LMFDB - Embedded newform 392.2.z.a.109.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			109.16
Character	$\chi$	$=$	392.109
Dual form			392.2.z.a.205.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849554 + 1.13060i) q^{2} +(0.209889 + 1.39252i) q^{3} +(-0.556517 - 1.92101i) q^{4} +(-1.73139 - 0.679519i) q^{5} +(-1.75270 - 0.945723i) q^{6} +(-0.592319 - 2.57860i) q^{7} +(2.64469 + 1.00281i) q^{8} +(0.971651 - 0.299715i) q^{9} +O(q^{10})$	\(q+(-0.849554 + 1.13060i) q^{2} +(0.209889 + 1.39252i) q^{3} +(-0.556517 - 1.92101i) q^{4} +(-1.73139 - 0.679519i) q^{5} +(-1.75270 - 0.945723i) q^{6} +(-0.592319 - 2.57860i) q^{7} +(2.64469 + 1.00281i) q^{8} +(0.971651 - 0.299715i) q^{9} +(2.23917 - 1.38022i) q^{10} +(0.224646 - 0.728285i) q^{11} +(2.55825 - 1.17816i) q^{12} +(-1.74405 + 0.398067i) q^{13} +(3.41857 + 1.52098i) q^{14} +(0.582847 - 2.55362i) q^{15} +(-3.38058 + 2.13815i) q^{16} +(4.21955 - 2.87684i) q^{17} +(-0.486612 + 1.35317i) q^{18} +(7.23191 - 4.17535i) q^{19} +(-0.341820 + 3.70418i) q^{20} +(3.46643 - 1.36604i) q^{21} +(0.632550 + 0.872702i) q^{22} +(-0.115232 - 0.0785636i) q^{23} +(-0.841339 + 3.89327i) q^{24} +(-1.12931 - 1.04784i) q^{25} +(1.03161 - 2.31000i) q^{26} +(2.45435 + 5.09651i) q^{27} +(-4.62388 + 2.57288i) q^{28} +(-2.76656 + 5.74483i) q^{29} +(2.39197 + 2.82841i) q^{30} +(3.93613 - 6.81758i) q^{31} +(0.454589 - 5.63856i) q^{32} +(1.06130 + 0.159966i) q^{33} +(-0.332177 + 7.21466i) q^{34} +(-0.726673 + 4.86704i) q^{35} +(-1.11650 - 1.69976i) q^{36} +(-4.03411 + 0.302315i) q^{37} +(-1.42325 + 11.7236i) q^{38} +(-0.920374 - 2.34508i) q^{39} +(-3.89755 - 3.53336i) q^{40} +(2.31407 + 2.90175i) q^{41} +(-1.40048 + 5.07968i) q^{42} +(-6.71348 - 5.35382i) q^{43} +(-1.52406 - 0.0262455i) q^{44} +(-1.88597 - 0.141334i) q^{45} +(0.186720 - 0.0635370i) q^{46} +(4.15655 - 3.85672i) q^{47} +(-3.68697 - 4.25876i) q^{48} +(-6.29832 + 3.05470i) q^{49} +(2.14410 - 0.386595i) q^{50} +(4.89171 + 5.27201i) q^{51} +(1.73528 + 3.12880i) q^{52} +(7.02866 + 0.526726i) q^{53} +(-7.84723 - 1.55487i) q^{54} +(-0.883833 + 1.10829i) q^{55} +(1.01933 - 7.41357i) q^{56} +(7.33217 + 9.19425i) q^{57} +(-4.14476 - 8.00842i) q^{58} +(7.74518 - 3.03976i) q^{59} +(-5.22990 + 0.301475i) q^{60} +(7.47238 - 0.559977i) q^{61} +(4.36401 + 10.2421i) q^{62} +(-1.34837 - 2.32797i) q^{63} +(5.98876 + 5.30422i) q^{64} +(3.29011 + 0.495905i) q^{65} +(-1.08249 + 1.06401i) q^{66} +(-6.85847 - 3.95974i) q^{67} +(-7.87470 - 6.50481i) q^{68} +(0.0852158 - 0.176952i) q^{69} +(-4.88533 - 4.95639i) q^{70} +(2.31572 - 1.11519i) q^{71} +(2.87027 + 0.181725i) q^{72} +(0.0710248 + 0.0659013i) q^{73} +(3.08540 - 4.81781i) q^{74} +(1.22212 - 1.79251i) q^{75} +(-12.0456 - 11.5689i) q^{76} +(-2.01101 - 0.147895i) q^{77} +(3.43325 + 0.951692i) q^{78} +(-2.79738 - 4.84520i) q^{79} +(7.30600 - 1.40480i) q^{80} +(-4.06145 + 2.76905i) q^{81} +(-5.24665 + 0.151095i) q^{82} +(-9.51251 - 2.17117i) q^{83} +(-4.55330 - 5.89884i) q^{84} +(-9.26055 + 2.11366i) q^{85} +(11.7565 - 3.04191i) q^{86} +(-8.58048 - 2.64673i) q^{87} +(1.32445 - 1.70081i) q^{88} +(-0.741049 + 0.228583i) q^{89} +(1.76202 - 2.01220i) q^{90} +(2.05949 + 4.26141i) q^{91} +(-0.0867934 + 0.265083i) q^{92} +(10.3198 + 4.05022i) q^{93} +(0.829192 + 7.97589i) q^{94} +(-15.3585 + 2.31492i) q^{95} +(7.94724 - 0.550446i) q^{96} -12.3959 q^{97} +(1.89711 - 9.71602i) q^{98} -0.774968i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−0.849554	+	1.13060i	−0.600725	+	0.799456i
$2$	−0.849554	+	1.13060i	−0.600725	+	0.799456i
$3$	0.209889	+	1.39252i	0.121180	+	0.803974i	0.964024	+	0.265816i	$0.0856414\pi$
$3$	0.209889	+	1.39252i	0.121180	+	0.803974i	−0.842844	+	0.538158i	$0.819121\pi$
$4$	−0.556517	−	1.92101i	−0.278258	−	0.960506i
$5$	−1.73139	−	0.679519i	−0.774300	−	0.303890i	−0.0549049	−	0.998492i	$-0.517486\pi$
$5$	−1.73139	−	0.679519i	−0.774300	−	0.303890i	−0.719395	+	0.694601i	$0.755581\pi$
$6$	−1.75270	−	0.945723i	−0.715537	−	0.386090i
$7$	−0.592319	−	2.57860i	−0.223875	−	0.974618i
$7$	−0.592319	−	2.57860i	−0.223875	−	0.974618i
$8$	2.64469	+	1.00281i	0.935039	+	0.354545i
$9$	0.971651	−	0.299715i	0.323884	−	0.0999049i
$10$	2.23917	−	1.38022i	0.708088	−	0.436464i
$11$	0.224646	−	0.728285i	0.0677333	−	0.219586i	−0.915378	−	0.402596i	$-0.868108\pi$
$11$	0.224646	−	0.728285i	0.0677333	−	0.219586i	0.983111	+	0.183010i	$0.0585841\pi$
$12$	2.55825	−	1.17816i	0.738503	−	0.340106i
$13$	−1.74405	+	0.398067i	−0.483712	+	0.110404i	−0.457421	−	0.889250i	$-0.651227\pi$
$13$	−1.74405	+	0.398067i	−0.483712	+	0.110404i	−0.0262907	+	0.999654i	$0.508370\pi$
$14$	3.41857	+	1.52098i	0.913651	+	0.406499i
$15$	0.582847	−	2.55362i	0.150490	−	0.659342i
$16$	−3.38058	+	2.13815i	−0.845145	+	0.534538i
$17$	4.21955	−	2.87684i	1.02339	−	0.697737i	0.0694063	−	0.997588i	$-0.477890\pi$
$17$	4.21955	−	2.87684i	1.02339	−	0.697737i	0.953986	+	0.299851i	$0.0969371\pi$
$18$	−0.486612	+	1.35317i	−0.114696	+	0.318946i
$19$	7.23191	−	4.17535i	1.65911	−	0.957890i	0.685990	−	0.727611i	$-0.259370\pi$
$19$	7.23191	−	4.17535i	1.65911	−	0.957890i	0.973125	−	0.230279i	$-0.0739638\pi$
$20$	−0.341820	+	3.70418i	−0.0764332	+	0.828280i
$21$	3.46643	−	1.36604i	0.756438	−	0.298094i
$22$	0.632550	+	0.872702i	0.134860	+	0.186061i
$23$	−0.115232	−	0.0785636i	−0.0240275	−	0.0163816i	0.551247	−	0.834342i	$-0.314152\pi$
$23$	−0.115232	−	0.0785636i	−0.0240275	−	0.0163816i	−0.575274	+	0.817961i	$0.695105\pi$
$24$	−0.841339	+	3.89327i	−0.171738	+	0.794710i
$25$	−1.12931	−	1.04784i	−0.225861	−	0.209568i
$26$	1.03161	−	2.31000i	0.202315	−	0.453028i
$27$	2.45435	+	5.09651i	0.472340	+	0.980825i
$28$	−4.62388	+	2.57288i	−0.873831	+	0.486229i
$29$	−2.76656	+	5.74483i	−0.513738	+	1.06679i	0.469241	+	0.883070i	$0.344528\pi$
$29$	−2.76656	+	5.74483i	−0.513738	+	1.06679i	−0.982979	+	0.183718i	$0.941187\pi$
$30$	2.39197	+	2.82841i	0.436711	+	0.516394i
$31$	3.93613	−	6.81758i	0.706951	−	1.22447i	−0.259032	−	0.965869i	$-0.583404\pi$
$31$	3.93613	−	6.81758i	0.706951	−	1.22447i	0.965983	−	0.258606i	$-0.0832630\pi$
$32$	0.454589	−	5.63856i	0.0803608	−	0.996766i
$33$	1.06130	+	0.159966i	0.184749	+	0.0278465i
$34$	−0.332177	+	7.21466i	−0.0569679	+	1.23730i
$35$	−0.726673	+	4.86704i	−0.122830	+	0.822680i
$36$	−1.11650	−	1.69976i	−0.186083	−	0.283293i
$37$	−4.03411	+	0.302315i	−0.663204	+	0.0497003i	−0.402080	−	0.915605i	$-0.631712\pi$
$37$	−4.03411	+	0.302315i	−0.663204	+	0.0497003i	−0.261125	+	0.965305i	$0.584093\pi$
$38$	−1.42325	+	11.7236i	−0.230881	+	1.90182i
$39$	−0.920374	−	2.34508i	−0.147378	−	0.375513i
$40$	−3.89755	−	3.53336i	−0.616257	−	0.558674i
$41$	2.31407	+	2.90175i	0.361397	+	0.453177i	0.928975	−	0.370142i	$-0.120691\pi$
$41$	2.31407	+	2.90175i	0.361397	+	0.453177i	−0.567578	+	0.823319i	$0.692120\pi$
$42$	−1.40048	+	5.07968i	−0.216099	+	0.783811i
$43$	−6.71348	−	5.35382i	−1.02380	−	0.816450i	−0.0406320	−	0.999174i	$-0.512937\pi$
$43$	−6.71348	−	5.35382i	−1.02380	−	0.816450i	−0.983164	+	0.182724i	$0.941509\pi$
$44$	−1.52406	−	0.0262455i	−0.229761	−	0.00395666i
$45$	−1.88597	−	0.141334i	−0.281143	−	0.0210688i
$46$	0.186720	−	0.0635370i	0.0275303	−	0.00936802i
$47$	4.15655	−	3.85672i	0.606295	−	0.562560i	−0.316140	−	0.948713i	$-0.602387\pi$
$47$	4.15655	−	3.85672i	0.606295	−	0.562560i	0.922435	+	0.386153i	$0.126196\pi$
$48$	−3.68697	−	4.25876i	−0.532168	−	0.614699i
$49$	−6.29832	+	3.05470i	−0.899760	+	0.436386i
$50$	2.14410	−	0.386595i	0.303221	−	0.0546728i
$51$	4.89171	+	5.27201i	0.684976	+	0.738229i
$52$	1.73528	+	3.12880i	0.240640	+	0.433887i
$53$	7.02866	+	0.526726i	0.965461	+	0.0723513i	0.548121	−	0.836399i	$-0.315343\pi$
$53$	7.02866	+	0.526726i	0.965461	+	0.0723513i	0.417340	+	0.908750i	$0.362962\pi$
$54$	−7.84723	−	1.55487i	−1.06787	−	0.211591i
$55$	−0.883833	+	1.10829i	−0.119176	+	0.149442i
$56$	1.01933	−	7.41357i	0.136214	−	0.990679i
$57$	7.33217	+	9.19425i	0.971169	+	1.21781i
$58$	−4.14476	−	8.00842i	−0.544234	−	1.05156i
$59$	7.74518	−	3.03976i	1.00834	−	0.395743i	0.197052	−	0.980393i	$-0.436863\pi$
$59$	7.74518	−	3.03976i	1.00834	−	0.395743i	0.811286	+	0.584650i	$0.198768\pi$
$60$	−5.22990	+	0.301475i	−0.675177	+	0.0389203i
$61$	7.47238	−	0.559977i	0.956740	−	0.0716978i	0.412800	−	0.910822i	$-0.364551\pi$
$61$	7.47238	−	0.559977i	0.956740	−	0.0716978i	0.543940	+	0.839124i	$0.316932\pi$
$62$	4.36401	+	10.2421i	0.554230	+	1.30075i
$63$	−1.34837	−	2.32797i	−0.169879	−	0.293296i
$64$	5.98876	+	5.30422i	0.748595	+	0.663027i
$65$	3.29011	+	0.495905i	0.408088	+	0.0615094i
$66$	−1.08249	+	1.06401i	−0.133246	+	0.130971i
$67$	−6.85847	−	3.95974i	−0.837895	−	0.483759i	0.0186529	−	0.999826i	$-0.494062\pi$
$67$	−6.85847	−	3.95974i	−0.837895	−	0.483759i	−0.856548	+	0.516067i	$0.827396\pi$
$68$	−7.87470	−	6.50481i	−0.954948	−	0.788824i
$69$	0.0852158	−	0.176952i	0.0102588	−	0.0213026i
$70$	−4.88533	−	4.95639i	−0.583909	−	0.592402i
$71$	2.31572	−	1.11519i	0.274825	−	0.132349i	−0.291395	−	0.956603i	$-0.594119\pi$
$71$	2.31572	−	1.11519i	0.274825	−	0.132349i	0.566220	+	0.824254i	$0.308405\pi$
$72$	2.87027	+	0.181725i	0.338265	+	0.0214165i
$73$	0.0710248	+	0.0659013i	0.00831282	+	0.00771317i	0.684318	−	0.729184i	$-0.260100\pi$
$73$	0.0710248	+	0.0659013i	0.00831282	+	0.00771317i	−0.676005	+	0.736897i	$0.736290\pi$
$74$	3.08540	−	4.81781i	0.358670	−	0.560059i
$75$	1.22212	−	1.79251i	0.141118	−	0.206982i
$76$	−12.0456	−	11.5689i	−1.38172	−	1.32705i
$77$	−2.01101	−	0.147895i	−0.229176	−	0.0168542i
$78$	3.43325	+	0.951692i	0.388739	+	0.107758i
$79$	−2.79738	−	4.84520i	−0.314729	−	0.545127i	0.664651	−	0.747154i	$-0.268580\pi$
$79$	−2.79738	−	4.84520i	−0.314729	−	0.545127i	−0.979380	+	0.202027i	$0.935247\pi$
$80$	7.30600	−	1.40480i	0.816836	−	0.157061i
$81$	−4.06145	+	2.76905i	−0.451272	+	0.307672i
$82$	−5.24665	+	0.151095i	−0.579395	+	0.0166856i
$83$	−9.51251	−	2.17117i	−1.04413	−	0.238317i	−0.334139	−	0.942524i	$-0.608445\pi$
$83$	−9.51251	−	2.17117i	−1.04413	−	0.238317i	−0.709994	+	0.704207i	$0.751303\pi$
$84$	−4.55330	−	5.89884i	−0.496806	−	0.643616i
$85$	−9.26055	+	2.11366i	−1.00445	+	0.229259i
$86$	11.7565	−	3.04191i	1.26774	−	0.328017i
$87$	−8.58048	−	2.64673i	−0.919924	−	0.283759i
$88$	1.32445	−	1.70081i	0.141187	−	0.181307i
$89$	−0.741049	+	0.228583i	−0.0785510	+	0.0242298i	−0.333782	−	0.942650i	$-0.608325\pi$
$89$	−0.741049	+	0.228583i	−0.0785510	+	0.0242298i	0.255231	+	0.966880i	$0.417849\pi$
$90$	1.76202	−	2.01220i	0.185733	−	0.212105i
$91$	2.05949	+	4.26141i	0.215893	+	0.446717i
$92$	−0.0867934	+	0.265083i	−0.00904884	+	0.0276369i
$93$	10.3198	+	4.05022i	1.07011	+	0.419988i
$94$	0.829192	+	7.97589i	0.0855246	+	0.822650i
$95$	−15.3585	+	2.31492i	−1.57575	+	0.237505i
$96$	7.94724	−	0.550446i	0.811112	−	0.0561797i
$97$	−12.3959			−1.25862			−0.629308	−	0.777156i	$-0.716662\pi$
$97$	−12.3959			−1.25862			−0.629308	+	0.777156i	$0.716662\pi$
$98$	1.89711	−	9.71602i	0.191637	−	0.981466i
$99$		−	0.774968i		−	0.0778872i
$100$	−1.38444	+	2.75255i	−0.138444	+	0.275255i
$101$	−0.149844	−	0.994147i	−0.0149100	−	0.0989214i	0.980138	−	0.198316i	$-0.0635473\pi$
$101$	−0.149844	−	0.994147i	−0.0149100	−	0.0989214i	−0.995048	+	0.0993950i	$0.968309\pi$
$102$	−10.1163	+	1.05172i	−1.00166	+	0.104135i
$103$	−1.59764	+	4.07071i	−0.157420	+	0.401099i	−0.987724	−	0.156212i	$-0.950072\pi$
$103$	−1.59764	+	4.07071i	−0.157420	+	0.401099i	0.830304	+	0.557311i	$0.188167\pi$
$104$	−5.01165	−	0.696176i	−0.491432	−	0.0682656i
$105$	−6.92999	+	0.00962995i	−0.676297	+	0.000939787i
$106$	−6.56675	+	7.49913i	−0.637819	+	0.728380i
$107$	−4.98847	−	16.1722i	−0.482253	−	1.56343i	−0.790711	−	0.612189i	$-0.790289\pi$
$107$	−4.98847	−	16.1722i	−0.482253	−	1.56343i	0.308458	−	0.951238i	$-0.400187\pi$
$108$	8.42458	−	7.55113i	0.810656	−	0.726608i
$109$	4.46093	−	14.4620i	0.427280	−	1.38521i	−0.444706	−	0.895676i	$-0.646692\pi$
$109$	4.46093	−	14.4620i	0.427280	−	1.38521i	0.871986	−	0.489531i	$-0.162832\pi$
$110$	−0.502171	−	1.94081i	−0.0478802	−	0.185049i
$111$	−1.26770	−	5.55415i	−0.120325	−	0.527176i
$112$	7.51581	+	7.45068i	0.710177	+	0.704023i
$113$	−3.21616	+	14.0909i	−0.302551	+	1.32556i	0.563712	+	0.825971i	$0.309373\pi$
$113$	−3.21616	+	14.0909i	−0.302551	+	1.32556i	−0.866263	+	0.499589i	$0.833484\pi$
$114$	−16.6241	+	0.478746i	−1.55699	+	0.0448387i
$115$	0.146125	+	0.214326i	0.0136262	+	0.0199860i
$116$	12.5755	+	2.11751i	1.16761	+	0.196606i
$117$	−1.57530	+	0.909499i	−0.145636	+	0.0840832i
$118$	−3.14320	+	11.3392i	−0.289355	+	1.04385i
$119$	−9.91754	−	9.17652i	−0.909139	−	0.841210i
$120$	4.10223	−	6.16905i	0.374481	−	0.563155i
$121$	8.60869	+	5.86931i	0.782609	+	0.533573i
$122$	−5.71508	+	8.92401i	−0.517419	+	0.807942i
$123$	−3.55506	+	3.83144i	−0.320549	+	0.345469i
$124$	−15.2872	−	3.76726i	−1.37283	−	0.338310i
$125$	5.27826	+	10.9604i	0.472102	+	0.980331i
$126$	3.77752	+	0.453266i	0.336528	+	0.0403802i
$127$	7.99416	+	3.84978i	0.709367	+	0.341613i	0.753532	−	0.657411i	$-0.228349\pi$
$127$	7.99416	+	3.84978i	0.709367	+	0.341613i	−0.0441652	+	0.999024i	$0.514063\pi$
$128$	−11.0847	+	2.26468i	−0.979761	+	0.200171i
$129$	6.04624	−	10.4724i	0.532341	−	0.922042i
$130$	−3.35580	+	3.29851i	−0.294323	+	0.289298i
$131$	−1.97653	+	13.1134i	−0.172690	+	1.14572i	0.719643	+	0.694344i	$0.244306\pi$
$131$	−1.97653	+	13.1134i	−0.172690	+	1.14572i	−0.892333	+	0.451378i	$0.850933\pi$
$132$	−0.283337	−	2.12780i	−0.0246613	−	0.185201i
$133$	−15.0501	−	16.1750i	−1.30501	−	1.40255i
$134$	10.3035	−	4.39018i	0.890089	−	0.379254i
$135$	−0.786253	−	10.4918i	−0.0676699	−	0.902992i
$136$	14.0443	−	3.37696i	1.20429	−	0.289572i
$137$	6.98926	+	17.8083i	0.597133	+	1.52147i	0.835044	+	0.550183i	$0.185442\pi$
$137$	6.98926	+	17.8083i	0.597133	+	1.52147i	−0.237911	+	0.971287i	$0.576463\pi$
$138$	0.127667	+	0.246676i	0.0108678	+	0.0209984i
$139$	8.66321	−	6.90868i	0.734804	−	0.585986i	−0.182957	−	0.983121i	$-0.558567\pi$
$139$	8.66321	−	6.90868i	0.734804	−	0.585986i	0.917760	+	0.397135i	$0.129995\pi$
$140$	9.75405	−	1.31264i	0.824368	−	0.110938i
$141$	6.24298	+	4.97861i	0.525754	+	0.419275i
$142$	−0.706491	+	3.56557i	−0.0592874	+	0.299216i
$143$	−0.101887	+	1.35959i	−0.00852021	+	0.113694i
$144$	−2.64391	+	3.09074i	−0.220326	+	0.257562i
$145$	8.69372	−	8.06659i	0.721974	−	0.669894i
$146$	−0.134847	+	0.0243139i	−0.0111601	+	0.00201223i
$147$	−5.57569	−	8.12940i	−0.459875	−	0.670502i
$148$	2.82580	+	7.58134i	0.232280	+	0.623182i
$149$	−11.0409	−	11.8993i	−0.904508	−	0.974828i	0.0952792	−	0.995451i	$-0.469626\pi$
$149$	−11.0409	−	11.8993i	−0.904508	−	0.974828i	−0.999787	+	0.0206227i	$0.993435\pi$
$150$	0.988366	+	2.90456i	0.0806997	+	0.237157i
$151$	−1.40221	+	18.7112i	−0.114110	+	1.52269i	0.586968	+	0.809610i	$0.300321\pi$
$151$	−1.40221	+	18.7112i	−0.114110	+	1.52269i	−0.701078	+	0.713085i	$0.747298\pi$
$152$	23.3132	−	3.79029i	1.89095	−	0.307433i
$153$	3.23770	−	4.05995i	0.261753	−	0.328227i
$154$	1.87567	−	2.14801i	0.151146	−	0.173092i
$155$	−11.4477	+	9.12920i	−0.919497	+	0.733275i
$156$	−3.99272	+	3.07312i	−0.319673	+	0.246047i
$157$	−0.121724	+	0.0477732i	−0.00971463	+	0.00381271i	−0.370193	−	0.928955i	$-0.620709\pi$
$157$	−0.121724	+	0.0477732i	−0.00971463	+	0.00381271i	0.360479	+	0.932767i	$0.382613\pi$
$158$	7.85450	+	0.953540i	0.624871	+	0.0758596i
$159$	0.741763	+	9.89813i	0.0588256	+	0.784973i
$160$	−4.61858	+	9.45362i	−0.365131	+	0.747375i
$161$	−0.134330	+	0.343671i	−0.0105867	+	0.0270850i
$162$	0.319731	−	6.94434i	0.0251204	−	0.545599i
$163$	−2.73005	+	18.1127i	−0.213834	+	1.41869i	0.582005	+	0.813185i	$0.302269\pi$
$163$	−2.73005	+	18.1127i	−0.213834	+	1.41869i	−0.795838	+	0.605509i	$0.792970\pi$
$164$	4.28648	−	6.06023i	0.334718	−	0.473224i
$165$	−1.72883	−	0.998139i	−0.134589	−	0.0777050i
$166$	10.5361	−	8.91032i	0.817761	−	0.691575i
$167$	20.5598	+	9.90107i	1.59096	+	0.766168i	0.999202	−	0.0399448i	$-0.0127182\pi$
$167$	20.5598	+	9.90107i	1.59096	+	0.766168i	0.591762	+	0.806113i	$0.298432\pi$
$168$	10.5375	−	0.136584i	0.812987	−	0.0105377i
$169$	−8.82935	+	4.25199i	−0.679181	+	0.327076i
$170$	5.47763	−	12.2657i	0.420115	−	0.940733i
$171$	5.77548	−	6.22449i	0.441662	−	0.475998i
$172$	−6.54860	+	15.8762i	−0.499326	+	1.21055i
$173$	−9.59645	+	14.0754i	−0.729604	+	1.07013i	0.264780	+	0.964309i	$0.414701\pi$
$173$	−9.59645	+	14.0754i	−0.729604	+	1.07013i	−0.994385	+	0.105824i	$0.966252\pi$
$174$	10.2820	−	7.45256i	0.779474	−	0.564977i
$175$	−2.03305	+	3.53268i	−0.153684	+	0.267045i
$176$	0.797748	+	2.94235i	0.0601325	+	0.221788i
$177$	5.85857	+	10.1473i	0.440357	+	0.762721i
$178$	0.371124	−	1.03202i	0.0278170	−	0.0773535i
$179$	−5.18554	−	7.60580i	−0.387586	−	0.568484i	0.582014	−	0.813178i	$-0.302265\pi$
$179$	−5.18554	−	7.60580i	−0.387586	−	0.568484i	−0.969600	+	0.244695i	$0.921312\pi$
$180$	0.778067	+	3.70162i	0.0579937	+	0.275902i
$181$	−3.01225	−	0.687527i	−0.223899	−	0.0511035i	0.109099	−	0.994031i	$-0.465203\pi$
$181$	−3.01225	−	0.687527i	−0.223899	−	0.0511035i	−0.332999	+	0.942927i	$0.608060\pi$
$182$	−6.56760	−	1.29184i	−0.486823	−	0.0957575i
$183$	2.34815	+	10.2879i	0.173580	+	0.760506i
$184$	−0.225968	−	0.323331i	−0.0166586	−	0.0238363i
$185$	7.19004	+	2.21783i	0.528622	+	0.163058i
$186$	−13.3464	+	8.22669i	−0.978606	+	0.603210i
$187$	−1.14725	−	3.71931i	−0.0838956	−	0.271983i
$188$	−9.72199	−	5.83846i	−0.709049	−	0.425813i
$189$	11.6881	−	9.34754i	0.850184	−	0.679934i
$190$	10.4306	−	19.3309i	0.756715	−	1.40241i
$191$	4.49771	−	11.4600i	0.325443	−	0.829215i	−0.670721	−	0.741710i	$-0.734015\pi$
$191$	4.49771	−	11.4600i	0.325443	−	0.829215i	0.996164	−	0.0875053i	$-0.0278895\pi$
$192$	−6.12927	+	9.45279i	−0.442342	+	0.682196i
$193$	−10.5584	+	1.59142i	−0.760010	+	0.114553i	−0.517602	−	0.855621i	$-0.673175\pi$
$193$	−10.5584	+	1.59142i	−0.760010	+	0.114553i	−0.242408	+	0.970174i	$0.577937\pi$
$194$	10.5310	−	14.0149i	0.756083	−	1.00621i
$195$			4.68565i			0.335546i
$196$	9.37324	+	10.3992i	0.669517	+	0.742797i
$197$			8.00498i			0.570331i	0.958478	+	0.285166i	$0.0920486\pi$
$197$			8.00498i			0.570331i	−0.958478	+	0.285166i	$0.907951\pi$
$198$	0.876180	+	0.658377i	0.0622674	+	0.0467888i
$199$	−4.49928	+	0.678158i	−0.318946	+	0.0480733i	−0.306564	−	0.951850i	$-0.599179\pi$
$199$	−4.49928	+	0.678158i	−0.318946	+	0.0480733i	−0.0123815	+	0.999923i	$0.503941\pi$
$200$	−1.93588	−	3.90369i	−0.136887	−	0.276033i
$201$	4.07451	−	10.3817i	0.287394	−	0.732267i
$202$	1.25128	+	0.675168i	0.0880400	+	0.0475047i
$203$	16.4523	+	3.73108i	1.15472	+	0.261871i
$204$	7.40528	−	12.3310i	0.518473	−	0.863342i
$205$	−2.03475	−	6.59651i	−0.142113	−	0.460720i
$206$	−3.24507	−	5.26457i	−0.226095	−	0.366800i
$207$	−0.135512	−	0.0417998i	−0.00941871	−	0.00290529i
$208$	5.04476	−	5.07473i	0.349791	−	0.351869i
$209$	−1.41622	−	6.20487i	−0.0979620	−	0.429200i
$210$	5.87651	−	7.84323i	0.405518	−	0.541234i
$211$	9.75717	+	2.22701i	0.671711	+	0.153314i	0.544756	−	0.838595i	$-0.316622\pi$
$211$	9.75717	+	2.22701i	0.671711	+	0.153314i	0.126955	+	0.991908i	$0.459480\pi$
$212$	−2.89972	−	13.7953i	−0.199154	−	0.947464i
$213$	2.03897	+	2.99063i	0.139708	+	0.204914i
$214$	22.5223	+	8.09920i	1.53959	+	0.553650i
$215$	7.98561	+	13.8315i	0.544614	+	0.943299i
$216$	1.38018	+	15.9399i	0.0939097	+	1.08458i
$217$	−19.9112	−	6.11152i	−1.35166	−	0.414877i
$218$	12.5609	+	17.3298i	0.850734	+	1.17372i
$219$	−0.0768618	+	0.112736i	−0.00519384	+	0.00761797i
$220$	2.62091	+	1.08107i	0.176702	+	0.0728858i
$221$	−6.21392	+	6.69702i	−0.417994	+	0.450490i
$222$	7.35650	+	3.28529i	0.493736	+	0.220494i
$223$	14.1199	−	6.79979i	0.945538	−	0.455347i	0.103419	−	0.994638i	$-0.467022\pi$
$223$	14.1199	−	6.79979i	0.945538	−	0.455347i	0.842120	+	0.539291i	$0.181308\pi$
$224$	−14.8088	+	2.16762i	−0.989456	+	0.144830i
$225$	−1.41134	−	0.679668i	−0.0940896	−	0.0453112i
$226$	−13.1989	−	15.6072i	−0.877977	−	1.03817i
$227$	6.49559	+	3.75023i	0.431128	+	0.248912i	0.699827	−	0.714312i	$-0.253260\pi$
$227$	6.49559	+	3.75023i	0.431128	+	0.248912i	−0.268699	+	0.963224i	$0.586594\pi$
$228$	13.5818	−	19.2019i	0.899476	−	1.27168i
$229$	−1.93289	+	12.8239i	−0.127729	+	0.847429i	0.829585	+	0.558380i	$0.188577\pi$
$229$	−1.93289	+	12.8239i	−0.127729	+	0.847429i	−0.957314	+	0.289048i	$0.906661\pi$
$230$	−0.366458	−	0.0168725i	−0.0241636	−	0.00111254i
$231$	−0.216143	−	2.83143i	−0.0142212	−	0.186294i
$232$	−13.0777	+	12.4190i	−0.858590	+	0.815345i
$233$	−0.411273	−	5.48806i	−0.0269434	−	0.359535i	−0.994338	−	0.106262i	$-0.966112\pi$
$233$	−0.411273	−	5.48806i	−0.0269434	−	0.359535i	0.967395	−	0.253273i	$-0.0815072\pi$
$234$	0.310020	−	2.55370i	0.0202667	−	0.166941i
$235$	−9.81731	+	3.85301i	−0.640411	+	0.251343i
$236$	−10.1497	−	13.1869i	−0.660692	−	0.858395i
$237$	6.15991	−	4.91236i	0.400129	−	0.319092i
$238$	18.8005	−	3.41683i	1.21865	−	0.221480i
$239$	5.70270	−	7.15096i	0.368877	−	0.462557i	−0.562402	−	0.826864i	$-0.690123\pi$
$239$	5.70270	−	7.15096i	0.368877	−	0.462557i	0.931279	+	0.364307i	$0.118694\pi$
$240$	3.48966	+	9.87893i	0.225257	+	0.637682i
$241$	0.530096	−	7.07364i	0.0341465	−	0.455653i	−0.953757	−	0.300580i	$-0.902820\pi$
$241$	0.530096	−	7.07364i	0.0341465	−	0.455653i	0.987903	−	0.155073i	$-0.0495612\pi$
$242$	−13.9494	+	4.74670i	−0.896701	+	0.305130i
$243$	6.83419	+	7.36550i	0.438413	+	0.472497i
$244$	−5.23423	−	14.0429i	−0.335087	−	0.899005i
$245$	12.9806	−	1.00904i	0.829297	−	0.0644654i
$246$	−1.31162	−	7.27437i	−0.0836257	−	0.463797i
$247$	−10.9507	+	10.1608i	−0.696778	+	0.646515i
$248$	17.2466	−	14.0832i	1.09516	−	0.894285i
$249$	1.02683	−	13.7021i	0.0650727	−	0.868335i
$250$	−16.8760	−	3.34386i	−1.06733	−	0.211485i
$251$	−6.39440	−	5.09936i	−0.403611	−	0.321869i	0.400556	−	0.916272i	$-0.368817\pi$
$251$	−6.39440	−	5.09936i	−0.403611	−	0.321869i	−0.804167	+	0.594403i	$0.797388\pi$
$252$	−3.72167	+	3.88579i	−0.234443	+	0.244782i
$253$	−0.0831030	+	0.0662725i	−0.00522464	+	0.00416651i
$254$	−11.1440	+	5.76760i	−0.699239	+	0.361892i
$255$	−4.88701	−	12.4519i	−0.306036	−	0.779768i
$256$	6.85663	−	14.4564i	0.428539	−	0.903523i
$257$	0.745048	+	9.94198i	0.0464748	+	0.620163i	0.971006	+	0.239056i	$0.0768381\pi$
$257$	0.745048	+	9.94198i	0.0464748	+	0.620163i	−0.924531	+	0.381107i	$0.875543\pi$
$258$	6.70349	+	15.7327i	0.417341	+	0.979477i
$259$	3.16903	+	10.2233i	0.196914	+	0.635244i
$260$	−0.878363	−	6.59633i	−0.0544738	−	0.409087i
$261$	−0.966325	+	6.41115i	−0.0598140	+	0.396840i
$262$	−13.1469	−	13.3752i	−0.812215	−	0.826322i
$263$	−15.2262	+	26.3726i	−0.938888	+	1.62620i	−0.171339	+	0.985212i	$0.554809\pi$
$263$	−15.2262	+	26.3726i	−0.938888	+	1.62620i	−0.767549	+	0.640990i	$0.778524\pi$
$264$	2.64640	+	1.48734i	0.162875	+	0.0915396i
$265$	−11.8114	−	5.68808i	−0.725570	−	0.349416i
$266$	31.0734	−	3.27412i	1.90523	−	0.200749i
$267$	−0.473846	−	0.983951i	−0.0289989	−	0.0602168i
$268$	−3.78986	+	15.3789i	−0.231502	+	0.939414i
$269$	−0.774505	+	0.834718i	−0.0472224	+	0.0508937i	−0.756221	−	0.654316i	$-0.772957\pi$
$269$	−0.774505	+	0.834718i	−0.0472224	+	0.0508937i	0.708999	+	0.705210i	$0.249147\pi$
$270$	12.5300	+	8.02442i	0.762553	+	0.488351i
$271$	15.2999	+	10.4313i	0.929400	+	0.633654i	0.930479	−	0.366345i	$-0.119391\pi$
$271$	15.2999	+	10.4313i	0.929400	+	0.633654i	−0.00107918	+	0.999999i	$0.500344\pi$
$272$	−8.11341	+	18.7474i	−0.491948	+	1.13673i
$273$	−5.50185	+	3.76231i	−0.332987	+	0.227705i
$274$	−26.0719	−	7.22709i	−1.57506	−	0.436604i
$275$	−1.01682	+	0.587062i	−0.0613166	+	0.0354012i
$276$	−0.387352	−	0.0652237i	−0.0233158	−	0.00392600i
$277$	10.4357	+	15.3063i	0.627018	+	0.919666i	0.999966	−	0.00818574i	$-0.00260563\pi$
$277$	10.4357	+	15.3063i	0.627018	+	0.919666i	−0.372949	+	0.927852i	$0.621653\pi$
$278$	0.451095	+	15.6639i	0.0270549	+	0.939460i
$279$	1.78122	−	7.80403i	0.106639	−	0.467215i
$280$	−6.80252	+	12.1431i	−0.406528	+	0.725689i
$281$	5.53059	+	24.2311i	0.329927	+	1.44551i	0.819267	+	0.573413i	$0.194381\pi$
$281$	5.53059	+	24.2311i	0.329927	+	1.44551i	−0.489339	+	0.872094i	$0.662762\pi$
$282$	−10.9326	+	2.82872i	−0.651025	+	0.168448i
$283$	1.40146	−	4.54341i	0.0833079	−	0.270078i	−0.904329	−	0.426836i	$-0.859628\pi$
$283$	1.40146	−	4.54341i	0.0833079	−	0.270078i	0.987637	+	0.156758i	$0.0501044\pi$
$284$	−3.43103	−	3.82790i	−0.203594	−	0.227144i
$285$	−6.44715	−	20.9011i	−0.381896	−	1.23808i
$286$	−1.45059	−	1.27024i	−0.0857753	−	0.0751106i
$287$	6.11178	−	7.68581i	0.360767	−	0.453679i
$288$	−1.24826	−	5.61496i	−0.0735542	−	0.330865i
$289$	3.31761	−	8.45314i	0.195154	−	0.497243i
$290$	1.73431	+	16.6821i	0.101842	+	0.979608i
$291$	−2.60177	−	17.2616i	−0.152519	−	1.01189i
$292$	0.0870709	−	0.173115i	0.00509544	−	0.0101308i
$293$		−	13.2778i		−	0.775698i	−0.921723	−	0.387849i	$-0.873218\pi$
$293$		−	13.2778i		−	0.775698i	0.921723	−	0.387849i	$-0.126782\pi$
$294$	13.9280	+	0.602484i	0.812295	+	0.0351376i
$295$	−15.4755			−0.901018
$296$	−10.9721	−	3.24590i	−0.637743	−	0.188664i
$297$	4.26307	−	0.642555i	0.247369	−	0.0372848i
$298$	22.8332	−	2.37379i	1.32269	−	0.137510i
$299$	0.232243	+	0.0911487i	0.0134310	+	0.00527126i
$300$	−4.12357	−	1.35014i	−0.238075	−	0.0779501i
$301$	−9.82883	+	20.4825i	−0.566524	+	1.18059i
$302$	−19.9636	−	17.4815i	−1.14878	−	1.00595i
$303$	1.35292	−	0.417321i	0.0777234	−	0.0239745i
$304$	−15.5205	+	29.5780i	−0.890163	+	1.69641i
$305$	−13.3181	−	4.10809i	−0.762592	−	0.235228i
$306$	1.83958	+	7.10969i	0.105162	+	0.406434i
$307$	6.90277	−	1.57551i	0.393962	−	0.0899193i	−0.0209506	−	0.999781i	$-0.506669\pi$
$307$	6.90277	−	1.57551i	0.393962	−	0.0899193i	0.414913	+	0.909861i	$0.363812\pi$
$308$	0.835055	+	3.94549i	0.0475817	+	0.224815i
$309$	−6.00388	−	1.37035i	−0.341549	−	0.0779563i
$310$	−0.596082	−	20.6985i	−0.0338552	−	1.17559i
$311$	−25.4855	+	17.3757i	−1.44515	+	0.985288i	−0.449388	+	0.893337i	$0.648358\pi$
$311$	−25.4855	+	17.3757i	−1.44515	+	0.985288i	−0.995764	+	0.0919508i	$0.970690\pi$
$312$	−0.0824491	−	7.12495i	−0.00466776	−	0.403371i
$313$	−13.2680	−	22.9809i	−0.749953	−	1.29896i	−0.947844	−	0.318733i	$-0.896743\pi$
$313$	−13.2680	−	22.9809i	−0.749953	−	1.29896i	0.197891	−	0.980224i	$-0.436591\pi$
$314$	0.0493987	−	0.178207i	0.00278773	−	0.0100568i
$315$	0.752651	+	4.94686i	0.0424071	+	0.278724i
$316$	−7.75090	+	8.07022i	−0.436022	+	0.453986i
$317$	−4.54047	+	6.65964i	−0.255018	+	0.374043i	−0.932303	−	0.361678i	$-0.882204\pi$
$317$	−4.54047	+	6.65964i	−0.255018	+	0.374043i	0.677285	+	0.735721i	$0.263156\pi$
$318$	−11.8210	−	7.57036i	−0.662889	−	0.424525i
$319$	3.56237	+	3.30540i	0.199455	+	0.185067i
$320$	−6.76454	−	13.2531i	−0.378150	−	0.740873i
$321$	21.4732	−	10.3409i	1.19852	−	0.577174i
$322$	−0.274434	−	0.443840i	−0.0152936	−	0.0247343i
$323$	18.5036	−	38.4232i	1.02957	−	2.13792i
$324$	7.57964	+	6.26108i	0.421091	+	0.347838i
$325$	2.38667	+	1.37795i	0.132389	+	0.0764347i
$326$	−18.1589	−	18.4743i	−1.00573	−	1.02320i
$327$	21.0750	+	3.17654i	1.16545	+	0.175663i
$328$	3.21010	+	9.99479i	0.177248	+	0.551870i
$329$	−12.4069	−	8.43366i	−0.684015	−	0.464963i
$330$	2.59723	−	1.10664i	0.142973	−	0.0609186i
$331$	9.71208	−	0.727820i	0.533824	−	0.0400046i	0.194909	−	0.980821i	$-0.437559\pi$
$331$	9.71208	−	0.727820i	0.533824	−	0.0400046i	0.338916	+	0.940817i	$0.389940\pi$
$332$	1.12303	+	19.4819i	0.0616341	+	1.06921i
$333$	−3.82914	+	1.50283i	−0.209836	+	0.0823545i
$334$	−28.6608	+	14.8334i	−1.56825	+	0.811649i
$335$	9.18394	+	11.5163i	0.501772	+	0.629203i
$336$	−8.79776	+	12.0298i	−0.479957	+	0.656277i
$337$	4.10315	−	5.14519i	0.223513	−	0.280276i	−0.657413	−	0.753530i	$-0.728349\pi$
$337$	4.10315	−	5.14519i	0.223513	−	0.280276i	0.880926	+	0.473254i	$0.156921\pi$
$338$	2.69371	−	13.5948i	0.146518	−	0.739458i
$339$	−20.2969	−	1.52105i	−1.10238	−	0.0826119i
$340$	9.21402	+	16.6133i	0.499700	+	0.900985i
$341$	−4.08090	−	4.39817i	−0.220993	−	0.238174i
$342$	2.13083	+	11.8178i	0.115222	+	0.639033i
$343$	11.6075	+	14.4315i	0.626744	+	0.779225i
$344$	−12.3862	−	20.8915i	−0.667821	−	1.12639i
$345$	−0.267784	+	0.248467i	−0.0144170	+	0.0133770i
$346$	−7.76096	−	22.8076i	−0.417232	−	1.22614i
$347$	−9.65290	−	0.723385i	−0.518195	−	0.0388333i	−0.186934	−	0.982372i	$-0.559855\pi$
$347$	−9.65290	−	0.723385i	−0.518195	−	0.0388333i	−0.331261	+	0.943539i	$0.607474\pi$
$348$	−0.309218	+	17.9562i	−0.0165758	+	0.962551i
$349$	12.8430	+	10.2420i	0.687472	+	0.548240i	0.903734	−	0.428095i	$-0.140815\pi$
$349$	12.8430	+	10.2420i	0.687472	+	0.548240i	−0.216262	+	0.976335i	$0.569387\pi$
$350$	−2.26686	−	5.29977i	−0.121169	−	0.283285i
$351$	−6.30926	−	7.91156i	−0.336763	−	0.422288i
$352$	−4.00435	−	1.59775i	−0.213433	−	0.0851604i
$353$	−1.99591	−	5.08549i	−0.106231	−	0.270673i	0.867867	−	0.496796i	$-0.165490\pi$
$353$	−1.99591	−	5.08549i	−0.106231	−	0.270673i	−0.974099	+	0.226123i	$0.927395\pi$
$354$	−16.4498	−	1.99701i	−0.874295	−	0.106140i
$355$	−4.76720	+	0.357252i	−0.253017	+	0.0189610i
$356$	0.851517	+	1.29635i	0.0451303	+	0.0687066i
$357$	10.6969	−	15.7365i	0.566142	−	0.832862i
$358$	13.0045	+	0.598753i	0.687310	+	0.0316451i
$359$	−8.05567	−	1.21420i	−0.425162	−	0.0640828i	−0.0670235	−	0.997751i	$-0.521350\pi$
$359$	−8.05567	−	1.21420i	−0.425162	−	0.0640828i	−0.358138	+	0.933669i	$0.616588\pi$
$360$	−4.84606	−	2.26504i	−0.255410	−	0.119378i
$361$	25.3670	−	43.9370i	1.33511	−	2.31247i
$362$	3.33639	−	2.82157i	0.175357	−	0.148298i
$363$	−6.36628	+	13.2197i	−0.334143	+	0.693855i
$364$	7.04008	−	6.32784i	0.369001	−	0.331669i
$365$	−0.0781901	−	0.162363i	−0.00409266	−	0.00849849i
$366$	−13.6264	−	6.08533i	−0.712265	−	0.318085i
$367$	−9.72965	−	9.02779i	−0.507883	−	0.471247i	0.384115	−	0.923285i	$-0.374507\pi$
$367$	−9.72965	−	9.02779i	−0.507883	−	0.471247i	−0.891999	+	0.452038i	$0.850697\pi$
$368$	0.557531	+	0.0192079i	0.0290633	+	0.00100128i
$369$	3.11816	+	2.12593i	0.162325	+	0.110671i
$370$	−8.61581	+	6.24490i	−0.447915	+	0.324657i
$371$	−2.80500	−	18.4361i	−0.145628	−	0.957153i
$372$	2.03739	−	22.0785i	0.105634	−	1.14472i
$373$	12.8772	−	7.43465i	0.666756	−	0.384952i	−0.128090	−	0.991763i	$-0.540885\pi$
$373$	12.8772	−	7.43465i	0.666756	−	0.384952i	0.794846	+	0.606811i	$0.207551\pi$
$374$	5.17971	+	1.86267i	0.267836	+	0.0963161i
$375$	−14.1548	+	9.65058i	−0.730951	+	0.498354i
$376$	14.8603	−	6.03160i	0.766363	−	0.311056i
$377$	2.53819	−	11.1205i	0.130723	−	0.572736i
$378$	0.638676	+	21.1558i	0.0328500	+	1.08814i
$379$	3.59089	−	0.819598i	0.184452	−	0.0420999i	−0.129297	−	0.991606i	$-0.541272\pi$
$379$	3.59089	−	0.819598i	0.184452	−	0.0420999i	0.313749	+	0.949506i	$0.398415\pi$
$380$	12.9942	+	28.2155i	0.666590	+	1.44743i
$381$	−3.68303	+	11.9401i	−0.188687	+	0.611709i
$382$	9.13561	+	14.8210i	0.467419	+	0.758307i
$383$	4.46475	−	1.37719i	0.228138	−	0.0703713i	−0.178578	−	0.983926i	$-0.557150\pi$
$383$	4.46475	−	1.37719i	0.228138	−	0.0703713i	0.406717	+	0.913554i	$0.366674\pi$
$384$	−5.48018	−	14.9604i	−0.279659	−	0.763445i
$385$	3.38135	+	1.62259i	0.172329	+	0.0826946i
$386$	7.17066	−	13.2893i	0.364977	−	0.676409i
$387$	−8.12778	−	3.18992i	−0.413158	−	0.162153i
$388$	6.89854	+	23.8127i	0.350220	+	1.20891i
$389$	−4.43104	−	29.3980i	−0.224663	−	1.49054i	−0.762223	−	0.647314i	$-0.775892\pi$
$389$	−4.43104	−	29.3980i	−0.224663	−	1.49054i	0.537561	−	0.843225i	$-0.319346\pi$
$390$	−5.29759	−	3.98071i	−0.268254	−	0.201571i
$391$	−0.712242			−0.0360196
$392$	−19.7204	+	1.76275i	−0.996029	+	0.0890324i
$393$	−18.6756			−0.942057
$394$	−9.05044	−	6.80066i	−0.455954	−	0.342612i
$395$	1.55093	+	10.2898i	0.0780360	+	0.517735i
$396$	−1.48872	+	0.431283i	−0.0748112	+	0.0216728i
$397$	4.19835	+	1.64773i	0.210709	+	0.0826972i	0.468348	−	0.883544i	$-0.344849\pi$
$397$	4.19835	+	1.64773i	0.210709	+	0.0826972i	−0.257639	+	0.966241i	$0.582945\pi$
$398$	3.05566	−	5.66302i	0.153166	−	0.283862i
$399$	19.3653	−	24.3526i	0.969476	−	1.21916i
$400$	6.05815	+	1.12769i	0.302908	+	0.0563844i
$401$	2.41053	−	0.743551i	0.120376	−	0.0371312i	−0.233982	−	0.972241i	$-0.575176\pi$
$401$	2.41053	−	0.743551i	0.120376	−	0.0371312i	0.354358	+	0.935110i	$0.384699\pi$
$402$	8.27602	+	13.4264i	0.412771	+	0.669650i
$403$	−4.15094	+	13.4570i	−0.206773	+	0.670342i
$404$	−1.82638	+	0.841111i	−0.0908658	+	0.0418468i
$405$	8.91356	−	2.03446i	0.442919	−	0.101093i
$406$	−18.1955	+	15.4312i	−0.903026	+	0.765838i
$407$	−0.686077	+	3.00590i	−0.0340076	+	0.148997i
$408$	7.65025	+	18.8483i	0.378744	+	0.933128i
$409$	−2.63591	+	1.79713i	−0.130337	+	0.0888626i	−0.626734	−	0.779233i	$-0.715609\pi$
$409$	−2.63591	+	1.79713i	−0.130337	+	0.0888626i	0.496396	+	0.868096i	$0.334656\pi$
$410$	9.18665	+	3.30359i	0.453696	+	0.163153i
$411$	−23.3316	+	13.4705i	−1.15086	+	0.664450i
$412$	8.70899	+	0.803661i	0.429061	+	0.0395936i
$413$	−12.4259	−	18.1712i	−0.611440	−	0.894146i
$414$	0.162383	−	0.117698i	0.00798070	−	0.00578456i
$415$	14.9945	+	10.2231i	0.736050	+	0.501830i
$416$	1.45170	+	10.0149i	0.0711755	+	0.491019i
$417$	11.4388	+	10.6137i	0.560161	+	0.519753i
$418$	8.21838	+	3.67019i	0.401974	+	0.179515i
$419$	1.82209	+	3.78360i	0.0890147	+	0.184841i	0.940723	−	0.339174i	$-0.110148\pi$
$419$	1.82209	+	3.78360i	0.0890147	+	0.184841i	−0.851709	+	0.524015i	$0.824433\pi$
$420$	3.87515	+	13.3072i	0.189088	+	0.649326i
$421$	9.08934	−	18.8742i	0.442987	−	0.919872i	−0.553234	−	0.833026i	$-0.686607\pi$
$421$	9.08934	−	18.8742i	0.442987	−	0.919872i	0.996222	−	0.0868469i	$-0.0276791\pi$
$422$	−10.8071	+	9.13950i	−0.526081	+	0.444904i
$423$	2.88280	−	4.99316i	0.140167	−	0.242776i
$424$	18.0604	+	8.44141i	0.877092	+	0.409951i
$425$	−7.77964	−	1.17259i	−0.377368	−	0.0568791i
$426$	−5.11342	−	0.235432i	−0.247746	−	0.0114067i
$427$	−5.86999	−	18.9366i	−0.284069	−	0.916405i
$428$	−28.2909	+	18.5830i	−1.36749	+	0.898244i
$429$	−1.91464	+	0.143483i	−0.0924397	+	0.00692740i
$430$	−22.4221	−	2.72205i	−1.08129	−	0.131269i
$431$	3.97811	+	10.1361i	0.191619	+	0.488237i	0.994103	−	0.108436i	$-0.0345842\pi$
$431$	3.97811	+	10.1361i	0.191619	+	0.488237i	−0.802484	+	0.596673i	$0.796489\pi$
$432$	−19.1942	−	11.9814i	−0.923483	−	0.576455i
$433$	−15.6673	−	19.6462i	−0.752922	−	0.944134i	0.246767	−	0.969075i	$-0.420632\pi$
$433$	−15.6673	−	19.6462i	−0.752922	−	0.944134i	−0.999689	+	0.0249406i	$0.992060\pi$
$434$	23.8254	−	17.3196i	1.14365	−	0.831368i
$435$	13.0576	+	10.4131i	0.626065	+	0.499271i
$436$	−30.2642	−	0.521172i	−1.44939	−	0.0249596i
$437$	−1.16138	−	0.0870331i	−0.0555561	−	0.00416336i
$438$	−0.0621607	−	0.182675i	−0.00297015	−	0.00872855i
$439$	−15.0169	+	13.9337i	−0.716718	+	0.665017i	−0.951716	−	0.306978i	$-0.900682\pi$
$439$	−15.0169	+	13.9337i	−0.716718	+	0.665017i	0.234998	+	0.971996i	$0.424492\pi$
$440$	−3.44886	+	2.04477i	−0.164418	+	0.0974807i
$441$	−5.20423	+	4.85580i	−0.247820	+	0.231229i
$442$	−2.29259	−	12.7149i	−0.109047	−	0.604788i
$443$	13.0667	+	14.0825i	0.620816	+	0.669080i	0.962672	−	0.270672i	$-0.0872459\pi$
$443$	13.0667	+	14.0825i	0.620816	+	0.669080i	−0.341856	+	0.939752i	$0.611055\pi$
$444$	−9.96409	+	5.52624i	−0.472875	+	0.262264i
$445$	1.43837	+	0.107791i	0.0681852	+	0.00510978i
$446$	−4.30777	+	21.7408i	−0.203979	+	1.02945i
$447$	14.2527	−	17.8723i	0.674128	−	0.845330i
$448$	10.1302	−	18.5844i	0.478606	−	0.878030i
$449$	3.73037	+	4.67774i	0.176047	+	0.220756i	0.862024	−	0.506867i	$-0.169196\pi$
$449$	3.73037	+	4.67774i	0.176047	+	0.220756i	−0.685977	+	0.727623i	$0.740625\pi$
$450$	1.96745	−	1.01825i	0.0927463	−	0.0480009i
$451$	2.63315	−	1.03343i	0.123990	−	0.0486625i
$452$	28.8586	−	1.66354i	1.35740	−	0.0782465i
$453$	−26.3501	+	1.97466i	−1.23803	+	0.0927778i
$454$	−9.75837	+	4.15790i	−0.457983	+	0.195140i
$455$	−0.670058	−	8.77761i	−0.0314128	−	0.411501i
$456$	10.1713	+	31.6687i	0.476313	+	1.48302i
$457$	13.0047	+	1.96014i	0.608334	+	0.0916916i	0.445983	−	0.895041i	$-0.352854\pi$
$457$	13.0047	+	1.96014i	0.608334	+	0.0916916i	0.162351	+	0.986733i	$0.448092\pi$
$458$	−12.8566	−	13.0799i	−0.600751	−	0.611186i
$459$	25.0181	+	14.4442i	1.16775	+	0.674199i
$460$	0.330402	−	0.399984i	0.0154051	−	0.0186494i
$461$	−2.18926	+	4.54605i	−0.101964	+	0.211731i	−0.945710	−	0.325013i	$-0.894631\pi$
$461$	−2.18926	+	4.54605i	−0.101964	+	0.211731i	0.843746	+	0.536743i	$0.180346\pi$
$462$	3.38484	+	2.16108i	0.157477	+	0.100542i
$463$	20.5018	−	9.87313i	0.952797	−	0.458843i	0.108131	−	0.994137i	$-0.465513\pi$
$463$	20.5018	−	9.87313i	0.952797	−	0.458843i	0.844666	+	0.535294i	$0.179799\pi$
$464$	−2.93072	−	25.3362i	−0.136055	−	1.17620i
$465$	−15.1154	−	14.0250i	−0.700958	−	0.650394i
$466$	6.55421	+	4.19742i	0.303618	+	0.194442i
$467$	−16.2449	+	23.8268i	−0.751722	+	1.10257i	0.239568	+	0.970880i	$0.422994\pi$
$467$	−16.2449	+	23.8268i	−0.751722	+	1.10257i	−0.991290	+	0.131694i	$0.957958\pi$
$468$	2.62384	+	2.52002i	0.121287	+	0.116488i
$469$	−6.14817	+	20.0306i	−0.283896	+	0.924929i
$470$	3.98412	−	14.3728i	0.183774	−	0.662968i
$471$	−0.0920738	−	0.159476i	−0.00424254	−	0.00734829i
$472$	23.5319	−	0.272308i	1.08314	−	0.0125340i
$473$	−5.40726	+	3.68661i	−0.248626	+	0.169511i
$474$	0.320748	+	11.1377i	0.0147324	+	0.511572i
$475$	−12.5421	−	2.86266i	−0.575473	−	0.131348i
$476$	−12.1089	+	24.1586i	−0.555012	+	1.10731i
$477$	6.98728	−	1.59480i	0.319925	−	0.0730209i
$478$	3.24013	+	12.5226i	0.148200	+	0.572771i
$479$	−7.67288	−	2.36677i	−0.350583	−	0.108141i	0.114462	−	0.993428i	$-0.463486\pi$
$479$	−7.67288	−	2.36677i	−0.350583	−	0.108141i	−0.465045	+	0.885287i	$0.653962\pi$
$480$	−14.1338	−	4.44727i	−0.645116	−	0.202989i
$481$	6.91534	−	2.13310i	0.315312	−	0.0972610i
$482$	7.54711	+	6.60876i	0.343762	+	0.301021i
$483$	−0.506764	−	0.114925i	−0.0230586	−	0.00522926i
$484$	6.48413	−	19.8038i	0.294733	−	0.900172i
$485$	21.4622	+	8.42328i	0.974546	+	0.382481i
$486$	−14.1335	+	1.46935i	−0.641106	+	0.0666509i
$487$	21.0799	−	3.17728i	0.955221	−	0.143976i	0.347107	−	0.937826i	$-0.387164\pi$
$487$	21.0799	−	3.17728i	0.955221	−	0.143976i	0.608115	+	0.793849i	$0.291926\pi$
$488$	20.3237	+	6.01238i	0.920009	+	0.272168i
$489$	−25.7953			−1.16651
$490$	−9.88685	+	15.5331i	−0.446642	+	0.701712i
$491$			30.9539i			1.39693i	0.715645	+	0.698464i	$0.246133\pi$
$491$			30.9539i			1.39693i	−0.715645	+	0.698464i	$0.753867\pi$
$492$	9.33869	+	4.69705i	0.421021	+	0.211759i
$493$	4.85331	+	32.1996i	0.218582	+	1.45020i
$494$	−2.18456	−	21.0130i	−0.0982882	−	0.945421i
$495$	−0.526606	+	1.34177i	−0.0236692	+	0.0603081i
$496$	1.27061	+	31.4634i	0.0570520	+	1.41275i
$497$	−4.24727	−	5.31075i	−0.190516	−	0.238220i
$498$	14.6192	+	12.8016i	0.655104	+	0.573653i
$499$	−4.43132	−	14.3660i	−0.198373	−	0.643109i	−0.999032	−	0.0439891i	$-0.985993\pi$
$499$	−4.43132	−	14.3660i	−0.198373	−	0.643109i	0.800659	−	0.599120i	$-0.204483\pi$
$500$	18.1177	−	16.2393i	0.810247	−	0.726242i
$501$	−9.47220	+	30.7081i	−0.423187	+	1.37194i
$502$	11.1977	−	2.89733i	0.499779	−	0.129314i
$503$	−1.01460	−	4.44523i	−0.0452386	−	0.198203i	0.947259	−	0.320470i	$-0.103841\pi$
$503$	−1.01460	−	4.44523i	−0.0452386	−	0.198203i	−0.992497	+	0.122267i	$0.960984\pi$
$504$	−1.23152	−	7.50891i	−0.0548562	−	0.334473i
$505$	−0.416105	+	1.82308i	−0.0185164	+	0.0811258i
$506$	−0.00432719	−	0.150258i	−0.000192367	−	0.00667980i
$507$	−7.77418	−	11.4026i	−0.345264	−	0.506409i
$508$	2.94660	−	17.4993i	0.130734	−	0.776408i
$509$	37.7567	−	21.7988i	1.67353	−	0.966216i	0.707900	−	0.706312i	$-0.249643\pi$
$509$	37.7567	−	21.7988i	1.67353	−	0.966216i	0.965635	−	0.259903i	$-0.0836907\pi$
$510$	18.2299	+	5.05330i	0.807234	+	0.223764i
$511$	0.127864	−	0.222179i	0.00565635	−	0.00982861i
$512$	10.5193	+	20.0336i	0.464892	+	0.885367i
$513$	39.0294	+	26.6098i	1.72319	+	1.17485i
$514$	−11.8734	−	7.60389i	−0.523712	−	0.335393i
$515$	5.53225	−	5.96235i	0.243780	−	0.262732i
$516$	−23.4824	−	5.78684i	−1.03376	−	0.254751i
$517$	−1.87503	−	3.89355i	−0.0824639	−	0.171238i
$518$	−14.2507	−	5.10232i	−0.626141	−	0.224183i
$519$	−21.6145	−	10.4090i	−0.948772	−	0.456905i
$520$	8.20403	+	4.61086i	0.359771	+	0.202200i
$521$	9.39684	−	16.2758i	0.411683	−	0.713056i	−0.583391	−	0.812192i	$-0.698274\pi$
$521$	9.39684	−	16.2758i	0.411683	−	0.713056i	0.995074	+	0.0991355i	$0.0316077\pi$
$522$	−6.42750	−	6.53914i	−0.281324	−	0.286211i
$523$	4.03395	−	26.7635i	0.176392	−	1.17029i	−0.708919	−	0.705290i	$-0.750817\pi$
$523$	4.03395	−	26.7635i	0.176392	−	1.17029i	0.885312	−	0.464998i	$-0.153945\pi$
$524$	26.2910	−	3.50089i	1.14853	−	0.152937i
$525$	−5.34605	−	2.08960i	−0.233321	−	0.0911978i
$526$	−16.8814	−	39.6197i	−0.736062	−	1.72750i
$527$	−3.00439	−	40.0908i	−0.130873	−	1.74638i
$528$	−3.92985	+	1.72845i	−0.171025	+	0.0752212i
$529$	−8.39574	−	21.3920i	−0.365032	−	0.930087i
$530$	16.4654	−	8.52167i	0.715210	−	0.370158i
$531$	6.61455	−	5.27493i	0.287047	−	0.228913i
$532$	−22.6968	+	37.9132i	−0.984032	+	1.64374i
$533$	−5.19094	−	4.13963i	−0.224844	−	0.179307i
$534$	1.51501	+	0.300189i	0.0655610	+	0.0129904i
$535$	−2.35236	+	31.3901i	−0.101702	+	1.35711i
$536$	−14.1677	−	17.3500i	−0.611950	−	0.749405i
$537$	9.50286	−	8.81736i	0.410079	−	0.380497i
$538$	−0.285749	−	1.58479i	−0.0123195	−	0.0683253i
$539$	0.809801	+	5.27319i	0.0348806	+	0.227133i
$540$	−19.7173	+	7.34927i	−0.848500	+	0.316262i
$541$	28.3589	+	30.5636i	1.21924	+	1.31403i	0.934729	+	0.355361i	$0.115642\pi$
$541$	28.3589	+	30.5636i	1.21924	+	1.31403i	0.284515	+	0.958672i	$0.408167\pi$
$542$	−24.7916	+	8.43611i	−1.06489	+	0.362362i
$543$	0.325158	−	4.33894i	0.0139539	−	0.186202i
$544$	−14.3031	−	25.1000i	−0.613240	−	1.07615i
$545$	−17.5508	+	22.0080i	−0.751794	+	0.942719i
$546$	0.420449	−	9.41668i	0.0179936	−	0.402997i
$547$	−16.2634	+	12.9696i	−0.695372	+	0.554540i	−0.906131	−	0.422998i	$-0.860978\pi$
$547$	−16.2634	+	12.9696i	−0.695372	+	0.554540i	0.210759	+	0.977538i	$0.432406\pi$
$548$	30.3204	−	23.3371i	1.29522	−	0.996911i
$549$	7.09271	−	2.78368i	0.302710	−	0.118805i
$550$	0.200112	−	1.64836i	0.00853279	−	0.0702863i
$551$	3.97911	+	53.0975i	0.169516	+	2.26203i
$552$	0.402818	−	0.382529i	0.0171451	−	0.0162815i
$553$	−10.8369	+	10.0832i	−0.460830	+	0.428781i
$554$	−26.1710	−	1.20496i	−1.11190	−	0.0511939i
$555$	−1.57927	+	10.4778i	−0.0670365	+	0.444758i
$556$	−18.0929	−	12.7973i	−0.767309	−	0.542728i
$557$	−23.0033	−	13.2810i	−0.974682	−	0.562733i	−0.0740217	−	0.997257i	$-0.523583\pi$
$557$	−23.0033	−	13.2810i	−0.974682	−	0.562733i	−0.900660	+	0.434524i	$0.856917\pi$
$558$	7.31000	+	8.64379i	0.309457	+	0.365921i
$559$	13.8398	+	6.66490i	0.585361	+	0.281895i
$560$	−7.94989	−	18.0071i	−0.335944	−	0.760941i
$561$	4.93843	−	2.37822i	0.208501	−	0.100409i
$562$	−32.0942	−	14.3327i	−1.35381	−	0.604590i
$563$	21.5549	−	23.2306i	0.908429	−	0.979054i	−0.0914301	−	0.995811i	$-0.529144\pi$
$563$	21.5549	−	23.2306i	0.908429	−	0.979054i	0.999860	+	0.0167574i	$0.00533430\pi$
$564$	6.08965	−	14.7635i	0.256421	−	0.621656i
$565$	15.1434	−	22.2114i	0.637090	−	0.934439i
$566$	3.94617	+	5.44436i	0.165870	+	0.228843i
$567$	9.54594	+	8.83268i	0.400892	+	0.370938i
$568$	7.24268	−	0.627119i	0.303896	−	0.0263133i
$569$	16.4634	+	28.5154i	0.690180	+	1.19543i	0.971779	+	0.235895i	$0.0758020\pi$
$569$	16.4634	+	28.5154i	0.690180	+	1.19543i	−0.281599	+	0.959532i	$0.590865\pi$
$570$	29.1081	+	10.4675i	1.21920	+	0.438435i
$571$	14.7034	+	21.5659i	0.615317	+	0.902505i	0.999787	−	0.0206329i	$-0.00656812\pi$
$571$	14.7034	+	21.5659i	0.615317	+	0.902505i	−0.384470	+	0.923138i	$0.625616\pi$
$572$	2.66848	−	0.560906i	0.111575	−	0.0234527i
$573$	16.9023	+	3.85784i	0.706104	+	0.161164i
$574$	3.49730	+	13.4395i	0.145975	+	0.560953i
$575$	0.0478095	+	0.209467i	0.00199379	+	0.00873538i
$576$	7.40874	+	3.35893i	0.308697	+	0.139955i
$577$	30.1149	+	9.28920i	1.25370	+	0.386715i	0.849320	−	0.527878i	$-0.177012\pi$
$577$	30.1149	+	9.28920i	1.25370	+	0.386715i	0.404378	+	0.914592i	$0.367488\pi$
$578$	6.73864	+	10.9323i	0.280290	+	0.454723i
$579$	−4.43219	−	14.3688i	−0.184195	−	0.597147i
$580$	−20.3342	−	12.2115i	−0.844332	−	0.507057i
$581$	0.0358726	+	25.8149i	0.00148825	+	1.07098i
$582$	21.7264	+	11.7231i	0.900586	+	0.485939i
$583$	1.96257	−	5.00054i	0.0812813	−	0.207101i
$584$	0.121752	+	0.245513i	0.00503814	+	0.0101594i
$585$	3.34547	−	0.504249i	0.138318	−	0.0208481i
$586$	15.0119	+	11.2802i	0.620136	+	0.465981i
$587$			12.0181i			0.496040i	0.968755	+	0.248020i	$0.0797799\pi$
$587$			12.0181i			0.496040i	−0.968755	+	0.248020i	$0.920220\pi$
$588$	−12.5137	+	15.2351i	−0.516057	+	0.628286i
$589$		−	65.7389i		−	2.70872i
$590$	13.1473	−	17.4966i	0.541264	−	0.720324i
$591$	−11.1471	+	1.68016i	−0.458531	+	0.0691125i
$592$	12.9912	−	9.64754i	0.533937	−	0.396512i
$593$	−3.87293	+	9.86806i	−0.159042	+	0.405233i	−0.988076	−	0.153965i	$-0.950796\pi$
$593$	−3.87293	+	9.86806i	−0.159042	+	0.405233i	0.829034	+	0.559198i	$0.188891\pi$
$594$	−2.89524	+	5.36572i	−0.118793	+	0.220158i
$595$	10.9355	+	22.6273i	0.448311	+	0.927627i
$596$	−16.7142	+	27.8319i	−0.684642	+	1.14004i
$597$	−1.88870	−	6.12302i	−0.0772994	−	0.250598i
$598$	−0.300356	+	0.185138i	−0.0122825	+	0.00757087i
$599$	−36.5004	−	11.2589i	−1.49137	−	0.460026i	−0.561361	−	0.827571i	$-0.689722\pi$
$599$	−36.5004	−	11.2589i	−1.49137	−	0.460026i	−0.930006	+	0.367545i	$0.880198\pi$
$600$	5.02966	−	3.51510i	0.205335	−	0.143503i
$601$	−8.81242	−	38.6097i	−0.359466	−	1.57492i	−0.754528	−	0.656268i	$-0.772134\pi$
$601$	−8.81242	−	38.6097i	−0.359466	−	1.57492i	0.395062	−	0.918655i	$-0.370723\pi$
$602$	−14.8074	−	28.5135i	−0.603506	−	1.16212i
$603$	−7.85083	−	1.79190i	−0.319710	−	0.0729718i
$604$	36.7248	−	7.71942i	1.49431	−	0.314099i
$605$	−10.9167	−	16.0118i	−0.443826	−	0.650973i
$606$	−0.677557	+	1.88415i	−0.0275239	+	0.0765385i
$607$	−7.64832	−	13.2473i	−0.310436	−	0.537690i	0.668021	−	0.744142i	$-0.267142\pi$
$607$	−7.64832	−	13.2473i	−0.310436	−	0.537690i	−0.978457	+	0.206452i	$0.933808\pi$
$608$	−20.2554	−	42.6756i	−0.821464	−	1.73073i
$609$	−1.74246	+	23.6933i	−0.0706081	+	0.960101i
$610$	15.9590	−	11.5674i	0.646163	−	0.468351i
$611$	−5.71399	+	8.38088i	−0.231163	+	0.339054i
$612$	−9.60105	−	3.96024i	−0.388099	−	0.160083i
$613$	−18.2011	+	19.6161i	−0.735137	+	0.792289i	−0.984362	−	0.176157i	$-0.943633\pi$
$613$	−18.2011	+	19.6161i	−0.735137	+	0.792289i	0.249226	+	0.968445i	$0.419824\pi$
$614$	−4.08300	+	9.14277i	−0.164777	+	0.368972i
$615$	8.75872	−	4.21798i	0.353186	−	0.170085i
$616$	−5.17020	−	2.40779i	−0.208313	−	0.0970127i
$617$	−3.66784	−	1.76634i	−0.147661	−	0.0711100i	0.358594	−	0.933494i	$-0.383256\pi$
$617$	−3.66784	−	1.76634i	−0.147661	−	0.0711100i	−0.506255	+	0.862384i	$0.668971\pi$
$618$	6.64994	−	5.62381i	0.267500	−	0.226223i
$619$	1.16858	+	0.674682i	0.0469693	+	0.0271178i	0.523301	−	0.852148i	$-0.324700\pi$
$619$	1.16858	+	0.674682i	0.0469693	+	0.0271178i	−0.476331	+	0.879266i	$0.658034\pi$
$620$	23.9081	+	16.9105i	0.960173	+	0.679143i
$621$	0.117582	−	0.780103i	0.00471839	−	0.0313044i
$622$	2.00630	−	43.5756i	0.0804454	−	1.74722i
$623$	1.02836	+	1.77547i	0.0412004	+	0.0711328i
$624$	8.12552	+	5.95981i	0.325281	+	0.238584i
$625$	−1.11527	−	14.8822i	−0.0446107	−	0.595288i
$626$	37.2541	+	4.52267i	1.48897	+	0.180762i
$627$	8.34317	−	3.27445i	0.333194	−	0.130769i
$628$	0.159514	+	0.207247i	0.00636531	+	0.00827005i
$629$	−16.1525	+	12.8812i	−0.644040	+	0.513605i
$630$	−6.23234	−	3.35167i	−0.248302	−	0.133534i
$631$	24.1085	−	30.2311i	0.959745	−	1.20348i	−0.0192945	−	0.999814i	$-0.506142\pi$
$631$	24.1085	−	30.2311i	0.959745	−	1.20348i	0.979040	−	0.203669i	$-0.0652866\pi$
$632$	−2.53940	−	15.6193i	−0.101012	−	0.621301i
$633$	−1.05324	+	14.0545i	−0.0418625	+	0.558616i
$634$	−3.67203	−	10.7912i	−0.145835	−	0.428573i
$635$	−11.2250	−	12.0976i	−0.445450	−	0.480081i
$636$	18.6016	−	6.93341i	0.737603	−	0.274928i
$637$	9.76858	−	7.83470i	0.387045	−	0.310422i
$638$	−6.76352	+	1.21951i	−0.267770	+	0.0482808i
$639$	1.91583	−	1.77763i	0.0757891	−	0.0703220i
$640$	20.7308	+	3.61125i	0.819459	+	0.142747i
$641$	0.910719	−	12.1527i	0.0359713	−	0.480003i	−0.949906	−	0.312535i	$-0.898822\pi$
$641$	0.910719	−	12.1527i	0.0359713	−	0.480003i	0.985878	−	0.167468i	$-0.0535591\pi$
$642$	−6.55114	+	33.0628i	−0.258553	+	1.30488i
$643$	−12.5805	−	10.0326i	−0.496128	−	0.395649i	0.343210	−	0.939259i	$-0.388486\pi$
$643$	−12.5805	−	10.0326i	−0.496128	−	0.395649i	−0.839338	+	0.543610i	$0.817057\pi$
$644$	0.734953	+	0.0667912i	0.0289612	+	0.00263194i
$645$	−17.5846	+	14.0232i	−0.692391	+	0.552164i
$646$	27.7214	+	53.5628i	1.09069	+	2.10740i
$647$	−10.9579	−	27.9204i	−0.430801	−	1.09766i	−0.967271	−	0.253744i	$-0.918338\pi$
$647$	−10.9579	−	27.9204i	−0.430801	−	1.09766i	0.536470	−	0.843919i	$-0.319757\pi$
$648$	−13.5181	+	3.25043i	−0.531041	+	0.127689i
$649$	−0.473886	−	6.32357i	−0.0186017	−	0.248222i
$650$	−3.58551	+	1.52774i	−0.140635	+	0.0599227i
$651$	4.33128	−	29.0096i	0.169756	−	1.13698i
$652$	36.3140	−	4.83555i	1.42217	−	0.189375i
$653$	−1.21179	+	8.03969i	−0.0474209	+	0.314617i	0.952527	+	0.304453i	$0.0984736\pi$
$653$	−1.21179	+	8.03969i	−0.0474209	+	0.314617i	−0.999948	+	0.0101645i	$0.996764\pi$
$654$	−21.4957	+	21.1287i	−0.840549	+	0.826198i
$655$	12.3329	−	21.3613i	0.481888	−	0.834654i
$656$	−14.0273	−	4.86177i	−0.547673	−	0.189820i
$657$	0.0887629	+	0.0427459i	0.00346297	+	0.00166768i
$658$	20.0754	−	6.86242i	0.782622	−	0.267525i
$659$	−6.44111	−	13.3751i	−0.250910	−	0.521020i	0.737029	−	0.675861i	$-0.236228\pi$
$659$	−6.44111	−	13.3751i	−0.250910	−	0.521020i	−0.987939	+	0.154841i	$0.950514\pi$
$660$	−0.955317	+	3.87658i	−0.0371857	+	0.150896i
$661$	25.6785	−	27.6749i	0.998779	−	1.07643i	0.00170430	−	0.999999i	$-0.499458\pi$
$661$	25.6785	−	27.6749i	0.998779	−	1.07643i	0.997075	−	0.0764295i	$-0.0243520\pi$
$662$	−7.42806	+	11.5988i	−0.288700	+	0.450801i
$663$	−10.6300	−	7.24740i	−0.412834	−	0.281466i
$664$	−22.9804	−	15.2813i	−0.891811	−	0.593028i
$665$	15.0663	+	38.2321i	0.584248	+	1.48258i
$666$	1.55396	−	5.60596i	0.0602149	−	0.217227i
$667$	0.770131	−	0.444635i	0.0298196	−	0.0172163i
$668$	7.57822	−	45.0057i	0.293210	−	1.74132i
$669$	12.4325	+	18.2351i	0.480667	+	0.705009i
$670$	−20.8226	+	0.599656i	−0.804447	+	0.0231667i
$671$	1.27082	−	5.56782i	0.0490594	−	0.214943i
$672$	−6.12668	−	20.1667i	−0.236342	−	0.777947i
$673$	8.02957	+	35.1798i	0.309517	+	1.35608i	0.855290	+	0.518150i	$0.173379\pi$
$673$	8.02957	+	35.1798i	0.309517	+	1.35608i	−0.545773	+	0.837933i	$0.683764\pi$
$674$	2.33131	+	9.01014i	0.0897986	+	0.347058i
$675$	2.56863	−	8.32729i	0.0988666	−	0.320518i
$676$	13.0818	+	14.5950i	0.503147	+	0.561346i
$677$	14.4148	+	46.7317i	0.554007	+	1.79605i	0.603613	+	0.797278i	$0.293727\pi$
$677$	14.4148	+	46.7317i	0.554007	+	1.79605i	−0.0496060	+	0.998769i	$0.515797\pi$
$678$	18.9630	−	21.6555i	0.728271	−	0.831676i
$679$	7.34235	+	31.9641i	0.281773	+	1.22667i
$680$	−26.6109	−	3.69656i	−1.02048	−	0.141757i
$681$	−3.85893	+	9.83240i	−0.147875	+	0.376778i
$682$	8.43952	−	0.877393i	0.323166	−	0.0335971i
$683$	−0.769230	−	5.10351i	−0.0294338	−	0.195280i	0.969282	−	0.245954i	$-0.0791012\pi$
$683$	−0.769230	−	5.10351i	−0.0294338	−	0.195280i	−0.998715	+	0.0506738i	$0.983863\pi$
$684$	−15.1715	−	7.63074i	−0.580096	−	0.291769i
$685$		−	35.5825i		−	1.35954i
$686$	−26.1774	+	0.863098i	−0.999457	+	0.0329532i
$687$	−18.2633			−0.696788
$688$	34.1427	+	3.74459i	1.30168	+	0.142761i
$689$	−12.4680	+	1.87925i	−0.474993	+	0.0715936i
$690$	−0.0534204	−	0.513843i	−0.00203368	−	0.0195617i
$691$	18.3938	+	7.21905i	0.699735	+	0.274626i	0.688422	−	0.725310i	$-0.258304\pi$
$691$	18.3938	+	7.21905i	0.699735	+	0.274626i	0.0113128	+	0.999936i	$0.496399\pi$
$692$	32.3796	+	10.6017i	1.23089	+	0.403016i
$693$	−1.99833	+	0.459028i	−0.0759103	+	0.0174370i
$694$	9.01852	−	10.2990i	0.342338	−	0.390946i
$695$	−19.6939	+	6.07478i	−0.747034	+	0.230429i
$696$	−20.0386	−	15.6043i	−0.759559	−	0.591481i
$697$	18.1122	+	5.58688i	0.686049	+	0.211618i
$698$	−22.4904	+	5.81923i	−0.851275	+	0.220261i
$699$	7.55593	−	1.72459i	0.285792	−	0.0652301i
$700$	7.91775	+	1.93953i	0.299263	+	0.0733072i
$701$	−38.4640	−	8.77916i	−1.45277	−	0.331584i	−0.577963	−	0.816063i	$-0.696152\pi$
$701$	−38.4640	−	8.77916i	−1.45277	−	0.331584i	−0.874803	+	0.484479i	$0.839009\pi$
$702$	14.3049	−	0.411957i	0.539903	−	0.0155483i
$703$	−27.9121	+	19.0301i	−1.05272	+	0.717735i
$704$	5.20833	−	3.16995i	0.196296	−	0.119472i
$705$	−7.42595	−	12.8621i	−0.279678	−	0.484416i
$706$	7.44529	+	2.06382i	0.280207	+	0.0776730i
$707$	−2.47475	+	0.975238i	−0.0930725	+	0.0366776i
$708$	16.2328	−	16.9015i	0.610065	−	0.635199i
$709$	−16.9658	+	24.8842i	−0.637163	+	0.934547i	0.362833	+	0.931854i	$0.381810\pi$
$709$	−16.9658	+	24.8842i	−0.637163	+	0.934547i	−0.999996	+	0.00269297i	$0.999143\pi$
$710$	3.64608	−	5.69330i	0.136835	−	0.213666i
$711$	−4.17025	−	3.86942i	−0.156397	−	0.145115i
$712$	−2.18907	−	0.138596i	−0.0820388	−	0.00519411i
$713$	−0.989181	+	0.476365i	−0.0370451	+	0.0178400i
$714$	8.70403	+	25.4629i	0.325740	+	0.952926i
$715$	1.10027	−	2.28474i	0.0411478	−	0.0854443i
$716$	−11.7250	+	14.1942i	−0.438183	+	0.530464i
$717$	11.1548	+	6.44024i	0.416584	+	0.240515i
$718$	8.21649	−	8.07622i	0.306637	−	0.301402i
$719$	−0.509782	−	0.0768372i	−0.0190116	−	0.00286554i	0.139530	−	0.990218i	$-0.455441\pi$
$719$	−0.509782	−	0.0768372i	−0.0190116	−	0.00286554i	−0.158541	+	0.987352i	$0.550679\pi$
$720$	6.67785	−	3.55469i	0.248869	−	0.132475i
$721$	11.4430	+	1.70850i	0.426161	+	0.0636278i
$722$	28.1245	+	66.0068i	1.04669	+	2.45652i
$723$	9.96146	−	0.746509i	0.370471	−	0.0277630i
$724$	0.355620	+	6.16920i	0.0132165	+	0.229276i
$725$	9.14397	−	3.58874i	0.339599	−	0.133283i
$726$	−9.53772	−	18.4286i	−0.353978	−	0.683949i
$727$	3.78295	+	4.74367i	0.140302	+	0.175933i	0.847018	−	0.531564i	$-0.178396\pi$
$727$	3.78295	+	4.74367i	0.140302	+	0.175933i	−0.706716	+	0.707497i	$0.749824\pi$
$728$	1.17334	+	13.3354i	0.0434867	+	0.494242i
$729$	−18.0167	+	22.5922i	−0.667284	+	0.836748i
$730$	0.249995	+	0.0495347i	0.00925273	+	0.00183336i
$731$	−43.7300	−	3.27711i	−1.61741	−	0.121208i
$732$	18.4565	−	10.2362i	0.682170	−	0.378342i
$733$	−1.39887	−	1.50762i	−0.0516685	−	0.0556854i	0.706689	−	0.707525i	$-0.250188\pi$
$733$	−1.39887	−	1.50762i	−0.0516685	−	0.0556854i	−0.758357	+	0.651839i	$0.773998\pi$
$734$	18.4727	−	3.33075i	0.681839	−	0.122940i
$735$	4.12959	+	17.8639i	0.152322	+	0.658921i
$736$	−0.495369	+	0.614026i	−0.0182595	+	0.0226333i
$737$	−4.42454	+	4.10538i	−0.162980	+	0.151224i
$738$	−5.05262	+	1.71931i	−0.185990	+	0.0632886i
$739$	4.94198	+	0.370350i	0.181794	+	0.0136236i	0.165316	−	0.986241i	$-0.447136\pi$
$739$	4.94198	+	0.370350i	0.181794	+	0.0136236i	0.0164779	+	0.999864i	$0.494755\pi$
$740$	0.259110	−	15.0464i	0.00952509	−	0.553118i
$741$	−16.4476	−	13.1165i	−0.604217	−	0.481847i
$742$	23.2268	+	12.4911i	0.852684	+	0.458563i
$743$	2.68870	+	3.37152i	0.0986388	+	0.123689i	0.828701	−	0.559692i	$-0.189080\pi$
$743$	2.68870	+	3.37152i	0.0986388	+	0.123689i	−0.730062	+	0.683381i	$0.760509\pi$
$744$	23.2311	+	21.0603i	0.851692	+	0.772109i
$745$	11.0303	+	28.1048i	0.404120	+	1.02968i
$746$	−2.53425	+	20.8751i	−0.0927854	+	0.764292i
$747$	−9.89356	+	0.741420i	−0.361987	+	0.0271271i
$748$	−6.50637	+	4.27375i	−0.237897	+	0.156264i
$749$	−38.7469	+	22.4424i	−1.41578	+	0.820026i
$750$	1.11431	−	24.2021i	0.0406889	−	0.883737i
$751$	6.26088	+	0.943677i	0.228463	+	0.0344352i	0.262276	−	0.964993i	$-0.415527\pi$
$751$	6.26088	+	0.943677i	0.228463	+	0.0344352i	−0.0338130	+	0.999428i	$0.510765\pi$
$752$	−5.80531	+	21.9253i	−0.211698	+	0.799532i
$753$	5.75887	−	9.97465i	0.209865	−	0.363497i
$754$	10.4166	+	12.3172i	0.379349	+	0.448565i
$755$	15.1424	−	31.4435i	0.551088	−	1.14435i
$756$	−24.4614	−	17.2509i	−0.889651	−	0.627410i
$757$	21.8359	+	45.3427i	0.793639	+	1.64801i	0.761185	+	0.648535i	$0.224618\pi$
$757$	21.8359	+	45.3427i	0.793639	+	1.64801i	0.0324546	+	0.999473i	$0.489668\pi$
$758$	−2.12402	+	4.75616i	−0.0771478	+	0.172751i
$759$	−0.109728	−	0.101813i	−0.00398289	−	0.00369558i
$760$	−42.9398	−	9.27932i	−1.55759	−	0.336596i
$761$	38.5196	+	26.2622i	1.39633	+	0.952003i	0.999417	+	0.0341485i	$0.0108719\pi$
$761$	38.5196	+	26.2622i	1.39633	+	0.952003i	0.396916	+	0.917855i	$0.370080\pi$
$762$	−10.3705	−	14.3078i	−0.375685	−	0.518316i
$763$	−39.9339	−	2.93684i	−1.44570	−	0.106321i
$764$	−24.5178	−	2.26249i	−0.887023	−	0.0818540i
$765$	−8.36453	+	4.82926i	−0.302420	+	0.174602i
$766$	−2.23599	+	6.21786i	−0.0807897	+	0.224660i
$767$	−12.2979	+	8.38459i	−0.444053	+	0.302750i
$768$	21.5700	+	6.51378i	0.778339	+	0.235046i
$769$	−5.65279	+	24.7665i	−0.203845	+	0.893102i	0.764724	+	0.644357i	$0.222875\pi$
$769$	−5.65279	+	24.7665i	−0.203845	+	0.893102i	−0.968569	+	0.248744i	$0.919982\pi$
$770$	−4.70713	+	2.44448i	−0.169633	+	0.0880929i
$771$	−13.6881	+	3.12421i	−0.492963	+	0.112516i
$772$	8.93307	+	19.3972i	0.321508	+	0.698119i
$773$	6.16300	−	19.9800i	0.221668	−	0.718629i	−0.774611	−	0.632438i	$-0.782054\pi$
$773$	6.16300	−	19.9800i	0.221668	−	0.718629i	0.996279	−	0.0861912i	$-0.0274696\pi$
$774$	10.5115	−	6.47927i	0.377828	−	0.232892i
$775$	−11.5889	+	3.57469i	−0.416284	+	0.128407i
$776$	−32.7834	−	12.4307i	−1.17686	−	0.446237i
$777$	−13.5710	+	6.55871i	−0.486858	+	0.235292i
$778$	37.0018	+	19.9655i	1.32658	+	0.715797i
$779$	28.8510	+	11.3232i	1.03369	+	0.405694i
$780$	9.00118	−	2.60764i	0.322294	−	0.0933684i
$781$	−0.291960	−	1.93703i	−0.0104471	−	0.0693122i
$782$	0.605088	−	0.805261i	0.0216379	−	0.0287961i
$783$	−36.0687			−1.28899
$784$	14.7605	−	23.7934i	0.527162	−	0.849765i
$785$	0.243214			0.00868069
$786$	15.8659	−	21.1146i	0.565918	−	0.753133i
$787$	−1.51759	−	10.0685i	−0.0540962	−	0.358905i	−0.999459	−	0.0328851i	$-0.989530\pi$
$787$	−1.51759	−	10.0685i	−0.0540962	−	0.358905i	0.945363	−	0.326020i	$-0.105708\pi$
$788$	15.3777	−	4.45490i	0.547807	−	0.158699i
$789$	−39.9202	−	15.6675i	−1.42120	−	0.557779i
$790$	−12.9512	−	6.98823i	−0.460784	−	0.248630i
$791$	38.2397	−	0.0531382i	1.35965	−	0.00188938i
$792$	0.777142	−	2.04955i	0.0276145	−	0.0728276i
$793$	−12.8093	+	3.95114i	−0.454871	+	0.140309i
$794$	−5.42965	+	3.34682i	−0.192691	+	0.118774i
$795$	5.44169	−	17.6415i	0.192997	−	0.625681i
$796$	3.80667	+	8.26577i	0.134924	+	0.292972i
$797$	−31.2226	+	7.12636i	−1.10596	+	0.252429i	−0.736245	−	0.676715i	$-0.763403\pi$
$797$	−31.2226	+	7.12636i	−1.10596	+	0.252429i	−0.369718	+	0.929144i	$0.620546\pi$
$798$	11.0813	+	42.5833i	0.392272	+	1.50743i
$799$	6.44362	−	28.2314i	0.227959	−	0.998754i
$800$	−6.42169	+	5.89132i	−0.227041	+	0.208290i
$801$	−0.651531	+	0.444206i	−0.0230207	+	0.0156953i
$802$	−1.20722	+	3.35704i	−0.0426283	+	0.118541i
$803$	0.0639504	−	0.0369218i	0.00225676	−	0.00130294i
$804$	−22.2109	−	2.04961i	−0.783317	−	0.0722841i
$805$	0.466108	−	0.503747i	0.0164281	−	0.0177548i
$806$	−11.6881	−	16.1255i	−0.411695	−	0.567998i
$807$	−1.32492	−	0.903318i	−0.0466396	−	0.0317983i
$808$	0.600647	−	2.77947i	0.0211307	−	0.0977816i
$809$	16.6425	+	15.4420i	0.585118	+	0.542911i	0.916215	−	0.400686i	$-0.131228\pi$
$809$	16.6425	+	15.4420i	0.585118	+	0.542911i	−0.331097	+	0.943597i	$0.607419\pi$
$810$	−5.27239	+	11.8061i	−0.185253	+	0.414823i
$811$	23.0719	+	47.9092i	0.810163	+	1.68232i	0.727872	+	0.685713i	$0.240509\pi$
$811$	23.0719	+	47.9092i	0.810163	+	1.68232i	0.0822910	+	0.996608i	$0.473776\pi$
$812$	−1.98851	−	33.6815i	−0.0697832	−	1.18199i
$813$	−11.3145	+	23.4948i	−0.396817	+	0.823999i
$814$	−2.81561	−	3.32935i	−0.0986871	−	0.116694i
$815$	17.0347	−	29.5049i	0.596699	−	1.03351i
$816$	−27.8092	−	7.36323i	−0.973515	−	0.257765i
$817$	−70.9054	−	10.6873i	−2.48066	−	0.373900i
$818$	0.207508	−	4.50693i	0.00725533	−	0.157581i
$819$	3.27831	+	3.52334i	0.114553	+	0.123116i
$820$	−11.5396	+	7.57985i	−0.402980	+	0.264700i
$821$	−32.1753	+	2.41121i	−1.12293	+	0.0841517i	−0.623222	−	0.782045i	$-0.714177\pi$
$821$	−32.1753	+	2.41121i	−1.12293	+	0.0841517i	−0.499704	+	0.866196i	$0.666558\pi$
$822$	4.59168	−	37.8226i	0.160153	−	1.31921i
$823$	4.18252	+	10.6569i	0.145793	+	0.371475i	0.985052	−	0.172257i	$-0.0551059\pi$
$823$	4.18252	+	10.6569i	0.145793	+	0.371475i	−0.839259	+	0.543732i	$0.817011\pi$
$824$	−8.30738	+	9.16364i	−0.289401	+	0.319231i
$825$	−1.03092	−	1.29273i	−0.0358919	−	0.0450071i
$826$	31.1009	+	1.38864i	1.08214	+	0.0483169i
$827$	36.2588	+	28.9155i	1.26084	+	1.00549i	0.999187	+	0.0403277i	$0.0128402\pi$
$827$	36.2588	+	28.9155i	1.26084	+	1.00549i	0.261656	+	0.965161i	$0.415731\pi$
$828$	−0.00488349	+	0.283582i	−0.000169713	+	0.00985515i
$829$	−51.0719	−	3.82731i	−1.77380	−	0.132928i	−0.852736	−	0.522342i	$-0.825059\pi$
$829$	−51.0719	−	3.82731i	−1.77380	−	0.132928i	−0.921063	+	0.389414i	$0.872678\pi$
$830$	−24.2968	+	8.26773i	−0.843355	+	0.286977i
$831$	−19.1240	+	17.7445i	−0.663406	+	0.615551i
$832$	−12.5561	−	6.86687i	−0.435305	−	0.238066i
$833$	−17.7882	+	31.0088i	−0.616324	+	1.07439i
$834$	−21.7177	+	3.91585i	−0.752022	+	0.135595i
$835$	−28.8690	−	31.1134i	−0.999052	−	1.07672i
$836$	−11.1315	+	6.17369i	−0.384990	+	0.213521i
$837$	44.4066	+	3.32781i	1.53492	+	0.115026i
$838$	−5.82570	−	1.15432i	−0.201245	−	0.0398753i
$839$	−32.1642	+	40.3327i	−1.11043	+	1.39244i	−0.199492	+	0.979899i	$0.563929\pi$
$839$	−32.1642	+	40.3327i	−1.11043	+	1.39244i	−0.910940	+	0.412539i	$0.864642\pi$
$840$	−18.3373	−	6.92396i	−0.632698	−	0.238899i
$841$	−7.26799	−	9.11377i	−0.250620	−	0.314268i
$842$	13.6173	+	26.3111i	0.469283	+	0.906739i
$843$	−32.5816	+	12.7873i	−1.12217	+	0.440419i
$844$	−1.15191	−	19.9830i	−0.0396504	−	0.687843i
$845$	18.1763	−	1.36213i	0.625285	−	0.0468586i
$846$	3.19617	+	7.50126i	0.109887	+	0.257898i
$847$	10.0355	−	25.6748i	0.344823	−	0.882198i
$848$	−24.8872	+	13.2477i	−0.854629	+	0.454928i
$849$	6.62095	+	0.997948i	0.227230	+	0.0342495i
$850$	7.93496	−	7.79949i	0.272167	−	0.267520i
$851$	0.488609	+	0.282098i	0.0167493	+	0.00967021i
$852$	4.61031	−	5.58123i	0.157947	−	0.191210i
$853$	12.9322	−	26.8540i	0.442790	−	0.919463i	−0.553454	−	0.832880i	$-0.686691\pi$
$853$	12.9322	−	26.8540i	0.442790	−	0.919463i	0.996245	−	0.0865839i	$-0.0275951\pi$
$854$	26.3966	+	9.45102i	0.903272	+	0.323407i
$855$	−14.2293	+	6.85245i	−0.486630	+	0.234349i
$856$	3.02464	−	47.7730i	0.103380	−	1.63285i
$857$	14.9905	+	13.9092i	0.512067	+	0.475128i	0.893370	−	0.449321i	$-0.148334\pi$
$857$	14.9905	+	13.9092i	0.512067	+	0.475128i	−0.381303	+	0.924450i	$0.624525\pi$
$858$	1.46437	−	2.28659i	0.0499927	−	0.0780629i
$859$	−4.10106	+	6.01515i	−0.139926	+	0.205234i	−0.889805	−	0.456341i	$-0.849160\pi$
$859$	−4.10106	+	6.01515i	−0.139926	+	0.205234i	0.749878	+	0.661576i	$0.230112\pi$
$860$	22.1263	−	23.0379i	0.754501	−	0.785586i
$861$	11.9855	+	6.89762i	0.408464	+	0.235070i
$862$	−14.8395	−	4.11348i	−0.505434	−	0.140106i
$863$	−15.1295	−	26.2051i	−0.515014	−	0.892031i	−0.999848	−	0.0174245i	$-0.994453\pi$
$863$	−15.1295	−	26.2051i	−0.515014	−	0.892031i	0.484834	−	0.874606i	$-0.338880\pi$
$864$	29.8527	−	11.5222i	1.01561	−	0.391993i
$865$	26.1797	−	17.8490i	0.890136	−	0.606884i
$866$	35.5222	−	1.02298i	1.20709	−	0.0347623i
$867$	12.4675	+	2.84563i	0.423419	+	0.0966427i
$868$	−0.659365	+	41.6509i	−0.0223803	+	1.41372i
$869$	−4.15710	+	0.948831i	−0.141020	+	0.0321869i
$870$	−22.8662	+	5.91647i	−0.775238	+	0.200587i
$871$	13.5377	+	4.17584i	0.458709	+	0.141493i
$872$	26.3003	−	33.7740i	0.890642	−	1.14373i
$873$	−12.0445	+	3.71524i	−0.407645	+	0.125742i
$874$	1.08505	−	1.23911i	0.0367024	−	0.0419136i
$875$	25.1361	−	20.1026i	0.849756	−	0.679591i
$876$	0.259341	+	0.0849133i	0.00876233	+	0.00286896i
$877$	−50.1199	−	19.6706i	−1.69243	−	0.664230i	−0.693985	−	0.719989i	$-0.744147\pi$
$877$	−50.1199	−	19.6706i	−1.69243	−	0.664230i	−0.998444	+	0.0557594i	$0.982242\pi$
$878$	−2.99573	−	28.8155i	−0.101101	−	0.972477i
$879$	18.4897	−	2.78687i	0.623641	−	0.0939987i
$880$	0.618173	−	5.63643i	0.0208386	−	0.190004i
$881$	4.28528			0.144375			0.0721874	−	0.997391i	$-0.477002\pi$
$881$	4.28528			0.144375			0.0721874	+	0.997391i	$0.477002\pi$
$882$	−1.06870	−	10.0092i	−0.0359851	−	0.337026i
$883$			15.3063i			0.515098i	0.966265	+	0.257549i	$0.0829148\pi$
$883$			15.3063i			0.515098i	−0.966265	+	0.257549i	$0.917085\pi$
$884$	16.3232	+	8.21002i	0.549009	+	0.276133i
$885$	−3.24814	−	21.5500i	−0.109185	−	0.724395i
$886$	−27.0225	+	2.80933i	−0.907840	+	0.0943812i
$887$	14.5356	−	37.0360i	0.488057	−	1.24355i	−0.448736	−	0.893664i	$-0.648126\pi$
$887$	14.5356	−	37.0360i	0.488057	−	1.24355i	0.936793	−	0.349884i	$-0.113779\pi$
$888$	2.21706	−	15.9602i	0.0743998	−	0.535591i
$889$	5.19195	−	22.8940i	0.174132	−	0.767840i
$890$	−1.34384	+	1.53465i	−0.0450456	+	0.0514415i
$891$	1.10427	+	3.57995i	0.0369944	+	0.119933i
$892$	−20.9204	−	23.3403i	−0.700468	−	0.781491i
$893$	13.9567	−	45.2465i	0.467043	−	1.51412i
$894$	8.09801	+	31.2975i	0.270838	+	1.04675i
$895$	3.80990	+	16.6923i	0.127351	+	0.557960i
$896$	12.4054	+	27.2416i	0.414435	+	0.910079i
$897$	−0.0781814	+	0.342535i	−0.00261040	+	0.0114369i
$898$	−8.45780	+	0.243571i	−0.282241	+	0.00812806i
$899$	28.2763	+	41.4737i	0.943067	+	1.38323i
$900$	−0.520214	+	3.08946i	−0.0173405	+	0.102982i
$901$	31.1731	−	17.9978i	1.03853	−	0.599594i
$902$	−1.06860	+	3.85500i	−0.0355804	+	0.128357i
$903$	−30.5854	−	9.38781i	−1.01782	−	0.312407i
$904$	−22.6362	+	34.0409i	−0.752868	+	1.13218i
$905$	4.74819	+	3.23726i	0.157835	+	0.107610i
$906$	20.1532	−	31.4690i	0.669547	−	1.04549i
$907$	34.1764	−	36.8334i	1.13481	−	1.22303i	0.163161	−	0.986600i	$-0.447831\pi$
$907$	34.1764	−	36.8334i	1.13481	−	1.22303i	0.971648	−	0.236433i	$-0.0759784\pi$
$908$	3.58934	−	14.5652i	0.119116	−	0.483363i
$909$	−0.443556	−	0.921054i	−0.0147118	−	0.0305494i
$910$	10.4932	+	6.69948i	0.347847	+	0.222086i
$911$	−32.7833	−	15.7876i	−1.08616	−	0.523067i	−0.196878	−	0.980428i	$-0.563080\pi$
$911$	−32.7833	−	15.7876i	−1.08616	−	0.523067i	−0.889281	+	0.457361i	$0.848795\pi$
$912$	−44.4456	−	15.4046i	−1.47174	−	0.510097i
$913$	−3.71817	+	6.44007i	−0.123054	+	0.213135i
$914$	−13.2643	+	13.0379i	−0.438745	+	0.431255i
$915$	2.92529	−	19.4080i	0.0967070	−	0.641609i
$916$	25.7106	−	3.42361i	0.849502	−	0.113119i
$917$	34.9849	−	2.67065i	1.15530	−	0.0881926i
$918$	−37.5849	+	16.0144i	−1.24049	+	0.528553i
$919$	0.0812289	+	1.08392i	0.00267949	+	0.0357554i	0.998383	−	0.0568404i	$-0.0181026\pi$
$919$	0.0812289	+	1.08392i	0.00267949	+	0.0357554i	−0.995704	+	0.0925958i	$0.970484\pi$
$920$	0.171528	+	0.713361i	0.00565511	+	0.0235188i
$921$	3.64276	+	9.28159i	0.120033	+	0.305839i
$922$	−3.27987	−	6.33730i	−0.108017	−	0.208708i
$923$	−3.59480	+	2.86676i	−0.118324	+	0.0943605i
$924$	−5.31892	+	1.99095i	−0.174980	+	0.0654974i
$925$	4.87253	+	3.88571i	0.160208	+	0.127761i
$926$	−6.25478	+	31.5671i	−0.205545	+	1.03736i
$927$	−0.332293	+	4.43414i	−0.0109139	+	0.145636i
$928$	31.1349	+	18.2110i	1.02205	+	0.597805i
$929$	−21.5650	+	20.0094i	−0.707525	+	0.656488i	−0.949490	−	0.313797i	$-0.898399\pi$
$929$	−21.5650	+	20.0094i	−0.707525	+	0.656488i	0.241965	+	0.970285i	$0.422208\pi$
$930$	28.6980	−	5.17444i	0.941044	−	0.169677i
$931$	−32.7944	+	48.3890i	−1.07479	+	1.58589i
$932$	−10.3138	+	3.84426i	−0.337838	+	0.125923i
$933$	−29.5452	−	31.8422i	−0.967268	−	1.04247i
$934$	−13.1377	−	38.6086i	−0.429880	−	1.26331i
$935$	−0.541000	+	7.21914i	−0.0176926	+	0.236091i
$936$	−5.07822	+	0.825624i	−0.165987	+	0.0269864i
$937$	−35.9657	+	45.0996i	−1.17495	+	1.47334i	−0.325600	+	0.945508i	$0.605566\pi$
$937$	−35.9657	+	45.0996i	−1.17495	+	1.47334i	−0.849349	+	0.527831i	$0.823005\pi$
$938$	−17.4235	−	23.9682i	−0.568896	−	0.782591i
$939$	29.2166	−	23.2995i	0.953449	−	0.760350i
$940$	12.8652	+	16.7149i	0.419616	+	0.545180i
$941$	20.4253	−	8.01632i	0.665844	−	0.261325i	−0.00825434	−	0.999966i	$-0.502627\pi$
$941$	20.4253	−	8.01632i	0.665844	−	0.261325i	0.674099	+	0.738641i	$0.264532\pi$
$942$	0.258526	+	0.0313852i	0.00842323	+	0.00102258i
$943$	−0.0386820	−	0.516175i	−0.00125966	−	0.0168090i
$944$	−19.6837	+	26.8365i	−0.640651	+	0.873454i
$945$	−26.5884	+	8.24193i	−0.864922	+	0.268110i
$946$	0.425677	−	9.24543i	0.0138400	−	0.300595i
$947$	3.54943	−	23.5489i	0.115341	−	0.765237i	−0.854135	−	0.520051i	$-0.825913\pi$
$947$	3.54943	−	23.5489i	0.115341	−	0.765237i	0.969476	−	0.245186i	$-0.0788491\pi$
$948$	−12.8648	−	9.09945i	−0.417829	−	0.295536i
$949$	−0.150104	−	0.0866624i	−0.00487257	−	0.00281318i
$950$	13.8918	−	11.7482i	0.450708	−	0.381161i
$951$	−10.2267	−	4.92492i	−0.331624	−	0.159702i
$952$	−17.0265	−	34.2144i	−0.551833	−	1.10890i
$953$	19.2103	−	9.25120i	0.622283	−	0.299676i	−0.0960485	−	0.995377i	$-0.530620\pi$
$953$	19.2103	−	9.25120i	0.622283	−	0.299676i	0.718332	+	0.695701i	$0.244906\pi$
$954$	−4.13298	+	9.25469i	−0.133810	+	0.299632i
$955$	−15.5746	+	16.7854i	−0.503981	+	0.543162i
$956$	−16.9107	−	6.97534i	−0.546932	−	0.225598i
$957$	−3.85514	+	5.65446i	−0.124619	+	0.182783i
$958$	9.19440	−	6.66427i	0.297058	−	0.215313i
$959$	41.7807	−	28.5707i	1.34917	−	0.922596i
$960$	17.0355	−	12.2015i	0.549818	−	0.393801i
$961$	−15.4863	−	26.8231i	−0.499558	−	0.865260i
$962$	−3.46327	+	9.63068i	−0.111660	+	0.310505i
$963$	−9.69410	−	14.2186i	−0.312388	−	0.458189i
$964$	−13.8836	+	2.91827i	−0.447159	+	0.0939913i
$965$	19.3621	+	4.41927i	0.623287	+	0.142261i
$966$	0.560457	−	0.475313i	0.0180324	−	0.0152929i
$967$	−5.01186	−	21.9584i	−0.161171	−	0.706135i	−0.989336	−	0.145651i	$-0.953472\pi$
$967$	−5.01186	−	21.9584i	−0.161171	−	0.706135i	0.828165	−	0.560484i	$-0.189385\pi$
$968$	16.8815	+	24.1553i	0.542593	+	0.776382i
$969$	57.3889	+	17.7021i	1.84360	+	0.568674i
$970$	−27.7566	+	17.1091i	−0.891211	+	0.549340i
$971$	−11.0948	−	35.9685i	−0.356050	−	1.15429i	−0.939619	−	0.342222i	$-0.888821\pi$
$971$	−11.0948	−	35.9685i	−0.356050	−	1.15429i	0.583569	−	0.812063i	$-0.301656\pi$
$972$	10.3459	−	17.2276i	0.331844	−	0.552575i
$973$	−22.9461	−	18.2468i	−0.735617	−	0.584965i
$974$	−14.3163	+	26.5322i	−0.458723	+	0.850147i
$975$	−1.41789	+	3.61271i	−0.0454087	+	0.115699i
$976$	−24.0637	+	17.8701i	−0.770259	+	0.572009i
$977$	−25.3727	+	3.82431i	−0.811743	+	0.122351i	−0.541780	−	0.840520i	$-0.682250\pi$
$977$	−25.3727	+	3.82431i	−0.811743	+	0.122351i	−0.269963	+	0.962871i	$0.587011\pi$
$978$	21.9145	−	29.1642i	0.700749	−	0.932569i
$979$			0.591045i			0.0188899i
$980$	−9.16228	−	24.3743i	−0.292678	−	0.778607i
$981$		−	15.3890i		−	0.491333i
$982$	−34.9965	−	26.2970i	−1.11678	−	0.839170i
$983$	−17.5647	+	2.64745i	−0.560227	+	0.0844406i	−0.423051	−	0.906106i	$-0.639041\pi$
$983$	−17.5647	+	2.64745i	−0.560227	+	0.0844406i	−0.137176	+	0.990547i	$0.543803\pi$
$984$	−13.2442	+	6.56794i	−0.422210	+	0.209378i
$985$	5.43954	−	13.8597i	0.173318	−	0.441607i
$986$	−40.5280	−	21.8681i	−1.29068	−	0.696423i
$987$	9.13999	−	19.0471i	0.290929	−	0.606274i
$988$	25.6133	+	15.3818i	0.814866	+	0.489361i
$989$	0.352990	+	1.14437i	0.0112244	+	0.0363887i
$990$	−1.06963	−	1.73529i	−0.0339949	−	0.0551510i
$991$	39.4776	+	12.1772i	1.25405	+	0.386822i	0.849448	−	0.527672i	$-0.176935\pi$
$991$	39.4776	+	12.1772i	1.25405	+	0.386822i	0.404599	+	0.914494i	$0.367411\pi$
$992$	−36.6520	−	25.2933i	−1.16370	−	0.803064i
$993$	3.05197	+	13.3715i	0.0968513	+	0.424333i
$994$	9.61263	−	0.290197i	0.304894	−	0.00920450i
$995$	8.25082	+	1.88320i	0.261568	+	0.0597013i
$996$	−26.8933	+	5.65289i	−0.852148	+	0.179119i
$997$	18.1250	+	26.5845i	0.574024	+	0.841939i	0.997966	−	0.0637507i	$-0.0203062\pi$
$997$	18.1250	+	26.5845i	0.574024	+	0.841939i	−0.423942	+	0.905689i	$0.639354\pi$
$998$	20.0068	+	7.19462i	0.633305	+	0.227742i
$999$	−11.4419	−	19.8179i	−0.362005	−	0.627012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.109.16	yes	648
8.5	even	2	inner	392.2.z.a.109.11	✓	648
49.9	even	21	inner	392.2.z.a.205.11	yes	648
392.205	even	42	inner	392.2.z.a.205.16	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.109.11	✓	648	8.5	even	2	inner
392.2.z.a.109.16	yes	648	1.1	even	1	trivial
392.2.z.a.205.11	yes	648	49.9	even	21	inner
392.2.z.a.205.16	yes	648	392.205	even	42	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849554 + 1.13060i) q^{2} +(0.209889 + 1.39252i) q^{3} +(-0.556517 - 1.92101i) q^{4} +(-1.73139 - 0.679519i) q^{5} +(-1.75270 - 0.945723i) q^{6} +(-0.592319 - 2.57860i) q^{7} +(2.64469 + 1.00281i) q^{8} +(0.971651 - 0.299715i) q^{9} +O(q^{10})\)	\(q+(-0.849554 + 1.13060i) q^{2} +(0.209889 + 1.39252i) q^{3} +(-0.556517 - 1.92101i) q^{4} +(-1.73139 - 0.679519i) q^{5} +(-1.75270 - 0.945723i) q^{6} +(-0.592319 - 2.57860i) q^{7} +(2.64469 + 1.00281i) q^{8} +(0.971651 - 0.299715i) q^{9} +(2.23917 - 1.38022i) q^{10} +(0.224646 - 0.728285i) q^{11} +(2.55825 - 1.17816i) q^{12} +(-1.74405 + 0.398067i) q^{13} +(3.41857 + 1.52098i) q^{14} +(0.582847 - 2.55362i) q^{15} +(-3.38058 + 2.13815i) q^{16} +(4.21955 - 2.87684i) q^{17} +(-0.486612 + 1.35317i) q^{18} +(7.23191 - 4.17535i) q^{19} +(-0.341820 + 3.70418i) q^{20} +(3.46643 - 1.36604i) q^{21} +(0.632550 + 0.872702i) q^{22} +(-0.115232 - 0.0785636i) q^{23} +(-0.841339 + 3.89327i) q^{24} +(-1.12931 - 1.04784i) q^{25} +(1.03161 - 2.31000i) q^{26} +(2.45435 + 5.09651i) q^{27} +(-4.62388 + 2.57288i) q^{28} +(-2.76656 + 5.74483i) q^{29} +(2.39197 + 2.82841i) q^{30} +(3.93613 - 6.81758i) q^{31} +(0.454589 - 5.63856i) q^{32} +(1.06130 + 0.159966i) q^{33} +(-0.332177 + 7.21466i) q^{34} +(-0.726673 + 4.86704i) q^{35} +(-1.11650 - 1.69976i) q^{36} +(-4.03411 + 0.302315i) q^{37} +(-1.42325 + 11.7236i) q^{38} +(-0.920374 - 2.34508i) q^{39} +(-3.89755 - 3.53336i) q^{40} +(2.31407 + 2.90175i) q^{41} +(-1.40048 + 5.07968i) q^{42} +(-6.71348 - 5.35382i) q^{43} +(-1.52406 - 0.0262455i) q^{44} +(-1.88597 - 0.141334i) q^{45} +(0.186720 - 0.0635370i) q^{46} +(4.15655 - 3.85672i) q^{47} +(-3.68697 - 4.25876i) q^{48} +(-6.29832 + 3.05470i) q^{49} +(2.14410 - 0.386595i) q^{50} +(4.89171 + 5.27201i) q^{51} +(1.73528 + 3.12880i) q^{52} +(7.02866 + 0.526726i) q^{53} +(-7.84723 - 1.55487i) q^{54} +(-0.883833 + 1.10829i) q^{55} +(1.01933 - 7.41357i) q^{56} +(7.33217 + 9.19425i) q^{57} +(-4.14476 - 8.00842i) q^{58} +(7.74518 - 3.03976i) q^{59} +(-5.22990 + 0.301475i) q^{60} +(7.47238 - 0.559977i) q^{61} +(4.36401 + 10.2421i) q^{62} +(-1.34837 - 2.32797i) q^{63} +(5.98876 + 5.30422i) q^{64} +(3.29011 + 0.495905i) q^{65} +(-1.08249 + 1.06401i) q^{66} +(-6.85847 - 3.95974i) q^{67} +(-7.87470 - 6.50481i) q^{68} +(0.0852158 - 0.176952i) q^{69} +(-4.88533 - 4.95639i) q^{70} +(2.31572 - 1.11519i) q^{71} +(2.87027 + 0.181725i) q^{72} +(0.0710248 + 0.0659013i) q^{73} +(3.08540 - 4.81781i) q^{74} +(1.22212 - 1.79251i) q^{75} +(-12.0456 - 11.5689i) q^{76} +(-2.01101 - 0.147895i) q^{77} +(3.43325 + 0.951692i) q^{78} +(-2.79738 - 4.84520i) q^{79} +(7.30600 - 1.40480i) q^{80} +(-4.06145 + 2.76905i) q^{81} +(-5.24665 + 0.151095i) q^{82} +(-9.51251 - 2.17117i) q^{83} +(-4.55330 - 5.89884i) q^{84} +(-9.26055 + 2.11366i) q^{85} +(11.7565 - 3.04191i) q^{86} +(-8.58048 - 2.64673i) q^{87} +(1.32445 - 1.70081i) q^{88} +(-0.741049 + 0.228583i) q^{89} +(1.76202 - 2.01220i) q^{90} +(2.05949 + 4.26141i) q^{91} +(-0.0867934 + 0.265083i) q^{92} +(10.3198 + 4.05022i) q^{93} +(0.829192 + 7.97589i) q^{94} +(-15.3585 + 2.31492i) q^{95} +(7.94724 - 0.550446i) q^{96} -12.3959 q^{97} +(1.89711 - 9.71602i) q^{98} -0.774968i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

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