LMFDB - Embedded newform 700.2.k.b.43.14

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			43.14
Character	$\chi$	$=$	700.43
Dual form			700.2.k.b.407.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08834 + 0.903055i) q^{2} +(-1.00798 + 1.00798i) q^{3} +(0.368985 + 1.96567i) q^{4} +(-2.00729 + 0.186768i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.37352 + 2.47254i) q^{8} +0.967954i q^{9} +O(q^{10})$	\(q+(1.08834 + 0.903055i) 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} +(-1.37352 + 2.47254i) q^{8} +0.967954i q^{9} -0.466996i q^{11} +(-2.35328 - 1.60942i) 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} +(-0.874115 + 1.05347i) q^{18} -6.88797 q^{19} +1.42550 q^{21} +(0.421723 - 0.508252i) 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} +(1.12903 - 1.65085i) q^{28} +2.62093i q^{29} +3.30718i q^{31} +(-5.36699 - 1.78756i) 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} +(-7.49648 - 6.22021i) q^{38} -5.37031 q^{39} -2.58124 q^{41} +(1.55143 + 1.28730i) 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} +(2.29527 - 5.21962i) q^{48} +1.00000i q^{49} -6.57516i q^{51} +(-4.25340 + 6.21928i) 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} +(-2.36684 + 2.85247i) q^{58} +11.4584 q^{59} +2.41339 q^{61} +(-2.98657 + 3.59935i) 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} +(-7.61459 - 5.20766i) q^{68} +4.49529i q^{69} +9.62009i q^{71} +(-2.39330 - 1.32951i) 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} +(-5.84475 - 4.84969i) q^{78} -2.91496 q^{79} +5.15920 q^{81} +(-2.80928 - 2.33100i) 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} +(1.15467 + 0.641430i) q^{88} -1.89554i q^{89} -3.76732i q^{91} +(5.20593 + 3.56037i) 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} +(-0.903055 + 1.08834i) 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 $

$2$	1.08834	+	0.903055i	0.769575	+	0.638556i
$2$	1.08834	+	0.903055i	0.769575	+	0.638556i
$3$	−1.00798	+	1.00798i	−0.581957	+	0.581957i	−0.935441	−	0.353483i	$-0.884997\pi$
$3$	−1.00798	+	1.00798i	−0.581957	+	0.581957i	0.353483	+	0.935441i	$0.384997\pi$
$4$	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
$8$	−1.37352	+	2.47254i	−0.485614	+	0.874173i
$9$			0.967954i			0.322651i
$10$		0			0
$11$		−	0.466996i		−	0.140805i	−0.997519	−	0.0704023i	$-0.977572\pi$
$11$		−	0.466996i		−	0.140805i	0.997519	−	0.0704023i	$-0.0224283\pi$
$12$	−2.35328	−	1.60942i	−0.679334	−	0.464601i
$13$	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	$0.438950\pi$
$18$	−0.874115	+	1.05347i	−0.206031	+	0.248304i
$19$	−6.88797			−1.58021			−0.790105	−	0.612972i	$-0.789974\pi$
$19$	−6.88797			−1.58021			−0.790105	+	0.612972i	$0.789974\pi$
$20$		0			0
$21$	1.42550			0.311069
$22$	0.421723	−	0.508252i	0.0899117	−	0.108360i
$23$	2.22985	−	2.22985i	0.464956	−	0.464956i	−0.435320	−	0.900276i	$-0.643365\pi$
$23$	2.22985	−	2.22985i	0.464956	−	0.464956i	0.900276	+	0.435320i	$0.143365\pi$
$24$	−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
$28$	1.12903	−	1.65085i	0.213366	−	0.311981i
$29$			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	$0.0959841\pi$
$31$			3.30718i			0.593988i	−0.954879	+	0.296994i	$0.904016\pi$
$32$	−5.36699	−	1.78756i	−0.948759	−	0.315999i
$33$	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	$-0.0695280\pi$
$38$	−7.49648	−	6.22021i	−1.21609	−	1.00905i
$39$	−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	$0.564601\pi$
$42$	1.55143	+	1.28730i	0.239391	+	0.198635i
$43$	−1.82521	+	1.82521i	−0.278342	+	0.278342i	−0.832447	−	0.554105i	$-0.813061\pi$
$43$	−1.82521	+	1.82521i	−0.278342	+	0.278342i	0.554105	+	0.832447i	$0.313061\pi$
$44$	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	0.513327	−	0.858193i	$-0.328413\pi$
$47$	−2.36428	−	2.36428i	−0.344865	−	0.344865i	−0.858193	+	0.513327i	$0.828413\pi$
$48$	2.29527	−	5.21962i	0.331293	−	0.753388i
$49$			1.00000i			0.142857i
$50$		0			0
$51$		−	6.57516i		−	0.920706i
$52$	−4.25340	+	6.21928i	−0.589841	+	0.862459i
$53$	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
$58$	−2.36684	+	2.85247i	−0.310781	+	0.374547i
$59$	11.4584			1.49176			0.745878	−	0.666083i	$-0.232030\pi$
$59$	11.4584			1.49176			0.745878	+	0.666083i	$0.232030\pi$
$60$		0			0
$61$	2.41339			0.309002			0.154501	−	0.987993i	$-0.450623\pi$
$61$	2.41339			0.309002			0.154501	+	0.987993i	$0.450623\pi$
$62$	−2.98657	+	3.59935i	−0.379294	+	0.457118i
$63$	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	$0.133556\pi$
$67$	10.8099	+	10.8099i	1.32064	+	1.32064i	0.407374	+	0.913261i	$0.366444\pi$
$68$	−7.61459	−	5.20766i	−0.923405	−	0.631522i
$69$			4.49529i			0.541169i
$70$		0			0
$71$			9.62009i			1.14169i	0.821056	+	0.570847i	$0.193385\pi$
$71$			9.62009i			1.14169i	−0.821056	+	0.570847i	$0.806615\pi$
$72$	−2.39330	−	1.32951i	−0.282053	−	0.156684i
$73$	−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
$78$	−5.84475	−	4.84969i	−0.661787	−	0.549119i
$79$	−2.91496			−0.327958			−0.163979	−	0.986464i	$-0.552433\pi$
$79$	−2.91496			−0.327958			−0.163979	+	0.986464i	$0.552433\pi$
$80$		0			0
$81$	5.15920			0.573245
$82$	−2.80928	−	2.33100i	−0.310233	−	0.257416i
$83$	−8.69820	+	8.69820i	−0.954752	+	0.954752i	−0.999020	−	0.0442680i	$-0.985904\pi$
$83$	−8.69820	+	8.69820i	−0.954752	+	0.954752i	0.0442680	+	0.999020i	$0.485904\pi$
$84$	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
$88$	1.15467	+	0.641430i	0.123088	+	0.0683767i
$89$		−	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
$92$	5.20593	+	3.56037i	0.542756	+	0.371194i
$93$	−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	$0.107148\pi$
$98$	−0.903055	+	1.08834i	−0.0912223	+	0.109939i
$99$	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	$0.598975\pi$
$102$	5.93773	−	7.15603i	0.587922	−	0.708553i
$103$	2.45266	−	2.45266i	0.241668	−	0.241668i	−0.575872	−	0.817540i	$-0.695337\pi$
$103$	2.45266	−	2.45266i	0.241668	−	0.241668i	0.817540	+	0.575872i	$0.195337\pi$
$104$	−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	0.954157	−	0.299307i	$-0.0967556\pi$
$107$	6.77382	+	6.77382i	0.654850	+	0.654850i	−0.299307	+	0.954157i	$0.596756\pi$
$108$	6.38612	−	9.33772i	0.614505	−	0.898522i
$109$			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
$112$	3.66161	+	1.61015i	0.345990	+	0.152145i
$113$	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
$118$	12.4707	+	10.3476i	1.14802	+	0.952570i
$119$	4.61253			0.422830
$120$		0			0
$121$	10.7819			0.980174
$122$	2.62659	+	2.17942i	0.237801	+	0.197315i
$123$	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	0.307664	−	0.951495i	$-0.400453\pi$
$127$	−7.25561	−	7.25561i	−0.643832	−	0.643832i	−0.951495	+	0.307664i	$0.900453\pi$
$128$	1.53341	−	11.2093i	0.135536	−	0.990772i
$129$		−	3.67955i		−	0.323967i
$130$		0			0
$131$		−	7.05985i		−	0.616822i	−0.951253	−	0.308411i	$-0.900203\pi$
$131$		−	7.05985i		−	0.616822i	0.951253	−	0.308411i	$-0.0997972\pi$
$132$	−0.751595	+	1.09897i	−0.0654180	+	0.0956534i
$133$	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	$0.356303\pi$
$138$	−4.05949	+	4.89242i	−0.345567	+	0.416471i
$139$	18.2195			1.54536			0.772680	−	0.634796i	$-0.218916\pi$
$139$	18.2195			1.54536			0.772680	+	0.634796i	$0.218916\pi$
$140$		0			0
$141$	4.76629			0.401394
$142$	−8.68746	+	10.4700i	−0.729036	+	0.878620i
$143$	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
$148$	16.9410	+	11.5861i	1.39254	+	0.952370i
$149$		−	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	$-0.990032\pi$
$151$		−	0.769488i		−	0.0626201i	0.999510	−	0.0313100i	$-0.00996792\pi$
$152$	9.46079	−	17.0308i	0.767371	−	1.38138i
$153$	−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	$0.409789\pi$
$158$	−3.17248	−	2.63237i	−0.252389	−	0.209420i
$159$	−15.5561			−1.23368
$160$		0			0
$161$	−3.15349			−0.248530
$162$	5.61499	+	4.65904i	0.441155	+	0.366049i
$163$	9.27269	−	9.27269i	0.726293	−	0.726293i	−0.243586	−	0.969879i	$-0.578324\pi$
$163$	9.27269	−	9.27269i	0.726293	−	0.726293i	0.969879	+	0.243586i	$0.0783239\pi$
$164$	−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	0.968074	−	0.250663i	$-0.0806487\pi$
$167$	9.27099	+	9.27099i	0.717411	+	0.717411i	−0.250663	+	0.968074i	$0.580649\pi$
$168$	−1.95796	+	3.52460i	−0.151060	+	0.271929i
$169$			1.19272i			0.0917480i
$170$		0			0
$171$		−	6.66724i		−	0.509856i
$172$	−4.26124	−	2.91429i	−0.324916	−	0.222212i
$173$	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
$178$	1.71177	−	2.06300i	0.128303	−	0.154628i
$179$	13.5772			1.01481			0.507405	−	0.861708i	$-0.330605\pi$
$179$	13.5772			1.01481			0.507405	+	0.861708i	$0.330605\pi$
$180$		0			0
$181$	19.8656			1.47660			0.738299	−	0.674474i	$-0.235629\pi$
$181$	19.8656			1.47660			0.738299	+	0.674474i	$0.235629\pi$
$182$	3.40210	−	4.10014i	0.252180	−	0.303923i
$183$	−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
$188$	3.77500	−	5.51977i	0.275320	−	0.402570i
$189$			5.65631i			0.411436i
$190$		0			0
$191$		−	14.9537i		−	1.08201i	−0.841019	−	0.541006i	$-0.818044\pi$
$191$		−	14.9537i		−	1.08201i	0.841019	−	0.541006i	$-0.181956\pi$
$192$	11.1070	+	2.58577i	0.801576	+	0.186612i
$193$	−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	$0.290602\pi$
$198$	0.491965	+	0.408208i	0.0349624	+	0.0290101i
$199$	2.30679			0.163524			0.0817621	−	0.996652i	$-0.473945\pi$
$199$	2.30679			0.163524			0.0817621	+	0.996652i	$0.473945\pi$
$200$		0			0
$201$	−21.7923			−1.53711
$202$	−6.69286	−	5.55341i	−0.470908	−	0.390737i
$203$	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
$208$	−13.7945	−	6.06596i	−0.956475	−	0.420599i
$209$			3.21666i			0.222501i
$210$		0			0
$211$		−	28.3975i		−	1.95496i	−0.211018	−	0.977482i	$-0.567678\pi$
$211$		−	28.3975i		−	1.95496i	0.211018	−	0.977482i	$-0.432322\pi$
$212$	−12.3208	+	18.0153i	−0.846194	+	1.23730i
$213$	−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
$218$	−14.4122	+	17.3693i	−0.976116	+	1.17640i
$219$	4.61718			0.312000
$220$		0			0
$221$	−17.3769			−1.16890
$222$	−13.2103	+	15.9208i	−0.886619	+	1.06854i
$223$	−2.46338	+	2.46338i	−0.164960	+	0.164960i	−0.784760	−	0.619800i	$-0.787214\pi$
$223$	−2.46338	+	2.46338i	−0.164960	+	0.164960i	0.619800	+	0.784760i	$0.287214\pi$
$224$	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	0.696617	−	0.717443i	$-0.254688\pi$
$227$	−0.313778	−	0.313778i	−0.0208262	−	0.0208262i	−0.717443	+	0.696617i	$0.754688\pi$
$228$	16.2093	+	11.0857i	1.07349	+	0.734166i
$229$		−	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
$232$	−6.48033	−	3.59990i	−0.425455	−	0.236345i
$233$	−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
$238$	5.02002	+	4.16537i	0.325400	+	0.270001i
$239$	−17.4027			−1.12569			−0.562844	−	0.826563i	$-0.690293\pi$
$239$	−17.4027			−1.12569			−0.562844	+	0.826563i	$0.690293\pi$
$240$		0			0
$241$	−22.0824			−1.42245			−0.711225	−	0.702965i	$-0.751859\pi$
$241$	−22.0824			−1.42245			−0.711225	+	0.702965i	$0.751859\pi$
$242$	11.7344	+	9.73666i	0.754318	+	0.625896i
$243$	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
$248$	−8.17713	−	4.54249i	−0.519248	−	0.288449i
$249$		−	17.5352i		−	1.11125i
$250$		0			0
$251$			25.0897i			1.58365i	0.610751	+	0.791823i	$0.290868\pi$
$251$			25.0897i			1.58365i	−0.610751	+	0.791823i	$0.709132\pi$
$252$	1.59795	+	1.09284i	0.100661	+	0.0688427i
$253$	−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	$0.335961\pi$
$258$	3.32284	−	4.00462i	0.206871	−	0.249317i
$259$	−10.2620			−0.637651
$260$		0			0
$261$	−2.53693			−0.157032
$262$	6.37543	−	7.68354i	0.393875	−	0.474691i
$263$	−11.3720	+	11.3720i	−0.701229	+	0.701229i	−0.964674	−	0.263446i	$-0.915141\pi$
$263$	−11.3720	+	11.3720i	−0.701229	+	0.701229i	0.263446	+	0.964674i	$0.415141\pi$
$264$	−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
$268$	−17.2599	+	25.2373i	−1.05432	+	1.54161i
$269$		−	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	$0.0417653\pi$
$271$			4.30758i			0.261667i	−0.991404	+	0.130833i	$0.958235\pi$
$272$	7.42687	−	16.8893i	0.450320	−	1.02406i
$273$	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	$-0.0887077\pi$
$278$	19.8291	+	16.4532i	1.18927	+	0.986799i
$279$	−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	$0.409206\pi$
$282$	5.18736	+	4.30422i	0.308903	+	0.256312i
$283$	−4.48860	+	4.48860i	−0.266819	+	0.266819i	−0.827817	−	0.560998i	$-0.810418\pi$
$283$	−4.48860	+	4.48860i	−0.266819	+	0.266819i	0.560998	+	0.827817i	$0.310418\pi$
$284$	−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
$288$	1.73028	−	5.19500i	0.101958	−	0.306118i
$289$		−	4.27544i		−	0.251497i
$290$		0			0
$291$			12.1826i			0.714157i
$292$	3.65691	−	5.34709i	0.214004	−	0.312915i
$293$	−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
$298$	13.8413	−	16.6813i	0.801806	−	0.966321i
$299$	11.8802			0.687050
$300$		0			0
$301$	2.58124			0.148780
$302$	0.694890	−	0.837468i	0.0399864	−	0.0481909i
$303$	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	0.909252	−	0.416246i	$-0.136654\pi$
$307$	8.63817	+	8.63817i	0.493006	+	0.493006i	−0.416246	+	0.909252i	$0.636654\pi$
$308$	−0.770940	−	0.527251i	−0.0439284	−	0.0300429i
$309$			4.94446i			0.281280i
$310$		0			0
$311$			14.5511i			0.825118i	0.910931	+	0.412559i	$0.135365\pi$
$311$			14.5511i			0.825118i	−0.910931	+	0.412559i	$0.864635\pi$
$312$	7.37625	−	13.2783i	0.417598	−	0.751735i
$313$	−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	$0.267294\pi$
$318$	−16.9304	−	14.0480i	−0.949410	−	0.787774i
$319$	1.22396			0.0685287
$320$		0			0
$321$	−13.6557			−0.762189
$322$	−3.43208	−	2.84777i	−0.191262	−	0.158700i
$323$	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
$328$	3.54539	−	6.38221i	0.195762	−	0.352399i
$329$			3.34359i			0.184338i
$330$		0			0
$331$			5.86317i			0.322269i	0.986932	+	0.161134i	$0.0515153\pi$
$331$			5.86317i			0.322269i	−0.986932	+	0.161134i	$0.948485\pi$
$332$	−20.3073	−	13.8883i	−1.11451	−	0.762218i
$333$	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	$0.216605\pi$
$338$	−1.07709	+	1.29809i	−0.0585862	+	0.0706070i
$339$	−14.6812			−0.797375
$340$		0			0
$341$	1.54444			0.0836363
$342$	6.02088	−	7.25625i	0.325572	−	0.392373i
$343$	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	0.333876	−	0.942617i	$-0.391643\pi$
$347$	−11.3396	−	11.3396i	−0.608741	−	0.608741i	−0.942617	+	0.333876i	$0.891643\pi$
$348$	4.21818	−	6.16778i	0.226118	−	0.330628i
$349$		−	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
$352$	−0.834785	+	2.50637i	−0.0444942	+	0.133590i
$353$	−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
$358$	14.7767	+	12.2610i	0.780973	+	0.648013i
$359$	−19.2502			−1.01599			−0.507994	−	0.861361i	$-0.669613\pi$
$359$	−19.2502			−1.01599			−0.507994	+	0.861361i	$0.669613\pi$
$360$		0			0
$361$	28.4442			1.49706
$362$	21.6206	+	17.9397i	1.13635	+	0.942890i
$363$	−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	0.962812	−	0.270171i	$-0.0870802\pi$
$367$	13.2691	+	13.2691i	0.692641	+	0.692641i	−0.270171	+	0.962812i	$0.587080\pi$
$368$	−5.07759	+	11.5468i	−0.264688	+	0.601921i
$369$		−	2.49852i		−	0.130068i
$370$		0			0
$371$		−	10.9128i		−	0.566562i
$372$	5.32266	−	7.78274i	0.275967	−	0.403516i
$373$	−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
$378$	−5.10796	+	6.15601i	−0.262725	+	0.316631i
$379$	−13.2251			−0.679326			−0.339663	−	0.940547i	$-0.610313\pi$
$379$	−13.2251			−0.679326			−0.339663	+	0.940547i	$0.610313\pi$
$380$		0			0
$381$	14.6270			0.749365
$382$	13.5040	−	16.2748i	0.690925	−	0.832690i
$383$	−19.4575	+	19.4575i	−0.994229	+	0.994229i	−0.999983	−	0.00575414i	$-0.998168\pi$
$383$	−19.4575	+	19.4575i	−0.994229	+	0.994229i	0.00575414	+	0.999983i	$0.498168\pi$
$384$	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
$388$	14.1085	+	9.64888i	0.716250	+	0.489848i
$389$			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
$392$	−2.47254	−	1.37352i	−0.124882	−	0.0693734i
$393$	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	$0.211494\pi$
$398$	2.51058	+	2.08316i	0.125844	+	0.104419i
$399$	−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	$0.584966\pi$
$402$	−23.7175	−	19.6796i	−1.18292	−	0.981529i
$403$	−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
$408$	16.2573	+	9.03113i	0.804857	+	0.447108i
$409$		−	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
$412$	5.72610	+	3.91612i	0.282105	+	0.192933i
$413$	−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
$418$	−2.90482	+	3.50083i	−0.142079	+	0.171231i
$419$	17.5164			0.855733			0.427867	−	0.903842i	$-0.359265\pi$
$419$	17.5164			0.855733			0.427867	+	0.903842i	$0.359265\pi$
$420$		0			0
$421$	−10.6568			−0.519379			−0.259689	−	0.965692i	$-0.583620\pi$
$421$	−10.6568			−0.519379			−0.259689	+	0.965692i	$0.583620\pi$
$422$	25.6445	−	30.9062i	1.24835	−	1.50449i
$423$	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
$428$	−10.8156	+	15.8145i	−0.522794	+	0.764423i
$429$			2.50792i			0.121083i
$430$		0			0
$431$			38.9415i			1.87575i	0.346976	+	0.937874i	$0.387209\pi$
$431$			38.9415i			1.87575i	−0.346976	+	0.937874i	$0.612791\pi$
$432$	20.7112	+	9.10752i	0.996470	+	0.438186i
$433$	−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
$438$	5.02508	+	4.16957i	0.240108	+	0.199230i
$439$	27.0296			1.29005			0.645026	−	0.764161i	$-0.276847\pi$
$439$	27.0296			1.29005			0.645026	+	0.764161i	$0.276847\pi$
$440$		0			0
$441$	−0.967954			−0.0460930
$442$	−18.9120	−	15.6923i	−0.899554	−	0.746406i
$443$	−12.2298	+	12.2298i	−0.581057	+	0.581057i	−0.935194	−	0.354137i	$-0.884775\pi$
$443$	−12.2298	+	12.2298i	−0.581057	+	0.581057i	0.354137	+	0.935194i	$0.384775\pi$
$444$	−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
$448$	−1.81394	+	7.79164i	−0.0857007	+	0.368120i
$449$			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
$452$	−11.6279	+	17.0021i	−0.546928	+	0.799712i
$453$	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	$0.147129\pi$
$458$	3.37594	−	4.06862i	0.157747	−	0.190114i
$459$	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	$0.577958\pi$
$462$	0.601166	−	0.724513i	0.0279688	−	0.0337074i
$463$	14.1517	−	14.1517i	0.657683	−	0.657683i	−0.297148	−	0.954831i	$-0.596035\pi$
$463$	14.1517	−	14.1517i	0.657683	−	0.657683i	0.954831	+	0.297148i	$0.0960355\pi$
$464$	−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	0.834005	−	0.551757i	$-0.186043\pi$
$467$	6.09942	+	6.09942i	0.282247	+	0.282247i	−0.551757	+	0.834005i	$0.686043\pi$
$468$	−6.01998	−	4.11710i	−0.278273	−	0.190313i
$469$		−	15.2875i		−	0.705909i
$470$		0			0
$471$		−	17.1889i		−	0.792021i
$472$	−15.7384	+	28.3313i	−0.724417	+	1.30405i
$473$	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
$478$	−18.9401	−	15.7156i	−0.866302	−	0.718815i
$479$	−12.0719			−0.551580			−0.275790	−	0.961218i	$-0.588940\pi$
$479$	−12.0719			−0.551580			−0.275790	+	0.961218i	$0.588940\pi$
$480$		0			0
$481$	38.6603			1.76276
$482$	−24.0332	−	19.9416i	−1.09468	−	0.908314i
$483$	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	0.0406645	−	0.999173i	$-0.487053\pi$
$487$	−21.1524	−	21.1524i	−0.958508	−	0.958508i	−0.999173	+	0.0406645i	$0.987053\pi$
$488$	−3.31484	+	5.96718i	−0.150056	+	0.270122i
$489$			18.6934i			0.845343i
$490$		0			0
$491$			19.2585i			0.869125i	0.900642	+	0.434562i	$0.143097\pi$
$491$			19.2585i			0.869125i	−0.900642	+	0.434562i	$0.856903\pi$
$492$	6.07439	+	4.15431i	0.273855	+	0.187291i
$493$	−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
$498$	15.8353	−	19.0844i	0.709595	−	0.855190i
$499$	−9.48925			−0.424797			−0.212399	−	0.977183i	$-0.568128\pi$
$499$	−9.48925			−0.424797			−0.212399	+	0.977183i	$0.568128\pi$
$500$		0			0
$501$	−18.6899			−0.835005
$502$	−22.6573	+	27.3062i	−1.01125	+	1.21873i
$503$	−24.1569	+	24.1569i	−1.07710	+	1.07710i	−0.0803368	+	0.996768i	$0.525600\pi$
$503$	−24.1569	+	24.1569i	−1.07710	+	1.07710i	−0.996768	+	0.0803368i	$0.974400\pi$
$504$	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
$508$	11.5849	−	16.9393i	0.513997	−	0.751561i
$509$			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
$512$	22.5996	−	1.12188i	0.998770	−	0.0495806i
$513$	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
$518$	−11.1686	−	9.26716i	−0.490720	−	0.407176i
$519$	−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	$0.538759\pi$
$522$	−2.76106	−	2.29099i	−0.120848	−	0.100274i
$523$	26.1183	−	26.1183i	1.14207	−	1.14207i	0.154003	−	0.988070i	$-0.450783\pi$
$523$	26.1183	−	26.1183i	1.14207	−	1.14207i	0.988070	−	0.154003i	$-0.0492166\pi$
$524$	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
$528$	−2.43755	−	1.07188i	−0.106081	−	0.0466477i
$529$			13.0555i			0.567631i
$530$		0			0
$531$			11.0912i			0.481317i
$532$	−7.77670	+	11.3710i	−0.337163	+	0.492995i
$533$	−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
$538$	6.10089	−	7.35267i	0.263028	−	0.316996i
$539$	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	$0.674112\pi$
$542$	−3.88998	+	4.68813i	−0.167089	+	0.201372i
$543$	−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	0.924179	−	0.381960i	$-0.124751\pi$
$547$	12.6814	+	12.6814i	0.542219	+	0.542219i	−0.381960	+	0.924179i	$0.624751\pi$
$548$	−12.6674	−	8.66332i	−0.541125	−	0.370079i
$549$			2.33605i			0.0997000i
$550$		0			0
$551$		−	18.0529i		−	0.769078i
$552$	−11.1148	−	6.17439i	−0.473076	−	0.262799i
$553$	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	$0.201503\pi$
$558$	−3.48401	−	2.89086i	−0.147490	−	0.122380i
$559$	−9.72436			−0.411297
$560$		0			0
$561$	−3.07057			−0.129640
$562$	10.2672	+	8.51923i	0.433096	+	0.359362i
$563$	28.2090	−	28.2090i	1.18887	−	1.18887i	0.211487	−	0.977381i	$-0.432169\pi$
$563$	28.2090	−	28.2090i	1.18887	−	1.18887i	0.977381	−	0.211487i	$-0.0678305\pi$
$564$	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
$568$	−23.7860	−	13.2134i	−0.998039	−	0.554423i
$569$			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	$0.0515623\pi$
$571$			7.70777i			0.322560i	−0.986909	+	0.161280i	$0.948438\pi$
$572$	2.90438	+	1.98632i	0.121438	+	0.0830524i
$573$	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	$0.0403909\pi$
$578$	3.86096	−	4.65315i	0.160595	−	0.193546i
$579$	9.12769			0.379334
$580$		0			0
$581$	12.3011			0.510336
$582$	−11.0016	+	13.2589i	−0.456029	+	0.549598i
$583$	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	0.997102	−	0.0760739i	$-0.0242385\pi$
$587$	22.3147	+	22.3147i	0.921028	+	0.921028i	−0.0760739	+	0.997102i	$0.524238\pi$
$588$	1.60942	−	2.35328i	0.0663715	−	0.0970477i
$589$		−	22.7798i		−	0.938625i
$590$		0			0
$591$		−	5.09034i		−	0.209389i
$592$	−16.5234	+	37.5755i	−0.679107	+	1.54434i
$593$	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
$598$	12.9297	+	10.7285i	0.528737	+	0.438720i
$599$	10.6863			0.436632			0.218316	−	0.975878i	$-0.429944\pi$
$599$	10.6863			0.436632			0.218316	+	0.975878i	$0.429944\pi$
$600$		0			0
$601$	−25.4476			−1.03803			−0.519014	−	0.854766i	$-0.673701\pi$
$601$	−25.4476			−1.03803			−0.519014	+	0.854766i	$0.673701\pi$
$602$	2.80928	+	2.33100i	0.114498	+	0.0950045i
$603$	−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	0.954743	−	0.297432i	$-0.0961303\pi$
$607$	16.1944	+	16.1944i	0.657310	+	0.657310i	−0.297432	+	0.954743i	$0.596130\pi$
$608$	36.9677	+	12.3127i	1.49924	+	0.499345i
$609$			3.73613i			0.151395i
$610$		0			0
$611$		−	12.5964i		−	0.509596i
$612$	5.04078	−	7.37057i	0.203761	−	0.297938i
$613$	−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	$0.0670131\pi$
$618$	−4.46512	+	5.38127i	−0.179613	+	0.216466i
$619$	17.5491			0.705356			0.352678	−	0.935745i	$-0.385271\pi$
$619$	17.5491			0.705356			0.352678	+	0.935745i	$0.385271\pi$
$620$		0			0
$621$	−17.8371			−0.715778
$622$	−13.1404	+	15.8366i	−0.526884	+	0.634990i
$623$	−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
$628$	−19.9062	−	13.6139i	−0.794342	−	0.543256i
$629$			47.3339i			1.88732i
$630$		0			0
$631$		−	47.5527i		−	1.89304i	−0.322642	−	0.946521i	$-0.604571\pi$
$631$		−	47.5527i		−	1.89304i	0.322642	−	0.946521i	$-0.395429\pi$
$632$	4.00376	−	7.20734i	0.159261	−	0.286692i
$633$	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
$638$	1.33209	+	1.10530i	0.0527380	+	0.0437594i
$639$	−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	$0.461358\pi$
$642$	−14.8621	−	12.3319i	−0.586562	−	0.486700i
$643$	12.9856	−	12.9856i	0.512101	−	0.512101i	−0.403069	−	0.915170i	$-0.632057\pi$
$643$	12.9856	−	12.9856i	0.512101	−	0.512101i	0.915170	+	0.403069i	$0.132057\pi$
$644$	−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	0.467300	−	0.884099i	$-0.345227\pi$
$647$	−10.6018	−	10.6018i	−0.416799	−	0.416799i	−0.884099	+	0.467300i	$0.845227\pi$
$648$	−7.08629	+	12.7563i	−0.278376	+	0.501116i
$649$		−	5.35103i		−	0.210046i
$650$		0			0
$651$			4.71439i			0.184771i
$652$	21.6485	+	14.8055i	0.847821	+	0.579830i
$653$	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
$658$	−3.01945	+	3.63898i	−0.117710	+	0.141862i
$659$	10.1563			0.395635			0.197817	−	0.980239i	$-0.436615\pi$
$659$	10.1563			0.395635			0.197817	+	0.980239i	$0.436615\pi$
$660$		0			0
$661$	42.5695			1.65576			0.827880	−	0.560905i	$-0.189547\pi$
$661$	42.5695			1.65576			0.827880	+	0.560905i	$0.189547\pi$
$662$	−5.29476	+	6.38114i	−0.205787	+	0.248010i
$663$	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
$668$	−14.8028	+	21.6445i	−0.572739	+	0.837453i
$669$		−	4.96608i		−	0.192000i
$670$		0			0
$671$		−	1.12704i		−	0.0435090i
$672$	−7.65064	−	2.54817i	−0.295130	−	0.0982977i
$673$	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	$-0.0787951\pi$
$678$	−15.9782	−	13.2580i	−0.613640	−	0.509169i
$679$	−8.54621			−0.327973
$680$		0			0
$681$	0.632565			0.0242399
$682$	1.68088	+	1.39472i	0.0643644	+	0.0534064i
$683$	6.54248	−	6.54248i	0.250341	−	0.250341i	−0.570769	−	0.821110i	$-0.693355\pi$
$683$	6.54248	−	6.54248i	0.250341	−	0.250341i	0.821110	+	0.570769i	$0.193355\pi$
$684$	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
$688$	4.15619	−	9.45150i	0.158453	−	0.360335i
$689$			41.1119i			1.56624i
$690$		0			0
$691$		−	29.4625i		−	1.12081i	−0.828219	−	0.560404i	$-0.810646\pi$
$691$		−	29.4625i		−	1.12081i	0.828219	−	0.560404i	$-0.189354\pi$
$692$	−4.46773	+	6.53266i	−0.169837	+	0.248334i
$693$	−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
$698$	22.2918	−	26.8657i	0.843758	−	1.01688i
$699$	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	$0.464938\pi$
$702$	19.2433	−	23.1917i	0.726293	−	0.875314i
$703$	−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
$708$	−26.9648	−	18.4414i	−1.01340	−	0.693071i
$709$			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
$712$	4.68678	+	2.60356i	0.175645	+	0.0975726i
$713$	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
$718$	−20.9508	−	17.3840i	−0.781879	−	0.648765i
$719$	−14.8792			−0.554902			−0.277451	−	0.960740i	$-0.589490\pi$
$719$	−14.8792			−0.554902			−0.277451	+	0.960740i	$0.589490\pi$
$720$		0			0
$721$	−3.46858			−0.129177
$722$	30.9570	+	25.6866i	1.15210	+	0.955957i
$723$	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	0.0966625	−	0.995317i	$-0.469183\pi$
$727$	−24.2304	−	24.2304i	−0.898655	−	0.898655i	−0.995317	+	0.0966625i	$0.969183\pi$
$728$	9.31484	+	5.17451i	0.345231	+	0.191780i
$729$			29.1831i			1.08085i
$730$		0			0
$731$		−	11.9060i		−	0.440361i
$732$	−5.67938	−	3.88416i	−0.209916	−	0.143563i
$733$	−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
$738$	2.25630	−	2.71925i	0.0830556	−	0.100097i
$739$	−35.7816			−1.31625			−0.658123	−	0.752910i	$-0.728650\pi$
$739$	−35.7816			−1.31625			−0.658123	+	0.752910i	$0.728650\pi$
$740$		0			0
$741$	36.9906			1.35888
$742$	9.85481	−	11.8768i	0.361781	−	0.436012i
$743$	−1.83282	+	1.83282i	−0.0672397	+	0.0672397i	−0.739927	−	0.672687i	$-0.765140\pi$
$743$	−1.83282	+	1.83282i	−0.0672397	+	0.0672397i	0.672687	+	0.739927i	$0.265140\pi$
$744$	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
$748$	−2.43196	+	3.55599i	−0.0889213	+	0.130020i
$749$		−	9.57962i		−	0.350032i
$750$		0			0
$751$			1.38920i			0.0506926i	0.999679	+	0.0253463i	$0.00806884\pi$
$751$			1.38920i			0.0506926i	−0.999679	+	0.0253463i	$0.991931\pi$
$752$	12.2429	+	5.38369i	0.446454	+	0.196323i
$753$	−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	$0.394813\pi$
$758$	−14.3934	−	11.9430i	−0.522792	−	0.433788i
$759$	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	$0.189067\pi$
$762$	15.9192	+	13.2090i	0.576693	+	0.478512i
$763$	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
$768$	−0.984468	+	22.7867i	−0.0355239	+	0.822245i
$769$		−	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
$772$	7.22933	−	10.5706i	0.260189	−	0.380446i
$773$	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
$778$	−9.60718	+	11.5784i	−0.344434	+	0.415105i
$779$	17.7795			0.637017
$780$		0			0
$781$	4.49254			0.160756
$782$	−13.1354	+	15.8306i	−0.469722	+	0.566100i
$783$	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	0.900203	−	0.435470i	$-0.143418\pi$
$787$	13.0374	+	13.0374i	0.464733	+	0.464733i	−0.435470	+	0.900203i	$0.643418\pi$
$788$	−5.89505	−	4.03166i	−0.210002	−	0.143622i
$789$		−	22.9255i		−	0.816170i
$790$		0			0
$791$		−	10.2990i		−	0.366191i
$792$	−0.620875	+	1.11766i	−0.0220618	+	0.0397144i
$793$	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	$0.835298\pi$
$798$	−10.6862	−	8.86691i	−0.378288	−	0.313885i
$799$	15.4224			0.545606
$800$		0			0
$801$	1.83479			0.0648292
$802$	−11.4973	−	9.53986i	−0.405982	−	0.336864i
$803$	−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
$808$	8.44660	−	15.2051i	0.297150	−	0.534913i
$809$		−	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	$0.140697\pi$
$811$			24.3635i			0.855518i	−0.903893	+	0.427759i	$0.859303\pi$
$812$	4.32675	+	2.95909i	0.151839	+	0.103844i
$813$	−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
$818$	25.7070	−	30.9816i	0.898824	−	1.08325i
$819$	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	$0.305434\pi$
$822$	9.87783	−	11.9046i	0.344529	−	0.415220i
$823$	14.0730	−	14.0730i	0.490553	−	0.490553i	−0.417928	−	0.908480i	$-0.637243\pi$
$823$	14.0730	−	14.0730i	0.490553	−	0.490553i	0.908480	+	0.417928i	$0.137243\pi$
$824$	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	0.181433	−	0.983403i	$-0.441926\pi$
$827$	−23.0627	−	23.0627i	−0.801970	−	0.801970i	−0.983403	+	0.181433i	$0.941926\pi$
$828$	−3.44627	+	5.03910i	−0.119766	+	0.175121i
$829$			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
$832$	6.83371	−	29.3536i	0.236916	−	1.01765i
$833$	−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
$838$	19.0639	+	15.8183i	0.658551	+	0.546434i
$839$	11.4626			0.395732			0.197866	−	0.980229i	$-0.436599\pi$
$839$	11.4626			0.395732			0.197866	+	0.980229i	$0.436599\pi$
$840$		0			0
$841$	22.1308			0.763129
$842$	−11.5982	−	9.62363i	−0.399701	−	0.331652i
$843$	−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
$848$	−39.9583	−	17.5712i	−1.37217	−	0.603397i
$849$		−	9.04883i		−	0.310555i
$850$		0			0
$851$		−	32.3611i		−	1.10933i
$852$	15.4828	−	22.6388i	0.530432	−	0.775592i
$853$	−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	$0.125685\pi$
$858$	−2.26479	+	2.72948i	−0.0773185	+	0.0931828i
$859$	6.31565			0.215487			0.107744	−	0.994179i	$-0.465637\pi$
$859$	6.31565			0.215487			0.107744	+	0.994179i	$0.465637\pi$
$860$		0			0
$861$	−3.67955			−0.125399
$862$	−35.1663	+	42.3818i	−1.19777	+	1.44353i
$863$	16.9489	−	16.9489i	0.576948	−	0.576948i	−0.357113	−	0.934061i	$-0.616239\pi$
$863$	16.9489	−	16.9489i	0.576948	−	0.576948i	0.934061	+	0.357113i	$0.116239\pi$
$864$	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
$868$	5.45966	+	3.73390i	0.185313	+	0.126737i
$869$			1.36127i			0.0461781i
$870$		0			0
$871$			57.5928i			1.95146i
$872$	−39.4601	−	21.9206i	−1.33629	−	0.742324i
$873$	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	$0.997715\pi$
$878$	29.4175	+	24.4092i	0.992792	+	0.823770i
$879$	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	$0.665012\pi$
$882$	−1.05347	−	0.874115i	−0.0354721	−	0.0294330i
$883$	−9.65095	+	9.65095i	−0.324780	+	0.324780i	−0.850598	−	0.525817i	$-0.823760\pi$
$883$	−9.65095	+	9.65095i	−0.324780	+	0.324780i	0.525817	+	0.850598i	$0.323760\pi$
$884$	−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	0.905419	−	0.424518i	$-0.139556\pi$
$887$	14.3225	+	14.3225i	0.480901	+	0.480901i	−0.424518	+	0.905419i	$0.639556\pi$
$888$	−36.1695	−	20.0926i	−1.21377	−	0.674262i
$889$			10.2610i			0.344142i
$890$		0			0
$891$		−	2.40933i		−	0.0807156i
$892$	−5.75114	−	3.93324i	−0.192562	−	0.131695i
$893$	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
$898$	−2.57244	+	3.10026i	−0.0858435	+	0.103457i
$899$	−8.66788			−0.289090
$900$		0			0
$901$	−50.3354			−1.67692
$902$	−1.08857	+	1.31192i	−0.0362454	+	0.0436822i
$903$	−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	0.881619	−	0.471962i	$-0.156454\pi$
$907$	12.3374	+	12.3374i	0.409657	+	0.409657i	−0.471962	+	0.881619i	$0.656454\pi$
$908$	0.501005	−	0.732564i	0.0166264	−	0.0243110i
$909$		−	5.95251i		−	0.197432i
$910$		0			0
$911$			58.6655i			1.94368i	0.235652	+	0.971838i	$0.424277\pi$
$911$			58.6655i			1.94368i	−0.235652	+	0.971838i	$0.575723\pi$
$912$	−15.8097	+	35.9526i	−0.523513	+	1.19051i
$913$	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
$918$	28.3948	+	23.5606i	0.937168	+	0.777616i
$919$	−54.8655			−1.80985			−0.904923	−	0.425575i	$-0.860072\pi$
$919$	−54.8655			−1.80985			−0.904923	+	0.425575i	$0.860072\pi$
$920$		0			0
$921$	−17.4142			−0.573817
$922$	−11.3321	−	9.40279i	−0.373201	−	0.309664i
$923$	−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
$928$	4.68507	−	14.0665i	0.153795	−	0.461755i
$929$			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
$932$	21.8438	−	31.9398i	0.715517	−	1.04622i
$933$	−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	$0.160701\pi$
$938$	13.8054	−	16.6380i	0.450763	−	0.543250i
$939$	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	$0.572112\pi$
$942$	15.5225	−	18.7074i	0.505750	−	0.609520i
$943$	−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	0.354478	−	0.935064i	$-0.384659\pi$
$947$	−17.8666	−	17.8666i	−0.580586	−	0.580586i	−0.935064	+	0.354478i	$0.884659\pi$
$948$	6.85972	+	4.69140i	0.222793	+	0.152370i
$949$		−	12.2023i		−	0.396105i
$950$		0			0
$951$		−	2.75644i		−	0.0893837i
$952$	−6.33542	+	11.4046i	−0.205332	+	0.369627i
$953$	−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
$958$	−13.1384	−	10.9016i	−0.424483	−	0.352215i
$959$	7.67328			0.247783
$960$		0			0
$961$	20.0625			0.647179
$962$	42.0757	+	34.9124i	1.35658	+	1.12562i
$963$	−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	0.443808	−	0.896122i	$-0.353627\pi$
$967$	−14.0654	−	14.0654i	−0.452314	−	0.452314i	−0.896122	+	0.443808i	$0.853627\pi$
$968$	−14.8092	+	26.6587i	−0.475986	+	0.856842i
$969$			45.2895i			1.45491i
$970$		0			0
$971$		−	32.5677i		−	1.04515i	−0.852594	−	0.522574i	$-0.824972\pi$
$971$		−	32.5677i		−	1.04515i	0.852594	−	0.522574i	$-0.175028\pi$
$972$	15.8721	+	10.8550i	0.509097	+	0.348175i
$973$	−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	$0.912685\pi$
$978$	−16.8811	+	20.3448i	−0.539799	+	0.650555i
$979$	−0.885208			−0.0282914
$980$		0			0
$981$	−15.4479			−0.493214
$982$	−17.3915	+	20.9599i	−0.554985	+	0.668857i
$983$	7.67704	−	7.67704i	0.244860	−	0.244860i	−0.573997	−	0.818857i	$-0.694608\pi$
$983$	7.67704	−	7.67704i	0.244860	−	0.244860i	0.818857	+	0.573997i	$0.194608\pi$
$984$	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
$988$	29.2973	−	42.8382i	0.932072	−	1.36287i
$989$			8.13991i			0.258834i
$990$		0			0
$991$			17.6551i			0.560832i	0.959879	+	0.280416i	$0.0904724\pi$
$991$			17.6551i			0.560832i	−0.959879	+	0.280416i	$0.909528\pi$
$992$	5.91180	−	17.7496i	0.187700	−	0.563552i
$993$	−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	$0.0857993\pi$
$998$	−10.3276	−	8.56931i	−0.326913	−	0.271257i
$999$	−58.0452			−1.83647

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.08834 + 0.903055i) q^{2} +(-1.00798 + 1.00798i) q^{3} +(0.368985 + 1.96567i) q^{4} +(-2.00729 + 0.186768i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-1.37352 + 2.47254i) q^{8} +0.967954i q^{9} +O(q^{10})\)	\(q+(1.08834 + 0.903055i) 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} +(-1.37352 + 2.47254i) q^{8} +0.967954i q^{9} -0.466996i q^{11} +(-2.35328 - 1.60942i) 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} +(-0.874115 + 1.05347i) q^{18} -6.88797 q^{19} +1.42550 q^{21} +(0.421723 - 0.508252i) 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} +(1.12903 - 1.65085i) q^{28} +2.62093i q^{29} +3.30718i q^{31} +(-5.36699 - 1.78756i) 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} +(-7.49648 - 6.22021i) q^{38} -5.37031 q^{39} -2.58124 q^{41} +(1.55143 + 1.28730i) 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} +(2.29527 - 5.21962i) q^{48} +1.00000i q^{49} -6.57516i q^{51} +(-4.25340 + 6.21928i) 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} +(-2.36684 + 2.85247i) q^{58} +11.4584 q^{59} +2.41339 q^{61} +(-2.98657 + 3.59935i) 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} +(-7.61459 - 5.20766i) q^{68} +4.49529i q^{69} +9.62009i q^{71} +(-2.39330 - 1.32951i) 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} +(-5.84475 - 4.84969i) q^{78} -2.91496 q^{79} +5.15920 q^{81} +(-2.80928 - 2.33100i) 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} +(1.15467 + 0.641430i) q^{88} -1.89554i q^{89} -3.76732i q^{91} +(5.20593 + 3.56037i) 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} +(-0.903055 + 1.08834i) 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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