LMFDB - Embedded newform 380.2.u.a.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} + 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			301.3
Root			$-0.443867 - 2.51729i$ of defining polynomial
Character	$\chi$	$=$	380.301
Dual form			380.2.u.a.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.40197 - 0.874246i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-0.118043 - 0.204456i) q^{7} +(2.70703 - 2.27147i) q^{9} +O(q^{10})$	\(q+(2.40197 - 0.874246i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-0.118043 - 0.204456i) q^{7} +(2.70703 - 2.27147i) q^{9} +(2.60901 - 4.51894i) q^{11} +(-1.93810 - 0.705410i) q^{13} +(0.443867 + 2.51729i) q^{15} +(4.62527 + 3.88107i) q^{17} +(1.86541 + 3.93958i) q^{19} +(-0.462280 - 0.387899i) q^{21} +(-0.685398 - 3.88708i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(0.682201 - 1.18161i) q^{27} +(-6.90607 + 5.79488i) q^{29} +(-1.86652 - 3.23290i) q^{31} +(2.31611 - 13.1353i) q^{33} +(0.221847 - 0.0807459i) q^{35} +1.73098 q^{37} -5.27196 q^{39} +(-11.1003 + 4.04019i) q^{41} +(-0.0112258 + 0.0636649i) q^{43} +(1.76689 + 3.06034i) q^{45} +(-6.65712 + 5.58599i) q^{47} +(3.47213 - 6.01391i) q^{49} +(14.5028 + 5.27858i) q^{51} +(0.300841 + 1.70615i) q^{53} +(3.99724 + 3.35408i) q^{55} +(7.92481 + 7.83193i) q^{57} +(0.134661 + 0.112994i) q^{59} +(-1.78040 - 10.0971i) q^{61} +(-0.783959 - 0.285338i) q^{63} +(1.03124 - 1.78616i) q^{65} +(-0.759172 + 0.637021i) q^{67} +(-5.04458 - 8.73746i) q^{69} +(-0.860306 + 4.87904i) q^{71} +(-2.27800 + 0.829123i) q^{73} -2.55613 q^{75} -1.23190 q^{77} +(6.14146 - 2.23531i) q^{79} +(-1.23529 + 7.00568i) q^{81} +(2.39473 + 4.14780i) q^{83} +(-4.62527 + 3.88107i) q^{85} +(-11.5220 + 19.9568i) q^{87} +(-5.51716 - 2.00808i) q^{89} +(0.0845529 + 0.479523i) q^{91} +(-7.30968 - 6.13355i) q^{93} +(-4.20365 + 1.15297i) q^{95} +(-2.70875 - 2.27291i) q^{97} +(-3.20196 - 18.1592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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
$3$	2.40197	−	0.874246i	1.38678	−	0.504746i	0.462553	−	0.886592i	$-0.346933\pi$
$3$	2.40197	−	0.874246i	1.38678	−	0.504746i	0.924226	+	0.381845i	$0.124711\pi$
$4$		0			0
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$6$		0			0
$7$	−0.118043	−	0.204456i	−0.0446159	−	0.0772770i	0.842855	−	0.538141i	$-0.180873\pi$
$7$	−0.118043	−	0.204456i	−0.0446159	−	0.0772770i	−0.887471	+	0.460864i	$0.847540\pi$
$8$		0			0
$9$	2.70703	−	2.27147i	0.902344	−	0.757156i
$10$		0			0
$11$	2.60901	−	4.51894i	0.786646	−	1.36251i	−0.141364	−	0.989958i	$-0.545149\pi$
$11$	2.60901	−	4.51894i	0.786646	−	1.36251i	0.928011	−	0.372554i	$-0.121518\pi$
$12$		0			0
$13$	−1.93810	−	0.705410i	−0.537532	−	0.195645i	0.0589666	−	0.998260i	$-0.481219\pi$
$13$	−1.93810	−	0.705410i	−0.537532	−	0.195645i	−0.596498	+	0.802614i	$0.703442\pi$
$14$		0			0
$15$	0.443867	+	2.51729i	0.114606	+	0.649962i
$16$		0			0
$17$	4.62527	+	3.88107i	1.12179	+	0.941297i	0.998694	−	0.0510977i	$-0.0162720\pi$
$17$	4.62527	+	3.88107i	1.12179	+	0.941297i	0.123100	+	0.992394i	$0.460716\pi$
$18$		0			0
$19$	1.86541	+	3.93958i	0.427953	+	0.903801i
$19$	1.86541	+	3.93958i	0.427953	+	0.903801i
$20$		0			0
$21$	−0.462280	−	0.387899i	−0.100878	−	0.0846464i
$22$		0			0
$23$	−0.685398	−	3.88708i	−0.142915	−	0.810513i	−0.969017	−	0.246993i	$-0.920558\pi$
$23$	−0.685398	−	3.88708i	−0.142915	−	0.810513i	0.826102	−	0.563521i	$-0.190553\pi$
$24$		0			0
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$		0			0
$27$	0.682201	−	1.18161i	0.131290	−	0.227400i
$28$		0			0
$29$	−6.90607	+	5.79488i	−1.28243	+	1.07608i	−0.289520	+	0.957172i	$0.593496\pi$
$29$	−6.90607	+	5.79488i	−1.28243	+	1.07608i	−0.992905	+	0.118911i	$0.962060\pi$
$30$		0			0
$31$	−1.86652	−	3.23290i	−0.335237	−	0.580647i	0.648294	−	0.761390i	$-0.275483\pi$
$31$	−1.86652	−	3.23290i	−0.335237	−	0.580647i	−0.983530	+	0.180744i	$0.942150\pi$
$32$		0			0
$33$	2.31611	−	13.1353i	0.403182	−	2.28656i
$34$		0			0
$35$	0.221847	−	0.0807459i	0.0374991	−	0.0136485i
$36$		0			0
$37$	1.73098			0.284572			0.142286	−	0.989826i	$-0.454555\pi$
$37$	1.73098			0.284572			0.142286	+	0.989826i	$0.454555\pi$
$38$		0			0
$39$	−5.27196			−0.844189
$40$		0			0
$41$	−11.1003	+	4.04019i	−1.73358	+	0.630972i	−0.998875	−	0.0474136i	$-0.984902\pi$
$41$	−11.1003	+	4.04019i	−1.73358	+	0.630972i	−0.734706	+	0.678386i	$0.762680\pi$
$42$		0			0
$43$	−0.0112258	+	0.0636649i	−0.00171193	+	0.00970881i	−0.985652	−	0.168792i	$-0.946013\pi$
$43$	−0.0112258	+	0.0636649i	−0.00171193	+	0.00970881i	0.983940	+	0.178500i	$0.0571246\pi$
$44$		0			0
$45$	1.76689	+	3.06034i	0.263392	+	0.456209i
$46$		0			0
$47$	−6.65712	+	5.58599i	−0.971041	+	0.814800i	−0.982714	−	0.185132i	$-0.940729\pi$
$47$	−6.65712	+	5.58599i	−0.971041	+	0.814800i	0.0116727	+	0.999932i	$0.496284\pi$
$48$		0			0
$49$	3.47213	−	6.01391i	0.496019	−	0.859130i
$50$		0			0
$51$	14.5028	+	5.27858i	2.03080	+	0.739149i
$52$		0			0
$53$	0.300841	+	1.70615i	0.0413237	+	0.234358i	0.998473	−	0.0552354i	$-0.0175909\pi$
$53$	0.300841	+	1.70615i	0.0413237	+	0.234358i	−0.957150	+	0.289594i	$0.906480\pi$
$54$		0			0
$55$	3.99724	+	3.35408i	0.538987	+	0.452264i
$56$		0			0
$57$	7.92481	+	7.83193i	1.04967	+	1.03736i
$58$		0			0
$59$	0.134661	+	0.112994i	0.0175313	+	0.0147105i	0.651511	−	0.758639i	$-0.274135\pi$
$59$	0.134661	+	0.112994i	0.0175313	+	0.0147105i	−0.633980	+	0.773350i	$0.718580\pi$
$60$		0			0
$61$	−1.78040	−	10.0971i	−0.227956	−	1.29280i	−0.856952	−	0.515396i	$-0.827645\pi$
$61$	−1.78040	−	10.0971i	−0.227956	−	1.29280i	0.628996	−	0.777409i	$-0.283466\pi$
$62$		0			0
$63$	−0.783959	−	0.285338i	−0.0987696	−	0.0359492i
$64$		0			0
$65$	1.03124	−	1.78616i	0.127910	−	0.221546i
$66$		0			0
$67$	−0.759172	+	0.637021i	−0.0927477	+	0.0778245i	−0.687983	−	0.725727i	$-0.741503\pi$
$67$	−0.759172	+	0.637021i	−0.0927477	+	0.0778245i	0.595235	+	0.803552i	$0.297059\pi$
$68$		0			0
$69$	−5.04458	−	8.73746i	−0.607296	−	1.05187i
$70$		0			0
$71$	−0.860306	+	4.87904i	−0.102099	+	0.579035i	0.890240	+	0.455492i	$0.150537\pi$
$71$	−0.860306	+	4.87904i	−0.102099	+	0.579035i	−0.992339	+	0.123543i	$0.960574\pi$
$72$		0			0
$73$	−2.27800	+	0.829123i	−0.266619	+	0.0970415i	−0.471871	−	0.881668i	$-0.656421\pi$
$73$	−2.27800	+	0.829123i	−0.266619	+	0.0970415i	0.205251	+	0.978709i	$0.434199\pi$
$74$		0			0
$75$	−2.55613			−0.295156
$76$		0			0
$77$	−1.23190			−0.140388
$78$		0			0
$79$	6.14146	−	2.23531i	0.690968	−	0.251492i	0.0274184	−	0.999624i	$-0.491271\pi$
$79$	6.14146	−	2.23531i	0.690968	−	0.251492i	0.663550	+	0.748132i	$0.269049\pi$
$80$		0			0
$81$	−1.23529	+	7.00568i	−0.137254	+	0.778408i
$82$		0			0
$83$	2.39473	+	4.14780i	0.262856	+	0.455280i	0.967000	−	0.254777i	$-0.0820022\pi$
$83$	2.39473	+	4.14780i	0.262856	+	0.455280i	−0.704143	+	0.710058i	$0.748669\pi$
$84$		0			0
$85$	−4.62527	+	3.88107i	−0.501681	+	0.420961i
$86$		0			0
$87$	−11.5220	+	19.9568i	−1.23529	+	2.13959i
$88$		0			0
$89$	−5.51716	−	2.00808i	−0.584818	−	0.212856i	0.0326309	−	0.999467i	$-0.489611\pi$
$89$	−5.51716	−	2.00808i	−0.584818	−	0.212856i	−0.617449	+	0.786611i	$0.711834\pi$
$90$		0			0
$91$	0.0845529	+	0.479523i	0.00886355	+	0.0502677i
$92$		0			0
$93$	−7.30968	−	6.13355i	−0.757978	−	0.636019i
$94$		0			0
$95$	−4.20365	+	1.15297i	−0.431285	+	0.118292i
$96$		0			0
$97$	−2.70875	−	2.27291i	−0.275032	−	0.230780i	0.494830	−	0.868990i	$-0.335230\pi$
$97$	−2.70875	−	2.27291i	−0.275032	−	0.230780i	−0.769862	+	0.638211i	$0.779675\pi$
$98$		0			0
$99$	−3.20196	−	18.1592i	−0.321809	−	1.82507i
$100$		0			0
$101$	−10.9459	−	3.98397i	−1.08915	−	0.396420i	−0.265847	−	0.964015i	$-0.585651\pi$
$101$	−10.9459	−	3.98397i	−1.08915	−	0.396420i	−0.823307	+	0.567596i	$0.807874\pi$
$102$		0			0
$103$	−4.76990	+	8.26171i	−0.469992	+	0.814050i	−0.999411	−	0.0343103i	$-0.989077\pi$
$103$	−4.76990	+	8.26171i	−0.469992	+	0.814050i	0.529419	+	0.848360i	$0.322410\pi$
$104$		0			0
$105$	0.462280	−	0.387899i	0.0451139	−	0.0378550i
$106$		0			0
$107$	9.94308	+	17.2219i	0.961234	+	1.66491i	0.719411	+	0.694585i	$0.244412\pi$
$107$	9.94308	+	17.2219i	0.961234	+	1.66491i	0.241823	+	0.970320i	$0.422255\pi$
$108$		0			0
$109$	2.26241	−	12.8308i	0.216700	−	1.22896i	−0.661233	−	0.750180i	$-0.729967\pi$
$109$	2.26241	−	12.8308i	0.216700	−	1.22896i	0.877933	−	0.478784i	$-0.158922\pi$
$110$		0			0
$111$	4.15777	−	1.51330i	0.394638	−	0.143636i
$112$		0			0
$113$	6.57342			0.618376			0.309188	−	0.951001i	$-0.399943\pi$
$113$	6.57342			0.618376			0.309188	+	0.951001i	$0.399943\pi$
$114$		0			0
$115$	3.94705			0.368064
$116$		0			0
$117$	−6.84880	+	2.49276i	−0.633172	+	0.230456i
$118$		0			0
$119$	0.247527	−	1.40379i	0.0226907	−	0.128686i
$120$		0			0
$121$	−8.11387	−	14.0536i	−0.737625	−	1.27760i
$122$		0			0
$123$	−23.1306	+	19.4089i	−2.08561	+	1.75004i
$124$		0			0
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	11.4305	+	4.16037i	1.01429	+	0.369173i	0.795080	−	0.606504i	$-0.207429\pi$
$127$	11.4305	+	4.16037i	1.01429	+	0.369173i	0.219214	+	0.975677i	$0.429651\pi$
$128$		0			0
$129$	0.0286947	+	0.162736i	0.00252643	+	0.0143281i
$130$		0			0
$131$	−0.637106	−	0.534596i	−0.0556642	−	0.0467078i	0.614531	−	0.788893i	$-0.289345\pi$
$131$	−0.637106	−	0.534596i	−0.0556642	−	0.0467078i	−0.670195	+	0.742185i	$0.733790\pi$
$132$		0			0
$133$	0.585272	−	0.846431i	0.0507495	−	0.0733948i
$134$		0			0
$135$	1.04519	+	0.877021i	0.0899558	+	0.0754819i
$136$		0			0
$137$	−3.09683	−	17.5630i	−0.264580	−	1.50051i	−0.770227	−	0.637770i	$-0.779857\pi$
$137$	−3.09683	−	17.5630i	−0.264580	−	1.50051i	0.505647	−	0.862741i	$-0.331254\pi$
$138$		0			0
$139$	−13.7175	−	4.99275i	−1.16350	−	0.423480i	−0.313154	−	0.949702i	$-0.601386\pi$
$139$	−13.7175	−	4.99275i	−1.16350	−	0.423480i	−0.850347	+	0.526222i	$0.823608\pi$
$140$		0			0
$141$	−11.1067	+	19.2374i	−0.935352	+	1.62008i
$142$		0			0
$143$	−8.24422	+	6.91772i	−0.689416	+	0.578489i
$144$		0			0
$145$	−4.50762	−	7.80742i	−0.374337	−	0.648371i
$146$		0			0
$147$	3.08233	−	17.4807i	0.254226	−	1.44179i
$148$		0			0
$149$	11.8453	−	4.31134i	0.970406	−	0.353199i	0.192303	−	0.981336i	$-0.438404\pi$
$149$	11.8453	−	4.31134i	0.970406	−	0.353199i	0.778103	+	0.628137i	$0.216182\pi$
$150$		0			0
$151$	19.6626			1.60012			0.800059	−	0.599922i	$-0.204802\pi$
$151$	19.6626			1.60012			0.800059	+	0.599922i	$0.204802\pi$
$152$		0			0
$153$	21.3365			1.72495
$154$		0			0
$155$	3.50791	−	1.27677i	0.281762	−	0.102553i
$156$		0			0
$157$	−3.00747	+	17.0562i	−0.240022	+	1.36123i	0.591752	+	0.806120i	$0.298437\pi$
$157$	−3.00747	+	17.0562i	−0.240022	+	1.36123i	−0.831774	+	0.555114i	$0.812675\pi$
$158$		0			0
$159$	2.21421	+	3.83513i	0.175598	+	0.304145i
$160$		0			0
$161$	−0.713830	+	0.598975i	−0.0562577	+	0.0472058i
$162$		0			0
$163$	5.89573	−	10.2117i	0.461789	−	0.799843i	−0.537261	−	0.843416i	$-0.680541\pi$
$163$	5.89573	−	10.2117i	0.461789	−	0.799843i	0.999050	+	0.0435735i	$0.0138743\pi$
$164$		0			0
$165$	12.5335	+	4.56184i	0.975735	+	0.355138i
$166$		0			0
$167$	−0.0232720	−	0.131982i	−0.00180084	−	0.0102131i	0.983894	−	0.178752i	$-0.0572061\pi$
$167$	−0.0232720	−	0.131982i	−0.00180084	−	0.0102131i	−0.985695	+	0.168539i	$0.946095\pi$
$168$		0			0
$169$	−6.69996	−	5.62193i	−0.515381	−	0.432456i
$170$		0			0
$171$	13.9983	+	6.42734i	1.07048	+	0.491511i
$172$		0			0
$173$	18.3629	+	15.4083i	1.39610	+	1.17147i	0.962798	+	0.270221i	$0.0870968\pi$
$173$	18.3629	+	15.4083i	1.39610	+	1.17147i	0.433304	+	0.901248i	$0.357348\pi$
$174$		0			0
$175$	0.0409957	+	0.232498i	0.00309899	+	0.0175752i
$176$		0			0
$177$	0.422236	+	0.153681i	0.0317372	+	0.0115514i
$178$		0			0
$179$	5.89792	−	10.2155i	0.440831	−	0.763542i	−0.556920	−	0.830566i	$-0.688017\pi$
$179$	5.89792	−	10.2155i	0.440831	−	0.763542i	0.997751	+	0.0670239i	$0.0213504\pi$
$180$		0			0
$181$	−0.682360	+	0.572568i	−0.0507194	+	0.0425586i	−0.667795	−	0.744345i	$-0.732762\pi$
$181$	−0.682360	+	0.572568i	−0.0507194	+	0.0425586i	0.617076	+	0.786904i	$0.288317\pi$
$182$		0			0
$183$	−13.1038	−	22.6965i	−0.968664	−	1.67777i
$184$		0			0
$185$	−0.300582	+	1.70468i	−0.0220992	+	0.125331i
$186$		0			0
$187$	29.6057	−	10.7756i	2.16498	−	0.787989i
$188$		0			0
$189$	−0.322115			−0.0234304
$190$		0			0
$191$	5.07774			0.367412			0.183706	−	0.982981i	$-0.441191\pi$
$191$	5.07774			0.367412			0.183706	+	0.982981i	$0.441191\pi$
$192$		0			0
$193$	8.33614	−	3.03411i	0.600049	−	0.218400i	−0.0240946	−	0.999710i	$-0.507670\pi$
$193$	8.33614	−	3.03411i	0.600049	−	0.218400i	0.624143	+	0.781310i	$0.285448\pi$
$194$		0			0
$195$	0.915466	−	5.19187i	0.0655579	−	0.371797i
$196$		0			0
$197$	11.4388	+	19.8126i	0.814983	+	1.41159i	0.909340	+	0.416054i	$0.136587\pi$
$197$	11.4388	+	19.8126i	0.814983	+	1.41159i	−0.0943565	+	0.995538i	$0.530079\pi$
$198$		0			0
$199$	5.20879	−	4.37069i	0.369241	−	0.309830i	−0.439220	−	0.898379i	$-0.644745\pi$
$199$	5.20879	−	4.37069i	0.369241	−	0.309830i	0.808461	+	0.588549i	$0.200301\pi$
$200$		0			0
$201$	−1.26660	+	2.19381i	−0.0893389	+	0.154739i
$202$		0			0
$203$	2.00001	+	0.727943i	0.140373	+	0.0510916i
$204$		0			0
$205$	−2.05126	−	11.6333i	−0.143266	−	0.812503i
$206$		0			0
$207$	−10.6848	−	8.96560i	−0.742644	−	0.623152i
$208$		0			0
$209$	22.6696	+	1.84874i	1.56809	+	0.127880i
$210$		0			0
$211$	8.29874	+	6.96347i	0.571309	+	0.479385i	0.882080	−	0.471100i	$-0.156143\pi$
$211$	8.29874	+	6.96347i	0.571309	+	0.479385i	−0.310771	+	0.950485i	$0.600587\pi$
$212$		0			0
$213$	2.19905	+	12.4714i	0.150676	+	0.854528i
$214$		0			0
$215$	−0.0607484	−	0.0221106i	−0.00414301	−	0.00150793i
$216$		0			0
$217$	−0.440657	+	0.763241i	−0.0299138	+	0.0518121i
$218$		0			0
$219$	−4.74682	+	3.98306i	−0.320761	+	0.269150i
$220$		0			0
$221$	−6.22649	−	10.7846i	−0.418839	−	0.725450i
$222$		0			0
$223$	4.17205	−	23.6609i	0.279381	−	1.58445i	−0.445311	−	0.895376i	$-0.646907\pi$
$223$	4.17205	−	23.6609i	0.279381	−	1.58445i	0.724692	−	0.689073i	$-0.241982\pi$
$224$		0			0
$225$	−3.32066	+	1.20862i	−0.221378	+	0.0805749i
$226$		0			0
$227$	−20.0082			−1.32799			−0.663995	−	0.747737i	$-0.731141\pi$
$227$	−20.0082			−1.32799			−0.663995	+	0.747737i	$0.731141\pi$
$228$		0			0
$229$	6.88943			0.455266			0.227633	−	0.973747i	$-0.426901\pi$
$229$	6.88943			0.455266			0.227633	+	0.973747i	$0.426901\pi$
$230$		0			0
$231$	−2.95898	+	1.07698i	−0.194687	+	0.0708602i
$232$		0			0
$233$	1.40492	−	7.96771i	0.0920396	−	0.521982i	−0.903575	−	0.428430i	$-0.859067\pi$
$233$	1.40492	−	7.96771i	0.0920396	−	0.521982i	0.995614	−	0.0935520i	$-0.0298221\pi$
$234$		0			0
$235$	−4.34513	−	7.52598i	−0.283445	−	0.490941i
$236$		0			0
$237$	12.7974	−	10.7383i	0.831281	−	0.697527i
$238$		0			0
$239$	−6.11728	+	10.5954i	−0.395694	+	0.685362i	−0.993189	−	0.116510i	$-0.962829\pi$
$239$	−6.11728	+	10.5954i	−0.395694	+	0.685362i	0.597496	+	0.801872i	$0.296162\pi$
$240$		0			0
$241$	0.885693	+	0.322366i	0.0570525	+	0.0207654i	0.370389	−	0.928877i	$-0.379224\pi$
$241$	0.885693	+	0.322366i	0.0570525	+	0.0207654i	−0.313336	+	0.949642i	$0.601447\pi$
$242$		0			0
$243$	3.86833	+	21.9384i	0.248154	+	1.40735i
$244$		0			0
$245$	5.31961	+	4.46369i	0.339858	+	0.285174i
$246$		0			0
$247$	−0.836322	−	8.95116i	−0.0532139	−	0.569549i
$248$		0			0
$249$	9.37829	+	7.86932i	0.594325	+	0.498698i
$250$		0			0
$251$	−3.01716	−	17.1112i	−0.190442	−	1.08005i	−0.918762	−	0.394811i	$-0.870810\pi$
$251$	−3.01716	−	17.1112i	−0.190442	−	1.08005i	0.728321	−	0.685236i	$-0.240301\pi$
$252$		0			0
$253$	−19.3537	−	7.04417i	−1.21676	−	0.442863i
$254$		0			0
$255$	−7.71677	+	13.3658i	−0.483243	+	0.837001i
$256$		0			0
$257$	−3.34243	+	2.80463i	−0.208495	+	0.174948i	−0.741055	−	0.671444i	$-0.765674\pi$
$257$	−3.34243	+	2.80463i	−0.208495	+	0.174948i	0.532560	+	0.846392i	$0.321230\pi$
$258$		0			0
$259$	−0.204329	−	0.353909i	−0.0126964	−	0.0219908i
$260$		0			0
$261$	−5.53206	+	31.3738i	−0.342426	+	1.94199i
$262$		0			0
$263$	9.63727	−	3.50768i	0.594260	−	0.216293i	−0.0273423	−	0.999626i	$-0.508704\pi$
$263$	9.63727	−	3.50768i	0.594260	−	0.216293i	0.621602	+	0.783333i	$0.286482\pi$
$264$		0			0
$265$	−1.73247			−0.106425
$266$		0			0
$267$	−15.0076			−0.918451
$268$		0			0
$269$	−21.2011	+	7.71658i	−1.29266	+	0.470488i	−0.894598	−	0.446872i	$-0.852538\pi$
$269$	−21.2011	+	7.71658i	−1.29266	+	0.470488i	−0.398058	+	0.917360i	$0.630316\pi$
$270$		0			0
$271$	4.86690	−	27.6016i	0.295643	−	1.67667i	−0.368934	−	0.929455i	$-0.620277\pi$
$271$	4.86690	−	27.6016i	0.295643	−	1.67667i	0.664577	−	0.747220i	$-0.268612\pi$
$272$		0			0
$273$	0.622315	+	1.07788i	0.0376642	+	0.0652364i
$274$		0			0
$275$	−3.99724	+	3.35408i	−0.241042	+	0.202259i
$276$		0			0
$277$	−5.33746	+	9.24475i	−0.320697	+	0.555463i	−0.980632	−	0.195859i	$-0.937250\pi$
$277$	−5.33746	+	9.24475i	−0.320697	+	0.555463i	0.659935	+	0.751323i	$0.270584\pi$
$278$		0			0
$279$	−12.3962	−	4.51183i	−0.742139	−	0.270116i
$280$		0			0
$281$	−3.29343	−	18.6780i	−0.196469	−	1.11423i	−0.910311	−	0.413926i	$-0.864157\pi$
$281$	−3.29343	−	18.6780i	−0.196469	−	1.11423i	0.713841	−	0.700308i	$-0.246954\pi$
$282$		0			0
$283$	1.96247	+	1.64670i	0.116656	+	0.0978864i	0.699250	−	0.714877i	$-0.253518\pi$
$283$	1.96247	+	1.64670i	0.116656	+	0.0978864i	−0.582593	+	0.812764i	$0.697962\pi$
$284$		0			0
$285$	−9.08907	+	6.44442i	−0.538390	+	0.381734i
$286$		0			0
$287$	2.13635	+	1.79261i	0.126105	+	0.105815i
$288$		0			0
$289$	3.37847	+	19.1602i	0.198733	+	1.12707i
$290$		0			0
$291$	−8.49344	−	3.09136i	−0.497894	−	0.181219i
$292$		0			0
$293$	1.40995	−	2.44211i	0.0823704	−	0.142670i	−0.821897	−	0.569636i	$-0.807084\pi$
$293$	1.40995	−	2.44211i	0.0823704	−	0.142670i	0.904268	+	0.426966i	$0.140418\pi$
$294$		0			0
$295$	−0.134661	+	0.112994i	−0.00784025	+	0.00657875i
$296$		0			0
$297$	−3.55974	−	6.16565i	−0.206557	−	0.357767i
$298$		0			0
$299$	−1.41362	+	8.01703i	−0.0817517	+	0.463637i
$300$		0			0
$301$	0.0143418	−	0.00521998i	0.000826647	−	0.000300875i
$302$		0			0
$303$	−29.7746			−1.71051
$304$		0			0
$305$	10.2529			0.587079
$306$		0			0
$307$	−10.2154	+	3.71810i	−0.583023	+	0.212203i	−0.616658	−	0.787231i	$-0.711514\pi$
$307$	−10.2154	+	3.71810i	−0.583023	+	0.212203i	0.0336350	+	0.999434i	$0.489292\pi$
$308$		0			0
$309$	−4.23440	+	24.0145i	−0.240886	+	1.36613i
$310$		0			0
$311$	−14.8848	−	25.7812i	−0.844039	−	1.46192i	−0.886454	−	0.462818i	$-0.846839\pi$
$311$	−14.8848	−	25.7812i	−0.844039	−	1.46192i	0.0424150	−	0.999100i	$-0.486495\pi$
$312$		0			0
$313$	26.9762	−	22.6357i	1.52478	−	1.27944i	0.699692	−	0.714444i	$-0.253320\pi$
$313$	26.9762	−	22.6357i	1.52478	−	1.27944i	0.825090	−	0.565001i	$-0.191124\pi$
$314$		0			0
$315$	0.417136	−	0.722501i	0.0235030	−	0.0407083i
$316$		0			0
$317$	−27.7278	−	10.0921i	−1.55735	−	0.566829i	−0.587223	−	0.809425i	$-0.699779\pi$
$317$	−27.7278	−	10.0921i	−1.55735	−	0.566829i	−0.970127	+	0.242596i	$0.922001\pi$
$318$		0			0
$319$	8.16870	+	46.3270i	0.457360	+	2.59382i
$320$		0			0
$321$	38.9392	+	32.6739i	2.17337	+	1.82368i
$322$		0			0
$323$	−6.66174	+	25.4614i	−0.370669	+	1.41671i
$324$		0			0
$325$	1.57995	+	1.32574i	0.0876399	+	0.0735386i
$326$		0			0
$327$	−5.78300	−	32.7970i	−0.319801	−	1.81368i
$328$		0			0
$329$	1.92791	+	0.701702i	0.106289	+	0.0386861i
$330$		0			0
$331$	−5.69418	+	9.86261i	−0.312981	+	0.542098i	−0.979006	−	0.203831i	$-0.934661\pi$
$331$	−5.69418	+	9.86261i	−0.312981	+	0.542098i	0.666026	+	0.745929i	$0.267994\pi$
$332$		0			0
$333$	4.68582	−	3.93187i	0.256781	−	0.215465i
$334$		0			0
$335$	−0.495515	−	0.858256i	−0.0270728	−	0.0468916i
$336$		0			0
$337$	4.72558	−	26.8001i	0.257419	−	1.45989i	−0.532369	−	0.846512i	$-0.678698\pi$
$337$	4.72558	−	26.8001i	0.257419	−	1.45989i	0.789788	−	0.613381i	$-0.210191\pi$
$338$		0			0
$339$	15.7892	−	5.74679i	0.857551	−	0.312123i
$340$		0			0
$341$	−19.4791			−1.05485
$342$		0			0
$343$	−3.29203			−0.177753
$344$		0			0
$345$	9.48070	−	3.45069i	0.510424	−	0.185779i
$346$		0			0
$347$	4.30641	−	24.4229i	0.231180	−	1.31109i	−0.619330	−	0.785130i	$-0.712596\pi$
$347$	4.30641	−	24.4229i	0.231180	−	1.31109i	0.850511	−	0.525958i	$-0.176293\pi$
$348$		0			0
$349$	5.63267	+	9.75608i	0.301510	+	0.522231i	0.976478	−	0.215616i	$-0.0691760\pi$
$349$	5.63267	+	9.75608i	0.301510	+	0.522231i	−0.674968	+	0.737847i	$0.735843\pi$
$350$		0			0
$351$	−2.15569	+	1.80884i	−0.115062	+	0.0965486i
$352$		0			0
$353$	−13.1589	+	22.7920i	−0.700380	+	1.21309i	0.267953	+	0.963432i	$0.413653\pi$
$353$	−13.1589	+	22.7920i	−0.700380	+	1.21309i	−0.968333	+	0.249662i	$0.919681\pi$
$354$		0			0
$355$	−4.65552	−	1.69447i	−0.247089	−	0.0899332i
$356$		0			0
$357$	−0.632710	−	3.58827i	−0.0334865	−	0.189912i
$358$		0			0
$359$	1.03308	+	0.866856i	0.0545238	+	0.0457509i	0.669642	−	0.742684i	$-0.266447\pi$
$359$	1.03308	+	0.866856i	0.0545238	+	0.0457509i	−0.615119	+	0.788435i	$0.710892\pi$
$360$		0			0
$361$	−12.0405	+	14.6978i	−0.633712	+	0.773569i
$362$		0			0
$363$	−31.7756	−	26.6629i	−1.66779	−	1.39944i
$364$		0			0
$365$	−0.420957	−	2.38736i	−0.0220339	−	0.124960i
$366$		0			0
$367$	27.2974	+	9.93543i	1.42491	+	0.518625i	0.935469	−	0.353410i	$-0.114978\pi$
$367$	27.2974	+	9.93543i	1.42491	+	0.518625i	0.489443	+	0.872035i	$0.337200\pi$
$368$		0			0
$369$	−20.8718	+	36.1510i	−1.08654	+	1.88195i
$370$		0			0
$371$	0.313321	−	0.262907i	0.0162668	−	0.0136495i
$372$		0			0
$373$	1.77239	+	3.06988i	0.0917711	+	0.158952i	0.908256	−	0.418414i	$-0.137414\pi$
$373$	1.77239	+	3.06988i	0.0917711	+	0.158952i	−0.816485	+	0.577366i	$0.804081\pi$
$374$		0			0
$375$	0.443867	−	2.51729i	0.0229212	−	0.129992i
$376$		0			0
$377$	17.4724	−	6.35944i	0.899875	−	0.327528i
$378$		0			0
$379$	−15.3268			−0.787286			−0.393643	−	0.919263i	$-0.628785\pi$
$379$	−15.3268			−0.787286			−0.393643	+	0.919263i	$0.628785\pi$
$380$		0			0
$381$	31.0930			1.59294
$382$		0			0
$383$	13.1607	−	4.79009i	0.672479	−	0.244762i	0.0168642	−	0.999858i	$-0.494632\pi$
$383$	13.1607	−	4.79009i	0.672479	−	0.244762i	0.655615	+	0.755095i	$0.272409\pi$
$384$		0			0
$385$	0.213917	−	1.21318i	0.0109022	−	0.0618295i
$386$		0			0
$387$	0.114224	+	0.197842i	0.00580634	+	0.0100569i
$388$		0			0
$389$	−15.3712	+	12.8979i	−0.779349	+	0.653952i	−0.943085	−	0.332553i	$-0.892090\pi$
$389$	−15.3712	+	12.8979i	−0.779349	+	0.653952i	0.163735	+	0.986504i	$0.447646\pi$
$390$		0			0
$391$	11.9159	−	20.6389i	0.602612	−	1.04375i
$392$		0			0
$393$	−1.99768	−	0.727096i	−0.100770	−	0.0366771i
$394$		0			0
$395$	1.13490	+	6.43631i	0.0571028	+	0.323846i
$396$		0			0
$397$	6.64859	+	5.57883i	0.333683	+	0.279993i	0.794199	−	0.607658i	$-0.207891\pi$
$397$	6.64859	+	5.57883i	0.333683	+	0.279993i	−0.460516	+	0.887652i	$0.652335\pi$
$398$		0			0
$399$	0.665817	−	2.54477i	0.0333326	−	0.127398i
$400$		0			0
$401$	12.0981	+	10.1515i	0.604149	+	0.506941i	0.892776	−	0.450500i	$-0.148754\pi$
$401$	12.0981	+	10.1515i	0.604149	+	0.506941i	−0.288627	+	0.957442i	$0.593199\pi$
$402$		0			0
$403$	1.33697	+	7.58234i	0.0665993	+	0.377703i
$404$		0			0
$405$	−6.68474	−	2.43305i	−0.332167	−	0.120899i
$406$		0			0
$407$	4.51615	−	7.82220i	0.223857	−	0.387732i
$408$		0			0
$409$	9.76460	−	8.19347i	0.482829	−	0.405141i	−0.368619	−	0.929580i	$-0.620169\pi$
$409$	9.76460	−	8.19347i	0.482829	−	0.405141i	0.851448	+	0.524439i	$0.175725\pi$
$410$		0			0
$411$	−22.7929	−	39.4785i	−1.12429	−	1.94733i
$412$		0			0
$413$	0.00720652	−	0.0408702i	0.000354610	−	0.00201109i
$414$		0			0
$415$	−4.50063	+	1.63809i	−0.220927	+	0.0804109i
$416$		0			0
$417$	−37.3139			−1.82727
$418$		0			0
$419$	1.77915			0.0869172			0.0434586	−	0.999055i	$-0.486162\pi$
$419$	1.77915			0.0869172			0.0434586	+	0.999055i	$0.486162\pi$
$420$		0			0
$421$	−30.1320	+	10.9671i	−1.46854	+	0.534506i	−0.947704	−	0.319150i	$-0.896603\pi$
$421$	−30.1320	+	10.9671i	−1.46854	+	0.534506i	−0.520838	+	0.853655i	$0.674381\pi$
$422$		0			0
$423$	−5.33264	+	30.2429i	−0.259282	+	1.47046i
$424$		0			0
$425$	−3.01893	−	5.22895i	−0.146440	−	0.253641i
$426$		0			0
$427$	−1.85425	+	1.55590i	−0.0897336	+	0.0752954i
$428$		0			0
$429$	−13.7546	+	23.8237i	−0.664078	+	1.15022i
$430$		0			0
$431$	12.8374	+	4.67243i	0.618356	+	0.225063i	0.632155	−	0.774842i	$-0.282170\pi$
$431$	12.8374	+	4.67243i	0.618356	+	0.225063i	−0.0137993	+	0.999905i	$0.504393\pi$
$432$		0			0
$433$	−2.36578	−	13.4170i	−0.113692	−	0.644781i	−0.987389	−	0.158311i	$-0.949395\pi$
$433$	−2.36578	−	13.4170i	−0.113692	−	0.644781i	0.873697	−	0.486471i	$-0.161716\pi$
$434$		0			0
$435$	−17.6528	−	14.8124i	−0.846386	−	0.710202i
$436$		0			0
$437$	14.0349	−	9.95117i	0.671381	−	0.476029i
$438$		0			0
$439$	9.83630	+	8.25363i	0.469461	+	0.393924i	0.846598	−	0.532233i	$-0.178647\pi$
$439$	9.83630	+	8.25363i	0.469461	+	0.393924i	−0.377137	+	0.926157i	$0.623091\pi$
$440$		0			0
$441$	−4.26124	−	24.1667i	−0.202916	−	1.15079i
$442$		0			0
$443$	38.9124	+	14.1630i	1.84878	+	0.672902i	0.985860	+	0.167568i	$0.0535915\pi$
$443$	38.9124	+	14.1630i	1.84878	+	0.672902i	0.862924	+	0.505334i	$0.168631\pi$
$444$		0			0
$445$	2.93562	−	5.08464i	0.139162	−	0.241035i
$446$		0			0
$447$	24.6829	−	20.7114i	1.16746	−	0.979618i
$448$		0			0
$449$	4.19525	+	7.26638i	0.197986	+	0.342922i	0.947875	−	0.318642i	$-0.103227\pi$
$449$	4.19525	+	7.26638i	0.197986	+	0.342922i	−0.749889	+	0.661563i	$0.769893\pi$
$450$		0			0
$451$	−10.7035	+	60.7027i	−0.504009	+	2.85838i
$452$		0			0
$453$	47.2290	−	17.1899i	2.21901	−	0.807654i
$454$		0			0
$455$	−0.486921			−0.0228272
$456$		0			0
$457$	−40.4467			−1.89202			−0.946008	−	0.324145i	$-0.894924\pi$
$457$	−40.4467			−1.89202			−0.946008	+	0.324145i	$0.894924\pi$
$458$		0			0
$459$	7.74126	−	2.81759i	0.361331	−	0.131514i
$460$		0			0
$461$	5.11750	−	29.0228i	0.238346	−	1.35173i	−0.597106	−	0.802162i	$-0.703683\pi$
$461$	5.11750	−	29.0228i	0.238346	−	1.35173i	0.835452	−	0.549564i	$-0.185206\pi$
$462$		0			0
$463$	−3.75782	−	6.50873i	−0.174641	−	0.302486i	0.765396	−	0.643559i	$-0.222543\pi$
$463$	−3.75782	−	6.50873i	−0.174641	−	0.302486i	−0.940037	+	0.341073i	$0.889210\pi$
$464$		0			0
$465$	7.30968	−	6.13355i	0.338978	−	0.284437i
$466$		0			0
$467$	−15.4358	+	26.7355i	−0.714282	+	1.23717i	0.248954	+	0.968515i	$0.419913\pi$
$467$	−15.4358	+	26.7355i	−0.714282	+	1.23717i	−0.963236	+	0.268657i	$0.913420\pi$
$468$		0			0
$469$	0.219857	+	0.0800215i	0.0101521	+	0.00369505i
$470$		0			0
$471$	7.68747	+	43.5978i	0.354220	+	2.00888i
$472$		0			0
$473$	0.258410	+	0.216831i	0.0118817	+	0.00996992i
$474$		0			0
$475$	−0.405494	−	4.34000i	−0.0186053	−	0.199133i
$476$		0			0
$477$	4.68986	+	3.93526i	0.214734	+	0.180183i
$478$		0			0
$479$	4.58448	+	25.9999i	0.209470	+	1.18796i	0.890249	+	0.455474i	$0.150530\pi$
$479$	4.58448	+	25.9999i	0.209470	+	1.18796i	−0.680779	+	0.732489i	$0.738359\pi$
$480$		0			0
$481$	−3.35481	−	1.22105i	−0.152966	−	0.0556751i
$482$		0			0
$483$	−1.19095	+	2.06278i	−0.0541901	+	0.0938599i
$484$		0			0
$485$	2.70875	−	2.27291i	0.122998	−	0.103208i
$486$		0			0
$487$	−15.5999	−	27.0197i	−0.706897	−	1.22438i	−0.966003	−	0.258533i	$-0.916761\pi$
$487$	−15.5999	−	27.0197i	−0.706897	−	1.22438i	0.259105	−	0.965849i	$-0.416572\pi$
$488$		0			0
$489$	5.23384	−	29.6826i	0.236682	−	1.34229i
$490$		0			0
$491$	−24.9835	+	9.09324i	−1.12749	+	0.410372i	−0.837380	−	0.546622i	$-0.815914\pi$
$491$	−24.9835	+	9.09324i	−1.12749	+	0.410372i	−0.290109	+	0.956994i	$0.593691\pi$
$492$		0			0
$493$	−54.4328			−2.45153
$494$		0			0
$495$	18.4393			0.828786
$496$		0			0
$497$	1.09910	−	0.400039i	0.0493013	−	0.0179442i
$498$		0			0
$499$	5.92353	−	33.5940i	0.265173	−	1.50387i	−0.503367	−	0.864072i	$-0.667906\pi$
$499$	5.92353	−	33.5940i	0.265173	−	1.50387i	0.768541	−	0.639801i	$-0.220983\pi$
$500$		0			0
$501$	−0.171283	−	0.296671i	−0.00765237	−	0.0132543i
$502$		0			0
$503$	10.0478	−	8.43114i	0.448011	−	0.375926i	−0.390686	−	0.920524i	$-0.627762\pi$
$503$	10.0478	−	8.43114i	0.448011	−	0.375926i	0.838697	+	0.544598i	$0.183318\pi$
$504$		0			0
$505$	5.82417	−	10.0878i	0.259172	−	0.448899i
$506$		0			0
$507$	−21.0081	−	7.64631i	−0.933001	−	0.339585i
$508$		0			0
$509$	−4.69483	−	26.6257i	−0.208095	−	1.18016i	−0.892495	−	0.451057i	$-0.851047\pi$
$509$	−4.69483	−	26.6257i	−0.208095	−	1.18016i	0.684401	−	0.729106i	$-0.260064\pi$
$510$		0			0
$511$	0.438419	+	0.367877i	0.0193945	+	0.0162739i
$512$		0			0
$513$	5.92761	+	0.483407i	0.261710	+	0.0213429i
$514$		0			0
$515$	−7.30791	−	6.13206i	−0.322025	−	0.270211i
$516$		0			0
$517$	7.87424	+	44.6570i	0.346309	+	1.96401i
$518$		0			0
$519$	57.5777	+	20.9566i	2.52738	+	0.919891i
$520$		0			0
$521$	−14.5020	+	25.1182i	−0.635344	+	1.10045i	0.351098	+	0.936339i	$0.385808\pi$
$521$	−14.5020	+	25.1182i	−0.635344	+	1.10045i	−0.986442	+	0.164109i	$0.947525\pi$
$522$		0			0
$523$	−32.5685	+	27.3283i	−1.42412	+	1.19498i	−0.475037	+	0.879966i	$0.657565\pi$
$523$	−32.5685	+	27.3283i	−1.42412	+	1.19498i	−0.949087	+	0.315015i	$0.897990\pi$
$524$		0			0
$525$	0.301732	+	0.522614i	0.0131686	+	0.0228088i
$526$		0			0
$527$	3.91396	−	22.1971i	0.170495	−	0.966923i
$528$		0			0
$529$	6.97328	−	2.53807i	0.303186	−	0.110351i
$530$		0			0
$531$	0.621193			0.0269575
$532$		0			0
$533$	24.3635			1.05530
$534$		0			0
$535$	−18.6869	+	6.80147i	−0.807904	+	0.294053i
$536$		0			0
$537$	5.23578	−	29.6936i	0.225941	−	1.28137i
$538$		0			0
$539$	−18.1177	−	31.3807i	−0.780383	−	1.35166i
$540$		0			0
$541$	6.62959	−	5.56288i	0.285028	−	0.239167i	−0.489052	−	0.872255i	$-0.662657\pi$
$541$	6.62959	−	5.56288i	0.285028	−	0.239167i	0.774080	+	0.633088i	$0.218213\pi$
$542$		0			0
$543$	−1.13844	+	1.97184i	−0.0488553	+	0.0846199i
$544$		0			0
$545$	12.2430	+	4.45608i	0.524431	+	0.190877i
$546$		0			0
$547$	5.39244	+	30.5820i	0.230564	+	1.30759i	0.851757	+	0.523936i	$0.175537\pi$
$547$	5.39244	+	30.5820i	0.230564	+	1.30759i	−0.621193	+	0.783657i	$0.713352\pi$
$548$		0			0
$549$	−27.7549	−	23.2891i	−1.18455	−	0.993956i
$550$		0			0
$551$	−35.7120	−	16.3972i	−1.52138	−	0.698544i
$552$		0			0
$553$	−1.18198	−	0.991795i	−0.0502627	−	0.0421754i
$554$		0			0
$555$	0.768325	+	4.35738i	0.0326136	+	0.184961i
$556$		0			0
$557$	−15.0627	−	5.48237i	−0.638227	−	0.232296i	0.00258113	−	0.999997i	$-0.499178\pi$
$557$	−15.0627	−	5.48237i	−0.638227	−	0.232296i	−0.640808	+	0.767701i	$0.721401\pi$
$558$		0			0
$559$	0.0666667	−	0.115470i	0.00281970	−	0.00488386i
$560$		0			0
$561$	61.6915	−	51.7653i	2.60462	−	2.18553i
$562$		0			0
$563$	7.28944	+	12.6257i	0.307213	+	0.532109i	0.977752	−	0.209766i	$-0.0672701\pi$
$563$	7.28944	+	12.6257i	0.307213	+	0.532109i	−0.670538	+	0.741875i	$0.733937\pi$
$564$		0			0
$565$	−1.14146	+	6.47356i	−0.0480217	+	0.272345i
$566$		0			0
$567$	1.57817	−	0.574406i	0.0662768	−	0.0241228i
$568$		0			0
$569$	11.4134			0.478474			0.239237	−	0.970961i	$-0.423103\pi$
$569$	11.4134			0.478474			0.239237	+	0.970961i	$0.423103\pi$
$570$		0			0
$571$	42.2764			1.76921			0.884606	−	0.466340i	$-0.154428\pi$
$571$	42.2764			1.76921			0.884606	+	0.466340i	$0.154428\pi$
$572$		0			0
$573$	12.1966	−	4.43919i	0.509520	−	0.185450i
$574$		0			0
$575$	−0.685398	+	3.88708i	−0.0285831	+	0.162103i
$576$		0			0
$577$	−6.88137	−	11.9189i	−0.286475	−	0.496189i	0.686491	−	0.727139i	$-0.259150\pi$
$577$	−6.88137	−	11.9189i	−0.286475	−	0.496189i	−0.972966	+	0.230949i	$0.925817\pi$
$578$		0			0
$579$	17.3706	−	14.5757i	0.721899	−	0.605745i
$580$		0			0
$581$	0.565361	−	0.979234i	0.0234551	−	0.0406255i
$582$		0			0
$583$	8.49491	+	3.09189i	0.351823	+	0.128053i
$584$		0			0
$585$	−1.26561	−	7.17762i	−0.0523264	−	0.296758i
$586$		0			0
$587$	−16.7949	−	14.0926i	−0.693201	−	0.581664i	0.226630	−	0.973981i	$-0.427229\pi$
$587$	−16.7949	−	14.0926i	−0.693201	−	0.581664i	−0.919830	+	0.392317i	$0.871674\pi$
$588$		0			0
$589$	9.25446	−	13.3840i	0.381323	−	0.551477i
$590$		0			0
$591$	44.7969	+	37.5891i	1.84270	+	1.54621i
$592$		0			0
$593$	7.48981	+	42.4768i	0.307570	+	1.74432i	0.611155	+	0.791511i	$0.290705\pi$
$593$	7.48981	+	42.4768i	0.307570	+	1.74432i	−0.303585	+	0.952804i	$0.598184\pi$
$594$		0			0
$595$	1.33949	+	0.487533i	0.0549135	+	0.0199869i
$596$		0			0
$597$	8.69030	−	15.0520i	0.355670	−	0.616039i
$598$		0			0
$599$	0.277780	−	0.233085i	0.0113498	−	0.00952360i	−0.637095	−	0.770785i	$-0.719864\pi$
$599$	0.277780	−	0.233085i	0.0113498	−	0.00952360i	0.648445	+	0.761262i	$0.275420\pi$
$600$		0			0
$601$	8.61809	+	14.9270i	0.351539	+	0.608884i	0.986519	−	0.163645i	$-0.0523251\pi$
$601$	8.61809	+	14.9270i	0.351539	+	0.608884i	−0.634980	+	0.772528i	$0.718992\pi$
$602$		0			0
$603$	−0.608129	+	3.44887i	−0.0247649	+	0.140449i
$604$		0			0
$605$	15.2491	−	5.55022i	0.619964	−	0.225648i
$606$		0			0
$607$	43.4646			1.76417			0.882086	−	0.471088i	$-0.156139\pi$
$607$	43.4646			1.76417			0.882086	+	0.471088i	$0.156139\pi$
$608$		0			0
$609$	5.44036			0.220455
$610$		0			0
$611$	16.8426	−	6.13019i	0.681377	−	0.248001i
$612$		0			0
$613$	−3.33887	+	18.9357i	−0.134856	+	0.764805i	0.840104	+	0.542425i	$0.182494\pi$
$613$	−3.33887	+	18.9357i	−0.134856	+	0.764805i	−0.974960	+	0.222380i	$0.928617\pi$
$614$		0			0
$615$	−15.0974	−	26.1495i	−0.608786	−	1.05445i
$616$		0			0
$617$	15.8140	−	13.2695i	0.636647	−	0.534210i	−0.266340	−	0.963879i	$-0.585814\pi$
$617$	15.8140	−	13.2695i	0.636647	−	0.534210i	0.902986	+	0.429669i	$0.141370\pi$
$618$		0			0
$619$	−12.2404	+	21.2011i	−0.491985	+	0.852143i	−0.999957	−	0.00923061i	$-0.997062\pi$
$619$	−12.2404	+	21.2011i	−0.491985	+	0.852143i	0.507973	+	0.861373i	$0.330395\pi$
$620$		0			0
$621$	−5.06058	−	1.84190i	−0.203074	−	0.0739130i
$622$		0			0
$623$	0.240696	+	1.36505i	0.00964327	+	0.0546897i
$624$		0			0
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$		0			0
$627$	56.0679	−	15.3782i	2.23914	−	0.614145i
$628$		0			0
$629$	8.00626	+	6.71805i	0.319231	+	0.267866i
$630$		0			0
$631$	−5.95880	−	33.7940i	−0.237216	−	1.34532i	−0.837896	−	0.545829i	$-0.816215\pi$
$631$	−5.95880	−	33.7940i	−0.237216	−	1.34532i	0.600680	−	0.799489i	$-0.294896\pi$
$632$		0			0
$633$	26.0211	+	9.47092i	1.03425	+	0.376435i
$634$		0			0
$635$	−6.08205	+	10.5344i	−0.241359	+	0.418046i
$636$		0			0
$637$	−10.9716	+	9.20627i	−0.434711	+	0.364766i
$638$		0			0
$639$	8.75370	+	15.1619i	0.346291	+	0.599794i
$640$		0			0
$641$	0.820906	−	4.65559i	0.0324238	−	0.183885i	−0.964295	−	0.264832i	$-0.914683\pi$
$641$	0.820906	−	4.65559i	0.0324238	−	0.183885i	0.996718	+	0.0809474i	$0.0257946\pi$
$642$		0			0
$643$	−3.58886	+	1.30624i	−0.141531	+	0.0515130i	−0.411814	−	0.911268i	$-0.635105\pi$
$643$	−3.58886	+	1.30624i	−0.141531	+	0.0515130i	0.270284	+	0.962781i	$0.412883\pi$
$644$		0			0
$645$	−0.165246			−0.00650656
$646$		0			0
$647$	7.12252			0.280015			0.140008	−	0.990150i	$-0.455287\pi$
$647$	7.12252			0.280015			0.140008	+	0.990150i	$0.455287\pi$
$648$		0			0
$649$	0.861943	−	0.313722i	0.0338342	−	0.0123147i
$650$		0			0
$651$	−0.391186	+	2.21853i	−0.0153318	+	0.0869509i
$652$		0			0
$653$	−5.16829	−	8.95175i	−0.202251	−	0.350309i	0.747002	−	0.664821i	$-0.231492\pi$
$653$	−5.16829	−	8.95175i	−0.202251	−	0.350309i	−0.949253	+	0.314512i	$0.898159\pi$
$654$		0			0
$655$	0.637106	−	0.534596i	0.0248938	−	0.0208884i
$656$		0			0
$657$	−4.28328	+	7.41885i	−0.167107	+	0.289437i
$658$		0			0
$659$	−1.81962	−	0.662288i	−0.0708824	−	0.0257991i	0.306336	−	0.951924i	$-0.400897\pi$
$659$	−1.81962	−	0.662288i	−0.0708824	−	0.0257991i	−0.377218	+	0.926124i	$0.623119\pi$
$660$		0			0
$661$	6.66418	+	37.7945i	0.259207	+	1.47003i	0.785039	+	0.619446i	$0.212643\pi$
$661$	6.66418	+	37.7945i	0.259207	+	1.47003i	−0.525832	+	0.850588i	$0.676246\pi$
$662$		0			0
$663$	−24.3842	−	20.4608i	−0.947006	−	0.794632i
$664$		0			0
$665$	0.731940	+	0.723361i	0.0283834	+	0.0280507i
$666$		0			0
$667$	27.2586	+	22.8727i	1.05546	+	0.885634i
$668$		0			0
$669$	−10.6643	−	60.4802i	−0.412305	−	2.33830i
$670$		0			0
$671$	−50.2734	−	18.2980i	−1.94078	−	0.706387i
$672$		0			0
$673$	−20.6769	+	35.8134i	−0.797035	+	1.38050i	0.124504	+	0.992219i	$0.460266\pi$
$673$	−20.6769	+	35.8134i	−0.797035	+	1.38050i	−0.921539	+	0.388286i	$0.873067\pi$
$674$		0			0
$675$	−1.04519	+	0.877021i	−0.0402295	+	0.0337565i
$676$		0			0
$677$	6.63593	+	11.4938i	0.255039	+	0.441741i	0.964906	−	0.262595i	$-0.0845782\pi$
$677$	6.63593	+	11.4938i	0.255039	+	0.441741i	−0.709867	+	0.704336i	$0.751245\pi$
$678$		0			0
$679$	−0.144962	+	0.822121i	−0.00556313	+	0.0315501i
$680$		0			0
$681$	−48.0591	+	17.4921i	−1.84163	+	0.670299i
$682$		0			0
$683$	8.82787			0.337789			0.168894	−	0.985634i	$-0.445980\pi$
$683$	8.82787			0.337789			0.168894	+	0.985634i	$0.445980\pi$
$684$		0			0
$685$	17.8340			0.681401
$686$		0			0
$687$	16.5482	−	6.02306i	0.631354	−	0.229794i
$688$		0			0
$689$	0.620479	−	3.51891i	0.0236384	−	0.134060i
$690$		0			0
$691$	−0.657277	−	1.13844i	−0.0250040	−	0.0433082i	0.853253	−	0.521498i	$-0.174627\pi$
$691$	−0.657277	−	1.13844i	−0.0250040	−	0.0433082i	−0.878257	+	0.478190i	$0.841293\pi$
$692$		0			0
$693$	−3.33478	+	2.79822i	−0.126678	+	0.106295i
$694$		0			0
$695$	7.29892	−	12.6421i	0.276864	−	0.479542i
$696$		0			0
$697$	−67.0223	−	24.3941i	−2.53865	−	0.923994i
$698$		0			0
$699$	−3.59116	−	20.3665i	−0.135830	−	0.770331i
$700$		0			0
$701$	10.7483	+	9.01893i	0.405959	+	0.340640i	0.822792	−	0.568343i	$-0.192415\pi$
$701$	10.7483	+	9.01893i	0.405959	+	0.340640i	−0.416832	+	0.908983i	$0.636860\pi$
$702$		0			0
$703$	3.22898	+	6.81933i	0.121783	+	0.257196i
$704$		0			0
$705$	−17.0164	−	14.2785i	−0.640876	−	0.537759i
$706$		0			0
$707$	0.477533	+	2.70822i	0.0179595	+	0.101853i
$708$		0			0
$709$	−29.7957	−	10.8447i	−1.11900	−	0.407283i	−0.284713	−	0.958613i	$-0.591898\pi$
$709$	−29.7957	−	10.8447i	−1.11900	−	0.407283i	−0.834287	+	0.551330i	$0.814121\pi$
$710$		0			0
$711$	11.5477	−	20.0012i	0.433072	−	0.750103i
$712$		0			0
$713$	−11.2873	+	9.47114i	−0.422711	+	0.354697i
$714$		0			0
$715$	−5.38103	−	9.32022i	−0.201239	−	0.348557i
$716$		0			0
$717$	−5.43051	+	30.7979i	−0.202806	+	1.15017i
$718$		0			0
$719$	21.2941	−	7.75043i	0.794137	−	0.289042i	0.0870823	−	0.996201i	$-0.472246\pi$
$719$	21.2941	−	7.75043i	0.794137	−	0.289042i	0.707055	+	0.707159i	$0.250023\pi$
$720$		0			0
$721$	2.25220			0.0838764
$722$		0			0
$723$	2.40924			0.0896005
$724$		0			0
$725$	8.47155	−	3.08339i	0.314625	−	0.114514i
$726$		0			0
$727$	−6.03930	+	34.2506i	−0.223985	+	1.27028i	0.640630	+	0.767850i	$0.278673\pi$
$727$	−6.03930	+	34.2506i	−0.223985	+	1.27028i	−0.864615	+	0.502434i	$0.832438\pi$
$728$		0			0
$729$	17.8006	+	30.8315i	0.659281	+	1.14191i
$730$		0			0
$731$	−0.299010	+	0.250900i	−0.0110593	+	0.00927985i
$732$		0			0
$733$	2.83708	−	4.91397i	0.104790	−	0.181502i	−0.808862	−	0.587998i	$-0.799916\pi$
$733$	2.83708	−	4.91397i	0.104790	−	0.181502i	0.913652	+	0.406496i	$0.133250\pi$
$734$		0			0
$735$	16.6799	+	6.07100i	0.615248	+	0.223932i
$736$		0			0
$737$	0.897971	+	5.09265i	0.0330772	+	0.187590i
$738$		0			0
$739$	19.8424	+	16.6497i	0.729913	+	0.612470i	0.930108	−	0.367286i	$-0.119713\pi$
$739$	19.8424	+	16.6497i	0.729913	+	0.612470i	−0.200195	+	0.979756i	$0.564158\pi$
$740$		0			0
$741$	−9.83434	−	20.7693i	−0.361274	−	0.762979i
$742$		0			0
$743$	−19.7891	−	16.6050i	−0.725992	−	0.609179i	0.203044	−	0.979170i	$-0.434917\pi$
$743$	−19.7891	−	16.6050i	−0.725992	−	0.609179i	−0.929036	+	0.369990i	$0.879361\pi$
$744$		0			0
$745$	2.18893	+	12.4140i	0.0801960	+	0.454814i
$746$		0			0
$747$	15.9042	+	5.78866i	0.581905	+	0.211796i
$748$		0			0
$749$	2.34741	−	4.06584i	0.0857726	−	0.148562i
$750$		0			0
$751$	−22.1536	+	18.5891i	−0.808397	+	0.678325i	−0.950225	−	0.311566i	$-0.899147\pi$
$751$	−22.1536	+	18.5891i	−0.808397	+	0.678325i	0.141828	+	0.989891i	$0.454702\pi$
$752$		0			0
$753$	−22.2065	−	38.4628i	−0.809250	−	1.40166i
$754$		0			0
$755$	−3.41437	+	19.3639i	−0.124262	+	0.704723i
$756$		0			0
$757$	−0.0387621	+	0.0141082i	−0.00140883	+	0.000512773i	−0.342724	−	0.939436i	$-0.611350\pi$
$757$	−0.0387621	+	0.0141082i	−0.00140883	+	0.000512773i	0.341316	+	0.939949i	$0.389128\pi$
$758$		0			0
$759$	−52.6454			−1.91091
$760$		0			0
$761$	−18.9666			−0.687538			−0.343769	−	0.939054i	$-0.611704\pi$
$761$	−18.9666			−0.687538			−0.343769	+	0.939054i	$0.611704\pi$
$762$		0			0
$763$	−2.89038	+	1.05201i	−0.104639	+	0.0380854i
$764$		0			0
$765$	−3.70504	+	21.0123i	−0.133956	+	0.759702i
$766$		0			0
$767$	−0.181279	−	0.313984i	−0.00654559	−	0.0113373i
$768$		0			0
$769$	−22.9870	+	19.2883i	−0.828931	+	0.695556i	−0.955045	−	0.296460i	$-0.904194\pi$
$769$	−22.9870	+	19.2883i	−0.828931	+	0.695556i	0.126114	+	0.992016i	$0.459749\pi$
$770$		0			0
$771$	−5.57648	+	9.65874i	−0.200832	+	0.347851i
$772$		0			0
$773$	46.8749	+	17.0611i	1.68597	+	0.613644i	0.994109	−	0.108383i	$-0.0345674\pi$
$773$	46.8749	+	17.0611i	1.68597	+	0.613644i	0.691864	+	0.722028i	$0.256790\pi$
$774$		0			0
$775$	0.648235	+	3.67632i	0.0232853	+	0.132057i
$776$		0			0
$777$	−0.800197	−	0.671445i	−0.0287069	−	0.0240880i
$778$		0			0
$779$	−36.6233	−	36.1940i	−1.31217	−	1.29679i
$780$		0			0
$781$	19.8035	+	16.6171i	0.708626	+	0.594607i
$782$		0			0
$783$	2.13594	+	12.1135i	0.0763324	+	0.432902i
$784$		0			0
$785$	−16.2749	−	5.92356i	−0.580874	−	0.211421i
$786$		0			0
$787$	6.07584	−	10.5237i	0.216580	−	0.375128i	−0.737180	−	0.675696i	$-0.763843\pi$
$787$	6.07584	−	10.5237i	0.216580	−	0.375128i	0.953760	+	0.300568i	$0.0971764\pi$
$788$		0			0
$789$	20.0819	−	16.8507i	0.714934	−	0.599901i
$790$		0			0
$791$	−0.775944	−	1.34397i	−0.0275894	−	0.0477862i
$792$		0			0
$793$	−3.67203	+	20.8251i	−0.130398	+	0.739522i
$794$		0			0
$795$	−4.16136	+	1.51461i	−0.147588	+	0.0537177i
$796$		0			0
$797$	−26.2815			−0.930938			−0.465469	−	0.885064i	$-0.654114\pi$
$797$	−26.2815			−0.930938			−0.465469	+	0.885064i	$0.654114\pi$
$798$		0			0
$799$	−52.4706			−1.85628
$800$		0			0
$801$	−19.4964	+	7.09611i	−0.688872	+	0.250729i
$802$		0			0
$803$	−2.19656	+	12.4573i	−0.0775149	+	0.439609i
$804$		0			0
$805$	−0.465920	−	0.806997i	−0.0164215	−	0.0284429i
$806$		0			0
$807$	−44.1783	+	37.0700i	−1.55515	+	1.30493i
$808$		0			0
$809$	−10.1543	+	17.5878i	−0.357007	+	0.618354i	−0.987459	−	0.157874i	$-0.949536\pi$
$809$	−10.1543	+	17.5878i	−0.357007	+	0.618354i	0.630453	+	0.776228i	$0.282869\pi$
$810$		0			0
$811$	−16.0707	−	5.84926i	−0.564319	−	0.205395i	0.0440781	−	0.999028i	$-0.485965\pi$
$811$	−16.0707	−	5.84926i	−0.564319	−	0.205395i	−0.608397	+	0.793633i	$0.708187\pi$
$812$		0			0
$813$	−12.4404	−	70.5530i	−0.436304	−	2.47440i
$814$		0			0
$815$	9.03279	+	7.57941i	0.316405	+	0.265495i
$816$		0			0
$817$	−0.271754	+	0.0745359i	−0.00950746	+	0.00260768i
$818$		0			0
$819$	1.31811	+	1.10603i	0.0460585	+	0.0386477i
$820$		0			0
$821$	0.505075	+	2.86442i	0.0176272	+	0.0999690i	0.992352	−	0.123440i	$-0.0393926\pi$
$821$	0.505075	+	2.86442i	0.0176272	+	0.0999690i	−0.974725	+	0.223409i	$0.928281\pi$
$822$		0			0
$823$	−27.3184	−	9.94309i	−0.952260	−	0.346594i	−0.181264	−	0.983434i	$-0.558019\pi$
$823$	−27.3184	−	9.94309i	−0.952260	−	0.346594i	−0.770996	+	0.636840i	$0.780241\pi$
$824$		0			0
$825$	−6.66896	+	11.5510i	−0.232183	+	0.402153i
$826$		0			0
$827$	−43.6367	+	36.6155i	−1.51740	+	1.27325i	−0.669891	+	0.742459i	$0.733659\pi$
$827$	−43.6367	+	36.6155i	−1.51740	+	1.27325i	−0.847505	+	0.530788i	$0.821896\pi$
$828$		0			0
$829$	5.23885	+	9.07395i	0.181953	+	0.315151i	0.942545	−	0.334078i	$-0.108425\pi$
$829$	5.23885	+	9.07395i	0.181953	+	0.315151i	−0.760593	+	0.649229i	$0.775092\pi$
$830$		0			0
$831$	−4.73824	+	26.8719i	−0.164368	+	0.932176i
$832$		0			0
$833$	39.3999	−	14.3404i	1.36513	−	0.496866i
$834$		0			0
$835$	0.134018			0.00463788
$836$		0			0
$837$	−5.09336			−0.176052
$838$		0			0
$839$	−4.60654	+	1.67664i	−0.159036	+	0.0578842i	−0.420311	−	0.907380i	$-0.638079\pi$
$839$	−4.60654	+	1.67664i	−0.159036	+	0.0578842i	0.261276	+	0.965264i	$0.415857\pi$
$840$		0			0
$841$	9.07737	−	51.4803i	0.313013	−	1.77518i
$842$		0			0
$843$	−24.2399	−	41.9847i	−0.834865	−	1.44603i
$844$		0			0
$845$	6.69996	−	5.62193i	0.230486	−	0.193400i
$846$		0			0
$847$	−1.91556	+	3.31786i	−0.0658196	+	0.114003i
$848$		0			0
$849$	6.15341	+	2.23966i	0.211185	+	0.0768649i
$850$		0			0
$851$	−1.18641	−	6.72847i	−0.0406696	−	0.230649i
$852$		0			0
$853$	−23.8434	−	20.0070i	−0.816382	−	0.685026i	0.135740	−	0.990745i	$-0.456659\pi$
$853$	−23.8434	−	20.0070i	−0.816382	−	0.685026i	−0.952122	+	0.305719i	$0.901103\pi$
$854$		0			0
$855$	−8.76048	+	12.6696i	−0.299602	+	0.433290i
$856$		0			0
$857$	−2.70967	−	2.27369i	−0.0925607	−	0.0776677i	0.595333	−	0.803479i	$-0.297020\pi$
$857$	−2.70967	−	2.27369i	−0.0925607	−	0.0776677i	−0.687894	+	0.725811i	$0.741465\pi$
$858$		0			0
$859$	4.03531	+	22.8854i	0.137683	+	0.780838i	0.972954	+	0.231000i	$0.0741997\pi$
$859$	4.03531	+	22.8854i	0.137683	+	0.780838i	−0.835271	+	0.549839i	$0.814689\pi$
$860$		0			0
$861$	6.69864	+	2.43811i	0.228289	+	0.0830905i
$862$		0			0
$863$	13.3464	−	23.1166i	0.454315	−	0.786897i	−0.544333	−	0.838869i	$-0.683217\pi$
$863$	13.3464	−	23.1166i	0.454315	−	0.786897i	0.998649	+	0.0519720i	$0.0165507\pi$
$864$		0			0
$865$	−18.3629	+	15.4083i	−0.624356	+	0.523897i
$866$		0			0
$867$	24.8658	+	43.0688i	0.844486	+	1.46269i
$868$		0			0
$869$	5.92191	−	33.5848i	0.200887	−	1.13929i
$870$		0			0
$871$	1.92071	−	0.699082i	0.0650808	−	0.0236875i
$872$		0			0
$873$	−12.4955			−0.422910
$874$		0			0
$875$	−0.236085			−0.00798113
$876$		0			0
$877$	−22.2343	+	8.09263i	−0.750799	+	0.273269i	−0.688942	−	0.724816i	$-0.741925\pi$
$877$	−22.2343	+	8.09263i	−0.750799	+	0.273269i	−0.0618573	+	0.998085i	$0.519702\pi$
$878$		0			0
$879$	1.25166	−	7.09853i	0.0422175	−	0.239428i
$880$		0			0
$881$	−4.69582	−	8.13340i	−0.158206	−	0.274021i	0.776016	−	0.630714i	$-0.217238\pi$
$881$	−4.69582	−	8.13340i	−0.158206	−	0.274021i	−0.934222	+	0.356692i	$0.883904\pi$
$882$		0			0
$883$	28.3016	−	23.7479i	0.952424	−	0.799179i	−0.0272797	−	0.999628i	$-0.508684\pi$
$883$	28.3016	−	23.7479i	0.952424	−	0.799179i	0.979704	+	0.200449i	$0.0642400\pi$
$884$		0			0
$885$	−0.224667	+	0.389135i	−0.00755210	+	0.0130806i
$886$		0			0
$887$	5.81504	+	2.11650i	0.195250	+	0.0710652i	0.437794	−	0.899075i	$-0.355760\pi$
$887$	5.81504	+	2.11650i	0.195250	+	0.0710652i	−0.242544	+	0.970140i	$0.577982\pi$
$888$		0			0
$889$	−0.498676	−	2.82813i	−0.0167251	−	0.0948526i
$890$		0			0
$891$	28.4353	+	23.8601i	0.952620	+	0.799343i
$892$		0			0
$893$	−34.4247	−	15.8061i	−1.15198	−	0.528931i
$894$		0			0
$895$	9.03614	+	7.58222i	0.302045	+	0.253446i
$896$		0			0
$897$	3.61339	+	20.4925i	0.120648	+	0.684226i
$898$		0			0
$899$	31.6246	+	11.5104i	1.05474	+	0.383894i
$900$		0			0
$901$	−5.23022	+	9.05901i	−0.174244	+	0.301800i
$902$		0			0
$903$	0.0298850	−	0.0250765i	0.000994511	−	0.000834494i
$904$		0			0
$905$	−0.445379	−	0.771419i	−0.0148049	−	0.0256428i
$906$		0			0
$907$	4.47030	−	25.3523i	0.148434	−	0.841811i	−0.816112	−	0.577894i	$-0.803875\pi$
$907$	4.47030	−	25.3523i	0.148434	−	0.841811i	0.964546	−	0.263917i	$-0.0850143\pi$
$908$		0			0
$909$	−38.6802	+	14.0785i	−1.28294	+	0.466953i
$910$		0			0
$911$	39.2207			1.29944			0.649721	−	0.760173i	$-0.274886\pi$
$911$	39.2207			1.29944			0.649721	+	0.760173i	$0.274886\pi$
$912$		0			0
$913$	24.9916			0.827100
$914$		0			0
$915$	24.6272	−	8.96356i	0.814149	−	0.296326i
$916$		0			0
$917$	−0.0340955	+	0.193365i	−0.00112593	+	0.00638548i
$918$		0			0
$919$	12.6535	+	21.9166i	0.417401	+	0.722961i	0.995677	−	0.0928808i	$-0.0296076\pi$
$919$	12.6535	+	21.9166i	0.417401	+	0.722961i	−0.578276	+	0.815841i	$0.696274\pi$
$920$		0			0
$921$	−21.2865	+	17.8615i	−0.701415	+	0.588557i
$922$		0			0
$923$	5.10908	−	8.84918i	0.168167	−	0.291274i
$924$		0			0
$925$	−1.62659	−	0.592030i	−0.0534820	−	0.0194658i
$926$		0			0
$927$	5.85394	+	33.1994i	0.192269	+	1.09041i
$928$		0			0
$929$	36.0605	+	30.2583i	1.18311	+	0.992744i	0.999953	+	0.00965926i	$0.00307469\pi$
$929$	36.0605	+	30.2583i	1.18311	+	0.992744i	0.183153	+	0.983084i	$0.441370\pi$
$930$		0			0
$931$	30.1692	+	2.46035i	0.988755	+	0.0806347i
$932$		0			0
$933$	−58.2920	−	48.9128i	−1.90839	−	1.60133i
$934$		0			0
$935$	5.47091	+	31.0271i	0.178918	+	1.01469i
$936$		0			0
$937$	21.7175	+	7.90454i	0.709481	+	0.258230i	0.671453	−	0.741047i	$-0.265670\pi$
$937$	21.7175	+	7.90454i	0.709481	+	0.258230i	0.0380275	+	0.999277i	$0.487893\pi$
$938$		0			0
$939$	45.0068	−	77.9541i	1.46874	−	2.54394i
$940$		0			0
$941$	22.9733	−	19.2769i	0.748908	−	0.628408i	−0.186306	−	0.982492i	$-0.559652\pi$
$941$	22.9733	−	19.2769i	0.748908	−	0.628408i	0.935214	+	0.354084i	$0.115207\pi$
$942$		0			0
$943$	23.3127	+	40.3788i	0.759166	+	1.31491i
$944$		0			0
$945$	0.0559347	−	0.317221i	0.00181956	−	0.0103192i
$946$		0			0
$947$	6.19288	−	2.25402i	0.201241	−	0.0732459i	−0.239433	−	0.970913i	$-0.576962\pi$
$947$	6.19288	−	2.25402i	0.201241	−	0.0732459i	0.440674	+	0.897667i	$0.354739\pi$
$948$		0			0
$949$	4.99985			0.162302
$950$		0			0
$951$	−75.4245			−2.44581
$952$		0			0
$953$	19.7024	−	7.17110i	0.638225	−	0.232295i	−0.00258241	−	0.999997i	$-0.500822\pi$
$953$	19.7024	−	7.17110i	0.638225	−	0.232295i	0.640807	+	0.767702i	$0.278600\pi$
$954$		0			0
$955$	−0.881740	+	5.00060i	−0.0285324	+	0.161815i
$956$		0			0
$957$	60.1222	+	104.135i	1.94348	+	3.36620i
$958$		0			0
$959$	−3.22530	+	2.70635i	−0.104150	+	0.0873926i
$960$		0			0
$961$	8.53222	−	14.7782i	0.275233	−	0.476717i
$962$		0			0
$963$	66.0352	+	24.0349i	2.12796	+	0.774513i
$964$		0			0
$965$	1.54046	+	8.73637i	0.0495891	+	0.281234i
$966$		0			0
$967$	−17.6688	−	14.8259i	−0.568189	−	0.476768i	0.312855	−	0.949801i	$-0.398715\pi$
$967$	−17.6688	−	14.8259i	−0.568189	−	0.476768i	−0.881045	+	0.473033i	$0.843159\pi$
$968$		0			0
$969$	6.25820	+	66.9815i	0.201042	+	2.15176i
$970$		0			0
$971$	−5.59628	−	4.69583i	−0.179593	−	0.150696i	0.548560	−	0.836111i	$-0.315176\pi$
$971$	−5.59628	−	4.69583i	−0.179593	−	0.150696i	−0.728153	+	0.685415i	$0.759621\pi$
$972$		0			0
$973$	0.598449	+	3.39397i	0.0191854	+	0.108806i
$974$		0			0
$975$	4.95402	+	1.80312i	0.158656	+	0.0577459i
$976$		0			0
$977$	14.8565	−	25.7323i	0.475303	−	0.823248i	−0.524297	−	0.851535i	$-0.675672\pi$
$977$	14.8565	−	25.7323i	0.475303	−	0.823248i	0.999600	+	0.0282870i	$0.00900523\pi$
$978$		0			0
$979$	−23.4687	+	19.6926i	−0.750064	+	0.629378i
$980$		0			0
$981$	−23.0203	−	39.8723i	−0.734980	−	1.27302i
$982$		0			0
$983$	10.5587	−	59.8814i	0.336770	−	1.90992i	−0.0722359	−	0.997388i	$-0.523013\pi$
$983$	10.5587	−	59.8814i	0.336770	−	1.90992i	0.409006	−	0.912532i	$-0.365875\pi$
$984$		0			0
$985$	−21.4980	+	7.82463i	−0.684983	+	0.249313i
$986$		0			0
$987$	5.24425			0.166926
$988$		0			0
$989$	0.255165			0.00811378
$990$		0			0
$991$	34.1295	−	12.4221i	1.08416	−	0.394602i	0.262705	−	0.964876i	$-0.415385\pi$
$991$	34.1295	−	12.4221i	1.08416	−	0.394602i	0.821454	+	0.570275i	$0.193163\pi$
$992$		0			0
$993$	−5.05491	+	28.6678i	−0.160413	+	0.909746i
$994$		0			0
$995$	3.39979	+	5.88862i	0.107781	+	0.186682i
$996$		0			0
$997$	39.4636	−	33.1139i	1.24982	−	1.04873i	0.253134	−	0.967431i	$-0.418539\pi$
$997$	39.4636	−	33.1139i	1.24982	−	1.04873i	0.996690	−	0.0812952i	$-0.0259056\pi$
$998$		0			0
$999$	1.18088	−	2.04534i	0.0373613	−	0.0647117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.a.301.3	yes	18
19.5	even	9		7220.2.a.v.1.2		9
19.6	even	9	inner	380.2.u.a.101.3	✓	18
19.14	odd	18		7220.2.a.x.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.a.101.3	✓	18	19.6	even	9	inner
380.2.u.a.301.3	yes	18	1.1	even	1	trivial
7220.2.a.v.1.2		9	19.5	even	9
7220.2.a.x.1.8		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)

\(f(q)\)	\(=\)	\(q+(2.40197 - 0.874246i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-0.118043 - 0.204456i) q^{7} +(2.70703 - 2.27147i) q^{9} +O(q^{10})\)	\(q+(2.40197 - 0.874246i) q^{3} +(-0.173648 + 0.984808i) q^{5} +(-0.118043 - 0.204456i) q^{7} +(2.70703 - 2.27147i) q^{9} +(2.60901 - 4.51894i) q^{11} +(-1.93810 - 0.705410i) q^{13} +(0.443867 + 2.51729i) q^{15} +(4.62527 + 3.88107i) q^{17} +(1.86541 + 3.93958i) q^{19} +(-0.462280 - 0.387899i) q^{21} +(-0.685398 - 3.88708i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(0.682201 - 1.18161i) q^{27} +(-6.90607 + 5.79488i) q^{29} +(-1.86652 - 3.23290i) q^{31} +(2.31611 - 13.1353i) q^{33} +(0.221847 - 0.0807459i) q^{35} +1.73098 q^{37} -5.27196 q^{39} +(-11.1003 + 4.04019i) q^{41} +(-0.0112258 + 0.0636649i) q^{43} +(1.76689 + 3.06034i) q^{45} +(-6.65712 + 5.58599i) q^{47} +(3.47213 - 6.01391i) q^{49} +(14.5028 + 5.27858i) q^{51} +(0.300841 + 1.70615i) q^{53} +(3.99724 + 3.35408i) q^{55} +(7.92481 + 7.83193i) q^{57} +(0.134661 + 0.112994i) q^{59} +(-1.78040 - 10.0971i) q^{61} +(-0.783959 - 0.285338i) q^{63} +(1.03124 - 1.78616i) q^{65} +(-0.759172 + 0.637021i) q^{67} +(-5.04458 - 8.73746i) q^{69} +(-0.860306 + 4.87904i) q^{71} +(-2.27800 + 0.829123i) q^{73} -2.55613 q^{75} -1.23190 q^{77} +(6.14146 - 2.23531i) q^{79} +(-1.23529 + 7.00568i) q^{81} +(2.39473 + 4.14780i) q^{83} +(-4.62527 + 3.88107i) q^{85} +(-11.5220 + 19.9568i) q^{87} +(-5.51716 - 2.00808i) q^{89} +(0.0845529 + 0.479523i) q^{91} +(-7.30968 - 6.13355i) q^{93} +(-4.20365 + 1.15297i) q^{95} +(-2.70875 - 2.27291i) q^{97} +(-3.20196 - 18.1592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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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