9637i	0.261932	−	0.453679i
$585$	−0.831606	+	0.202054i	−0.0343827	+	0.00835391i
$586$	−32.3719	−	56.0697i	−1.33727	−	2.31622i
$587$	21.3628	+	9.96163i	0.881737	+	0.411161i	0.810115	−	0.586271i	$-0.199405\pi$
$587$	21.3628	+	9.96163i	0.881737	+	0.411161i	0.0716220	+	0.997432i	$0.477182\pi$
$588$	33.9232	−	7.56780i	1.39897	−	0.312091i
$589$	0.299874	+	0.357375i	0.0123561	+	0.0147254i
$590$	−19.8031	+	4.95273i	−0.815279	+	0.203901i
$591$	−34.6866	+	16.0329i	−1.42681	+	0.659506i
$592$	−0.549741	+	1.17892i	−0.0225942	+	0.0484535i
$593$	−4.28377	−	15.9873i	−0.175914	−	0.656518i	−0.996394	−	0.0848440i	$-0.972961\pi$
$593$	−4.28377	−	15.9873i	−0.175914	−	0.656518i	0.820481	−	0.571674i	$-0.193706\pi$
$594$	20.1556	+	44.3869i	0.826995	+	1.82122i
$595$	−7.30641	−	8.57715i	−0.299533	−	0.351629i
$596$	4.59267	+	0.809811i	0.188123	+	0.0331711i
$597$	6.61549	+	2.43305i	0.270754	+	0.0995782i
$598$	0.856672	−	1.22345i	0.0350319	−	0.0500307i
$599$	11.8247	+	4.30385i	0.483146	+	0.175851i	0.572098	−	0.820185i	$-0.306130\pi$
$599$	11.8247	+	4.30385i	0.483146	+	0.175851i	−0.0889523	+	0.996036i	$0.528352\pi$
$600$	−16.4313	−	2.04937i	−0.670806	−	0.0836651i
$601$	1.79328	−	0.652699i	0.0731493	−	0.0266242i	−0.305186	−	0.952293i	$-0.598719\pi$
$601$	1.79328	−	0.652699i	0.0731493	−	0.0266242i	0.378336	+	0.925668i	$0.376497\pi$
$602$	71.2581	−	7.97307i	2.90426	−	0.324958i
$603$	−10.2459	−	39.2928i	−0.417246	−	1.60013i
$604$		−	4.27075i		−	0.173774i
$605$	2.48981	+	15.6466i	0.101225	+	0.636123i
$606$	35.1333	+	16.5269i	1.42719	+	0.671359i
$607$	−8.65700	+	4.03683i	−0.351377	+	0.163850i	−0.590290	−	0.807191i	$-0.700987\pi$
$607$	−8.65700	+	4.03683i	−0.351377	+	0.163850i	0.238913	+	0.971041i	$0.423209\pi$
$608$	15.0870	+	10.5640i	0.611857	+	0.428427i
$609$	0.815516	−	12.2514i	0.0330464	−	0.496451i
$610$	4.55974	+	10.2214i	0.184618	+	0.413851i
$611$		−	0.496857i		−	0.0201007i
$612$	11.6594	−	11.5037i	0.471302	−	0.465008i
$613$	6.25210	+	6.25210i	0.252520	+	0.252520i	0.822003	−	0.569483i	$-0.192857\pi$
$613$	6.25210	+	6.25210i	0.252520	+	0.252520i	−0.569483	+	0.822003i	$0.692857\pi$
$614$	−10.8358	+	61.4526i	−0.437296	+	2.48003i
$615$	29.9584	+	26.1814i	1.20804	+	1.05573i
$616$	0.519714	+	21.5070i	0.0209399	+	0.866543i
$617$	3.62688	+	7.77786i	0.146013	+	0.313125i	0.965689	−	0.259702i	$-0.0836244\pi$
$617$	3.62688	+	7.77786i	0.146013	+	0.313125i	−0.819676	+	0.572827i	$0.805847\pi$
$618$	15.0855	+	5.54815i	0.606826	+	0.223179i
$619$	−2.59150	−	7.12010i	−0.104161	−	0.286181i	0.876654	−	0.481122i	$-0.159771\pi$
$619$	−2.59150	−	7.12010i	−0.104161	−	0.286181i	−0.980815	+	0.194941i	$0.937548\pi$
$620$	−0.762825	+	0.878817i	−0.0306358	+	0.0352941i
$621$	−11.4013	−	25.1080i	−0.457517	−	1.00755i
$622$	−42.6485	+	42.6485i	−1.71005	+	1.71005i
$623$	19.3554	+	39.0181i	0.775458	+	1.56323i
$624$	−0.0303048	+	0.333473i	−0.00121316	+	0.0133496i
$625$	−11.0245	−	22.4379i	−0.440979	−	0.897518i
$626$	−14.7936	+	40.6451i	−0.591271	+	1.62450i
$627$	−16.4244	+	9.40918i	−0.655928	+	0.375767i
$628$	−20.8588	+	14.6055i	−0.832357	+	0.582822i
$629$	−0.817417	+	1.41581i	−0.0325925	+	0.0564519i
$630$	−25.1462	+	30.0114i	−1.00185	+	1.19568i
$631$	−19.1622	−	33.1899i	−0.762836	−	1.32127i	−0.941383	−	0.337339i	$-0.890473\pi$
$631$	−19.1622	−	33.1899i	−0.762836	−	1.32127i	0.178547	−	0.983931i	$-0.442860\pi$
$632$	21.9319	+	10.2270i	0.872403	+	0.406808i
$633$	−10.4049	+	12.3158i	−0.413559	+	0.489510i
$634$	−11.5021	−	13.7077i	−0.456808	−	0.544403i
$635$	−11.9279	+	11.5354i	−0.473345	+	0.457768i
$636$	54.3299	−	4.56931i	2.15432	−	0.181185i
$637$	−0.600227	+	0.661229i	−0.0237819	+	0.0261988i
$638$	24.2807	+	6.50599i	0.961282	+	0.257575i
$639$	7.61011	−	8.94656i	0.301051	−	0.353920i
$640$	−13.5657	+	27.8650i	−0.536229	+	1.10146i
$641$	−13.0508	+	15.5533i	−0.515475	+	0.614319i	−0.959505	−	0.281693i	$-0.909104\pi$
$641$	−13.0508	+	15.5533i	−0.515475	+	0.614319i	0.444030	+	0.896012i	$0.353549\pi$
$642$	7.77773	+	13.5766i	0.306962	+	0.535825i
$643$	28.8830	+	2.52694i	1.13904	+	0.0996527i	0.641026	−	0.767519i	$-0.278509\pi$
$643$	28.8830	+	2.52694i	1.13904	+	0.0996527i	0.498009	+	0.867172i	$0.334064\pi$
$644$	−0.972366	−	40.2389i	−0.0383166	−	1.58563i
$645$	−34.3124	+	32.9608i	−1.35105	+	1.29783i
$646$	8.27087	+	6.94009i	0.325413	+	0.273054i
$647$	5.73550	−	21.4052i	0.225486	−	0.841524i	−0.756724	−	0.653735i	$-0.773201\pi$
$647$	5.73550	−	21.4052i	0.225486	−	0.841524i	0.982209	−	0.187789i	$-0.0601322\pi$
$648$	−13.9622	−	10.0588i	−0.548487	−	0.395149i
$649$	−15.2405	−	8.79910i	−0.598241	−	0.345395i
$650$	1.24152	−	0.662441i	0.0486964	−	0.0259831i
$651$	0.231985	+	0.798927i	0.00909219	+	0.0313124i
$652$	0.451107	−	0.210355i	0.0176667	−	0.00823812i
$653$	14.9764	+	10.4866i	0.586072	+	0.410372i	0.828656	−	0.559758i	$-0.189106\pi$
$653$	14.9764	+	10.4866i	0.586072	+	0.410372i	−0.242584	+	0.970130i	$0.577995\pi$
$654$	−8.54207	−	8.59969i	−0.334022	−	0.336274i
$655$	6.29876	−	16.4445i	0.246113	−	0.642540i
$656$	13.4816	−	7.78361i	0.526368	−	0.303899i
$657$	17.9454	+	8.51542i	0.700118	+	0.332218i
$658$	−13.4844	−	18.3003i	−0.525677	−	0.713420i
$659$	−31.4861	−	26.4200i	−1.22653	−	1.02918i	−0.998457	−	0.0555315i	$-0.982315\pi$
$659$	−31.4861	−	26.4200i	−1.22653	−	1.02918i	−0.228068	−	0.973645i	$-0.573241\pi$
$660$	−29.6175	−	36.7723i	−1.15286	−	1.43136i
$661$	10.0061	−	8.39609i	0.389191	−	0.326570i	−0.427107	−	0.904201i	$-0.640467\pi$
$661$	10.0061	−	8.39609i	0.389191	−	0.326570i	0.816298	+	0.577631i	$0.196023\pi$
$662$	26.8195	+	2.34640i	1.04237	+	0.0911955i
$663$	−0.0744696	+	0.414193i	−0.00289216	+	0.0160859i
$664$	3.64756	−	4.34699i	0.141553	−	0.168696i
$665$	−12.5180	−	8.62728i	−0.485429	−	0.334552i
$666$	5.32526	+	1.97887i	0.206350	+	0.0766798i
$667$	−13.7347	−	3.68019i	−0.531809	−	0.142498i
$668$	65.6427	−	5.74299i	2.53979	−	0.222203i
$669$	−25.7062	−	6.98063i	−0.993858	−	0.269887i
$670$	32.4130	+	58.3746i	1.25222	+	2.25521i
$671$	−3.30014	+	9.06706i	−0.127400	+	0.350030i
$672$	17.0098	+	28.0957i	0.656168	+	1.08382i
$673$	−23.9765	+	16.7885i	−0.924225	+	0.647149i	−0.935705	−	0.352785i	$-0.885235\pi$
$673$	−23.9765	+	16.7885i	−0.924225	+	0.647149i	0.0114794	+	0.999934i	$0.496346\pi$
$674$	−34.1398	+	59.1318i	−1.31502	+	2.27767i
$675$	1.13078	−	25.9561i	0.0435239	−	0.999052i
$676$	−18.6103	−	32.2340i	−0.715781	−	1.23977i
$677$	1.17801	+	13.4647i	0.0452747	+	0.517492i	0.984643	+	0.174581i	$0.0558572\pi$
$677$	1.17801	+	13.4647i	0.0452747	+	0.517492i	−0.939368	+	0.342911i	$0.888587\pi$
$678$	−10.4059	+	1.79880i	−0.399636	+	0.0690825i
$679$	−15.3325	+	0.370508i	−0.588409	+	0.0142188i
$680$	−4.18868	+	6.98262i	−0.160629	+	0.267771i
$681$	−31.4390	+	31.2284i	−1.20475	+	1.19668i
$682$	−1.69669	+	0.148441i	−0.0649695	+	0.00568409i
$683$	−0.714300	+	0.714300i	−0.0273319	+	0.0273319i	−0.720641	−	0.693309i	$-0.756152\pi$
$683$	−0.714300	+	0.714300i	−0.0273319	+	0.0273319i	0.693309	+	0.720641i	$0.256152\pi$
$684$	11.1786	−	19.0648i	0.427425	−	0.728962i
$685$	2.50973	+	35.5204i	0.0958920	+	1.35716i
$686$	−4.16231	+	40.6443i	−0.158918	+	1.55181i
$687$	−1.03056	+	5.73186i	−0.0393182	+	0.218684i
$688$	7.86751	+	16.8719i	0.299946	+	0.643236i
$689$	−1.07311	+	0.900446i	−0.0408822	+	0.0343043i
$690$	28.4418	+	35.3126i	1.08276	+	1.34433i
$691$	7.75384	−	2.82217i	0.294970	−	0.107360i	−0.190296	−	0.981727i	$-0.560945\pi$
$691$	7.75384	−	2.82217i	0.294970	−	0.107360i	0.485266	+	0.874366i	$0.338723\pi$
$692$	4.88997	−	18.2496i	0.185889	−	0.693747i
$693$	−33.5698	+	3.52783i	−1.27521	+	0.134011i
$694$	−58.9735	−	34.0484i	−2.23861	−	1.29246i
$695$	−50.3629	+	8.01417i	−1.91037	+	0.303995i
$696$	−8.57872	+	2.26779i	−0.325176	+	0.0859602i
$697$	17.7317	−	8.26843i	0.671636	−	0.313189i
$698$	4.46866	−	51.0770i	0.169141	−	1.93329i
$699$	−19.2594	+	27.3094i	−0.728457	+	1.03294i
$700$	16.3458	−	34.2195i	0.617811	−	1.29338i
$701$		−	25.3011i		−	0.955610i	−0.878466	−	0.477805i	$-0.841433\pi$
$701$		−	25.3011i		−	0.955610i	0.878466	−	0.477805i	$-0.158567\pi$
$702$	1.46233	+	0.0147446i	0.0551919	+	0.000556498i
$703$	−0.570928	+	2.13073i	−0.0215329	+	0.0803620i
$704$	−51.0728	+	18.5890i	−1.92488	+	0.700598i
$705$	14.4885	+	4.19585i	0.545667	+	0.158025i
$706$	30.2757	+	11.0194i	1.13944	+	0.414722i
$707$	−18.5452	+	19.4637i	−0.697464	+	0.732007i
$708$	20.5469	+	0.0690559i	0.772201	+	0.00259528i
$709$	−28.5545	−	5.03493i	−1.07239	−	0.189091i	−0.390540	−	0.920586i	$-0.627712\pi$
$709$	−28.5545	−	5.03493i	−1.07239	−	0.189091i	−0.681847	+	0.731495i	$0.738823\pi$
$710$	−8.45367	+	17.3646i	−0.317260	+	0.651680i
$711$	−13.2256	+	35.5909i	−0.496000	+	1.33476i
$712$	22.2571	−	22.2571i	0.834121	−	0.834121i
$713$	0.959751	−	0.0839673i	0.0359430	−	0.00314460i
$714$	8.49807	+	17.2767i	0.318032	+	0.646563i
$715$	1.16640	+	0.333543i	0.0436208	+	0.0124738i
$716$	−9.87161	+	27.1220i	−0.368920	+	1.01360i
$717$	−47.3472	−	8.51275i	−1.76821	−	0.317915i
$718$	−41.6781	+	29.1833i	−1.55541	+	1.08911i
$719$	7.37478			0.275033			0.137516	−	0.990499i	$-0.456088\pi$
$719$	7.37478			0.275033			0.137516	+	0.990499i	$0.456088\pi$
$720$	−9.46825	−	3.69981i	−0.352861	−	0.137884i
$721$	−6.94588	+	8.69606i	−0.258678	+	0.323858i
$722$	−24.7847	−	11.5573i	−0.922392	−	0.430118i
$723$	23.0621	−	13.2117i	0.857687	−	0.491350i
$724$	−2.57492	+	7.07454i	−0.0956962	+	0.262923i
$725$	−9.96886	−	8.94984i	−0.370234	−	0.332389i
$726$	2.45023	−	26.9623i	0.0909366	−	1.00066i
$727$	−20.4474	−	29.2018i	−0.758350	−	1.08304i	−0.993804	−	0.111151i	$-0.964546\pi$
$727$	−20.4474	−	29.2018i	−0.758350	−	1.08304i	0.235453	−	0.971886i	$-0.424343\pi$
$728$	0.591323	+	0.258536i	0.0219159	+	0.00958198i
$729$	13.9687	−	23.1057i	0.517361	−	0.855767i
$730$	−32.0657	−	6.20880i	−1.18681	−	0.229798i
$731$	8.00211	+	21.9856i	0.295969	+	0.813167i
$732$	−1.91898	−	11.1011i	−0.0709277	−	0.410310i
$733$	27.3148	+	2.38973i	1.00889	+	0.0882668i	0.579603	−	0.814899i	$-0.303208\pi$
$733$	27.3148	+	2.38973i	1.00889	+	0.0882668i	0.429292	+	0.903166i	$0.358763\pi$
$734$	15.0696	−	12.6449i	0.556229	−	0.466732i
$735$	−14.2128	−	23.0867i	−0.524247	−	0.851566i
$736$	35.7410	−	13.0087i	1.31743	−	0.479505i
$737$	−14.8983	+	55.6012i	−0.548786	+	2.04810i
$738$	−38.6209	−	55.9531i	−1.42165	−	2.05966i
$739$	28.1617	+	16.2592i	1.03595	+	0.598103i	0.918682	−	0.394997i	$-0.129255\pi$
$739$	28.1617	+	16.2592i	1.03595	+	0.598103i	0.117263	+	0.993101i	$0.462588\pi$
$740$	−5.47276	−	0.571195i	−0.201183	−	0.0209975i
$741$	0.0475886	+	0.565837i	0.00174821	+	0.0207866i
$742$	−15.0874	+	62.2890i	−0.553875	+	2.28670i
$743$	−25.9629	−	18.1794i	−0.952487	−	0.666939i	−0.00956573	−	0.999954i	$-0.503045\pi$
$743$	−25.9629	−	18.1794i	−0.952487	−	0.666939i	−0.942921	+	0.333016i	$0.891934\pi$
$744$	0.493643	−	0.343186i	0.0180978	−	0.0125818i
$745$	−0.571652	−	3.59239i	−0.0209437	−	0.131615i
$746$	4.91949	+	2.84027i	0.180115	+	0.103990i
$747$	7.25885	+	5.15576i	0.265588	+	0.188639i
$748$	−22.4273	+	6.00937i	−0.820022	+	0.219724i
$749$	−10.6209	+	2.13852i	−0.388079	+	0.0781397i
$750$	8.83257	+	41.7972i	0.322520	+	1.52622i
$751$	−1.60367	−	9.09488i	−0.0585188	−	0.331877i	0.941468	−	0.337104i	$-0.109447\pi$
$751$	−1.60367	−	9.09488i	−0.0585188	−	0.331877i	−0.999986	+	0.00522694i	$0.998336\pi$
$752$	3.38514	−	4.83448i	0.123443	−	0.176295i
$753$	23.5002	+	8.64294i	0.856396	+	0.314966i
$754$	0.484716	−	0.577662i	0.0176523	−	0.0210372i
$755$	−3.14895	+	1.08683i	−0.114602	+	0.0395537i
$756$	31.9620	−	23.0573i	1.16245	−	0.838587i
$757$	−26.4769	+	26.4769i	−0.962320	+	0.962320i	−0.999315	−	0.0369950i	$-0.988221\pi$
$757$	−26.4769	+	26.4769i	−0.962320	+	0.962320i	0.0369950	+	0.999315i	$0.488221\pi$
$758$	20.7038	−	1.81135i	0.751997	−	0.0657912i
$759$	−3.53776	+	38.9294i	−0.128412	+	1.41305i
$760$	−3.02073	+	10.5635i	−0.109573	+	0.383177i
$761$	44.4159	−	7.83173i	1.61008	−	0.283900i	0.705019	−	0.709189i	$-0.250938\pi$
$761$	44.4159	−	7.83173i	1.61008	−	0.283900i	0.905058	+	0.425289i	$0.139827\pi$
$762$	24.6036	−	14.0949i	0.891295	−	0.510603i
$763$	7.51866	−	3.72973i	0.272194	−	0.135025i
$764$	−11.7673	+	20.3815i	−0.425725	+	0.737377i
$765$	−11.4491	−	5.66932i	−0.413943	−	0.204975i
$766$	3.25249	−	5.63347i	0.117517	−	0.203546i
$767$	−0.432449	+	0.302804i	−0.0156148	+	0.0109336i
$768$	5.60611	−	6.63568i	0.202293	−	0.239444i
$769$	28.3491	−	4.99871i	1.02230	−	0.180258i	0.362721	−	0.931898i	$-0.381848\pi$
$769$	28.3491	−	4.99871i	1.02230	−	0.180258i	0.659574	+	0.751640i	$0.270737\pi$
$770$	52.0132	−	19.3702i	1.87442	−	0.698055i
$771$	−20.6852	−	29.7539i	−0.744960	−	1.07156i
$772$	−13.1995	+	28.3065i	−0.475061	+	1.01877i
$773$	0.432314	+	1.61342i	0.0155492	+	0.0580306i	0.973265	−	0.229687i	$-0.0737702\pi$
$773$	0.432314	+	1.61342i	0.0155492	+	0.0580306i	−0.957715	+	0.287718i	$0.907104\pi$
$774$	70.6823	−	40.1774i	2.54062	−	1.44415i
$775$	0.842103	+	0.338811i	0.0302492	+	0.0121704i
$776$	3.79086	+	10.4153i	0.136084	+	0.373887i
$777$	−2.46530	+	3.06531i	−0.0884422	+	0.109967i
$778$	−16.3244	−	1.42820i	−0.585257	−	0.0512033i
$779$	20.2227	−	16.9689i	0.724555	−	0.607974i
$780$	−1.37526	+	0.339044i	−0.0492421	+	0.0121397i
$781$	−15.6458	+	5.69459i	−0.559849	+	0.203769i
$782$	21.5370	−	5.77082i	0.770161	−	0.206364i
$783$	−4.62963	−	13.1302i	−0.165449	−	0.469236i
$784$	−10.3453	+	2.34443i	−0.369476	+	0.0837295i
$785$	16.0773	+	11.6630i	0.573822	+	0.416270i
$786$	−17.3424	+	24.5912i	−0.618584	+	0.877140i
$787$	36.6797	+	25.6834i	1.30749	+	0.915515i	0.999358	−	0.0358289i	$-0.0114071\pi$
$787$	36.6797	+	25.6834i	1.30749	+	0.915515i	0.308132	+	0.951343i	$0.400296\pi$
$788$	−57.3202	+	26.7288i	−2.04195	+	0.952175i
$789$	51.5438	−	13.6256i	1.83501	−	0.485085i
$790$	6.48088	−	62.0949i	0.230579	−	2.20924i
$791$	1.09540	−	7.22960i	0.0389481	−	0.257055i
$792$	10.1604	+	22.1771i	0.361035	+	0.788028i
$793$	0.204676	+	0.204676i	0.00726827	+	0.00726827i
$794$	−8.35138	+	47.3631i	−0.296380	+	1.68085i
$795$	−17.1951	−	38.8962i	−0.609846	−	1.37951i
$796$	10.9628	+	3.99012i	0.388565	+	0.141426i
$797$	−3.89448	+	5.56190i	−0.137950	+	0.197013i	−0.882182	−	0.470908i	$-0.843926\pi$
$797$	−3.89448	+	5.56190i	−0.137950	+	0.197013i	0.744233	+	0.667920i	$0.232815\pi$
$798$	17.1093	+	19.5495i	0.605662	+	0.692044i
$799$	4.76779	−	5.68203i	0.168672	−	0.201016i
$800$	35.5745	+	4.31560i	1.25775	+	0.152579i
$801$	37.6183	+	31.9988i	1.32918	+	1.13062i
$802$	−5.97065	+	5.97065i	−0.210831	+	0.210831i
$803$	−16.1505	−	23.0653i	−0.569938	−	0.813957i
$804$	−17.1765	−	64.9761i	−0.605767	−	2.29153i
$805$	−29.4219	+	10.9570i	−1.03698	+	0.386184i
$806$	−0.0174748	+	0.0480115i	−0.000615522	+	0.00169113i
$807$	−20.9032	−	25.0822i	−0.735827	−	0.882934i
$808$	17.6083	+	8.21089i	0.619459	+	0.288858i
$809$	−1.18960	−	2.06045i	−0.0418241	−	0.0724415i	0.844356	−	0.535783i	$-0.179984\pi$
$809$	−1.18960	−	2.06045i	−0.0418241	−	0.0724415i	−0.886180	+	0.463342i	$0.846650\pi$
$810$	−12.7790	+	42.5173i	−0.449008	+	1.49390i
$811$	34.7681			1.22087			0.610436	−	0.792065i	$-0.290994\pi$
$811$	34.7681			1.22087			0.610436	+	0.792065i	$0.290994\pi$
$812$	1.28160	−	20.2817i	0.0449755	−	0.711747i
$813$	10.3343	−	28.0991i	0.362440	−	0.985478i
$814$	−5.17653	−	6.16915i	−0.181437	−	0.216229i
$815$	−0.269899	−	0.279083i	−0.00945416	−	0.00977586i
$816$	−3.54654	+	3.52278i	−0.124154	+	0.123322i
$817$	18.1074	+	25.8600i	0.633497	+	0.904727i
$818$	13.1253	+	48.9843i	0.458915	+	1.71269i
$819$	−0.329683	+	0.957424i	−0.0115201	+	0.0334551i
$820$	49.7295	+	43.1658i	1.73663	+	1.50742i
$821$	0.124677	+	0.342546i	0.00435125	+	0.0119550i	0.941849	−	0.336036i	$-0.109086\pi$
$821$	0.124677	+	0.342546i	0.00435125	+	0.0119550i	−0.937498	+	0.347991i	$0.886864\pi$
$822$	10.7676	−	59.8886i	0.375564	−	2.08886i
$823$	−6.88707	−	0.602540i	−0.240068	−	0.0210032i	−0.0335133	−	0.999438i	$-0.510670\pi$
$823$	−6.88707	−	0.602540i	−0.240068	−	0.0210032i	−0.206555	+	0.978435i	$0.566225\pi$
$824$	7.55802	+	2.75089i	0.263296	+	0.0958320i
$825$	−19.5762	+	31.1958i	−0.681556	+	1.08610i
$826$	−7.71011	+	22.8893i	−0.268269	+	0.796422i
$827$	3.89257	−	14.5273i	0.135358	−	0.505162i	−0.864638	−	0.502395i	$-0.832452\pi$
$827$	3.89257	−	14.5273i	0.135358	−	0.505162i	0.999996	−	0.00276736i	$-0.000880881\pi$
$828$	−19.0098	−	41.4925i	−0.660636	−	1.44196i
$829$		−	20.0583i		−	0.696653i	−0.937373	−	0.348327i	$-0.886750\pi$
$829$		−	20.0583i		−	0.696653i	0.937373	−	0.348327i	$-0.113250\pi$
$830$	−13.6715	−	5.23662i	−0.474545	−	0.181766i
$831$	27.8469	−	7.36133i	0.965998	−	0.255362i
$832$	−0.142103	+	1.62424i	−0.00492652	+	0.0563104i
$833$	−13.2092	+	1.80205i	−0.457673	+	0.0624375i
$834$	86.7857	+	7.88676i	3.00514	+	0.273096i
$835$	−20.9394	−	46.9389i	−0.724637	−	1.62439i
$836$	−27.1315	+	15.6644i	−0.938364	+	0.541765i
$837$	0.599035	+	0.728699i	0.0207057	+	0.0251875i
$838$	63.5218	−	17.0206i	2.19433	−	0.587968i
$839$	−4.67340	+	26.5041i	−0.161344	+	0.915025i	0.791411	+	0.611284i	$0.209347\pi$
$839$	−4.67340	+	26.5041i	−0.161344	+	0.915025i	−0.952755	+	0.303741i	$0.901764\pi$
$840$	−12.5326	+	15.0598i	−0.432415	+	0.519614i
$841$	20.5049	+	7.46318i	0.707066	+	0.257351i
$842$	22.7089	−	32.4316i	0.782600	−	1.11767i
$843$	13.7500	−	23.6320i	0.473577	−	0.813929i
$844$	−17.1526	+	20.4417i	−0.590417	+	0.703631i
$845$	−19.0311	+	21.9249i	−0.654690	+	0.754240i
$846$	−22.2350	−	13.0374i	−0.764454	−	0.448236i
$847$	17.1762	+	7.50973i	0.590183	+	0.258037i
$848$	−16.5763	+	1.45024i	−0.569234	+	0.0498015i
$849$	13.2864	−	1.11743i	0.455990	−	0.0383501i
$850$	20.5546	+	4.33785i	0.705019	+	0.148787i
$851$	2.92817	+	3.48965i	0.100376	+	0.119624i
$852$	12.5456	−	14.8497i	0.429807	−	0.508742i
$853$	−1.32398	−	15.1332i	−0.0453323	−	0.518151i	−0.984583	−	0.174919i	$-0.944034\pi$
$853$	−1.32398	−	15.1332i	−0.0453323	−	0.518151i	0.939251	−	0.343232i	$-0.111522\pi$
$854$	13.0935	+	1.98388i	0.448049	+	0.0678869i
$855$	−16.9018	−	3.39068i	−0.578031	−	0.115959i
$856$	3.91477	+	6.78058i	0.133804	+	0.231755i
$857$	−1.34656	−	15.3912i	−0.0459975	−	0.525753i	−0.983884	−	0.178810i	$-0.942775\pi$
$857$	−1.34656	−	15.3912i	−0.0459975	−	0.525753i	0.937886	−	0.346943i	$-0.112780\pi$
$858$	−1.79182	−	1.04255i	−0.0611716	−	0.0355921i
$859$	−26.2215	+	4.62355i	−0.894664	+	0.157753i	−0.602032	−	0.798472i	$-0.705642\pi$
$859$	−26.2215	+	4.62355i	−0.894664	+	0.157753i	−0.292632	+	0.956225i	$0.594531\pi$
$860$	−56.6067	+	54.7439i	−1.93027	+	1.86675i
$861$	45.2088	−	13.1273i	1.54071	−	0.447376i
$862$	−22.5670	−	32.2291i	−0.768636	−	1.09773i
$863$	5.22300	+	19.4925i	0.177793	+	0.663532i	0.996059	+	0.0886927i	$0.0282689\pi$
$863$	5.22300	+	19.4925i	0.177793	+	0.663532i	−0.818266	+	0.574840i	$0.805064\pi$
$864$	30.2893	+	21.6672i	1.03046	+	0.737132i
$865$	−14.7004	+	1.03867i	−0.499829	+	0.0353160i
$866$	−48.6974	+	58.0353i	−1.65481	+	1.97212i
$867$	17.7934	−	14.8288i	0.604295	−	0.503612i
$868$	0.388399	+	1.32101i	0.0131831	+	0.0448379i
$869$	41.2310	−	34.5969i	1.39867	−	1.17362i
$870$	12.7514	+	19.0127i	0.432314	+	0.644590i
$871$	1.32281	+	1.10997i	0.0448216	+	0.0376098i
$872$	−4.28888	−	4.28888i	−0.145240	−	0.145240i
$873$	−15.8102	+	7.24345i	−0.535095	+	0.245154i
$874$	26.0545	−	15.0426i	0.881307	−	0.508823i
$875$	−29.3908	−	3.34397i	−0.993590	−	0.113047i
$876$	29.7487	+	13.9940i	1.00511	+	0.472812i
$877$	45.9525	−	21.4280i	1.55171	−	0.723573i	0.557411	−	0.830237i	$-0.311795\pi$
$877$	45.9525	−	21.4280i	1.55171	−	0.723573i	0.994295	+	0.106664i	$0.0340169\pi$
$878$	−0.284308	+	3.24965i	−0.00959492	+	0.109670i
$879$	41.7372	−	29.0161i	1.40776	−	0.978690i
$880$	9.07675	+	11.1922i	0.305977	+	0.377290i
$881$	−0.590192	+	0.340747i	−0.0198841	+	0.0114801i	−0.509909	−	0.860228i	$-0.670321\pi$
$881$	−0.590192	+	0.340747i	−0.0198841	+	0.0114801i	0.490025	+	0.871708i	$0.336988\pi$
$882$	13.8410	+	44.2114i	0.466050	+	1.48868i
$883$	30.9651	−	8.29706i	1.04206	−	0.279218i	0.303091	−	0.952961i	$-0.401981\pi$
$883$	30.9651	−	8.29706i	1.04206	−	0.279218i	0.738966	+	0.673743i	$0.235315\pi$
$884$	−0.120950	+	0.685940i	−0.00406798	+	0.0230707i
$885$	−5.17790	−	15.1674i	−0.174053	−	0.509848i
$886$	−0.429676	−	0.156389i	−0.0144352	−	0.00525400i
$887$	−28.2374	−	2.47045i	−0.948119	−	0.0829497i	−0.397405	−	0.917643i	$-0.630089\pi$
$887$	−28.2374	−	2.47045i	−0.948119	−	0.0829497i	−0.550714	+	0.834694i	$0.685645\pi$
$888$	2.66806	+	0.981263i	0.0895343	+	0.0329290i
$889$	3.87544	+	19.2473i	0.129978	+	0.645533i
$890$	−73.0141	−	35.5458i	−2.44744	−	1.19150i
$891$	−33.4007	+	18.6898i	−1.11897	+	0.626132i
$892$	−42.5848	−	11.4106i	−1.42585	−	0.382054i
$893$	4.22969	−	9.07060i	0.141541	−	0.303536i
$894$	−0.562564	+	6.19044i	−0.0188150	+	0.207039i
$895$	22.5100	+	0.376572i	0.752428	+	0.0125874i
$896$	19.0968	+	31.3049i	0.637978	+	1.04582i
$897$	1.01356	+	0.589731i	0.0338419	+	0.0196906i
$898$	−28.6295	+	20.0466i	−0.955380	+	0.668964i
$899$	0.486419			0.0162230
$900$	1.72717	−	42.9660i	0.0575722	−	1.43220i
$901$	−20.9126			−0.696700
$902$	8.39979	+	96.0101i	0.279683	+	3.19679i
$903$	10.9266	+	55.2255i	0.363616	+	1.83779i
$904$	−5.20403	+	0.917611i	−0.173083	+	0.0305193i
$905$	5.87154	+	0.0982255i	0.195177	+	0.00326513i
$906$	5.67241	−	0.477067i	0.188453	−	0.0158495i
$907$	15.4240	+	22.0277i	0.512145	+	0.731419i	0.989057	−	0.147532i	$-0.0471330\pi$
$907$	15.4240	+	22.0277i	0.512145	+	0.731419i	−0.476912	+	0.878951i	$0.658244\pi$
$908$	−51.8607	+	51.8607i	−1.72106	+	1.72106i
$909$	−10.6184	+	28.5747i	−0.352190	+	0.947763i
$910$	0.132783	−	1.65971i	0.00440173	−	0.0550189i
$911$	−13.4026	−	36.8233i	−0.444047	−	1.22001i	−0.936808	−	0.349844i	$-0.886234\pi$
$911$	−13.4026	−	36.8233i	−0.444047	−	1.22001i	0.492761	−	0.870165i	$-0.335988\pi$
$912$	−3.39207	+	5.82990i	−0.112323	+	0.193047i
$913$	−5.33400	−	11.4388i	−0.176530	−	0.378569i
$914$	16.1489	+	91.5848i	0.534157	+	3.02935i
$915$	−7.69686	+	4.23997i	−0.254450	+	0.140169i
$916$	−1.67378	+	9.49247i	−0.0553032	+	0.313640i
$917$	−12.3598	−	16.7741i	−0.408157	−	0.553929i
$918$	16.5816	+	14.2009i	0.547274	+	0.468701i
$919$	−9.23068	−	5.32934i	−0.304492	−	0.175799i	0.339967	−	0.940437i	$-0.389584\pi$
$919$	−9.23068	−	5.32934i	−0.304492	−	0.175799i	−0.644459	+	0.764639i	$0.722917\pi$
$920$	14.2915	+	17.6224i	0.471178	+	0.580994i
$921$	−48.7917	−	4.43401i	−1.60774	−	0.146105i
$922$	6.37339	−	72.8482i	0.209896	−	2.39913i
$923$	−0.0435321	+	0.497574i	−0.00143288	+	0.0163778i
$924$	−55.5415	+	6.02560i	−1.82718	+	0.198228i
$925$	0.971559	+	4.18059i	0.0319447	+	0.137457i
$926$	57.6178	−	33.2656i	1.89344	−	1.09318i
$927$	−3.34808	+	12.1675i	−0.109965	+	0.399632i
$928$	18.5490	−	4.97019i	0.608901	−	0.163155i
$929$	−24.6459	+	8.97038i	−0.808607	+	0.294309i	−0.713048	−	0.701115i	$-0.752686\pi$
$929$	−24.6459	+	8.97038i	−0.808607	+	0.294309i	−0.0955585	+	0.995424i	$0.530464\pi$
$930$	−1.25246	−	0.915015i	−0.0410697	−	0.0300045i
$931$	−16.5867	+	6.96169i	−0.543607	+	0.228160i
$932$	−31.7241	+	45.3067i	−1.03916	+	1.48407i
$933$	−36.1731	−	30.5606i	−1.18425	−	1.00051i
$934$	−1.54745	−	0.272858i	−0.0506343	−	0.00892818i
$935$	10.1382	+	15.0070i	0.331555	+	0.490782i
$936$	0.731765	+	0.00491882i	0.0239185	+	0.000160777i
$937$	−11.4523	−	42.7407i	−0.374131	−	1.39628i	−0.854610	−	0.519270i	$-0.826204\pi$
$937$	−11.4523	−	42.7407i	−0.374131	−	1.39628i	0.480479	−	0.877006i	$-0.340463\pi$
$938$	78.8457	+	4.98228i	2.57440	+	0.162677i
$939$	−32.7729	−	8.89963i	−1.06950	−	0.290428i
$940$	24.0031	+	6.86392i	0.782893	+	0.223876i
$941$	−24.2520	+	4.27628i	−0.790592	+	0.139403i	−0.554341	−	0.832289i	$-0.687030\pi$
$941$	−24.2520	+	4.27628i	−0.790592	+	0.139403i	−0.236251	+	0.971692i	$0.575919\pi$
$942$	−21.7291	−	26.0731i	−0.707971	−	0.849509i
$943$	−4.75144	−	54.3093i	−0.154728	−	1.76855i
$944$	−6.27082			−0.204098
$945$	−25.1346	−	17.6989i	−0.817629	−	0.575745i
$946$	−115.253			−3.74718
$947$	2.44515	+	27.9481i	0.0794566	+	0.908193i	0.926408	+	0.376522i	$0.122880\pi$
$947$	2.44515	+	27.9481i	0.0794566	+	0.908193i	−0.846951	+	0.531671i	$0.821564\pi$
$948$	−21.6916	+	58.9797i	−0.704511	+	1.91557i
$949$	−0.831856	+	0.146679i	−0.0270032	+	0.00476139i
$950$	28.3044	−	1.52457i	0.918316	−	0.0494637i
$951$	9.96766	−	9.90089i	0.323224	−	0.321058i
$952$	4.28145	+	8.63087i	0.138763	+	0.279728i
$953$	−8.50165	−	31.7286i	−0.275396	−	1.02779i	−0.955576	−	0.294745i	$-0.904765\pi$
$953$	−8.50165	−	31.7286i	−0.275396	−	1.02779i	0.680180	−	0.733045i	$-0.261901\pi$
$954$	12.1379	+	71.6505i	0.392979	+	2.31977i
$955$	18.0225	+	3.48964i	0.583193	+	0.112922i
$956$	−78.4111	−	13.8260i	−2.53600	−	0.447165i
$957$	−3.49243	+	19.4246i	−0.112894	+	0.627907i
$958$	39.3339	−	56.1746i	1.27082	−	1.81492i
$959$	36.9866	+	20.1789i	1.19436	+	0.651611i
$960$	−46.1632	−	17.8601i	−1.48991	−	0.576432i
$961$	29.0995	−	10.5914i	0.938694	−	0.341657i
$962$	−0.233355	+	0.0625273i	−0.00752367	+	0.00201596i
$963$	−10.1101	+	6.97840i	−0.325795	+	0.224876i
$964$	38.0963	−	21.9949i	1.22700	−	0.708408i
$965$	24.2302	+	2.52892i	0.779999	+	0.0814089i
$966$	53.3366	−	5.78641i	1.71608	−	0.186175i
$967$	−3.45200	+	39.4566i	−0.111009	+	1.26884i	0.712556	+	0.701615i	$0.247538\pi$
$967$	−3.45200	+	39.4566i	−0.111009	+	1.26884i	−0.823565	+	0.567222i	$0.808018\pi$
$968$	1.18074	−	13.4959i	0.0379504	−	0.433775i
$969$	−4.88549	+	6.92754i	−0.156945	+	0.222545i
$970$	22.2097	−	18.0117i	0.713109	−	0.578322i
$971$	35.5260	+	20.5109i	1.14008	+	0.658228i	0.946451	−	0.322847i	$-0.104640\pi$
$971$	35.5260	+	20.5109i	1.14008	+	0.658228i	0.193632	+	0.981074i	$0.437973\pi$
$972$	22.9910	−	38.3197i	0.737436	−	1.22911i
$973$	−24.1722	+	55.2866i	−0.774925	+	1.77241i
$974$	−2.82753	+	16.0357i	−0.0906000	+	0.513818i
$975$	0.599965	+	0.927738i	0.0192143	+	0.0297114i
$976$	0.597045	+	3.38601i	0.0191109	+	0.108384i
$977$	−14.4120	−	30.9067i	−0.461081	−	0.988792i	−0.990124	−	0.140197i	$-0.955227\pi$
$977$	−14.4120	−	30.9067i	−0.461081	−	0.988792i	0.529042	−	0.848595i	$-0.322551\pi$
$978$	0.329784	+	0.575663i	0.0105453	+	0.0184077i
$979$	−23.9445	−	65.7869i	−0.765269	−	2.10256i
$980$	−23.6519	−	38.1315i	−0.755531	−	1.21807i
$981$	6.16607	−	7.24892i	0.196867	−	0.231440i
$982$	−35.3542	+	35.3542i	−1.12820	+	1.12820i
$983$	−8.66009	−	12.3679i	−0.276214	−	0.394474i	0.656945	−	0.753939i	$-0.271848\pi$
$983$	−8.66009	−	12.3679i	−0.276214	−	0.394474i	−0.933159	+	0.359464i	$0.882959\pi$
$984$	−19.4198	−	27.9337i	−0.619080	−	0.890493i
$985$	34.2949	+	35.4619i	1.09273	+	1.12991i
$986$	11.0864	−	1.95482i	0.353062	−	0.0622543i
$987$	13.4303	−	11.7539i	0.427493	−	0.374132i
$988$	0.0819110	+	0.936246i	0.00260593	+	0.0297860i
$989$	65.1940			2.07305
$990$	45.5325	−	43.4457i	1.44712	−	1.38079i
$991$	7.04356			0.223746			0.111873	−	0.993723i	$-0.464315\pi$
$991$	7.04356			0.223746			0.111873	+	0.993723i	$0.464315\pi$
$992$	−1.06581	+	0.746291i	−0.0338396	+	0.0236948i
$993$	−0.0710397	+	21.1372i	−0.00225438	+	0.670767i
$994$	11.9005	+	19.5081i	0.377460	+	0.618761i
$995$	0.152211	−	9.09859i	0.00482541	−	0.288445i
$996$	12.0427	+	8.49287i	0.381588	+	0.269107i
$997$	6.18229	−	13.2580i	0.195795	−	0.419884i	−0.783759	−	0.621065i	$-0.786700\pi$
$997$	6.18229	−	13.2580i	0.195795	−	0.419884i	0.979554	+	0.201181i	$0.0644780\pi$
$998$	29.8259	+	7.99182i	0.944121	+	0.252977i
$999$	−1.19781	+	4.29653i	−0.0378970	+	0.135936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.do.a.758.122	yes	1680
5.2	odd	4	inner	945.2.do.a.2.19	yes	1680
7.4	even	3		945.2.dh.a.893.19	yes	1680
27.14	odd	18		945.2.dh.a.338.122	yes	1680
35.32	odd	12		945.2.dh.a.137.122	✓	1680
135.122	even	36		945.2.dh.a.527.19	yes	1680
189.95	odd	18	inner	945.2.do.a.473.19	yes	1680
945.662	even	36	inner	945.2.do.a.662.122	yes	1680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.dh.a.137.122	✓	1680	35.32	odd	12
945.2.dh.a.338.122	yes	1680	27.14	odd	18
945.2.dh.a.527.19	yes	1680	135.122	even	36
945.2.dh.a.893.19	yes	1680	7.4	even	3
945.2.do.a.2.19	yes	1680	5.2	odd	4	inner
945.2.do.a.473.19	yes	1680	189.95	odd	18	inner
945.2.do.a.662.122	yes	1680	945.662	even	36	inner
945.2.do.a.758.122	yes	1680	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.do (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.192271 + 2.19767i) q^{2} +(-1.70674 + 0.295033i) q^{3} +(-2.82316 + 0.497800i) q^{4} +(1.08549 + 1.95492i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(2.64048 + 0.166853i) q^{7} +(-0.494869 - 1.84688i) q^{8} +(2.82591 - 1.00709i) q^{9} +O(q^{10})\)	\(q+(0.192271 + 2.19767i) q^{2} +(-1.70674 + 0.295033i) q^{3} +(-2.82316 + 0.497800i) q^{4} +(1.08549 + 1.95492i) q^{5} +(-0.976541 - 3.69412i) q^{6} +(2.64048 + 0.166853i) q^{7} +(-0.494869 - 1.84688i) q^{8} +(2.82591 - 1.00709i) q^{9} +(-4.08756 + 2.76141i) q^{10} +(-4.18808 - 0.738472i) q^{11} +(4.67153 - 1.68254i) q^{12} +(-0.0731741 + 0.104503i) q^{13} +(0.141002 + 5.83499i) q^{14} +(-2.42941 - 3.01629i) q^{15} +(-1.42399 + 0.518289i) q^{16} +(-1.83962 + 0.492925i) q^{17} +(2.75659 + 6.01678i) q^{18} +(-2.22549 + 1.28489i) q^{19} +(-4.03766 - 4.97871i) q^{20} +(-4.55584 + 0.494256i) q^{21} +(0.817670 - 9.34601i) q^{22} +(-0.462525 + 5.28668i) q^{23} +(1.38950 + 3.00613i) q^{24} +(-2.64344 + 4.24408i) q^{25} +(-0.243733 - 0.140719i) q^{26} +(-4.52597 + 2.55257i) q^{27} +(-7.53758 + 0.843380i) q^{28} +(-0.465271 + 2.63868i) q^{29} +(6.16169 - 5.91898i) q^{30} +(-0.0315243 - 0.178783i) q^{31} +(-3.02893 - 6.49557i) q^{32} +(7.36584 + 0.0247558i) q^{33} +(-1.43699 - 3.94810i) q^{34} +(2.54003 + 5.34306i) q^{35} +(-7.47668 + 4.24991i) q^{36} +(0.606980 - 0.606980i) q^{37} +(-3.25166 - 4.64385i) q^{38} +(0.0940571 - 0.199949i) q^{39} +(3.07333 - 2.97219i) q^{40} +(-10.1168 + 1.78386i) q^{41} +(-1.96217 - 9.91720i) q^{42} +(-1.07069 - 12.2381i) q^{43} +12.1913 q^{44} +(5.03627 + 4.43125i) q^{45} -11.7073 q^{46} +(-3.19029 + 2.23386i) q^{47} +(2.27746 - 1.30471i) q^{48} +(6.94432 + 0.881145i) q^{49} +(-9.83534 - 4.99339i) q^{50} +(2.99432 - 1.38404i) q^{51} +(0.154561 - 0.331456i) q^{52} +(10.6064 + 2.84198i) q^{53} +(-6.47992 - 9.45579i) q^{54} +(-3.10245 - 8.98898i) q^{55} +(-0.998538 - 4.95922i) q^{56} +(3.41925 - 2.84956i) q^{57} +(-5.88840 - 0.515169i) q^{58} +(3.88857 + 1.41532i) q^{59} +(8.36012 + 7.30611i) q^{60} +(0.393991 - 2.23444i) q^{61} +(0.386845 - 0.103655i) q^{62} +(7.62981 - 2.18769i) q^{63} +(11.0680 - 6.39013i) q^{64} +(-0.283726 - 0.0296126i) q^{65} +(1.36183 + 16.1924i) q^{66} +(1.17970 - 13.4841i) q^{67} +(4.94817 - 2.30737i) q^{68} +(-0.770337 - 9.15944i) q^{69} +(-11.2539 + 6.60945i) q^{70} +(3.39061 - 1.95757i) q^{71} +(-3.25842 - 4.72073i) q^{72} +(4.68183 + 4.68183i) q^{73} +(1.45065 + 1.21724i) q^{74} +(3.25951 - 8.02344i) q^{75} +(5.64331 - 4.73530i) q^{76} +(-10.9354 - 2.64872i) q^{77} +(0.457506 + 0.168262i) q^{78} +(-8.13529 + 9.69526i) q^{79} +(-2.55893 - 2.22119i) q^{80} +(6.97155 - 5.69188i) q^{81} +(-5.86550 - 21.8903i) q^{82} +(1.70228 + 2.43111i) q^{83} +(12.6158 - 3.66326i) q^{84} +(-2.96051 - 3.06125i) q^{85} +(26.6894 - 4.70605i) q^{86} +(0.0155972 - 4.64081i) q^{87} +(0.708686 + 8.10032i) q^{88} +(8.23114 + 14.2567i) q^{89} +(-8.77010 + 11.9200i) q^{90} +(-0.210652 + 0.263731i) q^{91} +(-1.32593 - 15.1554i) q^{92} +(0.106551 + 0.295836i) q^{93} +(-5.52269 - 6.58168i) q^{94} +(-4.92760 - 2.95593i) q^{95} +(7.08601 + 10.1926i) q^{96} +(-5.77479 + 0.505228i) q^{97} +(-0.601272 + 15.4307i) q^{98} +(-12.5789 + 2.13091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8}+O(q^{10}) \) 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8	\( 1680 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 36 q^{6} - 12 q^{7} - 36 q^{8} + 6 q^{10} + 12 q^{11} - 6 q^{12} - 24 q^{13} - 24 q^{15} - 12 q^{16} - 18 q^{17} - 6 q^{18} - 24 q^{20} - 24 q^{21} - 24 q^{22} + 42 q^{23} - 6 q^{25} - 24 q^{27} - 24 q^{28} + 30 q^{30} - 12 q^{31} + 90 q^{32} - 6 q^{33} - 18 q^{35} - 84 q^{36} - 12 q^{37} - 30 q^{38} - 54 q^{40} - 72 q^{41} - 108 q^{42} - 24 q^{43} - 6 q^{45} - 24 q^{46} - 6 q^{47} - 96 q^{48} - 72 q^{50} - 12 q^{51} - 30 q^{52} - 90 q^{53} - 48 q^{55} - 72 q^{56} - 24 q^{57} - 6 q^{58} + 186 q^{60} + 24 q^{61} - 36 q^{62} - 54 q^{63} + 138 q^{65} - 12 q^{66} - 6 q^{67} + 114 q^{68} - 12 q^{70} - 72 q^{71} + 18 q^{72} - 12 q^{73} - 150 q^{75} - 156 q^{77} - 84 q^{78} + 12 q^{81} - 12 q^{82} - 24 q^{83} - 24 q^{85} - 120 q^{86} - 102 q^{87} - 6 q^{88} + 30 q^{90} - 12 q^{91} + 108 q^{92} + 138 q^{93} - 66 q^{95} - 444 q^{96} - 24 q^{97} - 360 q^{98}+O(q^{100}) \) 1680 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 36 * q^6 - 12 * q^7 - 36 * q^8 + 6 * q^10 + 12 * q^11 - 6 * q^12 - 24 * q^13 - 24 * q^15 - 12 * q^16 - 18 * q^17 - 6 * q^18 - 24 * q^20 - 24 * q^21 - 24 * q^22 + 42 * q^23 - 6 * q^25 - 24 * q^27 - 24 * q^28 + 30 * q^30 - 12 * q^31 + 90 * q^32 - 6 * q^33 - 18 * q^35 - 84 * q^36 - 12 * q^37 - 30 * q^38 - 54 * q^40 - 72 * q^41 - 108 * q^42 - 24 * q^43 - 6 * q^45 - 24 * q^46 - 6 * q^47 - 96 * q^48 - 72 * q^50 - 12 * q^51 - 30 * q^52 - 90 * q^53 - 48 * q^55 - 72 * q^56 - 24 * q^57 - 6 * q^58 + 186 * q^60 + 24 * q^61 - 36 * q^62 - 54 * q^63 + 138 * q^65 - 12 * q^66 - 6 * q^67 + 114 * q^68 - 12 * q^70 - 72 * q^71 + 18 * q^72 - 12 * q^73 - 150 * q^75 - 156 * q^77 - 84 * q^78 + 12 * q^81 - 12 * q^82 - 24 * q^83 - 24 * q^85 - 120 * q^86 - 102 * q^87 - 6 * q^88 + 30 * q^90 - 12 * q^91 + 108 * q^92 + 138 * q^93 - 66 * q^95 - 444 * q^96 - 24 * q^97 - 360 * q^98

Introduction

L-functions

Modular forms

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