LMFDB - Embedded newform 380.2.u.b.301.3

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			301.3
Root			$1.55777 + 2.69813i$ of defining polynomial
Character	$\chi$	$=$	380.301
Dual form			380.2.u.b.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.92764 - 1.06558i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.643760 + 1.11502i) q^{7} +(5.13752 - 4.31089i) q^{9} +O(q^{10})$	\(q+(2.92764 - 1.06558i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.643760 + 1.11502i) q^{7} +(5.13752 - 4.31089i) q^{9} +(-2.25088 + 3.89864i) q^{11} +(-0.115094 - 0.0418907i) q^{13} +(-0.541007 - 3.06820i) q^{15} +(-0.730551 - 0.613005i) q^{17} +(-1.18925 - 4.19353i) q^{19} +(3.07284 + 2.57842i) q^{21} +(0.507981 + 2.88091i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(5.77395 - 10.0008i) q^{27} +(-5.12896 + 4.30371i) q^{29} +(-2.91189 - 5.04355i) q^{31} +(-2.43548 + 13.8123i) q^{33} +(1.20987 - 0.440358i) q^{35} -8.95982 q^{37} -0.381591 q^{39} +(7.45930 - 2.71496i) q^{41} +(-1.65520 + 9.38710i) q^{43} +(-3.35328 - 5.80804i) q^{45} +(-0.709210 + 0.595097i) q^{47} +(2.67115 - 4.62656i) q^{49} +(-2.79200 - 1.01620i) q^{51} +(-0.00414149 - 0.0234876i) q^{53} +(3.44855 + 2.89368i) q^{55} +(-7.95023 - 11.0099i) q^{57} +(8.19663 + 6.87779i) q^{59} +(1.02491 + 5.81255i) q^{61} +(8.11408 + 2.95328i) q^{63} +(-0.0612401 + 0.106071i) q^{65} +(12.0876 - 10.1427i) q^{67} +(4.55701 + 7.89297i) q^{69} +(-2.62142 + 14.8668i) q^{71} +(3.61254 - 1.31486i) q^{73} -3.11553 q^{75} -5.79610 q^{77} +(-2.80162 + 1.01971i) q^{79} +(2.75375 - 15.6173i) q^{81} +(-4.36455 - 7.55962i) q^{83} +(-0.730551 + 0.613005i) q^{85} +(-10.4299 + 18.0650i) q^{87} +(-14.0616 - 5.11801i) q^{89} +(-0.0273836 - 0.155300i) q^{91} +(-13.8993 - 11.6629i) q^{93} +(-4.33633 + 0.442988i) q^{95} +(-13.3023 - 11.1620i) q^{97} +(5.24266 + 29.7326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$1$

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
$3$	2.92764	−	1.06558i	1.69028	−	0.615210i	0.695616	−	0.718414i	$-0.255132\pi$
$3$	2.92764	−	1.06558i	1.69028	−	0.615210i	0.994660	+	0.103204i	$0.0329093\pi$
$4$		0			0
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$		0			0
$7$	0.643760	+	1.11502i	0.243318	+	0.421440i	0.961657	−	0.274253i	$-0.0884307\pi$
$7$	0.643760	+	1.11502i	0.243318	+	0.421440i	−0.718339	+	0.695693i	$0.755097\pi$
$8$		0			0
$9$	5.13752	−	4.31089i	1.71251	−	1.43696i
$10$		0			0
$11$	−2.25088	+	3.89864i	−0.678666	+	1.17548i	0.296717	+	0.954965i	$0.404108\pi$
$11$	−2.25088	+	3.89864i	−0.678666	+	1.17548i	−0.975383	+	0.220518i	$0.929225\pi$
$12$		0			0
$13$	−0.115094	−	0.0418907i	−0.0319213	−	0.0116184i	0.326010	−	0.945366i	$-0.394296\pi$
$13$	−0.115094	−	0.0418907i	−0.0319213	−	0.0116184i	−0.357931	+	0.933748i	$0.616518\pi$
$14$		0			0
$15$	−0.541007	−	3.06820i	−0.139687	−	0.792206i
$16$		0			0
$17$	−0.730551	−	0.613005i	−0.177185	−	0.148676i	0.549882	−	0.835242i	$-0.314673\pi$
$17$	−0.730551	−	0.613005i	−0.177185	−	0.148676i	−0.727067	+	0.686567i	$0.759117\pi$
$18$		0			0
$19$	−1.18925	−	4.19353i	−0.272834	−	0.962061i
$19$	−1.18925	−	4.19353i	−0.272834	−	0.962061i
$20$		0			0
$21$	3.07284	+	2.57842i	0.670549	+	0.562658i
$22$		0			0
$23$	0.507981	+	2.88091i	0.105921	+	0.600710i	0.990848	+	0.134980i	$0.0430971\pi$
$23$	0.507981	+	2.88091i	0.105921	+	0.600710i	−0.884927	+	0.465730i	$0.845792\pi$
$24$		0			0
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$		0			0
$27$	5.77395	−	10.0008i	1.11120	−	1.92465i
$28$		0			0
$29$	−5.12896	+	4.30371i	−0.952425	+	0.799179i	−0.979704	−	0.200449i	$-0.935760\pi$
$29$	−5.12896	+	4.30371i	−0.952425	+	0.799179i	0.0272796	+	0.999628i	$0.491316\pi$
$30$		0			0
$31$	−2.91189	−	5.04355i	−0.522991	−	0.905847i	−0.999642	−	0.0267547i	$-0.991483\pi$
$31$	−2.91189	−	5.04355i	−0.522991	−	0.905847i	0.476651	−	0.879093i	$-0.341851\pi$
$32$		0			0
$33$	−2.43548	+	13.8123i	−0.423963	+	2.40441i
$34$		0			0
$35$	1.20987	−	0.440358i	0.204506	−	0.0744340i
$36$		0			0
$37$	−8.95982			−1.47299			−0.736493	−	0.676445i	$-0.763520\pi$
$37$	−8.95982			−1.47299			−0.736493	+	0.676445i	$0.763520\pi$
$38$		0			0
$39$	−0.381591			−0.0611035
$40$		0			0
$41$	7.45930	−	2.71496i	1.16495	−	0.424006i	0.314085	−	0.949395i	$-0.398302\pi$
$41$	7.45930	−	2.71496i	1.16495	−	0.424006i	0.850862	+	0.525389i	$0.176080\pi$
$42$		0			0
$43$	−1.65520	+	9.38710i	−0.252415	+	1.43152i	0.550205	+	0.835030i	$0.314550\pi$
$43$	−1.65520	+	9.38710i	−0.252415	+	1.43152i	−0.802621	+	0.596490i	$0.796562\pi$
$44$		0			0
$45$	−3.35328	−	5.80804i	−0.499877	−	0.865812i
$46$		0			0
$47$	−0.709210	+	0.595097i	−0.103449	+	0.0868039i	−0.693045	−	0.720894i	$-0.743731\pi$
$47$	−0.709210	+	0.595097i	−0.103449	+	0.0868039i	0.589596	+	0.807698i	$0.299287\pi$
$48$		0			0
$49$	2.67115	−	4.62656i	0.381592	−	0.660937i
$50$		0			0
$51$	−2.79200	−	1.01620i	−0.390958	−	0.142297i
$52$		0			0
$53$	−0.00414149	−	0.0234876i	−0.000568878	−	0.00322627i	0.984522	−	0.175261i	$-0.0560770\pi$
$53$	−0.00414149	−	0.0234876i	−0.000568878	−	0.00322627i	−0.985091	+	0.172035i	$0.944966\pi$
$54$		0			0
$55$	3.44855	+	2.89368i	0.465002	+	0.390183i
$56$		0			0
$57$	−7.95023	−	11.0099i	−1.05303	−	1.45830i
$58$		0			0
$59$	8.19663	+	6.87779i	1.06711	+	0.895411i	0.994787	−	0.101970i	$-0.0325145\pi$
$59$	8.19663	+	6.87779i	1.06711	+	0.895411i	0.0723223	+	0.997381i	$0.476959\pi$
$60$		0			0
$61$	1.02491	+	5.81255i	0.131226	+	0.744221i	0.977414	+	0.211335i	$0.0677813\pi$
$61$	1.02491	+	5.81255i	0.131226	+	0.744221i	−0.846187	+	0.532886i	$0.821108\pi$
$62$		0			0
$63$	8.11408	+	2.95328i	1.02228	+	0.372079i
$64$		0			0
$65$	−0.0612401	+	0.106071i	−0.00759590	+	0.0131565i
$66$		0			0
$67$	12.0876	−	10.1427i	1.47673	−	1.23913i	0.567145	−	0.823618i	$-0.308048\pi$
$67$	12.0876	−	10.1427i	1.47673	−	1.23913i	0.909589	−	0.415509i	$-0.136397\pi$
$68$		0			0
$69$	4.55701	+	7.89297i	0.548600	+	0.950202i
$70$		0			0
$71$	−2.62142	+	14.8668i	−0.311106	+	1.76437i	0.282165	+	0.959366i	$0.408947\pi$
$71$	−2.62142	+	14.8668i	−0.311106	+	1.76437i	−0.593271	+	0.805003i	$0.702164\pi$
$72$		0			0
$73$	3.61254	−	1.31486i	0.422816	−	0.153892i	−0.121844	−	0.992549i	$-0.538881\pi$
$73$	3.61254	−	1.31486i	0.422816	−	0.153892i	0.544660	+	0.838657i	$0.316659\pi$
$74$		0			0
$75$	−3.11553			−0.359751
$76$		0			0
$77$	−5.79610			−0.660527
$78$		0			0
$79$	−2.80162	+	1.01971i	−0.315207	+	0.114726i	−0.494779	−	0.869019i	$-0.664751\pi$
$79$	−2.80162	+	1.01971i	−0.315207	+	0.114726i	0.179572	+	0.983745i	$0.442529\pi$
$80$		0			0
$81$	2.75375	−	15.6173i	0.305972	−	1.73525i
$82$		0			0
$83$	−4.36455	−	7.55962i	−0.479071	−	0.829776i	0.520641	−	0.853776i	$-0.325693\pi$
$83$	−4.36455	−	7.55962i	−0.479071	−	0.829776i	−0.999712	+	0.0240000i	$0.992360\pi$
$84$		0			0
$85$	−0.730551	+	0.613005i	−0.0792394	+	0.0664897i
$86$		0			0
$87$	−10.4299	+	18.0650i	−1.11820	+	1.93677i
$88$		0			0
$89$	−14.0616	−	5.11801i	−1.49053	−	0.542508i	−0.536939	−	0.843621i	$-0.680420\pi$
$89$	−14.0616	−	5.11801i	−1.49053	−	0.542508i	−0.953588	+	0.301113i	$0.902642\pi$
$90$		0			0
$91$	−0.0273836	−	0.155300i	−0.00287058	−	0.0162799i
$92$		0			0
$93$	−13.8993	−	11.6629i	−1.44129	−	1.20938i
$94$		0			0
$95$	−4.33633	+	0.442988i	−0.444898	+	0.0454496i
$96$		0			0
$97$	−13.3023	−	11.1620i	−1.35064	−	1.13332i	−0.978752	−	0.205048i	$-0.934265\pi$
$97$	−13.3023	−	11.1620i	−1.35064	−	1.13332i	−0.371891	−	0.928276i	$-0.621291\pi$
$98$		0			0
$99$	5.24266	+	29.7326i	0.526907	+	2.98824i
$100$		0			0
$101$	6.82879	+	2.48548i	0.679490	+	0.247314i	0.658629	−	0.752468i	$-0.271137\pi$
$101$	6.82879	+	2.48548i	0.679490	+	0.247314i	0.0208616	+	0.999782i	$0.493359\pi$
$102$		0			0
$103$	−0.425234	+	0.736527i	−0.0418996	+	0.0725722i	−0.886215	−	0.463275i	$-0.846674\pi$
$103$	−0.425234	+	0.736527i	−0.0418996	+	0.0725722i	0.844315	+	0.535847i	$0.180008\pi$
$104$		0			0
$105$	3.07284	−	2.57842i	0.299879	−	0.251628i
$106$		0			0
$107$	5.04809	+	8.74355i	0.488017	+	0.845271i	0.999905	−	0.0137816i	$-0.00438695\pi$
$107$	5.04809	+	8.74355i	0.488017	+	0.845271i	−0.511888	+	0.859052i	$0.671054\pi$
$108$		0			0
$109$	−0.521529	+	2.95774i	−0.0499534	+	0.283300i	−0.999544	−	0.0301927i	$-0.990388\pi$
$109$	−0.521529	+	2.95774i	−0.0499534	+	0.283300i	0.949591	+	0.313492i	$0.101499\pi$
$110$		0			0
$111$	−26.2312	+	9.54737i	−2.48975	+	0.906196i
$112$		0			0
$113$	−6.06424			−0.570475			−0.285238	−	0.958457i	$-0.592073\pi$
$113$	−6.06424			−0.570475			−0.285238	+	0.958457i	$0.592073\pi$
$114$		0			0
$115$	2.92535			0.272790
$116$		0			0
$117$	−0.771882	+	0.280942i	−0.0713605	+	0.0259731i
$118$		0			0
$119$	0.213216	−	1.20921i	0.0195455	−	0.110848i
$120$		0			0
$121$	−4.63292	−	8.02445i	−0.421174	−	0.729496i
$122$		0			0
$123$	18.9452	−	15.8969i	1.70823	−	1.43337i
$124$		0			0
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	−6.24161	−	2.27176i	−0.553854	−	0.201586i	0.0499042	−	0.998754i	$-0.484108\pi$
$127$	−6.24161	−	2.27176i	−0.553854	−	0.201586i	−0.603758	+	0.797168i	$0.706331\pi$
$128$		0			0
$129$	5.15683	+	29.2458i	0.454033	+	2.57495i
$130$		0			0
$131$	7.06862	+	5.93127i	0.617588	+	0.518218i	0.897044	−	0.441941i	$-0.145710\pi$
$131$	7.06862	+	5.93127i	0.617588	+	0.518218i	−0.279456	+	0.960158i	$0.590154\pi$
$132$		0			0
$133$	3.91029	−	4.02567i	0.339065	−	0.349070i
$134$		0			0
$135$	−8.84620	−	7.42284i	−0.761359	−	0.638856i
$136$		0			0
$137$	−0.634270	−	3.59712i	−0.0541893	−	0.307323i	0.945651	−	0.325183i	$-0.105426\pi$
$137$	−0.634270	−	3.59712i	−0.0541893	−	0.307323i	−0.999840	+	0.0178599i	$0.994315\pi$
$138$		0			0
$139$	17.6900	+	6.43863i	1.50044	+	0.546117i	0.956176	−	0.292794i	$-0.0945849\pi$
$139$	17.6900	+	6.43863i	1.50044	+	0.546117i	0.544269	+	0.838911i	$0.316807\pi$
$140$		0			0
$141$	−1.44219	+	2.49795i	−0.121454	+	0.210365i
$142$		0			0
$143$	0.422379	−	0.354418i	0.0353211	−	0.0296379i
$144$		0			0
$145$	3.34769	+	5.79837i	0.278011	+	0.481529i
$146$		0			0
$147$	2.89022	−	16.3912i	0.238381	−	1.35193i
$148$		0			0
$149$	−11.0670	+	4.02805i	−0.906641	+	0.329990i	−0.752911	−	0.658122i	$-0.771351\pi$
$149$	−11.0670	+	4.02805i	−0.906641	+	0.329990i	−0.153730	+	0.988113i	$0.549129\pi$
$150$		0			0
$151$	6.94029			0.564793			0.282396	−	0.959298i	$-0.408871\pi$
$151$	6.94029			0.564793			0.282396	+	0.959298i	$0.408871\pi$
$152$		0			0
$153$	−6.39581			−0.517071
$154$		0			0
$155$	−5.47257	+	1.99185i	−0.439567	+	0.159989i
$156$		0			0
$157$	3.03157	−	17.1929i	0.241946	−	1.37214i	−0.585534	−	0.810648i	$-0.699115\pi$
$157$	3.03157	−	17.1929i	0.241946	−	1.37214i	0.827480	−	0.561495i	$-0.189774\pi$
$158$		0			0
$159$	−0.0371526	−	0.0643502i	−0.00294639	−	0.00510330i
$160$		0			0
$161$	−2.88526	+	2.42102i	−0.227391	+	0.190803i
$162$		0			0
$163$	6.12605	−	10.6106i	0.479829	−	0.831089i	−0.519903	−	0.854225i	$-0.674032\pi$
$163$	6.12605	−	10.6106i	0.479829	−	0.831089i	0.999732	+	0.0231364i	$0.00736520\pi$
$164$		0			0
$165$	13.1796	+	4.79696i	1.02603	+	0.373443i
$166$		0			0
$167$	−4.09639	−	23.2318i	−0.316988	−	1.79773i	−0.560848	−	0.827919i	$-0.689525\pi$
$167$	−4.09639	−	23.2318i	−0.316988	−	1.79773i	0.243860	−	0.969811i	$-0.421586\pi$
$168$		0			0
$169$	−9.94709	−	8.34660i	−0.765160	−	0.642046i
$170$		0			0
$171$	−24.1876	−	16.4176i	−1.84968	−	1.25548i
$172$		0			0
$173$	−7.98365	−	6.69908i	−0.606986	−	0.509321i	0.286697	−	0.958021i	$-0.407443\pi$
$173$	−7.98365	−	6.69908i	−0.606986	−	0.509321i	−0.893683	+	0.448700i	$0.851887\pi$
$174$		0			0
$175$	−0.223575	−	1.26796i	−0.0169007	−	0.0958487i
$176$		0			0
$177$	31.3256	+	11.4016i	2.35458	+	0.856996i
$178$		0			0
$179$	−4.20212	+	7.27829i	−0.314081	+	0.544005i	−0.979242	−	0.202696i	$-0.935030\pi$
$179$	−4.20212	+	7.27829i	−0.314081	+	0.544005i	0.665160	+	0.746701i	$0.268363\pi$
$180$		0			0
$181$	17.2650	−	14.4870i	1.28329	−	1.07681i	0.290513	−	0.956871i	$-0.406174\pi$
$181$	17.2650	−	14.4870i	1.28329	−	1.07681i	0.992781	−	0.119940i	$-0.0382703\pi$
$182$		0			0
$183$	9.19428	+	15.9250i	0.679661	+	1.17721i
$184$		0			0
$185$	−1.55586	+	8.82370i	−0.114389	+	0.648732i
$186$		0			0
$187$	4.03427	−	1.46835i	0.295015	−	0.107377i
$188$		0			0
$189$	14.8681			1.08150
$190$		0			0
$191$	24.2967			1.75805			0.879025	−	0.476775i	$-0.158194\pi$
$191$	24.2967			1.75805			0.879025	+	0.476775i	$0.158194\pi$
$192$		0			0
$193$	4.36570	−	1.58898i	0.314250	−	0.114378i	−0.180080	−	0.983652i	$-0.557636\pi$
$193$	4.36570	−	1.58898i	0.314250	−	0.114378i	0.494330	+	0.869274i	$0.335413\pi$
$194$		0			0
$195$	−0.0662626	+	0.375794i	−0.00474516	+	0.0269112i
$196$		0			0
$197$	6.00361	+	10.3986i	0.427740	+	0.740867i	0.996672	−	0.0815174i	$-0.0259766\pi$
$197$	6.00361	+	10.3986i	0.427740	+	0.740867i	−0.568932	+	0.822384i	$0.692643\pi$
$198$		0			0
$199$	8.96006	−	7.51838i	0.635162	−	0.532964i	−0.267366	−	0.963595i	$-0.586153\pi$
$199$	8.96006	−	7.51838i	0.635162	−	0.532964i	0.902528	+	0.430631i	$0.141709\pi$
$200$		0			0
$201$	24.5804	−	42.5744i	1.73376	−	3.00297i
$202$		0			0
$203$	−8.10057	−	2.94836i	−0.568548	−	0.206935i
$204$		0			0
$205$	−1.37842	−	7.81742i	−0.0962732	−	0.545993i
$206$		0			0
$207$	15.0290	+	12.6108i	1.04459	+	0.876515i
$208$		0			0
$209$	19.0259	+	4.80266i	1.31605	+	0.332207i
$210$		0			0
$211$	9.63682	+	8.08626i	0.663426	+	0.556681i	0.911112	−	0.412160i	$-0.135225\pi$
$211$	9.63682	+	8.08626i	0.663426	+	0.556681i	−0.247685	+	0.968841i	$0.579670\pi$
$212$		0			0
$213$	8.16713	+	46.3181i	0.559603	+	3.17367i
$214$		0			0
$215$	8.95707	+	3.26011i	0.610867	+	0.222337i
$216$		0			0
$217$	3.74912	−	6.49366i	0.254507	−	0.440819i
$218$		0			0
$219$	9.17515	−	7.69887i	0.619999	−	0.520241i
$220$		0			0
$221$	0.0584026	+	0.101156i	0.00392858	+	0.00680451i
$222$		0			0
$223$	2.34163	−	13.2801i	0.156807	−	0.889299i	−0.800307	−	0.599590i	$-0.795330\pi$
$223$	2.34163	−	13.2801i	0.156807	−	0.889299i	0.957115	−	0.289709i	$-0.0935586\pi$
$224$		0			0
$225$	−6.30210	+	2.29378i	−0.420140	+	0.152918i
$226$		0			0
$227$	−21.1090			−1.40105			−0.700526	−	0.713627i	$-0.747051\pi$
$227$	−21.1090			−1.40105			−0.700526	+	0.713627i	$0.747051\pi$
$228$		0			0
$229$	−19.3629			−1.27954			−0.639770	−	0.768567i	$-0.720970\pi$
$229$	−19.3629			−1.27954			−0.639770	+	0.768567i	$0.720970\pi$
$230$		0			0
$231$	−16.9689	+	6.17619i	−1.11647	+	0.406363i
$232$		0			0
$233$	−0.321621	+	1.82400i	−0.0210701	+	0.119494i	−0.993529	−	0.113581i	$-0.963768\pi$
$233$	−0.321621	+	1.82400i	−0.0210701	+	0.119494i	0.972459	+	0.233075i	$0.0748789\pi$
$234$		0			0
$235$	0.462904	+	0.801773i	0.0301965	+	0.0523019i
$236$		0			0
$237$	−7.11558	+	5.97068i	−0.462207	+	0.387837i
$238$		0			0
$239$	10.6784	−	18.4956i	0.690730	−	1.19638i	−0.280869	−	0.959746i	$-0.590623\pi$
$239$	10.6784	−	18.4956i	0.690730	−	1.19638i	0.971599	−	0.236633i	$-0.0760441\pi$
$240$		0			0
$241$	5.67933	+	2.06711i	0.365838	+	0.133154i	0.518397	−	0.855140i	$-0.326529\pi$
$241$	5.67933	+	2.06711i	0.365838	+	0.133154i	−0.152559	+	0.988294i	$0.548751\pi$
$242$		0			0
$243$	−2.56358	−	14.5388i	−0.164454	−	0.932663i
$244$		0			0
$245$	−4.09243	−	3.43396i	−0.261456	−	0.219388i
$246$		0			0
$247$	−0.0387941	+	0.532467i	−0.00246841	+	0.0338801i
$248$		0			0
$249$	−20.8332	−	17.4811i	−1.32025	−	1.10782i
$250$		0			0
$251$	−0.425210	−	2.41149i	−0.0268390	−	0.152212i	0.968443	−	0.249235i	$-0.0801791\pi$
$251$	−0.425210	−	2.41149i	−0.0268390	−	0.152212i	−0.995282	+	0.0970230i	$0.969068\pi$
$252$		0			0
$253$	−12.3750	−	4.50414i	−0.778010	−	0.283173i
$254$		0			0
$255$	−1.48559	+	2.57312i	−0.0930313	+	0.161135i
$256$		0			0
$257$	7.75878	−	6.51039i	0.483979	−	0.406107i	−0.367884	−	0.929872i	$-0.619917\pi$
$257$	7.75878	−	6.51039i	0.483979	−	0.406107i	0.851863	+	0.523765i	$0.175473\pi$
$258$		0			0
$259$	−5.76798	−	9.99043i	−0.358405	−	0.620775i
$260$		0			0
$261$	−7.79732	+	44.2208i	−0.482642	+	2.73720i
$262$		0			0
$263$	−10.3651	+	3.77260i	−0.639141	+	0.232628i	−0.641205	−	0.767370i	$-0.721565\pi$
$263$	−10.3651	+	3.77260i	−0.639141	+	0.232628i	0.00206405	+	0.999998i	$0.499343\pi$
$264$		0			0
$265$	−0.0238499			−0.00146509
$266$		0			0
$267$	−46.6210			−2.85316
$268$		0			0
$269$	18.7568	−	6.82690i	1.14362	−	0.416243i	0.300400	−	0.953813i	$-0.402880\pi$
$269$	18.7568	−	6.82690i	1.14362	−	0.416243i	0.843219	+	0.537570i	$0.180658\pi$
$270$		0			0
$271$	−0.988320	+	5.60504i	−0.0600362	+	0.340482i	−1.00000		0.000792933i	$-0.999748\pi$
$271$	−0.988320	+	5.60504i	−0.0600362	+	0.340482i	0.939964	+	0.341275i	$0.110859\pi$
$272$		0			0
$273$	−0.245653	−	0.425484i	−0.0148676	−	0.0257514i
$274$		0			0
$275$	3.44855	−	2.89368i	0.207955	−	0.174495i
$276$		0			0
$277$	−16.0854	+	27.8607i	−0.966477	+	1.67399i	−0.260883	+	0.965370i	$0.584014\pi$
$277$	−16.0854	+	27.8607i	−0.966477	+	1.67399i	−0.705594	+	0.708616i	$0.749320\pi$
$278$		0			0
$279$	−36.7021	−	13.3585i	−2.19729	−	0.799750i
$280$		0			0
$281$	2.33744	+	13.2563i	0.139440	+	0.790805i	0.971664	+	0.236365i	$0.0759563\pi$
$281$	2.33744	+	13.2563i	0.139440	+	0.790805i	−0.832224	+	0.554440i	$0.812933\pi$
$282$		0			0
$283$	5.76933	+	4.84104i	0.342951	+	0.287770i	0.797952	−	0.602721i	$-0.205917\pi$
$283$	5.76933	+	4.84104i	0.342951	+	0.287770i	−0.455001	+	0.890491i	$0.650361\pi$
$284$		0			0
$285$	−12.2232	+	5.91760i	−0.724040	+	0.350528i
$286$		0			0
$287$	7.82925	+	6.56952i	0.462146	+	0.387787i
$288$		0			0
$289$	−2.79409	−	15.8461i	−0.164358	−	0.932122i
$290$		0			0
$291$	−50.8383	−	18.5036i	−2.98019	−	1.08470i
$292$		0			0
$293$	12.3915	−	21.4627i	0.723919	−	1.25386i	−0.235499	−	0.971875i	$-0.575672\pi$
$293$	12.3915	−	21.4627i	0.723919	−	1.25386i	0.959418	−	0.281989i	$-0.0909942\pi$
$294$		0			0
$295$	8.19663	−	6.87779i	0.477226	−	0.400440i
$296$		0			0
$297$	25.9929	+	45.0210i	1.50826	+	2.61239i
$298$		0			0
$299$	0.0622176	−	0.352854i	0.00359814	−	0.0204061i
$300$		0			0
$301$	−11.5324	+	4.19745i	−0.664717	+	0.241937i
$302$		0			0
$303$	22.6407			1.30068
$304$		0			0
$305$	5.90222			0.337960
$306$		0			0
$307$	16.1933	−	5.89388i	0.924200	−	0.336381i	0.164292	−	0.986412i	$-0.447466\pi$
$307$	16.1933	−	5.89388i	0.924200	−	0.336381i	0.759908	+	0.650031i	$0.225244\pi$
$308$		0			0
$309$	−0.460109	+	2.60941i	−0.0261747	+	0.148444i
$310$		0			0
$311$	4.22506	+	7.31802i	0.239581	+	0.414967i	0.960594	−	0.277955i	$-0.0896565\pi$
$311$	4.22506	+	7.31802i	0.239581	+	0.414967i	−0.721013	+	0.692922i	$0.756323\pi$
$312$		0			0
$313$	1.13129	−	0.949265i	0.0639443	−	0.0536556i	−0.610255	−	0.792205i	$-0.708933\pi$
$313$	1.13129	−	0.949265i	0.0639443	−	0.0536556i	0.674200	+	0.738549i	$0.264489\pi$
$314$		0			0
$315$	4.31741	−	7.47797i	0.243258	−	0.421336i
$316$		0			0
$317$	−2.10586	−	0.766472i	−0.118277	−	0.0430494i	0.282204	−	0.959355i	$-0.408935\pi$
$317$	−2.10586	−	0.766472i	−0.118277	−	0.0430494i	−0.400481	+	0.916305i	$0.631157\pi$
$318$		0			0
$319$	−5.23393	−	29.6831i	−0.293044	−	1.66193i
$320$		0			0
$321$	24.0959	+	20.2189i	1.34490	+	1.12851i
$322$		0			0
$323$	−1.70184	+	3.79260i	−0.0946931	+	0.211026i
$324$		0			0
$325$	0.0938253	+	0.0787287i	0.00520449	+	0.00436708i
$326$		0			0
$327$	1.62484	+	9.21493i	0.0898539	+	0.509587i
$328$		0			0
$329$	−1.12011	−	0.407686i	−0.0617536	−	0.0224765i
$330$		0			0
$331$	−1.35657	+	2.34964i	−0.0745637	+	0.129148i	−0.900896	−	0.434034i	$-0.857090\pi$
$331$	−1.35657	+	2.34964i	−0.0745637	+	0.129148i	0.826333	+	0.563182i	$0.190423\pi$
$332$		0			0
$333$	−46.0313	+	38.6248i	−2.52250	+	2.11663i
$334$		0			0
$335$	−7.88961	−	13.6652i	−0.431056	−	0.746610i
$336$		0			0
$337$	2.01515	−	11.4285i	0.109772	−	0.622549i	−0.879434	−	0.476020i	$-0.842079\pi$
$337$	2.01515	−	11.4285i	0.109772	−	0.622549i	0.989206	−	0.146529i	$-0.0468101\pi$
$338$		0			0
$339$	−17.7539	+	6.46190i	−0.964261	+	0.350962i
$340$		0			0
$341$	26.2173			1.41975
$342$		0			0
$343$	15.8909			0.858030
$344$		0			0
$345$	8.56438	−	3.11718i	0.461091	−	0.167823i
$346$		0			0
$347$	−5.33836	+	30.2754i	−0.286578	+	1.62527i	0.413014	+	0.910725i	$0.364476\pi$
$347$	−5.33836	+	30.2754i	−0.286578	+	1.62527i	−0.699593	+	0.714542i	$0.746635\pi$
$348$		0			0
$349$	9.56699	+	16.5705i	0.512109	+	0.886999i	0.999901	+	0.0140393i	$0.00446900\pi$
$349$	9.56699	+	16.5705i	0.512109	+	0.886999i	−0.487792	+	0.872960i	$0.662198\pi$
$350$		0			0
$351$	−1.08348	+	0.909151i	−0.0578321	+	0.0485269i
$352$		0			0
$353$	−9.74328	+	16.8759i	−0.518583	+	0.898211i	0.481184	+	0.876619i	$0.340207\pi$
$353$	−9.74328	+	16.8759i	−0.518583	+	0.898211i	−0.999767	+	0.0215918i	$0.993127\pi$
$354$		0			0
$355$	14.1858	+	5.16320i	0.752902	+	0.274034i
$356$		0			0
$357$	−0.664283	−	3.76734i	−0.0351576	−	0.199389i
$358$		0			0
$359$	−25.7000	−	21.5649i	−1.35639	−	1.13815i	−0.977078	−	0.212884i	$-0.931714\pi$
$359$	−25.7000	−	21.5649i	−1.35639	−	1.13815i	−0.379317	−	0.925267i	$-0.623841\pi$
$360$		0			0
$361$	−16.1714	+	9.97434i	−0.851124	+	0.524965i
$362$		0			0
$363$	−22.1142	−	18.5560i	−1.16069	−	0.973938i
$364$		0			0
$365$	−0.667571	−	3.78598i	−0.0349422	−	0.198167i
$366$		0			0
$367$	−10.1767	−	3.70401i	−0.531219	−	0.193348i	0.0624636	−	0.998047i	$-0.480104\pi$
$367$	−10.1767	−	3.70401i	−0.531219	−	0.193348i	−0.593683	+	0.804699i	$0.702327\pi$
$368$		0			0
$369$	26.6184	−	46.1044i	1.38570	−	2.40010i
$370$		0			0
$371$	0.0235231	−	0.0197382i	0.00122126	−	0.00102476i
$372$		0			0
$373$	−4.14975	−	7.18758i	−0.214866	−	0.372159i	0.738365	−	0.674401i	$-0.235598\pi$
$373$	−4.14975	−	7.18758i	−0.214866	−	0.372159i	−0.953231	+	0.302242i	$0.902265\pi$
$374$		0			0
$375$	−0.541007	+	3.06820i	−0.0279375	+	0.158441i
$376$		0			0
$377$	0.770597	−	0.280474i	0.0396878	−	0.0144452i
$378$		0			0
$379$	2.75557			0.141544			0.0707720	−	0.997493i	$-0.477454\pi$
$379$	2.75557			0.141544			0.0707720	+	0.997493i	$0.477454\pi$
$380$		0			0
$381$	−20.6940			−1.06018
$382$		0			0
$383$	2.15130	−	0.783010i	0.109926	−	0.0400100i	−0.286471	−	0.958089i	$-0.592482\pi$
$383$	2.15130	−	0.783010i	0.109926	−	0.0400100i	0.396398	+	0.918079i	$0.370260\pi$
$384$		0			0
$385$	−1.00648	+	5.70805i	−0.0512951	+	0.290909i
$386$		0			0
$387$	31.9631	+	55.3618i	1.62478	+	2.81420i
$388$		0			0
$389$	−8.46044	+	7.09915i	−0.428961	+	0.359941i	−0.831560	−	0.555436i	$-0.812552\pi$
$389$	−8.46044	+	7.09915i	−0.428961	+	0.359941i	0.402598	+	0.915377i	$0.368107\pi$
$390$		0			0
$391$	1.39490	−	2.41604i	0.0705433	−	0.122185i
$392$		0			0
$393$	27.0146	+	9.83252i	1.36271	+	0.495985i
$394$		0			0
$395$	0.517719	+	2.93613i	0.0260493	+	0.147733i
$396$		0			0
$397$	−14.4339	−	12.1114i	−0.724415	−	0.607856i	0.204188	−	0.978932i	$-0.434545\pi$
$397$	−14.4339	−	12.1114i	−0.724415	−	0.607856i	−0.928603	+	0.371076i	$0.878989\pi$
$398$		0			0
$399$	7.15829	−	15.9525i	0.358363	−	0.798621i
$400$		0			0
$401$	1.34821	+	1.13128i	0.0673263	+	0.0564935i	0.675830	−	0.737058i	$-0.263785\pi$
$401$	1.34821	+	1.13128i	0.0673263	+	0.0564935i	−0.608503	+	0.793551i	$0.708230\pi$
$402$		0			0
$403$	0.123863	+	0.702462i	0.00617005	+	0.0349921i
$404$		0			0
$405$	−14.9018	−	5.42382i	−0.740478	−	0.269512i
$406$		0			0
$407$	20.1675	−	34.9311i	0.999665	−	1.73147i
$408$		0			0
$409$	−9.30115	+	7.80459i	−0.459912	+	0.385912i	−0.843099	−	0.537759i	$-0.819271\pi$
$409$	−9.30115	+	7.80459i	−0.459912	+	0.385912i	0.383187	+	0.923671i	$0.374827\pi$
$410$		0			0
$411$	−5.68992	−	9.85523i	−0.280663	−	0.486123i
$412$		0			0
$413$	−2.39224	+	13.5671i	−0.117715	+	0.667593i
$414$		0			0
$415$	−8.20267	+	2.98553i	−0.402653	+	0.146554i
$416$		0			0
$417$	58.6508			2.87214
$418$		0			0
$419$	−16.4679			−0.804509			−0.402255	−	0.915528i	$-0.631773\pi$
$419$	−16.4679			−0.804509			−0.402255	+	0.915528i	$0.631773\pi$
$420$		0			0
$421$	0.999150	−	0.363661i	0.0486956	−	0.0177237i	−0.317558	−	0.948239i	$-0.602863\pi$
$421$	0.999150	−	0.363661i	0.0486956	−	0.0177237i	0.366253	+	0.930515i	$0.380640\pi$
$422$		0			0
$423$	−1.07818	+	6.11465i	−0.0524228	+	0.297304i
$424$		0			0
$425$	0.476833	+	0.825899i	0.0231298	+	0.0400620i
$426$		0			0
$427$	−5.82134	+	4.88469i	−0.281715	+	0.236387i
$428$		0			0
$429$	0.858916	−	1.48769i	0.0414688	−	0.0718261i
$430$		0			0
$431$	32.7978	+	11.9374i	1.57982	+	0.575006i	0.975164	−	0.221484i	$-0.0710902\pi$
$431$	32.7978	+	11.9374i	1.57982	+	0.575006i	0.604651	+	0.796490i	$0.293312\pi$
$432$		0			0
$433$	−1.23492	−	7.00358i	−0.0593465	−	0.336571i	0.940650	−	0.339379i	$-0.110217\pi$
$433$	−1.23492	−	7.00358i	−0.0593465	−	0.336571i	−0.999996	+	0.00280872i	$0.999106\pi$
$434$		0			0
$435$	15.9795	+	13.4084i	0.766156	+	0.642882i
$436$		0			0
$437$	11.4770	−	5.55636i	0.549021	−	0.265797i
$438$		0			0
$439$	−5.83392	−	4.89524i	−0.278438	−	0.233637i	0.492864	−	0.870106i	$-0.335950\pi$
$439$	−5.83392	−	4.89524i	−0.278438	−	0.233637i	−0.771302	+	0.636469i	$0.780394\pi$
$440$		0			0
$441$	−6.22153	−	35.2841i	−0.296263	−	1.68019i
$442$		0			0
$443$	−16.2738	−	5.92317i	−0.773191	−	0.281419i	−0.0748605	−	0.997194i	$-0.523851\pi$
$443$	−16.2738	−	5.92317i	−0.773191	−	0.281419i	−0.698330	+	0.715776i	$0.746073\pi$
$444$		0			0
$445$	−7.48203	+	12.9592i	−0.354682	+	0.614327i
$446$		0			0
$447$	−28.1080	+	23.5854i	−1.32946	+	1.11555i
$448$		0			0
$449$	0.462444	+	0.800976i	0.0218241	+	0.0378004i	0.876731	−	0.480981i	$-0.159719\pi$
$449$	0.462444	+	0.800976i	0.0218241	+	0.0378004i	−0.854907	+	0.518781i	$0.826386\pi$
$450$		0			0
$451$	−6.20533	+	35.1922i	−0.292197	+	1.65713i
$452$		0			0
$453$	20.3187	−	7.39540i	0.954656	−	0.347466i
$454$		0			0
$455$	−0.157696			−0.00739289
$456$		0			0
$457$	−20.6874			−0.967718			−0.483859	−	0.875146i	$-0.660765\pi$
$457$	−20.6874			−0.967718			−0.483859	+	0.875146i	$0.660765\pi$
$458$		0			0
$459$	−10.3487	+	3.76661i	−0.483035	+	0.175810i
$460$		0			0
$461$	2.46202	−	13.9628i	0.114667	−	0.650312i	−0.872247	−	0.489066i	$-0.837338\pi$
$461$	2.46202	−	13.9628i	0.114667	−	0.650312i	0.986914	−	0.161246i	$-0.0515512\pi$
$462$		0			0
$463$	18.7765	+	32.5218i	0.872616	+	1.51141i	0.859281	+	0.511504i	$0.170911\pi$
$463$	18.7765	+	32.5218i	0.872616	+	1.51141i	0.0133346	+	0.999911i	$0.495755\pi$
$464$		0			0
$465$	−13.8993	+	11.6629i	−0.644563	+	0.540852i
$466$		0			0
$467$	2.95532	−	5.11877i	0.136756	−	0.236868i	−0.789511	−	0.613736i	$-0.789666\pi$
$467$	2.95532	−	5.11877i	0.136756	−	0.236868i	0.926267	+	0.376868i	$0.122999\pi$
$468$		0			0
$469$	19.0909	+	6.94850i	0.881534	+	0.320852i
$470$		0			0
$471$	−9.44497	−	53.5651i	−0.435201	−	2.46815i
$472$		0			0
$473$	−32.8713	−	27.5823i	−1.51142	−	1.26823i
$474$		0			0
$475$	−0.316738	+	4.34738i	−0.0145329	+	0.199471i
$476$		0			0
$477$	−0.122529	−	0.102814i	−0.00561023	−	0.00470755i
$478$		0			0
$479$	1.61205	+	9.14240i	0.0736565	+	0.417727i	0.999233	+	0.0391656i	$0.0124700\pi$
$479$	1.61205	+	9.14240i	0.0736565	+	0.417727i	−0.925576	+	0.378561i	$0.876419\pi$
$480$		0			0
$481$	1.03122	+	0.375333i	0.0470196	+	0.0171137i
$482$		0			0
$483$	−5.86724	+	10.1624i	−0.266969	+	0.462403i
$484$		0			0
$485$	−13.3023	+	11.1620i	−0.604026	+	0.506838i
$486$		0			0
$487$	12.4983	+	21.6477i	0.566353	+	0.980951i	0.996922	+	0.0783942i	$0.0249793\pi$
$487$	12.4983	+	21.6477i	0.566353	+	0.980951i	−0.430570	+	0.902557i	$0.641687\pi$
$488$		0			0
$489$	6.62847	−	37.5919i	0.299750	−	1.69997i
$490$		0			0
$491$	−21.1513	+	7.69846i	−0.954547	+	0.347427i	−0.771894	−	0.635751i	$-0.780691\pi$
$491$	−21.1513	+	7.69846i	−0.954547	+	0.347427i	−0.182652	+	0.983178i	$0.558468\pi$
$492$		0			0
$493$	6.38516			0.287573
$494$		0			0
$495$	30.1913			1.35700
$496$		0			0
$497$	−18.2645	+	6.64772i	−0.819273	+	0.298191i
$498$		0			0
$499$	−4.60596	+	26.1217i	−0.206191	+	1.16937i	0.689364	+	0.724415i	$0.257890\pi$
$499$	−4.60596	+	26.1217i	−0.206191	+	1.16937i	−0.895555	+	0.444951i	$0.853221\pi$
$500$		0			0
$501$	−36.7480	−	63.6494i	−1.64178	−	2.84364i
$502$		0			0
$503$	−30.1792	+	25.3234i	−1.34563	+	1.12911i	−0.365484	+	0.930818i	$0.619096\pi$
$503$	−30.1792	+	25.3234i	−1.34563	+	1.12911i	−0.980142	+	0.198296i	$0.936459\pi$
$504$		0			0
$505$	3.63352	−	6.29345i	0.161690	−	0.280055i
$506$		0			0
$507$	−38.0155	−	13.8365i	−1.68833	−	0.614500i
$508$		0			0
$509$	−3.40757	−	19.3253i	−0.151038	−	0.856578i	−0.962319	−	0.271922i	$-0.912341\pi$
$509$	−3.40757	−	19.3253i	−0.151038	−	0.856578i	0.811281	−	0.584656i	$-0.198771\pi$
$510$		0			0
$511$	3.79171	+	3.18162i	0.167735	+	0.140747i
$512$		0			0
$513$	−48.8052	−	12.3198i	−2.15480	−	0.543930i
$514$		0			0
$515$	0.651497	+	0.546671i	0.0287084	+	0.0240892i
$516$		0			0
$517$	−0.723724	−	4.10444i	−0.0318294	−	0.180513i
$518$		0			0
$519$	−30.5117	−	11.1053i	−1.33931	−	0.487470i
$520$		0			0
$521$	−8.49964	+	14.7218i	−0.372376	+	0.644974i	−0.989931	−	0.141554i	$-0.954790\pi$
$521$	−8.49964	+	14.7218i	−0.372376	+	0.644974i	0.617554	+	0.786528i	$0.288124\pi$
$522$		0			0
$523$	25.3000	−	21.2293i	1.10629	−	0.928291i	0.108461	−	0.994101i	$-0.465408\pi$
$523$	25.3000	−	21.2293i	1.10629	−	0.928291i	0.997832	+	0.0658102i	$0.0209632\pi$
$524$		0			0
$525$	−2.00566	−	3.47390i	−0.0875340	−	0.151613i
$526$		0			0
$527$	−0.964433	+	5.46957i	−0.0420114	+	0.238258i
$528$		0			0
$529$	13.5714	−	4.93957i	0.590059	−	0.214764i
$530$		0			0
$531$	71.7597			3.11410
$532$		0			0
$533$	−0.972250			−0.0421128
$534$		0			0
$535$	9.48731	−	3.45310i	0.410172	−	0.149290i
$536$		0			0
$537$	−4.54675	+	25.7859i	−0.196207	+	1.11274i
$538$		0			0
$539$	12.0249	+	20.8277i	0.517947	+	0.897111i
$540$		0			0
$541$	−15.8252	+	13.2789i	−0.680378	+	0.570905i	−0.916117	−	0.400912i	$-0.868693\pi$
$541$	−15.8252	+	13.2789i	−0.680378	+	0.570905i	0.235739	+	0.971816i	$0.424249\pi$
$542$		0			0
$543$	35.1086	−	60.8099i	1.50666	−	2.60960i
$544$		0			0
$545$	2.82224	+	1.02721i	0.120891	+	0.0440009i
$546$		0			0
$547$	3.19901	+	18.1425i	0.136780	+	0.775717i	0.973604	+	0.228245i	$0.0732988\pi$
$547$	3.19901	+	18.1425i	0.136780	+	0.775717i	−0.836824	+	0.547472i	$0.815590\pi$
$548$		0			0
$549$	30.3228	+	25.4438i	1.29414	+	1.08592i
$550$		0			0
$551$	24.1474	+	16.3902i	1.02871	+	0.698248i
$552$		0			0
$553$	−2.94057	−	2.46743i	−0.125046	−	0.104926i
$554$		0			0
$555$	4.84733	+	27.4906i	0.205758	+	1.16691i
$556$		0			0
$557$	30.4882	+	11.0968i	1.29183	+	0.470186i	0.894326	−	0.447416i	$-0.147656\pi$
$557$	30.4882	+	11.0968i	1.29183	+	0.470186i	0.397500	+	0.917602i	$0.369878\pi$
$558$		0			0
$559$	0.583735	−	1.01106i	0.0246894	−	0.0427632i
$560$		0			0
$561$	10.2463	−	8.59763i	0.432597	−	0.362992i
$562$		0			0
$563$	−4.29185	−	7.43371i	−0.180880	−	0.313293i	0.761300	−	0.648399i	$-0.224561\pi$
$563$	−4.29185	−	7.43371i	−0.180880	−	0.313293i	−0.942180	+	0.335106i	$0.891228\pi$
$564$		0			0
$565$	−1.05304	+	5.97211i	−0.0443019	+	0.251248i
$566$		0			0
$567$	19.1864	−	6.98328i	0.805753	−	0.293270i
$568$		0			0
$569$	18.8173			0.788861			0.394431	−	0.918926i	$-0.370942\pi$
$569$	18.8173			0.788861			0.394431	+	0.918926i	$0.370942\pi$
$570$		0			0
$571$	−9.57993			−0.400907			−0.200454	−	0.979703i	$-0.564242\pi$
$571$	−9.57993			−0.400907			−0.200454	+	0.979703i	$0.564242\pi$
$572$		0			0
$573$	71.1322	−	25.8900i	2.97159	−	1.08157i
$574$		0			0
$575$	0.507981	−	2.88091i	0.0211843	−	0.120142i
$576$		0			0
$577$	6.41220	+	11.1063i	0.266943	+	0.462359i	0.968071	−	0.250676i	$-0.0806530\pi$
$577$	6.41220	+	11.1063i	0.266943	+	0.462359i	−0.701128	+	0.713036i	$0.747320\pi$
$578$		0			0
$579$	11.0880	−	9.30396i	0.460803	−	0.386660i
$580$		0			0
$581$	5.61944	−	9.73316i	0.233134	−	0.403799i
$582$		0			0
$583$	0.100892	+	0.0367215i	0.00417850	+	0.00152085i
$584$		0			0
$585$	0.142638	+	0.808941i	0.00589736	+	0.0334456i
$586$		0			0
$587$	−20.7329	−	17.3970i	−0.855739	−	0.718050i	0.105307	−	0.994440i	$-0.466417\pi$
$587$	−20.7329	−	17.3970i	−0.855739	−	0.718050i	−0.961046	+	0.276390i	$0.910862\pi$
$588$		0			0
$589$	−17.6873	+	18.2092i	−0.728791	+	0.750295i
$590$		0			0
$591$	28.6569	+	24.0460i	1.17879	+	0.989120i
$592$		0			0
$593$	−5.90373	−	33.4817i	−0.242437	−	1.37493i	−0.826370	−	0.563127i	$-0.809598\pi$
$593$	−5.90373	−	33.4817i	−0.242437	−	1.37493i	0.583933	−	0.811802i	$-0.301513\pi$
$594$		0			0
$595$	−1.15382	−	0.419954i	−0.0473018	−	0.0172164i
$596$		0			0
$597$	18.2205	−	31.5588i	0.745714	−	1.29161i
$598$		0			0
$599$	0.383051	−	0.321418i	0.0156510	−	0.0131328i	−0.634929	−	0.772571i	$-0.718970\pi$
$599$	0.383051	−	0.321418i	0.0156510	−	0.0131328i	0.650580	+	0.759438i	$0.274526\pi$
$600$		0			0
$601$	−3.43562	−	5.95066i	−0.140142	−	0.242733i	0.787408	−	0.616432i	$-0.211422\pi$
$601$	−3.43562	−	5.95066i	−0.140142	−	0.242733i	−0.927550	+	0.373699i	$0.878089\pi$
$602$		0			0
$603$	18.3762	−	104.217i	0.748336	−	4.24402i
$604$		0			0
$605$	−8.70704	+	3.16910i	−0.353991	+	0.128842i
$606$		0			0
$607$	−7.65201			−0.310586			−0.155293	−	0.987868i	$-0.549632\pi$
$607$	−7.65201			−0.310586			−0.155293	+	0.987868i	$0.549632\pi$
$608$		0			0
$609$	−26.8573			−1.08831
$610$		0			0
$611$	0.106555	−	0.0387827i	0.00431074	−	0.00156898i
$612$		0			0
$613$	−5.77627	+	32.7589i	−0.233302	+	1.32312i	0.612860	+	0.790192i	$0.290019\pi$
$613$	−5.77627	+	32.7589i	−0.233302	+	1.32312i	−0.846161	+	0.532927i	$0.821092\pi$
$614$		0			0
$615$	−12.3656	−	21.4178i	−0.498629	−	0.863650i
$616$		0			0
$617$	11.5490	−	9.69076i	0.464945	−	0.390135i	−0.380002	−	0.924986i	$-0.624077\pi$
$617$	11.5490	−	9.69076i	0.464945	−	0.390135i	0.844947	+	0.534851i	$0.179632\pi$
$618$		0			0
$619$	−15.4112	+	26.6930i	−0.619428	+	1.07288i	0.370162	+	0.928967i	$0.379302\pi$
$619$	−15.4112	+	26.6930i	−0.619428	+	1.07288i	−0.989590	+	0.143914i	$0.954031\pi$
$620$		0			0
$621$	31.7443	+	11.5540i	1.27386	+	0.463645i
$622$		0			0
$623$	−3.34560	−	18.9738i	−0.134038	−	0.760170i
$624$		0			0
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$		0			0
$627$	60.8187	−	6.21308i	2.42887	−	0.248126i
$628$		0			0
$629$	6.54561	+	5.49242i	0.260990	+	0.218997i
$630$		0			0
$631$	−5.76052	−	32.6695i	−0.229323	−	1.30055i	−0.854247	−	0.519868i	$-0.825981\pi$
$631$	−5.76052	−	32.6695i	−0.229323	−	1.30055i	0.624924	−	0.780685i	$-0.285130\pi$
$632$		0			0
$633$	36.8297	+	13.4049i	1.46385	+	0.532798i
$634$		0			0
$635$	−3.32109	+	5.75230i	−0.131794	+	0.228273i
$636$		0			0
$637$	−0.501242	+	0.420592i	−0.0198599	+	0.0166645i
$638$		0			0
$639$	50.6217	+	87.6793i	2.00256	+	3.46854i
$640$		0			0
$641$	−3.69073	+	20.9312i	−0.145775	+	0.826732i	0.820966	+	0.570977i	$0.193435\pi$
$641$	−3.69073	+	20.9312i	−0.145775	+	0.826732i	−0.966741	+	0.255756i	$0.917676\pi$
$642$		0			0
$643$	−43.7776	+	15.9338i	−1.72642	+	0.628366i	−0.998366	−	0.0571513i	$-0.981798\pi$
$643$	−43.7776	+	15.9338i	−1.72642	+	0.628366i	−0.728056	+	0.685517i	$0.759576\pi$
$644$		0			0
$645$	29.6970			1.16932
$646$		0			0
$647$	4.02896			0.158395			0.0791974	−	0.996859i	$-0.474764\pi$
$647$	4.02896			0.158395			0.0791974	+	0.996859i	$0.474764\pi$
$648$		0			0
$649$	−45.2636	+	16.4746i	−1.77675	+	0.646685i
$650$		0			0
$651$	4.05660	−	23.0061i	0.158991	−	0.901681i
$652$		0			0
$653$	−6.38069	−	11.0517i	−0.249696	−	0.432486i	0.713746	−	0.700405i	$-0.246997\pi$
$653$	−6.38069	−	11.0517i	−0.249696	−	0.432486i	−0.963441	+	0.267919i	$0.913664\pi$
$654$		0			0
$655$	7.06862	−	5.93127i	0.276194	−	0.231754i
$656$		0			0
$657$	12.8913	−	22.3284i	0.502937	−	0.871112i
$658$		0			0
$659$	17.6911	+	6.43902i	0.689146	+	0.250829i	0.662770	−	0.748823i	$-0.269381\pi$
$659$	17.6911	+	6.43902i	0.689146	+	0.250829i	0.0263766	+	0.999652i	$0.491603\pi$
$660$		0			0
$661$	2.07438	+	11.7644i	0.0806842	+	0.457583i	0.998205	+	0.0598944i	$0.0190764\pi$
$661$	2.07438	+	11.7644i	0.0806842	+	0.457583i	−0.917521	+	0.397688i	$0.869812\pi$
$662$		0			0
$663$	0.278772	+	0.233917i	0.0108266	+	0.00908459i
$664$		0			0
$665$	−3.28550	−	4.54994i	−0.127406	−	0.176439i
$666$		0			0
$667$	−15.0040	−	12.5899i	−0.580957	−	0.487481i
$668$		0			0
$669$	−7.29544	−	41.3745i	−0.282058	−	1.59963i
$670$		0			0
$671$	−24.9680	−	9.08760i	−0.963878	−	0.350823i
$672$		0			0
$673$	11.9605	−	20.7161i	0.461042	−	0.798547i	−0.537972	−	0.842963i	$-0.680809\pi$
$673$	11.9605	−	20.7161i	0.461042	−	0.798547i	0.999013	+	0.0444155i	$0.0141426\pi$
$674$		0			0
$675$	−8.84620	+	7.42284i	−0.340490	+	0.285705i
$676$		0			0
$677$	−5.45024	−	9.44010i	−0.209470	−	0.362812i	0.742078	−	0.670314i	$-0.233840\pi$
$677$	−5.45024	−	9.44010i	−0.209470	−	0.362812i	−0.951548	+	0.307501i	$0.900507\pi$
$678$		0			0
$679$	3.88237	−	22.0180i	0.148992	−	0.844973i
$680$		0			0
$681$	−61.7996	+	22.4932i	−2.36816	+	0.861941i
$682$		0			0
$683$	−0.353548			−0.0135282			−0.00676408	−	0.999977i	$-0.502153\pi$
$683$	−0.353548			−0.0135282			−0.00676408	+	0.999977i	$0.502153\pi$
$684$		0			0
$685$	−3.65261			−0.139559
$686$		0			0
$687$	−56.6878	+	20.6327i	−2.16278	+	0.787186i
$688$		0			0
$689$	−0.000507251		0.00287676i	−1.93247e−5		0.000109596i
$690$		0			0
$691$	−1.06320	−	1.84152i	−0.0404460	−	0.0700546i	0.845094	−	0.534618i	$-0.179545\pi$
$691$	−1.06320	−	1.84152i	−0.0404460	−	0.0700546i	−0.885540	+	0.464564i	$0.846211\pi$
$692$		0			0
$693$	−29.7776	+	24.9864i	−1.13116	+	0.949153i
$694$		0			0
$695$	9.41264	−	16.3032i	0.357042	−	0.618415i
$696$		0			0
$697$	−7.11368	−	2.58917i	−0.269450	−	0.0980718i
$698$		0			0
$699$	1.00202	+	5.68274i	0.0378999	+	0.214941i
$700$		0			0
$701$	16.4345	+	13.7902i	0.620722	+	0.520848i	0.898030	−	0.439933i	$-0.144998\pi$
$701$	16.4345	+	13.7902i	0.620722	+	0.520848i	−0.277308	+	0.960781i	$0.589442\pi$
$702$		0			0
$703$	10.6555	+	37.5733i	0.401880	+	1.41710i
$704$		0			0
$705$	2.20957	+	1.85405i	0.0832171	+	0.0698274i
$706$		0			0
$707$	1.62473	+	9.21432i	0.0611044	+	0.346540i
$708$		0			0
$709$	39.1314	+	14.2427i	1.46961	+	0.534895i	0.947995	−	0.318286i	$-0.103107\pi$
$709$	39.1314	+	14.2427i	1.46961	+	0.534895i	0.521616	+	0.853180i	$0.325329\pi$
$710$		0			0
$711$	−9.99754	+	17.3162i	−0.374937	+	0.649410i
$712$		0			0
$713$	13.0508	−	10.9509i	0.488756	−	0.410115i
$714$		0			0
$715$	−0.275688	−	0.477506i	−0.0103102	−	0.0178577i
$716$		0			0
$717$	11.5542	−	65.5272i	0.431500	−	2.44716i
$718$		0			0
$719$	11.1111	−	4.04411i	0.414374	−	0.150820i	−0.126416	−	0.991977i	$-0.540347\pi$
$719$	11.1111	−	4.04411i	0.414374	−	0.150820i	0.540790	+	0.841157i	$0.318125\pi$
$720$		0			0
$721$	−1.09499			−0.0407797
$722$		0			0
$723$	18.8297			0.700285
$724$		0			0
$725$	6.29160	−	2.28996i	0.233664	−	0.0850469i
$726$		0			0
$727$	1.05821	−	6.00138i	0.0392467	−	0.222579i	−0.958876	−	0.283825i	$-0.908396\pi$
$727$	1.05821	−	6.00138i	0.0392467	−	0.222579i	0.998123	+	0.0612463i	$0.0195075\pi$
$728$		0			0
$729$	0.789882	+	1.36812i	0.0292549	+	0.0506709i
$730$		0			0
$731$	6.96355	−	5.84311i	0.257556	−	0.216115i
$732$		0			0
$733$	−26.7539	+	46.3391i	−0.988177	+	1.71157i	−0.361310	+	0.932446i	$0.617670\pi$
$733$	−26.7539	+	46.3391i	−0.988177	+	1.71157i	−0.626867	+	0.779126i	$0.715663\pi$
$734$		0			0
$735$	−15.6403	−	5.69262i	−0.576902	−	0.209975i
$736$		0			0
$737$	12.3350	+	69.9551i	0.454365	+	2.57683i
$738$		0			0
$739$	22.9031	+	19.2180i	0.842504	+	0.706945i	0.958126	−	0.286348i	$-0.0924415\pi$
$739$	22.9031	+	19.2180i	0.842504	+	0.706945i	−0.115621	+	0.993293i	$0.536886\pi$
$740$		0			0
$741$	0.453809	+	1.60021i	0.0166711	+	0.0587853i
$742$		0			0
$743$	−36.6959	−	30.7915i	−1.34624	−	1.12963i	−0.979975	−	0.199122i	$-0.936191\pi$
$743$	−36.6959	−	30.7915i	−1.34624	−	1.12963i	−0.366268	−	0.930510i	$-0.619365\pi$
$744$		0			0
$745$	2.04509	+	11.5983i	0.0749264	+	0.424929i
$746$		0			0
$747$	−55.0116	−	20.0226i	−2.01277	−	0.732588i
$748$		0			0
$749$	−6.49952	+	11.2575i	−0.237487	+	0.411340i
$750$		0			0
$751$	19.4465	−	16.3175i	0.709611	−	0.595434i	−0.214879	−	0.976641i	$-0.568936\pi$
$751$	19.4465	−	16.3175i	0.709611	−	0.595434i	0.924490	+	0.381206i	$0.124491\pi$
$752$		0			0
$753$	−3.81448	−	6.60688i	−0.139008	−	0.240768i
$754$		0			0
$755$	1.20517	−	6.83485i	0.0438606	−	0.248746i
$756$		0			0
$757$	−24.9241	+	9.07161i	−0.905880	+	0.329713i	−0.752607	−	0.658470i	$-0.771204\pi$
$757$	−24.9241	+	9.07161i	−0.905880	+	0.329713i	−0.153274	+	0.988184i	$0.548982\pi$
$758$		0			0
$759$	−41.0291			−1.48926
$760$		0			0
$761$	42.9695			1.55764			0.778822	−	0.627244i	$-0.215817\pi$
$761$	42.9695			1.55764			0.778822	+	0.627244i	$0.215817\pi$
$762$		0			0
$763$	−3.63369	+	1.32255i	−0.131548	+	0.0478797i
$764$		0			0
$765$	−1.11062	+	6.29865i	−0.0401546	+	0.227728i
$766$		0			0
$767$	−0.655265	−	1.13495i	−0.0236602	−	0.0409807i
$768$		0			0
$769$	−36.0908	+	30.2838i	−1.30147	+	1.09206i	−0.311577	+	0.950221i	$0.600857\pi$
$769$	−36.0908	+	30.2838i	−1.30147	+	1.09206i	−0.989890	+	0.141839i	$0.954698\pi$
$770$		0			0
$771$	15.7776	−	27.3277i	0.568217	−	0.984182i
$772$		0			0
$773$	−20.4768	−	7.45294i	−0.736499	−	0.268064i	−0.0535859	−	0.998563i	$-0.517065\pi$
$773$	−20.4768	−	7.45294i	−0.736499	−	0.268064i	−0.682913	+	0.730499i	$0.739287\pi$
$774$		0			0
$775$	1.01129	+	5.73531i	0.0363266	+	0.206018i
$776$		0			0
$777$	−27.5321	−	23.1022i	−0.987710	−	0.828787i
$778$		0			0
$779$	−20.2563	−	28.0520i	−0.725756	−	1.00507i
$780$		0			0
$781$	−52.0599	−	43.6834i	−1.86285	−	1.56312i
$782$		0			0
$783$	13.4261	+	76.1430i	0.479808	+	2.72113i
$784$		0			0
$785$	−16.4053	−	5.97103i	−0.585530	−	0.213115i
$786$		0			0
$787$	−24.0963	+	41.7360i	−0.858940	+	1.48773i	0.0140010	+	0.999902i	$0.495543\pi$
$787$	−24.0963	+	41.7360i	−0.858940	+	1.48773i	−0.872941	+	0.487826i	$0.837790\pi$
$788$		0			0
$789$	−26.3254	+	22.0896i	−0.937210	+	0.786412i
$790$		0			0
$791$	−3.90391	−	6.76177i	−0.138807	−	0.240421i
$792$		0			0
$793$	0.125531	−	0.711922i	0.00445774	−	0.0252811i
$794$		0			0
$795$	−0.0698241	+	0.0254139i	−0.00247640	+	0.000901338i
$796$		0			0
$797$	22.8798			0.810443			0.405221	−	0.914219i	$-0.367194\pi$
$797$	22.8798			0.810443			0.405221	+	0.914219i	$0.367194\pi$
$798$		0			0
$799$	0.882911			0.0312352
$800$		0			0
$801$	−94.3049	+	34.3242i	−3.33210	+	1.21279i
$802$		0			0
$803$	−3.00524	+	17.0436i	−0.106053	+	0.601455i
$804$		0			0
$805$	1.88322	+	3.26184i	0.0663748	+	0.114965i
$806$		0			0
$807$	47.6385	−	39.9735i	1.67696	−	1.40713i
$808$		0			0
$809$	−5.54829	+	9.60992i	−0.195068	+	0.337867i	−0.946923	−	0.321461i	$-0.895826\pi$
$809$	−5.54829	+	9.60992i	−0.195068	+	0.337867i	0.751855	+	0.659328i	$0.229159\pi$
$810$		0			0
$811$	4.68468	+	1.70509i	0.164502	+	0.0598737i	0.422958	−	0.906149i	$-0.360992\pi$
$811$	4.68468	+	1.70509i	0.164502	+	0.0598737i	−0.258457	+	0.966023i	$0.583214\pi$
$812$		0			0
$813$	3.07914	+	17.4627i	0.107990	+	0.612443i
$814$		0			0
$815$	−9.38566	−	7.87550i	−0.328765	−	0.275867i
$816$		0			0
$817$	41.3335	−	4.22252i	1.44608	−	0.147727i
$818$		0			0
$819$	−0.810164	−	0.679808i	−0.0283094	−	0.0237544i
$820$		0			0
$821$	−4.09160	−	23.2046i	−0.142798	−	0.809847i	−0.969109	−	0.246633i	$-0.920676\pi$
$821$	−4.09160	−	23.2046i	−0.142798	−	0.809847i	0.826311	−	0.563214i	$-0.190435\pi$
$822$		0			0
$823$	41.1290	+	14.9697i	1.43367	+	0.521812i	0.937980	−	0.346689i	$-0.112694\pi$
$823$	41.1290	+	14.9697i	1.43367	+	0.521812i	0.495687	+	0.868501i	$0.334916\pi$
$824$		0			0
$825$	7.01269	−	12.1463i	0.244151	−	0.422881i
$826$		0			0
$827$	−6.73462	+	5.65102i	−0.234186	+	0.196505i	−0.752327	−	0.658790i	$-0.771069\pi$
$827$	−6.73462	+	5.65102i	−0.234186	+	0.196505i	0.518141	+	0.855295i	$0.326624\pi$
$828$		0			0
$829$	−16.3329	−	28.2894i	−0.567264	−	0.982530i	−0.996835	−	0.0794970i	$-0.974669\pi$
$829$	−16.3329	−	28.2894i	−0.567264	−	0.982530i	0.429571	−	0.903033i	$-0.358665\pi$
$830$		0			0
$831$	−17.4046	+	98.7064i	−0.603759	+	3.42409i
$832$		0			0
$833$	−4.78751	+	1.74251i	−0.165877	+	0.0603745i
$834$		0			0
$835$	−23.5902			−0.816372
$836$		0			0
$837$	−67.2524			−2.32458
$838$		0			0
$839$	18.5786	−	6.76204i	0.641403	−	0.233452i	−0.000783927	−	1.00000i	$-0.500250\pi$
$839$	18.5786	−	6.76204i	0.641403	−	0.233452i	0.642187	+	0.766548i	$0.278027\pi$
$840$		0			0
$841$	2.74854	−	15.5877i	0.0947771	−	0.537508i
$842$		0			0
$843$	20.9688	+	36.3190i	0.722204	+	1.25089i
$844$		0			0
$845$	−9.94709	+	8.34660i	−0.342190	+	0.287132i
$846$		0			0
$847$	5.96498	−	10.3316i	0.204959	−	0.354999i
$848$		0			0
$849$	22.0490	+	8.02519i	0.756721	+	0.275424i
$850$		0			0
$851$	−4.55142	−	25.8124i	−0.156021	−	0.884838i
$852$		0			0
$853$	26.0634	+	21.8698i	0.892394	+	0.748808i	0.968689	−	0.248278i	$-0.0798645\pi$
$853$	26.0634	+	21.8698i	0.892394	+	0.748808i	−0.0762946	+	0.997085i	$0.524309\pi$
$854$		0			0
$855$	−20.3683	+	20.9693i	−0.696581	+	0.717135i
$856$		0			0
$857$	12.9066	+	10.8299i	0.440881	+	0.369943i	0.836039	−	0.548670i	$-0.184866\pi$
$857$	12.9066	+	10.8299i	0.440881	+	0.369943i	−0.395158	+	0.918613i	$0.629310\pi$
$858$		0			0
$859$	−0.729186	−	4.13542i	−0.0248795	−	0.141099i	0.969838	−	0.243751i	$-0.0783781\pi$
$859$	−0.729186	−	4.13542i	−0.0248795	−	0.141099i	−0.994717	+	0.102653i	$0.967267\pi$
$860$		0			0
$861$	29.9216	+	10.8906i	1.01972	+	0.371149i
$862$		0			0
$863$	−18.5050	+	32.0517i	−0.629919	+	1.09105i	0.357649	+	0.933856i	$0.383579\pi$
$863$	−18.5050	+	32.0517i	−0.629919	+	1.09105i	−0.987568	+	0.157195i	$0.949755\pi$
$864$		0			0
$865$	−7.98365	+	6.69908i	−0.271452	+	0.227775i
$866$		0			0
$867$	−25.0653	−	43.4143i	−0.851262	−	1.47443i
$868$		0			0
$869$	2.33065	−	13.2178i	0.0790618	−	0.448382i
$870$		0			0
$871$	−1.81609	+	0.661003i	−0.0615359	+	0.0223972i
$872$		0			0
$873$	−116.459			−3.94153
$874$		0			0
$875$	−1.28752			−0.0435261
$876$		0			0
$877$	28.6083	−	10.4126i	0.966032	−	0.351607i	0.189638	−	0.981854i	$-0.439269\pi$
$877$	28.6083	−	10.4126i	0.966032	−	0.351607i	0.776395	+	0.630247i	$0.217046\pi$
$878$		0			0
$879$	13.4078	−	76.0392i	0.452233	−	2.56474i
$880$		0			0
$881$	5.10993	+	8.85066i	0.172158	+	0.298186i	0.939174	−	0.343442i	$-0.111593\pi$
$881$	5.10993	+	8.85066i	0.172158	+	0.298186i	−0.767016	+	0.641628i	$0.778259\pi$
$882$		0			0
$883$	−20.8764	+	17.5174i	−0.702548	+	0.589508i	−0.922497	−	0.386003i	$-0.873855\pi$
$883$	−20.8764	+	17.5174i	−0.702548	+	0.589508i	0.219949	+	0.975511i	$0.429411\pi$
$884$		0			0
$885$	16.6680	−	28.8698i	0.560289	−	0.970449i
$886$		0			0
$887$	−46.7138	−	17.0024i	−1.56849	−	0.570885i	−0.595832	−	0.803109i	$-0.703178\pi$
$887$	−46.7138	−	17.0024i	−1.56849	−	0.570885i	−0.972662	+	0.232223i	$0.925400\pi$
$888$		0			0
$889$	−1.48503	−	8.42202i	−0.0498063	−	0.282466i
$890$		0			0
$891$	54.6877	+	45.8884i	1.83211	+	1.53732i
$892$		0			0
$893$	3.33899	+	2.26637i	0.111735	+	0.0758411i
$894$		0			0
$895$	6.43803	+	5.40215i	0.215199	+	0.180574i
$896$		0			0
$897$	−0.193841	−	1.09933i	−0.00647217	−	0.0367055i
$898$		0			0
$899$	36.6410	+	13.3362i	1.22204	+	0.444788i
$900$		0			0
$901$	−0.0113724	+	0.0196976i	−0.000378871	+	0.000656223i
$902$		0			0
$903$	−29.2901	+	24.5773i	−0.974713	+	0.817881i
$904$		0			0
$905$	−11.2689	−	19.5183i	−0.374591	−	0.648810i
$906$		0			0
$907$	−3.81396	+	21.6301i	−0.126641	+	0.718215i	0.853679	+	0.520799i	$0.174366\pi$
$907$	−3.81396	+	21.6301i	−0.126641	+	0.718215i	−0.980320	+	0.197416i	$0.936745\pi$
$908$		0			0
$909$	45.7977	−	16.6690i	1.51901	−	0.552875i
$910$		0			0
$911$	−6.97667			−0.231148			−0.115574	−	0.993299i	$-0.536871\pi$
$911$	−6.97667			−0.231148			−0.115574	+	0.993299i	$0.536871\pi$
$912$		0			0
$913$	39.2963			1.30052
$914$		0			0
$915$	17.2796	−	6.28926i	0.571246	−	0.207917i
$916$		0			0
$917$	−2.06303	+	11.7000i	−0.0681271	+	0.386368i
$918$		0			0
$919$	−0.179981	−	0.311736i	−0.00593702	−	0.0102832i	0.863042	−	0.505133i	$-0.168556\pi$
$919$	−0.179981	−	0.311736i	−0.00593702	−	0.0102832i	−0.868979	+	0.494850i	$0.835223\pi$
$920$		0			0
$921$	41.1278	−	34.5103i	1.35521	−	1.13715i
$922$		0			0
$923$	0.924491	−	1.60127i	0.0304300	−	0.0527063i
$924$		0			0
$925$	8.41948	+	3.06444i	0.276831	+	0.100758i
$926$		0			0
$927$	0.990439	+	5.61706i	0.0325303	+	0.184488i
$928$		0			0
$929$	9.16646	+	7.69157i	0.300742	+	0.252352i	0.780653	−	0.624965i	$-0.214887\pi$
$929$	9.16646	+	7.69157i	0.300742	+	0.252352i	−0.479911	+	0.877317i	$0.659331\pi$
$930$		0			0
$931$	−22.5783	−	5.69937i	−0.739973	−	0.186789i
$932$		0			0
$933$	20.1674	+	16.9224i	0.660250	+	0.554016i
$934$		0			0
$935$	−0.745502	−	4.22795i	−0.0243805	−	0.138269i
$936$		0			0
$937$	26.8842	+	9.78505i	0.878269	+	0.319664i	0.741511	−	0.670941i	$-0.234110\pi$
$937$	26.8842	+	9.78505i	0.878269	+	0.319664i	0.136758	+	0.990604i	$0.456332\pi$
$938$		0			0
$939$	2.30050	−	3.98458i	0.0750740	−	0.130032i
$940$		0			0
$941$	15.4644	−	12.9762i	0.504126	−	0.423012i	−0.354930	−	0.934893i	$-0.615495\pi$
$941$	15.4644	−	12.9762i	0.504126	−	0.423012i	0.859057	+	0.511881i	$0.171051\pi$
$942$		0			0
$943$	11.6107	+	20.1104i	0.378098	+	0.654884i
$944$		0			0
$945$	2.58183	−	14.6423i	0.0839868	−	0.476313i
$946$		0			0
$947$	19.2743	−	7.01526i	0.626330	−	0.227965i	−0.00930331	−	0.999957i	$-0.502961\pi$
$947$	19.2743	−	7.01526i	0.626330	−	0.227965i	0.635633	+	0.771991i	$0.280739\pi$
$948$		0			0
$949$	−0.470861			−0.0152848
$950$		0			0
$951$	−6.98196			−0.226405
$952$		0			0
$953$	44.9752	−	16.3696i	1.45689	−	0.530265i	0.512384	−	0.858756i	$-0.328762\pi$
$953$	44.9752	−	16.3696i	1.45689	−	0.530265i	0.944507	+	0.328492i	$0.106540\pi$
$954$		0			0
$955$	4.21909	−	23.9276i	0.136526	−	0.774280i
$956$		0			0
$957$	−46.9527	−	81.3244i	−1.51776	−	2.62885i
$958$		0			0
$959$	3.60256	−	3.02291i	0.116333	−	0.0976148i
$960$		0			0
$961$	−1.45823	+	2.52573i	−0.0470398	+	0.0814752i
$962$		0			0
$963$	63.6271	+	23.1584i	2.05036	+	0.746268i
$964$		0			0
$965$	−0.806749	−	4.57530i	−0.0259702	−	0.147284i
$966$		0			0
$967$	−9.80608	−	8.22828i	−0.315342	−	0.264604i	0.471354	−	0.881944i	$-0.343766\pi$
$967$	−9.80608	−	8.22828i	−0.315342	−	0.264604i	−0.786696	+	0.617341i	$0.788210\pi$
$968$		0			0
$969$	−0.941086	+	12.9168i	−0.0302320	+	0.414949i
$970$		0			0
$971$	21.5441	+	18.0776i	0.691381	+	0.580138i	0.919307	−	0.393541i	$-0.128750\pi$
$971$	21.5441	+	18.0776i	0.691381	+	0.580138i	−0.227926	+	0.973679i	$0.573194\pi$
$972$		0			0
$973$	4.20887	+	23.8697i	0.134930	+	0.765227i
$974$		0			0
$975$	0.358578	+	0.130512i	0.0114837	+	0.00417972i
$976$		0			0
$977$	7.66796	−	13.2813i	0.245320	−	0.424906i	−0.716902	−	0.697174i	$-0.754440\pi$
$977$	7.66796	−	13.2813i	0.245320	−	0.424906i	0.962221	+	0.272268i	$0.0877737\pi$
$978$		0			0
$979$	51.6042	−	43.3011i	1.64928	−	1.38391i
$980$		0			0
$981$	10.0711	+	17.4437i	0.321546	+	0.556933i
$982$		0			0
$983$	5.27909	−	29.9392i	0.168377	−	0.954913i	−0.777137	−	0.629331i	$-0.783329\pi$
$983$	5.27909	−	29.9392i	0.168377	−	0.954913i	0.945514	−	0.325582i	$-0.105560\pi$
$984$		0			0
$985$	11.2831	−	4.10671i	0.359510	−	0.130851i
$986$		0			0
$987$	−3.71370			−0.118208
$988$		0			0
$989$	−27.8842			−0.886665
$990$		0			0
$991$	−6.16155	+	2.24262i	−0.195728	+	0.0712392i	−0.438024	−	0.898963i	$-0.644322\pi$
$991$	−6.16155	+	2.24262i	−0.195728	+	0.0712392i	0.242296	+	0.970202i	$0.422099\pi$
$992$		0			0
$993$	−1.46782	+	8.32445i	−0.0465800	+	0.264168i
$994$		0			0
$995$	−5.84826	−	10.1295i	−0.185402	−	0.321126i
$996$		0			0
$997$	−2.92015	+	2.45030i	−0.0924821	+	0.0776017i	−0.687856	−	0.725847i	$-0.741448\pi$
$997$	−2.92015	+	2.45030i	−0.0924821	+	0.0776017i	0.595374	+	0.803448i	$0.297004\pi$
$998$		0			0
$999$	−51.7335	+	89.6051i	−1.63678	+	2.83498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.301.3	yes	18
19.5	even	9		7220.2.a.w.1.1		9
19.6	even	9	inner	380.2.u.b.101.3	✓	18
19.14	odd	18		7220.2.a.y.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.101.3	✓	18	19.6	even	9	inner
380.2.u.b.301.3	yes	18	1.1	even	1	trivial
7220.2.a.w.1.1		9	19.5	even	9
7220.2.a.y.1.9		9	19.14	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)

\(f(q)\)	\(=\)	\(q+(2.92764 - 1.06558i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.643760 + 1.11502i) q^{7} +(5.13752 - 4.31089i) q^{9} +O(q^{10})\)	\(q+(2.92764 - 1.06558i) q^{3} +(0.173648 - 0.984808i) q^{5} +(0.643760 + 1.11502i) q^{7} +(5.13752 - 4.31089i) q^{9} +(-2.25088 + 3.89864i) q^{11} +(-0.115094 - 0.0418907i) q^{13} +(-0.541007 - 3.06820i) q^{15} +(-0.730551 - 0.613005i) q^{17} +(-1.18925 - 4.19353i) q^{19} +(3.07284 + 2.57842i) q^{21} +(0.507981 + 2.88091i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(5.77395 - 10.0008i) q^{27} +(-5.12896 + 4.30371i) q^{29} +(-2.91189 - 5.04355i) q^{31} +(-2.43548 + 13.8123i) q^{33} +(1.20987 - 0.440358i) q^{35} -8.95982 q^{37} -0.381591 q^{39} +(7.45930 - 2.71496i) q^{41} +(-1.65520 + 9.38710i) q^{43} +(-3.35328 - 5.80804i) q^{45} +(-0.709210 + 0.595097i) q^{47} +(2.67115 - 4.62656i) q^{49} +(-2.79200 - 1.01620i) q^{51} +(-0.00414149 - 0.0234876i) q^{53} +(3.44855 + 2.89368i) q^{55} +(-7.95023 - 11.0099i) q^{57} +(8.19663 + 6.87779i) q^{59} +(1.02491 + 5.81255i) q^{61} +(8.11408 + 2.95328i) q^{63} +(-0.0612401 + 0.106071i) q^{65} +(12.0876 - 10.1427i) q^{67} +(4.55701 + 7.89297i) q^{69} +(-2.62142 + 14.8668i) q^{71} +(3.61254 - 1.31486i) q^{73} -3.11553 q^{75} -5.79610 q^{77} +(-2.80162 + 1.01971i) q^{79} +(2.75375 - 15.6173i) q^{81} +(-4.36455 - 7.55962i) q^{83} +(-0.730551 + 0.613005i) q^{85} +(-10.4299 + 18.0650i) q^{87} +(-14.0616 - 5.11801i) q^{89} +(-0.0273836 - 0.155300i) q^{91} +(-13.8993 - 11.6629i) q^{93} +(-4.33633 + 0.442988i) q^{95} +(-13.3023 - 11.1620i) q^{97} +(5.24266 + 29.7326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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