LMFDB - Embedded newform 380.2.u.b.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 $ x^18 - 3x^17 + 21x^16 - 30x^15 + 192x^14 - 207x^13 + 1178x^12 - 705x^11 + 4413x^10 - 2224x^9 + 11430x^8 - 4101x^7 + 19237x^6 - 7125x^5 + 21573x^4 - 5266x^3 + 13851x^2 - 3285*x + 5329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.3
Root			$-1.14386 + 1.98122i$ of defining polynomial
Character	$\chi$	$=$	380.161
Dual form			380.2.u.b.321.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75249 - 1.47051i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(1.54340 - 2.67324i) q^{7} +(0.387867 - 2.19970i) q^{9} +O(q^{10})$	\(q+(1.75249 - 1.47051i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(1.54340 - 2.67324i) q^{7} +(0.387867 - 2.19970i) q^{9} +(-0.285125 - 0.493851i) q^{11} +(-1.79996 - 1.51035i) q^{13} +(-2.14975 + 0.782445i) q^{15} +(0.907938 + 5.14917i) q^{17} +(-2.34334 - 3.67543i) q^{19} +(-1.22625 - 6.95443i) q^{21} +(8.47060 - 3.08305i) q^{23} +(0.766044 + 0.642788i) q^{25} +(0.876608 + 1.51833i) q^{27} +(-0.559736 + 3.17442i) q^{29} +(-1.68171 + 2.91280i) q^{31} +(-1.22589 - 0.446189i) q^{33} +(-2.36462 + 1.98416i) q^{35} -8.95901 q^{37} -5.37541 q^{39} +(3.75201 - 3.14831i) q^{41} +(2.26039 + 0.822715i) q^{43} +(-1.11682 + 1.93439i) q^{45} +(-0.782003 + 4.43496i) q^{47} +(-1.26416 - 2.18959i) q^{49} +(9.16309 + 7.68875i) q^{51} +(12.4799 - 4.54230i) q^{53} +(0.0990228 + 0.561586i) q^{55} +(-9.51145 - 2.99524i) q^{57} +(0.866435 + 4.91379i) q^{59} +(1.59516 - 0.580591i) q^{61} +(-5.28172 - 4.43189i) q^{63} +(1.17484 + 2.03489i) q^{65} +(-2.49900 + 14.1725i) q^{67} +(10.3110 - 17.8592i) q^{69} +(-2.26795 - 0.825465i) q^{71} +(-6.11131 + 5.12800i) q^{73} +2.28771 q^{75} -1.76024 q^{77} +(5.59819 - 4.69744i) q^{79} +(10.0658 + 3.66364i) q^{81} +(-4.06853 + 7.04691i) q^{83} +(0.907938 - 5.14917i) q^{85} +(3.68710 + 6.38624i) q^{87} +(3.72950 + 3.12942i) q^{89} +(-6.81559 + 2.48067i) q^{91} +(1.33614 + 7.57764i) q^{93} +(0.944948 + 4.25524i) q^{95} +(1.72255 + 9.76905i) q^{97} +(-1.19692 + 0.435642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 15 * q^9	$ 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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
$3$	1.75249	−	1.47051i	1.01180	−	0.849002i	0.0232260	−	0.999730i	$-0.492606\pi$
$3$	1.75249	−	1.47051i	1.01180	−	0.849002i	0.988575	+	0.150728i	$0.0481618\pi$
$4$		0			0
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$		0			0
$7$	1.54340	−	2.67324i	0.583350	−	1.01039i	−0.411729	−	0.911306i	$-0.635075\pi$
$7$	1.54340	−	2.67324i	0.583350	−	1.01039i	0.995079	−	0.0990853i	$-0.0315917\pi$
$8$		0			0
$9$	0.387867	−	2.19970i	0.129289	−	0.733235i
$10$		0			0
$11$	−0.285125	−	0.493851i	−0.0859683	−	0.148902i	0.819835	−	0.572600i	$-0.194065\pi$
$11$	−0.285125	−	0.493851i	−0.0859683	−	0.148902i	−0.905803	+	0.423698i	$0.860732\pi$
$12$		0			0
$13$	−1.79996	−	1.51035i	−0.499220	−	0.418895i	0.358097	−	0.933684i	$-0.383426\pi$
$13$	−1.79996	−	1.51035i	−0.499220	−	0.418895i	−0.857317	+	0.514789i	$0.827870\pi$
$14$		0			0
$15$	−2.14975	+	0.782445i	−0.555063	+	0.202026i
$16$		0			0
$17$	0.907938	+	5.14917i	0.220207	+	1.24886i	0.871638	+	0.490150i	$0.163058\pi$
$17$	0.907938	+	5.14917i	0.220207	+	1.24886i	−0.651431	+	0.758708i	$0.725831\pi$
$18$		0			0
$19$	−2.34334	−	3.67543i	−0.537599	−	0.843201i
$19$	−2.34334	−	3.67543i	−0.537599	−	0.843201i
$20$		0			0
$21$	−1.22625	−	6.95443i	−0.267590	−	1.51758i
$22$		0			0
$23$	8.47060	−	3.08305i	1.76624	−	0.642860i	0.766243	−	0.642551i	$-0.222124\pi$
$23$	8.47060	−	3.08305i	1.76624	−	0.642860i	1.00000		0.000308691i	$-9.82594e-5\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$		0			0
$27$	0.876608	+	1.51833i	0.168703	+	0.292203i
$28$		0			0
$29$	−0.559736	+	3.17442i	−0.103940	+	0.589475i	0.887698	+	0.460426i	$0.152303\pi$
$29$	−0.559736	+	3.17442i	−0.103940	+	0.589475i	−0.991638	+	0.129049i	$0.958808\pi$
$30$		0			0
$31$	−1.68171	+	2.91280i	−0.302044	+	0.523155i	−0.976599	−	0.215069i	$-0.931002\pi$
$31$	−1.68171	+	2.91280i	−0.302044	+	0.523155i	0.674555	+	0.738225i	$0.264336\pi$
$32$		0			0
$33$	−1.22589	−	0.446189i	−0.213401	−	0.0776715i
$34$		0			0
$35$	−2.36462	+	1.98416i	−0.399694	+	0.335383i
$36$		0			0
$37$	−8.95901			−1.47285			−0.736426	−	0.676518i	$-0.763488\pi$
$37$	−8.95901			−1.47285			−0.736426	+	0.676518i	$0.763488\pi$
$38$		0			0
$39$	−5.37541			−0.860755
$40$		0			0
$41$	3.75201	−	3.14831i	0.585966	−	0.491684i	−0.300934	−	0.953645i	$-0.597298\pi$
$41$	3.75201	−	3.14831i	0.585966	−	0.491684i	0.886900	+	0.461961i	$0.152854\pi$
$42$		0			0
$43$	2.26039	+	0.822715i	0.344706	+	0.125463i	0.508571	−	0.861020i	$-0.330174\pi$
$43$	2.26039	+	0.822715i	0.344706	+	0.125463i	−0.163865	+	0.986483i	$0.552396\pi$
$44$		0			0
$45$	−1.11682	+	1.93439i	−0.166486	+	0.288361i
$46$		0			0
$47$	−0.782003	+	4.43496i	−0.114067	+	0.646905i	0.873141	+	0.487468i	$0.162079\pi$
$47$	−0.782003	+	4.43496i	−0.114067	+	0.646905i	−0.987208	+	0.159438i	$0.949032\pi$
$48$		0			0
$49$	−1.26416	−	2.18959i	−0.180594	−	0.312798i
$50$		0			0
$51$	9.16309	+	7.68875i	1.28309	+	1.07664i
$52$		0			0
$53$	12.4799	−	4.54230i	1.71424	−	0.623933i	0.716925	−	0.697150i	$-0.245549\pi$
$53$	12.4799	−	4.54230i	1.71424	−	0.623933i	0.997316	+	0.0732175i	$0.0233267\pi$
$54$		0			0
$55$	0.0990228	+	0.561586i	0.0133522	+	0.0757243i
$56$		0			0
$57$	−9.51145	−	2.99524i	−1.25982	−	0.396729i
$58$		0			0
$59$	0.866435	+	4.91379i	0.112800	+	0.639722i	0.987816	+	0.155627i	$0.0497398\pi$
$59$	0.866435	+	4.91379i	0.112800	+	0.639722i	−0.875016	+	0.484095i	$0.839149\pi$
$60$		0			0
$61$	1.59516	−	0.580591i	0.204239	−	0.0743371i	−0.237875	−	0.971296i	$-0.576451\pi$
$61$	1.59516	−	0.580591i	0.204239	−	0.0743371i	0.442114	+	0.896959i	$0.354229\pi$
$62$		0			0
$63$	−5.28172	−	4.43189i	−0.665434	−	0.558365i
$64$		0			0
$65$	1.17484	+	2.03489i	0.145721	+	0.252397i
$66$		0			0
$67$	−2.49900	+	14.1725i	−0.305302	+	1.73145i	0.316780	+	0.948499i	$0.397398\pi$
$67$	−2.49900	+	14.1725i	−0.305302	+	1.73145i	−0.622082	+	0.782952i	$0.713713\pi$
$68$		0			0
$69$	10.3110	−	17.8592i	1.24130	−	2.14999i
$70$		0			0
$71$	−2.26795	−	0.825465i	−0.269156	−	0.0979647i	0.203917	−	0.978988i	$-0.434633\pi$
$71$	−2.26795	−	0.825465i	−0.269156	−	0.0979647i	−0.473072	+	0.881024i	$0.656855\pi$
$72$		0			0
$73$	−6.11131	+	5.12800i	−0.715275	+	0.600187i	−0.926074	−	0.377343i	$-0.876838\pi$
$73$	−6.11131	+	5.12800i	−0.715275	+	0.600187i	0.210799	+	0.977529i	$0.432393\pi$
$74$		0			0
$75$	2.28771			0.264163
$76$		0			0
$77$	−1.76024			−0.200598
$78$		0			0
$79$	5.59819	−	4.69744i	0.629846	−	0.528503i	−0.271035	−	0.962569i	$-0.587366\pi$
$79$	5.59819	−	4.69744i	0.629846	−	0.528503i	0.900881	+	0.434066i	$0.142922\pi$
$80$		0			0
$81$	10.0658	+	3.66364i	1.11842	+	0.407071i
$82$		0			0
$83$	−4.06853	+	7.04691i	−0.446580	+	0.773499i	−0.998161	−	0.0606227i	$-0.980691\pi$
$83$	−4.06853	+	7.04691i	−0.446580	+	0.773499i	0.551581	+	0.834121i	$0.314025\pi$
$84$		0			0
$85$	0.907938	−	5.14917i	0.0984797	−	0.558506i
$86$		0			0
$87$	3.68710	+	6.38624i	0.395298	+	0.684677i
$88$		0			0
$89$	3.72950	+	3.12942i	0.395326	+	0.331718i	0.818684	−	0.574245i	$-0.194704\pi$
$89$	3.72950	+	3.12942i	0.395326	+	0.331718i	−0.423358	+	0.905963i	$0.639149\pi$
$90$		0			0
$91$	−6.81559	+	2.48067i	−0.714468	+	0.260045i
$92$		0			0
$93$	1.33614	+	7.57764i	0.138552	+	0.785765i
$94$		0			0
$95$	0.944948	+	4.25524i	0.0969496	+	0.436578i
$96$		0			0
$97$	1.72255	+	9.76905i	0.174898	+	0.991897i	0.938261	+	0.345927i	$0.112436\pi$
$97$	1.72255	+	9.76905i	0.174898	+	0.991897i	−0.763363	+	0.645970i	$0.776453\pi$
$98$		0			0
$99$	−1.19692	+	0.435642i	−0.120295	+	0.0437836i
$100$		0			0
$101$	−12.4977	−	10.4868i	−1.24357	−	1.04348i	−0.997237	−	0.0742916i	$-0.976330\pi$
$101$	−12.4977	−	10.4868i	−1.24357	−	1.04348i	−0.246331	−	0.969186i	$-0.579225\pi$
$102$		0			0
$103$	−0.967982	−	1.67659i	−0.0953781	−	0.165200i	0.814388	−	0.580320i	$-0.197073\pi$
$103$	−0.967982	−	1.67659i	−0.0953781	−	0.165200i	−0.909766	+	0.415121i	$0.863739\pi$
$104$		0			0
$105$	−1.22625	+	6.95443i	−0.119670	+	0.678683i
$106$		0			0
$107$	−4.08835	+	7.08123i	−0.395236	+	0.684569i	−0.993131	−	0.117005i	$-0.962670\pi$
$107$	−4.08835	+	7.08123i	−0.395236	+	0.684569i	0.597895	+	0.801574i	$0.296004\pi$
$108$		0			0
$109$	−5.86767	−	2.13566i	−0.562021	−	0.204559i	0.0453585	−	0.998971i	$-0.485557\pi$
$109$	−5.86767	−	2.13566i	−0.562021	−	0.204559i	−0.607379	+	0.794412i	$0.707779\pi$
$110$		0			0
$111$	−15.7006	+	13.1744i	−1.49023	+	1.25045i
$112$		0			0
$113$	−11.0563			−1.04009			−0.520043	−	0.854140i	$-0.674084\pi$
$113$	−11.0563			−1.04009			−0.520043	+	0.854140i	$0.674084\pi$
$114$		0			0
$115$	−9.01423			−0.840581
$116$		0			0
$117$	−4.02047	+	3.37357i	−0.371692	+	0.311887i
$118$		0			0
$119$	15.1663	+	5.52009i	1.39029	+	0.506026i
$120$		0			0
$121$	5.33741	−	9.24466i	0.485219	−	0.840424i
$122$		0			0
$123$	1.94573	−	11.0348i	0.175441	−	0.994973i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	−1.38569	−	1.16273i	−0.122960	−	0.103176i	0.579234	−	0.815161i	$-0.303352\pi$
$127$	−1.38569	−	1.16273i	−0.122960	−	0.103176i	−0.702194	+	0.711986i	$0.747796\pi$
$128$		0			0
$129$	5.17113	−	1.88214i	0.455293	−	0.165713i
$130$		0			0
$131$	1.78473	+	10.1217i	0.155933	+	0.884340i	0.957928	+	0.287009i	$0.0926610\pi$
$131$	1.78473	+	10.1217i	0.155933	+	0.884340i	−0.801995	+	0.597331i	$0.796228\pi$
$132$		0			0
$133$	−13.4420	+	0.591670i	−1.16557	+	0.0513043i
$134$		0			0
$135$	−0.304443	−	1.72658i	−0.0262023	−	0.148600i
$136$		0			0
$137$	1.34202	−	0.488457i	0.114657	−	0.0417317i	−0.284055	−	0.958808i	$-0.591680\pi$
$137$	1.34202	−	0.488457i	0.114657	−	0.0417317i	0.398711	+	0.917076i	$0.369457\pi$
$138$		0			0
$139$	14.5734	+	12.2285i	1.23610	+	1.03721i	0.997819	+	0.0660114i	$0.0210274\pi$
$139$	14.5734	+	12.2285i	1.23610	+	1.03721i	0.238278	+	0.971197i	$0.423417\pi$
$140$		0			0
$141$	5.15122	+	8.92217i	0.433811	+	0.751383i
$142$		0			0
$143$	−0.232672	+	1.31955i	−0.0194570	+	0.110346i
$144$		0			0
$145$	1.61169	−	2.79154i	0.133844	−	0.231825i
$146$		0			0
$147$	−5.43525	−	1.97827i	−0.448292	−	0.163165i
$148$		0			0
$149$	1.41523	−	1.18752i	0.115940	−	0.0972852i	−0.582974	−	0.812490i	$-0.698111\pi$
$149$	1.41523	−	1.18752i	0.115940	−	0.0972852i	0.698914	+	0.715205i	$0.253667\pi$
$150$		0			0
$151$	−11.2163			−0.912774			−0.456387	−	0.889781i	$-0.650857\pi$
$151$	−11.2163			−0.912774			−0.456387	+	0.889781i	$0.650857\pi$
$152$		0			0
$153$	11.6788			0.944177
$154$		0			0
$155$	2.57653	−	2.16196i	0.206952	−	0.173653i
$156$		0			0
$157$	−8.66378	−	3.15336i	−0.691445	−	0.251665i	−0.0276912	−	0.999617i	$-0.508815\pi$
$157$	−8.66378	−	3.15336i	−0.691445	−	0.251665i	−0.663754	+	0.747951i	$0.731038\pi$
$158$		0			0
$159$	15.1913	−	26.3122i	1.20475	−	2.08669i
$160$		0			0
$161$	4.83178	−	27.4024i	0.380797	−	2.15961i
$162$		0			0
$163$	−7.41466	−	12.8426i	−0.580761	−	1.00591i	−0.995389	−	0.0959170i	$-0.969422\pi$
$163$	−7.41466	−	12.8426i	−0.580761	−	1.00591i	0.414628	−	0.909991i	$-0.363912\pi$
$164$		0			0
$165$	0.999357	+	0.838560i	0.0777999	+	0.0652818i
$166$		0			0
$167$	14.1961	−	5.16695i	1.09852	−	0.399830i	0.271753	−	0.962367i	$-0.412397\pi$
$167$	14.1961	−	5.16695i	1.09852	−	0.399830i	0.826772	+	0.562537i	$0.190175\pi$
$168$		0			0
$169$	−1.29871	−	7.36535i	−0.0999008	−	0.566566i
$170$		0			0
$171$	−8.99376	+	3.72908i	−0.687770	+	0.285170i
$172$		0			0
$173$	−0.191331	−	1.08509i	−0.0145466	−	0.0824981i	0.976670	−	0.214745i	$-0.0688920\pi$
$173$	−0.191331	−	1.08509i	−0.0145466	−	0.0824981i	−0.991217	+	0.132247i	$0.957781\pi$
$174$		0			0
$175$	2.90064	−	1.05575i	0.219268	−	0.0798070i
$176$		0			0
$177$	8.74423	+	7.33728i	0.657256	+	0.551503i
$178$		0			0
$179$	−5.77224	−	9.99781i	−0.431437	−	0.747271i	0.565560	−	0.824707i	$-0.308660\pi$
$179$	−5.77224	−	9.99781i	−0.431437	−	0.747271i	−0.996997	+	0.0774357i	$0.975327\pi$
$180$		0			0
$181$	1.82662	−	10.3593i	0.135772	−	0.769999i	−0.838548	−	0.544828i	$-0.816595\pi$
$181$	1.82662	−	10.3593i	0.135772	−	0.769999i	0.974319	−	0.225171i	$-0.0722940\pi$
$182$		0			0
$183$	1.94174	−	3.36319i	0.143537	−	0.248614i
$184$		0			0
$185$	8.41871	+	3.06416i	0.618956	+	0.225282i
$186$		0			0
$187$	2.28405	−	1.91654i	0.167026	−	0.140151i
$188$		0			0
$189$	5.41182			0.393652
$190$		0			0
$191$	−4.44309			−0.321491			−0.160746	−	0.986996i	$-0.551390\pi$
$191$	−4.44309			−0.321491			−0.160746	+	0.986996i	$0.551390\pi$
$192$		0			0
$193$	−3.40457	+	2.85678i	−0.245067	+	0.205635i	−0.757044	−	0.653363i	$-0.773357\pi$
$193$	−3.40457	+	2.85678i	−0.245067	+	0.205635i	0.511978	+	0.858999i	$0.328913\pi$
$194$		0			0
$195$	5.05123	+	1.83850i	0.361726	+	0.131658i
$196$		0			0
$197$	6.56722	−	11.3748i	0.467895	−	0.810419i	−0.531432	−	0.847101i	$-0.678346\pi$
$197$	6.56722	−	11.3748i	0.467895	−	0.810419i	0.999327	+	0.0366826i	$0.0116791\pi$
$198$		0			0
$199$	4.13668	−	23.4603i	0.293242	−	1.66306i	−0.381022	−	0.924566i	$-0.624428\pi$
$199$	4.13668	−	23.4603i	0.293242	−	1.66306i	0.674264	−	0.738490i	$-0.264461\pi$
$200$		0			0
$201$	16.4615	+	28.5121i	1.16110	+	2.01109i
$202$		0			0
$203$	7.62210	+	6.39570i	0.534967	+	0.448890i
$204$		0			0
$205$	−4.60253	+	1.67518i	−0.321454	+	0.117000i
$206$		0			0
$207$	−3.49632	−	19.8286i	−0.243011	−	1.37819i
$208$		0			0
$209$	−1.14697	+	2.20521i	−0.0793374	+	0.152538i
$210$		0			0
$211$	−3.22833	−	18.3088i	−0.222247	−	1.26043i	−0.867878	−	0.496777i	$-0.834517\pi$
$211$	−3.22833	−	18.3088i	−0.222247	−	1.26043i	0.645631	−	0.763650i	$-0.276595\pi$
$212$		0			0
$213$	−5.18842	+	1.88843i	−0.355504	+	0.129393i
$214$		0			0
$215$	−1.84269	−	1.54620i	−0.125670	−	0.105450i
$216$		0			0
$217$	5.19109	+	8.99124i	0.352394	+	0.610365i
$218$		0			0
$219$	−3.16922	+	17.9735i	−0.214156	+	1.21454i
$220$		0			0
$221$	6.14279	−	10.6396i	0.413209	−	0.715699i
$222$		0			0
$223$	7.11744	+	2.59054i	0.476619	+	0.173475i	0.569148	−	0.822235i	$-0.307273\pi$
$223$	7.11744	+	2.59054i	0.476619	+	0.173475i	−0.0925293	+	0.995710i	$0.529495\pi$
$224$		0			0
$225$	1.71107	−	1.43576i	0.114071	−	0.0957170i
$226$		0			0
$227$	−24.1858			−1.60527			−0.802633	−	0.596473i	$-0.796568\pi$
$227$	−24.1858			−1.60527			−0.802633	+	0.596473i	$0.796568\pi$
$228$		0			0
$229$	−18.3373			−1.21176			−0.605880	−	0.795556i	$-0.707179\pi$
$229$	−18.3373			−1.21176			−0.605880	+	0.795556i	$0.707179\pi$
$230$		0			0
$231$	−3.08481	+	2.58847i	−0.202966	+	0.170309i
$232$		0			0
$233$	10.6418	+	3.87330i	0.697167	+	0.253748i	0.666201	−	0.745772i	$-0.267919\pi$
$233$	10.6418	+	3.87330i	0.697167	+	0.253748i	0.0309662	+	0.999520i	$0.490142\pi$
$234$		0			0
$235$	2.25169	−	3.90004i	0.146884	−	0.254410i
$236$		0			0
$237$	2.90313	−	16.4644i	0.188578	−	1.06948i
$238$		0			0
$239$	−5.03088	−	8.71375i	−0.325421	−	0.563645i	0.656177	−	0.754607i	$-0.272173\pi$
$239$	−5.03088	−	8.71375i	−0.325421	−	0.563645i	−0.981597	+	0.190962i	$0.938839\pi$
$240$		0			0
$241$	−19.1783	−	16.0925i	−1.23538	−	1.03661i	−0.997871	−	0.0652262i	$-0.979223\pi$
$241$	−19.1783	−	16.0925i	−1.23538	−	1.03661i	−0.237514	−	0.971384i	$-0.576332\pi$
$242$		0			0
$243$	18.0852	−	6.58246i	1.16016	−	0.422265i
$244$		0			0
$245$	0.439038	+	2.48991i	0.0280491	+	0.159074i
$246$		0			0
$247$	−1.33325	+	10.1549i	−0.0848328	+	0.646140i
$248$		0			0
$249$	3.23251	+	18.3325i	0.204852	+	1.16177i
$250$		0			0
$251$	13.4284	−	4.88755i	0.847595	−	0.308499i	0.118536	−	0.992950i	$-0.462180\pi$
$251$	13.4284	−	4.88755i	0.847595	−	0.308499i	0.729059	+	0.684451i	$0.239958\pi$
$252$		0			0
$253$	−3.93774	−	3.30416i	−0.247564	−	0.207731i
$254$		0			0
$255$	−5.98078	−	10.3590i	−0.374531	−	0.648707i
$256$		0			0
$257$	−3.05760	+	17.3405i	−0.190728	+	1.08167i	0.727645	+	0.685954i	$0.240615\pi$
$257$	−3.05760	+	17.3405i	−0.190728	+	1.08167i	−0.918372	+	0.395717i	$0.870496\pi$
$258$		0			0
$259$	−13.8273	+	23.9496i	−0.859188	+	1.48816i
$260$		0			0
$261$	6.76568	+	2.46251i	0.418785	+	0.152425i
$262$		0			0
$263$	−1.01134	+	0.848619i	−0.0623622	+	0.0523281i	−0.673436	−	0.739246i	$-0.735182\pi$
$263$	−1.01134	+	0.848619i	−0.0623622	+	0.0523281i	0.611074	+	0.791574i	$0.290738\pi$
$264$		0			0
$265$	−13.2808			−0.815833
$266$		0			0
$267$	11.1378			0.681621
$268$		0			0
$269$	−21.4196	+	17.9732i	−1.30598	+	1.09585i	−0.316898	+	0.948460i	$0.602641\pi$
$269$	−21.4196	+	17.9732i	−1.30598	+	1.09585i	−0.989079	+	0.147386i	$0.952914\pi$
$270$		0			0
$271$	28.1436	+	10.2434i	1.70960	+	0.622243i	0.996860	−	0.0791858i	$-0.0252320\pi$
$271$	28.1436	+	10.2434i	1.70960	+	0.622243i	0.712739	+	0.701429i	$0.247454\pi$
$272$		0			0
$273$	−8.29640	+	14.3698i	−0.502121	+	0.869699i
$274$		0			0
$275$	0.0990228	−	0.561586i	0.00597130	−	0.0338649i
$276$		0			0
$277$	−9.05979	−	15.6920i	−0.544350	−	0.942842i	−0.998648	−	0.0519916i	$-0.983443\pi$
$277$	−9.05979	−	15.6920i	−0.544350	−	0.942842i	0.454298	−	0.890850i	$-0.349890\pi$
$278$		0			0
$279$	5.75503	+	4.82904i	0.344545	+	0.289107i
$280$		0			0
$281$	−9.37092	+	3.41073i	−0.559022	+	0.203467i	−0.606050	−	0.795426i	$-0.707247\pi$
$281$	−9.37092	+	3.41073i	−0.559022	+	0.203467i	0.0470285	+	0.998894i	$0.485025\pi$
$282$		0			0
$283$	−5.42712	−	30.7787i	−0.322609	−	1.82960i	−0.525973	−	0.850501i	$-0.676299\pi$
$283$	−5.42712	−	30.7787i	−0.322609	−	1.82960i	0.203365	−	0.979103i	$-0.434812\pi$
$284$		0			0
$285$	7.91341	+	6.06771i	0.468750	+	0.359420i
$286$		0			0
$287$	−2.62536	−	14.8892i	−0.154970	−	0.878879i
$288$		0			0
$289$	−9.71487	+	3.53592i	−0.571463	+	0.207995i
$290$		0			0
$291$	17.3843	+	14.5871i	1.01908	+	0.855114i
$292$		0			0
$293$	10.2875	+	17.8184i	0.601001	+	1.04096i	0.992670	+	0.120858i	$0.0385645\pi$
$293$	10.2875	+	17.8184i	0.601001	+	1.04096i	−0.391669	+	0.920106i	$0.628102\pi$
$294$		0			0
$295$	0.866435	−	4.91379i	0.0504458	−	0.286092i
$296$		0			0
$297$	0.499885	−	0.865827i	0.0290063	−	0.0502404i
$298$		0			0
$299$	−19.9033	−	7.24419i	−1.15103	−	0.418942i
$300$		0			0
$301$	5.68800	−	4.77280i	0.327851	−	0.275100i
$302$		0			0
$303$	−37.3231			−2.14416
$304$		0			0
$305$	−1.69753			−0.0972006
$306$		0			0
$307$	21.7222	−	18.2271i	1.23975	−	1.04027i	0.242207	−	0.970225i	$-0.422129\pi$
$307$	21.7222	−	18.2271i	1.23975	−	1.04027i	0.997544	−	0.0700496i	$-0.0223158\pi$
$308$		0			0
$309$	−4.16184	−	1.51478i	−0.236759	−	0.0861731i
$310$		0			0
$311$	−16.3551	+	28.3278i	−0.927412	+	1.60632i	−0.139776	+	0.990183i	$0.544638\pi$
$311$	−16.3551	+	28.3278i	−0.927412	+	1.60632i	−0.787636	+	0.616141i	$0.788695\pi$
$312$		0			0
$313$	−2.16822	+	12.2966i	−0.122555	+	0.695046i	0.860175	+	0.510000i	$0.170355\pi$
$313$	−2.16822	+	12.2966i	−0.122555	+	0.695046i	−0.982730	+	0.185046i	$0.940757\pi$
$314$		0			0
$315$	3.44739	+	5.97106i	0.194239	+	0.336431i
$316$		0			0
$317$	15.1328	+	12.6980i	0.849944	+	0.713188i	0.959777	−	0.280762i	$-0.0905872\pi$
$317$	15.1328	+	12.6980i	0.849944	+	0.713188i	−0.109833	+	0.993950i	$0.535032\pi$
$318$		0			0
$319$	1.72728	−	0.628680i	0.0967093	−	0.0351993i
$320$		0			0
$321$	3.24826	+	18.4218i	0.181300	+	1.02820i
$322$		0			0
$323$	16.7978	−	15.4033i	0.934655	−	0.857064i
$324$		0			0
$325$	−0.408019	−	2.31399i	−0.0226328	−	0.128357i
$326$		0			0
$327$	−13.4236	+	4.88577i	−0.742324	+	0.270184i
$328$		0			0
$329$	10.6488	+	8.93540i	0.587087	+	0.492624i
$330$		0			0
$331$	−8.89182	−	15.4011i	−0.488738	−	0.846520i	0.511178	−	0.859475i	$-0.329209\pi$
$331$	−8.89182	−	15.4011i	−0.488738	−	0.846520i	−0.999916	+	0.0129553i	$0.995876\pi$
$332$		0			0
$333$	−3.47491	+	19.7072i	−0.190424	+	1.07995i
$334$		0			0
$335$	7.19559	−	12.4631i	0.393137	−	0.680933i
$336$		0			0
$337$	−23.9186	−	8.70567i	−1.30293	−	0.474228i	−0.404980	−	0.914325i	$-0.632722\pi$
$337$	−23.9186	−	8.70567i	−1.30293	−	0.474228i	−0.897950	+	0.440098i	$0.854944\pi$
$338$		0			0
$339$	−19.3760	+	16.2584i	−1.05236	+	0.883035i
$340$		0			0
$341$	1.91799			0.103865
$342$		0			0
$343$	13.8032			0.745302
$344$		0			0
$345$	−15.7974	+	13.2556i	−0.850501	+	0.713655i
$346$		0			0
$347$	5.83350	+	2.12322i	0.313159	+	0.113980i	0.493818	−	0.869565i	$-0.335601\pi$
$347$	5.83350	+	2.12322i	0.313159	+	0.113980i	−0.180659	+	0.983546i	$0.557823\pi$
$348$		0			0
$349$	−15.9635	+	27.6495i	−0.854505	+	1.48005i	0.0225985	+	0.999745i	$0.492806\pi$
$349$	−15.9635	+	27.6495i	−0.854505	+	1.48005i	−0.877104	+	0.480301i	$0.840527\pi$
$350$		0			0
$351$	0.715345	−	4.05692i	0.0381823	−	0.216543i
$352$		0			0
$353$	11.0062	+	19.0633i	0.585800	+	1.01464i	0.994775	+	0.102090i	$0.0325528\pi$
$353$	11.0062	+	19.0633i	0.585800	+	1.01464i	−0.408975	+	0.912545i	$0.634114\pi$
$354$		0			0
$355$	1.84885	+	1.55137i	0.0981266	+	0.0823380i
$356$		0			0
$357$	34.6962	−	12.6284i	1.83632	−	0.668365i
$358$		0			0
$359$	0.856397	+	4.85687i	0.0451989	+	0.256336i	0.999031	−	0.0440034i	$-0.0140112\pi$
$359$	0.856397	+	4.85687i	0.0451989	+	0.256336i	−0.953832	+	0.300339i	$0.902900\pi$
$360$		0			0
$361$	−8.01753	+	17.2255i	−0.421975	+	0.906607i
$362$		0			0
$363$	−4.24065	−	24.0499i	−0.222576	−	1.26229i
$364$		0			0
$365$	7.49663	−	2.72855i	0.392392	−	0.142819i
$366$		0			0
$367$	24.2096	+	20.3143i	1.26373	+	1.06040i	0.995274	+	0.0971072i	$0.0309590\pi$
$367$	24.2096	+	20.3143i	1.26373	+	1.06040i	0.268459	+	0.963291i	$0.413485\pi$
$368$		0			0
$369$	−5.47008	−	9.47445i	−0.284761	−	0.493220i
$370$		0			0
$371$	7.11873	−	40.3723i	0.369586	−	2.09603i
$372$		0			0
$373$	10.0856	−	17.4688i	0.522214	−	0.904500i	−0.477452	−	0.878658i	$-0.658440\pi$
$373$	10.0856	−	17.4688i	0.522214	−	0.904500i	0.999666	−	0.0258429i	$-0.00822696\pi$
$374$		0			0
$375$	−2.14975	−	0.782445i	−0.111013	−	0.0404053i
$376$		0			0
$377$	5.80198	−	4.86844i	0.298817	−	0.250738i
$378$		0			0
$379$	−11.8801			−0.610239			−0.305119	−	0.952314i	$-0.598696\pi$
$379$	−11.8801			−0.610239			−0.305119	+	0.952314i	$0.598696\pi$
$380$		0			0
$381$	−4.13822			−0.212007
$382$		0			0
$383$	−21.0413	+	17.6558i	−1.07516	+	0.902168i	−0.995510	−	0.0946544i	$-0.969825\pi$
$383$	−21.0413	+	17.6558i	−1.07516	+	0.902168i	−0.0796521	+	0.996823i	$0.525381\pi$
$384$		0			0
$385$	1.65409	+	0.602039i	0.0843002	+	0.0306828i
$386$		0			0
$387$	2.68646	−	4.65309i	0.136561	−	0.236530i
$388$		0			0
$389$	0.0727819	−	0.412767i	0.00369019	−	0.0209281i	−0.982907	−	0.184102i	$-0.941062\pi$
$389$	0.0727819	−	0.412767i	0.00369019	−	0.0209281i	0.986597	+	0.163174i	$0.0521733\pi$
$390$		0			0
$391$	23.5659	+	40.8174i	1.19178	+	2.06422i
$392$		0			0
$393$	18.0119	+	15.1138i	0.908580	+	0.762389i
$394$		0			0
$395$	−6.86720	+	2.49946i	−0.345526	+	0.125761i
$396$		0			0
$397$	−2.70976	−	15.3678i	−0.135999	−	0.771289i	−0.974159	−	0.225864i	$-0.927480\pi$
$397$	−2.70976	−	15.3678i	−0.135999	−	0.771289i	0.838160	−	0.545425i	$-0.183632\pi$
$398$		0			0
$399$	−22.6870	+	20.8036i	−1.13577	+	1.04148i
$400$		0			0
$401$	−4.10254	−	23.2667i	−0.204871	−	1.16188i	−0.897643	−	0.440724i	$-0.854722\pi$
$401$	−4.10254	−	23.2667i	−0.204871	−	1.16188i	0.692771	−	0.721157i	$-0.256389\pi$
$402$		0			0
$403$	7.42637	−	2.70298i	0.369934	−	0.134645i
$404$		0			0
$405$	−8.20570	−	6.88540i	−0.407744	−	0.342138i
$406$		0			0
$407$	2.55443	+	4.42441i	0.126619	+	0.219310i
$408$		0			0
$409$	−0.785457	+	4.45455i	−0.0388384	+	0.220263i	−0.998050	−	0.0624273i	$-0.980116\pi$
$409$	−0.785457	+	4.45455i	−0.0388384	+	0.220263i	0.959211	+	0.282691i	$0.0912270\pi$
$410$		0			0
$411$	1.63360	−	2.82948i	0.0805796	−	0.139568i
$412$		0			0
$413$	14.4730	+	5.26775i	0.712171	+	0.259209i
$414$		0			0
$415$	6.23336	−	5.23041i	0.305983	−	0.256751i
$416$		0			0
$417$	43.5219			2.13128
$418$		0			0
$419$	23.2692			1.13677			0.568386	−	0.822762i	$-0.307568\pi$
$419$	23.2692			1.13677			0.568386	+	0.822762i	$0.307568\pi$
$420$		0			0
$421$	−16.2997	+	13.6771i	−0.794401	+	0.666582i	−0.946831	−	0.321733i	$-0.895735\pi$
$421$	−16.2997	+	13.6771i	−0.794401	+	0.666582i	0.152429	+	0.988314i	$0.451290\pi$
$422$		0			0
$423$	9.45229	+	3.44035i	0.459586	+	0.167276i
$424$		0			0
$425$	−2.61430	+	4.52811i	−0.126812	+	0.219645i
$426$		0			0
$427$	0.909907	−	5.16034i	0.0440335	−	0.249726i
$428$		0			0
$429$	1.53266	+	2.65465i	0.0739976	+	0.128168i
$430$		0			0
$431$	−29.2038	−	24.5049i	−1.40670	−	1.18036i	−0.958033	−	0.286657i	$-0.907456\pi$
$431$	−29.2038	−	24.5049i	−1.40670	−	1.18036i	−0.448663	−	0.893701i	$-0.648100\pi$
$432$		0			0
$433$	−10.4460	+	3.80204i	−0.502003	+	0.182714i	−0.580595	−	0.814193i	$-0.697180\pi$
$433$	−10.4460	+	3.80204i	−0.502003	+	0.182714i	0.0785916	+	0.996907i	$0.474958\pi$
$434$		0			0
$435$	−1.28052	−	7.26216i	−0.0613960	−	0.348194i
$436$		0			0
$437$	−31.1810	−	23.9085i	−1.49159	−	1.14370i
$438$		0			0
$439$	1.10226	+	6.25125i	0.0526082	+	0.298356i	0.999748	−	0.0224664i	$-0.00715189\pi$
$439$	1.10226	+	6.25125i	0.0526082	+	0.298356i	−0.947139	+	0.320822i	$0.896041\pi$
$440$		0			0
$441$	−5.30677	+	1.93151i	−0.252703	+	0.0919765i
$442$		0			0
$443$	27.6358	+	23.1892i	1.31302	+	1.10175i	0.987736	+	0.156133i	$0.0499028\pi$
$443$	27.6358	+	23.1892i	1.31302	+	1.10175i	0.325279	+	0.945618i	$0.394542\pi$
$444$		0			0
$445$	−2.43426	−	4.21626i	−0.115395	−	0.199870i
$446$		0			0
$447$	0.733913	−	4.16223i	0.0347129	−	0.196867i
$448$		0			0
$449$	3.55923	−	6.16477i	0.167971	−	0.290933i	−0.769736	−	0.638363i	$-0.779612\pi$
$449$	3.55923	−	6.16477i	0.167971	−	0.290933i	0.937706	+	0.347429i	$0.112945\pi$
$450$		0			0
$451$	−2.62459	−	0.955272i	−0.123587	−	0.0449820i
$452$		0			0
$453$	−19.6566	+	16.4938i	−0.923545	+	0.774947i
$454$		0			0
$455$	7.25300			0.340026
$456$		0			0
$457$	35.9355			1.68099			0.840496	−	0.541817i	$-0.182263\pi$
$457$	35.9355			1.68099			0.840496	+	0.541817i	$0.182263\pi$
$458$		0			0
$459$	−7.02224	+	5.89236i	−0.327770	+	0.275032i
$460$		0			0
$461$	−25.1560	−	9.15604i	−1.17163	−	0.426439i	−0.318393	−	0.947959i	$-0.603143\pi$
$461$	−25.1560	−	9.15604i	−1.17163	−	0.426439i	−0.853239	+	0.521519i	$0.825365\pi$
$462$		0			0
$463$	−11.6850	+	20.2390i	−0.543048	+	0.940587i	0.455679	+	0.890144i	$0.349397\pi$
$463$	−11.6850	+	20.2390i	−0.543048	+	0.940587i	−0.998727	+	0.0504426i	$0.983937\pi$
$464$		0			0
$465$	1.33614	−	7.57764i	0.0619621	−	0.351405i
$466$		0			0
$467$	−8.10209	−	14.0332i	−0.374920	−	0.649380i	0.615395	−	0.788219i	$-0.288996\pi$
$467$	−8.10209	−	14.0332i	−0.374920	−	0.649380i	−0.990315	+	0.138838i	$0.955663\pi$
$468$		0			0
$469$	34.0297	+	28.5543i	1.57135	+	1.31852i
$470$		0			0
$471$	−19.8203	+	7.21398i	−0.913269	+	0.332403i
$472$		0			0
$473$	−0.238195	−	1.35087i	−0.0109522	−	0.0621131i
$474$		0			0
$475$	0.567417	−	4.32181i	0.0260349	−	0.198298i
$476$		0			0
$477$	−5.15118	−	29.2138i	−0.235857	−	1.33761i
$478$		0			0
$479$	−8.62752	+	3.14016i	−0.394202	+	0.143478i	−0.531513	−	0.847050i	$-0.678376\pi$
$479$	−8.62752	+	3.14016i	−0.394202	+	0.143478i	0.137311	+	0.990528i	$0.456154\pi$
$480$		0			0
$481$	16.1259	+	13.5312i	0.735277	+	0.616971i
$482$		0			0
$483$	−31.8279	−	55.1276i	−1.44822	−	2.50839i
$484$		0			0
$485$	1.72255	−	9.76905i	0.0782169	−	0.443590i
$486$		0			0
$487$	−18.5252	+	32.0866i	−0.839458	+	1.45398i	0.0508914	+	0.998704i	$0.483794\pi$
$487$	−18.5252	+	32.0866i	−0.839458	+	1.45398i	−0.890349	+	0.455279i	$0.849540\pi$
$488$		0			0
$489$	−31.8793	−	11.6031i	−1.44163	−	0.524711i
$490$		0			0
$491$	−23.3003	+	19.5513i	−1.05153	+	0.882337i	−0.993253	−	0.115964i	$-0.963004\pi$
$491$	−23.3003	+	19.5513i	−1.05153	+	0.882337i	−0.0582746	+	0.998301i	$0.518560\pi$
$492$		0			0
$493$	−16.8538			−0.759059
$494$		0			0
$495$	1.27373			0.0572500
$496$		0			0
$497$	−5.70702	+	4.78876i	−0.255995	+	0.214805i
$498$		0			0
$499$	−14.9454	−	5.43969i	−0.669049	−	0.243514i	−0.0149107	−	0.999889i	$-0.504746\pi$
$499$	−14.9454	−	5.43969i	−0.669049	−	0.243514i	−0.654138	+	0.756375i	$0.726969\pi$
$500$		0			0
$501$	17.2804	−	29.9306i	0.772032	−	1.33720i
$502$		0			0
$503$	−1.21681	+	6.90088i	−0.0542550	+	0.307695i	−0.999844	−	0.0176685i	$-0.994376\pi$
$503$	−1.21681	+	6.90088i	−0.0542550	+	0.307695i	0.945589	+	0.325364i	$0.105487\pi$
$504$		0			0
$505$	8.15730	+	14.1289i	0.362995	+	0.628726i
$506$		0			0
$507$	−13.1068	−	10.9979i	−0.582095	−	0.488436i
$508$		0			0
$509$	13.7407	−	5.00121i	0.609046	−	0.221675i	−0.0190398	−	0.999819i	$-0.506061\pi$
$509$	13.7407	−	5.00121i	0.609046	−	0.221675i	0.628086	+	0.778144i	$0.283839\pi$
$510$		0			0
$511$	4.27621	+	24.2516i	0.189168	+	1.07283i
$512$		0			0
$513$	3.52632	−	6.77987i	0.155691	−	0.299339i
$514$		0			0
$515$	0.336177	+	1.90655i	0.0148137	+	0.0840128i
$516$		0			0
$517$	2.41318	−	0.878324i	0.106131	−	0.0386286i
$518$		0			0
$519$	−1.93095	−	1.62026i	−0.0847594	−	0.0711216i
$520$		0			0
$521$	8.58227	+	14.8649i	0.375996	+	0.651244i	0.990476	−	0.137688i	$-0.0439673\pi$
$521$	8.58227	+	14.8649i	0.375996	+	0.651244i	−0.614479	+	0.788933i	$0.710634\pi$
$522$		0			0
$523$	−5.28473	+	29.9712i	−0.231085	+	1.31055i	0.619618	+	0.784903i	$0.287287\pi$
$523$	−5.28473	+	29.9712i	−0.231085	+	1.31055i	−0.850703	+	0.525646i	$0.823824\pi$
$524$		0			0
$525$	3.53086	−	6.11562i	0.154099	−	0.266908i
$526$		0			0
$527$	−16.5254	−	6.01476i	−0.719859	−	0.262007i
$528$		0			0
$529$	44.6269	−	37.4464i	1.94030	−	1.62811i
$530$		0			0
$531$	11.1450			0.483650
$532$		0			0
$533$	−11.5085			−0.498490
$534$		0			0
$535$	6.26372	−	5.25588i	0.270804	−	0.227232i
$536$		0			0
$537$	−24.8177	−	9.03291i	−1.07096	−	0.389799i
$538$		0			0
$539$	−0.720886	+	1.24861i	−0.0310508	+	0.0537815i
$540$		0			0
$541$	2.72643	−	15.4624i	0.117219	−	0.664779i	−0.868409	−	0.495848i	$-0.834857\pi$
$541$	2.72643	−	15.4624i	0.117219	−	0.664779i	0.985628	−	0.168931i	$-0.0540316\pi$
$542$		0			0
$543$	−12.0323	−	20.8406i	−0.516357	−	0.894356i
$544$		0			0
$545$	4.78337	+	4.01372i	0.204897	+	0.171929i
$546$		0			0
$547$	12.1733	−	4.43071i	0.520491	−	0.189443i	−0.0683963	−	0.997658i	$-0.521788\pi$
$547$	12.1733	−	4.43071i	0.520491	−	0.189443i	0.588888	+	0.808215i	$0.299566\pi$
$548$		0			0
$549$	−0.658418	−	3.73407i	−0.0281006	−	0.159366i
$550$		0			0
$551$	12.9790	−	5.38147i	0.552924	−	0.229258i
$552$		0			0
$553$	−3.91717	−	22.2154i	−0.166575	−	0.944693i
$554$		0			0
$555$	19.2596	−	7.00993i	0.817525	−	0.297555i
$556$		0			0
$557$	32.0401	+	26.8849i	1.35758	+	1.13915i	0.976720	+	0.214516i	$0.0688175\pi$
$557$	32.0401	+	26.8849i	1.35758	+	1.13915i	0.380863	+	0.924632i	$0.375627\pi$
$558$		0			0
$559$	−2.82603	−	4.89484i	−0.119529	−	0.207029i
$560$		0			0
$561$	1.18447	−	6.71745i	0.0500083	−	0.283611i
$562$		0			0
$563$	−4.72970	+	8.19209i	−0.199333	+	0.345255i	−0.948312	−	0.317338i	$-0.897211\pi$
$563$	−4.72970	+	8.19209i	−0.199333	+	0.345255i	0.748979	+	0.662594i	$0.230544\pi$
$564$		0			0
$565$	10.3895	+	3.78146i	0.437089	+	0.159087i
$566$		0			0
$567$	25.3293	−	21.2538i	1.06373	−	0.892577i
$568$		0			0
$569$	1.30763			0.0548186			0.0274093	−	0.999624i	$-0.491274\pi$
$569$	1.30763			0.0548186			0.0274093	+	0.999624i	$0.491274\pi$
$570$		0			0
$571$	11.7704			0.492576			0.246288	−	0.969197i	$-0.420789\pi$
$571$	11.7704			0.492576			0.246288	+	0.969197i	$0.420789\pi$
$572$		0			0
$573$	−7.78648	+	6.53363i	−0.325285	+	0.272947i
$574$		0			0
$575$	8.47060	+	3.08305i	0.353249	+	0.128572i
$576$		0			0
$577$	1.75149	−	3.03367i	0.0729155	−	0.126293i	−0.827262	−	0.561816i	$-0.810103\pi$
$577$	1.75149	−	3.03367i	0.0729155	−	0.126293i	0.900178	+	0.435522i	$0.143436\pi$
$578$		0			0
$579$	−1.76555	+	10.0130i	−0.0733739	+	0.416124i
$580$		0			0
$581$	12.5587	+	21.7524i	0.521024	+	0.902441i
$582$		0			0
$583$	−5.80153	−	4.86807i	−0.240275	−	0.201615i
$584$		0			0
$585$	4.93183	−	1.79504i	0.203906	−	0.0742158i
$586$		0			0
$587$	−1.47722	−	8.37771i	−0.0609713	−	0.345785i	−0.999998	−	0.00194144i	$-0.999382\pi$
$587$	−1.47722	−	8.37771i	−0.0609713	−	0.345785i	0.939027	−	0.343844i	$-0.111729\pi$
$588$		0			0
$589$	14.6466	−	0.644691i	0.603503	−	0.0265641i
$590$		0			0
$591$	−5.21776	−	29.5914i	−0.214630	−	1.21723i
$592$		0			0
$593$	−0.638258	+	0.232307i	−0.0262101	+	0.00953971i	−0.355092	−	0.934831i	$-0.615550\pi$
$593$	−0.638258	+	0.232307i	−0.0262101	+	0.00953971i	0.328882	+	0.944371i	$0.393328\pi$
$594$		0			0
$595$	−12.3637	−	10.3744i	−0.506862	−	0.425308i
$596$		0			0
$597$	−27.2492	−	47.1970i	−1.11524	−	1.93164i
$598$		0			0
$599$	−0.629002	+	3.56724i	−0.0257003	+	0.145754i	−0.994958	−	0.100295i	$-0.968021\pi$
$599$	−0.629002	+	3.56724i	−0.0257003	+	0.145754i	0.969257	+	0.246049i	$0.0791324\pi$
$600$		0			0
$601$	12.9137	−	22.3672i	0.526761	−	0.912376i	−0.472753	−	0.881195i	$-0.656740\pi$
$601$	12.9137	−	22.3672i	0.526761	−	0.912376i	0.999514	−	0.0311814i	$-0.00992697\pi$
$602$		0			0
$603$	30.2061	+	10.9941i	1.23009	+	0.447716i
$604$		0			0
$605$	−8.17738	+	6.86164i	−0.332458	+	0.278965i
$606$		0			0
$607$	2.64689			0.107434			0.0537169	−	0.998556i	$-0.482893\pi$
$607$	2.64689			0.107434			0.0537169	+	0.998556i	$0.482893\pi$
$608$		0			0
$609$	22.7626			0.922389
$610$		0			0
$611$	8.10591	−	6.80167i	0.327930	−	0.275166i
$612$		0			0
$613$	−27.8737	−	10.1452i	−1.12581	−	0.409760i	−0.289038	−	0.957318i	$-0.593335\pi$
$613$	−27.8737	−	10.1452i	−1.12581	−	0.409760i	−0.836768	+	0.547558i	$0.815558\pi$
$614$		0			0
$615$	−5.60251	+	9.70383i	−0.225915	+	0.391296i
$616$		0			0
$617$	1.69384	−	9.60623i	0.0681913	−	0.386732i	−0.931542	−	0.363634i	$-0.881536\pi$
$617$	1.69384	−	9.60623i	0.0681913	−	0.386732i	0.999733	−	0.0230981i	$-0.00735302\pi$
$618$		0			0
$619$	11.1539	+	19.3192i	0.448315	+	0.776504i	0.998276	−	0.0586859i	$-0.0186911\pi$
$619$	11.1539	+	19.3192i	0.448315	+	0.776504i	−0.549962	+	0.835190i	$0.685358\pi$
$620$		0			0
$621$	12.1065	+	10.1585i	0.485816	+	0.407648i
$622$		0			0
$623$	14.1218	−	5.13992i	0.565779	−	0.205927i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$		0			0
$627$	1.23275	+	5.55125i	0.0492313	+	0.221696i
$628$		0			0
$629$	−8.13423	−	46.1315i	−0.324333	−	1.83938i
$630$		0			0
$631$	43.7131	−	15.9103i	1.74019	−	0.633377i	0.740920	−	0.671593i	$-0.234390\pi$
$631$	43.7131	−	15.9103i	1.74019	−	0.633377i	0.999270	+	0.0382155i	$0.0121673\pi$
$632$		0			0
$633$	−32.5809	−	27.3386i	−1.29498	−	1.08661i
$634$		0			0
$635$	0.904443	+	1.56654i	0.0358917	+	0.0621663i
$636$		0			0
$637$	−1.03160	+	5.85050i	−0.0408735	+	0.231805i
$638$		0			0
$639$	−2.69544	+	4.66864i	−0.106630	+	0.184689i
$640$		0			0
$641$	−41.1061	−	14.9614i	−1.62359	−	0.590939i	−0.639531	−	0.768765i	$-0.720871\pi$
$641$	−41.1061	−	14.9614i	−1.62359	−	0.590939i	−0.984062	+	0.177826i	$0.943094\pi$
$642$		0			0
$643$	30.1438	−	25.2936i	1.18875	−	0.997483i	0.188874	−	0.982001i	$-0.439516\pi$
$643$	30.1438	−	25.2936i	1.18875	−	0.997483i	0.999880	−	0.0154814i	$-0.00492809\pi$
$644$		0			0
$645$	−5.50300			−0.216680
$646$		0			0
$647$	−9.53143			−0.374719			−0.187360	−	0.982291i	$-0.559993\pi$
$647$	−9.53143			−0.374719			−0.187360	+	0.982291i	$0.559993\pi$
$648$		0			0
$649$	2.17964	−	1.82893i	0.0855583	−	0.0717919i
$650$		0			0
$651$	22.3191	+	8.12348i	0.874754	+	0.318384i
$652$		0			0
$653$	−20.8821	+	36.1689i	−0.817180	+	1.41540i	0.0905712	+	0.995890i	$0.471131\pi$
$653$	−20.8821	+	36.1689i	−0.817180	+	1.41540i	−0.907752	+	0.419508i	$0.862203\pi$
$654$		0			0
$655$	1.78473	−	10.1217i	0.0697354	−	0.395489i
$656$		0			0
$657$	8.90970	+	15.4321i	0.347601	+	0.602062i
$658$		0			0
$659$	−9.64513	−	8.09322i	−0.375721	−	0.315267i	0.435299	−	0.900286i	$-0.356643\pi$
$659$	−9.64513	−	8.09322i	−0.375721	−	0.315267i	−0.811020	+	0.585019i	$0.801087\pi$
$660$		0			0
$661$	−41.2288	+	15.0060i	−1.60361	+	0.583667i	−0.980162	−	0.198196i	$-0.936492\pi$
$661$	−41.2288	+	15.0060i	−1.60361	+	0.583667i	−0.623450	+	0.781863i	$0.714270\pi$
$662$		0			0
$663$	−4.88054	−	27.6789i	−0.189545	−	1.07496i
$664$		0			0
$665$	12.8337	+	4.04145i	0.497671	+	0.156721i
$666$		0			0
$667$	5.04558	+	28.6149i	0.195366	+	1.10797i
$668$		0			0
$669$	16.2827	−	5.92641i	0.629525	−	0.229128i
$670$		0			0
$671$	−0.741545	−	0.622230i	−0.0286270	−	0.0240209i
$672$		0			0
$673$	6.37316	+	11.0386i	0.245667	+	0.425508i	0.962319	−	0.271923i	$-0.0876596\pi$
$673$	6.37316	+	11.0386i	0.245667	+	0.425508i	−0.716652	+	0.697431i	$0.754326\pi$
$674$		0			0
$675$	−0.304443	+	1.72658i	−0.0117180	+	0.0664561i
$676$		0			0
$677$	17.2366	−	29.8547i	0.662457	−	1.14741i	−0.317511	−	0.948255i	$-0.602847\pi$
$677$	17.2366	−	29.8547i	0.662457	−	1.14741i	0.979968	−	0.199155i	$-0.0638197\pi$
$678$		0			0
$679$	28.7737	+	10.4728i	1.10423	+	0.401907i
$680$		0			0
$681$	−42.3854	+	35.5655i	−1.62421	+	1.36287i
$682$		0			0
$683$	16.8008			0.642867			0.321433	−	0.946932i	$-0.395835\pi$
$683$	16.8008			0.642867			0.321433	+	0.946932i	$0.395835\pi$
$684$		0			0
$685$	−1.42815			−0.0545669
$686$		0			0
$687$	−32.1359	+	26.9652i	−1.22606	+	1.02879i
$688$		0			0
$689$	−29.3238	−	10.6730i	−1.11715	−	0.406608i
$690$		0			0
$691$	8.29618	−	14.3694i	0.315602	−	0.546638i	−0.663964	−	0.747765i	$-0.731127\pi$
$691$	8.29618	−	14.3694i	0.315602	−	0.546638i	0.979565	+	0.201127i	$0.0644604\pi$
$692$		0			0
$693$	−0.682741	+	3.87202i	−0.0259352	+	0.147086i
$694$		0			0
$695$	−9.51209	−	16.4754i	−0.360814	−	0.624948i
$696$		0			0
$697$	19.6178	+	16.4613i	0.743078	+	0.623516i
$698$		0			0
$699$	24.3454	−	8.86100i	0.920827	−	0.335154i
$700$		0			0
$701$	−2.49187	−	14.1321i	−0.0941167	−	0.533762i	−0.995014	−	0.0997310i	$-0.968202\pi$
$701$	−2.49187	−	14.1321i	−0.0941167	−	0.533762i	0.900898	−	0.434031i	$-0.142909\pi$
$702$		0			0
$703$	20.9940	+	32.9282i	0.791803	+	1.24191i
$704$		0			0
$705$	−1.78900	−	10.1459i	−0.0673776	−	0.382118i
$706$		0			0
$707$	−47.3228	+	17.2241i	−1.77976	+	0.647778i
$708$		0			0
$709$	20.3960	+	17.1143i	0.765987	+	0.642740i	0.939678	−	0.342061i	$-0.111125\pi$
$709$	20.3960	+	17.1143i	0.765987	+	0.642740i	−0.173690	+	0.984800i	$0.555569\pi$
$710$		0			0
$711$	−8.16162	−	14.1363i	−0.306085	−	0.530154i
$712$		0			0
$713$	−5.26477	+	29.8580i	−0.197167	+	1.11819i
$714$		0			0
$715$	0.669954	−	1.16039i	0.0250548	−	0.0433963i
$716$		0			0
$717$	−21.6303	−	7.87277i	−0.807797	−	0.294014i
$718$		0			0
$719$	19.9847	−	16.7692i	0.745304	−	0.625385i	−0.188952	−	0.981986i	$-0.560509\pi$
$719$	19.9847	−	16.7692i	0.745304	−	0.625385i	0.934256	+	0.356602i	$0.116065\pi$
$720$		0			0
$721$	−5.97593			−0.222555
$722$		0			0
$723$	−57.2741			−2.13005
$724$		0			0
$725$	−2.46926	+	2.07195i	−0.0917060	+	0.0769505i
$726$		0			0
$727$	8.47243	+	3.08371i	0.314225	+	0.114369i	0.494318	−	0.869281i	$-0.335418\pi$
$727$	8.47243	+	3.08371i	0.314225	+	0.114369i	−0.180093	+	0.983650i	$0.557640\pi$
$728$		0			0
$729$	5.94683	−	10.3002i	0.220253	−	0.381489i
$730$		0			0
$731$	−2.18401	+	12.3861i	−0.0807784	+	0.458117i
$732$		0			0
$733$	−17.8405	−	30.9006i	−0.658953	−	1.14134i	−0.980887	−	0.194578i	$-0.937666\pi$
$733$	−17.8405	−	30.9006i	−0.658953	−	1.14134i	0.321934	−	0.946762i	$-0.395667\pi$
$734$		0			0
$735$	4.43085	+	3.71793i	0.163434	+	0.137138i
$736$		0			0
$737$	7.71164	−	2.80681i	0.284062	−	0.103390i
$738$		0			0
$739$	−2.85870	−	16.2125i	−0.105159	−	0.596386i	−0.991157	−	0.132697i	$-0.957636\pi$
$739$	−2.85870	−	16.2125i	−0.105159	−	0.596386i	0.885998	−	0.463689i	$-0.153475\pi$
$740$		0			0
$741$	12.5964	+	19.7569i	0.462741	+	0.725789i
$742$		0			0
$743$	5.47679	+	31.0604i	0.200924	+	1.13950i	0.903726	+	0.428111i	$0.140821\pi$
$743$	5.47679	+	31.0604i	0.200924	+	1.13950i	−0.702802	+	0.711385i	$0.748068\pi$
$744$		0			0
$745$	−1.73603	+	0.631865i	−0.0636034	+	0.0231497i
$746$		0			0
$747$	13.9231	+	11.6828i	0.509418	+	0.427453i
$748$		0			0
$749$	12.6199	+	21.8583i	0.461122	+	0.798686i
$750$		0			0
$751$	1.55178	−	8.80057i	0.0566252	−	0.321138i	−0.943317	−	0.331893i	$-0.892313\pi$
$751$	1.55178	−	8.80057i	0.0566252	−	0.321138i	0.999942	+	0.0107557i	$0.00342373\pi$
$752$		0			0
$753$	16.3460	−	28.3121i	0.595681	−	1.03175i
$754$		0			0
$755$	10.5399	+	3.83622i	0.383587	+	0.139614i
$756$		0			0
$757$	5.34941	−	4.48869i	0.194428	−	0.163144i	−0.540377	−	0.841423i	$-0.681718\pi$
$757$	5.34941	−	4.48869i	0.194428	−	0.163144i	0.734805	+	0.678279i	$0.237274\pi$
$758$		0			0
$759$	−11.7597			−0.426849
$760$		0			0
$761$	−19.1207			−0.693124			−0.346562	−	0.938027i	$-0.612651\pi$
$761$	−19.1207			−0.693124			−0.346562	+	0.938027i	$0.612651\pi$
$762$		0			0
$763$	−14.7653	+	12.3895i	−0.534539	+	0.448532i
$764$		0			0
$765$	−10.9745	−	3.99439i	−0.396784	−	0.144418i
$766$		0			0
$767$	5.86199	−	10.1533i	0.211664	−	0.366613i
$768$		0			0
$769$	−1.92416	+	10.9125i	−0.0693870	+	0.393513i	0.930259	+	0.366904i	$0.119582\pi$
$769$	−1.92416	+	10.9125i	−0.0693870	+	0.393513i	−0.999646	+	0.0266095i	$0.991529\pi$
$770$		0			0
$771$	20.1411	+	34.8853i	0.725362	+	1.25636i
$772$		0			0
$773$	14.1680	+	11.8884i	0.509588	+	0.427595i	0.860984	−	0.508632i	$-0.169849\pi$
$773$	14.1680	+	11.8884i	0.509588	+	0.427595i	−0.351396	+	0.936227i	$0.614293\pi$
$774$		0			0
$775$	−3.16058	+	1.15036i	−0.113531	+	0.0413220i
$776$		0			0
$777$	10.9860	+	62.3048i	0.394121	+	2.23517i
$778$		0			0
$779$	−20.3636	−	6.41269i	−0.729603	−	0.229758i
$780$		0			0
$781$	0.238991	+	1.35539i	0.00855178	+	0.0484996i
$782$		0			0
$783$	−5.31048	+	1.93286i	−0.189781	+	0.0690747i
$784$		0			0
$785$	7.06278	+	5.92637i	0.252081	+	0.211521i
$786$		0			0
$787$	15.4354	+	26.7349i	0.550214	+	0.952998i	0.998259	+	0.0589870i	$0.0187871\pi$
$787$	15.4354	+	26.7349i	0.550214	+	0.952998i	−0.448045	+	0.894011i	$0.647880\pi$
$788$		0			0
$789$	−0.524466	+	2.97439i	−0.0186715	+	0.105891i
$790$		0			0
$791$	−17.0642	+	29.5561i	−0.606734	+	1.05089i
$792$		0			0
$793$	−3.74813	−	1.36421i	−0.133100	−	0.0484444i
$794$		0			0
$795$	−23.2745	+	19.5296i	−0.825460	+	0.692644i
$796$		0			0
$797$	−21.1177			−0.748026			−0.374013	−	0.927424i	$-0.622018\pi$
$797$	−21.1177			−0.748026			−0.374013	+	0.927424i	$0.622018\pi$
$798$		0			0
$799$	−23.5464			−0.833011
$800$		0			0
$801$	8.33035	−	6.99000i	0.294339	−	0.246979i
$802$		0			0
$803$	4.27495	+	1.55595i	0.150860	+	0.0549085i
$804$		0			0
$805$	−13.9125	+	24.0972i	−0.490353	+	0.849316i
$806$		0			0
$807$	−11.1078	+	62.9957i	−0.391015	+	2.21755i
$808$		0			0
$809$	−8.30657	−	14.3874i	−0.292043	−	0.505834i	0.682249	−	0.731120i	$-0.261002\pi$
$809$	−8.30657	−	14.3874i	−0.292043	−	0.505834i	−0.974293	+	0.225286i	$0.927669\pi$
$810$		0			0
$811$	13.5057	+	11.3326i	0.474249	+	0.397942i	0.848342	−	0.529449i	$-0.177601\pi$
$811$	13.5057	+	11.3326i	0.474249	+	0.397942i	−0.374092	+	0.927391i	$0.622046\pi$
$812$		0			0
$813$	64.3844	−	23.4340i	2.25806	−	0.821867i
$814$		0			0
$815$	2.57509	+	14.6040i	0.0902013	+	0.511557i
$816$		0			0
$817$	−2.27303	−	10.2358i	−0.0795234	−	0.358105i
$818$		0			0
$819$	2.81320	+	15.9545i	0.0983013	+	0.557494i
$820$		0			0
$821$	−16.4308	+	5.98034i	−0.573440	+	0.208715i	−0.612431	−	0.790524i	$-0.709808\pi$
$821$	−16.4308	+	5.98034i	−0.573440	+	0.208715i	0.0389903	+	0.999240i	$0.487586\pi$
$822$		0			0
$823$	23.4703	+	19.6939i	0.818124	+	0.686488i	0.952532	−	0.304438i	$-0.0984688\pi$
$823$	23.4703	+	19.6939i	0.818124	+	0.686488i	−0.134408	+	0.990926i	$0.542913\pi$
$824$		0			0
$825$	−0.652284	−	1.12979i	−0.0227096	−	0.0393342i
$826$		0			0
$827$	3.97960	−	22.5694i	0.138384	−	0.784816i	−0.834059	−	0.551676i	$-0.813989\pi$
$827$	3.97960	−	22.5694i	0.138384	−	0.784816i	0.972443	−	0.233141i	$-0.0749003\pi$
$828$		0			0
$829$	−21.4104	+	37.0839i	−0.743614	+	1.28798i	0.207226	+	0.978293i	$0.433556\pi$
$829$	−21.4104	+	37.0839i	−0.743614	+	1.28798i	−0.950840	+	0.309683i	$0.899777\pi$
$830$		0			0
$831$	−38.9525	−	14.1776i	−1.35125	−	0.491814i
$832$		0			0
$833$	10.1268	−	8.49738i	0.350872	−	0.294417i
$834$		0			0
$835$	−15.1071			−0.522804
$836$		0			0
$837$	−5.89680			−0.203823
$838$		0			0
$839$	3.01004	−	2.52572i	0.103918	−	0.0871977i	−0.589348	−	0.807879i	$-0.700615\pi$
$839$	3.01004	−	2.52572i	0.103918	−	0.0871977i	0.693266	+	0.720681i	$0.256171\pi$
$840$		0			0
$841$	17.4875	+	6.36491i	0.603016	+	0.219480i
$842$		0			0
$843$	−11.4069	+	19.7574i	−0.392875	+	0.680479i
$844$		0			0
$845$	−1.29871	+	7.36535i	−0.0446770	+	0.253376i
$846$		0			0
$847$	−16.4755	−	28.5364i	−0.566105	−	0.980522i
$848$		0			0
$849$	−54.7715	−	45.9588i	−1.87975	−	1.57730i
$850$		0			0
$851$	−75.8882	+	27.6210i	−2.60141	+	0.946837i
$852$		0			0
$853$	0.450339	+	2.55400i	0.0154193	+	0.0874473i	0.991546	−	0.129753i	$-0.0414185\pi$
$853$	0.450339	+	2.55400i	0.0154193	+	0.0874473i	−0.976127	+	0.217201i	$0.930307\pi$
$854$		0			0
$855$	9.72679	−	0.428138i	0.332649	−	0.0146420i
$856$		0			0
$857$	4.07304	+	23.0994i	0.139133	+	0.789060i	0.971892	+	0.235425i	$0.0756483\pi$
$857$	4.07304	+	23.0994i	0.139133	+	0.789060i	−0.832760	+	0.553634i	$0.813241\pi$
$858$		0			0
$859$	−1.92408	+	0.700308i	−0.0656488	+	0.0238942i	−0.374636	−	0.927172i	$-0.622232\pi$
$859$	−1.92408	+	0.700308i	−0.0656488	+	0.0238942i	0.308987	+	0.951066i	$0.400010\pi$
$860$		0			0
$861$	−26.4956	−	22.2325i	−0.902969	−	0.757681i
$862$		0			0
$863$	−6.82259	−	11.8171i	−0.232244	−	0.402258i	0.726224	−	0.687458i	$-0.241273\pi$
$863$	−6.82259	−	11.8171i	−0.232244	−	0.402258i	−0.958468	+	0.285200i	$0.907940\pi$
$864$		0			0
$865$	−0.191331	+	1.08509i	−0.00650546	+	0.0368943i
$866$		0			0
$867$	−11.8256	+	20.4825i	−0.401618	+	0.695623i
$868$		0			0
$869$	−3.91602	−	1.42531i	−0.132842	−	0.0483504i
$870$		0			0
$871$	25.9036	−	21.7357i	0.877710	−	0.736486i
$872$		0			0
$873$	22.1572			0.749906
$874$		0			0
$875$	−3.08680			−0.104353
$876$		0			0
$877$	−4.63051	+	3.88546i	−0.156361	+	0.131203i	−0.717612	−	0.696443i	$-0.754765\pi$
$877$	−4.63051	+	3.88546i	−0.156361	+	0.131203i	0.561251	+	0.827646i	$0.310320\pi$
$878$		0			0
$879$	44.2310	+	16.0988i	1.49187	+	0.542998i
$880$		0			0
$881$	26.6195	−	46.1063i	0.896833	−	1.55336i	0.0653124	−	0.997865i	$-0.479196\pi$
$881$	26.6195	−	46.1063i	0.896833	−	1.55336i	0.831520	−	0.555495i	$-0.187471\pi$
$882$		0			0
$883$	7.65782	−	43.4296i	0.257706	−	1.46152i	−0.531324	−	0.847169i	$-0.678305\pi$
$883$	7.65782	−	43.4296i	0.257706	−	1.46152i	0.789030	−	0.614355i	$-0.210584\pi$
$884$		0			0
$885$	−5.70739	−	9.88549i	−0.191852	−	0.332297i
$886$		0			0
$887$	−15.6614	−	13.1415i	−0.525858	−	0.441248i	0.340810	−	0.940132i	$-0.389299\pi$
$887$	−15.6614	−	13.1415i	−0.525858	−	0.441248i	−0.866668	+	0.498885i	$0.833743\pi$
$888$		0			0
$889$	−5.24693	+	1.90973i	−0.175976	+	0.0640501i
$890$		0			0
$891$	−1.06071	−	6.01558i	−0.0355351	−	0.201530i
$892$		0			0
$893$	18.1329	−	7.51842i	0.606793	−	0.251594i
$894$		0			0
$895$	2.00468	+	11.3691i	0.0670090	+	0.380027i
$896$		0			0
$897$	−45.5330	+	16.5726i	−1.52030	+	0.553345i
$898$		0			0
$899$	−8.30515	−	6.96885i	−0.276992	−	0.232424i
$900$		0			0
$901$	34.7200	+	60.1369i	1.15669	+	2.00345i
$902$		0			0
$903$	2.94970	−	16.7286i	0.0981599	−	0.556692i
$904$		0			0
$905$	−5.25954	+	9.10979i	−0.174833	+	0.302820i
$906$		0			0
$907$	32.2207	+	11.7274i	1.06987	+	0.389401i	0.816129	−	0.577870i	$-0.196116\pi$
$907$	32.2207	+	11.7274i	1.06987	+	0.389401i	0.253743	+	0.967272i	$0.418338\pi$
$908$		0			0
$909$	−27.9153	+	23.4238i	−0.925894	+	0.776917i
$910$		0			0
$911$	47.3608			1.56913			0.784567	−	0.620044i	$-0.212885\pi$
$911$	47.3608			1.56913			0.784567	+	0.620044i	$0.212885\pi$
$912$		0			0
$913$	4.64016			0.153567
$914$		0			0
$915$	−2.97491	+	2.49625i	−0.0983476	+	0.0825235i
$916$		0			0
$917$	29.8124	+	10.8508i	0.984493	+	0.358326i
$918$		0			0
$919$	16.3659	−	28.3466i	0.539861	−	0.935067i	−0.459050	−	0.888411i	$-0.651810\pi$
$919$	16.3659	−	28.3466i	0.539861	−	0.935067i	0.998911	−	0.0466566i	$-0.0148566\pi$
$920$		0			0
$921$	11.2648	−	63.8856i	0.371186	−	2.10510i
$922$		0			0
$923$	2.83548	+	4.91120i	0.0933310	+	0.161654i
$924$		0			0
$925$	−6.86300	−	5.75874i	−0.225654	−	0.189346i
$926$		0			0
$927$	−4.06346	+	1.47898i	−0.133462	+	0.0485760i
$928$		0			0
$929$	6.84874	+	38.8411i	0.224700	+	1.27434i	0.863258	+	0.504762i	$0.168420\pi$
$929$	6.84874	+	38.8411i	0.224700	+	1.27434i	−0.638559	+	0.769573i	$0.720469\pi$
$930$		0			0
$931$	−5.08531	+	9.77727i	−0.166664	+	0.320437i
$932$		0			0
$933$	12.9944	+	73.6947i	0.425416	+	2.41265i
$934$		0			0
$935$	−2.80180	+	1.01977i	−0.0916286	+	0.0333501i
$936$		0			0
$937$	−36.8139	−	30.8905i	−1.20266	−	1.00915i	−0.999550	−	0.0299933i	$-0.990451\pi$
$937$	−36.8139	−	30.8905i	−1.20266	−	1.00915i	−0.203108	−	0.979156i	$-0.565104\pi$
$938$		0			0
$939$	14.2826	+	24.7381i	0.466094	+	0.807298i
$940$		0			0
$941$	9.76795	−	55.3968i	0.318426	−	1.80588i	−0.233905	−	0.972259i	$-0.575150\pi$
$941$	9.76795	−	55.3968i	0.318426	−	1.80588i	0.552331	−	0.833625i	$-0.313738\pi$
$942$		0			0
$943$	22.0754	−	38.2358i	0.718875	−	1.24513i
$944$		0			0
$945$	−5.08545	−	1.85095i	−0.165430	−	0.0602115i
$946$		0			0
$947$	−3.79169	+	3.18161i	−0.123213	+	0.103388i	−0.702312	−	0.711869i	$-0.747849\pi$
$947$	−3.79169	+	3.18161i	−0.123213	+	0.103388i	0.579099	+	0.815257i	$0.303405\pi$
$948$		0			0
$949$	18.7452			0.608495
$950$		0			0
$951$	45.1927			1.46547
$952$		0			0
$953$	32.8444	−	27.5598i	1.06394	−	0.892748i	0.0694467	−	0.997586i	$-0.477877\pi$
$953$	32.8444	−	27.5598i	1.06394	−	0.892748i	0.994489	+	0.104837i	$0.0334322\pi$
$954$		0			0
$955$	4.17514	+	1.51963i	0.135104	+	0.0491740i
$956$		0			0
$957$	2.10257	−	3.64175i	0.0679663	−	0.117721i
$958$		0			0
$959$	0.765513	−	4.34144i	0.0247197	−	0.140192i
$960$		0			0
$961$	9.84371	+	17.0498i	0.317539	+	0.549994i
$962$		0			0
$963$	13.9909	+	11.7397i	0.450850	+	0.378308i
$964$		0			0
$965$	4.17633	−	1.52006i	0.134441	−	0.0489324i
$966$		0			0
$967$	−1.61776	−	9.17475i	−0.0520235	−	0.295040i	0.947684	−	0.319209i	$-0.103417\pi$
$967$	−1.61776	−	9.17475i	−0.0520235	−	0.295040i	−0.999708	+	0.0241688i	$0.992306\pi$
$968$		0			0
$969$	6.78720	−	51.6956i	0.218036	−	1.66070i
$970$		0			0
$971$	−1.59323	−	9.03568i	−0.0511293	−	0.289969i	0.948512	−	0.316740i	$-0.102588\pi$
$971$	−1.59323	−	9.03568i	−0.0511293	−	0.289969i	−0.999642	+	0.0267717i	$0.991477\pi$
$972$		0			0
$973$	55.1823	−	20.0847i	1.76906	−	0.643886i
$974$		0			0
$975$	−4.11780	−	3.45525i	−0.131875	−	0.110656i
$976$		0			0
$977$	18.2474	+	31.6055i	0.583787	+	1.01115i	0.995025	+	0.0996210i	$0.0317630\pi$
$977$	18.2474	+	31.6055i	0.583787	+	1.01115i	−0.411238	+	0.911528i	$0.634904\pi$
$978$		0			0
$979$	0.482094	−	2.73409i	0.0154078	−	0.0873819i
$980$		0			0
$981$	−6.97369	+	12.0788i	−0.222653	+	0.385646i
$982$		0			0
$983$	6.34437	+	2.30916i	0.202354	+	0.0736508i	0.441209	−	0.897404i	$-0.354550\pi$
$983$	6.34437	+	2.30916i	0.202354	+	0.0736508i	−0.238855	+	0.971055i	$0.576772\pi$
$984$		0			0
$985$	−10.0616	+	8.44266i	−0.320588	+	0.269006i
$986$		0			0
$987$	31.8015			1.01225
$988$		0			0
$989$	21.6833			0.689490
$990$		0			0
$991$	−1.81319	+	1.52145i	−0.0575979	+	0.0483304i	−0.671132	−	0.741338i	$-0.734192\pi$
$991$	−1.81319	+	1.52145i	−0.0575979	+	0.0483304i	0.613534	+	0.789668i	$0.289747\pi$
$992$		0			0
$993$	−38.2303	−	13.9147i	−1.21320	−	0.441570i
$994$		0			0
$995$	−11.9111	+	20.6306i	−0.377607	+	0.654035i
$996$		0			0
$997$	−2.04984	+	11.6252i	−0.0649190	+	0.368174i	0.934990	+	0.354675i	$0.115408\pi$
$997$	−2.04984	+	11.6252i	−0.0649190	+	0.368174i	−0.999909	+	0.0134997i	$0.995703\pi$
$998$		0			0
$999$	−7.85354	−	13.6027i	−0.248475	−	0.430371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.161.3	✓	18
19.6	even	9		7220.2.a.w.1.9		9
19.13	odd	18		7220.2.a.y.1.1		9
19.17	even	9	inner	380.2.u.b.321.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.161.3	✓	18	1.1	even	1	trivial
380.2.u.b.321.3	yes	18	19.17	even	9	inner
7220.2.a.w.1.9		9	19.6	even	9
7220.2.a.y.1.1		9	19.13	odd	18

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75249 - 1.47051i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(1.54340 - 2.67324i) q^{7} +(0.387867 - 2.19970i) q^{9} +O(q^{10})\)	\(q+(1.75249 - 1.47051i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(1.54340 - 2.67324i) q^{7} +(0.387867 - 2.19970i) q^{9} +(-0.285125 - 0.493851i) q^{11} +(-1.79996 - 1.51035i) q^{13} +(-2.14975 + 0.782445i) q^{15} +(0.907938 + 5.14917i) q^{17} +(-2.34334 - 3.67543i) q^{19} +(-1.22625 - 6.95443i) q^{21} +(8.47060 - 3.08305i) q^{23} +(0.766044 + 0.642788i) q^{25} +(0.876608 + 1.51833i) q^{27} +(-0.559736 + 3.17442i) q^{29} +(-1.68171 + 2.91280i) q^{31} +(-1.22589 - 0.446189i) q^{33} +(-2.36462 + 1.98416i) q^{35} -8.95901 q^{37} -5.37541 q^{39} +(3.75201 - 3.14831i) q^{41} +(2.26039 + 0.822715i) q^{43} +(-1.11682 + 1.93439i) q^{45} +(-0.782003 + 4.43496i) q^{47} +(-1.26416 - 2.18959i) q^{49} +(9.16309 + 7.68875i) q^{51} +(12.4799 - 4.54230i) q^{53} +(0.0990228 + 0.561586i) q^{55} +(-9.51145 - 2.99524i) q^{57} +(0.866435 + 4.91379i) q^{59} +(1.59516 - 0.580591i) q^{61} +(-5.28172 - 4.43189i) q^{63} +(1.17484 + 2.03489i) q^{65} +(-2.49900 + 14.1725i) q^{67} +(10.3110 - 17.8592i) q^{69} +(-2.26795 - 0.825465i) q^{71} +(-6.11131 + 5.12800i) q^{73} +2.28771 q^{75} -1.76024 q^{77} +(5.59819 - 4.69744i) q^{79} +(10.0658 + 3.66364i) q^{81} +(-4.06853 + 7.04691i) q^{83} +(0.907938 - 5.14917i) q^{85} +(3.68710 + 6.38624i) q^{87} +(3.72950 + 3.12942i) q^{89} +(-6.81559 + 2.48067i) q^{91} +(1.33614 + 7.57764i) q^{93} +(0.944948 + 4.25524i) q^{95} +(1.72255 + 9.76905i) q^{97} +(-1.19692 + 0.435642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 15 * q^9	\( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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