LMFDB - Embedded newform 380.2.u.a.61.1

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} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 $ x^18 - 3x^17 + 3x^15 + 36x^14 + 72x^13 - 134x^12 - 741x^11 + 486x^10 + 5700x^9 + 11637x^8 + 13878x^7 + 13978x^6 + 10005x^5 + 5949x^4 + 2649x^3 + 819x^2 + 135x + 9
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			61.1
Root			$-1.37827 - 1.15651i$ of defining polynomial
Character	$\chi$	$=$	380.61
Dual form			380.2.u.a.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.312429 - 1.77187i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-0.336777 + 0.583316i) q^{7} +(-0.222848 + 0.0811099i) q^{9} +O(q^{10})$	\(q+(-0.312429 - 1.77187i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-0.336777 + 0.583316i) q^{7} +(-0.222848 + 0.0811099i) q^{9} +(-3.21276 - 5.56466i) q^{11} +(0.791702 - 4.48996i) q^{13} +(1.37827 + 1.15651i) q^{15} +(1.21618 + 0.442652i) q^{17} +(-4.35314 + 0.223964i) q^{19} +(1.13878 + 0.414482i) q^{21} +(-1.04176 - 0.874144i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-2.48547 - 4.30496i) q^{27} +(-6.80288 + 2.47605i) q^{29} +(-2.97241 + 5.14836i) q^{31} +(-8.85612 + 7.43116i) q^{33} +(-0.116962 - 0.663322i) q^{35} +11.5704 q^{37} -8.20300 q^{39} +(-0.463683 - 2.62968i) q^{41} +(7.31756 - 6.14016i) q^{43} +(0.118575 - 0.205377i) q^{45} +(11.0445 - 4.01987i) q^{47} +(3.27316 + 5.66928i) q^{49} +(0.404354 - 2.29321i) q^{51} +(-2.74628 - 2.30440i) q^{53} +(6.03801 + 2.19766i) q^{55} +(1.75689 + 7.64324i) q^{57} +(0.150435 + 0.0547540i) q^{59} +(5.54965 + 4.65671i) q^{61} +(0.0277374 - 0.157306i) q^{63} +(2.27961 + 3.94841i) q^{65} +(-5.13512 + 1.86903i) q^{67} +(-1.22340 + 2.11898i) q^{69} +(9.00684 - 7.55764i) q^{71} +(-0.643012 - 3.64670i) q^{73} -1.79921 q^{75} +4.32794 q^{77} +(-1.11567 - 6.32728i) q^{79} +(-7.39632 + 6.20625i) q^{81} +(-2.52251 + 4.36912i) q^{83} +(-1.21618 + 0.442652i) q^{85} +(6.51266 + 11.2803i) q^{87} +(1.26006 - 7.14615i) q^{89} +(2.35244 + 1.97393i) q^{91} +(10.0509 + 3.65823i) q^{93} +(3.19074 - 2.96971i) q^{95} +(7.40807 + 2.69632i) q^{97} +(1.16730 + 0.979484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^9	$ 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.312429	−	1.77187i	−0.180381	−	1.02299i	−0.931748	−	0.363107i	$-0.881716\pi$
$3$	−0.312429	−	1.77187i	−0.180381	−	1.02299i	0.751366	−	0.659885i	$-0.229395\pi$
$4$		0			0
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$		0			0
$7$	−0.336777	+	0.583316i	−0.127290	+	0.220473i	−0.922626	−	0.385696i	$-0.873961\pi$
$7$	−0.336777	+	0.583316i	−0.127290	+	0.220473i	0.795336	+	0.606169i	$0.207295\pi$
$8$		0			0
$9$	−0.222848	+	0.0811099i	−0.0742825	+	0.0270366i
$10$		0			0
$11$	−3.21276	−	5.56466i	−0.968683	−	1.67781i	−0.699376	−	0.714754i	$-0.746539\pi$
$11$	−3.21276	−	5.56466i	−0.968683	−	1.67781i	−0.269307	−	0.963054i	$-0.586795\pi$
$12$		0			0
$13$	0.791702	−	4.48996i	0.219579	−	1.24529i	−0.653204	−	0.757182i	$-0.726576\pi$
$13$	0.791702	−	4.48996i	0.219579	−	1.24529i	0.872782	−	0.488110i	$-0.162313\pi$
$14$		0			0
$15$	1.37827	+	1.15651i	0.355869	+	0.298609i
$16$		0			0
$17$	1.21618	+	0.442652i	0.294966	+	0.107359i	0.485264	−	0.874367i	$-0.338723\pi$
$17$	1.21618	+	0.442652i	0.294966	+	0.107359i	−0.190299	+	0.981726i	$0.560946\pi$
$18$		0			0
$19$	−4.35314	+	0.223964i	−0.998679	+	0.0513810i
$19$	−4.35314	+	0.223964i	−0.998679	+	0.0513810i
$20$		0			0
$21$	1.13878	+	0.414482i	0.248502	+	0.0904475i
$22$		0			0
$23$	−1.04176	−	0.874144i	−0.217223	−	0.182272i	0.527683	−	0.849442i	$-0.323061\pi$
$23$	−1.04176	−	0.874144i	−0.217223	−	0.182272i	−0.744906	+	0.667170i	$0.767505\pi$
$24$		0			0
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$		0			0
$27$	−2.48547	−	4.30496i	−0.478329	−	0.828490i
$28$		0			0
$29$	−6.80288	+	2.47605i	−1.26326	+	0.459790i	−0.884863	−	0.465852i	$-0.845748\pi$
$29$	−6.80288	+	2.47605i	−1.26326	+	0.459790i	−0.378400	+	0.925642i	$0.623526\pi$
$30$		0			0
$31$	−2.97241	+	5.14836i	−0.533860	+	0.924673i	0.465358	+	0.885123i	$0.345926\pi$
$31$	−2.97241	+	5.14836i	−0.533860	+	0.924673i	−0.999218	+	0.0395498i	$0.987408\pi$
$32$		0			0
$33$	−8.85612	+	7.43116i	−1.54165	+	1.29360i
$34$		0			0
$35$	−0.116962	−	0.663322i	−0.0197701	−	0.112122i
$36$		0			0
$37$	11.5704			1.90216			0.951079	−	0.308948i	$-0.0999770\pi$
$37$	11.5704			1.90216			0.951079	+	0.308948i	$0.0999770\pi$
$38$		0			0
$39$	−8.20300			−1.31353
$40$		0			0
$41$	−0.463683	−	2.62968i	−0.0724151	−	0.410686i	−0.999369	−	0.0355118i	$-0.988694\pi$
$41$	−0.463683	−	2.62968i	−0.0724151	−	0.410686i	0.926954	−	0.375175i	$-0.122417\pi$
$42$		0			0
$43$	7.31756	−	6.14016i	1.11592	−	0.936366i	0.117526	−	0.993070i	$-0.462504\pi$
$43$	7.31756	−	6.14016i	1.11592	−	0.936366i	0.998391	+	0.0567043i	$0.0180592\pi$
$44$		0			0
$45$	0.118575	−	0.205377i	0.0176761	−	0.0306159i
$46$		0			0
$47$	11.0445	−	4.01987i	1.61100	−	0.586358i	0.629366	−	0.777109i	$-0.283314\pi$
$47$	11.0445	−	4.01987i	1.61100	−	0.586358i	0.981638	+	0.190751i	$0.0610922\pi$
$48$		0			0
$49$	3.27316	+	5.66928i	0.467595	+	0.809898i
$50$		0			0
$51$	0.404354	−	2.29321i	0.0566209	−	0.321113i
$52$		0			0
$53$	−2.74628	−	2.30440i	−0.377230	−	0.316534i	0.434384	−	0.900728i	$-0.356966\pi$
$53$	−2.74628	−	2.30440i	−0.377230	−	0.316534i	−0.811614	+	0.584194i	$0.801411\pi$
$54$		0			0
$55$	6.03801	+	2.19766i	0.814165	+	0.296332i
$56$		0			0
$57$	1.75689	+	7.64324i	0.232705	+	1.01237i
$58$		0			0
$59$	0.150435	+	0.0547540i	0.0195850	+	0.00712837i	0.351794	−	0.936077i	$-0.385572\pi$
$59$	0.150435	+	0.0547540i	0.0195850	+	0.00712837i	−0.332209	+	0.943206i	$0.607794\pi$
$60$		0			0
$61$	5.54965	+	4.65671i	0.710560	+	0.596231i	0.924756	−	0.380560i	$-0.124269\pi$
$61$	5.54965	+	4.65671i	0.710560	+	0.596231i	−0.214196	+	0.976791i	$0.568713\pi$
$62$		0			0
$63$	0.0277374	−	0.157306i	0.00349458	−	0.0198187i
$64$		0			0
$65$	2.27961	+	3.94841i	0.282751	+	0.489740i
$66$		0			0
$67$	−5.13512	+	1.86903i	−0.627354	+	0.228338i	−0.636079	−	0.771624i	$-0.719445\pi$
$67$	−5.13512	+	1.86903i	−0.627354	+	0.228338i	0.00872500	+	0.999962i	$0.497223\pi$
$68$		0			0
$69$	−1.22340	+	2.11898i	−0.147280	+	0.255096i
$70$		0			0
$71$	9.00684	−	7.55764i	1.06892	−	0.896927i	0.0739617	−	0.997261i	$-0.476436\pi$
$71$	9.00684	−	7.55764i	1.06892	−	0.896927i	0.994954	+	0.100334i	$0.0319913\pi$
$72$		0			0
$73$	−0.643012	−	3.64670i	−0.0752589	−	0.426815i	−0.999037	−	0.0438852i	$-0.986026\pi$
$73$	−0.643012	−	3.64670i	−0.0752589	−	0.426815i	0.923778	−	0.382929i	$-0.125085\pi$
$74$		0			0
$75$	−1.79921			−0.207755
$76$		0			0
$77$	4.32794			0.493214
$78$		0			0
$79$	−1.11567	−	6.32728i	−0.125523	−	0.711875i	−0.980996	−	0.194028i	$-0.937845\pi$
$79$	−1.11567	−	6.32728i	−0.125523	−	0.711875i	0.855473	−	0.517847i	$-0.173266\pi$
$80$		0			0
$81$	−7.39632	+	6.20625i	−0.821813	+	0.689583i
$82$		0			0
$83$	−2.52251	+	4.36912i	−0.276882	+	0.479573i	−0.970608	−	0.240666i	$-0.922634\pi$
$83$	−2.52251	+	4.36912i	−0.276882	+	0.479573i	0.693727	+	0.720238i	$0.255968\pi$
$84$		0			0
$85$	−1.21618	+	0.442652i	−0.131913	+	0.0480123i
$86$		0			0
$87$	6.51266	+	11.2803i	0.698230	+	1.20937i
$88$		0			0
$89$	1.26006	−	7.14615i	0.133566	−	0.757490i	−0.842282	−	0.539038i	$-0.818788\pi$
$89$	1.26006	−	7.14615i	0.133566	−	0.757490i	0.975848	−	0.218453i	$-0.0701009\pi$
$90$		0			0
$91$	2.35244	+	1.97393i	0.246603	+	0.206924i
$92$		0			0
$93$	10.0509	+	3.65823i	1.04223	+	0.379341i
$94$		0			0
$95$	3.19074	−	2.96971i	0.327363	−	0.304686i
$96$		0			0
$97$	7.40807	+	2.69632i	0.752176	+	0.273770i	0.689521	−	0.724266i	$-0.257821\pi$
$97$	7.40807	+	2.69632i	0.752176	+	0.273770i	0.0626549	+	0.998035i	$0.480043\pi$
$98$		0			0
$99$	1.16730	+	0.979484i	0.117318	+	0.0984419i
$100$		0			0
$101$	−2.35954	+	13.3816i	−0.234783	+	1.33152i	0.608289	+	0.793716i	$0.291856\pi$
$101$	−2.35954	+	13.3816i	−0.234783	+	1.33152i	−0.843071	+	0.537802i	$0.819255\pi$
$102$		0			0
$103$	5.39106	+	9.33758i	0.531197	+	0.920060i	0.999337	+	0.0364055i	$0.0115908\pi$
$103$	5.39106	+	9.33758i	0.531197	+	0.920060i	−0.468140	+	0.883654i	$0.655076\pi$
$104$		0			0
$105$	−1.13878	+	0.414482i	−0.111134	+	0.0404493i
$106$		0			0
$107$	−0.555176	+	0.961592i	−0.0536708	+	0.0929606i	−0.891613	−	0.452799i	$-0.850426\pi$
$107$	−0.555176	+	0.961592i	−0.0536708	+	0.0929606i	0.837942	+	0.545760i	$0.183759\pi$
$108$		0			0
$109$	1.91957	−	1.61071i	0.183862	−	0.154278i	−0.546211	−	0.837647i	$-0.683930\pi$
$109$	1.91957	−	1.61071i	0.183862	−	0.154278i	0.730073	+	0.683369i	$0.239486\pi$
$110$		0			0
$111$	−3.61492	−	20.5012i	−0.343113	−	1.94589i
$112$		0			0
$113$	−14.8298			−1.39507			−0.697536	−	0.716550i	$-0.745720\pi$
$113$	−14.8298			−1.39507			−0.697536	+	0.716550i	$0.745720\pi$
$114$		0			0
$115$	1.35993			0.126814
$116$		0			0
$117$	0.187752	+	1.06479i	0.0173576	+	0.0984401i
$118$		0			0
$119$	−0.667786	+	0.560339i	−0.0612158	+	0.0513662i
$120$		0			0
$121$	−15.1436	+	26.2295i	−1.37669	+	2.38450i
$122$		0			0
$123$	−4.51459	+	1.64317i	−0.407067	+	0.148160i
$124$		0			0
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$		0			0
$127$	−1.01635	+	5.76401i	−0.0901865	+	0.511473i	0.905930	+	0.423428i	$0.139173\pi$
$127$	−1.01635	+	5.76401i	−0.0901865	+	0.511473i	−0.996116	+	0.0880454i	$0.971938\pi$
$128$		0			0
$129$	−13.1658	−	11.0474i	−1.15918	−	0.972671i
$130$		0			0
$131$	7.64603	+	2.78293i	0.668037	+	0.243146i	0.653702	−	0.756752i	$-0.273215\pi$
$131$	7.64603	+	2.78293i	0.668037	+	0.243146i	0.0143345	+	0.999897i	$0.495437\pi$
$132$		0			0
$133$	1.33540	−	2.61468i	0.115794	−	0.226722i
$134$		0			0
$135$	4.67116	+	1.70016i	0.402029	+	0.146327i
$136$		0			0
$137$	3.81357	+	3.19997i	0.325816	+	0.273392i	0.790992	−	0.611826i	$-0.209565\pi$
$137$	3.81357	+	3.19997i	0.325816	+	0.273392i	−0.465177	+	0.885218i	$0.654009\pi$
$138$		0			0
$139$	0.364121	−	2.06503i	0.0308843	−	0.175154i	−0.965464	−	0.260537i	$-0.916100\pi$
$139$	0.364121	−	2.06503i	0.0308843	−	0.175154i	0.996348	+	0.0853833i	$0.0272115\pi$
$140$		0			0
$141$	−10.5733	−	18.3135i	−0.890434	−	1.54228i
$142$		0			0
$143$	−27.5287	+	10.0196i	−2.30206	+	0.837882i
$144$		0			0
$145$	3.61974	−	6.26957i	0.300603	−	0.520659i
$146$		0			0
$147$	9.02262	−	7.57088i	0.744173	−	0.624436i
$148$		0			0
$149$	−1.49492	−	8.47813i	−0.122469	−	0.694556i	−0.982779	−	0.184785i	$-0.940841\pi$
$149$	−1.49492	−	8.47813i	−0.122469	−	0.694556i	0.860310	−	0.509771i	$-0.170270\pi$
$150$		0			0
$151$	18.3265			1.49139			0.745693	−	0.666289i	$-0.232118\pi$
$151$	18.3265			1.49139			0.745693	+	0.666289i	$0.232118\pi$
$152$		0			0
$153$	−0.306925			−0.0248134
$154$		0			0
$155$	−1.03231	−	5.85450i	−0.0829168	−	0.470245i
$156$		0			0
$157$	10.2264	−	8.58096i	0.816155	−	0.684835i	−0.135913	−	0.990721i	$-0.543397\pi$
$157$	10.2264	−	8.58096i	0.816155	−	0.684835i	0.952068	+	0.305885i	$0.0989524\pi$
$158$		0			0
$159$	−3.22509	+	5.58602i	−0.255766	+	0.443000i
$160$		0			0
$161$	0.860745	−	0.313285i	0.0678362	−	0.0246904i
$162$		0			0
$163$	10.7658	+	18.6469i	0.843240	+	1.46053i	0.887141	+	0.461498i	$0.152688\pi$
$163$	10.7658	+	18.6469i	0.843240	+	1.46053i	−0.0439014	+	0.999036i	$0.513979\pi$
$164$		0			0
$165$	2.00752	−	11.3852i	0.156285	−	0.886337i
$166$		0			0
$167$	−9.32714	−	7.82640i	−0.721756	−	0.605625i	0.206115	−	0.978528i	$-0.433918\pi$
$167$	−9.32714	−	7.82640i	−0.721756	−	0.605625i	−0.927870	+	0.372903i	$0.878362\pi$
$168$		0			0
$169$	−7.31698	−	2.66316i	−0.562844	−	0.204859i
$170$		0			0
$171$	0.951921	−	0.402993i	0.0727952	−	0.0308176i
$172$		0			0
$173$	2.03095	+	0.739205i	0.154410	+	0.0562007i	0.418069	−	0.908415i	$-0.362707\pi$
$173$	2.03095	+	0.739205i	0.154410	+	0.0562007i	−0.263659	+	0.964616i	$0.584929\pi$
$174$		0			0
$175$	0.515973	+	0.432953i	0.0390039	+	0.0327282i
$176$		0			0
$177$	0.0500168	−	0.283659i	0.00375949	−	0.0213212i
$178$		0			0
$179$	−9.07390	−	15.7164i	−0.678215	−	1.17470i	−0.975518	−	0.219919i	$-0.929421\pi$
$179$	−9.07390	−	15.7164i	−0.678215	−	1.17470i	0.297303	−	0.954783i	$-0.403913\pi$
$180$		0			0
$181$	7.02363	−	2.55639i	0.522062	−	0.190015i	−0.0675283	−	0.997717i	$-0.521511\pi$
$181$	7.02363	−	2.55639i	0.522062	−	0.190015i	0.589591	+	0.807702i	$0.299289\pi$
$182$		0			0
$183$	6.51723	−	11.2882i	0.481768	−	0.834446i
$184$		0			0
$185$	−8.86342	+	7.43729i	−0.651652	+	0.546801i
$186$		0			0
$187$	−1.44407	−	8.18973i	−0.105601	−	0.598893i
$188$		0			0
$189$	3.34820			0.243546
$190$		0			0
$191$	−21.9662			−1.58942			−0.794710	−	0.606990i	$-0.792377\pi$
$191$	−21.9662			−1.58942			−0.794710	+	0.606990i	$0.792377\pi$
$192$		0			0
$193$	−2.07436	−	11.7643i	−0.149315	−	0.846810i	−0.963800	−	0.266625i	$-0.914091\pi$
$193$	−2.07436	−	11.7643i	−0.149315	−	0.846810i	0.814485	−	0.580185i	$-0.197020\pi$
$194$		0			0
$195$	6.28386	−	5.27279i	0.449997	−	0.377592i
$196$		0			0
$197$	3.87650	−	6.71430i	0.276189	−	0.478374i	−0.694245	−	0.719739i	$-0.744262\pi$
$197$	3.87650	−	6.71430i	0.276189	−	0.478374i	0.970435	+	0.241365i	$0.0775950\pi$
$198$		0			0
$199$	8.65867	−	3.15150i	0.613797	−	0.223404i	−0.0163667	−	0.999866i	$-0.505210\pi$
$199$	8.65867	−	3.15150i	0.613797	−	0.223404i	0.630164	+	0.776462i	$0.282988\pi$
$200$		0			0
$201$	4.91605	+	8.51484i	0.346751	+	0.600591i
$202$		0			0
$203$	0.846740	−	4.80210i	0.0594295	−	0.337042i
$204$		0			0
$205$	2.04552	+	1.71640i	0.142866	+	0.119879i
$206$		0			0
$207$	0.303056	+	0.110303i	0.0210639	+	0.00766662i
$208$		0			0
$209$	15.2319	+	23.5042i	1.05361	+	1.62582i
$210$		0			0
$211$	−19.3970	−	7.05994i	−1.33535	−	0.486027i	−0.427003	−	0.904250i	$-0.640431\pi$
$211$	−19.3970	−	7.05994i	−1.33535	−	0.486027i	−0.908344	+	0.418224i	$0.862653\pi$
$212$		0			0
$213$	−16.2052	−	13.5978i	−1.11036	−	0.931703i
$214$		0			0
$215$	−1.65876	+	9.40727i	−0.113126	+	0.641570i
$216$		0			0
$217$	−2.00208	−	3.46770i	−0.135910	−	0.235403i
$218$		0			0
$219$	−6.26061	+	2.27867i	−0.423053	+	0.153979i
$220$		0			0
$221$	2.95034	−	5.11013i	0.198461	−	0.343745i
$222$		0			0
$223$	−1.80840	+	1.51742i	−0.121099	+	0.101614i	−0.701326	−	0.712841i	$-0.747408\pi$
$223$	−1.80840	+	1.51742i	−0.121099	+	0.101614i	0.580227	+	0.814455i	$0.302964\pi$
$224$		0			0
$225$	0.0411806	+	0.233547i	0.00274537	+	0.0155698i
$226$		0			0
$227$	−15.3448			−1.01847			−0.509236	−	0.860627i	$-0.670072\pi$
$227$	−15.3448			−1.01847			−0.509236	+	0.860627i	$0.670072\pi$
$228$		0			0
$229$	9.54861			0.630990			0.315495	−	0.948927i	$-0.397829\pi$
$229$	9.54861			0.630990			0.315495	+	0.948927i	$0.397829\pi$
$230$		0			0
$231$	−1.35217	−	7.66856i	−0.0889665	−	0.504554i
$232$		0			0
$233$	19.8464	−	16.6531i	1.30018	−	1.09098i	0.310069	−	0.950714i	$-0.399648\pi$
$233$	19.8464	−	16.6531i	1.30018	−	1.09098i	0.990113	−	0.140269i	$-0.0447966\pi$
$234$		0			0
$235$	−5.87665	+	10.1787i	−0.383351	+	0.663983i
$236$		0			0
$237$	−10.8626	+	3.95365i	−0.705600	+	0.256817i
$238$		0			0
$239$	−7.42312	−	12.8572i	−0.480162	−	0.831665i	0.519579	−	0.854422i	$-0.326089\pi$
$239$	−7.42312	−	12.8572i	−0.480162	−	0.831665i	−0.999741	+	0.0227574i	$0.992755\pi$
$240$		0			0
$241$	3.35050	−	19.0016i	0.215825	−	1.22400i	−0.663645	−	0.748048i	$-0.730992\pi$
$241$	3.35050	−	19.0016i	0.215825	−	1.22400i	0.879470	−	0.475955i	$-0.157897\pi$
$242$		0			0
$243$	1.88363	+	1.58055i	0.120835	+	0.101392i
$244$		0			0
$245$	−6.15153	−	2.23897i	−0.393007	−	0.143043i
$246$		0			0
$247$	−2.44080	+	19.7228i	−0.155304	+	1.25493i
$248$		0			0
$249$	8.52963	+	3.10453i	0.540543	+	0.196742i
$250$		0			0
$251$	14.5731	+	12.2283i	0.919848	+	0.771844i	0.973967	−	0.226690i	$-0.0727905\pi$
$251$	14.5731	+	12.2283i	0.919848	+	0.771844i	−0.0541187	+	0.998535i	$0.517235\pi$
$252$		0			0
$253$	−1.51738	+	8.60548i	−0.0953967	+	0.541022i
$254$		0			0
$255$	1.16429	+	2.01661i	0.0729108	+	0.126285i
$256$		0			0
$257$	−11.1329	+	4.05205i	−0.694453	+	0.252760i	−0.665041	−	0.746807i	$-0.731586\pi$
$257$	−11.1329	+	4.05205i	−0.694453	+	0.252760i	−0.0294123	+	0.999567i	$0.509364\pi$
$258$		0			0
$259$	−3.89664	+	6.74918i	−0.242125	+	0.419374i
$260$		0			0
$261$	1.31517	−	1.10356i	0.0814072	−	0.0683087i
$262$		0			0
$263$	0.705433	+	4.00071i	0.0434989	+	0.246694i	0.998802	−	0.0489336i	$-0.0155823\pi$
$263$	0.705433	+	4.00071i	0.0434989	+	0.246694i	−0.955303	+	0.295628i	$0.904471\pi$
$264$		0			0
$265$	3.58501			0.220225
$266$		0			0
$267$	−13.0558			−0.798999
$268$		0			0
$269$	0.882623	+	5.00561i	0.0538145	+	0.305197i	0.999820	−	0.0189522i	$-0.00603304\pi$
$269$	0.882623	+	5.00561i	0.0538145	+	0.305197i	−0.946006	+	0.324149i	$0.894922\pi$
$270$		0			0
$271$	−11.4535	+	9.61062i	−0.695750	+	0.583804i	−0.920561	−	0.390599i	$-0.872268\pi$
$271$	−11.4535	+	9.61062i	−0.695750	+	0.583804i	0.224811	+	0.974402i	$0.427824\pi$
$272$		0			0
$273$	2.76259	−	4.78494i	0.167199	−	0.289598i
$274$		0			0
$275$	−6.03801	+	2.19766i	−0.364106	+	0.132524i
$276$		0			0
$277$	−6.04752	−	10.4746i	−0.363361	−	0.629359i	0.625151	−	0.780504i	$-0.285037\pi$
$277$	−6.04752	−	10.4746i	−0.363361	−	0.629359i	−0.988512	+	0.151145i	$0.951704\pi$
$278$		0			0
$279$	0.244811	−	1.38839i	0.0146564	−	0.0831208i
$280$		0			0
$281$	16.7076	+	14.0193i	0.996690	+	0.836322i	0.986522	−	0.163626i	$-0.0523190\pi$
$281$	16.7076	+	14.0193i	0.996690	+	0.836322i	0.0101678	+	0.999948i	$0.496763\pi$
$282$		0			0
$283$	15.0489	+	5.47733i	0.894561	+	0.325594i	0.748071	−	0.663618i	$-0.230980\pi$
$283$	15.0489	+	5.47733i	0.894561	+	0.325594i	0.146490	+	0.989212i	$0.453202\pi$
$284$		0			0
$285$	−6.25884	−	4.72576i	−0.370741	−	0.279930i
$286$		0			0
$287$	1.69009	+	0.615142i	0.0997628	+	0.0363107i
$288$		0			0
$289$	−11.7396	−	9.85071i	−0.690566	−	0.579453i
$290$		0			0
$291$	2.46304	−	13.9686i	0.144386	−	0.818853i
$292$		0			0
$293$	−3.15924	−	5.47196i	−0.184565	−	0.319675i	0.758865	−	0.651248i	$-0.225754\pi$
$293$	−3.15924	−	5.47196i	−0.184565	−	0.319675i	−0.943430	+	0.331573i	$0.892421\pi$
$294$		0			0
$295$	−0.150435	+	0.0547540i	−0.00875869	+	0.00318790i
$296$		0			0
$297$	−15.9704	+	27.6616i	−0.926699	+	1.60509i
$298$		0			0
$299$	−4.74964	+	3.98542i	−0.274679	+	0.230483i
$300$		0			0
$301$	1.11726	+	6.33631i	0.0643980	+	0.365219i
$302$		0			0
$303$	24.4477			1.40448
$304$		0			0
$305$	−7.24456			−0.414822
$306$		0			0
$307$	−0.139362	−	0.790360i	−0.00795380	−	0.0451082i	0.980573	−	0.196157i	$-0.0628461\pi$
$307$	−0.139362	−	0.790360i	−0.00795380	−	0.0451082i	−0.988526	+	0.151049i	$0.951735\pi$
$308$		0			0
$309$	14.8607	−	12.4696i	0.845396	−	0.709371i
$310$		0			0
$311$	−7.02192	+	12.1623i	−0.398176	+	0.689662i	−0.993501	−	0.113824i	$-0.963690\pi$
$311$	−7.02192	+	12.1623i	−0.398176	+	0.689662i	0.595325	+	0.803485i	$0.297023\pi$
$312$		0			0
$313$	−20.5637	+	7.48459i	−1.16233	+	0.423054i	−0.849930	−	0.526896i	$-0.823356\pi$
$313$	−20.5637	+	7.48459i	−1.16233	+	0.423054i	−0.312402	+	0.949950i	$0.601133\pi$
$314$		0			0
$315$	0.0798666	+	0.138333i	0.00449997	+	0.00779418i
$316$		0			0
$317$	5.41832	−	30.7288i	0.304323	−	1.72590i	−0.322350	−	0.946621i	$-0.604473\pi$
$317$	5.41832	−	30.7288i	0.304323	−	1.72590i	0.626673	−	0.779282i	$-0.284416\pi$
$318$		0			0
$319$	35.6344	+	29.9008i	1.99514	+	1.67412i
$320$		0			0
$321$	1.87727	+	0.683272i	0.104779	+	0.0381365i
$322$		0			0
$323$	−5.39332	−	1.65454i	−0.300092	−	0.0920613i
$324$		0			0
$325$	−4.28427	−	1.55935i	−0.237649	−	0.0864971i
$326$		0			0
$327$	−3.45371	−	2.89801i	−0.190991	−	0.160260i
$328$		0			0
$329$	−1.37469	+	7.79623i	−0.0757888	+	0.429820i
$330$		0			0
$331$	−5.88658	−	10.1959i	−0.323556	−	0.560415i	0.657663	−	0.753312i	$-0.271545\pi$
$331$	−5.88658	−	10.1959i	−0.323556	−	0.560415i	−0.981219	+	0.192897i	$0.938212\pi$
$332$		0			0
$333$	−2.57843	+	0.938471i	−0.141297	+	0.0514279i
$334$		0			0
$335$	2.73234	−	4.73255i	0.149284	−	0.258567i
$336$		0			0
$337$	7.27071	−	6.10085i	0.396061	−	0.332335i	−0.422908	−	0.906173i	$-0.638991\pi$
$337$	7.27071	−	6.10085i	0.396061	−	0.332335i	0.818969	+	0.573838i	$0.194546\pi$
$338$		0			0
$339$	4.63327	+	26.2766i	0.251645	+	1.42715i
$340$		0			0
$341$	38.1985			2.06856
$342$		0			0
$343$	−9.12419			−0.492660
$344$		0			0
$345$	−0.424881	−	2.40962i	−0.0228748	−	0.129730i
$346$		0			0
$347$	9.01036	−	7.56059i	0.483701	−	0.405874i	−0.368061	−	0.929802i	$-0.619978\pi$
$347$	9.01036	−	7.56059i	0.483701	−	0.405874i	0.851763	+	0.523928i	$0.175534\pi$
$348$		0			0
$349$	−6.21201	+	10.7595i	−0.332521	+	0.575944i	−0.983006	−	0.183576i	$-0.941233\pi$
$349$	−6.21201	+	10.7595i	−0.332521	+	0.575944i	0.650484	+	0.759520i	$0.274566\pi$
$350$		0			0
$351$	−21.2969	+	7.75143i	−1.13674	+	0.413741i
$352$		0			0
$353$	−5.73224	−	9.92852i	−0.305096	−	0.528442i	0.672187	−	0.740382i	$-0.265355\pi$
$353$	−5.73224	−	9.92852i	−0.305096	−	0.528442i	−0.977283	+	0.211940i	$0.932022\pi$
$354$		0			0
$355$	−2.04169	+	11.5790i	−0.108361	+	0.614548i
$356$		0			0
$357$	1.20149	+	1.00817i	0.0635894	+	0.0533578i
$358$		0			0
$359$	29.1144	+	10.5968i	1.53660	+	0.559277i	0.965227	−	0.261413i	$-0.0841885\pi$
$359$	29.1144	+	10.5968i	1.53660	+	0.559277i	0.571374	+	0.820690i	$0.306411\pi$
$360$		0			0
$361$	18.8997	−	1.94990i	0.994720	−	0.102626i
$362$		0			0
$363$	51.2067	+	18.6377i	2.68766	+	0.978227i
$364$		0			0
$365$	2.83663	+	2.38022i	0.148476	+	0.124586i
$366$		0			0
$367$	−0.782062	+	4.43529i	−0.0408233	+	0.231520i	−0.998392	−	0.0566842i	$-0.981947\pi$
$367$	−0.782062	+	4.43529i	−0.0408233	+	0.231520i	0.957569	+	0.288205i	$0.0930583\pi$
$368$		0			0
$369$	0.316623	+	0.548407i	0.0164827	+	0.0285490i
$370$		0			0
$371$	2.26908	−	0.825877i	0.117805	−	0.0428774i
$372$		0			0
$373$	9.56116	−	16.5604i	0.495058	−	0.857466i	−0.504926	−	0.863163i	$-0.668480\pi$
$373$	9.56116	−	16.5604i	0.495058	−	0.857466i	0.999984	+	0.00569689i	$0.00181339\pi$
$374$		0			0
$375$	1.37827	−	1.15651i	0.0711737	−	0.0597218i
$376$		0			0
$377$	5.73150	+	32.5050i	0.295187	+	1.67409i
$378$		0			0
$379$	−1.21152			−0.0622314			−0.0311157	−	0.999516i	$-0.509906\pi$
$379$	−1.21152			−0.0622314			−0.0311157	+	0.999516i	$0.509906\pi$
$380$		0			0
$381$	10.5306			0.539501
$382$		0			0
$383$	1.06603	+	6.04574i	0.0544715	+	0.308923i	0.999855	−	0.0170375i	$-0.00542347\pi$
$383$	1.06603	+	6.04574i	0.0544715	+	0.308923i	−0.945383	+	0.325960i	$0.894312\pi$
$384$		0			0
$385$	−3.31539	+	2.78194i	−0.168968	+	0.141781i
$386$		0			0
$387$	−1.13267	+	1.96185i	−0.0575769	+	0.0997262i
$388$		0			0
$389$	0.111964	−	0.0407516i	0.00567680	−	0.00206619i	−0.339180	−	0.940721i	$-0.610150\pi$
$389$	0.111964	−	0.0407516i	0.00567680	−	0.00206619i	0.344857	+	0.938655i	$0.387927\pi$
$390$		0			0
$391$	−0.880027	−	1.52425i	−0.0445049	−	0.0770847i
$392$		0			0
$393$	2.54215	−	14.4173i	0.128235	−	0.727255i
$394$		0			0
$395$	4.92175	+	4.12984i	0.247640	+	0.207795i
$396$		0			0
$397$	2.58876	+	0.942231i	0.129926	+	0.0472892i	0.406165	−	0.913800i	$-0.366866\pi$
$397$	2.58876	+	0.942231i	0.129926	+	0.0472892i	−0.276239	+	0.961089i	$0.589088\pi$
$398$		0			0
$399$	−5.05010	−	1.54925i	−0.252821	−	0.0775597i
$400$		0			0
$401$	−20.4922	−	7.45853i	−1.02333	−	0.372461i	−0.224792	−	0.974407i	$-0.572170\pi$
$401$	−20.4922	−	7.45853i	−1.02333	−	0.372461i	−0.798537	+	0.601945i	$0.794392\pi$
$402$		0			0
$403$	20.7627	+	17.4220i	1.03426	+	0.867850i
$404$		0			0
$405$	1.67661	−	9.50852i	0.0833114	−	0.472482i
$406$		0			0
$407$	−37.1728	−	64.3852i	−1.84259	−	3.19146i
$408$		0			0
$409$	−14.6340	+	5.32635i	−0.723605	+	0.263371i	−0.677456	−	0.735564i	$-0.736917\pi$
$409$	−14.6340	+	5.32635i	−0.723605	+	0.263371i	−0.0461499	+	0.998935i	$0.514695\pi$
$410$		0			0
$411$	4.47847	−	7.75694i	0.220907	−	0.382622i
$412$		0			0
$413$	−0.0826022	+	0.0693114i	−0.00406459	+	0.00341059i
$414$		0			0
$415$	−0.876059	−	4.96838i	−0.0430040	−	0.243888i
$416$		0			0
$417$	−3.77274			−0.184752
$418$		0			0
$419$	−15.2596			−0.745479			−0.372739	−	0.927936i	$-0.621581\pi$
$419$	−15.2596			−0.745479			−0.372739	+	0.927936i	$0.621581\pi$
$420$		0			0
$421$	1.42403	+	8.07607i	0.0694029	+	0.393603i	0.999645	+	0.0266562i	$0.00848593\pi$
$421$	1.42403	+	8.07607i	0.0694029	+	0.393603i	−0.930242	+	0.366947i	$0.880403\pi$
$422$		0			0
$423$	−2.13519	+	1.79163i	−0.103816	+	0.0871123i
$424$		0			0
$425$	0.647113	−	1.12083i	0.0313896	−	0.0543684i
$426$		0			0
$427$	−4.58533	+	1.66892i	−0.221900	+	0.0807649i
$428$		0			0
$429$	26.3543	+	45.6469i	1.27240	+	2.20385i
$430$		0			0
$431$	−1.44591	+	8.20017i	−0.0696471	+	0.394988i	0.929978	+	0.367615i	$0.119825\pi$
$431$	−1.44591	+	8.20017i	−0.0696471	+	0.394988i	−0.999625	+	0.0273736i	$0.991286\pi$
$432$		0			0
$433$	26.0125	+	21.8271i	1.25008	+	1.04894i	0.996666	+	0.0815863i	$0.0259986\pi$
$433$	26.0125	+	21.8271i	1.25008	+	1.04894i	0.253416	+	0.967357i	$0.418446\pi$
$434$		0			0
$435$	−12.2398	−	4.45492i	−0.586853	−	0.213597i
$436$		0			0
$437$	4.73072	+	3.57195i	0.226301	+	0.170870i
$438$		0			0
$439$	11.7612	+	4.28073i	0.561331	+	0.204308i	0.607074	−	0.794645i	$-0.292343\pi$
$439$	11.7612	+	4.28073i	0.561331	+	0.204308i	−0.0457426	+	0.998953i	$0.514565\pi$
$440$		0			0
$441$	−1.18925	−	0.997900i	−0.0566310	−	0.0475190i
$442$		0			0
$443$	−4.04892	+	22.9625i	−0.192370	+	1.09098i	0.723745	+	0.690068i	$0.242419\pi$
$443$	−4.04892	+	22.9625i	−0.192370	+	1.09098i	−0.916115	+	0.400916i	$0.868692\pi$
$444$		0			0
$445$	3.62820	+	6.28422i	0.171993	+	0.297901i
$446$		0			0
$447$	−14.5551	+	5.29763i	−0.688434	+	0.250569i
$448$		0			0
$449$	10.7619	−	18.6402i	0.507887	−	0.879686i	−0.492072	−	0.870555i	$-0.663760\pi$
$449$	10.7619	−	18.6402i	0.507887	−	0.879686i	0.999958	−	0.00913096i	$-0.00290651\pi$
$450$		0			0
$451$	−13.1436	+	11.0287i	−0.618906	+	0.519324i
$452$		0			0
$453$	−5.72572	−	32.4722i	−0.269018	−	1.52568i
$454$		0			0
$455$	−3.07089			−0.143966
$456$		0			0
$457$	−30.0765			−1.40692			−0.703459	−	0.710735i	$-0.748362\pi$
$457$	−30.0765			−1.40692			−0.703459	+	0.710735i	$0.748362\pi$
$458$		0			0
$459$	−1.11717	−	6.33579i	−0.0521450	−	0.295729i
$460$		0			0
$461$	14.5942	−	12.2459i	0.679717	−	0.570351i	−0.236206	−	0.971703i	$-0.575904\pi$
$461$	14.5942	−	12.2459i	0.679717	−	0.570351i	0.915924	+	0.401352i	$0.131460\pi$
$462$		0			0
$463$	10.2775	−	17.8012i	0.477637	−	0.827292i	−0.522034	−	0.852925i	$-0.674827\pi$
$463$	10.2775	−	17.8012i	0.477637	−	0.827292i	0.999671	+	0.0256324i	$0.00815994\pi$
$464$		0			0
$465$	−10.0509	+	3.65823i	−0.466100	+	0.169646i
$466$		0			0
$467$	20.2855	+	35.1354i	0.938699	+	1.62587i	0.767901	+	0.640568i	$0.221301\pi$
$467$	20.2855	+	35.1354i	0.938699	+	1.62587i	0.170798	+	0.985306i	$0.445366\pi$
$468$		0			0
$469$	0.639157	−	3.62484i	0.0295135	−	0.167380i
$470$		0			0
$471$	−18.3994	−	15.4389i	−0.847800	−	0.711389i
$472$		0			0
$473$	−57.6774	−	20.9929i	−2.65201	−	0.965253i
$474$		0			0
$475$	−0.535353	+	4.32590i	−0.0245637	+	0.198486i
$476$		0			0
$477$	0.798911	+	0.290780i	0.0365796	+	0.0133139i
$478$		0			0
$479$	9.78854	+	8.21356i	0.447250	+	0.375287i	0.838414	−	0.545034i	$-0.183483\pi$
$479$	9.78854	+	8.21356i	0.447250	+	0.375287i	−0.391164	+	0.920321i	$0.627928\pi$
$480$		0			0
$481$	9.16028	−	51.9506i	0.417673	−	2.36874i
$482$		0			0
$483$	−0.824024	−	1.42725i	−0.0374944	−	0.0649422i
$484$		0			0
$485$	−7.40807	+	2.69632i	−0.336383	+	0.122434i
$486$		0			0
$487$	0.754890	−	1.30751i	0.0342074	−	0.0592489i	−0.848415	−	0.529332i	$-0.822443\pi$
$487$	0.754890	−	1.30751i	0.0342074	−	0.0592489i	0.882622	+	0.470083i	$0.155776\pi$
$488$		0			0
$489$	29.6763	−	24.9014i	1.34201	−	1.12608i
$490$		0			0
$491$	5.10731	+	28.9650i	0.230490	+	1.30717i	0.851907	+	0.523693i	$0.175446\pi$
$491$	5.10731	+	28.9650i	0.230490	+	1.30717i	−0.621417	+	0.783480i	$0.713443\pi$
$492$		0			0
$493$	−9.36952			−0.421982
$494$		0			0
$495$	−1.52381			−0.0684900
$496$		0			0
$497$	1.37519	+	7.79907i	0.0616856	+	0.349836i
$498$		0			0
$499$	13.7504	−	11.5379i	0.615551	−	0.516509i	−0.280850	−	0.959752i	$-0.590616\pi$
$499$	13.7504	−	11.5379i	0.615551	−	0.516509i	0.896402	+	0.443243i	$0.146172\pi$
$500$		0			0
$501$	−10.9533	+	18.9717i	−0.489358	+	0.847594i
$502$		0			0
$503$	−6.63252	+	2.41404i	−0.295730	+	0.107637i	−0.485624	−	0.874168i	$-0.661408\pi$
$503$	−6.63252	+	2.41404i	−0.295730	+	0.107637i	0.189895	+	0.981804i	$0.439185\pi$
$504$		0			0
$505$	−6.79401	−	11.7676i	−0.302330	−	0.523650i
$506$		0			0
$507$	−2.43275	+	13.7968i	−0.108042	+	0.612738i
$508$		0			0
$509$	−5.30918	−	4.45493i	−0.235325	−	0.197461i	0.517497	−	0.855685i	$-0.326864\pi$
$509$	−5.30918	−	4.45493i	−0.235325	−	0.197461i	−0.752823	+	0.658224i	$0.771308\pi$
$510$		0			0
$511$	2.34373	+	0.853049i	0.103681	+	0.0377367i
$512$		0			0
$513$	11.7838	+	18.1835i	0.520266	+	0.802819i
$514$		0			0
$515$	−10.1319	−	3.68770i	−0.446464	−	0.162499i
$516$		0			0
$517$	−57.8525	−	48.5440i	−2.54435	−	2.13496i
$518$		0			0
$519$	0.675251	−	3.82954i	0.0296402	−	0.168098i
$520$		0			0
$521$	18.3552	+	31.7921i	0.804155	+	1.39284i	0.916860	+	0.399208i	$0.130715\pi$
$521$	18.3552	+	31.7921i	0.804155	+	1.39284i	−0.112705	+	0.993628i	$0.535952\pi$
$522$		0			0
$523$	3.83828	−	1.39702i	0.167836	−	0.0610874i	−0.256736	−	0.966482i	$-0.582647\pi$
$523$	3.83828	−	1.39702i	0.167836	−	0.0610874i	0.424572	+	0.905394i	$0.360425\pi$
$524$		0			0
$525$	0.605933	−	1.04951i	0.0264451	−	0.0458042i
$526$		0			0
$527$	−5.89390	+	4.94557i	−0.256742	+	0.215432i
$528$		0			0
$529$	−3.67276	−	20.8293i	−0.159685	−	0.905621i
$530$		0			0
$531$	−0.0379653			−0.00164755
$532$		0			0
$533$	−12.1742			−0.527325
$534$		0			0
$535$	−0.192810	−	1.09348i	−0.00833592	−	0.0472754i
$536$		0			0
$537$	−25.0126	+	20.9881i	−1.07937	+	0.905702i
$538$		0			0
$539$	21.0318	−	36.4281i	0.905902	−	1.56907i
$540$		0			0
$541$	−32.7657	+	11.9257i	−1.40871	+	0.512727i	−0.930750	−	0.365657i	$-0.880844\pi$
$541$	−32.7657	+	11.9257i	−1.40871	+	0.512727i	−0.477956	+	0.878384i	$0.658622\pi$
$542$		0			0
$543$	−6.72399	−	11.6463i	−0.288554	−	0.499790i
$544$		0			0
$545$	−0.435132	+	2.46776i	−0.0186390	+	0.105707i
$546$		0			0
$547$	−12.1746	−	10.2157i	−0.520548	−	0.436792i	0.344275	−	0.938869i	$-0.388125\pi$
$547$	−12.1746	−	10.2157i	−0.520548	−	0.436792i	−0.864823	+	0.502077i	$0.832569\pi$
$548$		0			0
$549$	−1.61443	−	0.587605i	−0.0689022	−	0.0250784i
$550$		0			0
$551$	29.0594	−	12.3022i	1.23797	−	0.524090i
$552$		0			0
$553$	4.06654	+	1.48010i	0.172927	+	0.0629402i
$554$		0			0
$555$	15.9471	+	13.3812i	0.676918	+	0.568002i
$556$		0			0
$557$	−1.82337	+	10.3409i	−0.0772588	+	0.438156i	0.921501	+	0.388375i	$0.126963\pi$
$557$	−1.82337	+	10.3409i	−0.0772588	+	0.438156i	−0.998760	+	0.0497811i	$0.984148\pi$
$558$		0			0
$559$	−21.7758	−	37.7167i	−0.921017	−	1.59525i
$560$		0			0
$561$	−14.0600	+	5.11742i	−0.593614	+	0.216058i
$562$		0			0
$563$	−3.48851	+	6.04227i	−0.147023	+	0.254651i	−0.930126	−	0.367241i	$-0.880302\pi$
$563$	−3.48851	+	6.04227i	−0.147023	+	0.254651i	0.783103	+	0.621892i	$0.213636\pi$
$564$		0			0
$565$	11.3603	−	9.53242i	0.477931	−	0.401032i
$566$		0			0
$567$	−1.12929	−	6.40451i	−0.0474257	−	0.268964i
$568$		0			0
$569$	−25.5455			−1.07092			−0.535461	−	0.844560i	$-0.679862\pi$
$569$	−25.5455			−1.07092			−0.535461	+	0.844560i	$0.679862\pi$
$570$		0			0
$571$	−1.23193			−0.0515548			−0.0257774	−	0.999668i	$-0.508206\pi$
$571$	−1.23193			−0.0515548			−0.0257774	+	0.999668i	$0.508206\pi$
$572$		0			0
$573$	6.86289	+	38.9214i	0.286701	+	1.62596i
$574$		0			0
$575$	−1.04176	+	0.874144i	−0.0434446	+	0.0364543i
$576$		0			0
$577$	−2.53389	+	4.38883i	−0.105487	+	0.182710i	−0.913937	−	0.405856i	$-0.866974\pi$
$577$	−2.53389	+	4.38883i	−0.105487	+	0.182710i	0.808450	+	0.588565i	$0.200307\pi$
$578$		0			0
$579$	−20.1967	+	7.35100i	−0.839346	+	0.305497i
$580$		0			0
$581$	−1.69905	−	2.94284i	−0.0704885	−	0.122090i
$582$		0			0
$583$	−4.00008	+	22.6856i	−0.165666	+	0.939541i
$584$		0			0
$585$	−0.828261	−	0.694994i	−0.0342444	−	0.0287344i
$586$		0			0
$587$	23.1177	+	8.41416i	0.954170	+	0.347290i	0.771746	−	0.635930i	$-0.219384\pi$
$587$	23.1177	+	8.41416i	0.954170	+	0.347290i	0.182424	+	0.983220i	$0.441606\pi$
$588$		0			0
$589$	11.7863	−	23.0772i	0.485644	−	0.950881i
$590$		0			0
$591$	−13.1080	−	4.77093i	−0.539192	−	0.196250i
$592$		0			0
$593$	16.6285	+	13.9530i	0.682852	+	0.572981i	0.916838	−	0.399259i	$-0.130733\pi$
$593$	16.6285	+	13.9530i	0.682852	+	0.572981i	−0.233986	+	0.972240i	$0.575177\pi$
$594$		0			0
$595$	0.151375	−	0.858489i	0.00620576	−	0.0351946i
$596$		0			0
$597$	−8.28928	−	14.3575i	−0.339258	−	0.587612i
$598$		0			0
$599$	35.2847	−	12.8426i	1.44169	−	0.524734i	0.501435	−	0.865195i	$-0.332806\pi$
$599$	35.2847	−	12.8426i	1.44169	−	0.524734i	0.940258	+	0.340461i	$0.110583\pi$
$600$		0			0
$601$	−9.31628	+	16.1363i	−0.380019	+	0.658212i	−0.991065	−	0.133383i	$-0.957416\pi$
$601$	−9.31628	+	16.1363i	−0.380019	+	0.658212i	0.611046	+	0.791595i	$0.290749\pi$
$602$		0			0
$603$	0.992751	−	0.833017i	0.0404280	−	0.0339231i
$604$		0			0
$605$	−5.25933	−	29.8271i	−0.213822	−	1.21264i
$606$		0			0
$607$	−43.4925			−1.76531			−0.882653	−	0.470025i	$-0.844245\pi$
$607$	−43.4925			−1.76531			−0.882653	+	0.470025i	$0.844245\pi$
$608$		0			0
$609$	−8.77327			−0.355511
$610$		0			0
$611$	−9.30511	−	52.7719i	−0.376444	−	2.13492i
$612$		0			0
$613$	37.0997	−	31.1304i	1.49844	−	1.25734i	0.615253	−	0.788330i	$-0.289054\pi$
$613$	37.0997	−	31.1304i	1.49844	−	1.25734i	0.883191	−	0.469014i	$-0.155391\pi$
$614$		0			0
$615$	2.40216	−	4.16066i	0.0968645	−	0.167774i
$616$		0			0
$617$	21.8080	−	7.93747i	0.877957	−	0.319550i	0.136572	−	0.990630i	$-0.456391\pi$
$617$	21.8080	−	7.93747i	0.877957	−	0.319550i	0.741385	+	0.671080i	$0.234169\pi$
$618$		0			0
$619$	2.33161	+	4.03847i	0.0937154	+	0.162320i	0.909072	−	0.416640i	$-0.136792\pi$
$619$	2.33161	+	4.03847i	0.0937154	+	0.162320i	−0.815356	+	0.578959i	$0.803459\pi$
$620$		0			0
$621$	−1.17388	+	6.65742i	−0.0471063	+	0.267153i
$622$		0			0
$623$	3.74410	+	3.14167i	0.150004	+	0.125869i
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$		0			0
$627$	36.8876	−	34.3324i	1.47315	−	1.37110i
$628$		0			0
$629$	14.0716	+	5.12164i	0.561071	+	0.204213i
$630$		0			0
$631$	6.92604	+	5.81163i	0.275721	+	0.231357i	0.770153	−	0.637859i	$-0.220180\pi$
$631$	6.92604	+	5.81163i	0.275721	+	0.231357i	−0.494432	+	0.869216i	$0.664624\pi$
$632$		0			0
$633$	−6.44913	+	36.5748i	−0.256330	+	1.45372i
$634$		0			0
$635$	−2.92646	−	5.06878i	−0.116133	−	0.201149i
$636$		0			0
$637$	28.0462	−	10.2080i	1.11123	−	0.404456i
$638$		0			0
$639$	−1.39415	+	2.41474i	−0.0551519	+	0.0955258i
$640$		0			0
$641$	4.88738	−	4.10100i	0.193040	−	0.161980i	−0.541145	−	0.840929i	$-0.682009\pi$
$641$	4.88738	−	4.10100i	0.193040	−	0.161980i	0.734185	+	0.678950i	$0.237565\pi$
$642$		0			0
$643$	−7.28320	−	41.3051i	−0.287221	−	1.62891i	−0.697241	−	0.716837i	$-0.745589\pi$
$643$	−7.28320	−	41.3051i	−0.287221	−	1.62891i	0.410020	−	0.912077i	$-0.365522\pi$
$644$		0			0
$645$	17.1867			0.676727
$646$		0			0
$647$	28.4481			1.11841			0.559205	−	0.829030i	$-0.311107\pi$
$647$	28.4481			1.11841			0.559205	+	0.829030i	$0.311107\pi$
$648$		0			0
$649$	−0.178625	−	1.01303i	−0.00701165	−	0.0397651i
$650$		0			0
$651$	−5.51882	+	4.63084i	−0.216300	+	0.181497i
$652$		0			0
$653$	−14.5691	+	25.2345i	−0.570134	+	0.987501i	0.426418	+	0.904526i	$0.359775\pi$
$653$	−14.5691	+	25.2345i	−0.570134	+	0.987501i	−0.996552	+	0.0829744i	$0.973558\pi$
$654$		0			0
$655$	−7.64603	+	2.78293i	−0.298755	+	0.108738i
$656$		0			0
$657$	0.439077	+	0.760504i	0.0171300	+	0.0296701i
$658$		0			0
$659$	−1.78347	+	10.1145i	−0.0694740	+	0.394006i	0.930165	+	0.367141i	$0.119664\pi$
$659$	−1.78347	+	10.1145i	−0.0694740	+	0.394006i	−0.999639	+	0.0268649i	$0.991448\pi$
$660$		0			0
$661$	13.4375	+	11.2754i	0.522658	+	0.438562i	0.865557	−	0.500810i	$-0.166965\pi$
$661$	13.4375	+	11.2754i	0.522658	+	0.438562i	−0.342899	+	0.939372i	$0.611409\pi$
$662$		0			0
$663$	−9.97628	−	3.63107i	−0.387447	−	0.141019i
$664$		0			0
$665$	0.657711	+	2.86134i	0.0255049	+	0.110958i
$666$		0			0
$667$	9.25142	+	3.36724i	0.358216	+	0.130380i
$668$		0			0
$669$	3.25368	+	2.73016i	0.125795	+	0.105554i
$670$		0			0
$671$	8.08332	−	45.8428i	0.312053	−	1.76974i
$672$		0			0
$673$	−18.8057	−	32.5724i	−0.724906	−	1.25557i	−0.959012	−	0.283364i	$-0.908550\pi$
$673$	−18.8057	−	32.5724i	−0.724906	−	1.25557i	0.234106	−	0.972211i	$-0.424784\pi$
$674$		0			0
$675$	−4.67116	+	1.70016i	−0.179793	+	0.0654393i
$676$		0			0
$677$	2.73960	−	4.74513i	0.105291	−	0.182370i	−0.808566	−	0.588406i	$-0.799756\pi$
$677$	2.73960	−	4.74513i	0.105291	−	0.182370i	0.913857	+	0.406036i	$0.133089\pi$
$678$		0			0
$679$	−4.06768	+	3.41319i	−0.156103	+	0.130986i
$680$		0			0
$681$	4.79417	+	27.1891i	0.183713	+	1.04189i
$682$		0			0
$683$	−7.75347			−0.296678			−0.148339	−	0.988937i	$-0.547393\pi$
$683$	−7.75347			−0.296678			−0.148339	+	0.988937i	$0.547393\pi$
$684$		0			0
$685$	−4.97827			−0.190210
$686$		0			0
$687$	−2.98326	−	16.9189i	−0.113819	−	0.645498i
$688$		0			0
$689$	−12.5209	+	10.5063i	−0.477009	+	0.400258i
$690$		0			0
$691$	−22.8718	+	39.6151i	−0.870084	+	1.50703i	−0.00817434	+	0.999967i	$0.502602\pi$
$691$	−22.8718	+	39.6151i	−0.870084	+	1.50703i	−0.861909	+	0.507062i	$0.830731\pi$
$692$		0			0
$693$	−0.964470	+	0.351038i	−0.0366372	+	0.0133348i
$694$		0			0
$695$	1.04844	+	1.81596i	0.0397698	+	0.0688833i
$696$		0			0
$697$	0.600111	−	3.40340i	0.0227308	−	0.128913i
$698$		0			0
$699$	−35.7078	−	29.9624i	−1.35059	−	1.13328i
$700$		0			0
$701$	9.17535	+	3.33956i	0.346548	+	0.126133i	0.509429	−	0.860512i	$-0.329856\pi$
$701$	9.17535	+	3.33956i	0.346548	+	0.126133i	−0.162881	+	0.986646i	$0.552079\pi$
$702$		0			0
$703$	−50.3675	+	2.59135i	−1.89965	+	0.0977347i
$704$		0			0
$705$	19.8713	+	7.23258i	0.748398	+	0.272395i
$706$		0			0
$707$	−7.01105	−	5.88297i	−0.263678	−	0.221252i
$708$		0			0
$709$	−5.49893	+	31.1860i	−0.206517	+	1.17121i	0.688518	+	0.725219i	$0.258261\pi$
$709$	−5.49893	+	31.1860i	−0.206517	+	1.17121i	−0.895035	+	0.445996i	$0.852850\pi$
$710$		0			0
$711$	0.761829	+	1.31953i	0.0285708	+	0.0494861i
$712$		0			0
$713$	7.59695	−	2.76507i	0.284508	−	0.103553i
$714$		0			0
$715$	14.6477	−	25.3706i	0.547793	−	0.948805i
$716$		0			0
$717$	−20.4622	+	17.1698i	−0.764174	+	0.641218i
$718$		0			0
$719$	5.66644	+	32.1360i	0.211322	+	1.19847i	0.887175	+	0.461433i	$0.152664\pi$
$719$	5.66644	+	32.1360i	0.211322	+	1.19847i	−0.675853	+	0.737037i	$0.736225\pi$
$720$		0			0
$721$	−7.26235			−0.270464
$722$		0			0
$723$	−34.7153			−1.29108
$724$		0			0
$725$	1.25712	+	7.12949i	0.0466883	+	0.264783i
$726$		0			0
$727$	25.4241	−	21.3333i	0.942927	−	0.791210i	−0.0351651	−	0.999382i	$-0.511196\pi$
$727$	25.4241	−	21.3333i	0.942927	−	0.791210i	0.978092	+	0.208172i	$0.0667513\pi$
$728$		0			0
$729$	−12.2708	+	21.2536i	−0.454473	+	0.787171i
$730$		0			0
$731$	11.6174	−	4.22838i	0.429684	−	0.156392i
$732$		0			0
$733$	3.60440	+	6.24300i	0.133132	+	0.230591i	0.924882	−	0.380254i	$-0.124163\pi$
$733$	3.60440	+	6.24300i	0.133132	+	0.230591i	−0.791751	+	0.610845i	$0.790830\pi$
$734$		0			0
$735$	−2.04526	+	11.5993i	−0.0754406	+	0.427845i
$736$		0			0
$737$	26.8984	+	22.5704i	0.990815	+	0.831393i
$738$		0			0
$739$	−23.3257	−	8.48987i	−0.858051	−	0.312305i	−0.124733	−	0.992190i	$-0.539807\pi$
$739$	−23.3257	−	8.48987i	−0.858051	−	0.312305i	−0.733318	+	0.679885i	$0.762030\pi$
$740$		0			0
$741$	35.7088	−	1.83718i	1.31180	−	0.0674905i
$742$		0			0
$743$	27.6624	+	10.0683i	1.01483	+	0.369370i	0.795288	−	0.606232i	$-0.207320\pi$
$743$	27.6624	+	10.0683i	1.01483	+	0.369370i	0.219547	+	0.975602i	$0.429542\pi$
$744$		0			0
$745$	6.59482	+	5.53371i	0.241615	+	0.202739i
$746$		0			0
$747$	0.207757	−	1.17825i	0.00760142	−	0.0431098i
$748$		0			0
$749$	−0.373941	−	0.647685i	−0.0136635	−	0.0236659i
$750$		0			0
$751$	−30.6975	+	11.1730i	−1.12017	+	0.407707i	−0.834713	−	0.550685i	$-0.814366\pi$
$751$	−30.6975	+	11.1730i	−1.12017	+	0.407707i	−0.285453	+	0.958393i	$0.592144\pi$
$752$		0			0
$753$	17.1140	−	29.6422i	0.623667	−	1.08022i
$754$		0			0
$755$	−14.0389	+	11.7800i	−0.510927	+	0.428719i
$756$		0			0
$757$	9.00156	+	51.0504i	0.327167	+	1.85546i	0.493986	+	0.869470i	$0.335539\pi$
$757$	9.00156	+	51.0504i	0.327167	+	1.85546i	−0.166819	+	0.985988i	$0.553349\pi$
$758$		0			0
$759$	15.7219			0.570669
$760$		0			0
$761$	29.7963			1.08011			0.540057	−	0.841628i	$-0.318403\pi$
$761$	29.7963			1.08011			0.540057	+	0.841628i	$0.318403\pi$
$762$		0			0
$763$	0.293085	+	1.66217i	0.0106104	+	0.0601746i
$764$		0			0
$765$	0.235118	−	0.197288i	0.00850072	−	0.00713295i
$766$		0			0
$767$	0.364944	−	0.632101i	0.0131774	−	0.0228238i
$768$		0			0
$769$	11.7119	−	4.26278i	0.422342	−	0.153720i	−0.122101	−	0.992518i	$-0.538963\pi$
$769$	11.7119	−	4.26278i	0.422342	−	0.153720i	0.544443	+	0.838798i	$0.316741\pi$
$770$		0			0
$771$	10.6580	+	18.4602i	0.383838	+	0.664827i
$772$		0			0
$773$	−5.08078	+	28.8145i	−0.182743	+	1.03639i	0.746078	+	0.665858i	$0.231934\pi$
$773$	−5.08078	+	28.8145i	−0.182743	+	1.03639i	−0.928821	+	0.370528i	$0.879177\pi$
$774$		0			0
$775$	4.55399	+	3.82125i	0.163584	+	0.137263i
$776$		0			0
$777$	13.1761	+	4.79572i	0.472691	+	0.172045i
$778$		0			0
$779$	2.60743	+	11.3435i	0.0934209	+	0.406423i
$780$		0			0
$781$	−70.9925	−	25.8392i	−2.54031	−	0.924598i
$782$		0			0
$783$	27.5676	+	23.1320i	0.985187	+	0.826670i
$784$		0			0
$785$	−2.31814	+	13.1468i	−0.0827378	+	0.469229i
$786$		0			0
$787$	16.1220	+	27.9240i	0.574686	+	0.995385i	0.996076	+	0.0885051i	$0.0282090\pi$
$787$	16.1220	+	27.9240i	0.574686	+	0.995385i	−0.421390	+	0.906879i	$0.638458\pi$
$788$		0			0
$789$	6.86836	−	2.49988i	0.244520	−	0.0889980i
$790$		0			0
$791$	4.99435	−	8.65047i	0.177579	−	0.307575i
$792$		0			0
$793$	25.3021	−	21.2310i	0.898505	−	0.753935i
$794$		0			0
$795$	−1.12006	−	6.35219i	−0.0397245	−	0.225289i
$796$		0			0
$797$	2.58966			0.0917304			0.0458652	−	0.998948i	$-0.485396\pi$
$797$	2.58966			0.0917304			0.0458652	+	0.998948i	$0.485396\pi$
$798$		0			0
$799$	15.2114			0.538142
$800$		0			0
$801$	0.298822	+	1.69470i	0.0105584	+	0.0598795i
$802$		0			0
$803$	−18.2268	+	15.2941i	−0.643211	+	0.539718i
$804$		0			0
$805$	−0.457993	+	0.793267i	−0.0161421	+	0.0279590i
$806$		0			0
$807$	8.59355	−	3.12780i	0.302507	−	0.110104i
$808$		0			0
$809$	−10.3087	−	17.8552i	−0.362435	−	0.627756i	0.625926	−	0.779883i	$-0.284721\pi$
$809$	−10.3087	−	17.8552i	−0.362435	−	0.627756i	−0.988361	+	0.152126i	$0.951388\pi$
$810$		0			0
$811$	2.10908	−	11.9612i	0.0740600	−	0.420015i	−0.925126	−	0.379661i	$-0.876040\pi$
$811$	2.10908	−	11.9612i	0.0740600	−	0.420015i	0.999185	−	0.0403535i	$-0.0128484\pi$
$812$		0			0
$813$	20.6072	+	17.2915i	0.722727	+	0.606440i
$814$		0			0
$815$	−20.2330	−	7.36422i	−0.708732	−	0.257957i
$816$		0			0
$817$	−30.4792	+	28.3679i	−1.06633	+	0.992466i
$818$		0			0
$819$	−0.684340	−	0.249080i	−0.0239128	−	0.00870354i
$820$		0			0
$821$	3.05042	+	2.55961i	0.106460	+	0.0893309i	0.694464	−	0.719527i	$-0.255642\pi$
$821$	3.05042	+	2.55961i	0.106460	+	0.0893309i	−0.588004	+	0.808858i	$0.700086\pi$
$822$		0			0
$823$	0.228416	−	1.29541i	0.00796207	−	0.0451551i	−0.980568	−	0.196180i	$-0.937146\pi$
$823$	0.228416	−	1.29541i	0.00796207	−	0.0451551i	0.988530	+	0.151025i	$0.0482574\pi$
$824$		0			0
$825$	5.78042	+	10.0120i	0.201248	+	0.348572i
$826$		0			0
$827$	2.87578	−	1.04670i	0.100001	−	0.0363972i	−0.291535	−	0.956560i	$-0.594166\pi$
$827$	2.87578	−	1.04670i	0.100001	−	0.0363972i	0.391536	+	0.920163i	$0.371944\pi$
$828$		0			0
$829$	−25.6472	+	44.4222i	−0.890763	+	1.54285i	−0.0518002	+	0.998657i	$0.516496\pi$
$829$	−25.6472	+	44.4222i	−0.890763	+	1.54285i	−0.838963	+	0.544189i	$0.816837\pi$
$830$		0			0
$831$	−16.6703	+	13.9880i	−0.578286	+	0.485239i
$832$		0			0
$833$	1.47122	+	8.34371i	0.0509748	+	0.289092i
$834$		0			0
$835$	12.1757			0.421358
$836$		0			0
$837$	29.5513			1.02144
$838$		0			0
$839$	2.38236	+	13.5110i	0.0822482	+	0.466453i	0.997917	+	0.0645179i	$0.0205510\pi$
$839$	2.38236	+	13.5110i	0.0822482	+	0.466453i	−0.915668	+	0.401935i	$0.868338\pi$
$840$		0			0
$841$	17.9331	−	15.0476i	0.618382	−	0.518884i
$842$		0			0
$843$	19.6205	−	33.9838i	0.675767	−	1.17046i
$844$		0			0
$845$	7.31698	−	2.66316i	0.251712	−	0.0916155i
$846$		0			0
$847$	−10.2001	−	17.6670i	−0.350478	−	0.607046i
$848$		0			0
$849$	5.00344	−	28.3759i	0.171718	−	0.973860i
$850$		0			0
$851$	−12.0536	−	10.1142i	−0.413192	−	0.346709i
$852$		0			0
$853$	−46.4590	−	16.9097i	−1.59072	−	0.578976i	−0.613224	−	0.789909i	$-0.710128\pi$
$853$	−46.4590	−	16.9097i	−1.59072	−	0.578976i	−0.977501	+	0.210933i	$0.932350\pi$
$854$		0			0
$855$	−0.470175	+	0.920593i	−0.0160797	+	0.0314836i
$856$		0			0
$857$	10.4491	+	3.80315i	0.356933	+	0.129913i	0.514262	−	0.857633i	$-0.328066\pi$
$857$	10.4491	+	3.80315i	0.356933	+	0.129913i	−0.157329	+	0.987546i	$0.550288\pi$
$858$		0			0
$859$	−29.5108	−	24.7625i	−1.00690	−	0.844886i	−0.0189707	−	0.999820i	$-0.506039\pi$
$859$	−29.5108	−	24.7625i	−1.00690	−	0.844886i	−0.987925	+	0.154934i	$0.950483\pi$
$860$		0			0
$861$	0.561921	−	3.18681i	0.0191502	−	0.108606i
$862$		0			0
$863$	3.92961	+	6.80628i	0.133765	+	0.231688i	0.925125	−	0.379662i	$-0.123960\pi$
$863$	3.92961	+	6.80628i	0.133765	+	0.231688i	−0.791360	+	0.611351i	$0.790626\pi$
$864$		0			0
$865$	−2.03095	+	0.739205i	−0.0690544	+	0.0251337i
$866$		0			0
$867$	−13.7864	+	23.8788i	−0.468211	+	0.810965i
$868$		0			0
$869$	−31.6248	+	26.5363i	−1.07280	+	0.900184i
$870$		0			0
$871$	4.32639	+	24.5362i	0.146594	+	0.831377i
$872$		0			0
$873$	−1.86957			−0.0632753
$874$		0			0
$875$	−0.673555			−0.0227703
$876$		0			0
$877$	7.02596	+	39.8462i	0.237250	+	1.34551i	0.837823	+	0.545941i	$0.183828\pi$
$877$	7.02596	+	39.8462i	0.237250	+	1.34551i	−0.600573	+	0.799570i	$0.705061\pi$
$878$		0			0
$879$	−8.70858	+	7.30737i	−0.293733	+	0.246471i
$880$		0			0
$881$	0.248999	−	0.431278i	0.00838898	−	0.0145301i	−0.861800	−	0.507247i	$-0.830663\pi$
$881$	0.248999	−	0.431278i	0.00838898	−	0.0145301i	0.870189	+	0.492717i	$0.163996\pi$
$882$		0			0
$883$	41.9080	−	15.2533i	1.41032	−	0.513314i	0.479095	−	0.877763i	$-0.340965\pi$
$883$	41.9080	−	15.2533i	1.41032	−	0.513314i	0.931223	+	0.364449i	$0.118743\pi$
$884$		0			0
$885$	0.144018	+	0.249446i	0.00484110	+	0.00838503i
$886$		0			0
$887$	−5.46596	+	30.9990i	−0.183529	+	1.04084i	0.744302	+	0.667843i	$0.232782\pi$
$887$	−5.46596	+	30.9990i	−0.183529	+	1.04084i	−0.927831	+	0.373001i	$0.878329\pi$
$888$		0			0
$889$	−3.01995	−	2.53404i	−0.101286	−	0.0849890i
$890$		0			0
$891$	58.2982	+	21.2188i	1.95306	+	0.710857i
$892$		0			0
$893$	−47.1779	+	19.9726i	−1.57875	+	0.668358i
$894$		0			0
$895$	17.0533	+	6.20691i	0.570030	+	0.207474i
$896$		0			0
$897$	8.54559	+	7.17060i	0.285329	+	0.239419i
$898$		0			0
$899$	7.47335	−	42.3835i	0.249250	−	1.41357i
$900$		0			0
$901$	−2.31991	−	4.01820i	−0.0772874	−	0.133866i
$902$		0			0
$903$	10.8781	−	3.95930i	0.362000	−	0.131757i
$904$		0			0
$905$	−3.73720	+	6.47301i	−0.124229	+	0.215170i
$906$		0			0
$907$	29.3861	−	24.6578i	0.975748	−	0.818750i	−0.00769425	−	0.999970i	$-0.502449\pi$
$907$	29.3861	−	24.6578i	0.975748	−	0.818750i	0.983443	+	0.181220i	$0.0580047\pi$
$908$		0			0
$909$	−0.559562	−	3.17344i	−0.0185595	−	0.105256i
$910$		0			0
$911$	48.1083			1.59390			0.796949	−	0.604046i	$-0.206446\pi$
$911$	48.1083			1.59390			0.796949	+	0.604046i	$0.206446\pi$
$912$		0			0
$913$	32.4169			1.07284
$914$		0			0
$915$	2.26341	+	12.8364i	0.0748260	+	0.424360i
$916$		0			0
$917$	−4.19834	+	3.52282i	−0.138641	+	0.116334i
$918$		0			0
$919$	4.30053	−	7.44874i	0.141861	−	0.245711i	−0.786336	−	0.617799i	$-0.788025\pi$
$919$	4.30053	−	7.44874i	0.141861	−	0.245711i	0.928198	+	0.372088i	$0.121358\pi$
$920$		0			0
$921$	−1.35688	+	0.493863i	−0.0447106	+	0.0162733i
$922$		0			0
$923$	−26.8028	−	46.4238i	−0.882224	−	1.52806i
$924$		0			0
$925$	2.00917	−	11.3946i	0.0660612	−	0.374652i
$926$		0			0
$927$	−1.95875	−	1.64359i	−0.0643339	−	0.0539826i
$928$		0			0
$929$	38.4554	+	13.9966i	1.26168	+	0.459214i	0.884332	−	0.466858i	$-0.154614\pi$
$929$	38.4554	+	13.9966i	1.26168	+	0.459214i	0.377348	+	0.926072i	$0.376836\pi$
$930$		0			0
$931$	−15.5183	−	23.9461i	−0.508590	−	0.784802i
$932$		0			0
$933$	23.7439	+	8.64209i	0.777342	+	0.282929i
$934$		0			0
$935$	6.37048	+	5.34547i	0.208337	+	0.174816i
$936$		0			0
$937$	5.06308	−	28.7142i	0.165404	−	0.938051i	−0.783244	−	0.621715i	$-0.786436\pi$
$937$	5.06308	−	28.7142i	0.165404	−	0.938051i	0.948647	−	0.316336i	$-0.102453\pi$
$938$		0			0
$939$	19.6865	+	34.0979i	0.642443	+	1.11274i
$940$		0			0
$941$	39.6205	−	14.4207i	1.29159	−	0.470100i	0.397342	−	0.917671i	$-0.369933\pi$
$941$	39.6205	−	14.4207i	1.29159	−	0.470100i	0.894249	+	0.447570i	$0.147711\pi$
$942$		0			0
$943$	−1.81567	+	3.14483i	−0.0591263	+	0.102410i
$944$		0			0
$945$	−2.56487	+	2.15218i	−0.0834353	+	0.0700105i
$946$		0			0
$947$	−3.78955	−	21.4916i	−0.123144	−	0.698383i	−0.982393	−	0.186826i	$-0.940180\pi$
$947$	−3.78955	−	21.4916i	−0.123144	−	0.698383i	0.859249	−	0.511557i	$-0.170931\pi$
$948$		0			0
$949$	−16.8826			−0.548034
$950$		0			0
$951$	−56.1404			−1.82048
$952$		0			0
$953$	−7.49487	−	42.5055i	−0.242783	−	1.37689i	−0.825587	−	0.564276i	$-0.809156\pi$
$953$	−7.49487	−	42.5055i	−0.242783	−	1.37689i	0.582804	−	0.812613i	$-0.301956\pi$
$954$		0			0
$955$	16.8271	−	14.1196i	0.544512	−	0.456900i
$956$		0			0
$957$	41.8472	−	72.4815i	1.35273	−	2.34299i
$958$		0			0
$959$	−3.15092	+	1.14684i	−0.101748	+	0.0370334i
$960$		0			0
$961$	−2.17040	−	3.75924i	−0.0700129	−	0.121266i
$962$		0			0
$963$	0.0457249	−	0.259319i	0.00147346	−	0.00835643i
$964$		0			0
$965$	9.15097	+	7.67857i	0.294580	+	0.247182i
$966$		0			0
$967$	54.0667	+	19.6787i	1.73867	+	0.632823i	0.999185	−	0.0403543i	$-0.0128487\pi$
$967$	54.0667	+	19.6787i	1.73867	+	0.632823i	0.739481	+	0.673177i	$0.235071\pi$
$968$		0			0
$969$	−1.24661	+	10.0732i	−0.0400470	+	0.323598i
$970$		0			0
$971$	−22.4251	−	8.16206i	−0.719655	−	0.261933i	−0.0438756	−	0.999037i	$-0.513971\pi$
$971$	−22.4251	−	8.16206i	−0.719655	−	0.261933i	−0.675779	+	0.737104i	$0.736193\pi$
$972$		0			0
$973$	1.08194	+	0.907854i	0.0346854	+	0.0291045i
$974$		0			0
$975$	−1.42444	+	8.07838i	−0.0456185	+	0.258715i
$976$		0			0
$977$	19.3169	+	33.4578i	0.618002	+	1.07041i	0.989850	+	0.142118i	$0.0453911\pi$
$977$	19.3169	+	33.4578i	0.618002	+	1.07041i	−0.371847	+	0.928294i	$0.621276\pi$
$978$		0			0
$979$	−43.8142	+	15.9470i	−1.40031	+	0.509670i
$980$		0			0
$981$	−0.297127	+	0.514640i	−0.00948655	+	0.0164312i
$982$		0			0
$983$	−11.7057	+	9.82225i	−0.373354	+	0.313281i	−0.810087	−	0.586310i	$-0.800580\pi$
$983$	−11.7057	+	9.82225i	−0.373354	+	0.313281i	0.436733	+	0.899591i	$0.356136\pi$
$984$		0			0
$985$	1.34630	+	7.63522i	0.0428965	+	0.243278i
$986$		0			0
$987$	14.2434			0.453373
$988$		0			0
$989$	−12.9906			−0.413076
$990$		0			0
$991$	0.957751	+	5.43167i	0.0304240	+	0.172543i	0.996234	−	0.0867092i	$-0.0276351\pi$
$991$	0.957751	+	5.43167i	0.0304240	+	0.172543i	−0.965810	+	0.259252i	$0.916524\pi$
$992$		0			0
$993$	−16.2266	+	13.6158i	−0.514936	+	0.432083i
$994$		0			0
$995$	−4.60718	+	7.97988i	−0.146058	+	0.252979i
$996$		0			0
$997$	28.1034	−	10.2288i	0.890044	−	0.323949i	0.143788	−	0.989609i	$-0.454072\pi$
$997$	28.1034	−	10.2288i	0.890044	−	0.323949i	0.746256	+	0.665659i	$0.231850\pi$
$998$		0			0
$999$	−28.7578	−	49.8100i	−0.909858	−	1.57592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.61.1	✓	18
19.5	even	9	inner	380.2.u.a.81.1	yes	18
19.9	even	9		7220.2.a.v.1.3		9
19.10	odd	18		7220.2.a.x.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.61.1	✓	18	1.1	even	1	trivial
380.2.u.a.81.1	yes	18	19.5	even	9	inner
7220.2.a.v.1.3		9	19.9	even	9
7220.2.a.x.1.7		9	19.10	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)

\(f(q)\)	\(=\)	\(q+(-0.312429 - 1.77187i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-0.336777 + 0.583316i) q^{7} +(-0.222848 + 0.0811099i) q^{9} +O(q^{10})\)	\(q+(-0.312429 - 1.77187i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-0.336777 + 0.583316i) q^{7} +(-0.222848 + 0.0811099i) q^{9} +(-3.21276 - 5.56466i) q^{11} +(0.791702 - 4.48996i) q^{13} +(1.37827 + 1.15651i) q^{15} +(1.21618 + 0.442652i) q^{17} +(-4.35314 + 0.223964i) q^{19} +(1.13878 + 0.414482i) q^{21} +(-1.04176 - 0.874144i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-2.48547 - 4.30496i) q^{27} +(-6.80288 + 2.47605i) q^{29} +(-2.97241 + 5.14836i) q^{31} +(-8.85612 + 7.43116i) q^{33} +(-0.116962 - 0.663322i) q^{35} +11.5704 q^{37} -8.20300 q^{39} +(-0.463683 - 2.62968i) q^{41} +(7.31756 - 6.14016i) q^{43} +(0.118575 - 0.205377i) q^{45} +(11.0445 - 4.01987i) q^{47} +(3.27316 + 5.66928i) q^{49} +(0.404354 - 2.29321i) q^{51} +(-2.74628 - 2.30440i) q^{53} +(6.03801 + 2.19766i) q^{55} +(1.75689 + 7.64324i) q^{57} +(0.150435 + 0.0547540i) q^{59} +(5.54965 + 4.65671i) q^{61} +(0.0277374 - 0.157306i) q^{63} +(2.27961 + 3.94841i) q^{65} +(-5.13512 + 1.86903i) q^{67} +(-1.22340 + 2.11898i) q^{69} +(9.00684 - 7.55764i) q^{71} +(-0.643012 - 3.64670i) q^{73} -1.79921 q^{75} +4.32794 q^{77} +(-1.11567 - 6.32728i) q^{79} +(-7.39632 + 6.20625i) q^{81} +(-2.52251 + 4.36912i) q^{83} +(-1.21618 + 0.442652i) q^{85} +(6.51266 + 11.2803i) q^{87} +(1.26006 - 7.14615i) q^{89} +(2.35244 + 1.97393i) q^{91} +(10.0509 + 3.65823i) q^{93} +(3.19074 - 2.96971i) q^{95} +(7.40807 + 2.69632i) q^{97} +(1.16730 + 0.979484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^9	\( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^9 + 9 * q^13 - 3 * q^15 + 12 * q^17 + 18 * q^19 + 15 * q^21 - 9 * q^23 - 33 * q^29 - 18 * q^31 + 9 * q^33 + 12 * q^35 + 60 * q^37 - 84 * q^39 - 18 * q^41 + 18 * q^43 + 6 * q^45 - 15 * q^47 - 15 * q^49 - 9 * q^51 + 24 * q^53 + 3 * q^55 + 66 * q^57 + 48 * q^59 - 18 * q^61 - 54 * q^63 + 3 * q^65 - 36 * q^67 - 9 * q^69 + 18 * q^73 - 6 * q^75 + 9 * q^79 - 9 * q^81 - 30 * q^83 - 12 * q^85 - 9 * q^87 + 6 * q^89 + 30 * q^91 + 21 * q^95 + 21 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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