LMFDB - Embedded newform 1380.2.r.c.737.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.8
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43142 + 0.975211i) q^{3} +(0.832554 + 2.07530i) q^{5} +(0.0455472 + 0.0455472i) q^{7} +(1.09793 - 2.79187i) q^{9} +O(q^{10})$	\(q+(-1.43142 + 0.975211i) q^{3} +(0.832554 + 2.07530i) q^{5} +(0.0455472 + 0.0455472i) q^{7} +(1.09793 - 2.79187i) q^{9} -4.88325i q^{11} +(-2.11410 + 2.11410i) q^{13} +(-3.21559 - 2.15870i) q^{15} +(-4.09837 + 4.09837i) q^{17} -0.731343i q^{19} +(-0.109615 - 0.0207790i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-3.61371 + 3.45559i) q^{25} +(1.15107 + 5.06705i) q^{27} -2.15209 q^{29} -6.73344 q^{31} +(4.76220 + 6.98998i) q^{33} +(-0.0566034 + 0.132444i) q^{35} +(-8.48292 - 8.48292i) q^{37} +(0.964470 - 5.08786i) q^{39} +4.34388i q^{41} +(0.623119 - 0.623119i) q^{43} +(6.70805 - 0.0458627i) q^{45} +(-2.23897 + 2.23897i) q^{47} -6.99585i q^{49} +(1.86971 - 9.86327i) q^{51} +(3.08535 + 3.08535i) q^{53} +(10.1342 - 4.06556i) q^{55} +(0.713214 + 1.04686i) q^{57} +11.4611 q^{59} -13.9103 q^{61} +(0.177169 - 0.0771546i) q^{63} +(-6.14748 - 2.62728i) q^{65} +(-3.10033 - 3.10033i) q^{67} +(-1.70175 - 0.322588i) q^{69} -10.1405i q^{71} +(3.66920 - 3.66920i) q^{73} +(1.80280 - 8.47053i) q^{75} +(0.222418 - 0.222418i) q^{77} -4.48862i q^{79} +(-6.58912 - 6.13054i) q^{81} +(3.25188 + 3.25188i) q^{83} +(-11.9175 - 5.09322i) q^{85} +(3.08054 - 2.09874i) q^{87} -12.6524 q^{89} -0.192583 q^{91} +(9.63838 - 6.56653i) q^{93} +(1.51775 - 0.608882i) q^{95} +(-10.3154 - 10.3154i) q^{97} +(-13.6334 - 5.36144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

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
$3$	−1.43142	+	0.975211i	−0.826431	+	0.563038i
$3$	−1.43142	+	0.975211i	−0.826431	+	0.563038i
$4$		0			0
$5$	0.832554	+	2.07530i	0.372329	+	0.928101i
$5$	0.832554	+	2.07530i	0.372329	+	0.928101i
$6$		0			0
$7$	0.0455472	+	0.0455472i	0.0172152	+	0.0172152i	0.715662	−	0.698447i	$-0.246125\pi$
$7$	0.0455472	+	0.0455472i	0.0172152	+	0.0172152i	−0.698447	+	0.715662i	$0.746125\pi$
$8$		0			0
$9$	1.09793	−	2.79187i	0.365975	−	0.930625i
$10$		0			0
$11$		−	4.88325i		−	1.47235i	−0.676789	−	0.736177i	$-0.736629\pi$
$11$		−	4.88325i		−	1.47235i	0.676789	−	0.736177i	$-0.263371\pi$
$12$		0			0
$13$	−2.11410	+	2.11410i	−0.586346	+	0.586346i	−0.936640	−	0.350294i	$-0.886082\pi$
$13$	−2.11410	+	2.11410i	−0.586346	+	0.586346i	0.350294	+	0.936640i	$0.386082\pi$
$14$		0			0
$15$	−3.21559	−	2.15870i	−0.830261	−	0.557375i
$16$		0			0
$17$	−4.09837	+	4.09837i	−0.994002	+	0.994002i	−0.999982	−	0.00598040i	$-0.998096\pi$
$17$	−4.09837	+	4.09837i	−0.994002	+	0.994002i	0.00598040	+	0.999982i	$0.498096\pi$
$18$		0			0
$19$		−	0.731343i		−	0.167781i	−0.996475	−	0.0838907i	$-0.973265\pi$
$19$		−	0.731343i		−	0.167781i	0.996475	−	0.0838907i	$-0.0267347\pi$
$20$		0			0
$21$	−0.109615	−	0.0207790i	−0.0239200	−	0.00453436i
$22$		0			0
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−3.61371	+	3.45559i	−0.722742	+	0.691118i
$26$		0			0
$27$	1.15107	+	5.06705i	0.221524	+	0.975155i
$28$		0			0
$29$	−2.15209			−0.399633			−0.199816	−	0.979833i	$-0.564035\pi$
$29$	−2.15209			−0.399633			−0.199816	+	0.979833i	$0.564035\pi$
$30$		0			0
$31$	−6.73344			−1.20936			−0.604681	−	0.796468i	$-0.706699\pi$
$31$	−6.73344			−1.20936			−0.604681	+	0.796468i	$0.706699\pi$
$32$		0			0
$33$	4.76220	+	6.98998i	0.828992	+	1.21680i
$34$		0			0
$35$	−0.0566034	+	0.132444i	−0.00956773	+	0.0223872i
$36$		0			0
$37$	−8.48292	−	8.48292i	−1.39458	−	1.39458i	−0.814699	−	0.579884i	$-0.803098\pi$
$37$	−8.48292	−	8.48292i	−1.39458	−	1.39458i	−0.579884	−	0.814699i	$-0.696902\pi$
$38$		0			0
$39$	0.964470	−	5.08786i	0.154439	−	0.814709i
$40$		0			0
$41$			4.34388i			0.678400i	0.940714	+	0.339200i	$0.110156\pi$
$41$			4.34388i			0.678400i	−0.940714	+	0.339200i	$0.889844\pi$
$42$		0			0
$43$	0.623119	−	0.623119i	0.0950247	−	0.0950247i	−0.657996	−	0.753021i	$-0.728596\pi$
$43$	0.623119	−	0.623119i	0.0950247	−	0.0950247i	0.753021	+	0.657996i	$0.228596\pi$
$44$		0			0
$45$	6.70805	−	0.0458627i	0.999977	−	0.00683680i
$46$		0			0
$47$	−2.23897	+	2.23897i	−0.326588	+	0.326588i	−0.851287	−	0.524700i	$-0.824178\pi$
$47$	−2.23897	+	2.23897i	−0.326588	+	0.326588i	0.524700	+	0.851287i	$0.324178\pi$
$48$		0			0
$49$		−	6.99585i		−	0.999407i
$50$		0			0
$51$	1.86971	−	9.86327i	0.261812	−	1.38113i
$52$		0			0
$53$	3.08535	+	3.08535i	0.423805	+	0.423805i	0.886511	−	0.462707i	$-0.153122\pi$
$53$	3.08535	+	3.08535i	0.423805	+	0.423805i	−0.462707	+	0.886511i	$0.653122\pi$
$54$		0			0
$55$	10.1342	−	4.06556i	1.36649	−	0.548201i
$56$		0			0
$57$	0.713214	+	1.04686i	0.0944674	+	0.138660i
$58$		0			0
$59$	11.4611			1.49211			0.746057	−	0.665882i	$-0.231945\pi$
$59$	11.4611			1.49211			0.746057	+	0.665882i	$0.231945\pi$
$60$		0			0
$61$	−13.9103			−1.78103			−0.890514	−	0.454956i	$-0.849655\pi$
$61$	−13.9103			−1.78103			−0.890514	+	0.454956i	$0.849655\pi$
$62$		0			0
$63$	0.177169	−	0.0771546i	0.0223213	−	0.00972056i
$64$		0			0
$65$	−6.14748	−	2.62728i	−0.762501	−	0.325874i
$66$		0			0
$67$	−3.10033	−	3.10033i	−0.378766	−	0.378766i	0.491891	−	0.870657i	$-0.336306\pi$
$67$	−3.10033	−	3.10033i	−0.378766	−	0.378766i	−0.870657	+	0.491891i	$0.836306\pi$
$68$		0			0
$69$	−1.70175	−	0.322588i	−0.204866	−	0.0388351i
$70$		0			0
$71$		−	10.1405i		−	1.20346i	−0.798701	−	0.601728i	$-0.794479\pi$
$71$		−	10.1405i		−	1.20346i	0.798701	−	0.601728i	$-0.205521\pi$
$72$		0			0
$73$	3.66920	−	3.66920i	0.429448	−	0.429448i	−0.458992	−	0.888440i	$-0.651789\pi$
$73$	3.66920	−	3.66920i	0.429448	−	0.429448i	0.888440	+	0.458992i	$0.151789\pi$
$74$		0			0
$75$	1.80280	−	8.47053i	0.208170	−	0.978093i
$76$		0			0
$77$	0.222418	−	0.222418i	0.0253469	−	0.0253469i
$78$		0			0
$79$		−	4.48862i		−	0.505009i	−0.967596	−	0.252505i	$-0.918746\pi$
$79$		−	4.48862i		−	0.505009i	0.967596	−	0.252505i	$-0.0812543\pi$
$80$		0			0
$81$	−6.58912	−	6.13054i	−0.732124	−	0.681171i
$82$		0			0
$83$	3.25188	+	3.25188i	0.356940	+	0.356940i	0.862684	−	0.505744i	$-0.168782\pi$
$83$	3.25188	+	3.25188i	0.356940	+	0.356940i	−0.505744	+	0.862684i	$0.668782\pi$
$84$		0			0
$85$	−11.9175	−	5.09322i	−1.29263	−	0.552438i
$86$		0			0
$87$	3.08054	−	2.09874i	0.330269	−	0.225009i
$88$		0			0
$89$	−12.6524			−1.34115			−0.670576	−	0.741841i	$-0.733953\pi$
$89$	−12.6524			−1.34115			−0.670576	+	0.741841i	$0.733953\pi$
$90$		0			0
$91$	−0.192583			−0.0201881
$92$		0			0
$93$	9.63838	−	6.56653i	0.999454	−	0.680917i
$94$		0			0
$95$	1.51775	−	0.608882i	0.155718	−	0.0624700i
$96$		0			0
$97$	−10.3154	−	10.3154i	−1.04737	−	1.04737i	−0.998821	−	0.0485505i	$-0.984540\pi$
$97$	−10.3154	−	10.3154i	−1.04737	−	1.04737i	−0.0485505	−	0.998821i	$-0.515460\pi$
$98$		0			0
$99$	−13.6334	−	5.36144i	−1.37021	−	0.538845i
$100$		0			0
$101$		−	0.305147i		−	0.0303633i	−0.999885	−	0.0151816i	$-0.995167\pi$
$101$		−	0.305147i		−	0.0303633i	0.999885	−	0.0151816i	$-0.00483265\pi$
$102$		0			0
$103$	13.8263	−	13.8263i	1.36235	−	1.36235i	0.491430	−	0.870917i	$-0.336475\pi$
$103$	13.8263	−	13.8263i	1.36235	−	1.36235i	0.870917	−	0.491430i	$-0.163525\pi$
$104$		0			0
$105$	−0.0481380	−	0.244784i	−0.00469779	−	0.0238885i
$106$		0			0
$107$	−13.1160	+	13.1160i	−1.26797	+	1.26797i	−0.320832	+	0.947136i	$0.603962\pi$
$107$	−13.1160	+	13.1160i	−1.26797	+	1.26797i	−0.947136	+	0.320832i	$0.896038\pi$
$108$		0			0
$109$			14.8879i			1.42601i	0.701161	+	0.713003i	$0.252665\pi$
$109$			14.8879i			1.42601i	−0.701161	+	0.713003i	$0.747335\pi$
$110$		0			0
$111$	20.4153	+	3.86998i	1.93773	+	0.367322i
$112$		0			0
$113$	1.79390	+	1.79390i	0.168756	+	0.168756i	0.786432	−	0.617676i	$-0.211926\pi$
$113$	1.79390	+	1.79390i	0.168756	+	0.168756i	−0.617676	+	0.786432i	$0.711926\pi$
$114$		0			0
$115$	−0.878752	+	2.05616i	−0.0819440	+	0.191738i
$116$		0			0
$117$	3.58117	+	8.22342i	0.331080	+	0.760256i
$118$		0			0
$119$	−0.373339			−0.0342239
$120$		0			0
$121$	−12.8461			−1.16783
$122$		0			0
$123$	−4.23620	−	6.21791i	−0.381965	−	0.560650i
$124$		0			0
$125$	−10.1800	−	4.62255i	−0.910525	−	0.413454i
$126$		0			0
$127$	−12.7575	−	12.7575i	−1.13204	−	1.13204i	−0.989837	−	0.142204i	$-0.954581\pi$
$127$	−12.7575	−	12.7575i	−1.13204	−	1.13204i	−0.142204	−	0.989837i	$-0.545419\pi$
$128$		0			0
$129$	−0.284272	+	1.49962i	−0.0250288	+	0.132034i
$130$		0			0
$131$			16.4202i			1.43464i	0.696746	+	0.717318i	$0.254630\pi$
$131$			16.4202i			1.43464i	−0.696746	+	0.717318i	$0.745370\pi$
$132$		0			0
$133$	0.0333106	−	0.0333106i	0.00288840	−	0.00288840i
$134$		0			0
$135$	−9.55731	+	6.60741i	−0.822562	+	0.568675i
$136$		0			0
$137$	−2.55398	+	2.55398i	−0.218202	+	0.218202i	−0.807740	−	0.589539i	$-0.799310\pi$
$137$	−2.55398	+	2.55398i	−0.218202	+	0.218202i	0.589539	+	0.807740i	$0.299310\pi$
$138$		0			0
$139$			3.73526i			0.316820i	0.987373	+	0.158410i	$0.0506368\pi$
$139$			3.73526i			0.316820i	−0.987373	+	0.158410i	$0.949363\pi$
$140$		0			0
$141$	1.02144	−	5.38838i	0.0860206	−	0.453783i
$142$		0			0
$143$	10.3237	+	10.3237i	0.863308	+	0.863308i
$144$		0			0
$145$	−1.79173	−	4.46622i	−0.148795	−	0.370899i
$146$		0			0
$147$	6.82243	+	10.0140i	0.562705	+	0.825941i
$148$		0			0
$149$	16.3938			1.34303			0.671516	−	0.740990i	$-0.265644\pi$
$149$	16.3938			1.34303			0.671516	+	0.740990i	$0.265644\pi$
$150$		0			0
$151$	−9.28321			−0.755457			−0.377728	−	0.925916i	$-0.623295\pi$
$151$	−9.28321			−0.755457			−0.377728	+	0.925916i	$0.623295\pi$
$152$		0			0
$153$	6.94243	+	15.9419i	0.561262	+	1.28882i
$154$		0			0
$155$	−5.60595	−	13.9739i	−0.450281	−	1.12241i
$156$		0			0
$157$	10.5257	+	10.5257i	0.840043	+	0.840043i	0.988864	−	0.148821i	$-0.0475478\pi$
$157$	10.5257	+	10.5257i	0.840043	+	0.840043i	−0.148821	+	0.988864i	$0.547548\pi$
$158$		0			0
$159$	−7.42529	−	1.40756i	−0.588864	−	0.111627i
$160$		0			0
$161$			0.0644135i			0.00507649i
$162$		0			0
$163$	−11.0549	+	11.0549i	−0.865889	+	0.865889i	−0.992014	−	0.126125i	$-0.959746\pi$
$163$	−11.0549	+	11.0549i	−0.865889	+	0.865889i	0.126125	+	0.992014i	$0.459746\pi$
$164$		0			0
$165$	−10.5415	+	15.7025i	−0.820654	+	1.22244i
$166$		0			0
$167$	16.4746	−	16.4746i	1.27484	−	1.27484i	0.331328	−	0.943516i	$-0.392503\pi$
$167$	16.4746	−	16.4746i	1.27484	−	1.27484i	0.943516	−	0.331328i	$-0.107497\pi$
$168$		0			0
$169$			4.06117i			0.312398i
$170$		0			0
$171$	−2.04182	−	0.802960i	−0.156142	−	0.0614039i
$172$		0			0
$173$	−4.53648	−	4.53648i	−0.344902	−	0.344902i	0.513305	−	0.858207i	$-0.328421\pi$
$173$	−4.53648	−	4.53648i	−0.344902	−	0.344902i	−0.858207	+	0.513305i	$0.828421\pi$
$174$		0			0
$175$	−0.321987	−	0.00720183i	−0.0243399	−	0.000544407i
$176$		0			0
$177$	−16.4057	+	11.1770i	−1.23313	+	0.840118i
$178$		0			0
$179$	−11.4570			−0.856335			−0.428168	−	0.903699i	$-0.640841\pi$
$179$	−11.4570			−0.856335			−0.428168	+	0.903699i	$0.640841\pi$
$180$		0			0
$181$	−0.349670			−0.0259908			−0.0129954	−	0.999916i	$-0.504137\pi$
$181$	−0.349670			−0.0259908			−0.0129954	+	0.999916i	$0.504137\pi$
$182$		0			0
$183$	19.9114	−	13.5655i	1.47190	−	1.00279i
$184$		0			0
$185$	10.5421	−	24.6671i	0.775069	−	1.81356i
$186$		0			0
$187$	20.0134	+	20.0134i	1.46352	+	1.46352i
$188$		0			0
$189$	−0.178362	+	0.283218i	−0.0129739	+	0.0206011i
$190$		0			0
$191$		−	18.1800i		−	1.31546i	−0.753256	−	0.657728i	$-0.771518\pi$
$191$		−	18.1800i		−	1.31546i	0.753256	−	0.657728i	$-0.228482\pi$
$192$		0			0
$193$	−1.01352	+	1.01352i	−0.0729550	+	0.0729550i	−0.742643	−	0.669688i	$-0.766428\pi$
$193$	−1.01352	+	1.01352i	−0.0729550	+	0.0729550i	0.669688	+	0.742643i	$0.266428\pi$
$194$		0			0
$195$	11.3618	−	2.23435i	0.813634	−	0.160005i
$196$		0			0
$197$	7.50078	−	7.50078i	0.534408	−	0.534408i	−0.387473	−	0.921881i	$-0.626652\pi$
$197$	7.50078	−	7.50078i	0.534408	−	0.534408i	0.921881	+	0.387473i	$0.126652\pi$
$198$		0			0
$199$		−	13.3742i		−	0.948070i	−0.880506	−	0.474035i	$-0.842797\pi$
$199$		−	13.3742i		−	0.948070i	0.880506	−	0.474035i	$-0.157203\pi$
$200$		0			0
$201$	7.46136	+	1.41440i	0.526284	+	0.0997640i
$202$		0			0
$203$	−0.0980216	−	0.0980216i	−0.00687977	−	0.00687977i
$204$		0			0
$205$	−9.01483	+	3.61651i	−0.629623	+	0.252588i
$206$		0			0
$207$	2.75050	−	1.19780i	0.191173	−	0.0832530i
$208$		0			0
$209$	−3.57133			−0.247034
$210$		0			0
$211$	14.7227			1.01356			0.506778	−	0.862077i	$-0.330837\pi$
$211$	14.7227			1.01356			0.506778	+	0.862077i	$0.330837\pi$
$212$		0			0
$213$	9.88913	+	14.5153i	0.677592	+	0.994572i
$214$		0			0
$215$	1.81194	+	0.774376i	0.123573	+	0.0528120i
$216$		0			0
$217$	−0.306689	−	0.306689i	−0.0208194	−	0.0208194i
$218$		0			0
$219$	−1.67392	+	8.83042i	−0.113113	+	0.596704i
$220$		0			0
$221$		−	17.3287i		−	1.16566i
$222$		0			0
$223$	−9.97647	+	9.97647i	−0.668074	+	0.668074i	−0.957270	−	0.289196i	$-0.906612\pi$
$223$	−9.97647	+	9.97647i	−0.668074	+	0.668074i	0.289196	+	0.957270i	$0.406612\pi$
$224$		0			0
$225$	5.67999	+	13.8830i	0.378666	+	0.925533i
$226$		0			0
$227$	−12.1267	+	12.1267i	−0.804875	+	0.804875i	−0.983853	−	0.178978i	$-0.942721\pi$
$227$	−12.1267	+	12.1267i	−0.804875	+	0.804875i	0.178978	+	0.983853i	$0.442721\pi$
$228$		0			0
$229$			23.4447i			1.54927i	0.632410	+	0.774634i	$0.282066\pi$
$229$			23.4447i			1.54927i	−0.632410	+	0.774634i	$0.717934\pi$
$230$		0			0
$231$	−0.101469	+	0.535279i	−0.00667618	+	0.0352187i
$232$		0			0
$233$	16.6467	+	16.6467i	1.09056	+	1.09056i	0.995469	+	0.0950908i	$0.0303142\pi$
$233$	16.6467	+	16.6467i	1.09056	+	1.09056i	0.0950908	+	0.995469i	$0.469686\pi$
$234$		0			0
$235$	−6.51059	−	2.78247i	−0.424704	−	0.181508i
$236$		0			0
$237$	4.37735	+	6.42510i	0.284340	+	0.417355i
$238$		0			0
$239$	−2.06471			−0.133555			−0.0667775	−	0.997768i	$-0.521272\pi$
$239$	−2.06471			−0.133555			−0.0667775	+	0.997768i	$0.521272\pi$
$240$		0			0
$241$	7.80330			0.502655			0.251328	−	0.967902i	$-0.419133\pi$
$241$	7.80330			0.502655			0.251328	+	0.967902i	$0.419133\pi$
$242$		0			0
$243$	15.4104	+	2.34960i	0.988575	+	0.150727i
$244$		0			0
$245$	14.5185	−	5.82442i	0.927551	−	0.372109i
$246$		0			0
$247$	1.54613	+	1.54613i	0.0983779	+	0.0983779i
$248$		0			0
$249$	−7.82607	−	1.48353i	−0.495957	−	0.0940152i
$250$		0			0
$251$		−	15.4862i		−	0.977482i	−0.872429	−	0.488741i	$-0.837456\pi$
$251$		−	15.4862i		−	0.977482i	0.872429	−	0.488741i	$-0.162544\pi$
$252$		0			0
$253$	3.45298	−	3.45298i	0.217087	−	0.217087i
$254$		0			0
$255$	22.0259	−	4.33150i	1.37931	−	0.271249i
$256$		0			0
$257$	−17.4332	+	17.4332i	−1.08745	+	1.08745i	−0.0916621	+	0.995790i	$0.529218\pi$
$257$	−17.4332	+	17.4332i	−1.08745	+	1.08745i	−0.995790	+	0.0916621i	$0.970782\pi$
$258$		0			0
$259$		−	0.772746i		−	0.0480161i
$260$		0			0
$261$	−2.36283	+	6.00836i	−0.146256	+	0.371908i
$262$		0			0
$263$	3.30971	+	3.30971i	0.204085	+	0.204085i	0.801748	−	0.597663i	$-0.203904\pi$
$263$	3.30971	+	3.30971i	0.204085	+	0.204085i	−0.597663	+	0.801748i	$0.703904\pi$
$264$		0			0
$265$	−3.83429	+	8.97172i	−0.235539	+	0.551128i
$266$		0			0
$267$	18.1109	−	12.3388i	1.10837	−	0.755120i
$268$		0			0
$269$	8.86518			0.540520			0.270260	−	0.962787i	$-0.412890\pi$
$269$	8.86518			0.540520			0.270260	+	0.962787i	$0.412890\pi$
$270$		0			0
$271$	−14.5237			−0.882251			−0.441126	−	0.897445i	$-0.645421\pi$
$271$	−14.5237			−0.882251			−0.441126	+	0.897445i	$0.645421\pi$
$272$		0			0
$273$	0.275667	−	0.187809i	0.0166841	−	0.0113667i
$274$		0			0
$275$	16.8745	+	17.6466i	1.01757	+	1.06413i
$276$		0			0
$277$	2.49953	+	2.49953i	0.150182	+	0.150182i	0.778199	−	0.628017i	$-0.216133\pi$
$277$	2.49953	+	2.49953i	0.150182	+	0.150182i	−0.628017	+	0.778199i	$0.716133\pi$
$278$		0			0
$279$	−7.39282	+	18.7989i	−0.442597	+	1.12546i
$280$		0			0
$281$		−	6.31149i		−	0.376512i	−0.982120	−	0.188256i	$-0.939717\pi$
$281$		−	6.31149i		−	0.376512i	0.982120	−	0.188256i	$-0.0602834\pi$
$282$		0			0
$283$	−12.2156	+	12.2156i	−0.726142	+	0.726142i	−0.969849	−	0.243707i	$-0.921636\pi$
$283$	−12.2156	+	12.2156i	−0.726142	+	0.726142i	0.243707	+	0.969849i	$0.421636\pi$
$284$		0			0
$285$	−1.57875	+	2.35170i	−0.0935172	+	0.139302i
$286$		0			0
$287$	−0.197851	+	0.197851i	−0.0116788	+	0.0116788i
$288$		0			0
$289$		−	16.5933i		−	0.976079i
$290$		0			0
$291$	24.8254	+	4.70598i	1.45529	+	0.275869i
$292$		0			0
$293$	13.0928	+	13.0928i	0.764888	+	0.764888i	0.977202	−	0.212313i	$-0.0680998\pi$
$293$	13.0928	+	13.0928i	0.764888	+	0.764888i	−0.212313	+	0.977202i	$0.568100\pi$
$294$		0			0
$295$	9.54202	+	23.7853i	0.555558	+	1.38483i
$296$		0			0
$297$	24.7437	−	5.62097i	1.43577	−	0.326162i
$298$		0			0
$299$	−2.98979			−0.172904
$300$		0			0
$301$	0.0567626			0.00327174
$302$		0			0
$303$	0.297583	+	0.436793i	0.0170957	+	0.0250931i
$304$		0			0
$305$	−11.5810	−	28.8679i	−0.663129	−	1.65297i
$306$		0			0
$307$	15.2344	+	15.2344i	0.869474	+	0.869474i	0.992414	−	0.122940i	$-0.0392322\pi$
$307$	15.2344	+	15.2344i	0.869474	+	0.869474i	−0.122940	+	0.992414i	$0.539232\pi$
$308$		0			0
$309$	−6.30768	+	33.2748i	−0.358832	+	1.89294i
$310$		0			0
$311$			0.129640i			0.00735119i	0.999993	+	0.00367559i	$0.00116998\pi$
$311$			0.129640i			0.00735119i	−0.999993	+	0.00367559i	$0.998830\pi$
$312$		0			0
$313$	−11.3250	+	11.3250i	−0.640127	+	0.640127i	−0.950587	−	0.310459i	$-0.899517\pi$
$313$	−11.3250	+	11.3250i	−0.640127	+	0.640127i	0.310459	+	0.950587i	$0.399517\pi$
$314$		0			0
$315$	0.307622	+	0.303444i	0.0173325	+	0.0170971i
$316$		0			0
$317$	−5.65691	+	5.65691i	−0.317724	+	0.317724i	−0.847892	−	0.530169i	$-0.822129\pi$
$317$	−5.65691	+	5.65691i	−0.317724	+	0.317724i	0.530169	+	0.847892i	$0.322129\pi$
$318$		0			0
$319$			10.5092i			0.588401i
$320$		0			0
$321$	5.98362	−	31.5653i	0.333973	−	1.76180i
$322$		0			0
$323$	2.99732	+	2.99732i	0.166775	+	0.166775i
$324$		0			0
$325$	0.334277	−	14.9452i	0.0185424	−	0.829011i
$326$		0			0
$327$	−14.5189	−	21.3109i	−0.802896	−	1.17849i
$328$		0			0
$329$	−0.203958			−0.0112446
$330$		0			0
$331$	−7.81387			−0.429489			−0.214745	−	0.976670i	$-0.568892\pi$
$331$	−7.81387			−0.429489			−0.214745	+	0.976670i	$0.568892\pi$
$332$		0			0
$333$	−32.9969	+	14.3696i	−1.80822	+	0.787450i
$334$		0			0
$335$	3.85292	−	9.01530i	0.210507	−	0.492559i
$336$		0			0
$337$	−3.65134	−	3.65134i	−0.198901	−	0.198901i	0.600628	−	0.799529i	$-0.294917\pi$
$337$	−3.65134	−	3.65134i	−0.198901	−	0.198901i	−0.799529	+	0.600628i	$0.794917\pi$
$338$		0			0
$339$	−4.31725	−	0.818392i	−0.234481	−	0.0444490i
$340$		0			0
$341$			32.8811i			1.78061i
$342$		0			0
$343$	0.637472	−	0.637472i	0.0344202	−	0.0344202i
$344$		0			0
$345$	−0.747328	−	3.80020i	−0.0402348	−	0.204596i
$346$		0			0
$347$	−16.8167	+	16.8167i	−0.902766	+	0.902766i	−0.995675	−	0.0929088i	$-0.970383\pi$
$347$	−16.8167	+	16.8167i	−0.902766	+	0.902766i	0.0929088	+	0.995675i	$0.470383\pi$
$348$		0			0
$349$		−	11.2744i		−	0.603505i	−0.953386	−	0.301752i	$-0.902428\pi$
$349$		−	11.2744i		−	0.603505i	0.953386	−	0.301752i	$-0.0975716\pi$
$350$		0			0
$351$	−13.1457	−	8.27877i	−0.701668	−	0.441888i
$352$		0			0
$353$	−5.91904	−	5.91904i	−0.315039	−	0.315039i	0.531819	−	0.846858i	$-0.321509\pi$
$353$	−5.91904	−	5.91904i	−0.315039	−	0.315039i	−0.846858	+	0.531819i	$0.821509\pi$
$354$		0			0
$355$	21.0445	−	8.44251i	1.11693	−	0.448082i
$356$		0			0
$357$	0.534405	−	0.364084i	0.0282837	−	0.0192694i
$358$		0			0
$359$	12.5303			0.661322			0.330661	−	0.943750i	$-0.392728\pi$
$359$	12.5303			0.661322			0.330661	+	0.943750i	$0.392728\pi$
$360$		0			0
$361$	18.4651			0.971849
$362$		0			0
$363$	18.3882	−	12.5277i	0.965128	−	0.657531i
$364$		0			0
$365$	10.6695	+	4.55988i	0.558467	+	0.238675i
$366$		0			0
$367$	−0.408224	−	0.408224i	−0.0213091	−	0.0213091i	0.696372	−	0.717681i	$-0.254796\pi$
$367$	−0.408224	−	0.408224i	−0.0213091	−	0.0213091i	−0.717681	+	0.696372i	$0.754796\pi$
$368$		0			0
$369$	12.1276	+	4.76926i	0.631335	+	0.248278i
$370$		0			0
$371$			0.281058i			0.0145918i
$372$		0			0
$373$	−12.2227	+	12.2227i	−0.632867	+	0.632867i	−0.948786	−	0.315919i	$-0.897687\pi$
$373$	−12.2227	+	12.2227i	−0.632867	+	0.632867i	0.315919	+	0.948786i	$0.397687\pi$
$374$		0			0
$375$	19.0798	−	3.31082i	0.985276	−	0.170970i
$376$		0			0
$377$	4.54973	−	4.54973i	0.234323	−	0.234323i
$378$		0			0
$379$		−	9.54936i		−	0.490518i	−0.969458	−	0.245259i	$-0.921127\pi$
$379$		−	9.54936i		−	0.490518i	0.969458	−	0.245259i	$-0.0788730\pi$
$380$		0			0
$381$	30.7025	+	5.82006i	1.57294	+	0.298171i
$382$		0			0
$383$	−0.700780	−	0.700780i	−0.0358082	−	0.0358082i	0.688976	−	0.724784i	$-0.258061\pi$
$383$	−0.700780	−	0.700780i	−0.0358082	−	0.0358082i	−0.724784	+	0.688976i	$0.758061\pi$
$384$		0			0
$385$	0.646759	+	0.276409i	0.0329619	+	0.0140871i
$386$		0			0
$387$	−1.05553	−	2.42381i	−0.0536556	−	0.123209i
$388$		0			0
$389$	−20.9173			−1.06055			−0.530275	−	0.847826i	$-0.677911\pi$
$389$	−20.9173			−1.06055			−0.530275	+	0.847826i	$0.677911\pi$
$390$		0			0
$391$	−5.79598			−0.293115
$392$		0			0
$393$	−16.0131	−	23.5041i	−0.807755	−	1.18563i
$394$		0			0
$395$	9.31521	−	3.73702i	0.468699	−	0.188030i
$396$		0			0
$397$	−2.49373	−	2.49373i	−0.125157	−	0.125157i	0.641754	−	0.766911i	$-0.278207\pi$
$397$	−2.49373	−	2.49373i	−0.125157	−	0.125157i	−0.766911	+	0.641754i	$0.778207\pi$
$398$		0			0
$399$	−0.0151966	+	0.0801663i	−0.000760781	+	0.00401334i
$400$		0			0
$401$			33.7265i			1.68422i	0.539307	+	0.842109i	$0.318686\pi$
$401$			33.7265i			1.68422i	−0.539307	+	0.842109i	$0.681314\pi$
$402$		0			0
$403$	14.2352	−	14.2352i	0.709104	−	0.709104i
$404$		0			0
$405$	7.23690	−	18.7784i	0.359604	−	0.933105i
$406$		0			0
$407$	−41.4242	+	41.4242i	−2.05332	+	2.05332i
$408$		0			0
$409$		−	1.48798i		−	0.0735759i	−0.999323	−	0.0367879i	$-0.988287\pi$
$409$		−	1.48798i		−	0.0735759i	0.999323	−	0.0367879i	$-0.0117126\pi$
$410$		0			0
$411$	1.16515	−	6.14650i	0.0574726	−	0.303184i
$412$		0			0
$413$	0.522023	+	0.522023i	0.0256871	+	0.0256871i
$414$		0			0
$415$	−4.04125	+	9.45597i	−0.198377	+	0.464175i
$416$		0			0
$417$	−3.64266	−	5.34672i	−0.178382	−	0.261830i
$418$		0			0
$419$	−6.01960			−0.294077			−0.147038	−	0.989131i	$-0.546974\pi$
$419$	−6.01960			−0.294077			−0.147038	+	0.989131i	$0.546974\pi$
$420$		0			0
$421$	−11.5345			−0.562157			−0.281079	−	0.959685i	$-0.590692\pi$
$421$	−11.5345			−0.562157			−0.281079	+	0.959685i	$0.590692\pi$
$422$		0			0
$423$	3.79270	+	8.70915i	0.184407	+	0.423453i
$424$		0			0
$425$	0.648027	−	28.9726i	0.0314339	−	1.40538i
$426$		0			0
$427$	−0.633574	−	0.633574i	−0.0306608	−	0.0306608i
$428$		0			0
$429$	−24.8453	−	4.70975i	−1.19954	−	0.227389i
$430$		0			0
$431$		−	18.1803i		−	0.875714i	−0.899045	−	0.437857i	$-0.855738\pi$
$431$		−	18.1803i		−	0.875714i	0.899045	−	0.437857i	$-0.144262\pi$
$432$		0			0
$433$	−1.94385	+	1.94385i	−0.0934156	+	0.0934156i	−0.752270	−	0.658855i	$-0.771041\pi$
$433$	−1.94385	+	1.94385i	−0.0934156	+	0.0934156i	0.658855	+	0.752270i	$0.271041\pi$
$434$		0			0
$435$	6.92023	+	4.64572i	0.331799	+	0.222745i
$436$		0			0
$437$	0.517137	−	0.517137i	0.0247380	−	0.0247380i
$438$		0			0
$439$		−	2.97482i		−	0.141980i	−0.997477	−	0.0709902i	$-0.977384\pi$
$439$		−	2.97482i		−	0.141980i	0.997477	−	0.0709902i	$-0.0226159\pi$
$440$		0			0
$441$	−19.5315	−	7.68093i	−0.930073	−	0.365758i
$442$		0			0
$443$	−5.62222	−	5.62222i	−0.267120	−	0.267120i	0.560819	−	0.827939i	$-0.310486\pi$
$443$	−5.62222	−	5.62222i	−0.267120	−	0.267120i	−0.827939	+	0.560819i	$0.810486\pi$
$444$		0			0
$445$	−10.5338	−	26.2575i	−0.499350	−	1.24472i
$446$		0			0
$447$	−23.4664	+	15.9874i	−1.10992	+	0.756179i
$448$		0			0
$449$	12.9005			0.608811			0.304405	−	0.952543i	$-0.401542\pi$
$449$	12.9005			0.608811			0.304405	+	0.952543i	$0.401542\pi$
$450$		0			0
$451$	21.2122			0.998844
$452$		0			0
$453$	13.2882	−	9.05309i	0.624333	−	0.425351i
$454$		0			0
$455$	−0.160335	−	0.399666i	−0.00751664	−	0.0187366i
$456$		0			0
$457$	16.1252	+	16.1252i	0.754307	+	0.754307i	0.975280	−	0.220973i	$-0.0709233\pi$
$457$	16.1252	+	16.1252i	0.754307	+	0.754307i	−0.220973	+	0.975280i	$0.570923\pi$
$458$		0			0
$459$	−25.4842	−	16.0492i	−1.18950	−	0.749110i
$460$		0			0
$461$			28.7047i			1.33691i	0.743752	+	0.668455i	$0.233044\pi$
$461$			28.7047i			1.33691i	−0.743752	+	0.668455i	$0.766956\pi$
$462$		0			0
$463$	9.53445	−	9.53445i	0.443104	−	0.443104i	−0.449950	−	0.893054i	$-0.648558\pi$
$463$	9.53445	−	9.53445i	0.443104	−	0.443104i	0.893054	+	0.449950i	$0.148558\pi$
$464$		0			0
$465$	21.6520	+	14.5355i	1.00409	+	0.674068i
$466$		0			0
$467$	−8.45237	+	8.45237i	−0.391129	+	0.391129i	−0.875090	−	0.483961i	$-0.839198\pi$
$467$	−8.45237	+	8.45237i	−0.391129	+	0.391129i	0.483961	+	0.875090i	$0.339198\pi$
$468$		0			0
$469$		−	0.282423i		−	0.0130411i
$470$		0			0
$471$	−25.3315	−	4.80192i	−1.16721	−	0.221261i
$472$		0			0
$473$	−3.04284	−	3.04284i	−0.139910	−	0.139910i
$474$		0			0
$475$	2.52722	+	2.64286i	0.115957	+	0.121263i
$476$		0			0
$477$	12.0014	−	5.22641i	0.549505	−	0.239301i
$478$		0			0
$479$	−33.7731			−1.54313			−0.771567	−	0.636148i	$-0.780527\pi$
$479$	−33.7731			−1.54313			−0.771567	+	0.636148i	$0.780527\pi$
$480$		0			0
$481$	35.8675			1.63542
$482$		0			0
$483$	−0.0628167	−	0.0922027i	−0.00285826	−	0.00419537i
$484$		0			0
$485$	12.8194	−	29.9957i	0.582099	−	1.36203i
$486$		0			0
$487$	−0.174152	−	0.174152i	−0.00789159	−	0.00789159i	0.703150	−	0.711042i	$-0.251776\pi$
$487$	−0.174152	−	0.174152i	−0.00789159	−	0.00789159i	−0.711042	+	0.703150i	$0.751776\pi$
$488$		0			0
$489$	5.04336	−	26.6052i	0.228069	−	1.20313i
$490$		0			0
$491$		−	25.0850i		−	1.13207i	−0.824382	−	0.566034i	$-0.808477\pi$
$491$		−	25.0850i		−	1.13207i	0.824382	−	0.566034i	$-0.191523\pi$
$492$		0			0
$493$	8.82006	−	8.82006i	0.397236	−	0.397236i
$494$		0			0
$495$	−0.223959	−	32.7570i	−0.0100662	−	1.47232i
$496$		0			0
$497$	0.461871	−	0.461871i	0.0207178	−	0.0207178i
$498$		0			0
$499$			26.9863i			1.20807i	0.796957	+	0.604036i	$0.206442\pi$
$499$			26.9863i			1.20807i	−0.796957	+	0.604036i	$0.793558\pi$
$500$		0			0
$501$	−7.51586	+	39.6483i	−0.335784	+	1.77136i
$502$		0			0
$503$	−0.864873	−	0.864873i	−0.0385628	−	0.0385628i	0.687562	−	0.726125i	$-0.258681\pi$
$503$	−0.864873	−	0.864873i	−0.0385628	−	0.0385628i	−0.726125	+	0.687562i	$0.758681\pi$
$504$		0			0
$505$	0.633270	−	0.254051i	0.0281802	−	0.0113051i
$506$		0			0
$507$	−3.96050	−	5.81324i	−0.175892	−	0.258175i
$508$		0			0
$509$	−34.5839			−1.53290			−0.766451	−	0.642303i	$-0.777979\pi$
$509$	−34.5839			−1.53290			−0.766451	+	0.642303i	$0.777979\pi$
$510$		0			0
$511$	0.334244			0.0147861
$512$		0			0
$513$	3.70575	−	0.841829i	0.163613	−	0.0371677i
$514$		0			0
$515$	40.2048	+	17.1825i	1.77164	+	0.757153i
$516$		0			0
$517$	10.9334	+	10.9334i	0.480853	+	0.480853i
$518$		0			0
$519$	10.9176	+	2.06958i	0.479231	+	0.0908445i
$520$		0			0
$521$			29.4550i			1.29045i	0.763993	+	0.645224i	$0.223236\pi$
$521$			29.4550i			1.29045i	−0.763993	+	0.645224i	$0.776764\pi$
$522$		0			0
$523$	5.89112	−	5.89112i	0.257601	−	0.257601i	−0.566477	−	0.824078i	$-0.691694\pi$
$523$	5.89112	−	5.89112i	0.257601	−	0.257601i	0.824078	+	0.566477i	$0.191694\pi$
$524$		0			0
$525$	0.467922	−	0.303696i	0.0204218	−	0.0132544i
$526$		0			0
$527$	27.5962	−	27.5962i	1.20211	−	1.20211i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	12.5835	−	31.9981i	0.546077	−	1.38860i
$532$		0			0
$533$	−9.18339	−	9.18339i	−0.397777	−	0.397777i
$534$		0			0
$535$	−38.1393	−	16.2998i	−1.64890	−	0.704700i
$536$		0			0
$537$	16.3998	−	11.1730i	0.707702	−	0.482150i
$538$		0			0
$539$	−34.1625			−1.47148
$540$		0			0
$541$	−17.6950			−0.760769			−0.380384	−	0.924829i	$-0.624208\pi$
$541$	−17.6950			−0.760769			−0.380384	+	0.924829i	$0.624208\pi$
$542$		0			0
$543$	0.500525	−	0.341002i	0.0214796	−	0.0146338i
$544$		0			0
$545$	−30.8969	+	12.3950i	−1.32348	+	0.530944i
$546$		0			0
$547$	−12.5572	−	12.5572i	−0.536907	−	0.536907i	0.385712	−	0.922619i	$-0.373956\pi$
$547$	−12.5572	−	12.5572i	−0.536907	−	0.536907i	−0.922619	+	0.385712i	$0.873956\pi$
$548$		0			0
$549$	−15.2725	+	38.8357i	−0.651812	+	1.65747i
$550$		0			0
$551$			1.57391i			0.0670510i
$552$		0			0
$553$	0.204444	−	0.204444i	0.00869384	−	0.00869384i
$554$		0			0
$555$	8.96544	+	45.5897i	0.380562	+	1.93517i
$556$		0			0
$557$	12.8257	−	12.8257i	0.543441	−	0.543441i	−0.381095	−	0.924536i	$-0.624453\pi$
$557$	12.8257	−	12.8257i	0.543441	−	0.543441i	0.924536	+	0.381095i	$0.124453\pi$
$558$		0			0
$559$			2.63467i			0.111435i
$560$		0			0
$561$	−48.1648	−	9.13027i	−2.03352	−	0.385480i
$562$		0			0
$563$	−19.3134	−	19.3134i	−0.813963	−	0.813963i	0.171262	−	0.985226i	$-0.445216\pi$
$563$	−19.3134	−	19.3134i	−0.813963	−	0.813963i	−0.985226	+	0.171262i	$0.945216\pi$
$564$		0			0
$565$	−2.22935	+	5.21639i	−0.0937896	+	0.219455i
$566$		0			0
$567$	−0.0208868	−	0.579345i	−0.000877163	−	0.0243302i
$568$		0			0
$569$	20.6077			0.863920			0.431960	−	0.901893i	$-0.357822\pi$
$569$	20.6077			0.863920			0.431960	+	0.901893i	$0.357822\pi$
$570$		0			0
$571$	−35.7521			−1.49618			−0.748089	−	0.663598i	$-0.769029\pi$
$571$	−35.7521			−1.49618			−0.748089	+	0.663598i	$0.769029\pi$
$572$		0			0
$573$	17.7293	+	26.0232i	0.740652	+	1.08713i
$574$		0			0
$575$	−4.99875	−	0.111806i	−0.208462	−	0.00466265i
$576$		0			0
$577$	−15.4657	−	15.4657i	−0.643845	−	0.643845i	0.307653	−	0.951499i	$-0.400456\pi$
$577$	−15.4657	−	15.4657i	−0.643845	−	0.643845i	−0.951499	+	0.307653i	$0.900456\pi$
$578$		0			0
$579$	0.462378	−	2.43918i	0.0192158	−	0.101369i
$580$		0			0
$581$			0.296228i			0.0122896i
$582$		0			0
$583$	15.0665	−	15.0665i	0.623991	−	0.623991i
$584$		0			0
$585$	−14.0845	+	14.2784i	−0.582323	+	0.590341i
$586$		0			0
$587$	12.9818	−	12.9818i	0.535816	−	0.535816i	−0.386481	−	0.922297i	$-0.626310\pi$
$587$	12.9818	−	12.9818i	0.535816	−	0.535816i	0.922297	+	0.386481i	$0.126310\pi$
$588$		0			0
$589$			4.92445i			0.202909i
$590$		0			0
$591$	−3.42192	+	18.0516i	−0.140759	+	0.742544i
$592$		0			0
$593$	21.0908	+	21.0908i	0.866097	+	0.866097i	0.992038	−	0.125941i	$-0.0401949\pi$
$593$	21.0908	+	21.0908i	0.866097	+	0.866097i	−0.125941	+	0.992038i	$0.540195\pi$
$594$		0			0
$595$	−0.310825	−	0.774789i	−0.0127426	−	0.0317632i
$596$		0			0
$597$	13.0426	+	19.1441i	0.533800	+	0.783514i
$598$		0			0
$599$	28.3682			1.15909			0.579546	−	0.814939i	$-0.303230\pi$
$599$	28.3682			1.15909			0.579546	+	0.814939i	$0.303230\pi$
$600$		0			0
$601$	26.6660			1.08773			0.543864	−	0.839173i	$-0.316961\pi$
$601$	26.6660			1.08773			0.543864	+	0.839173i	$0.316961\pi$
$602$		0			0
$603$	−12.0597	+	5.25180i	−0.491108	+	0.213870i
$604$		0			0
$605$	−10.6951	−	26.6594i	−0.434816	−	1.08386i
$606$		0			0
$607$	−16.1232	−	16.1232i	−0.654422	−	0.654422i	0.299633	−	0.954055i	$-0.403136\pi$
$607$	−16.1232	−	16.1232i	−0.654422	−	0.654422i	−0.954055	+	0.299633i	$0.903136\pi$
$608$		0			0
$609$	0.235902	+	0.0447183i	0.00955923	+	0.00181208i
$610$		0			0
$611$		−	9.46682i		−	0.382986i
$612$		0			0
$613$	−16.3147	+	16.3147i	−0.658945	+	0.658945i	−0.955131	−	0.296185i	$-0.904285\pi$
$613$	−16.3147	+	16.3147i	−0.658945	+	0.658945i	0.296185	+	0.955131i	$0.404285\pi$
$614$		0			0
$615$	9.37715	−	13.9681i	0.378123	−	0.563249i
$616$		0			0
$617$	−6.63101	+	6.63101i	−0.266954	+	0.266954i	−0.827872	−	0.560917i	$-0.810449\pi$
$617$	−6.63101	+	6.63101i	−0.266954	+	0.266954i	0.560917	+	0.827872i	$0.310449\pi$
$618$		0			0
$619$			22.8317i			0.917682i	0.888518	+	0.458841i	$0.151735\pi$
$619$			22.8317i			0.917682i	−0.888518	+	0.458841i	$0.848265\pi$
$620$		0			0
$621$	−2.76902	+	4.39688i	−0.111117	+	0.176441i
$622$		0			0
$623$	−0.576281	−	0.576281i	−0.0230882	−	0.0230882i
$624$		0			0
$625$	1.11778	−	24.9750i	0.0447113	−	0.999000i
$626$		0			0
$627$	5.11207	−	3.48280i	0.204156	−	0.139090i
$628$		0			0
$629$	69.5323			2.77244
$630$		0			0
$631$	35.5865			1.41668			0.708339	−	0.705873i	$-0.249445\pi$
$631$	35.5865			1.41668			0.708339	+	0.705873i	$0.249445\pi$
$632$		0			0
$633$	−21.0744	+	14.3578i	−0.837633	+	0.570670i
$634$		0			0
$635$	15.8542	−	37.0968i	0.629156	−	1.47214i
$636$		0			0
$637$	14.7899	+	14.7899i	0.585998	+	0.585998i
$638$		0			0
$639$	−28.3110	−	11.1335i	−1.11997	−	0.440435i
$640$		0			0
$641$			0.586866i			0.0231798i	0.999933	+	0.0115899i	$0.00368927\pi$
$641$			0.586866i			0.0231798i	−0.999933	+	0.0115899i	$0.996311\pi$
$642$		0			0
$643$	−0.775393	+	0.775393i	−0.0305785	+	0.0305785i	−0.722231	−	0.691652i	$-0.756883\pi$
$643$	−0.775393	+	0.775393i	−0.0305785	+	0.0305785i	0.691652	+	0.722231i	$0.256883\pi$
$644$		0			0
$645$	−3.34882	+	0.658562i	−0.131860	+	0.0259309i
$646$		0			0
$647$	2.32200	−	2.32200i	0.0912874	−	0.0912874i	−0.659988	−	0.751276i	$-0.729439\pi$
$647$	2.32200	−	2.32200i	0.0912874	−	0.0912874i	0.751276	+	0.659988i	$0.229439\pi$
$648$		0			0
$649$		−	55.9676i		−	2.19692i
$650$		0			0
$651$	0.738088	+	0.139914i	0.0289280	+	0.00548368i
$652$		0			0
$653$	−6.30140	−	6.30140i	−0.246593	−	0.246593i	0.572978	−	0.819571i	$-0.305788\pi$
$653$	−6.30140	−	6.30140i	−0.246593	−	0.246593i	−0.819571	+	0.572978i	$0.805788\pi$
$654$		0			0
$655$	−34.0767	+	13.6707i	−1.33149	+	0.534157i
$656$		0			0
$657$	−6.21544	−	14.2725i	−0.242487	−	0.556822i
$658$		0			0
$659$	26.7823			1.04329			0.521645	−	0.853163i	$-0.325319\pi$
$659$	26.7823			1.04329			0.521645	+	0.853163i	$0.325319\pi$
$660$		0			0
$661$	42.2270			1.64244			0.821219	−	0.570612i	$-0.193294\pi$
$661$	42.2270			1.64244			0.821219	+	0.570612i	$0.193294\pi$
$662$		0			0
$663$	16.8992	+	24.8047i	0.656310	+	0.963335i
$664$		0			0
$665$	0.0968622	+	0.0413965i	0.00375616	+	0.00160529i
$666$		0			0
$667$	−1.52176	−	1.52176i	−0.0589226	−	0.0589226i
$668$		0			0
$669$	4.55135	−	24.0097i	0.175965	−	0.928268i
$670$		0			0
$671$			67.9273i			2.62230i
$672$		0			0
$673$	8.30434	−	8.30434i	0.320109	−	0.320109i	−0.528700	−	0.848809i	$-0.677320\pi$
$673$	8.30434	−	8.30434i	0.320109	−	0.320109i	0.848809	+	0.528700i	$0.177320\pi$
$674$		0			0
$675$	−21.6693	−	14.3332i	−0.834052	−	0.551686i
$676$		0			0
$677$	3.86489	−	3.86489i	0.148540	−	0.148540i	−0.628926	−	0.777465i	$-0.716505\pi$
$677$	3.86489	−	3.86489i	0.148540	−	0.148540i	0.777465	+	0.628926i	$0.216505\pi$
$678$		0			0
$679$		−	0.939676i		−	0.0360615i
$680$		0			0
$681$	5.53229	−	29.1844i	0.211998	−	1.11835i
$682$		0			0
$683$	18.9020	+	18.9020i	0.723264	+	0.723264i	0.969269	−	0.246005i	$-0.0791179\pi$
$683$	18.9020	+	18.9020i	0.723264	+	0.723264i	−0.246005	+	0.969269i	$0.579118\pi$
$684$		0			0
$685$	−7.42660	−	3.17395i	−0.283756	−	0.121270i
$686$		0			0
$687$	−22.8635	−	33.5592i	−0.872297	−	1.28036i
$688$		0			0
$689$	−13.0455			−0.496992
$690$		0			0
$691$	−29.9570			−1.13962			−0.569808	−	0.821778i	$-0.692982\pi$
$691$	−29.9570			−1.13962			−0.569808	+	0.821778i	$0.692982\pi$
$692$		0			0
$693$	−0.376765	−	0.865162i	−0.0143121	−	0.0328648i
$694$		0			0
$695$	−7.75176	+	3.10980i	−0.294041	+	0.117961i
$696$		0			0
$697$	−17.8028	−	17.8028i	−0.674330	−	0.674330i
$698$		0			0
$699$	−40.0624	−	7.59435i	−1.51530	−	0.287245i
$700$		0			0
$701$		−	0.301918i		−	0.0114033i	−0.999984	−	0.00570165i	$-0.998185\pi$
$701$		−	0.301918i		−	0.0114033i	0.999984	−	0.00570165i	$-0.00181490\pi$
$702$		0			0
$703$	−6.20392	+	6.20392i	−0.233985	+	0.233985i
$704$		0			0
$705$	12.0329	−	2.36633i	0.453185	−	0.0891210i
$706$		0			0
$707$	0.0138986	−	0.0138986i	0.000522710	−	0.000522710i
$708$		0			0
$709$		−	16.2231i		−	0.609269i	−0.952469	−	0.304635i	$-0.901466\pi$
$709$		−	16.2231i		−	0.609269i	0.952469	−	0.304635i	$-0.0985344\pi$
$710$		0			0
$711$	−12.5317	−	4.92817i	−0.469974	−	0.184821i
$712$		0			0
$713$	−4.76126	−	4.76126i	−0.178311	−	0.178311i
$714$		0			0
$715$	−12.8297	+	30.0197i	−0.479802	+	1.12267i
$716$		0			0
$717$	2.95547	−	2.01353i	0.110374	−	0.0751966i
$718$		0			0
$719$	13.9633			0.520743			0.260372	−	0.965508i	$-0.416155\pi$
$719$	13.9633			0.520743			0.260372	+	0.965508i	$0.416155\pi$
$720$		0			0
$721$	1.25950			0.0469062
$722$		0			0
$723$	−11.1698	+	7.60987i	−0.415410	+	0.283014i
$724$		0			0
$725$	7.77702	−	7.43674i	0.288831	−	0.276193i
$726$		0			0
$727$	−0.832959	−	0.832959i	−0.0308927	−	0.0308927i	0.691492	−	0.722384i	$-0.256954\pi$
$727$	−0.832959	−	0.832959i	−0.0308927	−	0.0308927i	−0.722384	+	0.691492i	$0.756954\pi$
$728$		0			0
$729$	−24.3501	+	11.6651i	−0.901854	+	0.432041i
$730$		0			0
$731$			5.10755i			0.188909i
$732$		0			0
$733$	32.7878	−	32.7878i	1.21104	−	1.21104i	0.240361	−	0.970684i	$-0.422734\pi$
$733$	32.7878	−	32.7878i	1.21104	−	1.21104i	0.970684	−	0.240361i	$-0.0772658\pi$
$734$		0			0
$735$	−15.1020	+	22.4958i	−0.557045	+	0.829769i
$736$		0			0
$737$	−15.1397	+	15.1397i	−0.557678	+	0.557678i
$738$		0			0
$739$			11.4091i			0.419690i	0.977735	+	0.209845i	$0.0672959\pi$
$739$			11.4091i			0.419690i	−0.977735	+	0.209845i	$0.932704\pi$
$740$		0			0
$741$	−3.72097	−	0.705358i	−0.136693	−	0.0259120i
$742$		0			0
$743$	−36.2079	−	36.2079i	−1.32834	−	1.32834i	−0.906819	−	0.421521i	$-0.861497\pi$
$743$	−36.2079	−	36.2079i	−1.32834	−	1.32834i	−0.421521	−	0.906819i	$-0.638503\pi$
$744$		0			0
$745$	13.6487	+	34.0220i	0.500050	+	1.24647i
$746$		0			0
$747$	12.6492	−	5.50851i	0.462808	−	0.201546i
$748$		0			0
$749$	−1.19479			−0.0436567
$750$		0			0
$751$	−2.85874			−0.104317			−0.0521584	−	0.998639i	$-0.516610\pi$
$751$	−2.85874			−0.104317			−0.0521584	+	0.998639i	$0.516610\pi$
$752$		0			0
$753$	15.1023	+	22.1673i	0.550360	+	0.807821i
$754$		0			0
$755$	−7.72877	−	19.2654i	−0.281279	−	0.701140i
$756$		0			0
$757$	−22.8684	−	22.8684i	−0.831165	−	0.831165i	0.156511	−	0.987676i	$-0.449975\pi$
$757$	−22.8684	−	22.8684i	−0.831165	−	0.831165i	−0.987676	+	0.156511i	$0.949975\pi$
$758$		0			0
$759$	−1.57528	+	8.31004i	−0.0571790	+	0.301635i
$760$		0			0
$761$			14.9457i			0.541780i	0.962610	+	0.270890i	$0.0873179\pi$
$761$			14.9457i			0.541780i	−0.962610	+	0.270890i	$0.912682\pi$
$762$		0			0
$763$	−0.678104	+	0.678104i	−0.0245490	+	0.0245490i
$764$		0			0
$765$	−27.3041	+	27.6800i	−0.987183	+	1.00077i
$766$		0			0
$767$	−24.2300	+	24.2300i	−0.874895	+	0.874895i
$768$		0			0
$769$			50.0943i			1.80645i	0.429172	+	0.903223i	$0.358806\pi$
$769$			50.0943i			1.80645i	−0.429172	+	0.903223i	$0.641194\pi$
$770$		0			0
$771$	7.95317	−	41.9552i	0.286426	−	1.51098i
$772$		0			0
$773$	−24.6875	−	24.6875i	−0.887949	−	0.887949i	0.106377	−	0.994326i	$-0.466075\pi$
$773$	−24.6875	−	24.6875i	−0.887949	−	0.887949i	−0.994326	+	0.106377i	$0.966075\pi$
$774$		0			0
$775$	24.3327	−	23.2680i	0.874056	−	0.835812i
$776$		0			0
$777$	0.753591	+	1.10612i	0.0270349	+	0.0396820i
$778$		0			0
$779$	3.17686			0.113823
$780$		0			0
$781$	−49.5185			−1.77191
$782$		0			0
$783$	−2.47721	−	10.9047i	−0.0885283	−	0.389704i
$784$		0			0
$785$	−13.0807	+	30.6072i	−0.466872	+	1.09242i
$786$		0			0
$787$	30.7406	+	30.7406i	1.09578	+	1.09578i	0.994898	+	0.100885i	$0.0321674\pi$
$787$	30.7406	+	30.7406i	1.09578	+	1.09578i	0.100885	+	0.994898i	$0.467833\pi$
$788$		0			0
$789$	−7.96524	−	1.50992i	−0.283570	−	0.0537545i
$790$		0			0
$791$			0.163414i			0.00581034i
$792$		0			0
$793$	29.4077	−	29.4077i	1.04430	−	1.04430i
$794$		0			0
$795$	−3.26084	−	16.5815i	−0.115650	−	0.588087i
$796$		0			0
$797$	−26.1604	+	26.1604i	−0.926650	+	0.926650i	−0.997488	−	0.0708375i	$-0.977433\pi$
$797$	−26.1604	+	26.1604i	−0.926650	+	0.926650i	0.0708375	+	0.997488i	$0.477433\pi$
$798$		0			0
$799$		−	18.3523i		−	0.649257i
$800$		0			0
$801$	−13.8914	+	35.3239i	−0.490828	+	1.24811i
$802$		0			0
$803$	−17.9176	−	17.9176i	−0.632299	−	0.632299i
$804$		0			0
$805$	−0.133677	+	0.0536277i	−0.00471150	+	0.00189013i
$806$		0			0
$807$	−12.6898	+	8.64542i	−0.446702	+	0.304333i
$808$		0			0
$809$	18.5455			0.652023			0.326012	−	0.945366i	$-0.394295\pi$
$809$	18.5455			0.652023			0.326012	+	0.945366i	$0.394295\pi$
$810$		0			0
$811$	47.4347			1.66566			0.832829	−	0.553531i	$-0.186720\pi$
$811$	47.4347			1.66566			0.832829	+	0.553531i	$0.186720\pi$
$812$		0			0
$813$	20.7895	−	14.1637i	0.729119	−	0.496741i
$814$		0			0
$815$	−32.1461	−	13.7384i	−1.12603	−	0.481236i
$816$		0			0
$817$	−0.455713	−	0.455713i	−0.0159434	−	0.0159434i
$818$		0			0
$819$	−0.211441	+	0.537666i	−0.00738836	+	0.0187876i
$820$		0			0
$821$			36.0932i			1.25966i	0.776732	+	0.629831i	$0.216876\pi$
$821$			36.0932i			1.25966i	−0.776732	+	0.629831i	$0.783124\pi$
$822$		0			0
$823$	−28.7385	+	28.7385i	−1.00176	+	1.00176i	−0.00176151	+	0.999998i	$0.500561\pi$
$823$	−28.7385	+	28.7385i	−1.00176	+	1.00176i	−0.999998	+	0.00176151i	$0.999439\pi$
$824$		0			0
$825$	−41.3637	−	8.80354i	−1.44010	−	0.306500i
$826$		0			0
$827$	2.20874	−	2.20874i	0.0768056	−	0.0768056i	−0.667660	−	0.744466i	$-0.732704\pi$
$827$	2.20874	−	2.20874i	0.0768056	−	0.0768056i	0.744466	+	0.667660i	$0.232704\pi$
$828$		0			0
$829$		−	41.5603i		−	1.44345i	−0.692180	−	0.721725i	$-0.743350\pi$
$829$		−	41.5603i		−	1.44345i	0.692180	−	0.721725i	$-0.256650\pi$
$830$		0			0
$831$	−6.01544	−	1.14031i	−0.208673	−	0.0395568i
$832$		0			0
$833$	28.6716	+	28.6716i	0.993413	+	0.993413i
$834$		0			0
$835$	47.9057	+	20.4737i	1.65785	+	0.708522i
$836$		0			0
$837$	−7.75068	−	34.1187i	−0.267903	−	1.17932i
$838$		0			0
$839$	27.9200			0.963907			0.481953	−	0.876197i	$-0.339927\pi$
$839$	27.9200			0.963907			0.481953	+	0.876197i	$0.339927\pi$
$840$		0			0
$841$	−24.3685			−0.840294
$842$		0			0
$843$	6.15503	+	9.03439i	0.211991	+	0.311161i
$844$		0			0
$845$	−8.42813	+	3.38114i	−0.289936	+	0.116315i
$846$		0			0
$847$	−0.585104	−	0.585104i	−0.0201044	−	0.0201044i
$848$		0			0
$849$	5.57286	−	29.3984i	0.191260	−	1.00895i
$850$		0			0
$851$		−	11.9967i		−	0.411240i
$852$		0			0
$853$	−18.9115	+	18.9115i	−0.647517	+	0.647517i	−0.952392	−	0.304875i	$-0.901385\pi$
$853$	−18.9115	+	18.9115i	−0.647517	+	0.647517i	0.304875	+	0.952392i	$0.401385\pi$
$854$		0			0
$855$	−0.0335413	−	4.90588i	−0.00114709	−	0.167778i
$856$		0			0
$857$	32.1662	−	32.1662i	1.09878	−	1.09878i	0.104223	−	0.994554i	$-0.466765\pi$
$857$	32.1662	−	32.1662i	1.09878	−	1.09878i	0.994554	−	0.104223i	$-0.0332355\pi$
$858$		0			0
$859$			21.2914i			0.726455i	0.931701	+	0.363227i	$0.118325\pi$
$859$			21.2914i			0.726455i	−0.931701	+	0.363227i	$0.881675\pi$
$860$		0			0
$861$	0.0902616	−	0.476155i	0.00307611	−	0.0162273i
$862$		0			0
$863$	6.71401	+	6.71401i	0.228547	+	0.228547i	0.812086	−	0.583538i	$-0.198332\pi$
$863$	6.71401	+	6.71401i	0.228547	+	0.228547i	−0.583538	+	0.812086i	$0.698332\pi$
$864$		0			0
$865$	5.63767	−	13.1914i	0.191687	−	0.448521i
$866$		0			0
$867$	16.1820	+	23.7520i	0.549570	+	0.806661i
$868$		0			0
$869$	−21.9190			−0.743552
$870$		0			0
$871$	13.1088			0.444176
$872$		0			0
$873$	−40.1249	+	17.4738i	−1.35802	+	0.591397i
$874$		0			0
$875$	−0.253125	−	0.674214i	−0.00855720	−	0.0227926i
$876$		0			0
$877$	−10.6990	−	10.6990i	−0.361280	−	0.361280i	0.503004	−	0.864284i	$-0.332228\pi$
$877$	−10.6990	−	10.6990i	−0.361280	−	0.361280i	−0.864284	+	0.503004i	$0.832228\pi$
$878$		0			0
$879$	−31.5095	−	5.97304i	−1.06279	−	0.201466i
$880$		0			0
$881$		−	12.5400i		−	0.422484i	−0.977434	−	0.211242i	$-0.932249\pi$
$881$		−	12.5400i		−	0.422484i	0.977434	−	0.211242i	$-0.0677509\pi$
$882$		0			0
$883$	30.6857	−	30.6857i	1.03266	−	1.03266i	0.0332082	−	0.999448i	$-0.489428\pi$
$883$	30.6857	−	30.6857i	1.03266	−	1.03266i	0.999448	−	0.0332082i	$-0.0105725\pi$
$884$		0			0
$885$	−36.8543	−	24.7412i	−1.23884	−	0.831668i
$886$		0			0
$887$	−30.3563	+	30.3563i	−1.01927	+	1.01927i	−0.0194549	+	0.999811i	$0.506193\pi$
$887$	−30.3563	+	30.3563i	−1.01927	+	1.01927i	−0.999811	+	0.0194549i	$0.993807\pi$
$888$		0			0
$889$		−	1.16213i		−	0.0389767i
$890$		0			0
$891$	−29.9369	+	32.1763i	−1.00293	+	1.07795i
$892$		0			0
$893$	1.63746	+	1.63746i	0.0547954	+	0.0547954i
$894$		0			0
$895$	−9.53855	−	23.7766i	−0.318839	−	0.794765i
$896$		0			0
$897$	4.27964	−	2.91567i	0.142893	−	0.0973515i
$898$		0			0
$899$	14.4910			0.483301
$900$		0			0
$901$	−25.2898			−0.842525
$902$		0			0
$903$	−0.0812511	+	0.0553555i	−0.00270387	+	0.00184212i
$904$		0			0
$905$	−0.291119	−	0.725670i	−0.00967713	−	0.0241221i
$906$		0			0
$907$	−4.01034	−	4.01034i	−0.133161	−	0.133161i	0.637385	−	0.770546i	$-0.280016\pi$
$907$	−4.01034	−	4.01034i	−0.133161	−	0.133161i	−0.770546	+	0.637385i	$0.780016\pi$
$908$		0			0
$909$	−0.851932	−	0.335029i	−0.0282568	−	0.0111122i
$910$		0			0
$911$		−	42.5154i		−	1.40860i	−0.709903	−	0.704299i	$-0.751261\pi$
$911$		−	42.5154i		−	1.40860i	0.709903	−	0.704299i	$-0.248739\pi$
$912$		0			0
$913$	15.8797	−	15.8797i	0.525542	−	0.525542i
$914$		0			0
$915$	44.7297	+	30.0282i	1.47872	+	0.992701i
$916$		0			0
$917$	−0.747892	+	0.747892i	−0.0246976	+	0.0246976i
$918$		0			0
$919$		−	17.0909i		−	0.563777i	−0.959447	−	0.281889i	$-0.909039\pi$
$919$		−	17.0909i		−	0.563777i	0.959447	−	0.281889i	$-0.0909609\pi$
$920$		0			0
$921$	−36.6636	−	6.95008i	−1.20811	−	0.229013i
$922$		0			0
$923$	21.4380	+	21.4380i	0.705641	+	0.705641i
$924$		0			0
$925$	59.9683	+	1.34130i	1.97175	+	0.0441017i
$926$		0			0
$927$	−23.4210	−	53.7816i	−0.769248	−	1.76642i
$928$		0			0
$929$	−3.19021			−0.104667			−0.0523337	−	0.998630i	$-0.516666\pi$
$929$	−3.19021			−0.104667			−0.0523337	+	0.998630i	$0.516666\pi$
$930$		0			0
$931$	−5.11636			−0.167682
$932$		0			0
$933$	−0.126426	−	0.185569i	−0.00413900	−	0.00607525i
$934$		0			0
$935$	−24.8715	+	58.1959i	−0.813384	+	1.90321i
$936$		0			0
$937$	−22.5644	−	22.5644i	−0.737146	−	0.737146i	0.234879	−	0.972025i	$-0.424531\pi$
$937$	−22.5644	−	22.5644i	−0.737146	−	0.737146i	−0.972025	+	0.234879i	$0.924531\pi$
$938$		0			0
$939$	5.16657	−	27.2551i	0.168605	−	0.889437i
$940$		0			0
$941$		−	53.5049i		−	1.74421i	−0.489319	−	0.872105i	$-0.662755\pi$
$941$		−	53.5049i		−	1.74421i	0.489319	−	0.872105i	$-0.337245\pi$
$942$		0			0
$943$	−3.07159	+	3.07159i	−0.100025	+	0.100025i
$944$		0			0
$945$	−0.736258	−	0.134359i	−0.0239505	−	0.00437071i
$946$		0			0
$947$	0.475858	−	0.475858i	0.0154633	−	0.0154633i	−0.699333	−	0.714796i	$-0.746519\pi$
$947$	0.475858	−	0.475858i	0.0154633	−	0.0154633i	0.714796	+	0.699333i	$0.246519\pi$
$948$		0			0
$949$			15.5141i			0.503610i
$950$		0			0
$951$	2.58073	−	13.6141i	0.0836859	−	0.441467i
$952$		0			0
$953$	−7.21791	−	7.21791i	−0.233811	−	0.233811i	0.580470	−	0.814281i	$-0.302869\pi$
$953$	−7.21791	−	7.21791i	−0.233811	−	0.233811i	−0.814281	+	0.580470i	$0.802869\pi$
$954$		0			0
$955$	37.7288	−	15.1358i	1.22088	−	0.489783i
$956$		0			0
$957$	−10.2487	−	15.0430i	−0.331292	−	0.486273i
$958$		0			0
$959$	−0.232654			−0.00751278
$960$		0			0
$961$	14.3392			0.462556
$962$		0			0
$963$	22.2178	+	51.0185i	0.715957	+	1.64405i
$964$		0			0
$965$	−2.94718	−	1.25955i	−0.0948729	−	0.0405463i
$966$		0			0
$967$	−1.47307	−	1.47307i	−0.0473707	−	0.0473707i	0.683025	−	0.730395i	$-0.260664\pi$
$967$	−1.47307	−	1.47307i	−0.0473707	−	0.0473707i	−0.730395	+	0.683025i	$0.760664\pi$
$968$		0			0
$969$	−7.21343	−	1.36740i	−0.231729	−	0.0439273i
$970$		0			0
$971$		−	22.7537i		−	0.730201i	−0.930968	−	0.365100i	$-0.881035\pi$
$971$		−	22.7537i		−	0.730201i	0.930968	−	0.365100i	$-0.118965\pi$
$972$		0			0
$973$	−0.170130	+	0.170130i	−0.00545413	+	0.00545413i
$974$		0			0
$975$	14.0962	+	21.7188i	0.451441	+	0.695560i
$976$		0			0
$977$	10.5206	−	10.5206i	0.336585	−	0.336585i	−0.518495	−	0.855080i	$-0.673508\pi$
$977$	10.5206	−	10.5206i	0.336585	−	0.336585i	0.855080	+	0.518495i	$0.173508\pi$
$978$		0			0
$979$			61.7848i			1.97465i
$980$		0			0
$981$	41.5652	+	16.3459i	1.32708	+	0.521883i
$982$		0			0
$983$	−29.0475	−	29.0475i	−0.926471	−	0.926471i	0.0710046	−	0.997476i	$-0.477379\pi$
$983$	−29.0475	−	29.0475i	−0.926471	−	0.926471i	−0.997476	+	0.0710046i	$0.977379\pi$
$984$		0			0
$985$	21.8111	+	9.32154i	0.694961	+	0.297009i
$986$		0			0
$987$	0.291949	−	0.198902i	0.00929285	−	0.00633112i
$988$		0			0
$989$	0.881223			0.0280213
$990$		0			0
$991$	−5.05511			−0.160581			−0.0802905	−	0.996772i	$-0.525585\pi$
$991$	−5.05511			−0.160581			−0.0802905	+	0.996772i	$0.525585\pi$
$992$		0			0
$993$	11.1849	−	7.62017i	0.354943	−	0.241819i
$994$		0			0
$995$	27.7554	−	11.1347i	0.879905	−	0.352994i
$996$		0			0
$997$	−10.9112	−	10.9112i	−0.345562	−	0.345562i	0.512891	−	0.858453i	$-0.328574\pi$
$997$	−10.9112	−	10.9112i	−0.345562	−	0.345562i	−0.858453	+	0.512891i	$0.828574\pi$
$998$		0			0
$999$	33.2189	−	52.7479i	1.05100	−	1.66887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.8	✓	80
3.2	odd	2	inner	1380.2.r.c.737.12	yes	80
5.3	odd	4	inner	1380.2.r.c.1013.12	yes	80
15.8	even	4	inner	1380.2.r.c.1013.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.8	✓	80	1.1	even	1	trivial
1380.2.r.c.737.12	yes	80	3.2	odd	2	inner
1380.2.r.c.1013.8	yes	80	15.8	even	4	inner
1380.2.r.c.1013.12	yes	80	5.3	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43142 + 0.975211i) q^{3} +(0.832554 + 2.07530i) q^{5} +(0.0455472 + 0.0455472i) q^{7} +(1.09793 - 2.79187i) q^{9} +O(q^{10})\)	\(q+(-1.43142 + 0.975211i) q^{3} +(0.832554 + 2.07530i) q^{5} +(0.0455472 + 0.0455472i) q^{7} +(1.09793 - 2.79187i) q^{9} -4.88325i q^{11} +(-2.11410 + 2.11410i) q^{13} +(-3.21559 - 2.15870i) q^{15} +(-4.09837 + 4.09837i) q^{17} -0.731343i q^{19} +(-0.109615 - 0.0207790i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-3.61371 + 3.45559i) q^{25} +(1.15107 + 5.06705i) q^{27} -2.15209 q^{29} -6.73344 q^{31} +(4.76220 + 6.98998i) q^{33} +(-0.0566034 + 0.132444i) q^{35} +(-8.48292 - 8.48292i) q^{37} +(0.964470 - 5.08786i) q^{39} +4.34388i q^{41} +(0.623119 - 0.623119i) q^{43} +(6.70805 - 0.0458627i) q^{45} +(-2.23897 + 2.23897i) q^{47} -6.99585i q^{49} +(1.86971 - 9.86327i) q^{51} +(3.08535 + 3.08535i) q^{53} +(10.1342 - 4.06556i) q^{55} +(0.713214 + 1.04686i) q^{57} +11.4611 q^{59} -13.9103 q^{61} +(0.177169 - 0.0771546i) q^{63} +(-6.14748 - 2.62728i) q^{65} +(-3.10033 - 3.10033i) q^{67} +(-1.70175 - 0.322588i) q^{69} -10.1405i q^{71} +(3.66920 - 3.66920i) q^{73} +(1.80280 - 8.47053i) q^{75} +(0.222418 - 0.222418i) q^{77} -4.48862i q^{79} +(-6.58912 - 6.13054i) q^{81} +(3.25188 + 3.25188i) q^{83} +(-11.9175 - 5.09322i) q^{85} +(3.08054 - 2.09874i) q^{87} -12.6524 q^{89} -0.192583 q^{91} +(9.63838 - 6.56653i) q^{93} +(1.51775 - 0.608882i) q^{95} +(-10.3154 - 10.3154i) q^{97} +(-13.6334 - 5.36144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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