LMFDB - Embedded newform 700.2.k.b.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(43,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("700.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.k (of order $4$, degree $2$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	700.43
Dual form			700.2.k.b.407.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.903055 - 1.08834i) q^{2} +(1.00798 - 1.00798i) q^{3} +(-0.368985 + 1.96567i) q^{4} +(-2.00729 - 0.186768i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.47254 - 1.37352i) q^{8} +0.967954i q^{9} +O(q^{10})$	\(q+(-0.903055 - 1.08834i) q^{2} +(1.00798 - 1.00798i) q^{3} +(-0.368985 + 1.96567i) q^{4} +(-2.00729 - 0.186768i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.47254 - 1.37352i) q^{8} +0.967954i q^{9} +0.466996i q^{11} +(1.60942 + 2.35328i) q^{12} +(2.66390 + 2.66390i) q^{13} +(0.131019 - 1.40813i) q^{14} +(-3.72770 - 1.45060i) q^{16} +(-3.26155 + 3.26155i) q^{17} +(1.05347 - 0.874115i) q^{18} +6.88797 q^{19} +1.42550 q^{21} +(0.508252 - 0.421723i) q^{22} +(-2.22985 + 2.22985i) q^{23} +(1.10778 - 3.87675i) q^{24} +(0.493592 - 5.30489i) q^{26} +(3.99962 + 3.99962i) q^{27} +(-1.65085 + 1.12903i) q^{28} +2.62093i q^{29} -3.30718i q^{31} +(1.78756 + 5.36699i) q^{32} +(0.470723 + 0.470723i) q^{33} +(6.49505 + 0.604331i) q^{34} +(-1.90268 - 0.357160i) q^{36} +(7.25634 - 7.25634i) q^{37} +(-6.22021 - 7.49648i) q^{38} +5.37031 q^{39} -2.58124 q^{41} +(-1.28730 - 1.55143i) q^{42} +(1.82521 - 1.82521i) q^{43} +(-0.917960 - 0.172314i) q^{44} +(4.44052 + 0.413168i) q^{46} +(2.36428 + 2.36428i) q^{47} +(-5.21962 + 2.29527i) q^{48} +1.00000i q^{49} +6.57516i q^{51} +(-6.21928 + 4.25340i) q^{52} +(7.71648 + 7.71648i) q^{53} +(0.741086 - 7.96483i) q^{54} +(2.71957 + 0.777119i) q^{56} +(6.94294 - 6.94294i) q^{57} +(2.85247 - 2.36684i) q^{58} -11.4584 q^{59} +2.41339 q^{61} +(-3.59935 + 2.98657i) q^{62} +(-0.684447 + 0.684447i) q^{63} +(4.22687 - 6.79217i) q^{64} +(0.0872199 - 0.937397i) q^{66} +(-10.8099 - 10.8099i) q^{67} +(-5.20766 - 7.61459i) q^{68} +4.49529i q^{69} -9.62009i q^{71} +(1.32951 + 2.39330i) q^{72} +(-2.29031 - 2.29031i) q^{73} +(-14.4503 - 1.34452i) q^{74} +(-2.54156 + 13.5395i) q^{76} +(-0.330216 + 0.330216i) q^{77} +(-4.84969 - 5.84475i) q^{78} +2.91496 q^{79} +5.15920 q^{81} +(2.33100 + 2.80928i) q^{82} +(8.69820 - 8.69820i) q^{83} +(-0.525987 + 2.80206i) q^{84} +(-3.63472 - 0.338192i) q^{86} +(2.64184 + 2.64184i) q^{87} +(0.641430 + 1.15467i) q^{88} -1.89554i q^{89} +3.76732i q^{91} +(-3.56037 - 5.20593i) q^{92} +(-3.33357 - 3.33357i) q^{93} +(0.438075 - 4.70822i) q^{94} +(7.21165 + 3.60799i) q^{96} +(6.04308 - 6.04308i) q^{97} +(1.08834 - 0.903055i) q^{98} -0.452031 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{6}+O(q^{10}) $ 36 * q - 8 * q^6	$ 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) $ 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.903055	−	1.08834i	−0.638556	−	0.769575i
$2$	−0.903055	−	1.08834i	−0.638556	−	0.769575i
$3$	1.00798	−	1.00798i	0.581957	−	0.581957i	−0.353483	−	0.935441i	$-0.615003\pi$
$3$	1.00798	−	1.00798i	0.581957	−	0.581957i	0.935441	+	0.353483i	$0.115003\pi$
$4$	−0.368985	+	1.96567i	−0.184492	+	0.982834i
$5$		0			0
$5$		0			0
$6$	−2.00729	−	0.186768i	−0.819472	−	0.0762476i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.47254	−	1.37352i	0.874173	−	0.485614i
$9$			0.967954i			0.322651i
$10$		0			0
$11$			0.466996i			0.140805i	0.997519	+	0.0704023i	$0.0224283\pi$
$11$			0.466996i			0.140805i	−0.997519	+	0.0704023i	$0.977572\pi$
$12$	1.60942	+	2.35328i	0.464601	+	0.679334i
$13$	2.66390	+	2.66390i	0.738833	+	0.738833i	0.972352	−	0.233519i	$-0.0750242\pi$
$13$	2.66390	+	2.66390i	0.738833	+	0.738833i	−0.233519	+	0.972352i	$0.575024\pi$
$14$	0.131019	−	1.40813i	0.0350164	−	0.376339i
$15$		0			0
$16$	−3.72770	−	1.45060i	−0.931925	−	0.362651i
$17$	−3.26155	+	3.26155i	−0.791043	+	0.791043i	−0.981664	−	0.190621i	$-0.938950\pi$
$17$	−3.26155	+	3.26155i	−0.791043	+	0.791043i	0.190621	+	0.981664i	$0.438950\pi$
$18$	1.05347	−	0.874115i	0.248304	−	0.206031i
$19$	6.88797			1.58021			0.790105	−	0.612972i	$-0.210026\pi$
$19$	6.88797			1.58021			0.790105	+	0.612972i	$0.210026\pi$
$20$		0			0
$21$	1.42550			0.311069
$22$	0.508252	−	0.421723i	0.108360	−	0.0899117i
$23$	−2.22985	+	2.22985i	−0.464956	+	0.464956i	−0.900276	−	0.435320i	$-0.856635\pi$
$23$	−2.22985	+	2.22985i	−0.464956	+	0.464956i	0.435320	+	0.900276i	$0.356635\pi$
$24$	1.10778	−	3.87675i	0.226125	−	0.791338i
$25$		0			0
$26$	0.493592	−	5.30489i	0.0968014	−	1.04037i
$27$	3.99962	+	3.99962i	0.769727	+	0.769727i
$28$	−1.65085	+	1.12903i	−0.311981	+	0.213366i
$29$			2.62093i			0.486694i	0.969939	+	0.243347i	$0.0782453\pi$
$29$			2.62093i			0.486694i	−0.969939	+	0.243347i	$0.921755\pi$
$30$		0			0
$31$		−	3.30718i		−	0.593988i	−0.954879	−	0.296994i	$-0.904016\pi$
$31$		−	3.30718i		−	0.593988i	0.954879	−	0.296994i	$-0.0959841\pi$
$32$	1.78756	+	5.36699i	0.315999	+	0.948759i
$33$	0.470723	+	0.470723i	0.0819423	+	0.0819423i
$34$	6.49505	+	0.604331i	1.11389	+	0.103642i
$35$		0			0
$36$	−1.90268	−	0.357160i	−0.317113	−	0.0595267i
$37$	7.25634	−	7.25634i	1.19293	−	1.19293i	0.216696	−	0.976239i	$-0.430472\pi$
$37$	7.25634	−	7.25634i	1.19293	−	1.19293i	0.976239	−	0.216696i	$-0.0695280\pi$
$38$	−6.22021	−	7.49648i	−1.00905	−	1.21609i
$39$	5.37031			0.859938
$40$		0			0
$41$	−2.58124			−0.403122			−0.201561	−	0.979476i	$-0.564601\pi$
$41$	−2.58124			−0.403122			−0.201561	+	0.979476i	$0.564601\pi$
$42$	−1.28730	−	1.55143i	−0.198635	−	0.239391i
$43$	1.82521	−	1.82521i	0.278342	−	0.278342i	−0.554105	−	0.832447i	$-0.686939\pi$
$43$	1.82521	−	1.82521i	0.278342	−	0.278342i	0.832447	+	0.554105i	$0.186939\pi$
$44$	−0.917960	−	0.172314i	−0.138388	−	0.0259774i
$45$		0			0
$46$	4.44052	+	0.413168i	0.654719	+	0.0609182i
$47$	2.36428	+	2.36428i	0.344865	+	0.344865i	0.858193	−	0.513327i	$-0.171587\pi$
$47$	2.36428	+	2.36428i	0.344865	+	0.344865i	−0.513327	+	0.858193i	$0.671587\pi$
$48$	−5.21962	+	2.29527i	−0.753388	+	0.331293i
$49$			1.00000i			0.142857i
$50$		0			0
$51$			6.57516i			0.920706i
$52$	−6.21928	+	4.25340i	−0.862459	+	0.589841i
$53$	7.71648	+	7.71648i	1.05994	+	1.05994i	0.998085	+	0.0618550i	$0.0197016\pi$
$53$	7.71648	+	7.71648i	1.05994	+	1.05994i	0.0618550	+	0.998085i	$0.480298\pi$
$54$	0.741086	−	7.96483i	0.100849	−	1.08388i
$55$		0			0
$56$	2.71957	+	0.777119i	0.363418	+	0.103847i
$57$	6.94294	−	6.94294i	0.919614	−	0.919614i
$58$	2.85247	−	2.36684i	0.374547	−	0.310781i
$59$	−11.4584			−1.49176			−0.745878	−	0.666083i	$-0.767970\pi$
$59$	−11.4584			−1.49176			−0.745878	+	0.666083i	$0.767970\pi$
$60$		0			0
$61$	2.41339			0.309002			0.154501	−	0.987993i	$-0.450623\pi$
$61$	2.41339			0.309002			0.154501	+	0.987993i	$0.450623\pi$
$62$	−3.59935	+	2.98657i	−0.457118	+	0.379294i
$63$	−0.684447	+	0.684447i	−0.0862322	+	0.0862322i
$64$	4.22687	−	6.79217i	0.528359	−	0.849021i
$65$		0			0
$66$	0.0872199	−	0.937397i	0.0107360	−	0.115386i
$67$	−10.8099	−	10.8099i	−1.32064	−	1.32064i	−0.913261	−	0.407374i	$-0.866444\pi$
$67$	−10.8099	−	10.8099i	−1.32064	−	1.32064i	−0.407374	−	0.913261i	$-0.633556\pi$
$68$	−5.20766	−	7.61459i	−0.631522	−	0.923405i
$69$			4.49529i			0.541169i
$70$		0			0
$71$		−	9.62009i		−	1.14169i	−0.821056	−	0.570847i	$-0.806615\pi$
$71$		−	9.62009i		−	1.14169i	0.821056	−	0.570847i	$-0.193385\pi$
$72$	1.32951	+	2.39330i	0.156684	+	0.282053i
$73$	−2.29031	−	2.29031i	−0.268061	−	0.268061i	0.560258	−	0.828318i	$-0.310702\pi$
$73$	−2.29031	−	2.29031i	−0.268061	−	0.268061i	−0.828318	+	0.560258i	$0.810702\pi$
$74$	−14.4503	−	1.34452i	−1.67981	−	0.156297i
$75$		0			0
$76$	−2.54156	+	13.5395i	−0.291537	+	1.55308i
$77$	−0.330216	+	0.330216i	−0.0376316	+	0.0376316i
$78$	−4.84969	−	5.84475i	−0.549119	−	0.661787i
$79$	2.91496			0.327958			0.163979	−	0.986464i	$-0.447567\pi$
$79$	2.91496			0.327958			0.163979	+	0.986464i	$0.447567\pi$
$80$		0			0
$81$	5.15920			0.573245
$82$	2.33100	+	2.80928i	0.257416	+	0.310233i
$83$	8.69820	−	8.69820i	0.954752	−	0.954752i	−0.0442680	−	0.999020i	$-0.514096\pi$
$83$	8.69820	−	8.69820i	0.954752	−	0.954752i	0.999020	+	0.0442680i	$0.0140956\pi$
$84$	−0.525987	+	2.80206i	−0.0573899	+	0.305729i
$85$		0			0
$86$	−3.63472	−	0.338192i	−0.391942	−	0.0364682i
$87$	2.64184	+	2.64184i	0.283235	+	0.283235i
$88$	0.641430	+	1.15467i	0.0683767	+	0.123088i
$89$		−	1.89554i		−	0.200926i	−0.994941	−	0.100463i	$-0.967968\pi$
$89$		−	1.89554i		−	0.200926i	0.994941	−	0.100463i	$-0.0320325\pi$
$90$		0			0
$91$			3.76732i			0.394923i
$92$	−3.56037	−	5.20593i	−0.371194	−	0.542756i
$93$	−3.33357	−	3.33357i	−0.345676	−	0.345676i
$94$	0.438075	−	4.70822i	0.0451840	−	0.485616i
$95$		0			0
$96$	7.21165	+	3.60799i	0.736036	+	0.368239i
$97$	6.04308	−	6.04308i	0.613582	−	0.613582i	−0.330296	−	0.943878i	$-0.607148\pi$
$97$	6.04308	−	6.04308i	0.613582	−	0.613582i	0.943878	+	0.330296i	$0.107148\pi$
$98$	1.08834	−	0.903055i	0.109939	−	0.0912223i
$99$	−0.452031			−0.0454308
$100$		0			0
$101$	−6.14959			−0.611907			−0.305953	−	0.952047i	$-0.598975\pi$
$101$	−6.14959			−0.611907			−0.305953	+	0.952047i	$0.598975\pi$
$102$	7.15603	−	5.93773i	0.708553	−	0.587922i
$103$	−2.45266	+	2.45266i	−0.241668	+	0.241668i	−0.817540	−	0.575872i	$-0.804663\pi$
$103$	−2.45266	+	2.45266i	−0.241668	+	0.241668i	0.575872	+	0.817540i	$0.304663\pi$
$104$	10.2455	+	2.92766i	1.00466	+	0.287081i
$105$		0			0
$106$	1.42978	−	15.3666i	0.138873	−	1.49253i
$107$	−6.77382	−	6.77382i	−0.654850	−	0.654850i	0.299307	−	0.954157i	$-0.403244\pi$
$107$	−6.77382	−	6.77382i	−0.654850	−	0.654850i	−0.954157	+	0.299307i	$0.903244\pi$
$108$	−9.33772	+	6.38612i	−0.898522	+	0.614505i
$109$			15.9594i			1.52863i	0.644843	+	0.764315i	$0.276923\pi$
$109$			15.9594i			1.52863i	−0.644843	+	0.764315i	$0.723077\pi$
$110$		0			0
$111$		−	14.6285i		−	1.38847i
$112$	−1.61015	−	3.66161i	−0.152145	−	0.345990i
$113$	7.28250	+	7.28250i	0.685080	+	0.685080i	0.961140	−	0.276060i	$-0.0890289\pi$
$113$	7.28250	+	7.28250i	0.685080	+	0.685080i	−0.276060	+	0.961140i	$0.589029\pi$
$114$	−13.8262	−	1.28645i	−1.29494	−	0.120487i
$115$		0			0
$116$	−5.15187	−	0.967081i	−0.478339	−	0.0897913i
$117$	−2.57853	+	2.57853i	−0.238385	+	0.238385i
$118$	10.3476	+	12.4707i	0.952570	+	1.14802i
$119$	−4.61253			−0.422830
$120$		0			0
$121$	10.7819			0.980174
$122$	−2.17942	−	2.62659i	−0.197315	−	0.237801i
$123$	−2.60184	+	2.60184i	−0.234600	+	0.234600i
$124$	6.50083	+	1.22030i	0.583791	+	0.109586i
$125$		0			0
$126$	1.36301	+	0.126821i	0.121426	+	0.0112981i
$127$	7.25561	+	7.25561i	0.643832	+	0.643832i	0.951495	−	0.307664i	$-0.0995472\pi$
$127$	7.25561	+	7.25561i	0.643832	+	0.643832i	−0.307664	+	0.951495i	$0.599547\pi$
$128$	−11.2093	+	1.53341i	−0.990772	+	0.135536i
$129$		−	3.67955i		−	0.323967i
$130$		0			0
$131$			7.05985i			0.616822i	0.951253	+	0.308411i	$0.0997972\pi$
$131$			7.05985i			0.616822i	−0.951253	+	0.308411i	$0.900203\pi$
$132$	−1.09897	+	0.751595i	−0.0956534	+	0.0654180i
$133$	4.87053	+	4.87053i	0.422329	+	0.422329i
$134$	−2.00295	+	21.5268i	−0.173029	+	1.85963i
$135$		0			0
$136$	−3.58449	+	12.5441i	−0.307367	+	1.07565i
$137$	−5.42583	+	5.42583i	−0.463560	+	0.463560i	−0.899820	−	0.436261i	$-0.856303\pi$
$137$	−5.42583	+	5.42583i	−0.463560	+	0.463560i	0.436261	+	0.899820i	$0.356303\pi$
$138$	4.89242	−	4.05949i	0.416471	−	0.345567i
$139$	−18.2195			−1.54536			−0.772680	−	0.634796i	$-0.781084\pi$
$139$	−18.2195			−1.54536			−0.772680	+	0.634796i	$0.781084\pi$
$140$		0			0
$141$	4.76629			0.401394
$142$	−10.4700	+	8.68746i	−0.878620	+	0.729036i
$143$	−1.24403	+	1.24403i	−0.104031	+	0.104031i
$144$	1.40412	−	3.60824i	0.117010	−	0.300687i
$145$		0			0
$146$	−0.424371	+	4.56093i	−0.0351212	+	0.377465i
$147$	1.00798	+	1.00798i	0.0831368	+	0.0831368i
$148$	11.5861	+	16.9410i	0.952370	+	1.39254i
$149$		−	15.3272i		−	1.25565i	−0.778353	−	0.627827i	$-0.783944\pi$
$149$		−	15.3272i		−	1.25565i	0.778353	−	0.627827i	$-0.216056\pi$
$150$		0			0
$151$			0.769488i			0.0626201i	0.999510	+	0.0313100i	$0.00996792\pi$
$151$			0.769488i			0.0626201i	−0.999510	+	0.0313100i	$0.990032\pi$
$152$	17.0308	−	9.46079i	1.38138	−	0.767371i
$153$	−3.15703	−	3.15703i	−0.255231	−	0.255231i
$154$	0.657592	+	0.0611855i	0.0529903	+	0.00493047i
$155$		0			0
$156$	−1.98156	+	10.5563i	−0.158652	+	0.845177i
$157$	−8.52639	+	8.52639i	−0.680480	+	0.680480i	−0.960108	−	0.279628i	$-0.909789\pi$
$157$	−8.52639	+	8.52639i	−0.680480	+	0.680480i	0.279628	+	0.960108i	$0.409789\pi$
$158$	−2.63237	−	3.17248i	−0.209420	−	0.252389i
$159$	15.5561			1.23368
$160$		0			0
$161$	−3.15349			−0.248530
$162$	−4.65904	−	5.61499i	−0.366049	−	0.441155i
$163$	−9.27269	+	9.27269i	−0.726293	+	0.726293i	−0.969879	−	0.243586i	$-0.921676\pi$
$163$	−9.27269	+	9.27269i	−0.726293	+	0.726293i	0.243586	+	0.969879i	$0.421676\pi$
$164$	0.952438	−	5.07386i	0.0743729	−	0.396202i
$165$		0			0
$166$	−17.3216	−	1.61168i	−1.34442	−	0.125091i
$167$	−9.27099	−	9.27099i	−0.717411	−	0.717411i	0.250663	−	0.968074i	$-0.419351\pi$
$167$	−9.27099	−	9.27099i	−0.717411	−	0.717411i	−0.968074	+	0.250663i	$0.919351\pi$
$168$	3.52460	−	1.95796i	0.271929	−	0.151060i
$169$			1.19272i			0.0917480i
$170$		0			0
$171$			6.66724i			0.509856i
$172$	2.91429	+	4.26124i	0.222212	+	0.324916i
$173$	2.79813	+	2.79813i	0.212738	+	0.212738i	0.805429	−	0.592692i	$-0.201935\pi$
$173$	2.79813	+	2.79813i	0.212738	+	0.212738i	−0.592692	+	0.805429i	$0.701935\pi$
$174$	0.489505	−	5.26096i	0.0371092	−	0.398832i
$175$		0			0
$176$	0.677426	−	1.74082i	0.0510629	−	0.131219i
$177$	−11.5498	+	11.5498i	−0.868138	+	0.868138i
$178$	−2.06300	+	1.71177i	−0.154628	+	0.128303i
$179$	−13.5772			−1.01481			−0.507405	−	0.861708i	$-0.669395\pi$
$179$	−13.5772			−1.01481			−0.507405	+	0.861708i	$0.669395\pi$
$180$		0			0
$181$	19.8656			1.47660			0.738299	−	0.674474i	$-0.235629\pi$
$181$	19.8656			1.47660			0.738299	+	0.674474i	$0.235629\pi$
$182$	4.10014	−	3.40210i	0.303923	−	0.252180i
$183$	2.43264	−	2.43264i	0.179826	−	0.179826i
$184$	−2.45064	+	8.57614i	−0.180663	+	0.632242i
$185$		0			0
$186$	−0.617676	+	6.63848i	−0.0452902	+	0.486757i
$187$	−1.52313	−	1.52313i	−0.111382	−	0.111382i
$188$	−5.51977	+	3.77500i	−0.402570	+	0.275320i
$189$			5.65631i			0.411436i
$190$		0			0
$191$			14.9537i			1.08201i	0.841019	+	0.541006i	$0.181956\pi$
$191$			14.9537i			1.08201i	−0.841019	+	0.541006i	$0.818044\pi$
$192$	−2.58577	−	11.1070i	−0.186612	−	0.801576i
$193$	−4.52771	−	4.52771i	−0.325912	−	0.325912i	0.525118	−	0.851030i	$-0.324021\pi$
$193$	−4.52771	−	4.52771i	−0.325912	−	0.325912i	−0.851030	+	0.525118i	$0.824021\pi$
$194$	−12.0342	−	1.11972i	−0.864004	−	0.0803911i
$195$		0			0
$196$	−1.96567	−	0.368985i	−0.140405	−	0.0263561i
$197$	−2.52502	+	2.52502i	−0.179900	+	0.179900i	−0.791312	−	0.611412i	$-0.790602\pi$
$197$	−2.52502	+	2.52502i	−0.179900	+	0.179900i	0.611412	+	0.791312i	$0.290602\pi$
$198$	0.408208	+	0.491965i	0.0290101	+	0.0349624i
$199$	−2.30679			−0.163524			−0.0817621	−	0.996652i	$-0.526055\pi$
$199$	−2.30679			−0.163524			−0.0817621	+	0.996652i	$0.526055\pi$
$200$		0			0
$201$	−21.7923			−1.53711
$202$	5.55341	+	6.69286i	0.390737	+	0.470908i
$203$	−1.85327	+	1.85327i	−0.130074	+	0.130074i
$204$	−12.9246	−	2.42613i	−0.904901	−	0.169863i
$205$		0			0
$206$	4.88422	+	0.454451i	0.340300	+	0.0316631i
$207$	−2.15839	−	2.15839i	−0.150019	−	0.150019i
$208$	−6.06596	−	13.7945i	−0.420599	−	0.956475i
$209$			3.21666i			0.222501i
$210$		0			0
$211$			28.3975i			1.95496i	0.211018	+	0.977482i	$0.432322\pi$
$211$			28.3975i			1.95496i	−0.211018	+	0.977482i	$0.567678\pi$
$212$	−18.0153	+	12.3208i	−1.23730	+	0.846194i
$213$	−9.69685	−	9.69685i	−0.664417	−	0.664417i
$214$	−1.25512	+	13.4894i	−0.0857979	+	0.922114i
$215$		0			0
$216$	15.3828	+	4.39563i	1.04666	+	0.299085i
$217$	2.33853	−	2.33853i	0.158750	−	0.158750i
$218$	17.3693	−	14.4122i	1.17640	−	0.976116i
$219$	−4.61718			−0.312000
$220$		0			0
$221$	−17.3769			−1.16890
$222$	−15.9208	+	13.2103i	−1.06854	+	0.886619i
$223$	2.46338	−	2.46338i	0.164960	−	0.164960i	−0.619800	−	0.784760i	$-0.712786\pi$
$223$	2.46338	−	2.46338i	0.164960	−	0.164960i	0.784760	+	0.619800i	$0.212786\pi$
$224$	−2.53104	+	5.05903i	−0.169112	+	0.338021i
$225$		0			0
$226$	1.34937	−	14.5024i	0.0897587	−	0.964683i
$227$	0.313778	+	0.313778i	0.0208262	+	0.0208262i	0.717443	−	0.696617i	$-0.245312\pi$
$227$	0.313778	+	0.313778i	0.0208262	+	0.0208262i	−0.696617	+	0.717443i	$0.745312\pi$
$228$	11.0857	+	16.2093i	0.734166	+	1.07349i
$229$		−	3.73836i		−	0.247038i	−0.992342	−	0.123519i	$-0.960582\pi$
$229$		−	3.73836i		−	0.247038i	0.992342	−	0.123519i	$-0.0394179\pi$
$230$		0			0
$231$			0.665702i			0.0438000i
$232$	3.59990	+	6.48033i	0.236345	+	0.425455i
$233$	−13.6807	−	13.6807i	−0.896254	−	0.896254i	0.0988481	−	0.995103i	$-0.468484\pi$
$233$	−13.6807	−	13.6807i	−0.896254	−	0.896254i	−0.995103	+	0.0988481i	$0.968484\pi$
$234$	5.13488	+	0.477774i	0.335678	+	0.0312331i
$235$		0			0
$236$	4.22797	−	22.5234i	0.275218	−	1.46615i
$237$	2.93822	−	2.93822i	0.190858	−	0.190858i
$238$	4.16537	+	5.02002i	0.270001	+	0.325400i
$239$	17.4027			1.12569			0.562844	−	0.826563i	$-0.309707\pi$
$239$	17.4027			1.12569			0.562844	+	0.826563i	$0.309707\pi$
$240$		0			0
$241$	−22.0824			−1.42245			−0.711225	−	0.702965i	$-0.751859\pi$
$241$	−22.0824			−1.42245			−0.711225	+	0.702965i	$0.751859\pi$
$242$	−9.73666	−	11.7344i	−0.625896	−	0.754318i
$243$	−6.79848	+	6.79848i	−0.436123	+	0.436123i
$244$	−0.890503	+	4.74392i	−0.0570086	+	0.303698i
$245$		0			0
$246$	5.18130	+	0.482093i	0.330347	+	0.0307371i
$247$	18.3489	+	18.3489i	1.16751	+	1.16751i
$248$	−4.54249	−	8.17713i	−0.288449	−	0.519248i
$249$		−	17.5352i		−	1.11125i
$250$		0			0
$251$		−	25.0897i		−	1.58365i	−0.610751	−	0.791823i	$-0.709132\pi$
$251$		−	25.0897i		−	1.58365i	0.610751	−	0.791823i	$-0.290868\pi$
$252$	−1.09284	−	1.59795i	−0.0688427	−	0.100661i
$253$	−1.04133	−	1.04133i	−0.0654680	−	0.0654680i
$254$	1.34439	−	14.4488i	0.0843544	−	0.906599i
$255$		0			0
$256$	11.7915	+	10.8148i	0.736969	+	0.675927i
$257$	−6.04840	+	6.04840i	−0.377289	+	0.377289i	−0.870123	−	0.492834i	$-0.835961\pi$
$257$	−6.04840	+	6.04840i	−0.377289	+	0.377289i	0.492834	+	0.870123i	$0.335961\pi$
$258$	−4.00462	+	3.32284i	−0.249317	+	0.206871i
$259$	10.2620			0.637651
$260$		0			0
$261$	−2.53693			−0.157032
$262$	7.68354	−	6.37543i	0.474691	−	0.393875i
$263$	11.3720	−	11.3720i	0.701229	−	0.701229i	−0.263446	−	0.964674i	$-0.584859\pi$
$263$	11.3720	−	11.3720i	0.701229	−	0.701229i	0.964674	+	0.263446i	$0.0848590\pi$
$264$	1.81043	+	0.517330i	0.111424	+	0.0318395i
$265$		0			0
$266$	0.902457	−	9.69917i	0.0553332	−	0.594694i
$267$	−1.91066	−	1.91066i	−0.116931	−	0.116931i
$268$	25.2373	−	17.2599i	1.54161	−	1.05432i
$269$		−	6.75584i		−	0.411911i	−0.978561	−	0.205955i	$-0.933970\pi$
$269$		−	6.75584i		−	0.411911i	0.978561	−	0.205955i	$-0.0660302\pi$
$270$		0			0
$271$		−	4.30758i		−	0.261667i	−0.991404	−	0.130833i	$-0.958235\pi$
$271$		−	4.30758i		−	0.261667i	0.991404	−	0.130833i	$-0.0417653\pi$
$272$	16.8893	−	7.42687i	1.02406	−	0.450320i
$273$	3.79739	+	3.79739i	0.229828	+	0.229828i
$274$	10.8050	+	1.00535i	0.652753	+	0.0607352i
$275$		0			0
$276$	−8.83625	−	1.65869i	−0.531880	−	0.0998416i
$277$	20.5796	−	20.5796i	1.23651	−	1.23651i	0.275090	−	0.961418i	$-0.411292\pi$
$277$	20.5796	−	20.5796i	1.23651	−	1.23651i	0.961418	−	0.275090i	$-0.0887077\pi$
$278$	16.4532	+	19.8291i	0.986799	+	1.18927i
$279$	3.20120			0.191651
$280$		0			0
$281$	9.43379			0.562773			0.281387	−	0.959595i	$-0.409206\pi$
$281$	9.43379			0.562773			0.281387	+	0.959595i	$0.409206\pi$
$282$	−4.30422	−	5.18736i	−0.256312	−	0.308903i
$283$	4.48860	−	4.48860i	0.266819	−	0.266819i	−0.560998	−	0.827817i	$-0.689582\pi$
$283$	4.48860	−	4.48860i	0.266819	−	0.266819i	0.827817	+	0.560998i	$0.189582\pi$
$284$	18.9099	+	3.54967i	1.12210	+	0.210634i
$285$		0			0
$286$	2.47736	+	0.230506i	0.146489	+	0.0136301i
$287$	−1.82521	−	1.82521i	−0.107739	−	0.107739i
$288$	−5.19500	+	1.73028i	−0.306118	+	0.101958i
$289$		−	4.27544i		−	0.251497i
$290$		0			0
$291$		−	12.1826i		−	0.714157i
$292$	5.34709	−	3.65691i	0.312915	−	0.214004i
$293$	−0.355783	−	0.355783i	−0.0207851	−	0.0207851i	0.696638	−	0.717423i	$-0.254678\pi$
$293$	−0.355783	−	0.355783i	−0.0207851	−	0.0207851i	−0.717423	+	0.696638i	$0.754678\pi$
$294$	0.186768	−	2.00729i	0.0108925	−	0.117067i
$295$		0			0
$296$	7.97481	−	27.9083i	0.463526	−	1.62214i
$297$	−1.86781	+	1.86781i	−0.108381	+	0.108381i
$298$	−16.6813	+	13.8413i	−0.966321	+	0.801806i
$299$	−11.8802			−0.687050
$300$		0			0
$301$	2.58124			0.148780
$302$	0.837468	−	0.694890i	0.0481909	−	0.0399864i
$303$	−6.19866	+	6.19866i	−0.356104	+	0.356104i
$304$	−25.6763	−	9.99171i	−1.47264	−	0.573064i
$305$		0			0
$306$	−0.584964	+	6.28691i	−0.0334402	+	0.359399i
$307$	−8.63817	−	8.63817i	−0.493006	−	0.493006i	0.416246	−	0.909252i	$-0.363346\pi$
$307$	−8.63817	−	8.63817i	−0.493006	−	0.493006i	−0.909252	+	0.416246i	$0.863346\pi$
$308$	−0.527251	−	0.770940i	−0.0300429	−	0.0439284i
$309$			4.94446i			0.281280i
$310$		0			0
$311$		−	14.5511i		−	0.825118i	−0.910931	−	0.412559i	$-0.864635\pi$
$311$		−	14.5511i		−	0.825118i	0.910931	−	0.412559i	$-0.135365\pi$
$312$	13.2783	−	7.37625i	0.751735	−	0.417598i
$313$	−13.6090	−	13.6090i	−0.769229	−	0.769229i	0.208742	−	0.977971i	$-0.433063\pi$
$313$	−13.6090	−	13.6090i	−0.769229	−	0.769229i	−0.977971	+	0.208742i	$0.933063\pi$
$314$	16.9794	+	1.57985i	0.958206	+	0.0891560i
$315$		0			0
$316$	−1.07557	+	5.72984i	−0.0605058	+	0.322329i
$317$	−1.36731	+	1.36731i	−0.0767957	+	0.0767957i	−0.744461	−	0.667666i	$-0.767294\pi$
$317$	−1.36731	+	1.36731i	−0.0767957	+	0.0767957i	0.667666	+	0.744461i	$0.267294\pi$
$318$	−14.0480	−	16.9304i	−0.787774	−	0.949410i
$319$	−1.22396			−0.0685287
$320$		0			0
$321$	−13.6557			−0.762189
$322$	2.84777	+	3.43208i	0.158700	+	0.191262i
$323$	−22.4655	+	22.4655i	−1.25001	+	1.25001i
$324$	−1.90367	+	10.1413i	−0.105759	+	0.563405i
$325$		0			0
$326$	18.4656	+	1.71813i	1.02272	+	0.0951584i
$327$	16.0867	+	16.0867i	0.889598	+	0.889598i
$328$	−6.38221	+	3.54539i	−0.352399	+	0.195762i
$329$			3.34359i			0.184338i
$330$		0			0
$331$		−	5.86317i		−	0.322269i	−0.986932	−	0.161134i	$-0.948485\pi$
$331$		−	5.86317i		−	0.322269i	0.986932	−	0.161134i	$-0.0515153\pi$
$332$	13.8883	+	20.3073i	0.762218	+	1.11451i
$333$	7.02380	+	7.02380i	0.384902	+	0.384902i
$334$	−1.71782	+	18.4622i	−0.0939947	+	1.01021i
$335$		0			0
$336$	−5.31383	−	2.06783i	−0.289893	−	0.112810i
$337$	2.71874	−	2.71874i	0.148099	−	0.148099i	−0.629169	−	0.777268i	$-0.716605\pi$
$337$	2.71874	−	2.71874i	0.148099	−	0.148099i	0.777268	+	0.629169i	$0.216605\pi$
$338$	1.29809	−	1.07709i	0.0706070	−	0.0585862i
$339$	14.6812			0.797375
$340$		0			0
$341$	1.54444			0.0836363
$342$	7.25625	−	6.02088i	0.392373	−	0.325572i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	2.00593	−	7.01987i	0.108153	−	0.378486i
$345$		0			0
$346$	0.518463	−	5.57219i	0.0278728	−	0.299563i
$347$	11.3396	+	11.3396i	0.608741	+	0.608741i	0.942617	−	0.333876i	$-0.108357\pi$
$347$	11.3396	+	11.3396i	0.608741	+	0.608741i	−0.333876	+	0.942617i	$0.608357\pi$
$348$	−6.16778	+	4.21818i	−0.330628	+	0.226118i
$349$		−	24.6849i		−	1.32135i	−0.750671	−	0.660677i	$-0.770270\pi$
$349$		−	24.6849i		−	1.32135i	0.750671	−	0.660677i	$-0.229730\pi$
$350$		0			0
$351$			21.3092i			1.13740i
$352$	−2.50637	+	0.834785i	−0.133590	+	0.0444942i
$353$	−14.0941	−	14.0941i	−0.750153	−	0.750153i	0.224354	−	0.974508i	$-0.427973\pi$
$353$	−14.0941	−	14.0941i	−0.750153	−	0.750153i	−0.974508	+	0.224354i	$0.927973\pi$
$354$	23.0003	+	2.14006i	1.22245	+	0.113743i
$355$		0			0
$356$	3.72599	+	0.699424i	0.197477	+	0.0370694i
$357$	−4.64934	+	4.64934i	−0.246069	+	0.246069i
$358$	12.2610	+	14.7767i	0.648013	+	0.780973i
$359$	19.2502			1.01599			0.507994	−	0.861361i	$-0.330387\pi$
$359$	19.2502			1.01599			0.507994	+	0.861361i	$0.330387\pi$
$360$		0			0
$361$	28.4442			1.49706
$362$	−17.9397	−	21.6206i	−0.942890	−	1.13635i
$363$	10.8680	−	10.8680i	0.570420	−	0.570420i
$364$	−7.40531	−	1.39008i	−0.388144	−	0.0728602i
$365$		0			0
$366$	−4.84436	−	0.450743i	−0.253219	−	0.0235607i
$367$	−13.2691	−	13.2691i	−0.692641	−	0.692641i	0.270171	−	0.962812i	$-0.412920\pi$
$367$	−13.2691	−	13.2691i	−0.692641	−	0.692641i	−0.962812	+	0.270171i	$0.912920\pi$
$368$	11.5468	−	5.07759i	0.601921	−	0.264688i
$369$		−	2.49852i		−	0.130068i
$370$		0			0
$371$			10.9128i			0.566562i
$372$	7.78274	−	5.32266i	0.403516	−	0.275967i
$373$	−8.46024	−	8.46024i	−0.438055	−	0.438055i	0.453302	−	0.891357i	$-0.350246\pi$
$373$	−8.46024	−	8.46024i	−0.438055	−	0.438055i	−0.891357	+	0.453302i	$0.850246\pi$
$374$	−0.282220	+	3.03316i	−0.0145933	+	0.156841i
$375$		0			0
$376$	9.09315	+	2.59837i	0.468944	+	0.134001i
$377$	−6.98188	+	6.98188i	−0.359585	+	0.359585i
$378$	6.15601	−	5.10796i	0.316631	−	0.262725i
$379$	13.2251			0.679326			0.339663	−	0.940547i	$-0.389687\pi$
$379$	13.2251			0.679326			0.339663	+	0.940547i	$0.389687\pi$
$380$		0			0
$381$	14.6270			0.749365
$382$	16.2748	−	13.5040i	0.832690	−	0.690925i
$383$	19.4575	−	19.4575i	0.994229	−	0.994229i	−0.00575414	−	0.999983i	$-0.501832\pi$
$383$	19.4575	−	19.4575i	0.994229	−	0.994229i	0.999983	+	0.00575414i	$0.00183161\pi$
$384$	−9.75311	+	12.8444i	−0.497711	+	0.655463i
$385$		0			0
$386$	−0.838937	+	9.01648i	−0.0427008	+	0.458927i
$387$	1.76672	+	1.76672i	0.0898075	+	0.0898075i
$388$	9.64888	+	14.1085i	0.489848	+	0.716250i
$389$			10.6385i			0.539395i	0.962945	+	0.269698i	$0.0869238\pi$
$389$			10.6385i			0.539395i	−0.962945	+	0.269698i	$0.913076\pi$
$390$		0			0
$391$		−	14.5456i		−	0.735600i
$392$	1.37352	+	2.47254i	0.0693734	+	0.124882i
$393$	7.11618	+	7.11618i	0.358964	+	0.358964i
$394$	5.02832	+	0.467859i	0.253323	+	0.0235704i
$395$		0			0
$396$	0.166792	−	0.888542i	0.00838164	−	0.0446509i
$397$	3.40035	−	3.40035i	0.170659	−	0.170659i	−0.616610	−	0.787269i	$-0.711494\pi$
$397$	3.40035	−	3.40035i	0.170659	−	0.170659i	0.787269	+	0.616610i	$0.211494\pi$
$398$	2.08316	+	2.51058i	0.104419	+	0.125844i
$399$	9.81879			0.491555
$400$		0			0
$401$	−10.5640			−0.527541			−0.263770	−	0.964586i	$-0.584966\pi$
$401$	−10.5640			−0.527541			−0.263770	+	0.964586i	$0.584966\pi$
$402$	19.6796	+	23.7175i	0.981529	+	1.18292i
$403$	8.81001	−	8.81001i	0.438858	−	0.438858i
$404$	2.26910	−	12.0880i	0.112892	−	0.601403i
$405$		0			0
$406$	3.69061	+	0.343392i	0.183162	+	0.0170422i
$407$	3.38868	+	3.38868i	0.167971	+	0.167971i
$408$	9.03113	+	16.2573i	0.447108	+	0.804857i
$409$		−	28.4667i		−	1.40759i	−0.710404	−	0.703794i	$-0.751488\pi$
$409$		−	28.4667i		−	1.40759i	0.710404	−	0.703794i	$-0.248512\pi$
$410$		0			0
$411$			10.9382i			0.539544i
$412$	−3.91612	−	5.72610i	−0.192933	−	0.282105i
$413$	−8.10231	−	8.10231i	−0.398688	−	0.398688i
$414$	−0.399927	+	4.29822i	−0.0196553	+	0.211246i
$415$		0			0
$416$	−9.53525	+	19.0590i	−0.467504	+	0.934445i
$417$	−18.3649	+	18.3649i	−0.899334	+	0.899334i
$418$	3.50083	−	2.90482i	0.171231	−	0.142079i
$419$	−17.5164			−0.855733			−0.427867	−	0.903842i	$-0.640735\pi$
$419$	−17.5164			−0.855733			−0.427867	+	0.903842i	$0.640735\pi$
$420$		0			0
$421$	−10.6568			−0.519379			−0.259689	−	0.965692i	$-0.583620\pi$
$421$	−10.6568			−0.519379			−0.259689	+	0.965692i	$0.583620\pi$
$422$	30.9062	−	25.6445i	1.50449	−	1.24835i
$423$	−2.28851	+	2.28851i	−0.111271	+	0.111271i
$424$	29.6780	+	8.48051i	1.44129	+	0.411850i
$425$		0			0
$426$	−1.79672	+	19.3103i	−0.0870515	+	0.935587i
$427$	1.70652	+	1.70652i	0.0825844	+	0.0825844i
$428$	15.8145	−	10.8156i	0.764423	−	0.522794i
$429$			2.50792i			0.121083i
$430$		0			0
$431$		−	38.9415i		−	1.87575i	−0.346976	−	0.937874i	$-0.612791\pi$
$431$		−	38.9415i		−	1.87575i	0.346976	−	0.937874i	$-0.387209\pi$
$432$	−9.10752	−	20.7112i	−0.438186	−	0.996470i
$433$	−6.32139	−	6.32139i	−0.303787	−	0.303787i	0.538707	−	0.842493i	$-0.318913\pi$
$433$	−6.32139	−	6.32139i	−0.303787	−	0.303787i	−0.842493	+	0.538707i	$0.818913\pi$
$434$	−4.65695	−	0.433305i	−0.223541	−	0.0207993i
$435$		0			0
$436$	−31.3708	−	5.88876i	−1.50239	−	0.282021i
$437$	−15.3592	+	15.3592i	−0.734728	+	0.734728i
$438$	4.16957	+	5.02508i	0.199230	+	0.240108i
$439$	−27.0296			−1.29005			−0.645026	−	0.764161i	$-0.723153\pi$
$439$	−27.0296			−1.29005			−0.645026	+	0.764161i	$0.723153\pi$
$440$		0			0
$441$	−0.967954			−0.0460930
$442$	15.6923	+	18.9120i	0.746406	+	0.899554i
$443$	12.2298	−	12.2298i	0.581057	−	0.581057i	−0.354137	−	0.935194i	$-0.615225\pi$
$443$	12.2298	−	12.2298i	0.581057	−	0.581057i	0.935194	+	0.354137i	$0.115225\pi$
$444$	28.7547	+	5.39769i	1.36464	+	0.256163i
$445$		0			0
$446$	−4.90558	−	0.456438i	−0.232286	−	0.0216130i
$447$	−15.4495	−	15.4495i	−0.730738	−	0.730738i
$448$	7.79164	−	1.81394i	0.368120	−	0.0857007i
$449$			2.84860i			0.134434i	0.997738	+	0.0672169i	$0.0214119\pi$
$449$			2.84860i			0.134434i	−0.997738	+	0.0672169i	$0.978588\pi$
$450$		0			0
$451$		−	1.20543i		−	0.0567614i
$452$	−17.0021	+	11.6279i	−0.799712	+	0.546928i
$453$	0.775628	+	0.775628i	0.0364422	+	0.0364422i
$454$	0.0581398	−	0.624858i	0.00272863	−	0.0293260i
$455$		0			0
$456$	7.63038	−	26.7029i	0.357325	−	1.25048i
$457$	9.60132	−	9.60132i	0.449131	−	0.449131i	−0.445935	−	0.895066i	$-0.647129\pi$
$457$	9.60132	−	9.60132i	0.449131	−	0.449131i	0.895066	+	0.445935i	$0.147129\pi$
$458$	−4.06862	+	3.37594i	−0.190114	+	0.157747i
$459$	−26.0899			−1.21777
$460$		0			0
$461$	−10.4122			−0.484945			−0.242472	−	0.970158i	$-0.577958\pi$
$461$	−10.4122			−0.484945			−0.242472	+	0.970158i	$0.577958\pi$
$462$	0.724513	−	0.601166i	0.0337074	−	0.0279688i
$463$	−14.1517	+	14.1517i	−0.657683	+	0.657683i	−0.954831	−	0.297148i	$-0.903965\pi$
$463$	−14.1517	+	14.1517i	−0.657683	+	0.657683i	0.297148	+	0.954831i	$0.403965\pi$
$464$	3.80192	−	9.77002i	0.176500	−	0.453562i
$465$		0			0
$466$	−2.53489	+	27.2438i	−0.117427	+	1.26204i
$467$	−6.09942	−	6.09942i	−0.282247	−	0.282247i	0.551757	−	0.834005i	$-0.313957\pi$
$467$	−6.09942	−	6.09942i	−0.282247	−	0.282247i	−0.834005	+	0.551757i	$0.813957\pi$
$468$	−4.11710	−	6.01998i	−0.190313	−	0.278273i
$469$		−	15.2875i		−	0.705909i
$470$		0			0
$471$			17.1889i			0.792021i
$472$	−28.3313	+	15.7384i	−1.30405	+	0.724417i
$473$	0.852367	+	0.852367i	0.0391919	+	0.0391919i
$474$	−5.85116	−	0.544420i	−0.268753	−	0.0250060i
$475$		0			0
$476$	1.70195	−	9.06670i	0.0780089	−	0.415572i
$477$	−7.46920	+	7.46920i	−0.341991	+	0.341991i
$478$	−15.7156	−	18.9401i	−0.718815	−	0.866302i
$479$	12.0719			0.551580			0.275790	−	0.961218i	$-0.411060\pi$
$479$	12.0719			0.551580			0.275790	+	0.961218i	$0.411060\pi$
$480$		0			0
$481$	38.6603			1.76276
$482$	19.9416	+	24.0332i	0.908314	+	1.09468i
$483$	−3.17865	+	3.17865i	−0.144634	+	0.144634i
$484$	−3.97836	+	21.1937i	−0.180835	+	0.963348i
$485$		0			0
$486$	13.5385	+	1.25968i	0.614118	+	0.0571405i
$487$	21.1524	+	21.1524i	0.958508	+	0.958508i	0.999173	−	0.0406645i	$-0.0129475\pi$
$487$	21.1524	+	21.1524i	0.958508	+	0.958508i	−0.0406645	+	0.999173i	$0.512947\pi$
$488$	5.96718	−	3.31484i	0.270122	−	0.150056i
$489$			18.6934i			0.845343i
$490$		0			0
$491$		−	19.2585i		−	0.869125i	−0.900642	−	0.434562i	$-0.856903\pi$
$491$		−	19.2585i		−	0.869125i	0.900642	−	0.434562i	$-0.143097\pi$
$492$	−4.15431	−	6.07439i	−0.187291	−	0.273855i
$493$	−8.54828	−	8.54828i	−0.384995	−	0.384995i
$494$	3.39985	−	36.5399i	0.152966	−	1.64401i
$495$		0			0
$496$	−4.79741	+	12.3282i	−0.215410	+	0.553552i
$497$	6.80243	−	6.80243i	0.305131	−	0.305131i
$498$	−19.0844	+	15.8353i	−0.855190	+	0.709595i
$499$	9.48925			0.424797			0.212399	−	0.977183i	$-0.431872\pi$
$499$	9.48925			0.424797			0.212399	+	0.977183i	$0.431872\pi$
$500$		0			0
$501$	−18.6899			−0.835005
$502$	−27.3062	+	22.6573i	−1.21873	+	1.01125i
$503$	24.1569	−	24.1569i	1.07710	−	1.07710i	0.0803368	−	0.996768i	$-0.474400\pi$
$503$	24.1569	−	24.1569i	1.07710	−	1.07710i	0.996768	−	0.0803368i	$-0.0255996\pi$
$504$	−0.752216	+	2.63242i	−0.0335063	+	0.117257i
$505$		0			0
$506$	−0.192948	+	2.07371i	−0.00857757	+	0.0921876i
$507$	1.20224	+	1.20224i	0.0533934	+	0.0533934i
$508$	−16.9393	+	11.5849i	−0.751561	+	0.513997i
$509$			14.5829i			0.646374i	0.946335	+	0.323187i	$0.104754\pi$
$509$			14.5829i			0.646374i	−0.946335	+	0.323187i	$0.895246\pi$
$510$		0			0
$511$		−	3.23899i		−	0.143285i
$512$	1.12188	−	22.5996i	0.0495806	−	0.998770i
$513$	27.5492	+	27.5492i	1.21633	+	1.21633i
$514$	12.0448	+	1.12070i	0.531272	+	0.0494321i
$515$		0			0
$516$	7.23278	+	1.35770i	0.318405	+	0.0597694i
$517$	−1.10411	+	1.10411i	−0.0485587	+	0.0485587i
$518$	−9.26716	−	11.1686i	−0.407176	−	0.490720i
$519$	5.64091			0.247609
$520$		0			0
$521$	−5.54494			−0.242928			−0.121464	−	0.992596i	$-0.538759\pi$
$521$	−5.54494			−0.242928			−0.121464	+	0.992596i	$0.538759\pi$
$522$	2.29099	+	2.76106i	0.100274	+	0.120848i
$523$	−26.1183	+	26.1183i	−1.14207	+	1.14207i	−0.154003	+	0.988070i	$0.549217\pi$
$523$	−26.1183	+	26.1183i	−1.14207	+	1.14207i	−0.988070	+	0.154003i	$0.950783\pi$
$524$	−13.8773	−	2.60498i	−0.606233	−	0.113799i
$525$		0			0
$526$	−22.6462	−	2.10711i	−0.987422	−	0.0918745i
$527$	10.7866	+	10.7866i	0.469870	+	0.469870i
$528$	−1.07188	−	2.43755i	−0.0466477	−	0.106081i
$529$			13.0555i			0.567631i
$530$		0			0
$531$		−	11.0912i		−	0.481317i
$532$	−11.3710	+	7.77670i	−0.492995	+	0.337163i
$533$	−6.87616	−	6.87616i	−0.297840	−	0.297840i
$534$	−0.354025	+	3.80489i	−0.0153202	+	0.164654i
$535$		0			0
$536$	−41.5754	−	11.8802i	−1.79578	−	0.513146i
$537$	−13.6856	+	13.6856i	−0.590576	+	0.590576i
$538$	−7.35267	+	6.10089i	−0.316996	+	0.263028i
$539$	−0.466996			−0.0201150
$540$		0			0
$541$	−24.1953			−1.04024			−0.520119	−	0.854094i	$-0.674112\pi$
$541$	−24.1953			−1.04024			−0.520119	+	0.854094i	$0.674112\pi$
$542$	−4.68813	+	3.88998i	−0.201372	+	0.167089i
$543$	20.0241	−	20.0241i	0.859317	−	0.859317i
$544$	−23.3350	−	11.6745i	−1.00048	−	0.500540i
$545$		0			0
$546$	0.703615	−	7.56211i	0.0301119	−	0.323628i
$547$	−12.6814	−	12.6814i	−0.542219	−	0.542219i	0.381960	−	0.924179i	$-0.375249\pi$
$547$	−12.6814	−	12.6814i	−0.542219	−	0.542219i	−0.924179	+	0.381960i	$0.875249\pi$
$548$	−8.66332	−	12.6674i	−0.370079	−	0.541125i
$549$			2.33605i			0.0997000i
$550$		0			0
$551$			18.0529i			0.769078i
$552$	6.17439	+	11.1148i	0.262799	+	0.473076i
$553$	2.06119	+	2.06119i	0.0876505	+	0.0876505i
$554$	−40.9822	−	3.81318i	−1.74117	−	0.162006i
$555$		0			0
$556$	6.72273	−	35.8135i	0.285107	−	1.51883i
$557$	5.06552	−	5.06552i	0.214633	−	0.214633i	−0.591599	−	0.806232i	$-0.701503\pi$
$557$	5.06552	−	5.06552i	0.214633	−	0.214633i	0.806232	+	0.591599i	$0.201503\pi$
$558$	−2.89086	−	3.48401i	−0.122380	−	0.147490i
$559$	9.72436			0.411297
$560$		0			0
$561$	−3.07057			−0.129640
$562$	−8.51923	−	10.2672i	−0.359362	−	0.433096i
$563$	−28.2090	+	28.2090i	−1.18887	+	1.18887i	−0.211487	+	0.977381i	$0.567831\pi$
$563$	−28.2090	+	28.2090i	−1.18887	+	1.18887i	−0.977381	+	0.211487i	$0.932169\pi$
$564$	−1.75869	+	9.36894i	−0.0740541	+	0.394504i
$565$		0			0
$566$	−8.93859	−	0.831689i	−0.375717	−	0.0349585i
$567$	3.64811	+	3.64811i	0.153206	+	0.153206i
$568$	−13.2134	−	23.7860i	−0.554423	−	0.998039i
$569$			17.8458i			0.748133i	0.927402	+	0.374067i	$0.122037\pi$
$569$			17.8458i			0.748133i	−0.927402	+	0.374067i	$0.877963\pi$
$570$		0			0
$571$		−	7.70777i		−	0.322560i	−0.986909	−	0.161280i	$-0.948438\pi$
$571$		−	7.70777i		−	0.322560i	0.986909	−	0.161280i	$-0.0515623\pi$
$572$	−1.98632	−	2.90438i	−0.0830524	−	0.121438i
$573$	15.0730	+	15.0730i	0.629685	+	0.629685i
$574$	−0.338192	+	3.63472i	−0.0141159	+	0.151710i
$575$		0			0
$576$	6.57451	+	4.09141i	0.273938	+	0.170476i
$577$	20.7878	−	20.7878i	0.865409	−	0.865409i	−0.126551	−	0.991960i	$-0.540391\pi$
$577$	20.7878	−	20.7878i	0.865409	−	0.865409i	0.991960	+	0.126551i	$0.0403909\pi$
$578$	−4.65315	+	3.86096i	−0.193546	+	0.160595i
$579$	−9.12769			−0.379334
$580$		0			0
$581$	12.3011			0.510336
$582$	−13.2589	+	11.0016i	−0.549598	+	0.456029i
$583$	−3.60357	+	3.60357i	−0.149245	+	0.149245i
$584$	−8.80868	−	2.51708i	−0.364506	−	0.104158i
$585$		0			0
$586$	−0.0659228	+	0.708506i	−0.00272324	+	0.0292681i
$587$	−22.3147	−	22.3147i	−0.921028	−	0.921028i	0.0760739	−	0.997102i	$-0.475762\pi$
$587$	−22.3147	−	22.3147i	−0.921028	−	0.921028i	−0.997102	+	0.0760739i	$0.975762\pi$
$588$	−2.35328	+	1.60942i	−0.0970477	+	0.0663715i
$589$		−	22.7798i		−	0.938625i
$590$		0			0
$591$			5.09034i			0.209389i
$592$	−37.5755	+	16.5234i	−1.54434	+	0.679107i
$593$	13.8919	+	13.8919i	0.570471	+	0.570471i	0.932260	−	0.361789i	$-0.117834\pi$
$593$	13.8919	+	13.8919i	0.570471	+	0.570471i	−0.361789	+	0.932260i	$0.617834\pi$
$594$	3.71955	+	0.346084i	0.152615	+	0.0142000i
$595$		0			0
$596$	30.1282	+	5.65551i	1.23410	+	0.231659i
$597$	−2.32520	+	2.32520i	−0.0951641	+	0.0951641i
$598$	10.7285	+	12.9297i	0.438720	+	0.528737i
$599$	−10.6863			−0.436632			−0.218316	−	0.975878i	$-0.570056\pi$
$599$	−10.6863			−0.436632			−0.218316	+	0.975878i	$0.570056\pi$
$600$		0			0
$601$	−25.4476			−1.03803			−0.519014	−	0.854766i	$-0.673701\pi$
$601$	−25.4476			−1.03803			−0.519014	+	0.854766i	$0.673701\pi$
$602$	−2.33100	−	2.80928i	−0.0950045	−	0.114498i
$603$	10.4635	−	10.4635i	0.426105	−	0.426105i
$604$	−1.51256	−	0.283929i	−0.0615451	−	0.0115529i
$605$		0			0
$606$	12.3440	+	1.14854i	0.501441	+	0.0466564i
$607$	−16.1944	−	16.1944i	−0.657310	−	0.657310i	0.297432	−	0.954743i	$-0.403870\pi$
$607$	−16.1944	−	16.1944i	−0.657310	−	0.657310i	−0.954743	+	0.297432i	$0.903870\pi$
$608$	12.3127	+	36.9677i	0.499345	+	1.49924i
$609$			3.73613i			0.151395i
$610$		0			0
$611$			12.5964i			0.509596i
$612$	7.37057	−	5.04078i	0.297938	−	0.203761i
$613$	−5.21615	−	5.21615i	−0.210678	−	0.210678i	0.593877	−	0.804556i	$-0.297596\pi$
$613$	−5.21615	−	5.21615i	−0.210678	−	0.210678i	−0.804556	+	0.593877i	$0.797596\pi$
$614$	−1.60056	+	17.2020i	−0.0645933	+	0.694218i
$615$		0			0
$616$	−0.362912	+	1.27003i	−0.0146221	+	0.0511710i
$617$	19.1002	−	19.1002i	0.768945	−	0.768945i	−0.208976	−	0.977921i	$-0.567013\pi$
$617$	19.1002	−	19.1002i	0.768945	−	0.768945i	0.977921	+	0.208976i	$0.0670131\pi$
$618$	5.38127	−	4.46512i	0.216466	−	0.179613i
$619$	−17.5491			−0.705356			−0.352678	−	0.935745i	$-0.614729\pi$
$619$	−17.5491			−0.705356			−0.352678	+	0.935745i	$0.614729\pi$
$620$		0			0
$621$	−17.8371			−0.715778
$622$	−15.8366	+	13.1404i	−0.634990	+	0.526884i
$623$	1.34035	−	1.34035i	0.0536999	−	0.0536999i
$624$	−20.0189	−	7.79019i	−0.801398	−	0.311857i
$625$		0			0
$626$	−2.52161	+	27.1010i	−0.100784	+	1.08318i
$627$	3.24233	+	3.24233i	0.129486	+	0.129486i
$628$	−13.6139	−	19.9062i	−0.543256	−	0.794342i
$629$			47.3339i			1.88732i
$630$		0			0
$631$			47.5527i			1.89304i	0.322642	+	0.946521i	$0.395429\pi$
$631$			47.5527i			1.89304i	−0.322642	+	0.946521i	$0.604571\pi$
$632$	7.20734	−	4.00376i	0.286692	−	0.159261i
$633$	28.6241	+	28.6241i	1.13771	+	1.13771i
$634$	2.72286	+	0.253348i	0.108138	+	0.0100617i
$635$		0			0
$636$	−5.73997	+	30.5781i	−0.227605	+	1.21250i
$637$	−2.66390	+	2.66390i	−0.105548	+	0.105548i
$638$	1.10530	+	1.33209i	0.0437594	+	0.0527380i
$639$	9.31180			0.368369
$640$		0			0
$641$	6.13200			0.242199			0.121100	−	0.992640i	$-0.461358\pi$
$641$	6.13200			0.242199			0.121100	+	0.992640i	$0.461358\pi$
$642$	12.3319	+	14.8621i	0.486700	+	0.586562i
$643$	−12.9856	+	12.9856i	−0.512101	+	0.512101i	−0.915170	−	0.403069i	$-0.867943\pi$
$643$	−12.9856	+	12.9856i	−0.512101	+	0.512101i	0.403069	+	0.915170i	$0.367943\pi$
$644$	1.16359	−	6.19871i	0.0458518	−	0.244263i
$645$		0			0
$646$	44.7377	+	4.16261i	1.76018	+	0.163776i
$647$	10.6018	+	10.6018i	0.416799	+	0.416799i	0.884099	−	0.467300i	$-0.154773\pi$
$647$	10.6018	+	10.6018i	0.416799	+	0.416799i	−0.467300	+	0.884099i	$0.654773\pi$
$648$	12.7563	−	7.08629i	0.501116	−	0.278376i
$649$		−	5.35103i		−	0.210046i
$650$		0			0
$651$		−	4.71439i		−	0.184771i
$652$	−14.8055	−	21.6485i	−0.579830	−	0.847821i
$653$	15.4119	+	15.4119i	0.603114	+	0.603114i	0.941138	−	0.338024i	$-0.109758\pi$
$653$	15.4119	+	15.4119i	0.603114	+	0.603114i	−0.338024	+	0.941138i	$0.609758\pi$
$654$	2.98070	−	32.0351i	0.116554	−	1.25267i
$655$		0			0
$656$	9.62209	+	3.74435i	0.375679	+	0.146192i
$657$	2.21692	−	2.21692i	0.0864902	−	0.0864902i
$658$	3.63898	−	3.01945i	0.141862	−	0.117710i
$659$	−10.1563			−0.395635			−0.197817	−	0.980239i	$-0.563385\pi$
$659$	−10.1563			−0.395635			−0.197817	+	0.980239i	$0.563385\pi$
$660$		0			0
$661$	42.5695			1.65576			0.827880	−	0.560905i	$-0.189547\pi$
$661$	42.5695			1.65576			0.827880	+	0.560905i	$0.189547\pi$
$662$	−6.38114	+	5.29476i	−0.248010	+	0.205787i
$663$	−17.5156	+	17.5156i	−0.680248	+	0.680248i
$664$	9.55944	−	33.4538i	0.370978	−	1.29826i
$665$		0			0
$666$	1.30144	−	13.9872i	0.0504296	−	0.541992i
$667$	−5.84427	−	5.84427i	−0.226291	−	0.226291i
$668$	21.6445	−	14.8028i	0.837453	−	0.572739i
$669$		−	4.96608i		−	0.192000i
$670$		0			0
$671$			1.12704i			0.0435090i
$672$	2.54817	+	7.65064i	0.0982977	+	0.295130i
$673$	11.9276	+	11.9276i	0.459776	+	0.459776i	0.898582	−	0.438806i	$-0.144598\pi$
$673$	11.9276	+	11.9276i	0.459776	+	0.459776i	−0.438806	+	0.898582i	$0.644598\pi$
$674$	−5.41410	−	0.503754i	−0.208543	−	0.0194039i
$675$		0			0
$676$	−2.34450	−	0.440097i	−0.0901730	−	0.0169268i
$677$	31.6014	−	31.6014i	1.21454	−	1.21454i	0.245022	−	0.969518i	$-0.421205\pi$
$677$	31.6014	−	31.6014i	1.21454	−	1.21454i	0.969518	−	0.245022i	$-0.0787951\pi$
$678$	−13.2580	−	15.9782i	−0.509169	−	0.613640i
$679$	8.54621			0.327973
$680$		0			0
$681$	0.632565			0.0242399
$682$	−1.39472	−	1.68088i	−0.0534064	−	0.0643644i
$683$	−6.54248	+	6.54248i	−0.250341	+	0.250341i	−0.821110	−	0.570769i	$-0.806645\pi$
$683$	−6.54248	+	6.54248i	−0.250341	+	0.250341i	0.570769	+	0.821110i	$0.306645\pi$
$684$	−13.1056	−	2.46011i	−0.501104	−	0.0940646i
$685$		0			0
$686$	1.40813	+	0.131019i	0.0537627	+	0.00500234i
$687$	−3.76819	−	3.76819i	−0.143765	−	0.143765i
$688$	−9.45150	+	4.15619i	−0.360335	+	0.158453i
$689$			41.1119i			1.56624i
$690$		0			0
$691$			29.4625i			1.12081i	0.828219	+	0.560404i	$0.189354\pi$
$691$			29.4625i			1.12081i	−0.828219	+	0.560404i	$0.810646\pi$
$692$	−6.53266	+	4.46773i	−0.248334	+	0.169837i
$693$	−0.319634	−	0.319634i	−0.0121419	−	0.0121419i
$694$	2.10111	−	22.5817i	0.0797569	−	0.857188i
$695$		0			0
$696$	10.1607	+	2.90342i	0.385139	+	0.110054i
$697$	8.41885	−	8.41885i	0.318887	−	0.318887i
$698$	−26.8657	+	22.2918i	−1.01688	+	0.843758i
$699$	−27.5798			−1.04316
$700$		0			0
$701$	5.82092			0.219853			0.109926	−	0.993940i	$-0.464938\pi$
$701$	5.82092			0.219853			0.109926	+	0.993940i	$0.464938\pi$
$702$	23.1917	−	19.2433i	0.875314	−	0.726293i
$703$	49.9815	−	49.9815i	1.88509	−	1.88509i
$704$	3.17192	+	1.97393i	0.119546	+	0.0743953i
$705$		0			0
$706$	−2.61149	+	28.0670i	−0.0982846	+	1.05631i
$707$	−4.34841	−	4.34841i	−0.163539	−	0.163539i
$708$	−18.4414	−	26.9648i	−0.693071	−	1.01340i
$709$			7.42279i			0.278769i	0.990238	+	0.139384i	$0.0445124\pi$
$709$			7.42279i			0.278769i	−0.990238	+	0.139384i	$0.955488\pi$
$710$		0			0
$711$			2.82154i			0.105816i
$712$	−2.60356	−	4.68678i	−0.0975726	−	0.175645i
$713$	7.37453	+	7.37453i	0.276178	+	0.276178i
$714$	9.25868	+	0.861472i	0.346498	+	0.0322398i
$715$		0			0
$716$	5.00979	−	26.6883i	0.187225	−	0.997390i
$717$	17.5416	−	17.5416i	0.655102	−	0.655102i
$718$	−17.3840	−	20.9508i	−0.648765	−	0.781879i
$719$	14.8792			0.554902			0.277451	−	0.960740i	$-0.410510\pi$
$719$	14.8792			0.554902			0.277451	+	0.960740i	$0.410510\pi$
$720$		0			0
$721$	−3.46858			−0.129177
$722$	−25.6866	−	30.9570i	−0.955957	−	1.15210i
$723$	−22.2586	+	22.2586i	−0.827805	+	0.827805i
$724$	−7.33010	+	39.0491i	−0.272421	+	1.45125i
$725$		0			0
$726$	−21.6424	−	2.01371i	−0.803226	−	0.0747360i
$727$	24.2304	+	24.2304i	0.898655	+	0.898655i	0.995317	−	0.0966625i	$-0.0308168\pi$
$727$	24.2304	+	24.2304i	0.898655	+	0.898655i	−0.0966625	+	0.995317i	$0.530817\pi$
$728$	5.17451	+	9.31484i	0.191780	+	0.345231i
$729$			29.1831i			1.08085i
$730$		0			0
$731$			11.9060i			0.440361i
$732$	3.88416	+	5.67938i	0.143563	+	0.209916i
$733$	−7.24163	−	7.24163i	−0.267476	−	0.267476i	0.560607	−	0.828082i	$-0.310568\pi$
$733$	−7.24163	−	7.24163i	−0.267476	−	0.267476i	−0.828082	+	0.560607i	$0.810568\pi$
$734$	−2.45862	+	26.4241i	−0.0907494	+	0.975330i
$735$		0			0
$736$	−15.9536	−	7.98160i	−0.588057	−	0.294206i
$737$	5.04817	−	5.04817i	0.185952	−	0.185952i
$738$	−2.71925	+	2.25630i	−0.100097	+	0.0830556i
$739$	35.7816			1.31625			0.658123	−	0.752910i	$-0.271350\pi$
$739$	35.7816			1.31625			0.658123	+	0.752910i	$0.271350\pi$
$740$		0			0
$741$	36.9906			1.35888
$742$	11.8768	−	9.85481i	0.436012	−	0.361781i
$743$	1.83282	−	1.83282i	0.0672397	−	0.0672397i	−0.672687	−	0.739927i	$-0.734860\pi$
$743$	1.83282	−	1.83282i	0.0672397	−	0.0672397i	0.739927	+	0.672687i	$0.234860\pi$
$744$	−12.8211	−	3.66364i	−0.470045	−	0.134316i
$745$		0			0
$746$	−1.56759	+	16.8477i	−0.0573936	+	0.616839i
$747$	8.41946	+	8.41946i	0.308052	+	0.308052i
$748$	3.55599	−	2.43196i	0.130020	−	0.0889213i
$749$		−	9.57962i		−	0.350032i
$750$		0			0
$751$		−	1.38920i		−	0.0506926i	−0.999679	−	0.0253463i	$-0.991931\pi$
$751$		−	1.38920i		−	0.0506926i	0.999679	−	0.0253463i	$-0.00806884\pi$
$752$	−5.38369	−	12.2429i	−0.196323	−	0.446454i
$753$	−25.2899	−	25.2899i	−0.921614	−	0.921614i
$754$	13.9037	+	1.29367i	0.506343	+	0.0471126i
$755$		0			0
$756$	−11.1184	−	2.08709i	−0.404373	−	0.0759068i
$757$	−17.0976	+	17.0976i	−0.621423	+	0.621423i	−0.945895	−	0.324473i	$-0.894813\pi$
$757$	−17.0976	+	17.0976i	−0.621423	+	0.621423i	0.324473	+	0.945895i	$0.394813\pi$
$758$	−11.9430	−	14.3934i	−0.433788	−	0.522792i
$759$	−2.09928			−0.0761992
$760$		0			0
$761$	45.7228			1.65745			0.828725	−	0.559656i	$-0.189067\pi$
$761$	45.7228			1.65745			0.828725	+	0.559656i	$0.189067\pi$
$762$	−13.2090	−	15.9192i	−0.478512	−	0.576693i
$763$	−11.2850	+	11.2850i	−0.408544	+	0.408544i
$764$	−29.3940	−	5.51769i	−1.06344	−	0.199623i
$765$		0			0
$766$	−38.7475	−	3.60526i	−1.40001	−	0.130263i
$767$	−30.5240	−	30.5240i	−1.10216	−	1.10216i
$768$	22.7867	−	0.984468i	0.822245	−	0.0355239i
$769$		−	18.3997i		−	0.663512i	−0.943365	−	0.331756i	$-0.892359\pi$
$769$		−	18.3997i		−	0.663512i	0.943365	−	0.331756i	$-0.107641\pi$
$770$		0			0
$771$			12.1933i			0.439132i
$772$	10.5706	−	7.22933i	0.380446	−	0.260189i
$773$	14.9907	+	14.9907i	0.539179	+	0.539179i	0.923288	−	0.384109i	$-0.125491\pi$
$773$	14.9907	+	14.9907i	0.539179	+	0.539179i	−0.384109	+	0.923288i	$0.625491\pi$
$774$	0.327354	−	3.51825i	0.0117665	−	0.126461i
$775$		0			0
$776$	6.64142	−	23.2420i	0.238413	−	0.834341i
$777$	10.3439	−	10.3439i	0.371085	−	0.371085i
$778$	11.5784	−	9.60718i	0.415105	−	0.344434i
$779$	−17.7795			−0.637017
$780$		0			0
$781$	4.49254			0.160756
$782$	−15.8306	+	13.1354i	−0.566100	+	0.469722i
$783$	−10.4827	+	10.4827i	−0.374621	+	0.374621i
$784$	1.45060	−	3.72770i	0.0518073	−	0.133132i
$785$		0			0
$786$	1.31855	−	14.1712i	0.0470312	−	0.505468i
$787$	−13.0374	−	13.0374i	−0.464733	−	0.464733i	0.435470	−	0.900203i	$-0.356582\pi$
$787$	−13.0374	−	13.0374i	−0.464733	−	0.464733i	−0.900203	+	0.435470i	$0.856582\pi$
$788$	−4.03166	−	5.89505i	−0.143622	−	0.210002i
$789$		−	22.9255i		−	0.816170i
$790$		0			0
$791$			10.2990i			0.366191i
$792$	−1.11766	+	0.620875i	−0.0397144	+	0.0220618i
$793$	6.42902	+	6.42902i	0.228301	+	0.228301i
$794$	−6.77145	−	0.630048i	−0.240310	−	0.0223596i
$795$		0			0
$796$	0.851172	−	4.53439i	0.0301690	−	0.160717i
$797$	−38.5000	+	38.5000i	−1.36374	+	1.36374i	−0.494645	+	0.869095i	$0.664702\pi$
$797$	−38.5000	+	38.5000i	−1.36374	+	1.36374i	−0.869095	+	0.494645i	$0.835298\pi$
$798$	−8.86691	−	10.6862i	−0.313885	−	0.378288i
$799$	−15.4224			−0.545606
$800$		0			0
$801$	1.83479			0.0648292
$802$	9.53986	+	11.4973i	0.336864	+	0.405982i
$803$	1.06957	−	1.06957i	0.0377442	−	0.0377442i
$804$	8.04101	−	42.8363i	0.283585	−	1.51072i
$805$		0			0
$806$	−17.5442	−	1.63240i	−0.617969	−	0.0574988i
$807$	−6.80975	−	6.80975i	−0.239714	−	0.239714i
$808$	−15.2051	+	8.44660i	−0.534913	+	0.297150i
$809$		−	37.6505i		−	1.32372i	−0.749627	−	0.661860i	$-0.769767\pi$
$809$		−	37.6505i		−	1.32372i	0.749627	−	0.661860i	$-0.230233\pi$
$810$		0			0
$811$		−	24.3635i		−	0.855518i	−0.903893	−	0.427759i	$-0.859303\pi$
$811$		−	24.3635i		−	0.855518i	0.903893	−	0.427759i	$-0.140697\pi$
$812$	−2.95909	−	4.32675i	−0.103844	−	0.151839i
$813$	−4.34195	−	4.34195i	−0.152279	−	0.152279i
$814$	0.627887	−	6.74822i	0.0220074	−	0.236525i
$815$		0			0
$816$	9.53794	−	24.5102i	0.333895	−	0.858029i
$817$	12.5720	−	12.5720i	0.439839	−	0.439839i
$818$	−30.9816	+	25.7070i	−1.08325	+	0.898824i
$819$	−3.64659			−0.127422
$820$		0			0
$821$	32.8874			1.14778			0.573888	−	0.818934i	$-0.305434\pi$
$821$	32.8874			1.14778			0.573888	+	0.818934i	$0.305434\pi$
$822$	11.9046	−	9.87783i	0.415220	−	0.344529i
$823$	−14.0730	+	14.0730i	−0.490553	+	0.490553i	−0.908480	−	0.417928i	$-0.862757\pi$
$823$	−14.0730	+	14.0730i	−0.490553	+	0.490553i	0.417928	+	0.908480i	$0.362757\pi$
$824$	−2.69550	+	9.43307i	−0.0939023	+	0.328616i
$825$		0			0
$826$	−1.50127	+	16.1349i	−0.0522359	+	0.561406i
$827$	23.0627	+	23.0627i	0.801970	+	0.801970i	0.983403	−	0.181433i	$-0.0580737\pi$
$827$	23.0627	+	23.0627i	0.801970	+	0.801970i	−0.181433	+	0.983403i	$0.558074\pi$
$828$	5.03910	−	3.44627i	0.175121	−	0.119766i
$829$			11.6584i			0.404912i	0.979291	+	0.202456i	$0.0648923\pi$
$829$			11.6584i			0.404912i	−0.979291	+	0.202456i	$0.935108\pi$
$830$		0			0
$831$		−	41.4876i		−	1.43919i
$832$	29.3536	−	6.83371i	1.01765	−	0.236916i
$833$	−3.26155	−	3.26155i	−0.113006	−	0.113006i
$834$	36.5719	+	3.40282i	1.26638	+	0.117830i
$835$		0			0
$836$	−6.32288	−	1.18690i	−0.218681	−	0.0410497i
$837$	13.2275	−	13.2275i	0.457208	−	0.457208i
$838$	15.8183	+	19.0639i	0.546434	+	0.658551i
$839$	−11.4626			−0.395732			−0.197866	−	0.980229i	$-0.563401\pi$
$839$	−11.4626			−0.395732			−0.197866	+	0.980229i	$0.563401\pi$
$840$		0			0
$841$	22.1308			0.763129
$842$	9.62363	+	11.5982i	0.331652	+	0.399701i
$843$	9.50907	−	9.50907i	0.327510	−	0.327510i
$844$	−55.8200	−	10.4782i	−1.92141	−	0.360676i
$845$		0			0
$846$	4.55734	+	0.424037i	0.156685	+	0.0145787i
$847$	7.62396	+	7.62396i	0.261963	+	0.261963i
$848$	−17.5712	−	39.9583i	−0.603397	−	1.37217i
$849$		−	9.04883i		−	0.310555i
$850$		0			0
$851$			32.3611i			1.10933i
$852$	22.6388	−	15.4828i	0.775592	−	0.530432i
$853$	−0.313030	−	0.313030i	−0.0107179	−	0.0107179i	0.701728	−	0.712445i	$-0.252412\pi$
$853$	−0.313030	−	0.313030i	−0.0107179	−	0.0107179i	−0.712445	+	0.701728i	$0.752412\pi$
$854$	0.316200	−	3.39836i	0.0108201	−	0.116290i
$855$		0			0
$856$	−26.0525	−	7.44451i	−0.890456	−	0.254448i
$857$	15.7609	−	15.7609i	0.538382	−	0.538382i	−0.384672	−	0.923053i	$-0.625685\pi$
$857$	15.7609	−	15.7609i	0.538382	−	0.538382i	0.923053	+	0.384672i	$0.125685\pi$
$858$	2.72948	−	2.26479i	0.0931828	−	0.0773185i
$859$	−6.31565			−0.215487			−0.107744	−	0.994179i	$-0.534363\pi$
$859$	−6.31565			−0.215487			−0.107744	+	0.994179i	$0.534363\pi$
$860$		0			0
$861$	−3.67955			−0.125399
$862$	−42.3818	+	35.1663i	−1.44353	+	1.19777i
$863$	−16.9489	+	16.9489i	−0.576948	+	0.576948i	−0.934061	−	0.357113i	$-0.883761\pi$
$863$	−16.9489	+	16.9489i	−0.576948	+	0.576948i	0.357113	+	0.934061i	$0.383761\pi$
$864$	−14.3164	+	28.6155i	−0.487052	+	0.973518i
$865$		0			0
$866$	−1.17129	+	12.5884i	−0.0398019	+	0.427771i
$867$	−4.30956	−	4.30956i	−0.146360	−	0.146360i
$868$	3.73390	+	5.45966i	0.126737	+	0.185313i
$869$			1.36127i			0.0461781i
$870$		0			0
$871$		−	57.5928i		−	1.95146i
$872$	21.9206	+	39.4601i	0.742324	+	1.33629i
$873$	5.84942	+	5.84942i	0.197973	+	0.197973i
$874$	30.5862	+	2.84589i	1.03459	+	0.0962636i
$875$		0			0
$876$	1.70367	−	9.07584i	0.0575616	−	0.306644i
$877$	−29.8260	+	29.8260i	−1.00715	+	1.00715i	−0.00717832	+	0.999974i	$0.502285\pi$
$877$	−29.8260	+	29.8260i	−1.00715	+	1.00715i	−0.999974	+	0.00717832i	$0.997715\pi$
$878$	24.4092	+	29.4175i	0.823770	+	0.992792i
$879$	−0.717244			−0.0241920
$880$		0			0
$881$	−29.4140			−0.990982			−0.495491	−	0.868613i	$-0.665012\pi$
$881$	−29.4140			−0.990982			−0.495491	+	0.868613i	$0.665012\pi$
$882$	0.874115	+	1.05347i	0.0294330	+	0.0354721i
$883$	9.65095	−	9.65095i	0.324780	−	0.324780i	−0.525817	−	0.850598i	$-0.676240\pi$
$883$	9.65095	−	9.65095i	0.324780	−	0.324780i	0.850598	+	0.525817i	$0.176240\pi$
$884$	6.41181	−	34.1572i	0.215652	−	1.14883i
$885$		0			0
$886$	−24.3545	−	2.26606i	−0.818205	−	0.0761297i
$887$	−14.3225	−	14.3225i	−0.480901	−	0.480901i	0.424518	−	0.905419i	$-0.360444\pi$
$887$	−14.3225	−	14.3225i	−0.480901	−	0.480901i	−0.905419	+	0.424518i	$0.860444\pi$
$888$	−20.0926	−	36.1695i	−0.674262	−	1.21377i
$889$			10.2610i			0.344142i
$890$		0			0
$891$			2.40933i			0.0807156i
$892$	3.93324	+	5.75114i	0.131695	+	0.192562i
$893$	16.2851	+	16.2851i	0.544959	+	0.544959i
$894$	−2.86263	+	30.7662i	−0.0957407	+	1.02897i
$895$		0			0
$896$	−9.01047	−	6.84189i	−0.301019	−	0.228572i
$897$	−11.9750	+	11.9750i	−0.399834	+	0.399834i
$898$	3.10026	−	2.57244i	0.103457	−	0.0858435i
$899$	8.66788			0.289090
$900$		0			0
$901$	−50.3354			−1.67692
$902$	−1.31192	+	1.08857i	−0.0436822	+	0.0362454i
$903$	2.60184	−	2.60184i	0.0865837	−	0.0865837i
$904$	28.0089	+	8.00357i	0.931563	+	0.266195i
$905$		0			0
$906$	0.143716	−	1.54459i	0.00477463	−	0.0513154i
$907$	−12.3374	−	12.3374i	−0.409657	−	0.409657i	0.471962	−	0.881619i	$-0.343546\pi$
$907$	−12.3374	−	12.3374i	−0.409657	−	0.409657i	−0.881619	+	0.471962i	$0.843546\pi$
$908$	−0.732564	+	0.501005i	−0.0243110	+	0.0166264i
$909$		−	5.95251i		−	0.197432i
$910$		0			0
$911$		−	58.6655i		−	1.94368i	−0.235652	−	0.971838i	$-0.575723\pi$
$911$		−	58.6655i		−	1.94368i	0.235652	−	0.971838i	$-0.424277\pi$
$912$	−35.9526	+	15.8097i	−1.19051	+	0.523513i
$913$	4.06203	+	4.06203i	0.134433	+	0.134433i
$914$	−19.1201	−	1.77902i	−0.632435	−	0.0588448i
$915$		0			0
$916$	7.34837	+	1.37940i	0.242797	+	0.0455766i
$917$	−4.99207	+	4.99207i	−0.164853	+	0.164853i
$918$	23.5606	+	28.3948i	0.777616	+	0.937168i
$919$	54.8655			1.80985			0.904923	−	0.425575i	$-0.139928\pi$
$919$	54.8655			1.80985			0.904923	+	0.425575i	$0.139928\pi$
$920$		0			0
$921$	−17.4142			−0.573817
$922$	9.40279	+	11.3321i	0.309664	+	0.373201i
$923$	25.6269	−	25.6269i	0.843521	−	0.843521i
$924$	−1.30855	−	0.245634i	−0.0430481	−	0.00808077i
$925$		0			0
$926$	28.1816	+	2.62215i	0.926105	+	0.0861692i
$927$	−2.37406	−	2.37406i	−0.0779743	−	0.0779743i
$928$	−14.0665	+	4.68507i	−0.461755	+	0.153795i
$929$			27.2841i			0.895162i	0.894243	+	0.447581i	$0.147714\pi$
$929$			27.2841i			0.895162i	−0.894243	+	0.447581i	$0.852286\pi$
$930$		0			0
$931$			6.88797i			0.225744i
$932$	31.9398	−	21.8438i	1.04622	−	0.715517i
$933$	−14.6672	−	14.6672i	−0.480183	−	0.480183i
$934$	−1.13016	+	12.1464i	−0.0369799	+	0.397441i
$935$		0			0
$936$	−2.83384	+	9.91719i	−0.0926269	+	0.324153i
$937$	11.9859	−	11.9859i	0.391562	−	0.391562i	−0.483682	−	0.875244i	$-0.660701\pi$
$937$	11.9859	−	11.9859i	0.391562	−	0.391562i	0.875244	+	0.483682i	$0.160701\pi$
$938$	−16.6380	+	13.8054i	−0.543250	+	0.450763i
$939$	−27.4353			−0.895317
$940$		0			0
$941$	−13.7804			−0.449228			−0.224614	−	0.974448i	$-0.572112\pi$
$941$	−13.7804			−0.449228			−0.224614	+	0.974448i	$0.572112\pi$
$942$	18.7074	−	15.5225i	0.609520	−	0.505750i
$943$	5.75578	−	5.75578i	0.187434	−	0.187434i
$944$	42.7135	+	16.6216i	1.39020	+	0.540986i
$945$		0			0
$946$	0.157935	−	1.69740i	0.00513489	−	0.0551873i
$947$	17.8666	+	17.8666i	0.580586	+	0.580586i	0.935064	−	0.354478i	$-0.115341\pi$
$947$	17.8666	+	17.8666i	0.580586	+	0.580586i	−0.354478	+	0.935064i	$0.615341\pi$
$948$	4.69140	+	6.85972i	0.152370	+	0.222793i
$949$		−	12.2023i		−	0.396105i
$950$		0			0
$951$			2.75644i			0.0893837i
$952$	−11.4046	+	6.33542i	−0.369627	+	0.205332i
$953$	−14.0596	−	14.0596i	−0.455434	−	0.455434i	0.441719	−	0.897153i	$-0.354369\pi$
$953$	−14.0596	−	14.0596i	−0.455434	−	0.455434i	−0.897153	+	0.441719i	$0.854369\pi$
$954$	14.8741	+	1.38396i	0.481568	+	0.0448074i
$955$		0			0
$956$	−6.42134	+	34.2080i	−0.207681	+	1.10636i
$957$	−1.23373	+	1.23373i	−0.0398808	+	0.0398808i
$958$	−10.9016	−	13.1384i	−0.352215	−	0.424483i
$959$	−7.67328			−0.247783
$960$		0			0
$961$	20.0625			0.647179
$962$	−34.9124	−	42.0757i	−1.12562	−	1.35658i
$963$	6.55674	−	6.55674i	0.211288	−	0.211288i
$964$	8.14805	−	43.4066i	0.262431	−	1.39803i
$965$		0			0
$966$	6.32996	+	0.588970i	0.203663	+	0.0189498i
$967$	14.0654	+	14.0654i	0.452314	+	0.452314i	0.896122	−	0.443808i	$-0.146373\pi$
$967$	14.0654	+	14.0654i	0.452314	+	0.452314i	−0.443808	+	0.896122i	$0.646373\pi$
$968$	26.6587	−	14.8092i	0.856842	−	0.475986i
$969$			45.2895i			1.45491i
$970$		0			0
$971$			32.5677i			1.04515i	0.852594	+	0.522574i	$0.175028\pi$
$971$			32.5677i			1.04515i	−0.852594	+	0.522574i	$0.824972\pi$
$972$	−10.8550	−	15.8721i	−0.348175	−	0.509097i
$973$	−12.8831	−	12.8831i	−0.413015	−	0.413015i
$974$	3.91932	−	42.1229i	0.125583	−	1.34971i
$975$		0			0
$976$	−8.99638	−	3.50086i	−0.287967	−	0.112060i
$977$	−38.5553	+	38.5553i	−1.23349	+	1.23349i	−0.270880	+	0.962613i	$0.587315\pi$
$977$	−38.5553	+	38.5553i	−1.23349	+	1.23349i	−0.962613	+	0.270880i	$0.912685\pi$
$978$	20.3448	−	16.8811i	0.650555	−	0.539799i
$979$	0.885208			0.0282914
$980$		0			0
$981$	−15.4479			−0.493214
$982$	−20.9599	+	17.3915i	−0.668857	+	0.554985i
$983$	−7.67704	+	7.67704i	−0.244860	+	0.244860i	−0.818857	−	0.573997i	$-0.805392\pi$
$983$	−7.67704	+	7.67704i	−0.244860	+	0.244860i	0.573997	+	0.818857i	$0.305392\pi$
$984$	−2.85945	+	10.0068i	−0.0911560	+	0.319006i
$985$		0			0
$986$	−1.58391	+	17.0230i	−0.0504418	+	0.542124i
$987$	3.37027	+	3.37027i	0.107277	+	0.107277i
$988$	−42.8382	+	29.2973i	−1.36287	+	0.932072i
$989$			8.13991i			0.258834i
$990$		0			0
$991$		−	17.6551i		−	0.560832i	−0.959879	−	0.280416i	$-0.909528\pi$
$991$		−	17.6551i		−	0.560832i	0.959879	−	0.280416i	$-0.0904724\pi$
$992$	17.7496	−	5.91180i	0.563552	−	0.187700i
$993$	−5.90996	−	5.90996i	−0.187547	−	0.187547i
$994$	−13.5463	−	1.26042i	−0.429664	−	0.0399780i
$995$		0			0
$996$	34.4684	+	6.47023i	1.09217	+	0.205017i
$997$	22.0269	−	22.0269i	0.697598	−	0.697598i	−0.266294	−	0.963892i	$-0.585799\pi$
$997$	22.0269	−	22.0269i	0.697598	−	0.697598i	0.963892	+	0.266294i	$0.0857993\pi$
$998$	−8.56931	−	10.3276i	−0.271257	−	0.326913i
$999$	58.0452			1.83647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.k.b.43.5		36
4.3	odd	2	inner	700.2.k.b.43.14		36
5.2	odd	4	inner	700.2.k.b.407.14		36
5.3	odd	4		140.2.k.a.127.5	yes	36
5.4	even	2		140.2.k.a.43.14	yes	36
20.3	even	4		140.2.k.a.127.14	yes	36
20.7	even	4	inner	700.2.k.b.407.5		36
20.19	odd	2		140.2.k.a.43.5	✓	36
35.3	even	12		980.2.x.l.667.8		72
35.4	even	6		980.2.x.k.863.2		72
35.9	even	6		980.2.x.k.263.12		72
35.13	even	4		980.2.k.l.687.5		36
35.18	odd	12		980.2.x.k.667.8		72
35.19	odd	6		980.2.x.l.263.12		72
35.23	odd	12		980.2.x.k.67.16		72
35.24	odd	6		980.2.x.l.863.2		72
35.33	even	12		980.2.x.l.67.16		72
35.34	odd	2		980.2.k.l.883.14		36
140.3	odd	12		980.2.x.l.667.12		72
140.19	even	6		980.2.x.l.263.8		72
140.23	even	12		980.2.x.k.67.2		72
140.39	odd	6		980.2.x.k.863.16		72
140.59	even	6		980.2.x.l.863.16		72
140.79	odd	6		980.2.x.k.263.8		72
140.83	odd	4		980.2.k.l.687.14		36
140.103	odd	12		980.2.x.l.67.2		72
140.123	even	12		980.2.x.k.667.12		72
140.139	even	2		980.2.k.l.883.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.5	✓	36	20.19	odd	2
140.2.k.a.43.14	yes	36	5.4	even	2
140.2.k.a.127.5	yes	36	5.3	odd	4
140.2.k.a.127.14	yes	36	20.3	even	4
700.2.k.b.43.5		36	1.1	even	1	trivial
700.2.k.b.43.14		36	4.3	odd	2	inner
700.2.k.b.407.5		36	20.7	even	4	inner
700.2.k.b.407.14		36	5.2	odd	4	inner
980.2.k.l.687.5		36	35.13	even	4
980.2.k.l.687.14		36	140.83	odd	4
980.2.k.l.883.5		36	140.139	even	2
980.2.k.l.883.14		36	35.34	odd	2
980.2.x.k.67.2		72	140.23	even	12
980.2.x.k.67.16		72	35.23	odd	12
980.2.x.k.263.8		72	140.79	odd	6
980.2.x.k.263.12		72	35.9	even	6
980.2.x.k.667.8		72	35.18	odd	12
980.2.x.k.667.12		72	140.123	even	12
980.2.x.k.863.2		72	35.4	even	6
980.2.x.k.863.16		72	140.39	odd	6
980.2.x.l.67.2		72	140.103	odd	12
980.2.x.l.67.16		72	35.33	even	12
980.2.x.l.263.8		72	140.19	even	6
980.2.x.l.263.12		72	35.19	odd	6
980.2.x.l.667.8		72	35.3	even	12
980.2.x.l.667.12		72	140.3	odd	12
980.2.x.l.863.2		72	35.24	odd	6
980.2.x.l.863.16		72	140.59	even	6

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.903055 - 1.08834i) q^{2} +(1.00798 - 1.00798i) q^{3} +(-0.368985 + 1.96567i) q^{4} +(-2.00729 - 0.186768i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.47254 - 1.37352i) q^{8} +0.967954i q^{9} +O(q^{10})\)	\(q+(-0.903055 - 1.08834i) q^{2} +(1.00798 - 1.00798i) q^{3} +(-0.368985 + 1.96567i) q^{4} +(-2.00729 - 0.186768i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.47254 - 1.37352i) q^{8} +0.967954i q^{9} +0.466996i q^{11} +(1.60942 + 2.35328i) q^{12} +(2.66390 + 2.66390i) q^{13} +(0.131019 - 1.40813i) q^{14} +(-3.72770 - 1.45060i) q^{16} +(-3.26155 + 3.26155i) q^{17} +(1.05347 - 0.874115i) q^{18} +6.88797 q^{19} +1.42550 q^{21} +(0.508252 - 0.421723i) q^{22} +(-2.22985 + 2.22985i) q^{23} +(1.10778 - 3.87675i) q^{24} +(0.493592 - 5.30489i) q^{26} +(3.99962 + 3.99962i) q^{27} +(-1.65085 + 1.12903i) q^{28} +2.62093i q^{29} -3.30718i q^{31} +(1.78756 + 5.36699i) q^{32} +(0.470723 + 0.470723i) q^{33} +(6.49505 + 0.604331i) q^{34} +(-1.90268 - 0.357160i) q^{36} +(7.25634 - 7.25634i) q^{37} +(-6.22021 - 7.49648i) q^{38} +5.37031 q^{39} -2.58124 q^{41} +(-1.28730 - 1.55143i) q^{42} +(1.82521 - 1.82521i) q^{43} +(-0.917960 - 0.172314i) q^{44} +(4.44052 + 0.413168i) q^{46} +(2.36428 + 2.36428i) q^{47} +(-5.21962 + 2.29527i) q^{48} +1.00000i q^{49} +6.57516i q^{51} +(-6.21928 + 4.25340i) q^{52} +(7.71648 + 7.71648i) q^{53} +(0.741086 - 7.96483i) q^{54} +(2.71957 + 0.777119i) q^{56} +(6.94294 - 6.94294i) q^{57} +(2.85247 - 2.36684i) q^{58} -11.4584 q^{59} +2.41339 q^{61} +(-3.59935 + 2.98657i) q^{62} +(-0.684447 + 0.684447i) q^{63} +(4.22687 - 6.79217i) q^{64} +(0.0872199 - 0.937397i) q^{66} +(-10.8099 - 10.8099i) q^{67} +(-5.20766 - 7.61459i) q^{68} +4.49529i q^{69} -9.62009i q^{71} +(1.32951 + 2.39330i) q^{72} +(-2.29031 - 2.29031i) q^{73} +(-14.4503 - 1.34452i) q^{74} +(-2.54156 + 13.5395i) q^{76} +(-0.330216 + 0.330216i) q^{77} +(-4.84969 - 5.84475i) q^{78} +2.91496 q^{79} +5.15920 q^{81} +(2.33100 + 2.80928i) q^{82} +(8.69820 - 8.69820i) q^{83} +(-0.525987 + 2.80206i) q^{84} +(-3.63472 - 0.338192i) q^{86} +(2.64184 + 2.64184i) q^{87} +(0.641430 + 1.15467i) q^{88} -1.89554i q^{89} +3.76732i q^{91} +(-3.56037 - 5.20593i) q^{92} +(-3.33357 - 3.33357i) q^{93} +(0.438075 - 4.70822i) q^{94} +(7.21165 + 3.60799i) q^{96} +(6.04308 - 6.04308i) q^{97} +(1.08834 - 0.903055i) q^{98} -0.452031 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{6}+O(q^{10}) \) 36 * q - 8 * q^6	\( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

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