LMFDB - Embedded newform 675.2.y.a.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0963190 + 0.453145i) q^{2} +(1.63103 + 0.726180i) q^{4} +(2.22769 - 0.193424i) q^{5} +(1.95191 + 1.12694i) q^{7} +(-1.03077 + 1.41873i) q^{8} +O(q^{10})$	\(q+(-0.0963190 + 0.453145i) q^{2} +(1.63103 + 0.726180i) q^{4} +(2.22769 - 0.193424i) q^{5} +(1.95191 + 1.12694i) q^{7} +(-1.03077 + 1.41873i) q^{8} +(-0.126919 + 1.02810i) q^{10} +(-0.465072 - 0.0988542i) q^{11} +(0.730547 + 3.43695i) q^{13} +(-0.698673 + 0.775955i) q^{14} +(1.84570 + 2.04986i) q^{16} +(0.0636721 - 0.0876371i) q^{17} +(-4.61523 - 3.35316i) q^{19} +(3.77388 + 1.30222i) q^{20} +(0.0895906 - 0.201224i) q^{22} +(-3.93659 - 3.54452i) q^{23} +(4.92517 - 0.861776i) q^{25} -1.62780 q^{26} +(2.36526 + 3.25551i) q^{28} +(0.394133 + 3.74992i) q^{29} +(1.13402 - 10.7895i) q^{31} +(-4.14407 + 2.39258i) q^{32} +(0.0335795 + 0.0372938i) q^{34} +(4.56623 + 2.13292i) q^{35} +(1.63720 + 0.531959i) q^{37} +(1.96400 - 1.76839i) q^{38} +(-2.02181 + 3.35987i) q^{40} +(-7.48170 + 1.59028i) q^{41} +(-0.610331 - 0.352375i) q^{43} +(-0.686760 - 0.498960i) q^{44} +(1.98535 - 1.44244i) q^{46} +(1.87005 - 0.196550i) q^{47} +(-0.960022 - 1.66281i) q^{49} +(-0.0838782 + 2.31482i) q^{50} +(-1.30431 + 6.13628i) q^{52} +(4.01720 + 5.52920i) q^{53} +(-1.05516 - 0.130260i) q^{55} +(-3.61080 + 1.60763i) q^{56} +(-1.73722 - 0.182589i) q^{58} +(8.45126 - 1.79637i) q^{59} +(-6.65685 - 1.41496i) q^{61} +(4.77998 + 1.55311i) q^{62} +(1.01972 + 3.13838i) q^{64} +(2.29222 + 7.51515i) q^{65} +(10.9745 + 1.15346i) q^{67} +(0.167491 - 0.0967012i) q^{68} +(-1.40634 + 1.86372i) q^{70} +(1.33478 - 0.969773i) q^{71} +(-3.20933 + 1.04277i) q^{73} +(-0.398749 + 0.690653i) q^{74} +(-5.09256 - 8.82058i) q^{76} +(-0.796378 - 0.717062i) q^{77} +(0.595958 + 5.67016i) q^{79} +(4.50813 + 4.20943i) q^{80} -3.54347i q^{82} +(5.62685 + 12.6381i) q^{83} +(0.124890 - 0.207544i) q^{85} +(0.218463 - 0.242628i) q^{86} +(0.619630 - 0.557917i) q^{88} +(-5.42948 - 16.7102i) q^{89} +(-2.44727 + 7.53192i) q^{91} +(-3.84673 - 8.63989i) q^{92} +(-0.0910553 + 0.866334i) q^{94} +(-10.9299 - 6.57709i) q^{95} +(0.439012 - 0.0461420i) q^{97} +(0.845962 - 0.274870i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.0963190	+	0.453145i	−0.0681078	+	0.320422i	−0.998992	−	0.0448929i	$-0.985705\pi$
$2$	−0.0963190	+	0.453145i	−0.0681078	+	0.320422i	0.930884	+	0.365315i	$0.119039\pi$
$3$		0			0
$3$		0			0
$4$	1.63103	+	0.726180i	0.815514	+	0.363090i
$5$	2.22769	−	0.193424i	0.996252	−	0.0865018i
$5$	2.22769	−	0.193424i	0.996252	−	0.0865018i
$6$		0			0
$7$	1.95191	+	1.12694i	0.737754	+	0.425942i	0.821252	−	0.570565i	$-0.193276\pi$
$7$	1.95191	+	1.12694i	0.737754	+	0.425942i	−0.0834981	+	0.996508i	$0.526609\pi$
$8$	−1.03077	+	1.41873i	−0.364432	+	0.501598i
$9$		0			0
$10$	−0.126919	+	1.02810i	−0.0401354	+	0.325112i
$11$	−0.465072	−	0.0988542i	−0.140225	−	0.0298057i	0.137265	−	0.990534i	$-0.456169\pi$
$11$	−0.465072	−	0.0988542i	−0.140225	−	0.0298057i	−0.277489	+	0.960729i	$0.589502\pi$
$12$		0			0
$13$	0.730547	+	3.43695i	0.202617	+	0.953240i	0.955479	+	0.295060i	$0.0953398\pi$
$13$	0.730547	+	3.43695i	0.202617	+	0.953240i	−0.752861	+	0.658179i	$0.771327\pi$
$14$	−0.698673	+	0.775955i	−0.186728	+	0.207383i
$15$		0			0
$16$	1.84570	+	2.04986i	0.461425	+	0.512464i
$17$	0.0636721	−	0.0876371i	0.0154428	−	0.0212551i	−0.801226	−	0.598362i	$-0.795818\pi$
$17$	0.0636721	−	0.0876371i	0.0154428	−	0.0212551i	0.816669	+	0.577107i	$0.195818\pi$
$18$		0			0
$19$	−4.61523	−	3.35316i	−1.05881	−	0.769267i	−0.0849384	−	0.996386i	$-0.527069\pi$
$19$	−4.61523	−	3.35316i	−1.05881	−	0.769267i	−0.973867	+	0.227119i	$0.927069\pi$
$20$	3.77388	+	1.30222i	0.843865	+	0.291186i
$21$		0			0
$22$	0.0895906	−	0.201224i	0.0191008	−	0.0429010i
$23$	−3.93659	−	3.54452i	−0.820836	−	0.739084i	0.147412	−	0.989075i	$-0.452906\pi$
$23$	−3.93659	−	3.54452i	−0.820836	−	0.739084i	−0.968248	+	0.249991i	$0.919572\pi$
$24$		0			0
$25$	4.92517	−	0.861776i	0.985035	−	0.172355i
$26$	−1.62780			−0.319239
$27$		0			0
$28$	2.36526	+	3.25551i	0.446993	+	0.615233i
$29$	0.394133	+	3.74992i	0.0731887	+	0.696344i	0.968179	+	0.250258i	$0.0805155\pi$
$29$	0.394133	+	3.74992i	0.0731887	+	0.696344i	−0.894990	+	0.446085i	$0.852818\pi$
$30$		0			0
$31$	1.13402	−	10.7895i	0.203676	−	1.93785i	−0.122346	−	0.992487i	$-0.539042\pi$
$31$	1.13402	−	10.7895i	0.203676	−	1.93785i	0.326023	−	0.945362i	$-0.394291\pi$
$32$	−4.14407	+	2.39258i	−0.732575	+	0.422952i
$33$		0			0
$34$	0.0335795	+	0.0372938i	0.00575884	+	0.00639584i
$35$	4.56623	+	2.13292i	0.771833	+	0.360529i
$36$		0			0
$37$	1.63720	+	0.531959i	0.269154	+	0.0874536i	0.440485	−	0.897760i	$-0.354807\pi$
$37$	1.63720	+	0.531959i	0.269154	+	0.0874536i	−0.171330	+	0.985214i	$0.554807\pi$
$38$	1.96400	−	1.76839i	0.318603	−	0.286872i
$39$		0			0
$40$	−2.02181	+	3.35987i	−0.319677	+	0.531241i
$41$	−7.48170	+	1.59028i	−1.16845	+	0.248361i	−0.750975	−	0.660330i	$-0.770416\pi$
$41$	−7.48170	+	1.59028i	−1.16845	+	0.248361i	−0.417470	+	0.908691i	$0.637083\pi$
$42$		0			0
$43$	−0.610331	−	0.352375i	−0.0930746	−	0.0537366i	0.452740	−	0.891642i	$-0.350446\pi$
$43$	−0.610331	−	0.352375i	−0.0930746	−	0.0537366i	−0.545815	+	0.837906i	$0.683780\pi$
$44$	−0.686760	−	0.498960i	−0.103533	−	0.0752211i
$45$		0			0
$46$	1.98535	−	1.44244i	0.292724	−	0.212677i
$47$	1.87005	−	0.196550i	0.272774	−	0.0286697i	0.0328462	−	0.999460i	$-0.489543\pi$
$47$	1.87005	−	0.196550i	0.272774	−	0.0286697i	0.239928	+	0.970791i	$0.422876\pi$
$48$		0			0
$49$	−0.960022	−	1.66281i	−0.137146	−	0.237544i
$50$	−0.0838782	+	2.31482i	−0.0118622	+	0.327366i
$51$		0			0
$52$	−1.30431	+	6.13628i	−0.180875	+	0.850948i
$53$	4.01720	+	5.52920i	0.551804	+	0.759493i	0.990256	−	0.139261i	$-0.0444728\pi$
$53$	4.01720	+	5.52920i	0.551804	+	0.759493i	−0.438451	+	0.898755i	$0.644473\pi$
$54$		0			0
$55$	−1.05516	−	0.130260i	−0.142277	−	0.0175643i
$56$	−3.61080	+	1.60763i	−0.482513	+	0.214829i
$57$		0			0
$58$	−1.73722	−	0.182589i	−0.228109	−	0.0239752i
$59$	8.45126	−	1.79637i	1.10026	−	0.233868i	0.378218	−	0.925716i	$-0.376537\pi$
$59$	8.45126	−	1.79637i	1.10026	−	0.233868i	0.722042	+	0.691849i	$0.243204\pi$
$60$		0			0
$61$	−6.65685	−	1.41496i	−0.852323	−	0.181167i	−0.239020	−	0.971015i	$-0.576826\pi$
$61$	−6.65685	−	1.41496i	−0.852323	−	0.181167i	−0.613303	+	0.789848i	$0.710159\pi$
$62$	4.77998	+	1.55311i	0.607058	+	0.197245i
$63$		0			0
$64$	1.01972	+	3.13838i	0.127465	+	0.392298i
$65$	2.29222	+	7.51515i	0.284315	+	0.932140i
$66$		0			0
$67$	10.9745	+	1.15346i	1.34074	+	0.140918i	0.747584	−	0.664167i	$-0.231214\pi$
$67$	10.9745	+	1.15346i	1.34074	+	0.140918i	0.593159	+	0.805085i	$0.297880\pi$
$68$	0.167491	−	0.0967012i	0.0203113	−	0.0117267i
$69$		0			0
$70$	−1.40634	+	1.86372i	−0.168089	+	0.222758i
$71$	1.33478	−	0.969773i	0.158409	−	0.115091i	−0.505757	−	0.862676i	$-0.668787\pi$
$71$	1.33478	−	0.969773i	0.158409	−	0.115091i	0.664166	+	0.747585i	$0.268787\pi$
$72$		0			0
$73$	−3.20933	+	1.04277i	−0.375623	+	0.122047i	−0.490743	−	0.871304i	$-0.663275\pi$
$73$	−3.20933	+	1.04277i	−0.375623	+	0.122047i	0.115120	+	0.993352i	$0.463275\pi$
$74$	−0.398749	+	0.690653i	−0.0463536	+	0.0802868i
$75$		0			0
$76$	−5.09256	−	8.82058i	−0.584157	−	1.01179i
$77$	−0.796378	−	0.717062i	−0.0907557	−	0.0817168i
$78$		0			0
$79$	0.595958	+	5.67016i	0.0670505	+	0.637943i	0.975508	+	0.219965i	$0.0705944\pi$
$79$	0.595958	+	5.67016i	0.0670505	+	0.637943i	−0.908457	+	0.417978i	$0.862739\pi$
$80$	4.50813	+	4.20943i	0.504024	+	0.470629i
$81$		0			0
$82$		−	3.54347i		−	0.391311i
$83$	5.62685	+	12.6381i	0.617627	+	1.38721i	0.903352	+	0.428900i	$0.141099\pi$
$83$	5.62685	+	12.6381i	0.617627	+	1.38721i	−0.285725	+	0.958312i	$0.592234\pi$
$84$		0			0
$85$	0.124890	−	0.207544i	0.0135463	−	0.0225113i
$86$	0.218463	−	0.242628i	0.0235575	−	0.0261633i
$87$		0			0
$88$	0.619630	−	0.557917i	0.0660528	−	0.0594742i
$89$	−5.42948	−	16.7102i	−0.575523	−	1.77128i	−0.634390	−	0.773013i	$-0.718749\pi$
$89$	−5.42948	−	16.7102i	−0.575523	−	1.77128i	0.0588665	−	0.998266i	$-0.481251\pi$
$90$		0			0
$91$	−2.44727	+	7.53192i	−0.256543	+	0.789560i
$92$	−3.84673	−	8.63989i	−0.401049	−	0.900771i
$93$		0			0
$94$	−0.0910553	+	0.866334i	−0.00939164	+	0.0893555i
$95$	−10.9299	−	6.57709i	−1.12138	−	0.674795i
$96$		0			0
$97$	0.439012	−	0.0461420i	0.0445749	−	0.00468501i	−0.0822148	−	0.996615i	$-0.526199\pi$
$97$	0.439012	−	0.0461420i	0.0445749	−	0.00468501i	0.126790	+	0.991930i	$0.459533\pi$
$98$	0.845962	−	0.274870i	0.0854550	−	0.0277660i
$99$		0			0
$100$	8.65890	+	2.17098i	0.865890	+	0.217098i
$101$	−6.27977	+	10.8769i	−0.624860	+	1.08229i	0.363708	+	0.931513i	$0.381511\pi$
$101$	−6.27977	+	10.8769i	−0.624860	+	1.08229i	−0.988568	+	0.150777i	$0.951823\pi$
$102$		0			0
$103$	−5.19487	+	11.6679i	−0.511866	+	1.14967i	0.454088	+	0.890957i	$0.349965\pi$
$103$	−5.19487	+	11.6679i	−0.511866	+	1.14967i	−0.965954	+	0.258713i	$0.916702\pi$
$104$	−5.62914	−	2.50626i	−0.551983	−	0.245759i
$105$		0			0
$106$	−2.89246	+	1.28781i	−0.280941	+	0.125083i
$107$		−	19.9165i		−	1.92540i	−0.270562	−	0.962702i	$-0.587210\pi$
$107$		−	19.9165i		−	1.92540i	0.270562	−	0.962702i	$-0.412790\pi$
$108$		0			0
$109$	4.44163	−	13.6699i	0.425431	−	1.30934i	−0.477150	−	0.878822i	$-0.658330\pi$
$109$	4.44163	−	13.6699i	0.425431	−	1.30934i	0.902581	−	0.430521i	$-0.141670\pi$
$110$	0.160658	−	0.465592i	0.0153182	−	0.0443925i
$111$		0			0
$112$	1.29258	+	6.08113i	0.122138	+	0.574613i
$113$	−1.13013	−	5.31683i	−0.106313	−	0.500165i	−0.998795	−	0.0490808i	$-0.984371\pi$
$113$	−1.13013	−	5.31683i	−0.106313	−	0.500165i	0.892481	−	0.451084i	$-0.148963\pi$
$114$		0			0
$115$	−9.45509	−	7.13466i	−0.881692	−	0.665310i
$116$	−2.08028	+	6.40244i	−0.193149	+	0.594452i
$117$		0			0
$118$			4.00267i			0.368476i
$119$	0.223044	−	0.0993056i	0.0204464	−	0.00910333i
$120$		0			0
$121$	−9.84248	−	4.38215i	−0.894771	−	0.398378i
$122$	1.28236	−	2.88023i	0.116100	−	0.260764i
$123$		0			0
$124$	9.68473	−	16.7745i	0.869715	−	1.50639i
$125$	10.8051	−	2.87241i	0.966434	−	0.256916i
$126$		0			0
$127$	7.93872	−	2.57945i	0.704448	−	0.228889i	0.0651803	−	0.997874i	$-0.479238\pi$
$127$	7.93872	−	2.57945i	0.704448	−	0.228889i	0.639267	+	0.768985i	$0.279238\pi$
$128$	−11.0382	+	1.16017i	−0.975653	+	0.102545i
$129$		0			0
$130$	−3.62624	+	0.314856i	−0.318042	+	0.0276147i
$131$	1.41260	−	13.4400i	0.123419	−	1.17426i	−0.741007	−	0.671497i	$-0.765652\pi$
$131$	1.41260	−	13.4400i	0.123419	−	1.17426i	0.864426	−	0.502759i	$-0.167682\pi$
$132$		0			0
$133$	−5.22972	−	11.7461i	−0.453474	−	1.01852i
$134$	−1.57973	+	4.86192i	−0.136468	+	0.420006i
$135$		0			0
$136$	0.0587024	+	0.180667i	0.00503369	+	0.0154921i
$137$	−2.82955	+	2.54774i	−0.241745	+	0.217668i	−0.781093	−	0.624415i	$-0.785337\pi$
$137$	−2.82955	+	2.54774i	−0.241745	+	0.217668i	0.539348	+	0.842083i	$0.318671\pi$
$138$		0			0
$139$	3.51985	−	3.90919i	0.298550	−	0.331573i	−0.575141	−	0.818054i	$-0.695053\pi$
$139$	3.51985	−	3.90919i	0.298550	−	0.331573i	0.873691	+	0.486481i	$0.161720\pi$
$140$	5.89876	+	6.79475i	0.498536	+	0.574261i
$141$		0			0
$142$	0.310884	+	0.698256i	0.0260888	+	0.0585963i
$143$		−	1.67065i		−	0.139707i
$144$		0			0
$145$	1.60333	+	8.27742i	0.133149	+	0.687402i
$146$	−0.163409	−	1.55473i	−0.0135238	−	0.128670i
$147$		0			0
$148$	2.28402	+	2.05654i	0.187746	+	0.169047i
$149$	−3.97418	−	6.88348i	−0.325577	−	0.563917i	0.656052	−	0.754716i	$-0.272225\pi$
$149$	−3.97418	−	6.88348i	−0.325577	−	0.563917i	−0.981629	+	0.190799i	$0.938892\pi$
$150$		0			0
$151$	−1.90213	+	3.29458i	−0.154793	+	0.268109i	−0.932984	−	0.359919i	$-0.882804\pi$
$151$	−1.90213	+	3.29458i	−0.154793	+	0.268109i	0.778191	+	0.628028i	$0.216138\pi$
$152$	9.51446	−	3.09144i	0.771725	−	0.250749i
$153$		0			0
$154$	0.401640	−	0.291808i	0.0323651	−	0.0235146i
$155$	0.439298	−	24.2549i	0.0352852	−	1.94820i
$156$		0			0
$157$	−10.6410	+	6.14356i	−0.849241	+	0.490309i	−0.860395	−	0.509628i	$-0.829783\pi$
$157$	−10.6410	+	6.14356i	−0.849241	+	0.490309i	0.0111539	+	0.999938i	$0.496450\pi$
$158$	−2.62681	−	0.276089i	−0.208978	−	0.0219644i
$159$		0			0
$160$	−8.76890	+	6.13148i	−0.693243	+	0.484736i
$161$	−3.68943	−	11.3549i	−0.290768	−	0.894891i
$162$		0			0
$163$	−22.9116	−	7.44443i	−1.79457	−	0.583093i	−0.794856	−	0.606798i	$-0.792454\pi$
$163$	−22.9116	−	7.44443i	−1.79457	−	0.583093i	−0.999719	+	0.0237055i	$0.992454\pi$
$164$	−13.3577	−	2.83926i	−1.04306	−	0.221709i
$165$		0			0
$166$	−6.26887	+	1.33249i	−0.486559	+	0.103421i
$167$	6.24446	+	0.656319i	0.483210	+	0.0507875i	0.343002	−	0.939335i	$-0.388556\pi$
$167$	6.24446	+	0.656319i	0.483210	+	0.0507875i	0.140208	+	0.990122i	$0.455223\pi$
$168$		0			0
$169$	0.597136	−	0.265862i	0.0459335	−	0.0204509i
$170$	0.0820181	+	0.0765839i	0.00629050	+	0.00587372i
$171$		0			0
$172$	−0.739579	−	1.01794i	−0.0563924	−	0.0776174i
$173$	−1.54592	+	7.27296i	−0.117534	+	0.552953i	0.879494	+	0.475910i	$0.157881\pi$
$173$	−1.54592	+	7.27296i	−0.117534	+	0.552953i	−0.997028	+	0.0770430i	$0.975452\pi$
$174$		0			0
$175$	10.5847	+	3.86825i	0.800127	+	0.292412i
$176$	−0.655746	−	1.13579i	−0.0494287	−	0.0856131i
$177$		0			0
$178$	8.09511	−	0.850831i	0.606755	−	0.0637725i
$179$	16.9136	−	12.2884i	1.26418	−	0.918481i	0.265225	−	0.964187i	$-0.414554\pi$
$179$	16.9136	−	12.2884i	1.26418	−	0.918481i	0.998955	+	0.0457060i	$0.0145537\pi$
$180$		0			0
$181$	−1.42930	−	1.03845i	−0.106239	−	0.0771874i	0.533397	−	0.845865i	$-0.320915\pi$
$181$	−1.42930	−	1.03845i	−0.106239	−	0.0771874i	−0.639637	+	0.768678i	$0.720915\pi$
$182$	−3.17733	−	1.83443i	−0.235520	−	0.135977i
$183$		0			0
$184$	9.08645	−	1.93138i	0.669862	−	0.142384i
$185$	3.75007	+	0.868365i	0.275711	+	0.0638434i
$186$		0			0
$187$	−0.0382754	+	0.0344633i	−0.00279898	+	0.00252021i
$188$	3.19283	+	1.03741i	0.232861	+	0.0756611i
$189$		0			0
$190$	4.03313	−	4.31931i	0.292594	−	0.313356i
$191$	6.50683	+	7.22657i	0.470818	+	0.522896i	0.931045	−	0.364905i	$-0.118899\pi$
$191$	6.50683	+	7.22657i	0.470818	+	0.522896i	−0.460227	+	0.887801i	$0.652232\pi$
$192$		0			0
$193$	−11.4975	+	6.63811i	−0.827611	+	0.477822i	−0.853034	−	0.521855i	$-0.825240\pi$
$193$	−11.4975	+	6.63811i	−0.827611	+	0.477822i	0.0254229	+	0.999677i	$0.491907\pi$
$194$	−0.0213761	+	0.203380i	−0.00153472	+	0.0146019i
$195$		0			0
$196$	−0.358325	−	3.40923i	−0.0255946	−	0.243517i
$197$	7.37613	+	10.1524i	0.525527	+	0.723326i	0.986441	−	0.164119i	$-0.0524780\pi$
$197$	7.37613	+	10.1524i	0.525527	+	0.723326i	−0.460913	+	0.887445i	$0.652478\pi$
$198$		0			0
$199$	−23.3663			−1.65639			−0.828196	−	0.560438i	$-0.810633\pi$
$199$	−23.3663			−1.65639			−0.828196	+	0.560438i	$0.810633\pi$
$200$	−3.85409	+	7.87579i	−0.272525	+	0.556903i
$201$		0			0
$202$	−4.32394	−	3.89330i	−0.304232	−	0.273931i
$203$	−3.45662	+	7.76369i	−0.242607	+	0.544904i
$204$		0			0
$205$	−16.3593	+	4.98979i	−1.14258	+	0.348502i
$206$	−4.78688	−	3.47787i	−0.333517	−	0.242315i
$207$		0			0
$208$	−5.69689	+	7.84110i	−0.395008	+	0.543682i
$209$	1.81494	+	2.01570i	0.125542	+	0.139429i
$210$		0			0
$211$	3.16388	−	3.51385i	0.217811	−	0.241903i	−0.624331	−	0.781160i	$-0.714628\pi$
$211$	3.16388	−	3.51385i	0.217811	−	0.241903i	0.842141	+	0.539257i	$0.181295\pi$
$212$	2.53696	+	11.9355i	0.174239	+	0.819732i
$213$		0			0
$214$	9.02509	+	1.91834i	0.616942	+	0.131135i
$215$	−1.42778	−	0.666928i	−0.0973740	−	0.0454841i
$216$		0			0
$217$	14.3726	−	19.7822i	0.975675	−	1.34290i
$218$	5.76665	+	3.32938i	0.390567	+	0.225494i
$219$		0			0
$220$	−1.62640	−	0.978691i	−0.109652	−	0.0659833i
$221$	0.347720	+	0.154815i	0.0233902	+	0.0104140i
$222$		0			0
$223$	3.03985	−	14.3014i	0.203563	−	0.957689i	−0.751143	−	0.660139i	$-0.770497\pi$
$223$	3.03985	−	14.3014i	0.203563	−	0.957689i	0.954706	−	0.297550i	$-0.0961695\pi$
$224$	−10.7851			−0.720613
$225$		0			0
$226$	2.51815			0.167505
$227$	4.52072	−	21.2683i	0.300051	−	1.41163i	−0.527175	−	0.849757i	$-0.676749\pi$
$227$	4.52072	−	21.2683i	0.300051	−	1.41163i	0.827225	−	0.561871i	$-0.189918\pi$
$228$		0			0
$229$	21.9978	+	9.79405i	1.45365	+	0.647209i	0.973231	−	0.229828i	$-0.0738163\pi$
$229$	21.9978	+	9.79405i	1.45365	+	0.647209i	0.480424	+	0.877037i	$0.340483\pi$
$230$	4.14374	−	3.59733i	0.273230	−	0.237201i
$231$		0			0
$232$	−5.72640	−	3.30614i	−0.375956	−	0.217059i
$233$	−14.5941	+	20.0871i	−0.956091	+	1.31595i	−0.00732317	+	0.999973i	$0.502331\pi$
$233$	−14.5941	+	20.0871i	−0.956091	+	1.31595i	−0.948768	+	0.315973i	$0.897669\pi$
$234$		0			0
$235$	4.12786	−	0.799563i	0.269272	−	0.0521577i
$236$	15.0887	+	3.20721i	0.982193	+	0.208772i
$237$		0			0
$238$	0.0235165	+	0.110636i	0.00152435	+	0.00717149i
$239$	−11.1193	+	12.3493i	−0.719249	+	0.798807i	−0.986315	−	0.164871i	$-0.947279\pi$
$239$	−11.1193	+	12.3493i	−0.719249	+	0.798807i	0.267066	+	0.963678i	$0.413946\pi$
$240$		0			0
$241$	5.83074	+	6.47569i	0.375591	+	0.417136i	0.901072	−	0.433669i	$-0.142781\pi$
$241$	5.83074	+	6.47569i	0.375591	+	0.417136i	−0.525481	+	0.850805i	$0.676115\pi$
$242$	2.93377	−	4.03799i	0.188590	−	0.259572i
$243$		0			0
$244$	−9.83000	−	7.14191i	−0.629301	−	0.457214i
$245$	−2.46026	−	3.51852i	−0.157180	−	0.224790i
$246$		0			0
$247$	8.15301	−	18.3120i	0.518764	−	1.16516i
$248$	14.1385	+	12.7303i	0.897794	+	0.808378i
$249$		0			0
$250$	0.260888	+	5.17293i	0.0165000	+	0.327165i
$251$	−9.37202			−0.591557			−0.295778	−	0.955257i	$-0.595579\pi$
$251$	−9.37202			−0.591557			−0.295778	+	0.955257i	$0.595579\pi$
$252$		0			0
$253$	1.48041	+	2.03761i	0.0930725	+	0.128103i
$254$	0.404214	+	3.84584i	0.0253627	+	0.241310i
$255$		0			0
$256$	−0.152396	+	1.44995i	−0.00952477	+	0.0906222i
$257$	8.31682	−	4.80172i	0.518789	−	0.299523i	−0.217650	−	0.976027i	$-0.569839\pi$
$257$	8.31682	−	4.80172i	0.518789	−	0.299523i	0.736439	+	0.676504i	$0.236506\pi$
$258$		0			0
$259$	2.59619	+	2.88336i	0.161320	+	0.179164i
$260$	−1.71868	+	13.9220i	−0.106588	+	0.863405i
$261$		0			0
$262$	5.95420	+	1.93464i	0.367852	+	0.119522i
$263$	8.66161	−	7.79895i	0.534098	−	0.480904i	−0.357386	−	0.933957i	$-0.616332\pi$
$263$	8.66161	−	7.79895i	0.534098	−	0.480904i	0.891484	+	0.453053i	$0.149665\pi$
$264$		0			0
$265$	10.0185	+	11.5403i	0.615434	+	0.708915i
$266$	5.82643	−	1.23845i	0.357241	−	0.0759340i
$267$		0			0
$268$	17.0620	+	9.85076i	1.04223	+	0.601731i
$269$	−0.642833	−	0.467046i	−0.0391942	−	0.0284763i	0.568016	−	0.823018i	$-0.307711\pi$
$269$	−0.642833	−	0.467046i	−0.0391942	−	0.0284763i	−0.607210	+	0.794541i	$0.707711\pi$
$270$		0			0
$271$	9.36862	−	6.80670i	0.569103	−	0.413478i	−0.265676	−	0.964062i	$-0.585595\pi$
$271$	9.36862	−	6.80670i	0.569103	−	0.413478i	0.834779	+	0.550585i	$0.185595\pi$
$272$	0.297163	−	0.0312331i	0.0180182	−	0.00189378i
$273$		0			0
$274$	−0.881955	−	1.52759i	−0.0532809	−	0.0922852i
$275$	−2.37575	−	0.0860859i	−0.143263	−	0.00519118i
$276$		0			0
$277$	−0.512109	+	2.40928i	−0.0307696	+	0.144760i	−0.990851	−	0.134962i	$-0.956909\pi$
$277$	−0.512109	+	2.40928i	−0.0307696	+	0.144760i	0.960081	+	0.279722i	$0.0902422\pi$
$278$	1.43240	+	1.97153i	0.0859098	+	0.118245i
$279$		0			0
$280$	−7.73277	+	4.27971i	−0.462121	+	0.255762i
$281$	−4.01547	+	1.78780i	−0.239543	+	0.106651i	−0.522997	−	0.852334i	$-0.675186\pi$
$281$	−4.01547	+	1.78780i	−0.239543	+	0.106651i	0.283455	+	0.958986i	$0.408520\pi$
$282$		0			0
$283$	−21.4096	−	2.25024i	−1.27267	−	0.133763i	−0.556003	−	0.831180i	$-0.687666\pi$
$283$	−21.4096	−	2.25024i	−1.27267	−	0.133763i	−0.716665	+	0.697418i	$0.754332\pi$
$284$	2.88129	−	0.612437i	0.170973	−	0.0363415i
$285$		0			0
$286$	0.757047	+	0.160915i	0.0447651	+	0.00951512i
$287$	−16.3958	−	5.32731i	−0.967812	−	0.314461i
$288$		0			0
$289$	5.24966	+	16.1568i	0.308804	+	0.950400i
$290$	−3.90531	−	0.0707316i	−0.229327	−	0.00415350i
$291$		0			0
$292$	−5.99175	−	0.629758i	−0.350640	−	0.0368538i
$293$	−12.4038	+	7.16132i	−0.724636	+	0.418369i	−0.816457	−	0.577407i	$-0.804065\pi$
$293$	−12.4038	+	7.16132i	−0.724636	+	0.418369i	0.0918206	+	0.995776i	$0.470731\pi$
$294$		0			0
$295$	18.4793	−	5.63643i	1.07591	−	0.328166i
$296$	−2.44229	+	1.77442i	−0.141955	+	0.103136i
$297$		0			0
$298$	3.50201	−	1.13787i	0.202866	−	0.0659151i
$299$	9.30650	−	16.1193i	0.538209	−	0.932205i
$300$		0			0
$301$	−0.794209	−	1.37561i	−0.0457774	−	0.0792888i
$302$	−1.30971	−	1.17927i	−0.0753654	−	0.0678594i
$303$		0			0
$304$	−1.64483	−	15.6495i	−0.0943372	−	0.897558i
$305$	−15.1031	−	1.86449i	−0.864799	−	0.106760i
$306$		0			0
$307$			14.5621i			0.831102i	0.909570	+	0.415551i	$0.136411\pi$
$307$			14.5621i			0.831102i	−0.909570	+	0.415551i	$0.863589\pi$
$308$	−0.778199	−	1.74786i	−0.0443420	−	0.0995937i
$309$		0			0
$310$	10.9487	+	2.53528i	0.621844	+	0.143994i
$311$	−15.1541	+	16.8303i	−0.859310	+	0.954361i	−0.999360	−	0.0357837i	$-0.988607\pi$
$311$	−15.1541	+	16.8303i	−0.859310	+	0.954361i	0.140049	+	0.990145i	$0.455274\pi$
$312$		0			0
$313$	−9.87088	+	8.88778i	−0.557935	+	0.502367i	−0.899163	−	0.437614i	$-0.855824\pi$
$313$	−9.87088	+	8.88778i	−0.557935	+	0.502367i	0.341228	+	0.939980i	$0.389157\pi$
$314$	−1.75900	−	5.41364i	−0.0992660	−	0.305509i
$315$		0			0
$316$	−3.14554	+	9.68096i	−0.176950	+	0.544597i
$317$	11.8133	+	26.5330i	0.663500	+	1.49024i	0.860293	+	0.509799i	$0.170280\pi$
$317$	11.8133	+	26.5330i	0.663500	+	1.49024i	−0.196794	+	0.980445i	$0.563053\pi$
$318$		0			0
$319$	0.187395	−	1.78295i	0.0104921	−	0.0998259i
$320$	2.87866	+	6.79410i	0.160922	+	0.379802i
$321$		0			0
$322$	5.50078	−	0.578155i	0.306547	−	0.0322193i
$323$	−0.587722	+	0.190963i	−0.0327017	+	0.0106254i
$324$		0			0
$325$	6.55996	+	16.2980i	0.363881	+	0.904052i
$326$	5.58023	−	9.66524i	0.309060	−	0.535308i
$327$		0			0
$328$	5.45572	−	12.2537i	0.301242	−	0.676600i
$329$	3.87167	+	1.72378i	0.213452	+	0.0950349i
$330$		0			0
$331$	−14.5022	+	6.45681i	−0.797115	+	0.354899i	−0.764545	−	0.644571i	$-0.777036\pi$
$331$	−14.5022	+	6.45681i	−0.797115	+	0.354899i	−0.0325707	+	0.999469i	$0.510369\pi$
$332$			24.6992i			1.35554i
$333$		0			0
$334$	−0.898867	+	2.76643i	−0.0491838	+	0.151372i
$335$	24.6708	+	0.446829i	1.34791	+	0.0244129i
$336$		0			0
$337$	1.51242	+	7.11535i	0.0823865	+	0.387598i	0.999950	−	0.00999103i	$-0.00318030\pi$
$337$	1.51242	+	7.11535i	0.0823865	+	0.387598i	−0.917564	+	0.397589i	$0.869847\pi$
$338$	0.0629586	+	0.296197i	0.00342449	+	0.0161110i
$339$		0			0
$340$	0.354414	−	0.247817i	0.0192208	−	0.0134397i
$341$	−1.59399	+	4.90579i	−0.0863193	+	0.265663i
$342$		0			0
$343$		−	20.1047i		−	1.08555i
$344$	1.12904	−	0.502679i	0.0608735	−	0.0271026i
$345$		0			0
$346$	−3.14681	−	1.40105i	−0.169173	−	0.0753208i
$347$	7.75228	−	17.4119i	0.416164	−	0.934720i	−0.576864	−	0.816840i	$-0.695724\pi$
$347$	7.75228	−	17.4119i	0.416164	−	0.934720i	0.993028	−	0.117879i	$-0.0376096\pi$
$348$		0			0
$349$	5.38588	−	9.32861i	0.288299	−	0.499349i	−0.685105	−	0.728445i	$-0.740244\pi$
$349$	5.38588	−	9.32861i	0.288299	−	0.499349i	0.973404	+	0.229096i	$0.0735769\pi$
$350$	−2.77239	+	4.42381i	−0.148190	+	0.236463i
$351$		0			0
$352$	2.16381	−	0.703064i	0.115331	−	0.0374734i
$353$	−10.6361	+	1.11790i	−0.566101	+	0.0594997i	−0.383256	−	0.923642i	$-0.625197\pi$
$353$	−10.6361	+	1.11790i	−0.566101	+	0.0594997i	−0.182845	+	0.983142i	$0.558531\pi$
$354$		0			0
$355$	2.78589	−	2.41853i	0.147860	−	0.128362i
$356$	3.27900	−	31.1976i	0.173787	−	1.65347i
$357$		0			0
$358$	3.93935	+	8.84792i	0.208201	+	0.467627i
$359$	−4.51829	+	13.9059i	−0.238466	+	0.733923i	0.758176	+	0.652049i	$0.226091\pi$
$359$	−4.51829	+	13.9059i	−0.238466	+	0.733923i	−0.996643	+	0.0818741i	$0.973909\pi$
$360$		0			0
$361$	4.18532	+	12.8811i	0.220280	+	0.677952i
$362$	0.608238	−	0.547660i	0.0319683	−	0.0287844i
$363$		0			0
$364$	−9.46109	+	10.5076i	−0.495896	+	0.550748i
$365$	−6.94768	+	2.94373i	−0.363658	+	0.154082i
$366$		0			0
$367$	6.80742	+	15.2897i	0.355345	+	0.798117i	0.999449	+	0.0331799i	$0.0105634\pi$
$367$	6.80742	+	15.2897i	0.355345	+	0.798117i	−0.644105	+	0.764937i	$0.722770\pi$
$368$		−	14.6116i		−	0.761681i
$369$		0			0
$370$	−0.754698	+	1.61569i	−0.0392349	+	0.0839955i
$371$	1.61016	+	15.3196i	0.0835953	+	0.795356i
$372$		0			0
$373$	−3.27745	−	2.95103i	−0.169700	−	0.152798i	0.579905	−	0.814684i	$-0.303090\pi$
$373$	−3.27745	−	2.95103i	−0.169700	−	0.152798i	−0.749605	+	0.661886i	$0.769756\pi$
$374$	−0.0119303	−	0.0206638i	−0.000616899	−	0.00106850i
$375$		0			0
$376$	−1.64873	+	2.85569i	−0.0850270	+	0.147271i
$377$	−12.6004	+	4.09411i	−0.648953	+	0.210858i
$378$		0			0
$379$	−15.4394	+	11.2174i	−0.793071	+	0.576199i	−0.908873	−	0.417073i	$-0.863056\pi$
$379$	−15.4394	+	11.2174i	−0.793071	+	0.576199i	0.115803	+	0.993272i	$0.463056\pi$
$380$	−13.0507	−	18.6645i	−0.669489	−	0.957467i
$381$		0			0
$382$	−3.90142	+	2.25248i	−0.199614	+	0.115247i
$383$	0.480237	+	0.0504749i	0.0245389	+	0.00257915i	0.116790	−	0.993157i	$-0.462740\pi$
$383$	0.480237	+	0.0504749i	0.0245389	+	0.00257915i	−0.0922510	+	0.995736i	$0.529406\pi$
$384$		0			0
$385$	−1.91278	−	1.44335i	−0.0974842	−	0.0735600i
$386$	−1.90060	−	5.84943i	−0.0967378	−	0.297728i
$387$		0			0
$388$	0.749548	+	0.243543i	0.0380525	+	0.0123640i
$389$	−21.6678	−	4.60564i	−1.09860	−	0.233515i	−0.377270	−	0.926103i	$-0.623137\pi$
$389$	−21.6678	−	4.60564i	−1.09860	−	0.233515i	−0.721333	+	0.692588i	$0.756470\pi$
$390$		0			0
$391$	−0.561283	+	0.119304i	−0.0283853	+	0.00603348i
$392$	3.34864	+	0.351956i	0.169132	+	0.0177765i
$393$		0			0
$394$	−5.31096	+	2.36459i	−0.267562	+	0.119126i
$395$	2.42435	+	12.5161i	0.121982	+	0.629752i
$396$		0			0
$397$	−7.56291	−	10.4095i	−0.379572	−	0.522436i	0.575899	−	0.817521i	$-0.304652\pi$
$397$	−7.56291	−	10.4095i	−0.379572	−	0.522436i	−0.955471	+	0.295085i	$0.904652\pi$
$398$	2.25062	−	10.5883i	0.112813	−	0.530745i
$399$		0			0
$400$	10.8569	+	8.50532i	0.542845	+	0.425266i
$401$	12.0084	+	20.7991i	0.599671	+	1.03866i	0.992869	+	0.119207i	$0.0380351\pi$
$401$	12.0084	+	20.7991i	0.599671	+	1.03866i	−0.393199	+	0.919453i	$0.628632\pi$
$402$		0			0
$403$	37.9114	−	3.98465i	1.88850	−	0.198490i
$404$	−18.1410	+	13.1802i	−0.902551	+	0.655742i
$405$		0			0
$406$	−3.18514	−	2.31414i	−0.158076	−	0.114849i
$407$	−0.708831	−	0.409244i	−0.0351355	−	0.0202855i
$408$		0			0
$409$	26.4726	−	5.62694i	1.30899	−	0.278234i	0.499983	−	0.866035i	$-0.333340\pi$
$409$	26.4726	−	5.62694i	1.30899	−	0.278234i	0.809005	+	0.587801i	$0.200006\pi$
$410$	−0.685392	−	7.89374i	−0.0338491	−	0.389844i
$411$		0			0
$412$	−16.9460	+	15.2582i	−0.834867	+	0.751718i
$413$	18.5205	+	6.01769i	0.911336	+	0.296111i
$414$		0			0
$415$	14.9794	+	27.0654i	0.735308	+	1.32859i
$416$	−11.2506	−	12.4951i	−0.551607	−	0.612622i
$417$		0			0
$418$	−1.08822	+	0.628282i	−0.0532264	+	0.0307303i
$419$	−0.505370	+	4.80828i	−0.0246890	+	0.234900i	0.975218	+	0.221247i	$0.0710126\pi$
$419$	−0.505370	+	4.80828i	−0.0246890	+	0.234900i	−0.999907	+	0.0136529i	$0.995654\pi$
$420$		0			0
$421$	1.46471	+	13.9358i	0.0713855	+	0.679187i	0.970439	+	0.241348i	$0.0775895\pi$
$421$	1.46471	+	13.9358i	0.0713855	+	0.679187i	−0.899053	+	0.437839i	$0.855744\pi$
$422$	1.28754	+	1.77215i	0.0626765	+	0.0862669i
$423$		0			0
$424$	−11.9852			−0.582055
$425$	0.238073	−	0.486499i	0.0115482	−	0.0235987i
$426$		0			0
$427$	−11.3990	−	10.2637i	−0.551638	−	0.496697i
$428$	14.4630	−	32.4844i	0.699096	−	1.57019i
$429$		0			0
$430$	0.439738	−	0.582755i	0.0212060	−	0.0281030i
$431$	25.3074	+	18.3869i	1.21902	+	0.885667i	0.996018	−	0.0891516i	$-0.0284156\pi$
$431$	25.3074	+	18.3869i	1.21902	+	0.885667i	0.222998	+	0.974819i	$0.428416\pi$
$432$		0			0
$433$	22.0928	−	30.4081i	1.06171	−	1.46132i	0.183519	−	0.983016i	$-0.441251\pi$
$433$	22.0928	−	30.4081i	1.06171	−	1.46132i	0.878193	−	0.478306i	$-0.158749\pi$
$434$	7.57985	+	8.41827i	0.363844	+	0.404090i
$435$		0			0
$436$	17.1713	−	19.0706i	0.822354	−	0.913317i
$437$	6.28292	+	29.5588i	0.300553	+	1.41399i
$438$		0			0
$439$	−19.3461	−	4.11214i	−0.923338	−	0.196262i	−0.278372	−	0.960473i	$-0.589795\pi$
$439$	−19.3461	−	4.11214i	−0.923338	−	0.196262i	−0.644966	+	0.764212i	$0.723128\pi$
$440$	1.27243	−	1.36272i	0.0606605	−	0.0649649i
$441$		0			0
$442$	−0.103646	+	0.142656i	−0.00492993	+	0.00678546i
$443$	8.47262	+	4.89167i	0.402546	+	0.232410i	0.687582	−	0.726107i	$-0.258672\pi$
$443$	8.47262	+	4.89167i	0.402546	+	0.232410i	−0.285036	+	0.958517i	$0.592005\pi$
$444$		0			0
$445$	−15.3273	−	36.1749i	−0.726585	−	1.71486i
$446$	6.18779	+	2.75498i	0.293001	+	0.130452i
$447$		0			0
$448$	−1.54635	+	7.27502i	−0.0730583	+	0.343712i
$449$	10.7750			0.508505			0.254252	−	0.967138i	$-0.418171\pi$
$449$	10.7750			0.508505			0.254252	+	0.967138i	$0.418171\pi$
$450$		0			0
$451$	3.63674			0.171247
$452$	2.01771	−	9.49257i	0.0949050	−	0.446493i
$453$		0			0
$454$	9.20220	+	4.09708i	0.431881	+	0.192286i
$455$	−3.99489	+	17.2521i	−0.187284	+	0.808792i
$456$		0			0
$457$	34.9111	+	20.1559i	1.63307	+	0.942855i	0.983138	+	0.182864i	$0.0585369\pi$
$457$	34.9111	+	20.1559i	1.63307	+	0.942855i	0.649934	+	0.759990i	$0.274796\pi$
$458$	−6.55693	+	9.02484i	−0.306385	+	0.421703i
$459$		0			0
$460$	−10.2405	−	18.5029i	−0.477464	−	0.862703i
$461$	−21.8005	−	4.63383i	−1.01535	−	0.215819i	−0.329959	−	0.943995i	$-0.607035\pi$
$461$	−21.8005	−	4.63383i	−1.01535	−	0.215819i	−0.685390	+	0.728176i	$0.740368\pi$
$462$		0			0
$463$	4.97618	+	23.4111i	0.231263	+	1.08801i	0.928548	+	0.371213i	$0.121058\pi$
$463$	4.97618	+	23.4111i	0.231263	+	1.08801i	−0.697285	+	0.716794i	$0.745609\pi$
$464$	−6.95935	+	7.72915i	−0.323080	+	0.358817i
$465$		0			0
$466$	−7.69666	−	8.54801i	−0.356541	−	0.395979i
$467$	5.56984	−	7.66622i	0.257741	−	0.354751i	−0.660462	−	0.750859i	$-0.729640\pi$
$467$	5.56984	−	7.66622i	0.257741	−	0.354751i	0.918204	+	0.396109i	$0.129640\pi$
$468$		0			0
$469$	20.1213	+	14.6190i	0.929116	+	0.675042i
$470$	−0.0352731	+	1.94753i	−0.00162703	+	0.0898329i
$471$		0			0
$472$	−6.16273	+	13.8417i	−0.283663	+	0.637117i
$473$	0.249014	+	0.224213i	0.0114497	+	0.0103093i
$474$		0			0
$475$	−25.6205	−	12.5376i	−1.17555	−	0.575264i
$476$	0.435905			0.0199797
$477$		0			0
$478$	−4.52500	−	6.22813i	−0.206969	−	0.284868i
$479$	1.03004	+	9.80017i	0.0470637	+	0.447781i	0.992525	+	0.122045i	$0.0389453\pi$
$479$	1.03004	+	9.80017i	0.0470637	+	0.447781i	−0.945461	+	0.325736i	$0.894388\pi$
$480$		0			0
$481$	−0.632266	+	6.01561i	−0.0288289	+	0.274288i
$482$	−3.49604	+	2.01844i	−0.159240	+	0.0919374i
$483$		0			0
$484$	−12.8711	−	14.2948i	−0.585051	−	0.649765i
$485$	0.969056	−	0.187705i	0.0440026	−	0.00852326i
$486$		0			0
$487$	−19.5185	−	6.34193i	−0.884466	−	0.287380i	−0.168656	−	0.985675i	$-0.553943\pi$
$487$	−19.5185	−	6.34193i	−0.884466	−	0.287380i	−0.715811	+	0.698295i	$0.753943\pi$
$488$	8.86913	−	7.98580i	0.401486	−	0.361500i
$489$		0			0
$490$	1.83137	−	0.775953i	0.0827329	−	0.0350540i
$491$	−3.67951	+	0.782104i	−0.166054	+	0.0352959i	−0.290188	−	0.956970i	$-0.593718\pi$
$491$	−3.67951	+	0.782104i	−0.166054	+	0.0352959i	0.124134	+	0.992265i	$0.460385\pi$
$492$		0			0
$493$	0.353728	+	0.204225i	0.0159311	+	0.00919783i
$494$	7.51269	+	5.45829i	0.338012	+	0.245580i
$495$		0			0
$496$	24.2100	−	17.5896i	1.08706	−	0.789795i
$497$	3.69825	−	0.388701i	0.165889	−	0.0174356i
$498$		0			0
$499$	−12.8947	−	22.3343i	−0.577246	−	0.999819i	−0.995794	−	0.0916243i	$-0.970794\pi$
$499$	−12.8947	−	22.3343i	−0.577246	−	0.999819i	0.418548	−	0.908195i	$-0.362539\pi$
$500$	19.7092	+	3.16143i	0.881424	+	0.141384i
$501$		0			0
$502$	0.902704	−	4.24689i	0.0402896	−	0.189548i
$503$	−3.20988	−	4.41802i	−0.143121	−	0.196990i	0.731438	−	0.681908i	$-0.238849\pi$
$503$	−3.20988	−	4.41802i	−0.143121	−	0.196990i	−0.874560	+	0.484918i	$0.838849\pi$
$504$		0			0
$505$	−11.8855	+	25.4449i	−0.528898	+	1.13228i
$506$	−1.06592	+	0.474580i	−0.0473861	+	0.0210977i
$507$		0			0
$508$	14.8214	+	1.55779i	0.657594	+	0.0691159i
$509$	28.8973	−	6.14231i	1.28085	−	0.272253i	0.483273	−	0.875470i	$-0.339448\pi$
$509$	28.8973	−	6.14231i	1.28085	−	0.272253i	0.797578	+	0.603216i	$0.206114\pi$
$510$		0			0
$511$	−7.43947	−	1.58131i	−0.329103	−	0.0699530i
$512$	−21.7540	−	7.06831i	−0.961401	−	0.312378i
$513$		0			0
$514$	1.37481	+	4.23123i	0.0606402	+	0.186631i
$515$	−9.31570	+	26.9972i	−0.410499	+	1.18964i
$516$		0			0
$517$	−0.889136	−	0.0934520i	−0.0391042	−	0.00411001i
$518$	−1.55665	+	0.898730i	−0.0683951	+	0.0394879i
$519$		0			0
$520$	−13.0247	−	4.49434i	−0.571172	−	0.197090i
$521$	−0.476427	+	0.346145i	−0.0208727	+	0.0151649i	−0.598173	−	0.801367i	$-0.704106\pi$
$521$	−0.476427	+	0.346145i	−0.0208727	+	0.0151649i	0.577300	+	0.816532i	$0.304106\pi$
$522$		0			0
$523$	−2.57247	+	0.835847i	−0.112486	+	0.0365490i	−0.364719	−	0.931117i	$-0.618835\pi$
$523$	−2.57247	+	0.835847i	−0.112486	+	0.0365490i	0.252233	+	0.967667i	$0.418835\pi$
$524$	12.0638	−	20.8952i	0.527011	−	0.912810i
$525$		0			0
$526$	2.69978	+	4.67615i	0.117716	+	0.203890i
$527$	−0.873354	−	0.786372i	−0.0380439	−	0.0342549i
$528$		0			0
$529$	0.528957	+	5.03269i	0.0229981	+	0.218813i
$530$	−6.19440	+	3.42830i	−0.269068	+	0.148916i
$531$		0			0
$532$		−	22.9560i		−	0.995269i
$533$	−10.9315	−	24.5525i	−0.473494	−	1.06349i
$534$		0			0
$535$	−3.85234	−	44.3678i	−0.166551	−	1.91819i
$536$	−12.9486	+	14.3809i	−0.559294	+	0.621158i
$537$		0			0
$538$	0.273557	−	0.246311i	0.0117939	−	0.0106192i
$539$	0.282104	+	0.868228i	0.0121511	+	0.0373972i
$540$		0			0
$541$	7.06653	−	21.7486i	0.303814	−	0.935044i	−0.676303	−	0.736624i	$-0.736419\pi$
$541$	7.06653	−	21.7486i	0.303814	−	0.935044i	0.980117	−	0.198420i	$-0.0635810\pi$
$542$	2.18205	+	4.90096i	0.0937270	+	0.210514i
$543$		0			0
$544$	−0.0541828	+	0.515515i	−0.00232307	+	0.0221025i
$545$	7.25047	−	31.3115i	0.310576	−	1.34124i
$546$		0			0
$547$	16.6049	−	1.74525i	0.709975	−	0.0746214i	0.257345	−	0.966320i	$-0.417152\pi$
$547$	16.6049	−	1.74525i	0.709975	−	0.0746214i	0.452630	+	0.891698i	$0.350486\pi$
$548$	−6.46519	+	2.10067i	−0.276179	+	0.0897360i
$549$		0			0
$550$	0.267839	−	1.06827i	0.0114207	−	0.0455511i
$551$	10.7551	−	18.6283i	0.458182	−	0.793594i
$552$		0			0
$553$	−5.22666	+	11.7393i	−0.222260	+	0.499205i
$554$	−1.04243	−	0.464119i	−0.0442886	−	0.0197185i
$555$		0			0
$556$	8.57975	−	3.81995i	0.363863	−	0.162002i
$557$			10.8339i			0.459046i	0.973303	+	0.229523i	$0.0737167\pi$
$557$			10.8339i			0.459046i	−0.973303	+	0.229523i	$0.926283\pi$
$558$		0			0
$559$	0.765220	−	2.35511i	0.0323654	−	0.0996103i
$560$	4.05571	+	13.2968i	0.171385	+	0.561894i
$561$		0			0
$562$	−0.423368	−	1.99179i	−0.0178587	−	0.0840185i
$563$	−6.24048	−	29.3591i	−0.263005	−	1.23734i	−0.889144	−	0.457628i	$-0.848699\pi$
$563$	−6.24048	−	29.3591i	−0.263005	−	1.23734i	0.626139	−	0.779712i	$-0.284634\pi$
$564$		0			0
$565$	−3.54597	−	11.6256i	−0.149180	−	0.489094i
$566$	3.08183	−	9.48491i	0.129539	−	0.398680i
$567$		0			0
$568$			2.89330i			0.121400i
$569$	0.147223	−	0.0655479i	0.00617190	−	0.00274791i	−0.403648	−	0.914914i	$-0.632258\pi$
$569$	0.147223	−	0.0655479i	0.00617190	−	0.00274791i	0.409820	+	0.912166i	$0.365591\pi$
$570$		0			0
$571$	17.1364	+	7.62963i	0.717138	+	0.319290i	0.732665	−	0.680589i	$-0.238276\pi$
$571$	17.1364	+	7.62963i	0.717138	+	0.319290i	−0.0155276	+	0.999879i	$0.504943\pi$
$572$	1.21319	−	2.72488i	0.0507261	−	0.113933i
$573$		0			0
$574$	3.99327	−	6.91655i	0.166676	−	0.288691i
$575$	−22.4430	−	14.0649i	−0.935937	−	0.586548i
$576$		0			0
$577$	−2.48893	+	0.808701i	−0.103615	+	0.0336667i	−0.360366	−	0.932811i	$-0.617348\pi$
$577$	−2.48893	+	0.808701i	−0.103615	+	0.0336667i	0.256750	+	0.966478i	$0.417348\pi$
$578$	−7.82702	+	0.822653i	−0.325561	+	0.0342178i
$579$		0			0
$580$	−3.39583	+	14.6650i	−0.141004	+	0.608931i
$581$	−3.25924	+	31.0096i	−0.135216	+	1.28649i
$582$		0			0
$583$	−1.32170	−	2.96859i	−0.0547393	−	0.122947i
$584$	1.82866	−	5.62804i	0.0756705	−	0.232890i
$585$		0			0
$586$	−2.05040	−	6.31048i	−0.0847012	−	0.260684i
$587$	−16.4216	+	14.7861i	−0.677794	+	0.610288i	−0.934399	−	0.356228i	$-0.884063\pi$
$587$	−16.4216	+	14.7861i	−0.677794	+	0.610288i	0.256605	+	0.966516i	$0.417396\pi$
$588$		0			0
$589$	−41.4126	+	45.9934i	−1.70638	+	1.89512i
$590$	0.774213	+	8.91670i	0.0318738	+	0.367095i
$591$		0			0
$592$	1.93134	+	4.33787i	0.0793777	+	0.178285i
$593$		−	36.5395i		−	1.50050i	−0.661155	−	0.750249i	$-0.729933\pi$
$593$		−	36.5395i		−	1.50050i	0.661155	−	0.750249i	$-0.270067\pi$
$594$		0			0
$595$	0.477664	−	0.264364i	0.0195823	−	0.0108379i
$596$	−1.48335	−	14.1131i	−0.0607603	−	0.578096i
$597$		0			0
$598$	6.40801	+	5.76979i	0.262043	+	0.235944i
$599$	0.950626	+	1.64653i	0.0388415	+	0.0672755i	0.884793	−	0.465985i	$-0.154300\pi$
$599$	0.950626	+	1.64653i	0.0388415	+	0.0672755i	−0.845951	+	0.533260i	$0.820967\pi$
$600$		0			0
$601$	−1.99041	+	3.44750i	−0.0811906	+	0.140626i	−0.903762	−	0.428036i	$-0.859206\pi$
$601$	−1.99041	+	3.44750i	−0.0811906	+	0.140626i	0.822571	+	0.568662i	$0.192539\pi$
$602$	0.699848	−	0.227394i	0.0285237	−	0.00926791i
$603$		0			0
$604$	−5.49488	+	3.99226i	−0.223583	+	0.162443i
$605$	−22.7736	−	7.85829i	−0.925877	−	0.319485i
$606$		0			0
$607$	−34.0722	+	19.6716i	−1.38295	+	0.798445i	−0.992508	−	0.122184i	$-0.961010\pi$
$607$	−34.0722	+	19.6716i	−1.38295	+	0.798445i	−0.390440	+	0.920629i	$0.627677\pi$
$608$	27.1485	+	2.85342i	1.10102	+	0.115722i
$609$		0			0
$610$	2.29960	−	6.66430i	0.0931079	−	0.269830i
$611$	2.04169	+	6.28367i	0.0825979	+	0.254210i
$612$		0			0
$613$	−2.29903	−	0.747001i	−0.0928570	−	0.0301711i	0.262220	−	0.965008i	$-0.415545\pi$
$613$	−2.29903	−	0.747001i	−0.0928570	−	0.0301711i	−0.355077	+	0.934837i	$0.615545\pi$
$614$	−6.59874	−	1.40260i	−0.266303	−	0.0566045i
$615$		0			0
$616$	1.83820	−	0.390722i	0.0740633	−	0.0157426i
$617$	−35.6316	−	3.74503i	−1.43447	−	0.150769i	−0.644826	−	0.764330i	$-0.723070\pi$
$617$	−35.6316	−	3.74503i	−1.43447	−	0.150769i	−0.789648	+	0.613560i	$0.789737\pi$
$618$		0			0
$619$	−11.2787	+	5.02161i	−0.453330	+	0.201836i	−0.620683	−	0.784061i	$-0.713145\pi$
$619$	−11.2787	+	5.02161i	−0.453330	+	0.201836i	0.167353	+	0.985897i	$0.446478\pi$
$620$	18.3300	−	39.2415i	0.736149	−	1.57598i
$621$		0			0
$622$	−6.16696	−	8.48809i	−0.247273	−	0.340341i
$623$	8.23350	−	38.7356i	0.329868	−	1.55191i
$624$		0			0
$625$	23.5147	−	8.48879i	0.940587	−	0.339552i
$626$	−3.07670	−	5.32900i	−0.122970	−	0.212990i
$627$		0			0
$628$	−21.8170	+	2.29306i	−0.870594	+	0.0915031i
$629$	0.150864	−	0.109609i	0.00601532	−	0.00437039i
$630$		0			0
$631$	23.0034	+	16.7130i	0.915753	+	0.665333i	0.942463	−	0.334310i	$-0.108503\pi$
$631$	23.0034	+	16.7130i	0.915753	+	0.665333i	−0.0267104	+	0.999643i	$0.508503\pi$
$632$	−8.65874	−	4.99912i	−0.344426	−	0.198854i
$633$		0			0
$634$	−13.1612	+	2.79749i	−0.522697	+	0.111103i
$635$	17.1861	−	7.28174i	0.682008	−	0.288967i
$636$		0			0
$637$	5.01365	−	4.51431i	0.198648	−	0.178864i
$638$	0.789885	+	0.256649i	0.0312718	+	0.0101608i
$639$		0			0
$640$	−24.3654	+	4.71955i	−0.963125	+	0.186557i
$641$	−2.97291	−	3.30175i	−0.117423	−	0.130411i	0.681567	−	0.731755i	$-0.261299\pi$
$641$	−2.97291	−	3.30175i	−0.117423	−	0.130411i	−0.798990	+	0.601344i	$0.794632\pi$
$642$		0			0
$643$	−11.6058	+	6.70061i	−0.457688	+	0.264246i	−0.711072	−	0.703120i	$-0.751790\pi$
$643$	−11.6058	+	6.70061i	−0.457688	+	0.264246i	0.253384	+	0.967366i	$0.418456\pi$
$644$	2.22814	−	21.1993i	0.0878011	−	0.835371i
$645$		0			0
$646$	−0.0299249	−	0.284717i	−0.00117738	−	0.0112020i
$647$	1.08985	+	1.50005i	0.0428465	+	0.0589732i	0.829903	−	0.557908i	$-0.188396\pi$
$647$	1.08985	+	1.50005i	0.0428465	+	0.0589732i	−0.787056	+	0.616881i	$0.788396\pi$
$648$		0			0
$649$	−4.10803			−0.161254
$650$	−8.01722	+	1.40280i	−0.314461	+	0.0550225i
$651$		0			0
$652$	−31.9635	−	28.7800i	−1.25179	−	1.12711i
$653$	−6.90190	+	15.5019i	−0.270092	+	0.606637i	−0.996767	−	0.0803446i	$-0.974398\pi$
$653$	−6.90190	+	15.5019i	−0.270092	+	0.606637i	0.726675	+	0.686981i	$0.241065\pi$
$654$		0			0
$655$	0.547213	−	30.2133i	0.0213814	−	1.18053i
$656$	−17.0688	−	12.4012i	−0.666425	−	0.484186i
$657$		0			0
$658$	−1.15404	+	1.58839i	−0.0449890	+	0.0619221i
$659$	32.3243	+	35.8997i	1.25917	+	1.39846i	0.881272	+	0.472610i	$0.156688\pi$
$659$	32.3243	+	35.8997i	1.25917	+	1.39846i	0.377903	+	0.925845i	$0.376645\pi$
$660$		0			0
$661$	−8.76145	+	9.73058i	−0.340781	+	0.378476i	−0.889037	−	0.457835i	$-0.848625\pi$
$661$	−8.76145	+	9.73058i	−0.340781	+	0.378476i	0.548256	+	0.836310i	$0.315292\pi$
$662$	−1.52903	−	7.19354i	−0.0594276	−	0.279585i
$663$		0			0
$664$	−23.7301	−	5.04398i	−0.920905	−	0.195744i
$665$	−13.9222	−	25.1552i	−0.539878	−	0.975476i
$666$		0			0
$667$	11.7402	−	16.1589i	0.454581	−	0.625677i
$668$	9.70827	+	5.60507i	0.375624	+	0.216867i
$669$		0			0
$670$	−2.57874	+	11.1364i	−0.0996254	+	0.430236i
$671$	2.95604	+	1.31612i	0.114117	+	0.0508081i
$672$		0			0
$673$	−6.64193	+	31.2478i	−0.256028	+	1.20452i	0.642738	+	0.766086i	$0.277798\pi$
$673$	−6.64193	+	31.2478i	−0.256028	+	1.20452i	−0.898766	+	0.438429i	$0.855535\pi$
$674$	−3.36996			−0.129806
$675$		0			0
$676$	1.16701			0.0448850
$677$	7.31271	−	34.4036i	0.281050	−	1.32224i	−0.580374	−	0.814350i	$-0.697093\pi$
$677$	7.31271	−	34.4036i	0.281050	−	1.32224i	0.861424	−	0.507887i	$-0.169573\pi$
$678$		0			0
$679$	0.908912	+	0.404674i	0.0348809	+	0.0155300i
$680$	0.165716	+	0.391116i	0.00635491	+	0.0149986i
$681$		0			0
$682$	−2.06950	−	1.19483i	−0.0792454	−	0.0457524i
$683$	19.0663	−	26.2425i	0.729551	−	1.00414i	−0.269601	−	0.962972i	$-0.586892\pi$
$683$	19.0663	−	26.2425i	0.729551	−	1.00414i	0.999152	−	0.0411689i	$-0.0131082\pi$
$684$		0			0
$685$	−5.81055	+	6.22286i	−0.222010	+	0.237763i
$686$	9.11034	+	1.93646i	0.347834	+	0.0739344i
$687$		0			0
$688$	−0.404169	−	1.90147i	−0.0154088	−	0.0724928i
$689$	−16.0688	+	17.8463i	−0.612174	+	0.679888i
$690$		0			0
$691$	−7.79356	−	8.65563i	−0.296481	−	0.329276i	0.576438	−	0.817141i	$-0.304442\pi$
$691$	−7.79356	−	8.65563i	−0.296481	−	0.329276i	−0.872919	+	0.487865i	$0.837776\pi$
$692$	−7.80291	+	10.7398i	−0.296622	+	0.408265i
$693$		0			0
$694$	7.14343	+	5.19000i	0.271161	+	0.197010i
$695$	7.08499	−	9.38928i	0.268749	−	0.356156i
$696$		0			0
$697$	−0.337008	+	0.756931i	−0.0127651	+	0.0286708i
$698$	3.70845	+	3.33911i	0.140367	+	0.126387i
$699$		0			0
$700$	14.4549	+	13.9956i	0.546342	+	0.528985i
$701$	29.8405			1.12706			0.563530	−	0.826095i	$-0.309443\pi$
$701$	29.8405			1.12706			0.563530	+	0.826095i	$0.309443\pi$
$702$		0			0
$703$	−5.77232	−	7.94491i	−0.217707	−	0.299648i
$704$	−0.164002	−	1.56038i	−0.00618108	−	0.0588090i
$705$		0			0
$706$	0.517887	−	4.92736i	0.0194909	−	0.185444i
$707$	−24.5151	+	14.1538i	−0.921986	+	0.532309i
$708$		0			0
$709$	5.28689	+	5.87169i	0.198553	+	0.220516i	0.834197	−	0.551467i	$-0.185932\pi$
$709$	5.28689	+	5.87169i	0.198553	+	0.220516i	−0.635643	+	0.771983i	$0.719265\pi$
$710$	0.827610	+	1.49536i	0.0310597	+	0.0561200i
$711$		0			0
$712$	29.3039	+	9.52140i	1.09821	+	0.356830i
$713$	−42.7078	+	38.4543i	−1.59942	+	1.44012i
$714$		0			0
$715$	−0.323144	−	3.72168i	−0.0120849	−	0.139183i
$716$	36.5101	−	7.76047i	1.36445	−	0.290022i
$717$		0			0
$718$	−5.86618	−	3.38684i	−0.218924	−	0.126396i
$719$	0.863660	+	0.627486i	0.0322091	+	0.0234013i	0.603773	−	0.797156i	$-0.293663\pi$
$719$	0.863660	+	0.627486i	0.0322091	+	0.0234013i	−0.571564	+	0.820557i	$0.693663\pi$
$720$		0			0
$721$	−23.2889	+	16.9204i	−0.867324	+	0.630148i
$722$	−6.24013	+	0.655864i	−0.232234	+	0.0244087i
$723$		0			0
$724$	−1.57713	−	2.73167i	−0.0586137	−	0.101522i
$725$	5.17277	+	18.1294i	0.192112	+	0.673308i
$726$		0			0
$727$	3.82866	−	18.0124i	0.141997	−	0.668045i	−0.848350	−	0.529436i	$-0.822404\pi$
$727$	3.82866	−	18.0124i	0.141997	−	0.668045i	0.990347	−	0.138609i	$-0.0442630\pi$
$728$	−8.16321	−	11.2357i	−0.302549	−	0.416422i
$729$		0			0
$730$	−0.664746	−	3.43185i	−0.0246033	−	0.127018i
$731$	−0.0697421	+	0.0310512i	−0.00257951	+	0.00114847i
$732$		0			0
$733$	36.2524	+	3.81028i	1.33901	+	0.140736i	0.746801	−	0.665047i	$-0.231589\pi$
$733$	36.2524	+	3.81028i	1.33901	+	0.140736i	0.592211	+	0.805783i	$0.298255\pi$
$734$	−7.58415	+	1.61206i	−0.279936	+	0.0595023i
$735$		0			0
$736$	24.7941	+	5.27014i	0.913921	+	0.194260i
$737$	−4.98989	−	1.62131i	−0.183805	−	0.0597219i
$738$		0			0
$739$	10.2900	+	31.6695i	0.378525	+	1.16498i	0.941069	+	0.338214i	$0.109823\pi$
$739$	10.2900	+	31.6695i	0.378525	+	1.16498i	−0.562544	+	0.826767i	$0.690177\pi$
$740$	5.48588	+	4.13955i	0.201665	+	0.152173i
$741$		0			0
$742$	−7.09711	−	0.745936i	−0.260543	−	0.0273842i
$743$	−22.5931	+	13.0441i	−0.828860	+	0.478542i	−0.853462	−	0.521155i	$-0.825501\pi$
$743$	−22.5931	+	13.0441i	−0.828860	+	0.478542i	0.0246023	+	0.999697i	$0.492168\pi$
$744$		0			0
$745$	−10.1847	−	14.5655i	−0.373137	−	0.533640i
$746$	1.65292	−	1.20092i	0.0605179	−	0.0439688i
$747$		0			0
$748$	−0.0874549	+	0.0284158i	−0.00319767	+	0.00103899i
$749$	22.4447	−	38.8754i	0.820112	−	1.42048i
$750$		0			0
$751$	8.62884	+	14.9456i	0.314871	+	0.545372i	0.979410	−	0.201881i	$-0.0647055\pi$
$751$	8.62884	+	14.9456i	0.314871	+	0.545372i	−0.664539	+	0.747253i	$0.731372\pi$
$752$	3.85444	+	3.47055i	0.140557	+	0.126558i
$753$		0			0
$754$	−0.641572	−	6.10415i	−0.0233647	−	0.222300i
$755$	−3.60009	+	7.70721i	−0.131021	+	0.280494i
$756$		0			0
$757$			33.7370i			1.22619i	0.790008	+	0.613097i	$0.210076\pi$
$757$			33.7370i			1.22619i	−0.790008	+	0.613097i	$0.789924\pi$
$758$	−3.59600	−	8.07676i	−0.130613	−	0.293361i
$759$		0			0
$760$	20.5973	−	8.72708i	0.747142	−	0.316564i
$761$	26.6062	−	29.5492i	0.964476	−	1.07116i	−0.0329503	−	0.999457i	$-0.510490\pi$
$761$	26.6062	−	29.5492i	0.964476	−	1.07116i	0.997426	−	0.0717019i	$-0.0228430\pi$
$762$		0			0
$763$	24.0749	−	21.6771i	0.871568	−	0.784764i
$764$	5.36503	+	16.5119i	0.194100	+	0.597378i
$765$		0			0
$766$	−0.0691284	+	0.212755i	−0.00249771	+	0.00768716i
$767$	12.3481	+	27.7343i	0.445864	+	1.00143i
$768$		0			0
$769$	−4.86564	+	46.2935i	−0.175460	+	1.66939i	0.452974	+	0.891524i	$0.350363\pi$
$769$	−4.86564	+	46.2935i	−0.175460	+	1.66939i	−0.628434	+	0.777863i	$0.716304\pi$
$770$	0.838285	−	0.727744i	0.0302097	−	0.0262261i
$771$		0			0
$772$	−23.5733	+	2.47765i	−0.848421	+	0.0891726i
$773$	−25.7407	+	8.36366i	−0.925828	+	0.300820i	−0.732856	−	0.680384i	$-0.761813\pi$
$773$	−25.7407	+	8.36366i	−0.925828	+	0.300820i	−0.192973	+	0.981204i	$0.561813\pi$
$774$		0			0
$775$	−3.71287	−	54.1174i	−0.133370	−	1.94395i
$776$	−0.387057	+	0.670402i	−0.0138945	+	0.0240660i
$777$		0			0
$778$	4.17405	−	9.37507i	0.149647	−	0.336112i
$779$	39.8622	+	17.7478i	1.42821	+	0.635881i
$780$		0			0
$781$	−0.716634	+	0.319066i	−0.0256432	+	0.0114171i
$782$		−	0.265834i		−	0.00950620i
$783$		0			0
$784$	1.63660	−	5.03695i	0.0584501	−	0.179891i
$785$	−22.5164	+	15.7441i	−0.803645	+	0.561932i
$786$		0			0
$787$	2.42647	+	11.4157i	0.0864945	+	0.406925i	1.00000		9.82044e-5i	$3.12594e-5\pi$
$787$	2.42647	+	11.4157i	0.0864945	+	0.406925i	−0.913506	+	0.406826i	$0.866635\pi$
$788$	4.65822	+	21.9152i	0.165942	+	0.780697i
$789$		0			0
$790$	−5.90511	−	0.106951i	−0.210094	−	0.00380516i
$791$	3.78582	−	11.6516i	0.134608	−	0.414282i
$792$		0			0
$793$		−	23.9130i		−	0.849175i
$794$	5.44545	−	2.42447i	0.193252	−	0.0860412i
$795$		0			0
$796$	−38.1111	−	16.9681i	−1.35081	−	0.601420i
$797$	21.2084	−	47.6349i	0.751241	−	1.68731i	0.0251805	−	0.999683i	$-0.491984\pi$
$797$	21.2084	−	47.6349i	0.751241	−	1.68731i	0.726060	−	0.687631i	$-0.241349\pi$
$798$		0			0
$799$	0.101845	−	0.176400i	0.00360301	−	0.00624059i
$800$	−18.3484	+	15.3551i	−0.648714	+	0.542886i
$801$		0			0
$802$	−10.5817	+	3.43819i	−0.373652	+	0.121407i
$803$	1.59565	−	0.167710i	0.0563093	−	0.00591835i
$804$		0			0
$805$	−10.4152	−	24.5815i	−0.367088	−	0.866385i
$806$	−1.84596	+	17.5632i	−0.0650213	+	0.618637i
$807$		0			0
$808$	−8.95838	−	20.1209i	−0.315155	−	0.707849i
$809$	−10.3950	+	31.9926i	−0.365469	+	1.12480i	0.584217	+	0.811597i	$0.301402\pi$
$809$	−10.3950	+	31.9926i	−0.365469	+	1.12480i	−0.949687	+	0.313202i	$0.898598\pi$
$810$		0			0
$811$	3.90630	+	12.0224i	0.137169	+	0.422162i	0.995921	−	0.0902289i	$-0.0287599\pi$
$811$	3.90630	+	12.0224i	0.137169	+	0.422162i	−0.858752	+	0.512391i	$0.828760\pi$
$812$	−11.2757	+	10.1527i	−0.395699	+	0.356289i
$813$		0			0
$814$	0.253721	−	0.281786i	0.00889291	−	0.00987658i
$815$	−52.4798	−	12.1522i	−1.83829	−	0.425673i
$816$		0			0
$817$	1.63525	+	3.67282i	0.0572100	+	0.128496i
$818$			12.5379i			0.438379i
$819$		0			0
$820$	−30.3059	−	3.74129i	−1.05833	−	0.130652i
$821$	−3.51721	−	33.4640i	−0.122751	−	1.16790i	−0.866407	−	0.499339i	$-0.833576\pi$
$821$	−3.51721	−	33.4640i	−0.122751	−	1.16790i	0.743655	−	0.668563i	$-0.233090\pi$
$822$		0			0
$823$	−5.75260	−	5.17966i	−0.200523	−	0.180552i	0.562751	−	0.826626i	$-0.309743\pi$
$823$	−5.75260	−	5.17966i	−0.200523	−	0.180552i	−0.763274	+	0.646075i	$0.776410\pi$
$824$	−11.1989	−	19.3970i	−0.390131	−	0.675727i
$825$		0			0
$826$	−4.51076	+	7.81287i	−0.156950	+	0.271845i
$827$	−43.6791	+	14.1922i	−1.51887	+	0.493511i	−0.945455	−	0.325752i	$-0.894382\pi$
$827$	−43.6791	+	14.1922i	−1.51887	+	0.493511i	−0.573417	+	0.819264i	$0.694382\pi$
$828$		0			0
$829$	27.4660	−	19.9552i	0.953934	−	0.693074i	0.00220030	−	0.999998i	$-0.499300\pi$
$829$	27.4660	−	19.9552i	0.953934	−	0.693074i	0.951734	+	0.306924i	$0.0992996\pi$
$830$	−13.7073	+	4.18092i	−0.475789	+	0.145122i
$831$		0			0
$832$	−10.0415	+	5.79748i	−0.348127	+	0.200991i
$833$	−0.206850	−	0.0217408i	−0.00716694	−	0.000753276i
$834$		0			0
$835$	14.0376	+	0.254245i	0.485792	+	0.00879852i
$836$	1.49646	+	4.60563i	0.0517561	+	0.159289i
$837$		0			0
$838$	−2.13017	−	0.692134i	−0.0735855	−	0.0239094i
$839$	4.77476	+	1.01491i	0.164843	+	0.0350385i	0.289594	−	0.957150i	$-0.406480\pi$
$839$	4.77476	+	1.01491i	0.164843	+	0.0350385i	−0.124751	+	0.992188i	$0.539813\pi$
$840$		0			0
$841$	14.4597	−	3.07350i	0.498610	−	0.105983i
$842$	−6.45600	−	0.678553i	−0.222489	−	0.0233845i
$843$		0			0
$844$	7.71207	−	3.43363i	0.265460	−	0.118191i
$845$	1.27881	−	0.707758i	0.0439923	−	0.0243476i
$846$		0			0
$847$	−14.2733	−	19.6454i	−0.490435	−	0.675026i
$848$	−3.91952	+	18.4399i	−0.134597	+	0.633229i
$849$		0			0
$850$	0.197524	+	0.154741i	0.00677501	+	0.00530756i
$851$	−4.55946	−	7.89721i	−0.156296	−	0.270713i
$852$		0			0
$853$	−21.5299	+	2.26288i	−0.737168	+	0.0774795i	−0.465669	−	0.884959i	$-0.654186\pi$
$853$	−21.5299	+	2.26288i	−0.737168	+	0.0774795i	−0.271500	+	0.962439i	$0.587520\pi$
$854$	5.74891	−	4.17682i	0.196724	−	0.142928i
$855$		0			0
$856$	28.2562	+	20.5294i	0.965778	+	0.701679i
$857$	−0.0545858	−	0.0315151i	−0.00186462	−	0.00107654i	0.499067	−	0.866563i	$-0.333676\pi$
$857$	−0.0545858	−	0.0315151i	−0.00186462	−	0.00107654i	−0.500932	+	0.865487i	$0.667009\pi$
$858$		0			0
$859$	31.9152	−	6.78378i	1.08893	−	0.231460i	0.371741	−	0.928336i	$-0.378761\pi$
$859$	31.9152	−	6.78378i	1.08893	−	0.231460i	0.717191	+	0.696877i	$0.245427\pi$
$860$	−1.84444	−	2.12461i	−0.0628950	−	0.0724484i
$861$		0			0
$862$	−10.7695	+	9.69693i	−0.366812	+	0.330279i
$863$	0.356924	+	0.115972i	0.0121498	+	0.00394772i	0.315086	−	0.949063i	$-0.397967\pi$
$863$	0.356924	+	0.115972i	0.0121498	+	0.00394772i	−0.302936	+	0.953011i	$0.597967\pi$
$864$		0			0
$865$	−2.03705	+	16.5009i	−0.0692618	+	0.561047i
$866$	11.6513	+	12.9401i	0.395929	+	0.439724i
$867$		0			0
$868$	37.8075	−	21.8282i	1.28327	−	0.740897i
$869$	0.283356	−	2.69595i	0.00961218	−	0.0914538i
$870$		0			0
$871$	4.05296	+	38.5614i	0.137329	+	1.30660i
$872$	14.8157	+	20.3920i	0.501722	+	0.690561i
$873$		0			0
$874$	−13.9996			−0.473543
$875$	24.3276	+	6.56992i	0.822422	+	0.222104i
$876$		0			0
$877$	−17.9667	−	16.1773i	−0.606692	−	0.546268i	0.307501	−	0.951548i	$-0.400507\pi$
$877$	−17.9667	−	16.1773i	−0.606692	−	0.546268i	−0.914193	+	0.405280i	$0.867174\pi$
$878$	3.72679	−	8.37051i	0.125773	−	0.282491i
$879$		0			0
$880$	−1.68049	−	2.40334i	−0.0566492	−	0.0810165i
$881$	47.1738	+	34.2738i	1.58933	+	1.15471i	0.904895	+	0.425634i	$0.139949\pi$
$881$	47.1738	+	34.2738i	1.58933	+	1.15471i	0.684430	+	0.729078i	$0.260051\pi$
$882$		0			0
$883$	−15.3904	+	21.1831i	−0.517929	+	0.712868i	−0.985231	−	0.171229i	$-0.945226\pi$
$883$	−15.3904	+	21.1831i	−0.517929	+	0.712868i	0.467302	+	0.884098i	$0.345226\pi$
$884$	0.454718	+	0.505015i	0.0152938	+	0.0169855i
$885$		0			0
$886$	−3.03271	+	3.36817i	−0.101886	+	0.113156i
$887$	−0.756890	−	3.56089i	−0.0254139	−	0.119563i	0.963612	−	0.267304i	$-0.0861329\pi$
$887$	−0.756890	−	3.56089i	−0.0254139	−	0.119563i	−0.989026	+	0.147742i	$0.952800\pi$
$888$		0			0
$889$	18.4026	+	3.91159i	0.617202	+	0.131190i
$890$	17.8688	−	3.46117i	0.598964	−	0.116019i
$891$		0			0
$892$	15.3434	−	21.1184i	0.513736	−	0.707097i
$893$	−9.28974	−	5.36344i	−0.310869	−	0.179481i
$894$		0			0
$895$	35.3013	−	30.6463i	1.17999	−	1.02439i
$896$	−22.8531	−	10.1749i	−0.763470	−	0.339919i
$897$		0			0
$898$	−1.03784	+	4.88265i	−0.0346331	+	0.162936i
$899$	40.9067			1.36432
$900$		0			0
$901$	0.740346			0.0246645
$902$	−0.350287	+	1.64797i	−0.0116633	+	0.0548714i
$903$		0			0
$904$	8.70805	+	3.87707i	0.289625	+	0.128950i
$905$	−3.38490	−	2.03688i	−0.112518	−	0.0677082i
$906$		0			0
$907$	−8.64965	−	4.99388i	−0.287207	−	0.165819i	0.349475	−	0.936946i	$-0.386360\pi$
$907$	−8.64965	−	4.99388i	−0.287207	−	0.165819i	−0.636682	+	0.771127i	$0.719693\pi$
$908$	22.8180	−	31.4064i	0.757244	−	1.04226i
$909$		0			0
$910$	−7.43293	−	3.47197i	−0.246399	−	0.115095i
$911$	50.5154	+	10.7374i	1.67365	+	0.355746i	0.944476	−	0.328581i	$-0.106570\pi$
$911$	50.5154	+	10.7374i	1.67365	+	0.355746i	0.729176	+	0.684327i	$0.239904\pi$
$912$		0			0
$913$	−1.36756	−	6.43387i	−0.0452597	−	0.212930i
$914$	−12.4962	+	13.8784i	−0.413336	+	0.459057i
$915$		0			0
$916$	28.7668	+	31.9487i	0.950480	+	1.05562i
$917$	17.9033	−	24.6418i	0.591219	−	0.813743i
$918$		0			0
$919$	−5.97185	−	4.33880i	−0.196993	−	0.143124i	0.484916	−	0.874561i	$-0.338850\pi$
$919$	−5.97185	−	4.33880i	−0.196993	−	0.143124i	−0.681909	+	0.731437i	$0.738850\pi$
$920$	19.8682	−	6.06006i	0.655035	−	0.199794i
$921$		0			0
$922$	4.19960	−	9.43245i	0.138306	−	0.310641i
$923$	4.30818	+	3.87911i	0.141806	+	0.127682i
$924$		0			0
$925$	8.52194	+	1.20909i	0.280200	+	0.0397547i
$926$	−11.0879			−0.364372
$927$		0			0
$928$	−10.6053	−	14.5969i	−0.348136	−	0.479168i
$929$	4.51030	+	42.9126i	0.147978	+	1.40792i	0.776496	+	0.630122i	$0.216995\pi$
$929$	4.51030	+	42.9126i	0.147978	+	1.40792i	−0.628518	+	0.777795i	$0.716338\pi$
$930$		0			0
$931$	−1.14494	+	10.8933i	−0.0375238	+	0.357015i
$932$	−38.3902	+	22.1646i	−1.25751	+	0.726025i
$933$		0			0
$934$	2.93743	+	3.26235i	0.0961157	+	0.106747i
$935$	−0.0785996	+	0.0841769i	−0.00257048	+	0.00275288i
$936$		0			0
$937$	2.06458	+	0.670824i	0.0674470	+	0.0219149i	0.342546	−	0.939501i	$-0.388711\pi$
$937$	2.06458	+	0.670824i	0.0674470	+	0.0219149i	−0.275099	+	0.961416i	$0.588711\pi$
$938$	−8.56259	+	7.70979i	−0.279578	+	0.251734i
$939$		0			0
$940$	7.31328	+	1.69346i	0.238533	+	0.0552346i
$941$	−4.19357	+	0.891371i	−0.136706	+	0.0290578i	−0.275757	−	0.961227i	$-0.588928\pi$
$941$	−4.19357	+	0.891371i	−0.136706	+	0.0290578i	0.139050	+	0.990285i	$0.455595\pi$
$942$		0			0
$943$	35.0892	+	20.2588i	1.14266	+	0.659716i
$944$	19.2808	+	14.0083i	0.627536	+	0.455932i
$945$		0			0
$946$	−0.125586	+	0.0912436i	−0.00408315	+	0.00296659i
$947$	2.68671	−	0.282385i	0.0873064	−	0.00917627i	−0.0607745	−	0.998152i	$-0.519357\pi$
$947$	2.68671	−	0.282385i	0.0873064	−	0.00917627i	0.148081	+	0.988975i	$0.452690\pi$
$948$		0			0
$949$	−5.92853	−	10.2685i	−0.192448	−	0.333330i
$950$	8.14909	−	10.4022i	0.264391	−	0.337491i
$951$		0			0
$952$	−0.0890189	+	0.418801i	−0.00288512	+	0.0135734i
$953$	17.2857	+	23.7917i	0.559939	+	0.770689i	0.991319	−	0.131481i	$-0.0419732\pi$
$953$	17.2857	+	23.7917i	0.559939	+	0.770689i	−0.431380	+	0.902170i	$0.641973\pi$
$954$		0			0
$955$	15.8930	+	14.8400i	0.514285	+	0.480210i
$956$	−27.1037	+	12.0673i	−0.876596	+	0.390286i
$957$		0			0
$958$	−4.54011	−	0.477185i	−0.146684	−	0.0154171i
$959$	−8.39417	+	1.78424i	−0.271062	+	0.0576160i
$960$		0			0
$961$	−84.8045	−	18.0258i	−2.73563	−	0.581476i
$962$	−2.66505	−	0.865926i	−0.0859246	−	0.0279186i
$963$		0			0
$964$	4.80758	+	14.7962i	0.154842	+	0.476554i
$965$	−24.3289	+	17.0115i	−0.783177	+	0.547620i
$966$		0			0
$967$	−8.67117	−	0.911377i	−0.278846	−	0.0293079i	−0.0359268	−	0.999354i	$-0.511438\pi$
$967$	−8.67117	−	0.911377i	−0.278846	−	0.0293079i	−0.242919	+	0.970047i	$0.578105\pi$
$968$	16.3624	−	9.44685i	0.525908	−	0.303633i
$969$		0			0
$970$	−0.00828070	+	0.457203i	−0.000265877	+	0.0146799i
$971$	16.1493	−	11.7332i	0.518257	−	0.376536i	−0.297690	−	0.954663i	$-0.596216\pi$
$971$	16.1493	−	11.7332i	0.518257	−	0.376536i	0.815947	+	0.578127i	$0.196216\pi$
$972$		0			0
$973$	11.2759	−	3.66375i	0.361488	−	0.117454i
$974$	4.75382	−	8.23385i	0.152322	−	0.263830i
$975$		0			0
$976$	−9.38608	−	16.2572i	−0.300441	−	0.520380i
$977$	7.70268	+	6.93552i	0.246430	+	0.221887i	0.783084	−	0.621915i	$-0.213645\pi$
$977$	7.70268	+	6.93552i	0.246430	+	0.221887i	−0.536654	+	0.843802i	$0.680312\pi$
$978$		0			0
$979$	0.873225	+	8.30818i	0.0279084	+	0.265531i
$980$	−1.45766	−	7.52540i	−0.0465633	−	0.240390i
$981$		0			0
$982$		−	1.74268i		−	0.0556113i
$983$	8.02970	+	18.0350i	0.256108	+	0.575227i	0.995143	−	0.0984395i	$-0.0313851\pi$
$983$	8.02970	+	18.0350i	0.256108	+	0.575227i	−0.739035	+	0.673667i	$0.764718\pi$
$984$		0			0
$985$	18.3954	+	21.1896i	0.586127	+	0.675156i
$986$	−0.126614	+	0.140619i	−0.00403222	+	0.00447823i
$987$		0			0
$988$	26.5956	−	23.9468i	0.846118	−	0.761848i
$989$	1.15362	+	3.55049i	0.0366831	+	0.112899i
$990$		0			0
$991$	4.63805	−	14.2744i	0.147332	−	0.453442i	−0.849971	−	0.526829i	$-0.823381\pi$
$991$	4.63805	−	14.2744i	0.147332	−	0.453442i	0.997304	+	0.0733867i	$0.0233807\pi$
$992$	21.1152	+	47.4256i	0.670410	+	1.50576i
$993$		0			0
$994$	−0.180073	+	1.71328i	−0.00571157	+	0.0543420i
$995$	−52.0528	+	4.51960i	−1.65018	+	0.143281i
$996$		0			0
$997$	36.6723	−	3.85441i	1.16142	−	0.122070i	0.495853	−	0.868406i	$-0.334855\pi$
$997$	36.6723	−	3.85441i	1.16142	−	0.122070i	0.665569	+	0.746336i	$0.268189\pi$
$998$	11.3627	−	3.69196i	0.359679	−	0.116867i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.12		224
3.2	odd	2		225.2.u.a.169.17	yes	224
9.4	even	3	inner	675.2.y.a.469.12		224
9.5	odd	6		225.2.u.a.94.17	yes	224
25.4	even	10	inner	675.2.y.a.154.12		224
75.29	odd	10		225.2.u.a.79.17	yes	224
225.4	even	30	inner	675.2.y.a.604.12		224
225.104	odd	30		225.2.u.a.4.17	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.17	✓	224	225.104	odd	30
225.2.u.a.79.17	yes	224	75.29	odd	10
225.2.u.a.94.17	yes	224	9.5	odd	6
225.2.u.a.169.17	yes	224	3.2	odd	2
675.2.y.a.19.12		224	1.1	even	1	trivial
675.2.y.a.154.12		224	25.4	even	10	inner
675.2.y.a.469.12		224	9.4	even	3	inner
675.2.y.a.604.12		224	225.4	even	30	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0963190 + 0.453145i) q^{2} +(1.63103 + 0.726180i) q^{4} +(2.22769 - 0.193424i) q^{5} +(1.95191 + 1.12694i) q^{7} +(-1.03077 + 1.41873i) q^{8} +O(q^{10})\)	\(q+(-0.0963190 + 0.453145i) q^{2} +(1.63103 + 0.726180i) q^{4} +(2.22769 - 0.193424i) q^{5} +(1.95191 + 1.12694i) q^{7} +(-1.03077 + 1.41873i) q^{8} +(-0.126919 + 1.02810i) q^{10} +(-0.465072 - 0.0988542i) q^{11} +(0.730547 + 3.43695i) q^{13} +(-0.698673 + 0.775955i) q^{14} +(1.84570 + 2.04986i) q^{16} +(0.0636721 - 0.0876371i) q^{17} +(-4.61523 - 3.35316i) q^{19} +(3.77388 + 1.30222i) q^{20} +(0.0895906 - 0.201224i) q^{22} +(-3.93659 - 3.54452i) q^{23} +(4.92517 - 0.861776i) q^{25} -1.62780 q^{26} +(2.36526 + 3.25551i) q^{28} +(0.394133 + 3.74992i) q^{29} +(1.13402 - 10.7895i) q^{31} +(-4.14407 + 2.39258i) q^{32} +(0.0335795 + 0.0372938i) q^{34} +(4.56623 + 2.13292i) q^{35} +(1.63720 + 0.531959i) q^{37} +(1.96400 - 1.76839i) q^{38} +(-2.02181 + 3.35987i) q^{40} +(-7.48170 + 1.59028i) q^{41} +(-0.610331 - 0.352375i) q^{43} +(-0.686760 - 0.498960i) q^{44} +(1.98535 - 1.44244i) q^{46} +(1.87005 - 0.196550i) q^{47} +(-0.960022 - 1.66281i) q^{49} +(-0.0838782 + 2.31482i) q^{50} +(-1.30431 + 6.13628i) q^{52} +(4.01720 + 5.52920i) q^{53} +(-1.05516 - 0.130260i) q^{55} +(-3.61080 + 1.60763i) q^{56} +(-1.73722 - 0.182589i) q^{58} +(8.45126 - 1.79637i) q^{59} +(-6.65685 - 1.41496i) q^{61} +(4.77998 + 1.55311i) q^{62} +(1.01972 + 3.13838i) q^{64} +(2.29222 + 7.51515i) q^{65} +(10.9745 + 1.15346i) q^{67} +(0.167491 - 0.0967012i) q^{68} +(-1.40634 + 1.86372i) q^{70} +(1.33478 - 0.969773i) q^{71} +(-3.20933 + 1.04277i) q^{73} +(-0.398749 + 0.690653i) q^{74} +(-5.09256 - 8.82058i) q^{76} +(-0.796378 - 0.717062i) q^{77} +(0.595958 + 5.67016i) q^{79} +(4.50813 + 4.20943i) q^{80} -3.54347i q^{82} +(5.62685 + 12.6381i) q^{83} +(0.124890 - 0.207544i) q^{85} +(0.218463 - 0.242628i) q^{86} +(0.619630 - 0.557917i) q^{88} +(-5.42948 - 16.7102i) q^{89} +(-2.44727 + 7.53192i) q^{91} +(-3.84673 - 8.63989i) q^{92} +(-0.0910553 + 0.866334i) q^{94} +(-10.9299 - 6.57709i) q^{95} +(0.439012 - 0.0461420i) q^{97} +(0.845962 - 0.274870i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Introduction

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