LMFDB - Embedded newform 380.2.bh.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.362674 + 0.169118i) q^{3} +(1.57660 - 1.58566i) q^{5} +(1.00773 + 3.76091i) q^{7} +(-1.82543 + 2.17546i) q^{9} +O(q^{10})$	\(q+(-0.362674 + 0.169118i) q^{3} +(1.57660 - 1.58566i) q^{5} +(1.00773 + 3.76091i) q^{7} +(-1.82543 + 2.17546i) q^{9} +(0.973938 + 1.68691i) q^{11} +(2.46032 - 5.27618i) q^{13} +(-0.303629 + 0.841710i) q^{15} +(-0.350620 + 4.00760i) q^{17} +(4.22053 + 1.08956i) q^{19} +(-1.00151 - 1.19356i) q^{21} +(1.79737 - 1.25853i) q^{23} +(-0.0286516 - 4.99992i) q^{25} +(0.604839 - 2.25729i) q^{27} +(3.44950 + 2.89447i) q^{29} +(2.99397 + 1.72857i) q^{31} +(-0.638508 - 0.447088i) q^{33} +(7.55232 + 4.33153i) q^{35} +(-5.01505 - 5.01505i) q^{37} +2.32961i q^{39} +(-3.17796 + 8.73136i) q^{41} +(-1.28086 + 1.82925i) q^{43} +(0.571574 + 6.32436i) q^{45} +(-4.06756 + 0.355865i) q^{47} +(-7.06672 + 4.07998i) q^{49} +(-0.550596 - 1.51275i) q^{51} +(-4.39667 - 6.27909i) q^{53} +(4.21038 + 1.11525i) q^{55} +(-1.71494 + 0.318611i) q^{57} +(4.29987 - 3.60802i) q^{59} +(1.94572 - 11.0347i) q^{61} +(-10.0213 - 4.67299i) q^{63} +(-4.48729 - 12.2197i) q^{65} +(-0.637363 - 7.28509i) q^{67} +(-0.439018 + 0.760402i) q^{69} +(2.69808 - 0.475744i) q^{71} +(-1.74492 - 3.74199i) q^{73} +(0.855965 + 1.80849i) q^{75} +(-5.36285 + 5.36285i) q^{77} +(-8.14836 - 2.96576i) q^{79} +(-1.31702 - 7.46922i) q^{81} +(-14.3797 + 3.85303i) q^{83} +(5.80192 + 6.87436i) q^{85} +(-1.74055 - 0.466379i) q^{87} +(-1.72328 + 0.627223i) q^{89} +(22.3226 + 3.93607i) q^{91} +(-1.37817 - 0.120574i) q^{93} +(8.38177 - 4.97453i) q^{95} +(-0.221785 - 0.0194037i) q^{97} +(-5.44767 - 0.960571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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			0
$2$		0			0
$3$	−0.362674	+	0.169118i	−0.209390	+	0.0976401i	−0.524484	−	0.851420i	$-0.675742\pi$
$3$	−0.362674	+	0.169118i	−0.209390	+	0.0976401i	0.315094	+	0.949060i	$0.397964\pi$
$4$		0			0
$5$	1.57660	−	1.58566i	0.705078	−	0.709130i
$5$	1.57660	−	1.58566i	0.705078	−	0.709130i
$6$		0			0
$7$	1.00773	+	3.76091i	0.380887	+	1.42149i	0.844549	+	0.535478i	$0.179868\pi$
$7$	1.00773	+	3.76091i	0.380887	+	1.42149i	−0.463662	+	0.886012i	$0.653465\pi$
$8$		0			0
$9$	−1.82543	+	2.17546i	−0.608477	+	0.725155i
$10$		0			0
$11$	0.973938	+	1.68691i	0.293653	+	0.508623i	0.974671	−	0.223645i	$-0.0717955\pi$
$11$	0.973938	+	1.68691i	0.293653	+	0.508623i	−0.681017	+	0.732267i	$0.738462\pi$
$12$		0			0
$13$	2.46032	−	5.27618i	0.682370	−	1.46335i	−0.193649	−	0.981071i	$-0.562032\pi$
$13$	2.46032	−	5.27618i	0.682370	−	1.46335i	0.876019	−	0.482277i	$-0.160190\pi$
$14$		0			0
$15$	−0.303629	+	0.841710i	−0.0783967	+	0.217328i
$16$		0			0
$17$	−0.350620	+	4.00760i	−0.0850378	+	0.971986i	0.827087	+	0.562074i	$0.189996\pi$
$17$	−0.350620	+	4.00760i	−0.0850378	+	0.971986i	−0.912125	+	0.409913i	$0.865559\pi$
$18$		0			0
$19$	4.22053	+	1.08956i	0.968256	+	0.249962i
$19$	4.22053	+	1.08956i	0.968256	+	0.249962i
$20$		0			0
$21$	−1.00151	−	1.19356i	−0.218548	−	0.260456i
$22$		0			0
$23$	1.79737	−	1.25853i	0.374777	−	0.262421i	−0.370979	−	0.928641i	$-0.620978\pi$
$23$	1.79737	−	1.25853i	0.374777	−	0.262421i	0.745755	+	0.666220i	$0.232089\pi$
$24$		0			0
$25$	−0.0286516	−	4.99992i	−0.00573033	−	0.999984i
$26$		0			0
$27$	0.604839	−	2.25729i	0.116401	−	0.434416i
$28$		0			0
$29$	3.44950	+	2.89447i	0.640556	+	0.537490i	0.904189	−	0.427133i	$-0.140476\pi$
$29$	3.44950	+	2.89447i	0.640556	+	0.537490i	−0.263633	+	0.964623i	$0.584921\pi$
$30$		0			0
$31$	2.99397	+	1.72857i	0.537733	+	0.310460i	0.744160	−	0.668002i	$-0.232850\pi$
$31$	2.99397	+	1.72857i	0.537733	+	0.310460i	−0.206427	+	0.978462i	$0.566184\pi$
$32$		0			0
$33$	−0.638508	−	0.447088i	−0.111150	−	0.0778281i
$34$		0			0
$35$	7.55232	+	4.33153i	1.27658	+	0.732162i
$36$		0			0
$37$	−5.01505	−	5.01505i	−0.824469	−	0.824469i	0.162276	−	0.986745i	$-0.448116\pi$
$37$	−5.01505	−	5.01505i	−0.824469	−	0.824469i	−0.986745	+	0.162276i	$0.948116\pi$
$38$		0			0
$39$			2.32961i			0.373037i
$40$		0			0
$41$	−3.17796	+	8.73136i	−0.496313	+	1.36361i	0.398500	+	0.917168i	$0.369531\pi$
$41$	−3.17796	+	8.73136i	−0.496313	+	1.36361i	−0.894813	+	0.446441i	$0.852691\pi$
$42$		0			0
$43$	−1.28086	+	1.82925i	−0.195329	+	0.278959i	−0.904854	−	0.425721i	$-0.860020\pi$
$43$	−1.28086	+	1.82925i	−0.195329	+	0.278959i	0.709525	+	0.704680i	$0.248909\pi$
$44$		0			0
$45$	0.571574	+	6.32436i	0.0852051	+	0.942780i
$46$		0			0
$47$	−4.06756	+	0.355865i	−0.593314	+	0.0519083i	−0.379859	−	0.925045i	$-0.624027\pi$
$47$	−4.06756	+	0.355865i	−0.593314	+	0.0519083i	−0.213455	+	0.976953i	$0.568472\pi$
$48$		0			0
$49$	−7.06672	+	4.07998i	−1.00953	+	0.582854i
$50$		0			0
$51$	−0.550596	−	1.51275i	−0.0770988	−	0.211827i
$52$		0			0
$53$	−4.39667	−	6.27909i	−0.603929	−	0.862500i	0.394479	−	0.918905i	$-0.370925\pi$
$53$	−4.39667	−	6.27909i	−0.603929	−	0.862500i	−0.998408	+	0.0564053i	$0.982036\pi$
$54$		0			0
$55$	4.21038	+	1.11525i	0.567728	+	0.150380i
$56$		0			0
$57$	−1.71494	+	0.318611i	−0.227149	+	0.0422010i
$58$		0			0
$59$	4.29987	−	3.60802i	0.559795	−	0.469724i	−0.318447	−	0.947941i	$-0.603161\pi$
$59$	4.29987	−	3.60802i	0.559795	−	0.469724i	0.878242	+	0.478217i	$0.158717\pi$
$60$		0			0
$61$	1.94572	−	11.0347i	0.249124	−	1.41285i	−0.561592	−	0.827414i	$-0.689811\pi$
$61$	1.94572	−	11.0347i	0.249124	−	1.41285i	0.810716	−	0.585440i	$-0.199078\pi$
$62$		0			0
$63$	−10.0213	−	4.67299i	−1.26256	−	0.588742i
$64$		0			0
$65$	−4.48729	−	12.2197i	−0.556579	−	1.51566i
$66$		0			0
$67$	−0.637363	−	7.28509i	−0.0778663	−	0.890016i	−0.930209	−	0.367031i	$-0.880374\pi$
$67$	−0.637363	−	7.28509i	−0.0778663	−	0.890016i	0.852342	−	0.522984i	$-0.175181\pi$
$68$		0			0
$69$	−0.439018	+	0.760402i	−0.0528516	+	0.0915416i
$70$		0			0
$71$	2.69808	−	0.475744i	0.320203	−	0.0564604i	−0.0112367	−	0.999937i	$-0.503577\pi$
$71$	2.69808	−	0.475744i	0.320203	−	0.0564604i	0.331439	+	0.943476i	$0.392466\pi$
$72$		0			0
$73$	−1.74492	−	3.74199i	−0.204227	−	0.437967i	0.777341	−	0.629080i	$-0.216568\pi$
$73$	−1.74492	−	3.74199i	−0.204227	−	0.437967i	−0.981568	+	0.191113i	$0.938790\pi$
$74$		0			0
$75$	0.855965	+	1.80849i	0.0988384	+	0.208827i
$76$		0			0
$77$	−5.36285	+	5.36285i	−0.611153	+	0.611153i
$78$		0			0
$79$	−8.14836	−	2.96576i	−0.916763	−	0.333674i	−0.159813	−	0.987147i	$-0.551089\pi$
$79$	−8.14836	−	2.96576i	−0.916763	−	0.333674i	−0.756950	+	0.653473i	$0.773311\pi$
$80$		0			0
$81$	−1.31702	−	7.46922i	−0.146336	−	0.829913i
$82$		0			0
$83$	−14.3797	+	3.85303i	−1.57838	+	0.422925i	−0.938423	−	0.345488i	$-0.887713\pi$
$83$	−14.3797	+	3.85303i	−1.57838	+	0.422925i	−0.639954	+	0.768413i	$0.721047\pi$
$84$		0			0
$85$	5.80192	+	6.87436i	0.629306	+	0.745629i
$86$		0			0
$87$	−1.74055	−	0.466379i	−0.186607	−	0.0500011i
$88$		0			0
$89$	−1.72328	+	0.627223i	−0.182667	+	0.0664855i	−0.431734	−	0.902001i	$-0.642098\pi$
$89$	−1.72328	+	0.627223i	−0.182667	+	0.0664855i	0.249067	+	0.968486i	$0.419876\pi$
$90$		0			0
$91$	22.3226	+	3.93607i	2.34004	+	0.412612i
$92$		0			0
$93$	−1.37817	−	0.120574i	−0.142909	−	0.0125029i
$94$		0			0
$95$	8.38177	−	4.97453i	0.859951	−	0.510376i
$96$		0			0
$97$	−0.221785	−	0.0194037i	−0.0225189	−	0.00197015i	0.0758907	−	0.997116i	$-0.475820\pi$
$97$	−0.221785	−	0.0194037i	−0.0225189	−	0.00197015i	−0.0984096	+	0.995146i	$0.531376\pi$
$98$		0			0
$99$	−5.44767	−	0.960571i	−0.547511	−	0.0965410i
$100$		0			0
$101$	−11.5307	+	4.19682i	−1.14735	+	0.417600i	−0.844561	−	0.535459i	$-0.820138\pi$
$101$	−11.5307	+	4.19682i	−1.14735	+	0.417600i	−0.302785	+	0.953059i	$0.597916\pi$
$102$		0			0
$103$	−0.154208	−	0.0413200i	−0.0151946	−	0.00407138i	0.251214	−	0.967932i	$-0.419170\pi$
$103$	−0.154208	−	0.0413200i	−0.0151946	−	0.00407138i	−0.266408	+	0.963860i	$0.585837\pi$
$104$		0			0
$105$	−3.47157	−	0.293703i	−0.338790	−	0.0286624i
$106$		0			0
$107$	−12.6620	+	3.39277i	−1.22408	+	0.327991i	−0.812272	−	0.583279i	$-0.801770\pi$
$107$	−12.6620	+	3.39277i	−1.22408	+	0.327991i	−0.411809	+	0.911270i	$0.635103\pi$
$108$		0			0
$109$	1.22782	+	6.96332i	0.117604	+	0.666965i	0.985428	+	0.170094i	$0.0544070\pi$
$109$	1.22782	+	6.96332i	0.117604	+	0.666965i	−0.867824	+	0.496872i	$0.834482\pi$
$110$		0			0
$111$	2.66696	+	0.970694i	0.253137	+	0.0921342i
$112$		0			0
$113$	10.7019	−	10.7019i	1.00675	−	1.00675i	0.00677601	−	0.999977i	$-0.497843\pi$
$113$	10.7019	−	10.7019i	1.00675	−	1.00675i	0.999977	−	0.00677601i	$-0.00215689\pi$
$114$		0			0
$115$	0.838128	−	4.83421i	0.0781558	−	0.450793i
$116$		0			0
$117$	6.98698	+	14.9836i	0.645947	+	1.38524i
$118$		0			0
$119$	−15.4256	+	2.71994i	−1.41406	+	0.249337i
$120$		0			0
$121$	3.60289	−	6.24039i	0.327535	−	0.567308i
$122$		0			0
$123$	−0.324065	−	3.70409i	−0.0292200	−	0.333986i
$124$		0			0
$125$	−7.97335	−	7.83745i	−0.713159	−	0.701003i
$126$		0			0
$127$	6.15995	+	2.87243i	0.546607	+	0.254887i	0.676248	−	0.736674i	$-0.263605\pi$
$127$	6.15995	+	2.87243i	0.546607	+	0.254887i	−0.129641	+	0.991561i	$0.541382\pi$
$128$		0			0
$129$	0.155175	−	0.880039i	0.0136624	−	0.0774831i
$130$		0			0
$131$	−8.24688	+	6.91995i	−0.720533	+	0.604599i	−0.927533	−	0.373742i	$-0.878075\pi$
$131$	−8.24688	+	6.91995i	−0.720533	+	0.604599i	0.207000	+	0.978341i	$0.433630\pi$
$132$		0			0
$133$	0.155428	+	16.9710i	0.0134773	+	1.47157i
$134$		0			0
$135$	−2.62571	−	4.51792i	−0.225985	−	0.388840i
$136$		0			0
$137$	−9.16762	−	13.0927i	−0.783243	−	1.11859i	−0.990120	−	0.140220i	$-0.955219\pi$
$137$	−9.16762	−	13.0927i	−0.783243	−	1.11859i	0.206878	−	0.978367i	$-0.433670\pi$
$138$		0			0
$139$	7.02075	+	19.2894i	0.595492	+	1.63610i	0.760148	+	0.649750i	$0.225127\pi$
$139$	7.02075	+	19.2894i	0.595492	+	1.63610i	−0.164656	+	0.986351i	$0.552651\pi$
$140$		0			0
$141$	1.41501	−	0.816958i	0.119166	−	0.0688003i
$142$		0			0
$143$	11.2966	−	0.988327i	0.944672	−	0.0826481i
$144$		0			0
$145$	10.0282	−	0.906309i	0.832793	−	0.0752649i
$146$		0			0
$147$	1.87292	−	2.67481i	0.154476	−	0.220614i
$148$		0			0
$149$	2.12809	−	5.84688i	0.174340	−	0.478995i	−0.821490	−	0.570223i	$-0.806857\pi$
$149$	2.12809	−	5.84688i	0.174340	−	0.478995i	0.995830	+	0.0912279i	$0.0290792\pi$
$150$		0			0
$151$			18.0272i			1.46703i	0.679672	+	0.733516i	$0.262122\pi$
$151$			18.0272i			1.46703i	−0.679672	+	0.733516i	$0.737878\pi$
$152$		0			0
$153$	−8.07836	−	8.07836i	−0.653097	−	0.653097i
$154$		0			0
$155$	7.46123	−	2.02216i	0.599300	−	0.162424i
$156$		0			0
$157$	11.6215	+	8.13748i	0.927498	+	0.649441i	0.936556	−	0.350518i	$-0.113994\pi$
$157$	11.6215	+	8.13748i	0.927498	+	0.649441i	−0.00905785	+	0.999959i	$0.502883\pi$
$158$		0			0
$159$	2.65646	+	1.53371i	0.210671	+	0.121631i
$160$		0			0
$161$	6.54447	+	5.49146i	0.515777	+	0.432788i
$162$		0			0
$163$	5.57929	−	20.8222i	0.437004	−	1.63092i	−0.299220	−	0.954184i	$-0.596727\pi$
$163$	5.57929	−	20.8222i	0.437004	−	1.63092i	0.736224	−	0.676737i	$-0.236607\pi$
$164$		0			0
$165$	−1.71560	+	0.307578i	−0.133560	+	0.0239449i
$166$		0			0
$167$	11.5436	−	8.08291i	0.893270	−	0.625474i	−0.0341827	−	0.999416i	$-0.510883\pi$
$167$	11.5436	−	8.08291i	0.893270	−	0.625474i	0.927452	+	0.373942i	$0.121994\pi$
$168$		0			0
$169$	−13.4286	−	16.0036i	−1.03297	−	1.23105i
$170$		0			0
$171$	−10.0746	+	7.19269i	−0.770423	+	0.550039i
$172$		0			0
$173$	1.01214	−	11.5689i	0.0769519	−	0.879564i	−0.855390	−	0.517985i	$-0.826682\pi$
$173$	1.01214	−	11.5689i	0.0769519	−	0.879564i	0.932341	−	0.361579i	$-0.117762\pi$
$174$		0			0
$175$	18.7754	−	5.14633i	1.41928	−	0.389026i
$176$		0			0
$177$	−0.949270	+	2.03572i	−0.0713515	+	0.153014i
$178$		0			0
$179$	11.0677	+	19.1698i	0.827238	+	1.43282i	0.900197	+	0.435483i	$0.143422\pi$
$179$	11.0677	+	19.1698i	0.827238	+	1.43282i	−0.0729591	+	0.997335i	$0.523244\pi$
$180$		0			0
$181$	15.8520	−	18.8917i	1.17827	−	1.40421i	0.282743	−	0.959196i	$-0.408756\pi$
$181$	15.8520	−	18.8917i	1.17827	−	1.40421i	0.895526	−	0.445010i	$-0.146800\pi$
$182$		0			0
$183$	1.16051	+	4.33107i	0.0857871	+	0.320162i
$184$		0			0
$185$	−15.8589	+	0.0454388i	−1.16597	+	0.00334072i
$186$		0			0
$187$	−7.10195	+	3.31169i	−0.519346	+	0.242175i
$188$		0			0
$189$	9.09897			0.661853
$190$		0			0
$191$	−15.6365			−1.13142			−0.565709	−	0.824605i	$-0.691398\pi$
$191$	−15.6365			−1.13142			−0.565709	+	0.824605i	$0.691398\pi$
$192$		0			0
$193$	4.20793	−	1.96219i	0.302893	−	0.141242i	−0.265229	−	0.964185i	$-0.585448\pi$
$193$	4.20793	−	1.96219i	0.302893	−	0.141242i	0.568123	+	0.822944i	$0.307670\pi$
$194$		0			0
$195$	3.69398	+	3.67288i	0.264532	+	0.263020i
$196$		0			0
$197$	3.56624	+	13.3094i	0.254084	+	0.948255i	0.968598	+	0.248633i	$0.0799813\pi$
$197$	3.56624	+	13.3094i	0.254084	+	0.948255i	−0.714514	+	0.699621i	$0.753352\pi$
$198$		0			0
$199$	3.48073	−	4.14817i	0.246742	−	0.294056i	−0.628431	−	0.777865i	$-0.716303\pi$
$199$	3.48073	−	4.14817i	0.246742	−	0.294056i	0.875174	+	0.483809i	$0.160747\pi$
$200$		0			0
$201$	1.46319	+	2.53432i	0.103206	+	0.178757i
$202$		0			0
$203$	−7.40968	+	15.8901i	−0.520058	+	1.11527i
$204$		0			0
$205$	8.83462	+	18.8050i	0.617037	+	1.31340i
$206$		0			0
$207$	−0.543082	+	6.20746i	−0.0377468	+	0.431448i
$208$		0			0
$209$	2.27254	+	8.18082i	0.157195	+	0.565879i
$210$		0			0
$211$	−17.6436	−	21.0268i	−1.21464	−	1.44755i	−0.858269	−	0.513200i	$-0.828460\pi$
$211$	−17.6436	−	21.0268i	−1.21464	−	1.44755i	−0.356366	−	0.934346i	$-0.615984\pi$
$212$		0			0
$213$	−0.898065	+	0.628832i	−0.0615344	+	0.0430869i
$214$		0			0
$215$	0.881177	+	4.91502i	0.0600958	+	0.335201i
$216$		0			0
$217$	−3.48387	+	13.0020i	−0.236500	+	0.882632i
$218$		0			0
$219$	1.26567	+	1.06203i	0.0855263	+	0.0717651i
$220$		0			0
$221$	20.2822	+	11.7099i	1.36433	+	0.787694i
$222$		0			0
$223$	3.21418	+	2.25060i	0.215238	+	0.150711i	0.676224	−	0.736696i	$-0.263615\pi$
$223$	3.21418	+	2.25060i	0.215238	+	0.150711i	−0.460986	+	0.887407i	$0.652504\pi$
$224$		0			0
$225$	10.9294	+	9.06468i	0.728630	+	0.604312i
$226$		0			0
$227$	−12.0533	−	12.0533i	−0.800004	−	0.800004i	0.183092	−	0.983096i	$-0.441389\pi$
$227$	−12.0533	−	12.0533i	−0.800004	−	0.800004i	−0.983096	+	0.183092i	$0.941389\pi$
$228$		0			0
$229$			6.89642i			0.455728i	0.973693	+	0.227864i	$0.0731742\pi$
$229$			6.89642i			0.455728i	−0.973693	+	0.227864i	$0.926826\pi$
$230$		0			0
$231$	1.03801	−	2.85192i	0.0682962	−	0.187642i
$232$		0			0
$233$	−8.42351	+	12.0300i	−0.551842	+	0.788112i	−0.994064	−	0.108793i	$-0.965301\pi$
$233$	−8.42351	+	12.0300i	−0.551842	+	0.788112i	0.442222	+	0.896906i	$0.354190\pi$
$234$		0			0
$235$	−5.84864	+	7.01083i	−0.381523	+	0.457336i
$236$		0			0
$237$	3.45676	−	0.302427i	0.224541	−	0.0196448i
$238$		0			0
$239$	20.2687	−	11.7021i	1.31107	−	0.756947i	0.328797	−	0.944401i	$-0.393357\pi$
$239$	20.2687	−	11.7021i	1.31107	−	0.756947i	0.982273	+	0.187454i	$0.0600234\pi$
$240$		0			0
$241$	−5.32234	−	14.6230i	−0.342842	−	0.941952i	−0.984566	−	0.175015i	$-0.944002\pi$
$241$	−5.32234	−	14.6230i	−0.342842	−	0.941952i	0.641723	−	0.766936i	$-0.278220\pi$
$242$		0			0
$243$	5.76203	+	8.22903i	0.369634	+	0.527893i
$244$		0			0
$245$	−4.67195	+	17.6379i	−0.298480	+	1.12685i
$246$		0			0
$247$	16.1326	−	19.5876i	1.02649	−	1.24633i
$248$		0			0
$249$	4.56353	−	3.82925i	0.289202	−	0.242669i
$250$		0			0
$251$	1.15969	−	6.57695i	0.0731993	−	0.415134i	−0.926085	−	0.377314i	$-0.876848\pi$
$251$	1.15969	−	6.57695i	0.0731993	−	0.415134i	0.999285	−	0.0378195i	$-0.0120412\pi$
$252$		0			0
$253$	3.87355	+	1.80626i	0.243528	+	0.113559i
$254$		0			0
$255$	−3.26678	−	1.51194i	−0.204574	−	0.0946816i
$256$		0			0
$257$	0.338079	+	3.86426i	0.0210888	+	0.241046i	0.999422	+	0.0340074i	$0.0108270\pi$
$257$	0.338079	+	3.86426i	0.0210888	+	0.241046i	−0.978333	+	0.207038i	$0.933617\pi$
$258$		0			0
$259$	13.8073	−	23.9150i	0.857944	−	1.48600i
$260$		0			0
$261$	−12.5937	+	2.22060i	−0.779528	+	0.137452i
$262$		0			0
$263$	0.389328	+	0.834916i	0.0240070	+	0.0514831i	0.917946	−	0.396706i	$-0.129847\pi$
$263$	0.389328	+	0.834916i	0.0240070	+	0.0514831i	−0.893939	+	0.448189i	$0.852069\pi$
$264$		0			0
$265$	−16.8883	−	2.92800i	−1.03744	−	0.179866i
$266$		0			0
$267$	0.518915	−	0.518915i	0.0317571	−	0.0317571i
$268$		0			0
$269$	1.00822	+	0.366962i	0.0614723	+	0.0223741i	0.372573	−	0.928003i	$-0.378476\pi$
$269$	1.00822	+	0.366962i	0.0614723	+	0.0223741i	−0.311101	+	0.950377i	$0.600698\pi$
$270$		0			0
$271$	−0.921346	−	5.22521i	−0.0559678	−	0.317409i	0.943952	−	0.330083i	$-0.107077\pi$
$271$	−0.921346	−	5.22521i	−0.0559678	−	0.317409i	−0.999920	+	0.0126739i	$0.995966\pi$
$272$		0			0
$273$	−8.76147	+	2.34763i	−0.530268	+	0.142085i
$274$		0			0
$275$	8.40651	−	4.91794i	0.506932	−	0.296563i
$276$		0			0
$277$	18.0556	+	4.83800i	1.08486	+	0.290687i	0.756585	−	0.653896i	$-0.226866\pi$
$277$	18.0556	+	4.83800i	1.08486	+	0.290687i	0.328274	+	0.944583i	$0.393533\pi$
$278$		0			0
$279$	−9.22573	+	3.35789i	−0.552330	+	0.201032i
$280$		0			0
$281$	23.8982	+	4.21389i	1.42565	+	0.251380i	0.832638	−	0.553817i	$-0.186829\pi$
$281$	23.8982	+	4.21389i	1.42565	+	0.251380i	0.593007	+	0.805197i	$0.297941\pi$
$282$		0			0
$283$	−1.75141	−	0.153228i	−0.104110	−	0.00910846i	0.0349816	−	0.999388i	$-0.488863\pi$
$283$	−1.75141	−	0.153228i	−0.104110	−	0.00910846i	−0.139092	+	0.990279i	$0.544418\pi$
$284$		0			0
$285$	−2.19857	+	3.22164i	−0.130232	+	0.190833i
$286$		0			0
$287$	−36.0404	−	3.15312i	−2.12740	−	0.186123i
$288$		0			0
$289$	0.803787	+	0.141729i	0.0472816	+	0.00833702i
$290$		0			0
$291$	0.0837173	−	0.0304706i	0.00490759	−	0.00178622i
$292$		0			0
$293$	20.5743	+	5.51286i	1.20196	+	0.322064i	0.803603	−	0.595166i	$-0.202914\pi$
$293$	20.5743	+	5.51286i	1.20196	+	0.322064i	0.398358	+	0.917230i	$0.369580\pi$
$294$		0			0
$295$	1.05808	−	12.5065i	0.0616039	−	0.728159i
$296$		0			0
$297$	4.39692	−	1.17815i	0.255135	−	0.0683633i
$298$		0			0
$299$	−2.21812	−	12.5796i	−0.128277	−	0.727497i
$300$		0			0
$301$	−8.17042	−	2.97379i	−0.470935	−	0.171406i
$302$		0			0
$303$	3.47212	−	3.47212i	0.199468	−	0.199468i
$304$		0			0
$305$	−14.4297	−	20.4827i	−0.826245	−	1.17283i
$306$		0			0
$307$	−12.0025	−	25.7394i	−0.685016	−	1.46902i	−0.873439	−	0.486934i	$-0.838115\pi$
$307$	−12.0025	−	25.7394i	−0.685016	−	1.46902i	0.188422	−	0.982088i	$-0.439663\pi$
$308$		0			0
$309$	0.0629152	−	0.0110937i	0.00357912	−	0.000631096i
$310$		0			0
$311$	−14.4603	+	25.0460i	−0.819969	+	1.42023i	0.0857351	+	0.996318i	$0.472676\pi$
$311$	−14.4603	+	25.0460i	−0.819969	+	1.42023i	−0.905704	+	0.423910i	$0.860657\pi$
$312$		0			0
$313$	0.274958	+	3.14278i	0.0155415	+	0.177640i	0.999998	+	0.00201154i	$0.000640294\pi$
$313$	0.274958	+	3.14278i	0.0155415	+	0.177640i	−0.984456	+	0.175629i	$0.943804\pi$
$314$		0			0
$315$	−23.2093	+	8.52290i	−1.30770	+	0.480211i
$316$		0			0
$317$	−3.37043	−	1.57166i	−0.189302	−	0.0882730i	0.325656	−	0.945488i	$-0.394415\pi$
$317$	−3.37043	−	1.57166i	−0.189302	−	0.0882730i	−0.514958	+	0.857215i	$0.672193\pi$
$318$		0			0
$319$	−1.52312	+	8.63804i	−0.0852783	+	0.483637i
$320$		0			0
$321$	4.01840	−	3.37183i	0.224285	−	0.188197i
$322$		0			0
$323$	−5.84632	+	16.5322i	−0.325298	+	0.919875i
$324$		0			0
$325$	−26.4509	−	12.1502i	−1.46723	−	0.673974i
$326$		0			0
$327$	−1.62292	−	2.31777i	−0.0897476	−	0.128173i
$328$		0			0
$329$	−5.43738	−	14.9391i	−0.299773	−	0.823619i
$330$		0			0
$331$	−29.7206	+	17.1592i	−1.63359	+	0.943155i	−0.650619	+	0.759404i	$0.725491\pi$
$331$	−29.7206	+	17.1592i	−1.63359	+	0.943155i	−0.982973	+	0.183751i	$0.941176\pi$
$332$		0			0
$333$	20.0647	−	1.75543i	1.09954	−	0.0961971i
$334$		0			0
$335$	−12.5566	−	10.4750i	−0.686038	−	0.572313i
$336$		0			0
$337$	6.04900	−	8.63887i	0.329510	−	0.470589i	−0.619876	−	0.784700i	$-0.712817\pi$
$337$	6.04900	−	8.63887i	0.329510	−	0.470589i	0.949387	+	0.314110i	$0.101706\pi$
$338$		0			0
$339$	−2.07143	+	5.69120i	−0.112504	+	0.309103i
$340$		0			0
$341$			6.73408i			0.364671i
$342$		0			0
$343$	−3.19355	−	3.19355i	−0.172435	−	0.172435i
$344$		0			0
$345$	0.513584	+	1.89499i	0.0276504	+	0.102023i
$346$		0			0
$347$	21.2596	+	14.8861i	1.14127	+	0.799128i	0.982144	−	0.188129i	$-0.0602424\pi$
$347$	21.2596	+	14.8861i	1.14127	+	0.799128i	0.159129	+	0.987258i	$0.449131\pi$
$348$		0			0
$349$	−9.14413	−	5.27936i	−0.489474	−	0.282598i	0.234882	−	0.972024i	$-0.424530\pi$
$349$	−9.14413	−	5.27936i	−0.489474	−	0.282598i	−0.724356	+	0.689426i	$0.757863\pi$
$350$		0			0
$351$	−10.4218	−	8.74489i	−0.556272	−	0.466768i
$352$		0			0
$353$	0.503189	−	1.87793i	0.0267821	−	0.0999520i	−0.951241	−	0.308448i	$-0.900190\pi$
$353$	0.503189	−	1.87793i	0.0267821	−	0.0999520i	0.978023	+	0.208496i	$0.0668569\pi$
$354$		0			0
$355$	3.49942	−	5.02830i	0.185730	−	0.266874i
$356$		0			0
$357$	5.13446	−	3.59518i	0.271744	−	0.190277i
$358$		0			0
$359$	−4.69249	−	5.59229i	−0.247660	−	0.295150i	0.627865	−	0.778322i	$-0.283929\pi$
$359$	−4.69249	−	5.59229i	−0.247660	−	0.295150i	−0.875525	+	0.483172i	$0.839484\pi$
$360$		0			0
$361$	16.6257	+	9.19704i	0.875038	+	0.484055i
$362$		0			0
$363$	−0.251314	+	2.87254i	−0.0131906	+	0.150769i
$364$		0			0
$365$	−8.68458	−	3.13278i	−0.454572	−	0.163977i
$366$		0			0
$367$	−3.05650	+	6.55468i	−0.159548	+	0.342152i	−0.969789	−	0.243945i	$-0.921558\pi$
$367$	−3.05650	+	6.55468i	−0.159548	+	0.342152i	0.810241	+	0.586097i	$0.199336\pi$
$368$		0			0
$369$	−13.1936	−	22.8520i	−0.686833	−	1.18963i
$370$		0			0
$371$	19.1844	−	22.8631i	0.996006	−	1.18699i
$372$		0			0
$373$	8.83635	+	32.9777i	0.457529	+	1.70752i	0.680545	+	0.732706i	$0.261743\pi$
$373$	8.83635	+	32.9777i	0.457529	+	1.70752i	−0.223016	+	0.974815i	$0.571590\pi$
$374$		0			0
$375$	4.21718	+	1.49400i	0.217774	+	0.0771500i
$376$		0			0
$377$	23.7586	−	11.0788i	1.22363	−	0.570589i
$378$		0			0
$379$	−10.8584			−0.557756			−0.278878	−	0.960327i	$-0.589963\pi$
$379$	−10.8584			−0.557756			−0.278878	+	0.960327i	$0.589963\pi$
$380$		0			0
$381$	−2.71983			−0.139341
$382$		0			0
$383$	−31.5606	+	14.7169i	−1.61267	+	0.752000i	−0.999286	−	0.0377854i	$-0.987970\pi$
$383$	−31.5606	+	14.7169i	−1.61267	+	0.752000i	−0.613383	+	0.789785i	$0.710192\pi$
$384$		0			0
$385$	0.0485900	+	16.9587i	0.00247637	+	0.864297i
$386$		0			0
$387$	−1.64136	−	6.12564i	−0.0834350	−	0.311384i
$388$		0			0
$389$	−5.92451	+	7.06056i	−0.300385	+	0.357985i	−0.895032	−	0.446002i	$-0.852847\pi$
$389$	−5.92451	+	7.06056i	−0.300385	+	0.357985i	0.594647	+	0.803987i	$0.297292\pi$
$390$		0			0
$391$	4.41349	+	7.64439i	0.223200	+	0.386593i
$392$		0			0
$393$	1.82064	−	3.90438i	0.0918392	−	0.196950i
$394$		0			0
$395$	−17.5494	+	8.24473i	−0.883007	+	0.414837i
$396$		0			0
$397$	0.133600	−	1.52705i	0.00670518	−	0.0766406i	−0.992105	−	0.125412i	$-0.959975\pi$
$397$	0.133600	−	1.52705i	0.00670518	−	0.0766406i	0.998810	+	0.0487710i	$0.0155304\pi$
$398$		0			0
$399$	−2.92647	−	6.12865i	−0.146506	−	0.306816i
$400$		0			0
$401$	−3.11490	−	3.71219i	−0.155551	−	0.185378i	0.682641	−	0.730754i	$-0.260831\pi$
$401$	−3.11490	−	3.71219i	−0.155551	−	0.185378i	−0.838192	+	0.545376i	$0.816387\pi$
$402$		0			0
$403$	16.4864	−	11.5439i	0.821244	−	0.575041i
$404$		0			0
$405$	−13.9201	−	9.68763i	−0.691695	−	0.481382i
$406$		0			0
$407$	3.57559	−	13.3443i	0.177235	−	0.661452i
$408$		0			0
$409$	−26.2490	−	22.0255i	−1.29793	−	1.08909i	−0.990499	−	0.137521i	$-0.956087\pi$
$409$	−26.2490	−	22.0255i	−1.29793	−	1.08909i	−0.307430	−	0.951571i	$-0.599469\pi$
$410$		0			0
$411$	5.53907	+	3.19798i	0.273222	+	0.157745i
$412$		0			0
$413$	17.9025	+	12.5355i	0.880926	+	0.616831i
$414$		0			0
$415$	−16.5615	+	28.8760i	−0.812970	+	1.41747i
$416$		0			0
$417$	−5.80841	−	5.80841i	−0.284439	−	0.284439i
$418$		0			0
$419$		−	18.2280i		−	0.890495i	−0.895407	−	0.445248i	$-0.853116\pi$
$419$		−	18.2280i		−	0.890495i	0.895407	−	0.445248i	$-0.146884\pi$
$420$		0			0
$421$	−6.04504	+	16.6086i	−0.294617	+	0.809455i	0.700759	+	0.713399i	$0.252845\pi$
$421$	−6.04504	+	16.6086i	−0.294617	+	0.809455i	−0.995376	+	0.0960561i	$0.969377\pi$
$422$		0			0
$423$	6.65087	−	9.49843i	0.323377	−	0.461830i
$424$		0			0
$425$	20.0477	+	1.63825i	0.972458	+	0.0794666i
$426$		0			0
$427$	43.4614	−	3.80238i	2.10325	−	0.184010i
$428$		0			0
$429$	−3.92985	+	2.26890i	−0.189735	+	0.109544i
$430$		0			0
$431$	−8.44555	−	23.2039i	−0.406808	−	1.11769i	−0.958859	−	0.283884i	$-0.908377\pi$
$431$	−8.44555	−	23.2039i	−0.406808	−	1.11769i	0.552051	−	0.833810i	$-0.313845\pi$
$432$		0			0
$433$	4.14392	+	5.91813i	0.199144	+	0.284407i	0.906286	−	0.422664i	$-0.138905\pi$
$433$	4.14392	+	5.91813i	0.199144	+	0.284407i	−0.707142	+	0.707071i	$0.750016\pi$
$434$		0			0
$435$	−3.48368	+	2.02463i	−0.167029	+	0.0970736i
$436$		0			0
$437$	8.95707	−	3.35332i	0.428475	−	0.160411i
$438$		0			0
$439$	−12.0392	+	10.1021i	−0.574599	+	0.482146i	−0.883168	−	0.469056i	$-0.844594\pi$
$439$	−12.0392	+	10.1021i	−0.574599	+	0.482146i	0.308569	+	0.951202i	$0.400150\pi$
$440$		0			0
$441$	4.02398	−	22.8211i	0.191618	−	1.08672i
$442$		0			0
$443$	−20.6662	−	9.63683i	−0.981883	−	0.457859i	−0.135699	−	0.990750i	$-0.543328\pi$
$443$	−20.6662	−	9.63683i	−0.981883	−	0.457859i	−0.846184	+	0.532891i	$0.821106\pi$
$444$		0			0
$445$	−1.72236	+	3.72142i	−0.0816479	+	0.176412i
$446$		0			0
$447$	0.217007	+	2.48041i	0.0102641	+	0.117319i
$448$		0			0
$449$	−5.24763	+	9.08916i	−0.247651	+	0.428944i	−0.962874	−	0.269953i	$-0.912992\pi$
$449$	−5.24763	+	9.08916i	−0.247651	+	0.428944i	0.715223	+	0.698897i	$0.246325\pi$
$450$		0			0
$451$	−17.8242	+	3.14288i	−0.839307	+	0.147992i
$452$		0			0
$453$	−3.04872	−	6.53799i	−0.143241	−	0.307182i
$454$		0			0
$455$	41.4351	−	29.1904i	1.94251	−	1.36847i
$456$		0			0
$457$	−20.9707	+	20.9707i	−0.980967	+	0.980967i	−0.999822	−	0.0188554i	$-0.993998\pi$
$457$	−20.9707	+	20.9707i	−0.980967	+	0.980967i	0.0188554	+	0.999822i	$0.493998\pi$
$458$		0			0
$459$	8.83425	+	3.21540i	0.412348	+	0.150082i
$460$		0			0
$461$	0.207934	+	1.17925i	0.00968446	+	0.0549233i	0.989267	−	0.146119i	$-0.0466782\pi$
$461$	0.207934	+	1.17925i	0.00968446	+	0.0549233i	−0.979583	+	0.201042i	$0.935567\pi$
$462$		0			0
$463$	−9.49986	+	2.54548i	−0.441496	+	0.118298i	−0.472717	−	0.881214i	$-0.656727\pi$
$463$	−9.49986	+	2.54548i	−0.441496	+	0.118298i	0.0312217	+	0.999512i	$0.490060\pi$
$464$		0			0
$465$	−2.36401	+	1.99521i	−0.109628	+	0.0925256i
$466$		0			0
$467$	−33.0167	−	8.84679i	−1.52783	−	0.409381i	−0.605519	−	0.795831i	$-0.707034\pi$
$467$	−33.0167	−	8.84679i	−1.52783	−	0.409381i	−0.922310	+	0.386450i	$0.873701\pi$
$468$		0			0
$469$	26.7563	−	9.73848i	1.23549	−	0.449681i
$470$		0			0
$471$	−5.59101	−	0.985846i	−0.257620	−	0.0454254i
$472$		0			0
$473$	−4.33327	−	0.379112i	−0.199244	−	0.0174316i
$474$		0			0
$475$	5.32678	−	21.1335i	0.244410	−	0.969672i
$476$		0			0
$477$	21.6858	+	1.89726i	0.992922	+	0.0868695i
$478$		0			0
$479$	33.0238	+	5.82300i	1.50890	+	0.266059i	0.866059	−	0.499942i	$-0.166645\pi$
$479$	33.0238	+	5.82300i	1.50890	+	0.266059i	0.642839	+	0.766001i	$0.277756\pi$
$480$		0			0
$481$	−38.7989	+	14.1216i	−1.76908	+	0.643892i
$482$		0			0
$483$	−3.30221	−	0.884825i	−0.150256	−	0.0402609i
$484$		0			0
$485$	−0.380435	+	0.321085i	−0.0172747	+	0.0145797i
$486$		0			0
$487$	2.99168	−	0.801617i	0.135566	−	0.0363247i	−0.190398	−	0.981707i	$-0.560978\pi$
$487$	2.99168	−	0.801617i	0.135566	−	0.0363247i	0.325964	+	0.945382i	$0.394311\pi$
$488$		0			0
$489$	1.49794	+	8.49523i	0.0677391	+	0.384168i
$490$		0			0
$491$	16.0890	+	5.85594i	0.726089	+	0.264275i	0.678508	−	0.734593i	$-0.262627\pi$
$491$	16.0890	+	5.85594i	0.726089	+	0.264275i	0.0475804	+	0.998867i	$0.484849\pi$
$492$		0			0
$493$	−12.8094	+	12.8094i	−0.576905	+	0.576905i
$494$		0			0
$495$	−10.1119	+	7.12373i	−0.454498	+	0.320188i
$496$		0			0
$497$	4.50817	+	9.66779i	0.202219	+	0.433660i
$498$		0			0
$499$	28.5374	−	5.03191i	1.27751	−	0.225259i	0.506587	−	0.862189i	$-0.330907\pi$
$499$	28.5374	−	5.03191i	1.27751	−	0.225259i	0.770922	+	0.636930i	$0.219796\pi$
$500$		0			0
$501$	−2.81960	+	4.88368i	−0.125970	+	0.218187i
$502$		0			0
$503$	3.34280	+	38.2084i	0.149048	+	1.70363i	0.591066	+	0.806623i	$0.298707\pi$
$503$	3.34280	+	38.2084i	0.149048	+	1.70363i	−0.442018	+	0.897006i	$0.645737\pi$
$504$		0			0
$505$	−11.5245	+	24.9005i	−0.512836	+	1.10806i
$506$		0			0
$507$	7.57669	+	3.53307i	0.336493	+	0.156909i
$508$		0			0
$509$	4.04565	−	22.9440i	0.179320	−	1.01698i	−0.753718	−	0.657198i	$-0.771742\pi$
$509$	4.04565	−	22.9440i	0.179320	−	1.01698i	0.933038	−	0.359777i	$-0.117147\pi$
$510$		0			0
$511$	12.3149	−	10.3334i	0.544778	−	0.457123i
$512$		0			0
$513$	5.01219	−	8.86795i	0.221294	−	0.391529i
$514$		0			0
$515$	−0.308644	+	0.179377i	−0.0136005	+	0.00790430i
$516$		0			0
$517$	−4.56186	−	6.51501i	−0.200630	−	0.286530i
$518$		0			0
$519$	1.58942	+	4.36690i	0.0697678	+	0.191685i
$520$		0			0
$521$	5.45638	−	3.15025i	0.239049	−	0.138015i	−0.375691	−	0.926745i	$-0.622595\pi$
$521$	5.45638	−	3.15025i	0.239049	−	0.138015i	0.614739	+	0.788730i	$0.289261\pi$
$522$		0			0
$523$	26.8932	−	2.35285i	1.17596	−	0.102883i	0.517623	−	0.855609i	$-0.326817\pi$
$523$	26.8932	−	2.35285i	1.17596	−	0.102883i	0.658334	+	0.752726i	$0.271262\pi$
$524$		0			0
$525$	−5.93900	+	5.04168i	−0.259199	+	0.220037i
$526$		0			0
$527$	−7.97716	+	11.3926i	−0.347491	+	0.496268i
$528$		0			0
$529$	−6.21984	+	17.0889i	−0.270428	+	0.742994i
$530$		0			0
$531$			15.9404i			0.691754i
$532$		0			0
$533$	38.2494	+	38.2494i	1.65677	+	1.65677i
$534$		0			0
$535$	−14.5831	+	25.4267i	−0.630484	+	1.09929i
$536$		0			0
$537$	−7.25591	−	5.08064i	−0.313116	−	0.219246i
$538$		0			0
$539$	−13.7651	−	7.94729i	−0.592905	−	0.342314i
$540$		0			0
$541$	−2.37198	−	1.99033i	−0.101979	−	0.0855708i	0.590372	−	0.807131i	$-0.298981\pi$
$541$	−2.37198	−	1.99033i	−0.101979	−	0.0855708i	−0.692352	+	0.721560i	$0.743425\pi$
$542$		0			0
$543$	−2.55419	+	9.53236i	−0.109611	+	0.409073i
$544$		0			0
$545$	12.9773	+	9.03148i	0.555885	+	0.386866i
$546$		0			0
$547$	11.6352	−	8.14707i	0.497486	−	0.348344i	−0.297750	−	0.954644i	$-0.596236\pi$
$547$	11.6352	−	8.14707i	0.497486	−	0.348344i	0.795236	+	0.606301i	$0.207347\pi$
$548$		0			0
$549$	20.4539	+	24.3760i	0.872951	+	1.04034i
$550$		0			0
$551$	11.4050	+	15.9747i	0.485870	+	0.680543i
$552$		0			0
$553$	2.94259	−	33.6339i	0.125132	−	1.43026i
$554$		0			0
$555$	5.74393	−	2.69850i	0.243816	−	0.114545i
$556$		0			0
$557$	−0.679408	+	1.45700i	−0.0287875	+	0.0617349i	−0.920176	−	0.391506i	$-0.871954\pi$
$557$	−0.679408	+	1.45700i	−0.0287875	+	0.0617349i	0.891388	+	0.453241i	$0.149732\pi$
$558$		0			0
$559$	6.50015	+	11.2586i	0.274927	+	0.476187i
$560$		0			0
$561$	2.01563	−	2.40213i	0.0850998	−	0.101418i
$562$		0			0
$563$	−3.05000	−	11.3828i	−0.128542	−	0.479726i	0.871399	−	0.490575i	$-0.163213\pi$
$563$	−3.05000	−	11.3828i	−0.128542	−	0.479726i	−0.999941	+	0.0108488i	$0.996547\pi$
$564$		0			0
$565$	−0.0969647	−	33.8423i	−0.00407933	−	1.42376i
$566$		0			0
$567$	26.7638	−	12.4802i	1.12398	−	0.524118i
$568$		0			0
$569$	31.1070			1.30407			0.652036	−	0.758188i	$-0.273915\pi$
$569$	31.1070			1.30407			0.652036	+	0.758188i	$0.273915\pi$
$570$		0			0
$571$	22.9002			0.958345			0.479172	−	0.877721i	$-0.340937\pi$
$571$	22.9002			0.958345			0.479172	+	0.877721i	$0.340937\pi$
$572$		0			0
$573$	5.67096	−	2.64441i	0.236908	−	0.110472i
$574$		0			0
$575$	−6.34404	−	8.95062i	−0.264565	−	0.373267i
$576$		0			0
$577$	1.22808	+	4.58324i	0.0511255	+	0.190803i	0.986766	−	0.162152i	$-0.0518435\pi$
$577$	1.22808	+	4.58324i	0.0511255	+	0.190803i	−0.935640	+	0.352955i	$0.885177\pi$
$578$		0			0
$579$	−1.19427	+	1.42327i	−0.0496320	+	0.0591491i
$580$		0			0
$581$	−28.9818	−	50.1979i	−1.20237	−	2.08256i
$582$		0			0
$583$	6.31018	−	13.5322i	0.261341	−	0.560448i
$584$		0			0
$585$	34.7747	+	12.5442i	1.43776	+	0.518640i
$586$		0			0
$587$	−1.49191	+	17.0527i	−0.0615779	+	0.703838i	0.901175	+	0.433455i	$0.142706\pi$
$587$	−1.49191	+	17.0527i	−0.0615779	+	0.703838i	−0.962753	+	0.270383i	$0.912850\pi$
$588$		0			0
$589$	10.7528	+	10.5576i	0.443059	+	0.435018i
$590$		0			0
$591$	−3.54423	−	4.22385i	−0.145790	−	0.173746i
$592$		0			0
$593$	−7.61781	+	5.33404i	−0.312826	+	0.219043i	−0.719436	−	0.694559i	$-0.755600\pi$
$593$	−7.61781	+	5.33404i	−0.312826	+	0.219043i	0.406610	+	0.913602i	$0.366711\pi$
$594$		0			0
$595$	−20.0071	+	28.7480i	−0.820209	+	1.17855i
$596$		0			0
$597$	−0.560841	+	2.09309i	−0.0229537	+	0.0856643i
$598$		0			0
$599$	−17.9004	−	15.0202i	−0.731389	−	0.613708i	0.199121	−	0.979975i	$-0.436191\pi$
$599$	−17.9004	−	15.0202i	−0.731389	−	0.613708i	−0.930510	+	0.366267i	$0.880636\pi$
$600$		0			0
$601$	−15.0109	−	8.66657i	−0.612309	−	0.353517i	0.161560	−	0.986863i	$-0.448348\pi$
$601$	−15.0109	−	8.66657i	−0.612309	−	0.353517i	−0.773869	+	0.633346i	$0.781681\pi$
$602$		0			0
$603$	17.0119	+	11.9119i	0.692779	+	0.485089i
$604$		0			0
$605$	−4.21483	−	15.5516i	−0.171357	−	0.632261i
$606$		0			0
$607$	−5.10563	−	5.10563i	−0.207231	−	0.207231i	0.595858	−	0.803090i	$-0.296812\pi$
$607$	−5.10563	−	5.10563i	−0.207231	−	0.207231i	−0.803090	+	0.595858i	$0.796812\pi$
$608$		0			0
$609$		−	7.01603i		−	0.284304i
$610$		0			0
$611$	−8.12989	+	22.3367i	−0.328900	+	0.903646i
$612$		0			0
$613$	4.77602	−	6.82086i	0.192902	−	0.275492i	−0.711037	−	0.703155i	$-0.751774\pi$
$613$	4.77602	−	6.82086i	0.192902	−	0.275492i	0.903938	+	0.427663i	$0.140663\pi$
$614$		0			0
$615$	−6.38435	−	5.32601i	−0.257442	−	0.214765i
$616$		0			0
$617$	−2.58557	+	0.226208i	−0.104091	+	0.00910678i	−0.139082	−	0.990281i	$-0.544415\pi$
$617$	−2.58557	+	0.226208i	−0.104091	+	0.00910678i	0.0349912	+	0.999388i	$0.488860\pi$
$618$		0			0
$619$	14.3260	−	8.27110i	0.575809	−	0.332444i	−0.183657	−	0.982990i	$-0.558794\pi$
$619$	14.3260	−	8.27110i	0.575809	−	0.332444i	0.759466	+	0.650547i	$0.225460\pi$
$620$		0			0
$621$	−1.75375	−	4.81838i	−0.0703755	−	0.193355i
$622$		0			0
$623$	−4.09553	−	5.84903i	−0.164084	−	0.234336i
$624$		0			0
$625$	−24.9984	+	0.286512i	−0.999934	+	0.0114605i
$626$		0			0
$627$	−2.20771	−	2.58264i	−0.0881675	−	0.103141i
$628$		0			0
$629$	21.8567	−	18.3399i	0.871484	−	0.731262i
$630$		0			0
$631$	−0.733663	+	4.16081i	−0.0292067	+	0.165639i	−0.995922	−	0.0902134i	$-0.971245\pi$
$631$	−0.733663	+	4.16081i	−0.0292067	+	0.165639i	0.966716	+	0.255853i	$0.0823562\pi$
$632$		0			0
$633$	9.95488	+	4.64204i	0.395671	+	0.184504i
$634$		0			0
$635$	14.2665	−	5.23892i	0.566149	−	0.207900i
$636$		0			0
$637$	4.14025	+	47.3233i	0.164043	+	1.87502i
$638$		0			0
$639$	−3.89019	+	6.73801i	−0.153894	+	0.266551i
$640$		0			0
$641$	31.9675	−	5.63673i	1.26264	−	0.222637i	0.498046	−	0.867150i	$-0.334051\pi$
$641$	31.9675	−	5.63673i	1.26264	−	0.222637i	0.764593	+	0.644513i	$0.222940\pi$
$642$		0			0
$643$	8.36545	+	17.9398i	0.329901	+	0.707475i	0.999375	−	0.0353606i	$-0.0112580\pi$
$643$	8.36545	+	17.9398i	0.329901	+	0.707475i	−0.669473	+	0.742836i	$0.733480\pi$
$644$		0			0
$645$	−1.15080	−	1.63353i	−0.0453125	−	0.0643200i
$646$		0			0
$647$	−21.7829	+	21.7829i	−0.856375	+	0.856375i	−0.990909	−	0.134534i	$-0.957046\pi$
$647$	−21.7829	+	21.7829i	−0.856375	+	0.856375i	0.134534	+	0.990909i	$0.457046\pi$
$648$		0			0
$649$	10.2742	+	3.73951i	0.403298	+	0.146788i
$650$		0			0
$651$	−0.935355	−	5.30466i	−0.0366594	−	0.207906i
$652$		0			0
$653$	−2.86215	+	0.766911i	−0.112005	+	0.0300116i	−0.314386	−	0.949295i	$-0.601799\pi$
$653$	−2.86215	+	0.766911i	−0.112005	+	0.0300116i	0.202381	+	0.979307i	$0.435132\pi$
$654$		0			0
$655$	−2.02934	+	23.9868i	−0.0792927	+	0.937241i
$656$		0			0
$657$	11.3258	+	3.03474i	0.441862	+	0.118396i
$658$		0			0
$659$	−5.69461	+	2.07267i	−0.221831	+	0.0807397i	−0.450545	−	0.892754i	$-0.648770\pi$
$659$	−5.69461	+	2.07267i	−0.221831	+	0.0807397i	0.228714	+	0.973494i	$0.426548\pi$
$660$		0			0
$661$	−38.4949	−	6.78768i	−1.49728	−	0.264010i	−0.635818	−	0.771839i	$-0.719337\pi$
$661$	−38.4949	−	6.78768i	−1.49728	−	0.264010i	−0.861458	+	0.507829i	$0.830448\pi$
$662$		0			0
$663$	−9.33617	−	0.816809i	−0.362587	−	0.0317222i
$664$		0			0
$665$	27.1553	+	26.5101i	1.05304	+	1.02802i
$666$		0			0
$667$	9.84279	+	0.861133i	0.381114	+	0.0333432i
$668$		0			0
$669$	−1.54632	−	0.272657i	−0.0597840	−	0.0105415i
$670$		0			0
$671$	20.5096	−	7.46490i	0.791766	−	0.288179i
$672$		0			0
$673$	−14.4653	−	3.87597i	−0.557596	−	0.149408i	−0.0309946	−	0.999520i	$-0.509867\pi$
$673$	−14.4653	−	3.87597i	−0.557596	−	0.149408i	−0.526602	+	0.850112i	$0.676534\pi$
$674$		0			0
$675$	−11.3036	−	2.95947i	−0.435075	−	0.113910i
$676$		0			0
$677$	−27.5523	+	7.38263i	−1.05892	+	0.283738i	−0.745934	−	0.666019i	$-0.767997\pi$
$677$	−27.5523	+	7.38263i	−1.05892	+	0.283738i	−0.312988	+	0.949757i	$0.601330\pi$
$678$		0			0
$679$	−0.150525	−	0.853668i	−0.00577661	−	0.0327608i
$680$		0			0
$681$	6.40983	+	2.33299i	0.245625	+	0.0894003i
$682$		0			0
$683$	−17.6900	+	17.6900i	−0.676888	+	0.676888i	−0.959295	−	0.282407i	$-0.908867\pi$
$683$	−17.6900	+	17.6900i	−0.676888	+	0.676888i	0.282407	+	0.959295i	$0.408867\pi$
$684$		0			0
$685$	−35.2143	−	6.10526i	−1.34547	−	0.233270i
$686$		0			0
$687$	−1.16631	−	2.50115i	−0.0444973	−	0.0954249i
$688$		0			0
$689$	−43.9468	+	7.74901i	−1.67424	+	0.295214i
$690$		0			0
$691$	−5.11916	+	8.86665i	−0.194742	+	0.337303i	−0.946816	−	0.321776i	$-0.895720\pi$
$691$	−5.11916	+	8.86665i	−0.194742	+	0.337303i	0.752074	+	0.659079i	$0.229054\pi$
$692$		0			0
$693$	−1.87717	−	21.4562i	−0.0713079	−	0.815053i
$694$		0			0
$695$	41.6553	+	19.2791i	1.58008	+	0.731298i
$696$		0			0
$697$	−33.8776	−	15.7974i	−1.28320	−	0.598368i
$698$		0			0
$699$	1.02050	−	5.78754i	0.0385988	−	0.218905i
$700$		0			0
$701$	6.26653	−	5.25824i	0.236683	−	0.198601i	−0.516729	−	0.856149i	$-0.672851\pi$
$701$	6.26653	−	5.25824i	0.236683	−	0.198601i	0.753413	+	0.657548i	$0.228406\pi$
$702$		0			0
$703$	−15.7020	−	26.6303i	−0.592211	−	1.00438i
$704$		0			0
$705$	0.935493	−	3.53175i	0.0352327	−	0.133013i
$706$		0			0
$707$	−27.4037	−	39.1365i	−1.03062	−	1.47188i
$708$		0			0
$709$	−4.64302	−	12.7566i	−0.174372	−	0.479084i	0.821462	−	0.570263i	$-0.193159\pi$
$709$	−4.64302	−	12.7566i	−0.174372	−	0.479084i	−0.995835	+	0.0911790i	$0.970936\pi$
$710$		0			0
$711$	21.3262	−	12.3127i	0.799795	−	0.461762i
$712$		0			0
$713$	7.55671	−	0.661126i	0.283001	−	0.0247594i
$714$		0			0
$715$	16.2431	−	19.4708i	0.607459	−	0.728169i
$716$		0			0
$717$	−5.37188	+	7.67184i	−0.200617	+	0.286510i
$718$		0			0
$719$	1.04276	−	2.86496i	0.0388884	−	0.106845i	−0.918729	−	0.394889i	$-0.870783\pi$
$719$	1.04276	−	2.86496i	0.0388884	−	0.106845i	0.957617	+	0.288044i	$0.0930051\pi$
$720$		0			0
$721$		−	0.621602i		−	0.0231497i
$722$		0			0
$723$	4.40329	+	4.40329i	0.163760	+	0.163760i
$724$		0			0
$725$	14.3733	−	17.3302i	0.533811	−	0.643626i
$726$		0			0
$727$	18.6585	+	13.0649i	0.692007	+	0.484549i	0.865901	−	0.500216i	$-0.166746\pi$
$727$	18.6585	+	13.0649i	0.692007	+	0.484549i	−0.173894	+	0.984764i	$0.555635\pi$
$728$		0			0
$729$	16.2236	+	9.36667i	0.600872	+	0.346914i
$730$		0			0
$731$	−6.88183	−	5.77454i	−0.254534	−	0.213579i
$732$		0			0
$733$	4.51172	−	16.8380i	0.166644	−	0.621924i	−0.831181	−	0.556002i	$-0.812335\pi$
$733$	4.51172	−	16.8380i	0.166644	−	0.621924i	0.997825	−	0.0659219i	$-0.0209988\pi$
$734$		0			0
$735$	−1.28849	−	7.18693i	−0.0475268	−	0.265094i
$736$		0			0
$737$	11.6685	−	8.17040i	0.429816	−	0.300961i
$738$		0			0
$739$	−3.78660	−	4.51269i	−0.139292	−	0.166002i	0.691888	−	0.722004i	$-0.256779\pi$
$739$	−3.78660	−	4.51269i	−0.139292	−	0.166002i	−0.831181	+	0.556002i	$0.812335\pi$
$740$		0			0
$741$	−2.53825	+	9.83220i	−0.0932451	+	0.361195i
$742$		0			0
$743$	−0.199808	+	2.28381i	−0.00733024	+	0.0837850i	−0.998979	−	0.0451861i	$-0.985612\pi$
$743$	−0.199808	+	2.28381i	−0.00733024	+	0.0837850i	0.991648	+	0.128971i	$0.0411675\pi$
$744$		0			0
$745$	−5.91602	−	12.5926i	−0.216746	−	0.461358i
$746$		0			0
$747$	17.8670	−	38.3160i	0.653720	−	1.40191i
$748$		0			0
$749$	−25.5198	−	44.2016i	−0.932473	−	1.61509i
$750$		0			0
$751$	−2.71700	+	3.23800i	−0.0991449	+	0.118156i	−0.813335	−	0.581795i	$-0.802351\pi$
$751$	−2.71700	+	3.23800i	−0.0991449	+	0.118156i	0.714191	+	0.699951i	$0.246795\pi$
$752$		0			0
$753$	0.691688	+	2.58141i	0.0252065	+	0.0940720i
$754$		0			0
$755$	28.5850	+	28.4217i	1.04032	+	1.03437i
$756$		0			0
$757$	36.9125	−	17.2126i	1.34161	−	0.625602i	0.386617	−	0.922240i	$-0.373643\pi$
$757$	36.9125	−	17.2126i	1.34161	−	0.625602i	0.954990	+	0.296638i	$0.0958656\pi$
$758$		0			0
$759$	−1.71031			−0.0620802
$760$		0			0
$761$	9.70881			0.351944			0.175972	−	0.984395i	$-0.443693\pi$
$761$	9.70881			0.351944			0.175972	+	0.984395i	$0.443693\pi$
$762$		0			0
$763$	−24.9511	+	11.6349i	−0.903290	+	0.421211i
$764$		0			0
$765$	−25.5459	+	0.0731939i	−0.923615	+	0.00264633i
$766$		0			0
$767$	−8.45748	−	31.5637i	−0.305382	−	1.13970i
$768$		0			0
$769$	−33.1498	+	39.5064i	−1.19541	+	1.42464i	−0.315880	+	0.948799i	$0.602300\pi$
$769$	−33.1498	+	39.5064i	−1.19541	+	1.42464i	−0.879533	+	0.475839i	$0.842145\pi$
$770$		0			0
$771$	−0.776127	−	1.34429i	−0.0279515	−	0.0484134i
$772$		0			0
$773$	−11.9890	+	25.7104i	−0.431214	+	0.924741i	0.563885	+	0.825853i	$0.309306\pi$
$773$	−11.9890	+	25.7104i	−0.431214	+	0.924741i	−0.995099	+	0.0988873i	$0.968472\pi$
$774$		0			0
$775$	8.55692	−	15.0191i	0.307374	−	0.539503i
$776$		0			0
$777$	−0.963109	+	11.0084i	−0.0345514	+	0.394924i
$778$		0			0
$779$	−22.9260	+	33.3884i	−0.821409	+	1.19626i
$780$		0			0
$781$	3.43030	+	4.08807i	0.122746	+	0.146283i
$782$		0			0
$783$	8.62006	−	6.03583i	0.308056	−	0.215703i
$784$		0			0
$785$	31.2258	−	5.59825i	1.11450	−	0.199810i
$786$		0			0
$787$	−11.4267	+	42.6452i	−0.407319	+	1.52014i	0.392419	+	0.919787i	$0.371638\pi$
$787$	−11.4267	+	42.6452i	−0.407319	+	1.52014i	−0.799738	+	0.600349i	$0.795028\pi$
$788$		0			0
$789$	−0.282398	−	0.236960i	−0.0100536	−	0.00843600i
$790$		0			0
$791$	51.0337	+	29.4643i	1.81455	+	1.04763i
$792$		0			0
$793$	−53.4341	−	37.4150i	−1.89750	−	1.32864i
$794$		0			0
$795$	6.62013	−	1.79420i	0.234792	−	0.0636338i
$796$		0			0
$797$	−7.56963	−	7.56963i	−0.268130	−	0.268130i	0.560216	−	0.828346i	$-0.310718\pi$
$797$	−7.56963	−	7.56963i	−0.268130	−	0.268130i	−0.828346	+	0.560216i	$0.810718\pi$
$798$		0			0
$799$		−	16.4259i		−	0.581107i
$800$		0			0
$801$	1.78123	−	4.89389i	0.0629367	−	0.172917i
$802$		0			0
$803$	4.61296	−	6.58799i	0.162788	−	0.232485i
$804$		0			0
$805$	19.0256	−	1.71947i	0.670566	−	0.0606034i
$806$		0			0
$807$	−0.427715	+	0.0374202i	−0.0150563	+	0.00131725i
$808$		0			0
$809$	−32.2339	+	18.6103i	−1.13328	+	0.654302i	−0.944759	−	0.327766i	$-0.893704\pi$
$809$	−32.2339	+	18.6103i	−1.13328	+	0.654302i	−0.188526	+	0.982068i	$0.560371\pi$
$810$		0			0
$811$	13.5629	+	37.2637i	0.476257	+	1.30850i	0.912648	+	0.408747i	$0.134034\pi$
$811$	13.5629	+	37.2637i	0.476257	+	1.30850i	−0.436391	+	0.899757i	$0.643744\pi$
$812$		0			0
$813$	1.21782	+	1.73923i	0.0427110	+	0.0609976i
$814$		0			0
$815$	−24.2207	−	41.6752i	−0.848413	−	1.45982i
$816$		0			0
$817$	−7.39898	+	6.32485i	−0.258858	+	0.221279i
$818$		0			0
$819$	−49.3111	+	41.3769i	−1.72307	+	1.44583i
$820$		0			0
$821$	−4.49696	+	25.5035i	−0.156945	+	0.890080i	0.800041	+	0.599945i	$0.204811\pi$
$821$	−4.49696	+	25.5035i	−0.156945	+	0.890080i	−0.956986	+	0.290134i	$0.906300\pi$
$822$		0			0
$823$	−11.9997	−	5.59556i	−0.418283	−	0.195049i	0.202070	−	0.979371i	$-0.435233\pi$
$823$	−11.9997	−	5.59556i	−0.418283	−	0.195049i	−0.620354	+	0.784322i	$0.713011\pi$
$824$		0			0
$825$	−2.21711	+	3.20530i	−0.0771899	+	0.111594i
$826$		0			0
$827$	2.86033	+	32.6938i	0.0994635	+	1.13687i	0.867829	+	0.496862i	$0.165515\pi$
$827$	2.86033	+	32.6938i	0.0994635	+	1.13687i	−0.768366	+	0.640011i	$0.778930\pi$
$828$		0			0
$829$	−7.66854	+	13.2823i	−0.266339	+	0.461313i	−0.967914	−	0.251283i	$-0.919147\pi$
$829$	−7.66854	+	13.2823i	−0.266339	+	0.461313i	0.701574	+	0.712596i	$0.252481\pi$
$830$		0			0
$831$	−7.36650	+	1.29891i	−0.255541	+	0.0450588i
$832$		0			0
$833$	−13.8732	−	29.7511i	−0.480677	−	1.03082i
$834$		0			0
$835$	5.38288	−	31.0478i	0.186282	−	1.07445i
$836$		0			0
$837$	5.71275	−	5.71275i	0.197462	−	0.197462i
$838$		0			0
$839$	29.0261	+	10.5646i	1.00209	+	0.364732i	0.790391	−	0.612603i	$-0.209878\pi$
$839$	29.0261	+	10.5646i	1.00209	+	0.364732i	0.211701	+	0.977335i	$0.432100\pi$
$840$		0			0
$841$	−1.51473	−	8.59044i	−0.0522319	−	0.296222i
$842$		0			0
$843$	−9.37989	+	2.51333i	−0.323060	+	0.0865638i
$844$		0			0
$845$	−46.5479	−	3.93805i	−1.60130	−	0.135473i
$846$		0			0
$847$	27.1003	+	7.26149i	0.931176	+	0.249508i
$848$		0			0
$849$	0.661102	−	0.240622i	0.0226890	−	0.00825811i
$850$		0			0
$851$	−15.3255	−	2.70229i	−0.525350	−	0.0926333i
$852$		0			0
$853$	−6.88794	−	0.602617i	−0.235839	−	0.0206332i	−0.0313763	−	0.999508i	$-0.509989\pi$
$853$	−6.88794	−	0.602617i	−0.235839	−	0.0206332i	−0.204462	+	0.978874i	$0.565545\pi$
$854$		0			0
$855$	−4.47843	+	27.3149i	−0.153159	+	0.934150i
$856$		0			0
$857$	−5.74879	−	0.502954i	−0.196375	−	0.0171806i	−0.0114561	−	0.999934i	$-0.503647\pi$
$857$	−5.74879	−	0.502954i	−0.196375	−	0.0171806i	−0.184919	+	0.982754i	$0.559202\pi$
$858$		0			0
$859$	−27.4787	−	4.84523i	−0.937560	−	0.165317i	−0.316067	−	0.948737i	$-0.602362\pi$
$859$	−27.4787	−	4.84523i	−0.937560	−	0.165317i	−0.621493	+	0.783420i	$0.713474\pi$
$860$		0			0
$861$	13.6042	−	4.95151i	0.463628	−	0.168747i
$862$		0			0
$863$	25.9989	+	6.96639i	0.885014	+	0.237139i	0.672569	−	0.740034i	$-0.265191\pi$
$863$	25.9989	+	6.96639i	0.885014	+	0.237139i	0.212445	+	0.977173i	$0.431857\pi$
$864$		0			0
$865$	−16.7486	−	19.8444i	−0.569468	−	0.674730i
$866$		0			0
$867$	−0.315482	+	0.0845331i	−0.0107143	+	0.00287089i
$868$		0			0
$869$	−2.93303	−	16.6340i	−0.0994962	−	0.564271i
$870$		0			0
$871$	−40.0055	−	14.5608i	−1.35554	−	0.493375i
$872$		0			0
$873$	0.447066	−	0.447066i	0.0151309	−	0.0151309i
$874$		0			0
$875$	21.4409	−	37.8851i	0.724835	−	1.28075i
$876$		0			0
$877$	−10.6753	−	22.8932i	−0.360478	−	0.773048i	−0.999991	−	0.00426738i	$-0.998642\pi$
$877$	−10.6753	−	22.8932i	−0.360478	−	0.773048i	0.639513	−	0.768780i	$-0.279136\pi$
$878$		0			0
$879$	−8.39407	+	1.48010i	−0.283125	+	0.0499225i
$880$		0			0
$881$	−26.9250	+	46.6354i	−0.907125	+	1.57119i	−0.0890859	+	0.996024i	$0.528395\pi$
$881$	−26.9250	+	46.6354i	−0.907125	+	1.57119i	−0.818039	+	0.575163i	$0.804939\pi$
$882$		0			0
$883$	−4.49960	−	51.4306i	−0.151423	−	1.73078i	−0.569175	−	0.822217i	$-0.692737\pi$
$883$	−4.49960	−	51.4306i	−0.151423	−	1.73078i	0.417751	−	0.908562i	$-0.362818\pi$
$884$		0			0
$885$	1.73134	+	4.71474i	0.0581983	+	0.158484i
$886$		0			0
$887$	−27.3506	−	12.7538i	−0.918344	−	0.428231i	−0.0948082	−	0.995496i	$-0.530224\pi$
$887$	−27.3506	−	12.7538i	−0.918344	−	0.428231i	−0.823535	+	0.567265i	$0.808002\pi$
$888$		0			0
$889$	−4.59537	+	26.0617i	−0.154124	+	0.874080i
$890$		0			0
$891$	11.3172	−	9.49626i	0.379141	−	0.318137i
$892$		0			0
$893$	−17.5550	−	2.92991i	−0.587455	−	0.0980456i
$894$		0			0
$895$	47.8462	+	12.6735i	1.59932	+	0.423629i
$896$		0			0
$897$	2.93189	+	4.18717i	0.0978928	+	0.139805i
$898$		0			0
$899$	5.32440	+	14.6287i	0.177579	+	0.487893i
$900$		0			0
$901$	26.7057	−	15.4185i	0.889695	−	0.513665i
$902$		0			0
$903$	3.46612	−	0.303246i	0.115345	−	0.0100914i
$904$		0			0
$905$	−4.96352	−	54.9205i	−0.164993	−	1.82562i
$906$		0			0
$907$	−7.43343	+	10.6160i	−0.246823	+	0.352500i	−0.923378	−	0.383892i	$-0.874583\pi$
$907$	−7.43343	+	10.6160i	−0.246823	+	0.352500i	0.676555	+	0.736392i	$0.263472\pi$
$908$		0			0
$909$	11.9184	−	32.7456i	0.395309	−	1.08610i
$910$		0			0
$911$		−	1.63952i		−	0.0543198i	−0.999631	−	0.0271599i	$-0.991354\pi$
$911$		−	1.63952i		−	0.0543198i	0.999631	−	0.0271599i	$-0.00864633\pi$
$912$		0			0
$913$	−20.5047	−	20.5047i	−0.678605	−	0.678605i
$914$		0			0
$915$	8.69727	+	4.98820i	0.287523	+	0.164905i
$916$		0			0
$917$	−34.3359	−	24.0423i	−1.13387	−	0.793946i
$918$		0			0
$919$	32.7780	+	18.9244i	1.08125	+	0.624258i	0.931232	−	0.364426i	$-0.118735\pi$
$919$	32.7780	+	18.9244i	1.08125	+	0.624258i	0.150014	+	0.988684i	$0.452068\pi$
$920$		0			0
$921$	8.70596	+	7.30516i	0.286871	+	0.240713i
$922$		0			0
$923$	4.12803	−	15.4060i	0.135876	−	0.507095i
$924$		0			0
$925$	−24.9311	+	25.2185i	−0.819731	+	0.829180i
$926$		0			0
$927$	0.371387	−	0.260048i	0.0121979	−	0.00854109i
$928$		0			0
$929$	28.3217	+	33.7524i	0.929204	+	1.10738i	0.993989	+	0.109482i	$0.0349194\pi$
$929$	28.3217	+	33.7524i	0.929204	+	1.10738i	−0.0647851	+	0.997899i	$0.520636\pi$
$930$		0			0
$931$	−34.2707	+	9.52003i	−1.12318	+	0.312006i
$932$		0			0
$933$	1.00866	−	11.5290i	0.0330220	−	0.377443i
$934$		0			0
$935$	−5.94572	+	16.4825i	−0.194446	+	0.539036i
$936$		0			0
$937$	3.14116	−	6.73623i	0.102617	−	0.220063i	−0.848295	−	0.529524i	$-0.822371\pi$
$937$	3.14116	−	6.73623i	0.102617	−	0.220063i	0.950912	+	0.309461i	$0.100148\pi$
$938$		0			0
$939$	−0.631219	−	1.09330i	−0.0205991	−	0.0356786i
$940$		0			0
$941$	19.2240	−	22.9102i	0.626683	−	0.746852i	−0.355521	−	0.934668i	$-0.615696\pi$
$941$	19.2240	−	22.9102i	0.626683	−	0.746852i	0.982204	+	0.187816i	$0.0601409\pi$
$942$		0			0
$943$	5.27672	+	19.6930i	0.171834	+	0.641292i
$944$		0			0
$945$	14.3455	−	14.4279i	0.466658	−	0.469340i
$946$		0			0
$947$	−16.5528	+	7.71871i	−0.537895	+	0.250824i	−0.672529	−	0.740071i	$-0.734792\pi$
$947$	−16.5528	+	7.71871i	−0.537895	+	0.250824i	0.134634	+	0.990895i	$0.457014\pi$
$948$		0			0
$949$	−24.0365			−0.780257
$950$		0			0
$951$	1.48816			0.0482569
$952$		0			0
$953$	43.0745	−	20.0860i	1.39532	−	0.650649i	0.427901	−	0.903825i	$-0.359253\pi$
$953$	43.0745	−	20.0860i	1.39532	−	0.650649i	0.967420	+	0.253176i	$0.0814753\pi$
$954$		0			0
$955$	−24.6526	+	24.7942i	−0.797738	+	0.802323i
$956$		0			0
$957$	−0.908449	−	3.39038i	−0.0293660	−	0.109595i
$958$		0			0
$959$	40.0020	−	47.6725i	1.29173	−	1.53943i
$960$		0			0
$961$	−9.52410	−	16.4962i	−0.307229	−	0.532136i
$962$		0			0
$963$	15.7327	−	33.7390i	0.506981	−	1.08722i
$964$		0			0
$965$	3.52286	−	9.76595i	0.113405	−	0.314377i
$966$		0			0
$967$	−0.408147	+	4.66514i	−0.0131251	+	0.150021i	−0.999929	−	0.0118980i	$-0.996213\pi$
$967$	−0.408147	+	4.66514i	−0.0131251	+	0.150021i	0.986804	+	0.161919i	$0.0517682\pi$
$968$		0			0
$969$	−0.675574	−	6.98451i	−0.0217026	−	0.224375i
$970$		0			0
$971$	24.7733	+	29.5237i	0.795013	+	0.947459i	0.999507	−	0.0314085i	$-0.00999929\pi$
$971$	24.7733	+	29.5237i	0.795013	+	0.947459i	−0.204494	+	0.978868i	$0.565555\pi$
$972$		0			0
$973$	−65.4704	+	45.8429i	−2.09889	+	1.46966i
$974$		0			0
$975$	11.6479	−	0.0667473i	0.373031	−	0.00213762i
$976$		0			0
$977$	5.56801	−	20.7801i	0.178137	−	0.664815i	−0.817860	−	0.575418i	$-0.804839\pi$
$977$	5.56801	−	20.7801i	0.178137	−	0.664815i	0.995996	−	0.0893968i	$-0.0284939\pi$
$978$		0			0
$979$	−2.73644	−	2.29614i	−0.0874569	−	0.0733851i
$980$		0			0
$981$	−17.3898	−	10.0400i	−0.555212	−	0.320552i
$982$		0			0
$983$	−15.1505	−	10.6085i	−0.483227	−	0.338359i	0.306445	−	0.951888i	$-0.400860\pi$
$983$	−15.1505	−	10.6085i	−0.483227	−	0.338359i	−0.789672	+	0.613529i	$0.789749\pi$
$984$		0			0
$985$	26.7267	+	15.3288i	0.851585	+	0.488415i
$986$		0			0
$987$	4.49846	+	4.49846i	0.143188	+	0.143188i
$988$		0			0
$989$			4.89984i			0.155806i
$990$		0			0
$991$	17.9310	−	49.2651i	0.569597	−	1.56496i	−0.235538	−	0.971865i	$-0.575685\pi$
$991$	17.9310	−	49.2651i	0.569597	−	1.56496i	0.805135	−	0.593091i	$-0.202093\pi$
$992$		0			0
$993$	7.87696	−	11.2495i	0.249968	−	0.356991i
$994$		0			0
$995$	−1.08988	−	12.0593i	−0.0345514	−	0.382305i
$996$		0			0
$997$	−30.9945	+	2.71166i	−0.981604	+	0.0858792i	−0.566646	−	0.823961i	$-0.691759\pi$
$997$	−30.9945	+	2.71166i	−0.981604	+	0.0858792i	−0.414958	+	0.909841i	$0.636204\pi$
$998$		0			0
$999$	−14.3537	+	8.28712i	−0.454131	+	0.262193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.13.5	✓	120
5.2	odd	4	inner	380.2.bh.a.317.6	yes	120
19.3	odd	18	inner	380.2.bh.a.193.6	yes	120
95.22	even	36	inner	380.2.bh.a.117.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.5	✓	120	1.1	even	1	trivial
380.2.bh.a.117.5	yes	120	95.22	even	36	inner
380.2.bh.a.193.6	yes	120	19.3	odd	18	inner
380.2.bh.a.317.6	yes	120	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.362674 + 0.169118i) q^{3} +(1.57660 - 1.58566i) q^{5} +(1.00773 + 3.76091i) q^{7} +(-1.82543 + 2.17546i) q^{9} +O(q^{10})\)	\(q+(-0.362674 + 0.169118i) q^{3} +(1.57660 - 1.58566i) q^{5} +(1.00773 + 3.76091i) q^{7} +(-1.82543 + 2.17546i) q^{9} +(0.973938 + 1.68691i) q^{11} +(2.46032 - 5.27618i) q^{13} +(-0.303629 + 0.841710i) q^{15} +(-0.350620 + 4.00760i) q^{17} +(4.22053 + 1.08956i) q^{19} +(-1.00151 - 1.19356i) q^{21} +(1.79737 - 1.25853i) q^{23} +(-0.0286516 - 4.99992i) q^{25} +(0.604839 - 2.25729i) q^{27} +(3.44950 + 2.89447i) q^{29} +(2.99397 + 1.72857i) q^{31} +(-0.638508 - 0.447088i) q^{33} +(7.55232 + 4.33153i) q^{35} +(-5.01505 - 5.01505i) q^{37} +2.32961i q^{39} +(-3.17796 + 8.73136i) q^{41} +(-1.28086 + 1.82925i) q^{43} +(0.571574 + 6.32436i) q^{45} +(-4.06756 + 0.355865i) q^{47} +(-7.06672 + 4.07998i) q^{49} +(-0.550596 - 1.51275i) q^{51} +(-4.39667 - 6.27909i) q^{53} +(4.21038 + 1.11525i) q^{55} +(-1.71494 + 0.318611i) q^{57} +(4.29987 - 3.60802i) q^{59} +(1.94572 - 11.0347i) q^{61} +(-10.0213 - 4.67299i) q^{63} +(-4.48729 - 12.2197i) q^{65} +(-0.637363 - 7.28509i) q^{67} +(-0.439018 + 0.760402i) q^{69} +(2.69808 - 0.475744i) q^{71} +(-1.74492 - 3.74199i) q^{73} +(0.855965 + 1.80849i) q^{75} +(-5.36285 + 5.36285i) q^{77} +(-8.14836 - 2.96576i) q^{79} +(-1.31702 - 7.46922i) q^{81} +(-14.3797 + 3.85303i) q^{83} +(5.80192 + 6.87436i) q^{85} +(-1.74055 - 0.466379i) q^{87} +(-1.72328 + 0.627223i) q^{89} +(22.3226 + 3.93607i) q^{91} +(-1.37817 - 0.120574i) q^{93} +(8.38177 - 4.97453i) q^{95} +(-0.221785 - 0.0194037i) q^{97} +(-5.44767 - 0.960571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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