LMFDB - Embedded newform 380.2.bh.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80092 - 0.839782i) q^{3} +(-1.74340 - 1.40020i) q^{5} +(-0.755503 - 2.81958i) q^{7} +(0.609708 - 0.726622i) q^{9} +O(q^{10})$	\(q+(1.80092 - 0.839782i) q^{3} +(-1.74340 - 1.40020i) q^{5} +(-0.755503 - 2.81958i) q^{7} +(0.609708 - 0.726622i) q^{9} +(1.17270 + 2.03117i) q^{11} +(2.20631 - 4.73144i) q^{13} +(-4.31558 - 1.05758i) q^{15} +(0.125014 - 1.42892i) q^{17} +(-3.05201 - 3.11211i) q^{19} +(-3.72843 - 4.44337i) q^{21} +(2.21427 - 1.55045i) q^{23} +(1.07886 + 4.88222i) q^{25} +(-1.05506 + 3.93755i) q^{27} +(5.56573 + 4.67020i) q^{29} +(2.34635 + 1.35467i) q^{31} +(3.81768 + 2.67317i) q^{33} +(-2.63084 + 5.97350i) q^{35} +(-3.32665 - 3.32665i) q^{37} -10.3738i q^{39} +(-1.41908 + 3.89890i) q^{41} +(-3.51529 + 5.02035i) q^{43} +(-2.08038 + 0.413075i) q^{45} +(8.34312 - 0.729929i) q^{47} +(-1.31705 + 0.760401i) q^{49} +(-0.974838 - 2.67835i) q^{51} +(2.51445 + 3.59100i) q^{53} +(0.799577 - 5.18316i) q^{55} +(-8.10991 - 3.04164i) q^{57} +(7.59535 - 6.37326i) q^{59} +(-1.68347 + 9.54743i) q^{61} +(-2.50940 - 1.17015i) q^{63} +(-10.4715 + 5.15950i) q^{65} +(-0.534287 - 6.10693i) q^{67} +(2.68568 - 4.65173i) q^{69} +(4.76199 - 0.839668i) q^{71} +(5.54088 + 11.8824i) q^{73} +(6.04294 + 7.88646i) q^{75} +(4.84108 - 4.84108i) q^{77} +(-16.5155 - 6.01117i) q^{79} +(1.90073 + 10.7796i) q^{81} +(13.1282 - 3.51769i) q^{83} +(-2.21872 + 2.31612i) q^{85} +(13.9454 + 3.73665i) q^{87} +(-4.65929 + 1.69584i) q^{89} +(-15.0075 - 2.64623i) q^{91} +(5.36321 + 0.469220i) q^{93} +(0.963270 + 9.69908i) q^{95} +(5.32688 + 0.466041i) q^{97} +(2.19090 + 0.386315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.80092	−	0.839782i	1.03976	−	0.484848i	0.173706	−	0.984798i	$-0.444426\pi$
$3$	1.80092	−	0.839782i	1.03976	−	0.484848i	0.866055	+	0.499949i	$0.166648\pi$
$4$		0			0
$5$	−1.74340	−	1.40020i	−0.779671	−	0.626190i
$5$	−1.74340	−	1.40020i	−0.779671	−	0.626190i
$6$		0			0
$7$	−0.755503	−	2.81958i	−0.285553	−	1.06570i	−0.948434	−	0.316975i	$-0.897333\pi$
$7$	−0.755503	−	2.81958i	−0.285553	−	1.06570i	0.662880	−	0.748725i	$-0.269334\pi$
$8$		0			0
$9$	0.609708	−	0.726622i	0.203236	−	0.242207i
$10$		0			0
$11$	1.17270	+	2.03117i	0.353582	+	0.612422i	0.986874	−	0.161491i	$-0.0516302\pi$
$11$	1.17270	+	2.03117i	0.353582	+	0.612422i	−0.633292	+	0.773913i	$0.718297\pi$
$12$		0			0
$13$	2.20631	−	4.73144i	0.611920	−	1.31227i	−0.319247	−	0.947672i	$-0.603430\pi$
$13$	2.20631	−	4.73144i	0.611920	−	1.31227i	0.931166	−	0.364594i	$-0.118792\pi$
$14$		0			0
$15$	−4.31558	−	1.05758i	−1.11428	−	0.273065i
$16$		0			0
$17$	0.125014	−	1.42892i	0.0303204	−	0.346563i	−0.965848	−	0.259109i	$-0.916571\pi$
$17$	0.125014	−	1.42892i	0.0303204	−	0.346563i	0.996169	−	0.0874545i	$-0.0278732\pi$
$18$		0			0
$19$	−3.05201	−	3.11211i	−0.700179	−	0.713968i
$19$	−3.05201	−	3.11211i	−0.700179	−	0.713968i
$20$		0			0
$21$	−3.72843	−	4.44337i	−0.813610	−	0.969622i
$22$		0			0
$23$	2.21427	−	1.55045i	0.461707	−	0.323291i	−0.319474	−	0.947595i	$-0.603506\pi$
$23$	2.21427	−	1.55045i	0.461707	−	0.323291i	0.781181	+	0.624304i	$0.214617\pi$
$24$		0			0
$25$	1.07886	+	4.88222i	0.215773	+	0.976444i
$26$		0			0
$27$	−1.05506	+	3.93755i	−0.203047	+	0.757781i
$28$		0			0
$29$	5.56573	+	4.67020i	1.03353	+	0.867235i	0.991267	−	0.131871i	$-0.0420986\pi$
$29$	5.56573	+	4.67020i	1.03353	+	0.867235i	0.0422637	+	0.999106i	$0.486543\pi$
$30$		0			0
$31$	2.34635	+	1.35467i	0.421418	+	0.243306i	0.695684	−	0.718348i	$-0.255102\pi$
$31$	2.34635	+	1.35467i	0.421418	+	0.243306i	−0.274266	+	0.961654i	$0.588435\pi$
$32$		0			0
$33$	3.81768	+	2.67317i	0.664572	+	0.465339i
$34$		0			0
$35$	−2.63084	+	5.97350i	−0.444693	+	1.00971i
$36$		0			0
$37$	−3.32665	−	3.32665i	−0.546898	−	0.546898i	0.378644	−	0.925542i	$-0.376390\pi$
$37$	−3.32665	−	3.32665i	−0.546898	−	0.546898i	−0.925542	+	0.378644i	$0.876390\pi$
$38$		0			0
$39$		−	10.3738i		−	1.66113i
$40$		0			0
$41$	−1.41908	+	3.89890i	−0.221623	+	0.608905i	−0.999817	−	0.0191188i	$-0.993914\pi$
$41$	−1.41908	+	3.89890i	−0.221623	+	0.608905i	0.778194	+	0.628024i	$0.216136\pi$
$42$		0			0
$43$	−3.51529	+	5.02035i	−0.536076	+	0.765596i	−0.992245	−	0.124297i	$-0.960332\pi$
$43$	−3.51529	+	5.02035i	−0.536076	+	0.765596i	0.456169	+	0.889893i	$0.349221\pi$
$44$		0			0
$45$	−2.08038	+	0.413075i	−0.310125	+	0.0615776i
$46$		0			0
$47$	8.34312	−	0.729929i	1.21697	−	0.106471i	0.539477	−	0.842000i	$-0.318622\pi$
$47$	8.34312	−	0.729929i	1.21697	−	0.106471i	0.677493	+	0.735529i	$0.263066\pi$
$48$		0			0
$49$	−1.31705	+	0.760401i	−0.188150	+	0.108629i
$50$		0			0
$51$	−0.974838	−	2.67835i	−0.136505	−	0.375043i
$52$		0			0
$53$	2.51445	+	3.59100i	0.345386	+	0.493262i	0.953835	−	0.300330i	$-0.0970970\pi$
$53$	2.51445	+	3.59100i	0.345386	+	0.493262i	−0.608449	+	0.793593i	$0.708208\pi$
$54$		0			0
$55$	0.799577	−	5.18316i	0.107815	−	0.698897i
$56$		0			0
$57$	−8.10991	−	3.04164i	−1.07418	−	0.402875i
$58$		0			0
$59$	7.59535	−	6.37326i	0.988830	−	0.829727i	0.00343235	−	0.999994i	$-0.498907\pi$
$59$	7.59535	−	6.37326i	0.988830	−	0.829727i	0.985398	+	0.170267i	$0.0544630\pi$
$60$		0			0
$61$	−1.68347	+	9.54743i	−0.215546	+	1.22242i	0.664410	+	0.747368i	$0.268683\pi$
$61$	−1.68347	+	9.54743i	−0.215546	+	1.22242i	−0.879956	+	0.475055i	$0.842428\pi$
$62$		0			0
$63$	−2.50940	−	1.17015i	−0.316155	−	0.147425i
$64$		0			0
$65$	−10.4715	+	5.15950i	−1.29882	+	0.639958i
$66$		0			0
$67$	−0.534287	−	6.10693i	−0.0652736	−	0.746081i	−0.956349	−	0.292226i	$-0.905604\pi$
$67$	−0.534287	−	6.10693i	−0.0652736	−	0.746081i	0.891076	−	0.453855i	$-0.149951\pi$
$68$		0			0
$69$	2.68568	−	4.65173i	0.323318	−	0.560002i
$70$		0			0
$71$	4.76199	−	0.839668i	0.565145	−	0.0996502i	0.116226	−	0.993223i	$-0.462920\pi$
$71$	4.76199	−	0.839668i	0.565145	−	0.0996502i	0.448919	+	0.893573i	$0.351809\pi$
$72$		0			0
$73$	5.54088	+	11.8824i	0.648510	+	1.39074i	0.905511	+	0.424324i	$0.139488\pi$
$73$	5.54088	+	11.8824i	0.648510	+	1.39074i	−0.257000	+	0.966411i	$0.582734\pi$
$74$		0			0
$75$	6.04294	+	7.88646i	0.697779	+	0.910650i
$76$		0			0
$77$	4.84108	−	4.84108i	0.551692	−	0.551692i
$78$		0			0
$79$	−16.5155	−	6.01117i	−1.85814	−	0.676309i	−0.980348	−	0.197274i	$-0.936791\pi$
$79$	−16.5155	−	6.01117i	−1.85814	−	0.676309i	−0.877796	−	0.479035i	$-0.840987\pi$
$80$		0			0
$81$	1.90073	+	10.7796i	0.211193	+	1.19773i
$82$		0			0
$83$	13.1282	−	3.51769i	1.44101	−	0.386117i	0.548121	−	0.836399i	$-0.315343\pi$
$83$	13.1282	−	3.51769i	1.44101	−	0.386117i	0.892886	+	0.450282i	$0.148676\pi$
$84$		0			0
$85$	−2.21872	+	2.31612i	−0.240654	+	0.251219i
$86$		0			0
$87$	13.9454	+	3.73665i	1.49510	+	0.400611i
$88$		0			0
$89$	−4.65929	+	1.69584i	−0.493884	+	0.179759i	−0.576941	−	0.816786i	$-0.695754\pi$
$89$	−4.65929	+	1.69584i	−0.493884	+	0.179759i	0.0830572	+	0.996545i	$0.473532\pi$
$90$		0			0
$91$	−15.0075	−	2.64623i	−1.57322	−	0.277401i
$92$		0			0
$93$	5.36321	+	0.469220i	0.556139	+	0.0486559i
$94$		0			0
$95$	0.963270	+	9.69908i	0.0988294	+	0.995104i
$96$		0			0
$97$	5.32688	+	0.466041i	0.540862	+	0.0473193i	0.354314	−	0.935126i	$-0.384714\pi$
$97$	5.32688	+	0.466041i	0.540862	+	0.0473193i	0.186548	+	0.982446i	$0.440270\pi$
$98$		0			0
$99$	2.19090	+	0.386315i	0.220194	+	0.0388261i
$100$		0			0
$101$	−5.59932	+	2.03799i	−0.557153	+	0.202787i	−0.605222	−	0.796057i	$-0.706916\pi$
$101$	−5.59932	+	2.03799i	−0.557153	+	0.202787i	0.0480687	+	0.998844i	$0.484693\pi$
$102$		0			0
$103$	−1.09976	−	0.294681i	−0.108363	−	0.0290357i	0.204230	−	0.978923i	$-0.434531\pi$
$103$	−1.09976	−	0.294681i	−0.108363	−	0.0290357i	−0.312593	+	0.949887i	$0.601198\pi$
$104$		0			0
$105$	0.278513	+	12.9671i	0.0271801	+	1.26546i
$106$		0			0
$107$	−9.05442	+	2.42612i	−0.875324	+	0.234542i	−0.668388	−	0.743812i	$-0.733016\pi$
$107$	−9.05442	+	2.42612i	−0.875324	+	0.234542i	−0.206935	+	0.978355i	$0.566349\pi$
$108$		0			0
$109$	0.874181	+	4.95773i	0.0837314	+	0.474864i	0.997623	+	0.0689062i	$0.0219509\pi$
$109$	0.874181	+	4.95773i	0.0837314	+	0.474864i	−0.913892	+	0.405958i	$0.866938\pi$
$110$		0			0
$111$	−8.78469	−	3.19737i	−0.833806	−	0.303481i
$112$		0			0
$113$	−11.1805	+	11.1805i	−1.05178	+	1.05178i	−0.0531926	+	0.998584i	$0.516940\pi$
$113$	−11.1805	+	11.1805i	−1.05178	+	1.05178i	−0.998584	+	0.0531926i	$0.983060\pi$
$114$		0			0
$115$	−6.03129	−	0.397380i	−0.562421	−	0.0370559i
$116$		0			0
$117$	−2.09276	−	4.48795i	−0.193476	−	0.414911i
$118$		0			0
$119$	−4.12339	+	0.727065i	−0.377991	+	0.0666499i
$120$		0			0
$121$	2.74955	−	4.76237i	0.249959	−	0.432942i
$122$		0			0
$123$	0.718572	+	8.21331i	0.0647914	+	0.740569i
$124$		0			0
$125$	4.95521	−	10.0223i	0.443207	−	0.896419i
$126$		0			0
$127$	14.2763	+	6.65713i	1.26681	+	0.590724i	0.935677	−	0.352859i	$-0.114790\pi$
$127$	14.2763	+	6.65713i	1.26681	+	0.590724i	0.331136	+	0.943583i	$0.392568\pi$
$128$		0			0
$129$	−2.11474	+	11.9933i	−0.186193	+	1.05595i
$130$		0			0
$131$	−3.07381	+	2.57923i	−0.268560	+	0.225348i	−0.767115	−	0.641509i	$-0.778309\pi$
$131$	−3.07381	+	2.57923i	−0.268560	+	0.225348i	0.498555	+	0.866858i	$0.333864\pi$
$132$		0			0
$133$	−6.46904	+	10.9566i	−0.560937	+	0.950056i
$134$		0			0
$135$	7.35275	−	5.38740i	0.632824	−	0.463674i
$136$		0			0
$137$	7.16358	+	10.2306i	0.612026	+	0.874063i	0.998843	−	0.0480932i	$-0.0153144\pi$
$137$	7.16358	+	10.2306i	0.612026	+	0.874063i	−0.386817	+	0.922156i	$0.626426\pi$
$138$		0			0
$139$	−6.64077	−	18.2454i	−0.563263	−	1.54755i	−0.814823	−	0.579710i	$-0.803166\pi$
$139$	−6.64077	−	18.2454i	−0.563263	−	1.54755i	0.251561	−	0.967842i	$-0.419056\pi$
$140$		0			0
$141$	14.4123	−	8.32094i	1.21373	−	0.700750i
$142$		0			0
$143$	12.1977	−	1.06716i	1.02002	−	0.0892406i
$144$		0			0
$145$	−3.16405	−	15.9352i	−0.262760	−	1.32334i
$146$		0			0
$147$	−1.73333	+	2.47546i	−0.142963	+	0.204172i
$148$		0			0
$149$	−6.46703	+	17.7680i	−0.529800	+	1.45561i	0.329507	+	0.944153i	$0.393118\pi$
$149$	−6.46703	+	17.7680i	−0.529800	+	1.45561i	−0.859307	+	0.511460i	$0.829105\pi$
$150$		0			0
$151$		−	14.0862i		−	1.14632i	−0.819445	−	0.573158i	$-0.805718\pi$
$151$		−	14.0862i		−	1.14632i	0.819445	−	0.573158i	$-0.194282\pi$
$152$		0			0
$153$	−0.962060	−	0.962060i	−0.0777779	−	0.0777779i
$154$		0			0
$155$	−2.19381	−	5.64709i	−0.176211	−	0.453586i
$156$		0			0
$157$	−8.39622	−	5.87910i	−0.670091	−	0.469203i	0.188359	−	0.982100i	$-0.439683\pi$
$157$	−8.39622	−	5.87910i	−0.670091	−	0.469203i	−0.858450	+	0.512897i	$0.828572\pi$
$158$		0			0
$159$	7.54397	+	4.35551i	0.598276	+	0.345415i
$160$		0			0
$161$	−6.04449	−	5.07193i	−0.476373	−	0.399724i
$162$		0			0
$163$	3.16451	−	11.8101i	0.247864	−	0.925040i	−0.724059	−	0.689738i	$-0.757726\pi$
$163$	3.16451	−	11.8101i	0.247864	−	0.925040i	0.971922	−	0.235301i	$-0.0756077\pi$
$164$		0			0
$165$	−2.91275	−	10.0059i	−0.226757	−	0.778959i
$166$		0			0
$167$	−0.698293	+	0.488950i	−0.0540356	+	0.0378361i	−0.600282	−	0.799788i	$-0.704945\pi$
$167$	−0.698293	+	0.488950i	−0.0540356	+	0.0378361i	0.546247	+	0.837624i	$0.316056\pi$
$168$		0			0
$169$	−9.16252	−	10.9195i	−0.704809	−	0.839959i
$170$		0			0
$171$	−4.12216	+	0.320175i	−0.315230	+	0.0244844i
$172$		0			0
$173$	1.46950	−	16.7965i	0.111724	−	1.27701i	−0.708803	−	0.705407i	$-0.750764\pi$
$173$	1.46950	−	16.7965i	0.111724	−	1.27701i	0.820527	−	0.571608i	$-0.193680\pi$
$174$		0			0
$175$	12.9507	−	6.73047i	0.978981	−	0.508776i
$176$		0			0
$177$	8.32646	−	17.8561i	0.625855	−	1.34215i
$178$		0			0
$179$	−3.70717	−	6.42101i	−0.277087	−	0.479929i	0.693572	−	0.720387i	$-0.256036\pi$
$179$	−3.70717	−	6.42101i	−0.277087	−	0.479929i	−0.970660	+	0.240458i	$0.922702\pi$
$180$		0			0
$181$	7.51502	−	8.95606i	0.558587	−	0.665698i	−0.410660	−	0.911789i	$-0.634702\pi$
$181$	7.51502	−	8.95606i	0.558587	−	0.665698i	0.969247	+	0.246090i	$0.0791460\pi$
$182$		0			0
$183$	4.98597	+	18.6079i	0.368573	+	1.37553i
$184$		0			0
$185$	1.14169	+	10.4577i	0.0839385	+	0.768863i
$186$		0			0
$187$	3.04898	−	1.42176i	0.222964	−	0.103970i
$188$		0			0
$189$	11.8993			0.865548
$190$		0			0
$191$	−8.74367			−0.632670			−0.316335	−	0.948648i	$-0.602452\pi$
$191$	−8.74367			−0.632670			−0.316335	+	0.948648i	$0.602452\pi$
$192$		0			0
$193$	−13.3111	+	6.20707i	−0.958154	+	0.446794i	−0.837824	−	0.545940i	$-0.816173\pi$
$193$	−13.3111	+	6.20707i	−0.958154	+	0.446794i	−0.120329	+	0.992734i	$0.538395\pi$
$194$		0			0
$195$	−14.5254	+	18.0856i	−1.04018	+	1.29513i
$196$		0			0
$197$	−5.62534	−	20.9941i	−0.400789	−	1.49576i	−0.811692	−	0.584085i	$-0.801453\pi$
$197$	−5.62534	−	20.9941i	−0.400789	−	1.49576i	0.410903	−	0.911679i	$-0.365213\pi$
$198$		0			0
$199$	−4.18858	+	4.99175i	−0.296920	+	0.353856i	−0.893793	−	0.448480i	$-0.851965\pi$
$199$	−4.18858	+	4.99175i	−0.296920	+	0.353856i	0.596872	+	0.802336i	$0.296410\pi$
$200$		0			0
$201$	−6.09070	−	10.5494i	−0.429605	−	0.744097i
$202$		0			0
$203$	8.96307	−	19.2214i	0.629084	−	1.34908i
$204$		0			0
$205$	7.93327	−	4.81032i	0.554084	−	0.335967i
$206$		0			0
$207$	0.223468	−	2.55425i	0.0155321	−	0.177533i
$208$		0			0
$209$	2.74216	−	9.84873i	0.189679	−	0.681251i
$210$		0			0
$211$	3.67164	+	4.37569i	0.252766	+	0.301235i	0.877474	−	0.479623i	$-0.159227\pi$
$211$	3.67164	+	4.37569i	0.252766	+	0.301235i	−0.624709	+	0.780858i	$0.714782\pi$
$212$		0			0
$213$	7.87082	−	5.51121i	0.539300	−	0.377622i
$214$		0			0
$215$	13.1580	−	3.83035i	0.897371	−	0.261227i
$216$		0			0
$217$	2.04691	−	7.63918i	0.138953	−	0.518581i
$218$		0			0
$219$	19.9573	+	16.7462i	1.34859	+	1.13160i
$220$		0			0
$221$	−6.48502	−	3.74413i	−0.436230	−	0.251857i
$222$		0			0
$223$	1.32086	+	0.924876i	0.0884514	+	0.0619343i	0.616966	−	0.786990i	$-0.288362\pi$
$223$	1.32086	+	0.924876i	0.0884514	+	0.0619343i	−0.528514	+	0.848924i	$0.677251\pi$
$224$		0			0
$225$	4.20532	+	2.19280i	0.280354	+	0.146187i
$226$		0			0
$227$	6.53511	+	6.53511i	0.433751	+	0.433751i	0.889902	−	0.456152i	$-0.150773\pi$
$227$	6.53511	+	6.53511i	0.433751	+	0.433751i	−0.456152	+	0.889902i	$0.650773\pi$
$228$		0			0
$229$		−	16.0050i		−	1.05764i	−0.848733	−	0.528822i	$-0.822634\pi$
$229$		−	16.0050i		−	1.05764i	0.848733	−	0.528822i	$-0.177366\pi$
$230$		0			0
$231$	4.65293	−	12.7838i	0.306140	−	0.841114i
$232$		0			0
$233$	9.37482	−	13.3886i	0.614165	−	0.877118i	−0.384782	−	0.923008i	$-0.625723\pi$
$233$	9.37482	−	13.3886i	0.614165	−	0.877118i	0.998947	+	0.0458892i	$0.0146121\pi$
$234$		0			0
$235$	−15.5674	−	10.4095i	−1.01551	−	0.679042i
$236$		0			0
$237$	−34.7912	+	3.04384i	−2.25993	+	0.197718i
$238$		0			0
$239$	−21.7134	+	12.5362i	−1.40452	+	0.810902i	−0.994853	−	0.101332i	$-0.967690\pi$
$239$	−21.7134	+	12.5362i	−1.40452	+	0.810902i	−0.409670	+	0.912234i	$0.634356\pi$
$240$		0			0
$241$	8.86478	+	24.3558i	0.571031	+	1.56889i	0.802879	+	0.596142i	$0.203300\pi$
$241$	8.86478	+	24.3558i	0.571031	+	1.56889i	−0.231849	+	0.972752i	$0.574477\pi$
$242$		0			0
$243$	5.46111	+	7.79927i	0.350330	+	0.500324i
$244$		0			0
$245$	3.36086	+	0.518461i	0.214718	+	0.0331233i
$246$		0			0
$247$	−21.4585	+	7.57412i	−1.36537	+	0.481930i
$248$		0			0
$249$	20.6887	−	17.3599i	1.31109	−	1.10014i
$250$		0			0
$251$	−3.27260	+	18.5598i	−0.206565	+	1.17149i	0.688394	+	0.725337i	$0.258316\pi$
$251$	−3.27260	+	18.5598i	−0.206565	+	1.17149i	−0.894959	+	0.446149i	$0.852795\pi$
$252$		0			0
$253$	5.74590	+	2.67936i	0.361242	+	0.168450i
$254$		0			0
$255$	−2.05070	+	6.03439i	−0.128420	+	0.377888i
$256$		0			0
$257$	2.63053	+	30.0671i	0.164088	+	1.87554i	0.418191	+	0.908359i	$0.362664\pi$
$257$	2.63053	+	30.0671i	0.164088	+	1.87554i	−0.254103	+	0.967177i	$0.581780\pi$
$258$		0			0
$259$	−6.86646	+	11.8931i	−0.426661	+	0.738998i
$260$		0			0
$261$	6.78694	−	1.19672i	0.420101	−	0.0740752i
$262$		0			0
$263$	−7.06699	−	15.1552i	−0.435770	−	0.934511i	−0.994458	−	0.105133i	$-0.966473\pi$
$263$	−7.06699	−	15.1552i	−0.435770	−	0.934511i	0.558689	−	0.829378i	$-0.311305\pi$
$264$		0			0
$265$	0.644454	−	9.78128i	0.0395885	−	0.600859i
$266$		0			0
$267$	−6.96686	+	6.96686i	−0.426365	+	0.426365i
$268$		0			0
$269$	23.9237	+	8.70753i	1.45866	+	0.530907i	0.944995	−	0.327086i	$-0.106067\pi$
$269$	23.9237	+	8.70753i	1.45866	+	0.530907i	0.513661	+	0.857993i	$0.328289\pi$
$270$		0			0
$271$	−1.65903	−	9.40884i	−0.100779	−	0.571546i	−0.992823	−	0.119597i	$-0.961840\pi$
$271$	−1.65903	−	9.40884i	−0.100779	−	0.571546i	0.892044	−	0.451949i	$-0.149271\pi$
$272$		0			0
$273$	−29.2496	+	7.83741i	−1.77027	+	0.474342i
$274$		0			0
$275$	−8.65146	+	7.91673i	−0.521702	+	0.477397i
$276$		0			0
$277$	2.13763	+	0.572775i	0.128437	+	0.0344147i	0.322465	−	0.946581i	$-0.395488\pi$
$277$	2.13763	+	0.572775i	0.128437	+	0.0344147i	−0.194028	+	0.980996i	$0.562155\pi$
$278$		0			0
$279$	2.41492	−	0.878959i	0.144578	−	0.0526219i
$280$		0			0
$281$	−5.16659	−	0.911010i	−0.308213	−	0.0543463i	0.0174024	−	0.999849i	$-0.494460\pi$
$281$	−5.16659	−	0.911010i	−0.308213	−	0.0543463i	−0.325615	+	0.945502i	$0.605571\pi$
$282$		0			0
$283$	−4.90313	−	0.428968i	−0.291461	−	0.0254995i	−0.0595122	−	0.998228i	$-0.518955\pi$
$283$	−4.90313	−	0.428968i	−0.291461	−	0.0254995i	−0.231948	+	0.972728i	$0.574510\pi$
$284$		0			0
$285$	9.87988	+	16.6583i	0.585233	+	0.986753i
$286$		0			0
$287$	12.0654	+	1.05558i	0.712196	+	0.0623091i
$288$		0			0
$289$	14.7156	+	2.59475i	0.865621	+	0.152632i
$290$		0			0
$291$	9.98464	−	3.63411i	0.585310	−	0.213035i
$292$		0			0
$293$	−12.9174	−	3.46122i	−0.754645	−	0.202207i	−0.139068	−	0.990283i	$-0.544411\pi$
$293$	−12.9174	−	3.46122i	−0.754645	−	0.202207i	−0.615578	+	0.788076i	$0.711077\pi$
$294$		0			0
$295$	−22.1656	+	0.476081i	−1.29053	+	0.0277185i
$296$		0			0
$297$	−9.23511	+	2.47454i	−0.535876	+	0.143587i
$298$		0			0
$299$	−2.45050	−	13.8974i	−0.141716	−	0.803710i
$300$		0			0
$301$	16.8111	+	6.11873i	0.968974	+	0.352678i
$302$		0			0
$303$	−8.37245	+	8.37245i	−0.480985	+	0.480985i
$304$		0			0
$305$	16.3033	−	14.2878i	0.933524	−	0.818115i
$306$		0			0
$307$	−6.85299	−	14.6963i	−0.391121	−	0.838761i	−0.998999	−	0.0447309i	$-0.985757\pi$
$307$	−6.85299	−	14.6963i	−0.391121	−	0.838761i	0.607878	−	0.794030i	$-0.292021\pi$
$308$		0			0
$309$	−2.22805	+	0.392865i	−0.126749	+	0.0223493i
$310$		0			0
$311$	−6.10330	+	10.5712i	−0.346087	+	0.599440i	−0.985551	−	0.169381i	$-0.945823\pi$
$311$	−6.10330	+	10.5712i	−0.346087	+	0.599440i	0.639464	+	0.768821i	$0.279156\pi$
$312$		0			0
$313$	−2.08552	−	23.8376i	−0.117881	−	1.34738i	−0.792795	−	0.609488i	$-0.791375\pi$
$313$	−2.08552	−	23.8376i	−0.117881	−	1.34738i	0.674915	−	0.737896i	$-0.264180\pi$
$314$		0			0
$315$	2.73643	+	5.55371i	0.154180	+	0.312916i
$316$		0			0
$317$	15.7059	+	7.32377i	0.882129	+	0.411344i	0.810260	−	0.586070i	$-0.199326\pi$
$317$	15.7059	+	7.32377i	0.882129	+	0.411344i	0.0718692	+	0.997414i	$0.477104\pi$
$318$		0			0
$319$	−2.95907	+	16.7817i	−0.165676	+	0.939596i
$320$		0			0
$321$	−14.2688	+	11.9730i	−0.796409	+	0.668267i
$322$		0			0
$323$	−4.82849	+	3.97201i	−0.268665	+	0.221008i
$324$		0			0
$325$	25.4802	+	5.66710i	1.41339	+	0.314354i
$326$		0			0
$327$	5.73774	+	8.19434i	0.317298	+	0.453148i
$328$		0			0
$329$	−8.36135	−	22.9726i	−0.460976	−	1.26652i
$330$		0			0
$331$	17.2686	−	9.97004i	0.949169	−	0.548003i	0.0563464	−	0.998411i	$-0.482055\pi$
$331$	17.2686	−	9.97004i	0.949169	−	0.548003i	0.892823	+	0.450408i	$0.148722\pi$
$332$		0			0
$333$	−4.44550	+	0.388931i	−0.243612	+	0.0213133i
$334$		0			0
$335$	−7.61947	+	11.3949i	−0.416296	+	0.622571i
$336$		0			0
$337$	−5.04041	+	7.19845i	−0.274568	+	0.392124i	−0.932627	−	0.360843i	$-0.882489\pi$
$337$	−5.04041	+	7.19845i	−0.274568	+	0.392124i	0.658058	+	0.752967i	$0.271378\pi$
$338$		0			0
$339$	−10.7460	+	29.5244i	−0.583644	+	1.60355i
$340$		0			0
$341$			6.35447i			0.344114i
$342$		0			0
$343$	−11.3095	−	11.3095i	−0.610654	−	0.610654i
$344$		0			0
$345$	−11.1956	+	4.34932i	−0.602749	+	0.234159i
$346$		0			0
$347$	6.00376	+	4.20388i	0.322299	+	0.225676i	0.723517	−	0.690306i	$-0.242524\pi$
$347$	6.00376	+	4.20388i	0.322299	+	0.225676i	−0.401218	+	0.915982i	$0.631413\pi$
$348$		0			0
$349$	−31.1316	−	17.9738i	−1.66644	−	0.962117i	−0.969536	−	0.244950i	$-0.921229\pi$
$349$	−31.1316	−	17.9738i	−1.66644	−	0.962117i	−0.696901	−	0.717168i	$-0.745438\pi$
$350$		0			0
$351$	16.3025	+	13.6794i	0.870162	+	0.730153i
$352$		0			0
$353$	−5.49787	+	20.5183i	−0.292622	+	1.09208i	0.650465	+	0.759536i	$0.274574\pi$
$353$	−5.49787	+	20.5183i	−0.292622	+	1.09208i	−0.943088	+	0.332545i	$0.892093\pi$
$354$		0			0
$355$	−9.47775	−	5.20388i	−0.503027	−	0.276193i
$356$		0			0
$357$	−6.81531	+	4.77213i	−0.360704	+	0.252568i
$358$		0			0
$359$	7.73374	+	9.21672i	0.408171	+	0.486440i	0.930493	−	0.366309i	$-0.119379\pi$
$359$	7.73374	+	9.21672i	0.408171	+	0.486440i	−0.522322	+	0.852748i	$0.674934\pi$
$360$		0			0
$361$	−0.370497	+	18.9964i	−0.0194999	+	0.999810i
$362$		0			0
$363$	0.952371	−	10.8857i	0.0499865	−	0.571348i
$364$		0			0
$365$	6.97789	−	28.4742i	0.365240	−	1.49041i
$366$		0			0
$367$	−14.1316	+	30.3053i	−0.737664	+	1.58193i	0.0736285	+	0.997286i	$0.476542\pi$
$367$	−14.1316	+	30.3053i	−0.737664	+	1.58193i	−0.811293	+	0.584640i	$0.801236\pi$
$368$		0			0
$369$	1.96780	+	3.40832i	0.102439	+	0.177430i
$370$		0			0
$371$	8.22544	−	9.80270i	0.427044	−	0.508931i
$372$		0			0
$373$	−0.475497	−	1.77458i	−0.0246203	−	0.0918842i	0.952522	−	0.304468i	$-0.0984787\pi$
$373$	−0.475497	−	1.77458i	−0.0246203	−	0.0918842i	−0.977143	+	0.212584i	$0.931812\pi$
$374$		0			0
$375$	0.507404	−	22.2106i	0.0262022	−	1.14695i
$376$		0			0
$377$	34.3765	−	16.0300i	1.77048	−	0.825589i
$378$		0			0
$379$	28.4646			1.46213			0.731064	−	0.682309i	$-0.239024\pi$
$379$	28.4646			1.46213			0.731064	+	0.682309i	$0.239024\pi$
$380$		0			0
$381$	31.3009			1.60359
$382$		0			0
$383$	−8.21138	+	3.82903i	−0.419582	+	0.195654i	−0.620931	−	0.783865i	$-0.713245\pi$
$383$	−8.21138	+	3.82903i	−0.419582	+	0.195654i	0.201349	+	0.979520i	$0.435467\pi$
$384$		0			0
$385$	−15.2184	+	1.66143i	−0.775602	+	0.0846741i
$386$		0			0
$387$	1.50460	+	5.61523i	0.0764829	+	0.285438i
$388$		0			0
$389$	−6.60445	+	7.87087i	−0.334859	+	0.399069i	−0.907031	−	0.421065i	$-0.861657\pi$
$389$	−6.60445	+	7.87087i	−0.334859	+	0.399069i	0.572172	+	0.820134i	$0.306101\pi$
$390$		0			0
$391$	−1.93865	−	3.35783i	−0.0980415	−	0.169813i
$392$		0			0
$393$	−3.36968	+	7.22631i	−0.169978	+	0.364519i
$394$		0			0
$395$	20.3763	+	33.6050i	1.02524	+	1.69085i
$396$		0			0
$397$	0.649242	−	7.42087i	0.0325845	−	0.372443i	−0.962342	−	0.271841i	$-0.912368\pi$
$397$	0.649242	−	7.42087i	0.0325845	−	0.372443i	0.994927	−	0.100602i	$-0.0320769\pi$
$398$		0			0
$399$	−2.44907	+	25.1645i	−0.122607	+	1.25980i
$400$		0			0
$401$	15.0407	+	17.9248i	0.751097	+	0.895123i	0.997250	−	0.0741083i	$-0.0236111\pi$
$401$	15.0407	+	17.9248i	0.751097	+	0.895123i	−0.246153	+	0.969231i	$0.579167\pi$
$402$		0			0
$403$	11.5863	−	8.11282i	0.577155	−	0.404129i
$404$		0			0
$405$	11.7799	−	21.4545i	0.585347	−	1.06608i
$406$		0			0
$407$	2.85585	−	10.6582i	0.141559	−	0.528306i
$408$		0			0
$409$	17.7877	+	14.9257i	0.879547	+	0.738027i	0.966086	−	0.258221i	$-0.0831363\pi$
$409$	17.7877	+	14.9257i	0.879547	+	0.738027i	−0.0865392	+	0.996248i	$0.527581\pi$
$410$		0			0
$411$	21.4925	+	12.4087i	1.06015	+	0.612077i
$412$		0			0
$413$	−23.7082	−	16.6007i	−1.16660	−	0.816865i
$414$		0			0
$415$	−27.8132	−	12.2494i	−1.36529	−	0.601300i
$416$		0			0
$417$	−27.2816	−	27.2816i	−1.33599	−	1.33599i
$418$		0			0
$419$		−	0.259631i		−	0.0126838i	−0.999980	−	0.00634190i	$-0.997981\pi$
$419$		−	0.259631i		−	0.0126838i	0.999980	−	0.00634190i	$-0.00201870\pi$
$420$		0			0
$421$	−9.61145	+	26.4072i	−0.468433	+	1.28701i	0.450563	+	0.892745i	$0.351223\pi$
$421$	−9.61145	+	26.4072i	−0.468433	+	1.28701i	−0.918997	+	0.394266i	$0.870999\pi$
$422$		0			0
$423$	4.55649	−	6.50734i	0.221544	−	0.316398i
$424$		0			0
$425$	7.11116	−	0.931261i	0.344942	−	0.0451728i
$426$		0			0
$427$	28.1916	−	2.46644i	1.36429	−	0.119360i
$428$		0			0
$429$	21.0709	−	12.1653i	1.01731	−	0.587346i
$430$		0			0
$431$	−0.358599	−	0.985241i	−0.0172731	−	0.0474574i	0.930756	−	0.365640i	$-0.119150\pi$
$431$	−0.358599	−	0.985241i	−0.0172731	−	0.0474574i	−0.948030	+	0.318182i	$0.896928\pi$
$432$		0			0
$433$	7.27832	+	10.3945i	0.349774	+	0.499529i	0.955033	−	0.296500i	$-0.0958194\pi$
$433$	7.27832	+	10.3945i	0.349774	+	0.499529i	−0.605259	+	0.796028i	$0.706931\pi$
$434$		0			0
$435$	−19.0802	−	26.0408i	−0.914828	−	1.24856i
$436$		0			0
$437$	−11.5831	−	2.15908i	−0.554096	−	0.103283i
$438$		0			0
$439$	1.65946	−	1.39245i	0.0792015	−	0.0664579i	−0.602327	−	0.798249i	$-0.705760\pi$
$439$	1.65946	−	1.39245i	0.0792015	−	0.0664579i	0.681529	+	0.731791i	$0.261315\pi$
$440$		0			0
$441$	−0.250494	+	1.42062i	−0.0119283	+	0.0676486i
$442$		0			0
$443$	−22.6038	−	10.5403i	−1.07394	−	0.500787i	−0.196516	−	0.980501i	$-0.562963\pi$
$443$	−22.6038	−	10.5403i	−1.07394	−	0.500787i	−0.877425	+	0.479714i	$0.840740\pi$
$444$		0			0
$445$	10.4975	+	3.56743i	0.497630	+	0.169112i
$446$		0			0
$447$	3.27467	+	37.4297i	0.154887	+	1.77036i
$448$		0			0
$449$	−14.1301	+	24.4740i	−0.666841	+	1.15500i	0.311942	+	0.950101i	$0.399020\pi$
$449$	−14.1301	+	24.4740i	−0.666841	+	1.15500i	−0.978783	+	0.204901i	$0.934313\pi$
$450$		0			0
$451$	−9.58350	+	1.68983i	−0.451269	+	0.0795710i
$452$		0			0
$453$	−11.8293	−	25.3680i	−0.555790	−	1.19189i
$454$		0			0
$455$	22.4588	+	25.6270i	1.05289	+	1.20141i
$456$		0			0
$457$	−26.5786	+	26.5786i	−1.24329	+	1.24329i	−0.284666	+	0.958627i	$0.591883\pi$
$457$	−26.5786	+	26.5786i	−1.24329	+	1.24329i	−0.958627	+	0.284666i	$0.908117\pi$
$458$		0			0
$459$	5.49453	+	1.99984i	0.256463	+	0.0933447i
$460$		0			0
$461$	−7.17389	−	40.6852i	−0.334122	−	1.89490i	−0.435737	−	0.900074i	$-0.643512\pi$
$461$	−7.17389	−	40.6852i	−0.334122	−	1.89490i	0.101616	−	0.994824i	$-0.467599\pi$
$462$		0			0
$463$	−6.52392	+	1.74808i	−0.303192	+	0.0812402i	−0.407208	−	0.913336i	$-0.633498\pi$
$463$	−6.52392	+	1.74808i	−0.303192	+	0.0812402i	0.104015	+	0.994576i	$0.466831\pi$
$464$		0			0
$465$	−8.69321	−	8.32763i	−0.403138	−	0.386184i
$466$		0			0
$467$	22.0619	+	5.91148i	1.02090	+	0.273551i	0.730179	−	0.683256i	$-0.239437\pi$
$467$	22.0619	+	5.91148i	1.02090	+	0.273551i	0.290726	+	0.956806i	$0.406103\pi$
$468$		0			0
$469$	−16.8153	+	6.12027i	−0.776459	+	0.282608i
$470$		0			0
$471$	−20.0581	−	3.53678i	−0.924226	−	0.162966i
$472$		0			0
$473$	−14.3196	−	1.25280i	−0.658415	−	0.0576039i
$474$		0			0
$475$	11.9013	−	18.2581i	0.546070	−	0.837740i
$476$		0			0
$477$	4.14238	+	0.362411i	0.189667	+	0.0165937i
$478$		0			0
$479$	−10.1610	−	1.79166i	−0.464268	−	0.0818630i	−0.0633790	−	0.997990i	$-0.520188\pi$
$479$	−10.1610	−	1.79166i	−0.464268	−	0.0818630i	−0.400889	+	0.916126i	$0.631299\pi$
$480$		0			0
$481$	−23.0795	+	8.40025i	−1.05233	+	0.383018i
$482$		0			0
$483$	−15.1449	−	4.05808i	−0.689119	−	0.184649i
$484$		0			0
$485$	−8.63431	−	8.27120i	−0.392064	−	0.375576i
$486$		0			0
$487$	−18.0289	+	4.83082i	−0.816967	+	0.218906i	−0.643020	−	0.765850i	$-0.722319\pi$
$487$	−18.0289	+	4.83082i	−0.816967	+	0.218906i	−0.173947	+	0.984755i	$0.555652\pi$
$488$		0			0
$489$	−4.21890	−	23.9265i	−0.190785	−	1.08200i
$490$		0			0
$491$	−16.2077	−	5.89913i	−0.731445	−	0.266224i	−0.0506684	−	0.998716i	$-0.516135\pi$
$491$	−16.2077	−	5.89913i	−0.731445	−	0.266224i	−0.680776	+	0.732491i	$0.738357\pi$
$492$		0			0
$493$	7.36913	−	7.36913i	0.331889	−	0.331889i
$494$		0			0
$495$	−3.27869	−	3.74120i	−0.147366	−	0.168155i
$496$		0			0
$497$	−5.96521	−	12.7924i	−0.267576	−	0.573819i
$498$		0			0
$499$	27.6348	−	4.87276i	1.23710	−	0.218135i	0.483429	−	0.875384i	$-0.339391\pi$
$499$	27.6348	−	4.87276i	1.23710	−	0.218135i	0.753674	+	0.657249i	$0.228280\pi$
$500$		0			0
$501$	−0.846957	+	1.46697i	−0.0378393	+	0.0655395i
$502$		0			0
$503$	1.58352	+	18.0998i	0.0706059	+	0.807029i	0.946116	+	0.323829i	$0.104970\pi$
$503$	1.58352	+	18.0998i	0.0706059	+	0.807029i	−0.875510	+	0.483200i	$0.839474\pi$
$504$		0			0
$505$	12.6154	+	4.28717i	0.561379	+	0.190776i
$506$		0			0
$507$	−25.6709	−	11.9705i	−1.14008	−	0.531630i
$508$		0			0
$509$	−7.33486	+	41.5981i	−0.325112	+	1.84380i	0.183774	+	0.982968i	$0.441168\pi$
$509$	−7.33486	+	41.5981i	−0.325112	+	1.84380i	−0.508886	+	0.860834i	$0.669943\pi$
$510$		0			0
$511$	29.3173	−	24.6002i	1.29692	−	1.08825i
$512$		0			0
$513$	15.4741	−	8.73395i	0.683200	−	0.385613i
$514$		0			0
$515$	1.50471	+	2.05364i	0.0663055	+	0.0904940i
$516$		0			0
$517$	11.2666	+	16.0904i	0.495504	+	0.707653i
$518$		0			0
$519$	−11.4589	−	31.4832i	−0.502992	−	1.38196i
$520$		0			0
$521$	−4.44996	+	2.56919i	−0.194956	+	0.112558i	−0.594301	−	0.804243i	$-0.702571\pi$
$521$	−4.44996	+	2.56919i	−0.194956	+	0.112558i	0.399344	+	0.916801i	$0.369238\pi$
$522$		0			0
$523$	24.8703	−	2.17587i	1.08750	−	0.0951440i	0.470723	−	0.882281i	$-0.343993\pi$
$523$	24.8703	−	2.17587i	1.08750	−	0.0951440i	0.616778	+	0.787137i	$0.288438\pi$
$524$		0			0
$525$	17.6710	−	22.9968i	0.771227	−	1.00366i
$526$		0			0
$527$	2.22903	−	3.18339i	0.0970983	−	0.138671i
$528$		0			0
$529$	−5.36737	+	14.7467i	−0.233364	+	0.641162i
$530$		0			0
$531$		−	9.40477i		−	0.408132i
$532$		0			0
$533$	15.3165	+	15.3165i	0.663430	+	0.663430i
$534$		0			0
$535$	19.1825	+	8.44833i	0.829332	+	0.365253i
$536$		0			0
$537$	−12.0686	−	8.45050i	−0.520797	−	0.364666i
$538$		0			0
$539$	−3.08901	−	1.78344i	−0.133053	−	0.0768183i
$540$		0			0
$541$	−11.9249	−	10.0062i	−0.512693	−	0.430200i	0.349383	−	0.936980i	$-0.386391\pi$
$541$	−11.9249	−	10.0062i	−0.512693	−	0.430200i	−0.862076	+	0.506780i	$0.830836\pi$
$542$		0			0
$543$	6.01281	−	22.4401i	0.258034	−	0.962997i
$544$		0			0
$545$	5.41778	−	9.86732i	0.232072	−	0.422669i
$546$		0			0
$547$	−21.2182	+	14.8571i	−0.907223	+	0.635244i	−0.931216	−	0.364468i	$-0.881251\pi$
$547$	−21.2182	+	14.8571i	−0.907223	+	0.635244i	0.0239931	+	0.999712i	$0.492362\pi$
$548$		0			0
$549$	5.91094	+	7.04439i	0.252273	+	0.300647i
$550$		0			0
$551$	−2.45245	−	31.5747i	−0.104478	−	1.34513i
$552$		0			0
$553$	−4.47140	+	51.1083i	−0.190143	+	2.17335i
$554$		0			0
$555$	10.8382	+	17.8746i	0.460058	+	0.758736i
$556$		0			0
$557$	−1.62268	+	3.47984i	−0.0687550	+	0.147446i	−0.937682	−	0.347495i	$-0.887032\pi$
$557$	−1.62268	+	3.47984i	−0.0687550	+	0.147446i	0.868927	+	0.494941i	$0.164810\pi$
$558$		0			0
$559$	15.9977	+	27.7088i	0.676630	+	1.17196i
$560$		0			0
$561$	4.29700	−	5.12096i	0.181419	−	0.216207i
$562$		0			0
$563$	−3.84710	−	14.3576i	−0.162136	−	0.605099i	−0.998388	−	0.0567544i	$-0.981925\pi$
$563$	−3.84710	−	14.3576i	−0.162136	−	0.605099i	0.836252	−	0.548345i	$-0.184742\pi$
$564$		0			0
$565$	35.1471	−	3.83709i	1.47865	−	0.161428i
$566$		0			0
$567$	28.9579	−	13.5033i	1.21612	−	0.567085i
$568$		0			0
$569$	2.86898			0.120274			0.0601370	−	0.998190i	$-0.480846\pi$
$569$	2.86898			0.120274			0.0601370	+	0.998190i	$0.480846\pi$
$570$		0			0
$571$	33.0560			1.38335			0.691675	−	0.722209i	$-0.256873\pi$
$571$	33.0560			1.38335			0.691675	+	0.722209i	$0.256873\pi$
$572$		0			0
$573$	−15.7466	+	7.34277i	−0.657825	+	0.306749i
$574$		0			0
$575$	9.95852	+	9.13782i	0.415299	+	0.381073i
$576$		0			0
$577$	−3.43146	−	12.8064i	−0.142853	−	0.533136i	−0.999842	−	0.0178001i	$-0.994334\pi$
$577$	−3.43146	−	12.8064i	−0.142853	−	0.533136i	0.856988	−	0.515336i	$-0.172333\pi$
$578$		0			0
$579$	−18.7596	+	22.3568i	−0.779623	+	0.929118i
$580$		0			0
$581$	−19.8368	−	34.3584i	−0.822970	−	1.42543i
$582$		0			0
$583$	−4.34527	+	9.31845i	−0.179963	+	0.385931i
$584$		0			0
$585$	−2.63552	+	10.7546i	−0.108965	+	0.444647i
$586$		0			0
$587$	0.574333	−	6.56466i	0.0237053	−	0.270953i	−0.975087	−	0.221822i	$-0.928800\pi$
$587$	0.574333	−	6.56466i	0.0237053	−	0.270953i	0.998792	−	0.0491302i	$-0.0156449\pi$
$588$		0			0
$589$	−2.94521	−	11.4366i	−0.121355	−	0.471236i
$590$		0			0
$591$	−27.7612	−	33.0845i	−1.14194	−	1.36091i
$592$		0			0
$593$	26.2452	−	18.3771i	1.07776	−	0.754656i	0.106892	−	0.994271i	$-0.465910\pi$
$593$	26.2452	−	18.3771i	1.07776	−	0.754656i	0.970868	+	0.239615i	$0.0770212\pi$
$594$		0			0
$595$	8.20674	+	4.50602i	0.336444	+	0.184729i
$596$		0			0
$597$	−3.35130	+	12.5072i	−0.137160	+	0.511887i
$598$		0			0
$599$	−20.2588	−	16.9992i	−0.827754	−	0.694568i	0.127020	−	0.991900i	$-0.459459\pi$
$599$	−20.2588	−	16.9992i	−0.827754	−	0.694568i	−0.954774	+	0.297332i	$0.903903\pi$
$600$		0			0
$601$	8.77604	+	5.06685i	0.357982	+	0.206681i	0.668195	−	0.743986i	$-0.267067\pi$
$601$	8.77604	+	5.06685i	0.357982	+	0.206681i	−0.310213	+	0.950667i	$0.600400\pi$
$602$		0			0
$603$	−4.76319	−	3.33522i	−0.193972	−	0.135821i
$604$		0			0
$605$	−11.4618	+	4.45276i	−0.465990	+	0.181030i
$606$		0			0
$607$	−9.97125	−	9.97125i	−0.404720	−	0.404720i	0.475172	−	0.879893i	$-0.342386\pi$
$607$	−9.97125	−	9.97125i	−0.404720	−	0.404720i	−0.879893	+	0.475172i	$0.842386\pi$
$608$		0			0
$609$		−	42.1431i		−	1.70773i
$610$		0			0
$611$	14.9539	−	41.0855i	0.604969	−	1.66214i
$612$		0			0
$613$	−0.773975	+	1.10535i	−0.0312605	+	0.0446447i	−0.834478	−	0.551041i	$-0.814231\pi$
$613$	−0.773975	+	1.10535i	−0.0312605	+	0.0446447i	0.803218	+	0.595686i	$0.203120\pi$
$614$		0			0
$615$	10.2475	−	15.3252i	0.413221	−	0.617972i
$616$		0			0
$617$	17.6671	−	1.54567i	0.711252	−	0.0622265i	0.274213	−	0.961669i	$-0.411583\pi$
$617$	17.6671	−	1.54567i	0.711252	−	0.0622265i	0.437039	+	0.899443i	$0.356027\pi$
$618$		0			0
$619$	12.4605	−	7.19410i	0.500832	−	0.289155i	−0.228225	−	0.973608i	$-0.573292\pi$
$619$	12.4605	−	7.19410i	0.500832	−	0.289155i	0.729057	+	0.684453i	$0.239959\pi$
$620$		0			0
$621$	3.76877	+	10.3546i	0.151235	+	0.415516i
$622$		0			0
$623$	8.30167	+	11.8560i	0.332600	+	0.475001i
$624$		0			0
$625$	−22.6721	+	10.5345i	−0.906884	+	0.421380i
$626$		0			0
$627$	−3.33238	−	20.0396i	−0.133083	−	0.800303i
$628$		0			0
$629$	−5.16939	+	4.33763i	−0.206117	+	0.172953i
$630$		0			0
$631$	1.45310	−	8.24093i	0.0578469	−	0.328066i	−0.942127	−	0.335256i	$-0.891177\pi$
$631$	1.45310	−	8.24093i	0.0578469	−	0.328066i	0.999974	+	0.00718930i	$0.00228845\pi$
$632$		0			0
$633$	10.2869	+	4.79688i	0.408869	+	0.190659i
$634$		0			0
$635$	−15.5678	−	31.5957i	−0.617791	−	1.25384i
$636$		0			0
$637$	0.691969	+	7.90924i	0.0274168	+	0.313375i
$638$		0			0
$639$	2.29330	−	3.97212i	0.0907217	−	0.157135i
$640$		0			0
$641$	−27.4265	+	4.83603i	−1.08328	+	0.191012i	−0.686666	−	0.726973i	$-0.740926\pi$
$641$	−27.4265	+	4.83603i	−1.08328	+	0.191012i	−0.396615	+	0.917985i	$0.629815\pi$
$642$		0			0
$643$	−14.9144	−	31.9839i	−0.588165	−	1.26132i	−0.944974	−	0.327146i	$-0.893913\pi$
$643$	−14.9144	−	31.9839i	−0.588165	−	1.26132i	0.356809	−	0.934177i	$-0.383865\pi$
$644$		0			0
$645$	20.4799	−	17.9480i	0.806395	−	0.706703i
$646$		0			0
$647$	6.47728	−	6.47728i	0.254648	−	0.254648i	−0.568225	−	0.822873i	$-0.692370\pi$
$647$	6.47728	−	6.47728i	0.254648	−	0.254648i	0.822873	+	0.568225i	$0.192370\pi$
$648$		0			0
$649$	21.8523	+	7.95357i	0.857776	+	0.312205i
$650$		0			0
$651$	−2.72892	−	15.4765i	−0.106955	−	0.606572i
$652$		0			0
$653$	−30.8818	+	8.27476i	−1.20850	+	0.323816i	−0.806173	−	0.591680i	$-0.798465\pi$
$653$	−30.8818	+	8.27476i	−1.20850	+	0.323816i	−0.402326	+	0.915496i	$0.631798\pi$
$654$		0			0
$655$	8.97031	−	0.192668i	0.350499	−	0.00752816i
$656$		0			0
$657$	12.0124	+	3.21870i	0.468647	+	0.125573i
$658$		0			0
$659$	−25.7587	+	9.37540i	−1.00342	+	0.365214i	−0.790901	−	0.611944i	$-0.790388\pi$
$659$	−25.7587	+	9.37540i	−1.00342	+	0.365214i	−0.212516	+	0.977158i	$0.568166\pi$
$660$		0			0
$661$	4.38760	+	0.773653i	0.170658	+	0.0300916i	0.258324	−	0.966058i	$-0.416830\pi$
$661$	4.38760	+	0.773653i	0.170658	+	0.0300916i	−0.0876661	+	0.996150i	$0.527941\pi$
$662$		0			0
$663$	−14.8232	−	1.29686i	−0.575687	−	0.0503661i
$664$		0			0
$665$	26.6195	−	10.0437i	1.03226	−	0.389478i
$666$		0			0
$667$	19.5649	+	1.71171i	0.757557	+	0.0662777i
$668$		0			0
$669$	3.15545	+	0.556392i	0.121997	+	0.0215114i
$670$		0			0
$671$	−21.3667	+	7.77684i	−0.824852	+	0.300222i
$672$		0			0
$673$	22.8996	+	6.13594i	0.882717	+	0.236523i	0.671579	−	0.740933i	$-0.265616\pi$
$673$	22.8996	+	6.13594i	0.882717	+	0.236523i	0.211138	+	0.977456i	$0.432283\pi$
$674$		0			0
$675$	−20.3622	−	0.902969i	−0.783742	−	0.0347553i
$676$		0			0
$677$	−6.65672	+	1.78366i	−0.255839	+	0.0685517i	−0.384459	−	0.923142i	$-0.625612\pi$
$677$	−6.65672	+	1.78366i	−0.255839	+	0.0685517i	0.128620	+	0.991694i	$0.458945\pi$
$678$		0			0
$679$	−2.71043	−	15.3716i	−0.104017	−	0.589909i
$680$		0			0
$681$	17.2573	+	6.28113i	0.661300	+	0.240693i
$682$		0			0
$683$	−23.4039	+	23.4039i	−0.895524	+	0.895524i	−0.995036	−	0.0995128i	$-0.968272\pi$
$683$	−23.4039	+	23.4039i	−0.895524	+	0.895524i	0.0995128	+	0.995036i	$0.468272\pi$
$684$		0			0
$685$	1.83603	−	27.8665i	0.0701510	−	1.06473i
$686$		0			0
$687$	−13.4407	−	28.8238i	−0.512796	−	1.09970i
$688$		0			0
$689$	22.5383	−	3.97411i	0.858640	−	0.151401i
$690$		0			0
$691$	−23.6640	+	40.9873i	−0.900221	+	1.55923i	−0.0730145	+	0.997331i	$0.523262\pi$
$691$	−23.6640	+	40.9873i	−0.900221	+	1.55923i	−0.827207	+	0.561898i	$0.810071\pi$
$692$		0			0
$693$	−0.565988	−	6.46927i	−0.0215001	−	0.245747i
$694$		0			0
$695$	−13.9697	+	41.1073i	−0.529901	+	1.55929i
$696$		0			0
$697$	5.39379	+	2.51517i	0.204305	+	0.0952688i
$698$		0			0
$699$	5.63975	−	31.9846i	0.213315	−	1.20977i
$700$		0			0
$701$	29.6107	−	24.8463i	1.11838	−	0.938434i	0.119860	−	0.992791i	$-0.461755\pi$
$701$	29.6107	−	24.8463i	1.11838	−	0.938434i	0.998522	+	0.0543572i	$0.0173110\pi$
$702$		0			0
$703$	−0.199950	+	20.5059i	−0.00754125	+	0.773394i
$704$		0			0
$705$	−36.7774	−	5.67344i	−1.38512	−	0.213674i
$706$		0			0
$707$	9.97656	+	14.2480i	0.375207	+	0.535852i
$708$		0			0
$709$	7.24886	+	19.9161i	0.272237	+	0.747964i	0.998185	+	0.0602155i	$0.0191788\pi$
$709$	7.24886	+	19.9161i	0.272237	+	0.747964i	−0.725949	+	0.687749i	$0.758599\pi$
$710$		0			0
$711$	−14.4375	+	8.33550i	−0.541449	+	0.312605i
$712$		0			0
$713$	7.29580	−	0.638300i	0.273230	−	0.0239045i
$714$		0			0
$715$	−22.7597	−	15.2188i	−0.851165	−	0.569151i
$716$		0			0
$717$	−28.5763	+	40.8112i	−1.06720	+	1.52412i
$718$		0			0
$719$	−10.3126	+	28.3337i	−0.384596	+	1.05667i	0.584803	+	0.811176i	$0.301172\pi$
$719$	−10.3126	+	28.3337i	−0.384596	+	1.05667i	−0.969398	+	0.245493i	$0.921050\pi$
$720$		0			0
$721$			3.32350i			0.123774i
$722$		0			0
$723$	36.4183	+	36.4183i	1.35441	+	1.35441i
$724$		0			0
$725$	−16.7963	+	32.2116i	−0.623798	+	1.19631i
$726$		0			0
$727$	31.7258	+	22.2146i	1.17664	+	0.823895i	0.987433	−	0.158041i	$-0.0505178\pi$
$727$	31.7258	+	22.2146i	1.17664	+	0.823895i	0.189212	+	0.981936i	$0.439407\pi$
$728$		0			0
$729$	−12.0536	−	6.95913i	−0.446428	−	0.257745i
$730$		0			0
$731$	6.73420	+	5.65067i	0.249073	+	0.208997i
$732$		0			0
$733$	3.35443	−	12.5189i	0.123899	−	0.462396i	−0.875899	−	0.482494i	$-0.839731\pi$
$733$	3.35443	−	12.5189i	0.123899	−	0.462396i	0.999798	+	0.0200977i	$0.00639772\pi$
$734$		0			0
$735$	6.48803	−	1.88868i	0.239315	−	0.0696652i
$736$		0			0
$737$	11.7777	−	8.24683i	0.433837	−	0.303776i
$738$		0			0
$739$	−3.49091	−	4.16030i	−0.128415	−	0.153039i	0.698006	−	0.716092i	$-0.254071\pi$
$739$	−3.49091	−	4.16030i	−0.128415	−	0.153039i	−0.826421	+	0.563053i	$0.809627\pi$
$740$		0			0
$741$	−32.2843	+	31.6608i	−1.18599	+	1.16309i
$742$		0			0
$743$	4.44835	−	50.8449i	0.163194	−	1.86532i	−0.268474	−	0.963287i	$-0.586519\pi$
$743$	4.44835	−	50.8449i	0.163194	−	1.86532i	0.431668	−	0.902032i	$-0.357925\pi$
$744$		0			0
$745$	36.1535	−	21.9216i	1.32456	−	0.803144i
$746$		0			0
$747$	5.44834	−	11.6840i	0.199344	−	0.427495i
$748$		0			0
$749$	13.6813	+	23.6967i	0.499903	+	0.865858i
$750$		0			0
$751$	6.00839	−	7.16052i	0.219249	−	0.261291i	−0.645197	−	0.764016i	$-0.723225\pi$
$751$	6.00839	−	7.16052i	0.219249	−	0.261291i	0.864446	+	0.502725i	$0.167669\pi$
$752$		0			0
$753$	9.69252	+	36.1730i	0.353215	+	1.31822i
$754$		0			0
$755$	−19.7235	+	24.5578i	−0.717812	+	0.893750i
$756$		0			0
$757$	−14.0251	+	6.54003i	−0.509753	+	0.237702i	−0.660439	−	0.750880i	$-0.729630\pi$
$757$	−14.0251	+	6.54003i	−0.509753	+	0.237702i	0.150686	+	0.988582i	$0.451852\pi$
$758$		0			0
$759$	12.5980			0.457277
$760$		0			0
$761$	−43.4648			−1.57560			−0.787799	−	0.615932i	$-0.788780\pi$
$761$	−43.4648			−1.57560			−0.787799	+	0.615932i	$0.788780\pi$
$762$		0			0
$763$	13.3182	−	6.21040i	0.482153	−	0.224832i
$764$		0			0
$765$	0.330173	+	3.02433i	0.0119374	+	0.109345i
$766$		0			0
$767$	−13.3970	−	49.9983i	−0.483738	−	1.80534i
$768$		0			0
$769$	−11.3928	+	13.5774i	−0.410835	+	0.489614i	−0.931292	−	0.364274i	$-0.881317\pi$
$769$	−11.3928	+	13.5774i	−0.410835	+	0.489614i	0.520457	+	0.853888i	$0.325762\pi$
$770$		0			0
$771$	29.9872	+	51.9394i	1.07996	+	1.87055i
$772$		0			0
$773$	6.78584	−	14.5523i	0.244070	−	0.523409i	−0.745666	−	0.666320i	$-0.767868\pi$
$773$	6.78584	−	14.5523i	0.244070	−	0.523409i	0.989736	+	0.142911i	$0.0456462\pi$
$774$		0			0
$775$	−4.08239	+	12.9169i	−0.146644	+	0.463989i
$776$		0			0
$777$	−2.37836	+	27.1847i	−0.0853230	+	0.975247i
$778$		0			0
$779$	16.4649	−	7.48312i	0.589915	−	0.268111i
$780$		0			0
$781$	7.28990	+	8.68776i	0.260853	+	0.310873i
$782$		0			0
$783$	−24.2613	+	16.9880i	−0.867029	+	0.607100i
$784$		0			0
$785$	6.40601	+	22.0060i	0.228640	+	0.785428i
$786$		0			0
$787$	−8.04962	+	30.0416i	−0.286938	+	1.07087i	0.660474	+	0.750849i	$0.270355\pi$
$787$	−8.04962	+	30.0416i	−0.286938	+	1.07087i	−0.947412	+	0.320017i	$0.896311\pi$
$788$		0			0
$789$	−25.4541	−	21.3586i	−0.906192	−	0.760385i
$790$		0			0
$791$	39.9713	+	23.0775i	1.42122	+	0.820540i
$792$		0			0
$793$	41.4589	+	29.0298i	1.47225	+	1.03088i
$794$		0			0
$795$	−7.05353	−	18.1565i	−0.250163	−	0.643944i
$796$		0			0
$797$	−24.2039	−	24.2039i	−0.857346	−	0.857346i	0.133679	−	0.991025i	$-0.457321\pi$
$797$	−24.2039	−	24.2039i	−0.857346	−	0.857346i	−0.991025	+	0.133679i	$0.957321\pi$
$798$		0			0
$799$		−	12.0129i		−	0.424985i
$800$		0			0
$801$	−1.60857	+	4.41951i	−0.0568360	+	0.156156i
$802$		0			0
$803$	−17.6375	+	25.1890i	−0.622415	+	0.888901i
$804$		0			0
$805$	3.43622	+	17.3059i	0.121111	+	0.609953i
$806$		0			0
$807$	50.3971	−	4.40917i	1.77406	−	0.155210i
$808$		0			0
$809$	−22.6885	+	13.0992i	−0.797684	+	0.460543i	−0.842661	−	0.538445i	$-0.819012\pi$
$809$	−22.6885	+	13.0992i	−0.797684	+	0.460543i	0.0449769	+	0.998988i	$0.485679\pi$
$810$		0			0
$811$	8.32652	+	22.8769i	0.292384	+	0.803318i	0.995717	+	0.0924572i	$0.0294721\pi$
$811$	8.32652	+	22.8769i	0.292384	+	0.803318i	−0.703333	+	0.710861i	$0.748306\pi$
$812$		0			0
$813$	−10.8891	−	15.5513i	−0.381899	−	0.545409i
$814$		0			0
$815$	−22.0536	+	16.1588i	−0.772502	+	0.566017i
$816$		0			0
$817$	26.3526	−	4.38218i	0.921960	−	0.153313i
$818$		0			0
$819$	−11.0730	+	9.29137i	−0.386923	+	0.324667i
$820$		0			0
$821$	−8.20793	+	46.5495i	−0.286459	+	1.62459i	0.413569	+	0.910473i	$0.364282\pi$
$821$	−8.20793	+	46.5495i	−0.286459	+	1.62459i	−0.700028	+	0.714115i	$0.746829\pi$
$822$		0			0
$823$	−1.64779	−	0.768377i	−0.0574383	−	0.0267839i	0.393687	−	0.919245i	$-0.371199\pi$
$823$	−1.64779	−	0.768377i	−0.0574383	−	0.0267839i	−0.451125	+	0.892461i	$0.648977\pi$
$824$		0			0
$825$	−8.93223	+	21.5227i	−0.310980	+	0.749325i
$826$		0			0
$827$	−1.34740	−	15.4008i	−0.0468537	−	0.535540i	−0.982960	−	0.183822i	$-0.941153\pi$
$827$	−1.34740	−	15.4008i	−0.0468537	−	0.535540i	0.936106	−	0.351718i	$-0.114402\pi$
$828$		0			0
$829$	2.18489	−	3.78434i	0.0758843	−	0.131435i	−0.825586	−	0.564276i	$-0.809155\pi$
$829$	2.18489	−	3.78434i	0.0758843	−	0.131435i	0.901470	+	0.432841i	$0.142489\pi$
$830$		0			0
$831$	4.33069	−	0.763618i	0.150230	−	0.0264896i
$832$		0			0
$833$	0.921900	+	1.97702i	0.0319419	+	0.0684997i
$834$		0			0
$835$	1.90203	+	0.125318i	0.0658225	+	0.00433681i
$836$		0			0
$837$	−7.80961	+	7.80961i	−0.269940	+	0.269940i
$838$		0			0
$839$	0.219415	+	0.0798604i	0.00757504	+	0.00275709i	0.345805	−	0.938306i	$-0.387606\pi$
$839$	0.219415	+	0.0798604i	0.00757504	+	0.00275709i	−0.338230	+	0.941064i	$0.609828\pi$
$840$		0			0
$841$	4.13077	+	23.4268i	0.142440	+	0.807820i
$842$		0			0
$843$	−10.0697	+	2.69816i	−0.346817	+	0.0929294i
$844$		0			0
$845$	0.684438	+	31.8663i	0.0235454	+	1.09624i
$846$		0			0
$847$	−15.5052	−	4.15459i	−0.532763	−	0.142754i
$848$		0			0
$849$	−9.19037	+	3.34502i	−0.315413	+	0.114801i
$850$		0			0
$851$	−12.5239	−	2.20830i	−0.429314	−	0.0756996i
$852$		0			0
$853$	27.0627	+	2.36768i	0.926609	+	0.0810678i	0.540461	−	0.841369i	$-0.318250\pi$
$853$	27.0627	+	2.36768i	0.926609	+	0.0810678i	0.386148	+	0.922437i	$0.373805\pi$
$854$		0			0
$855$	7.63487	+	5.21367i	0.261107	+	0.178304i
$856$		0			0
$857$	5.71885	+	0.500335i	0.195352	+	0.0170911i	0.184412	−	0.982849i	$-0.440962\pi$
$857$	5.71885	+	0.500335i	0.195352	+	0.0170911i	0.0109404	+	0.999940i	$0.496518\pi$
$858$		0			0
$859$	−16.7939	−	2.96121i	−0.573000	−	0.101035i	−0.120362	−	0.992730i	$-0.538406\pi$
$859$	−16.7939	−	2.96121i	−0.573000	−	0.101035i	−0.452637	+	0.891695i	$0.649517\pi$
$860$		0			0
$861$	22.6152	−	8.23125i	0.770723	−	0.280520i
$862$		0			0
$863$	0.289113	+	0.0774676i	0.00984152	+	0.00263703i	0.263736	−	0.964595i	$-0.415045\pi$
$863$	0.289113	+	0.0774676i	0.00984152	+	0.00263703i	−0.253895	+	0.967232i	$0.581712\pi$
$864$		0			0
$865$	−26.0804	+	27.2254i	−0.886762	+	0.925690i
$866$		0			0
$867$	28.6805	−	7.68492i	0.974042	−	0.260994i
$868$		0			0
$869$	−7.15804	−	40.5953i	−0.242820	−	1.37710i
$870$		0			0
$871$	−30.0734	−	10.9458i	−1.01900	−	0.370885i
$872$		0			0
$873$	3.58647	−	3.58647i	0.121384	−	0.121384i
$874$		0			0
$875$	−32.0022	−	6.39973i	−1.08187	−	0.216351i
$876$		0			0
$877$	−9.47545	−	20.3202i	−0.319963	−	0.686163i	0.678880	−	0.734249i	$-0.262466\pi$
$877$	−9.47545	−	20.3202i	−0.319963	−	0.686163i	−0.998843	+	0.0480861i	$0.984688\pi$
$878$		0			0
$879$	−26.1699	+	4.61446i	−0.882690	+	0.155642i
$880$		0			0
$881$	19.6442	−	34.0247i	0.661829	−	1.14632i	−0.318305	−	0.947988i	$-0.603114\pi$
$881$	19.6442	−	34.0247i	0.661829	−	1.14632i	0.980135	−	0.198333i	$-0.0635529\pi$
$882$		0			0
$883$	−3.26412	−	37.3090i	−0.109846	−	1.25555i	−0.828424	−	0.560102i	$-0.810762\pi$
$883$	−3.26412	−	37.3090i	−0.109846	−	1.25555i	0.718577	−	0.695447i	$-0.244794\pi$
$884$		0			0
$885$	−39.5185	+	19.4716i	−1.32840	+	0.654531i
$886$		0			0
$887$	40.8025	+	19.0265i	1.37001	+	0.638848i	0.961728	−	0.274006i	$-0.0883487\pi$
$887$	40.8025	+	19.0265i	1.37001	+	0.638848i	0.408286	+	0.912854i	$0.366126\pi$
$888$		0			0
$889$	7.98452	−	45.2825i	0.267792	−	1.51873i
$890$		0			0
$891$	−19.6663	+	16.5019i	−0.658844	+	0.552836i
$892$		0			0
$893$	−27.7349	−	23.7370i	−0.928113	−	0.794328i
$894$		0			0
$895$	−2.52765	+	16.3852i	−0.0844899	+	0.547696i
$896$		0			0
$897$	−16.0840	−	22.9703i	−0.537028	−	0.766955i
$898$		0			0
$899$	6.73260	+	18.4977i	0.224545	+	0.616932i
$900$		0			0
$901$	5.44559	−	3.14401i	0.181419	−	0.104742i
$902$		0			0
$903$	35.4138	−	3.09830i	1.17850	−	0.103105i
$904$		0			0
$905$	−25.6420	+	5.09140i	−0.852368	+	0.169244i
$906$		0			0
$907$	10.1353	−	14.4747i	0.336537	−	0.480625i	−0.614841	−	0.788651i	$-0.710780\pi$
$907$	10.1353	−	14.4747i	0.336537	−	0.480625i	0.951378	+	0.308026i	$0.0996685\pi$
$908$		0			0
$909$	−1.93311	+	5.31116i	−0.0641170	+	0.176160i
$910$		0			0
$911$			53.9106i			1.78614i	0.449921	+	0.893068i	$0.351452\pi$
$911$			53.9106i			1.78614i	−0.449921	+	0.893068i	$0.648548\pi$
$912$		0			0
$913$	22.5405	+	22.5405i	0.745981	+	0.745981i
$914$		0			0
$915$	17.3623	−	39.4223i	0.573980	−	1.30326i
$916$		0			0
$917$	9.59461	+	6.71822i	0.316842	+	0.221855i
$918$		0			0
$919$	20.8428	+	12.0336i	0.687540	+	0.396951i	0.802690	−	0.596397i	$-0.203401\pi$
$919$	20.8428	+	12.0336i	0.687540	+	0.396951i	−0.115150	+	0.993348i	$0.536735\pi$
$920$		0			0
$921$	−24.6833	−	20.7118i	−0.813343	−	0.682476i
$922$		0			0
$923$	6.53358	−	24.3837i	0.215055	−	0.802598i
$924$		0			0
$925$	12.6524	−	19.8305i	0.416010	−	0.652021i
$926$		0			0
$927$	−0.884655	+	0.619442i	−0.0290559	+	0.0203452i
$928$		0			0
$929$	−23.8447	−	28.4170i	−0.782318	−	0.932330i	0.216718	−	0.976234i	$-0.430465\pi$
$929$	−23.8447	−	28.4170i	−0.782318	−	0.932330i	−0.999036	+	0.0439040i	$0.986020\pi$
$930$		0			0
$931$	6.38611	+	1.77807i	0.209296	+	0.0582738i
$932$		0			0
$933$	−2.11402	+	24.1634i	−0.0692099	+	0.791073i
$934$		0			0
$935$	−7.30635	−	1.79050i	−0.238943	−	0.0585555i
$936$		0			0
$937$	6.92411	−	14.8488i	0.226201	−	0.485089i	−0.760150	−	0.649748i	$-0.774874\pi$
$937$	6.92411	−	14.8488i	0.226201	−	0.485089i	0.986351	+	0.164659i	$0.0526522\pi$
$938$		0			0
$939$	−23.7743	−	41.1783i	−0.775844	−	1.34380i
$940$		0			0
$941$	4.66871	−	5.56396i	0.152196	−	0.181380i	−0.684559	−	0.728957i	$-0.740005\pi$
$941$	4.66871	−	5.56396i	0.152196	−	0.181380i	0.836755	+	0.547577i	$0.184450\pi$
$942$		0			0
$943$	2.90281	+	10.8334i	0.0945284	+	0.352785i
$944$		0			0
$945$	−20.7452	−	16.6615i	−0.674842	−	0.541997i
$946$		0			0
$947$	10.4783	−	4.88612i	0.340500	−	0.158778i	−0.244845	−	0.969562i	$-0.578737\pi$
$947$	10.4783	−	4.88612i	0.340500	−	0.158778i	0.585345	+	0.810785i	$0.300959\pi$
$948$		0			0
$949$	68.4460			2.22185
$950$		0			0
$951$	34.4353			1.11664
$952$		0			0
$953$	−13.4585	+	6.27582i	−0.435965	+	0.203294i	−0.628195	−	0.778056i	$-0.716206\pi$
$953$	−13.4585	+	6.27582i	−0.435965	+	0.203294i	0.192230	+	0.981350i	$0.438428\pi$
$954$		0			0
$955$	15.2437	+	12.2429i	0.493274	+	0.396171i
$956$		0			0
$957$	8.76394	+	32.7075i	0.283298	+	1.05728i
$958$		0			0
$959$	23.4340	−	27.9275i	0.756723	−	0.901828i
$960$		0			0
$961$	−11.8298	−	20.4897i	−0.381605	−	0.660959i
$962$		0			0
$963$	−3.75768	+	8.05836i	−0.121089	+	0.259677i
$964$		0			0
$965$	31.8977	+	7.81686i	1.02682	+	0.251634i
$966$		0			0
$967$	0.450638	−	5.15082i	0.0144915	−	0.165639i	−0.985500	−	0.169674i	$-0.945729\pi$
$967$	0.450638	−	5.15082i	0.0144915	−	0.165639i	0.999992	+	0.00403444i	$0.00128421\pi$
$968$		0			0
$969$	−5.36010	+	11.2081i	−0.172191	+	0.360057i
$970$		0			0
$971$	−3.43749	−	4.09664i	−0.110314	−	0.131467i	0.708062	−	0.706150i	$-0.249570\pi$
$971$	−3.43749	−	4.09664i	−0.110314	−	0.131467i	−0.818376	+	0.574683i	$0.805125\pi$
$972$		0			0
$973$	−46.4271	+	32.5086i	−1.48838	+	1.04218i
$974$		0			0
$975$	50.6469	−	11.1919i	1.62200	−	0.358427i
$976$		0			0
$977$	15.3092	−	57.1347i	0.489785	−	1.82790i	−0.0676895	−	0.997706i	$-0.521563\pi$
$977$	15.3092	−	57.1347i	0.489785	−	1.82790i	0.557474	−	0.830194i	$-0.311771\pi$
$978$		0			0
$979$	−8.90850	−	7.47512i	−0.284717	−	0.238906i
$980$		0			0
$981$	4.13539	+	2.38757i	0.132033	+	0.0762291i
$982$		0			0
$983$	34.4343	+	24.1112i	1.09828	+	0.769027i	0.974747	−	0.223313i	$-0.0716871\pi$
$983$	34.4343	+	24.1112i	1.09828	+	0.769027i	0.123538	+	0.992340i	$0.460576\pi$
$984$		0			0
$985$	−19.5887	+	44.4776i	−0.624149	+	1.41717i
$986$		0			0
$987$	−34.3501	−	34.3501i	−1.09338	−	1.09338i
$988$		0			0
$989$			16.5667i			0.526789i
$990$		0			0
$991$	5.68129	−	15.6092i	0.180472	−	0.495843i	−0.816162	−	0.577823i	$-0.803902\pi$
$991$	5.68129	−	15.6092i	0.180472	−	0.495843i	0.996634	+	0.0819803i	$0.0261244\pi$
$992$		0			0
$993$	22.7267	−	32.4571i	0.721210	−	1.02999i
$994$		0			0
$995$	14.2918	−	2.83775i	0.453081	−	0.0899626i
$996$		0			0
$997$	−13.6597	+	1.19507i	−0.432606	+	0.0378481i	−0.301380	−	0.953504i	$-0.597447\pi$
$997$	−13.6597	+	1.19507i	−0.432606	+	0.0378481i	−0.131227	+	0.991352i	$0.541892\pi$
$998$		0			0
$999$	16.6087	−	9.58902i	0.525475	−	0.303383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.13.8	✓	120
5.2	odd	4	inner	380.2.bh.a.317.3	yes	120
19.3	odd	18	inner	380.2.bh.a.193.3	yes	120
95.22	even	36	inner	380.2.bh.a.117.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.8	✓	120	1.1	even	1	trivial
380.2.bh.a.117.8	yes	120	95.22	even	36	inner
380.2.bh.a.193.3	yes	120	19.3	odd	18	inner
380.2.bh.a.317.3	yes	120	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80092 - 0.839782i) q^{3} +(-1.74340 - 1.40020i) q^{5} +(-0.755503 - 2.81958i) q^{7} +(0.609708 - 0.726622i) q^{9} +O(q^{10})\)	\(q+(1.80092 - 0.839782i) q^{3} +(-1.74340 - 1.40020i) q^{5} +(-0.755503 - 2.81958i) q^{7} +(0.609708 - 0.726622i) q^{9} +(1.17270 + 2.03117i) q^{11} +(2.20631 - 4.73144i) q^{13} +(-4.31558 - 1.05758i) q^{15} +(0.125014 - 1.42892i) q^{17} +(-3.05201 - 3.11211i) q^{19} +(-3.72843 - 4.44337i) q^{21} +(2.21427 - 1.55045i) q^{23} +(1.07886 + 4.88222i) q^{25} +(-1.05506 + 3.93755i) q^{27} +(5.56573 + 4.67020i) q^{29} +(2.34635 + 1.35467i) q^{31} +(3.81768 + 2.67317i) q^{33} +(-2.63084 + 5.97350i) q^{35} +(-3.32665 - 3.32665i) q^{37} -10.3738i q^{39} +(-1.41908 + 3.89890i) q^{41} +(-3.51529 + 5.02035i) q^{43} +(-2.08038 + 0.413075i) q^{45} +(8.34312 - 0.729929i) q^{47} +(-1.31705 + 0.760401i) q^{49} +(-0.974838 - 2.67835i) q^{51} +(2.51445 + 3.59100i) q^{53} +(0.799577 - 5.18316i) q^{55} +(-8.10991 - 3.04164i) q^{57} +(7.59535 - 6.37326i) q^{59} +(-1.68347 + 9.54743i) q^{61} +(-2.50940 - 1.17015i) q^{63} +(-10.4715 + 5.15950i) q^{65} +(-0.534287 - 6.10693i) q^{67} +(2.68568 - 4.65173i) q^{69} +(4.76199 - 0.839668i) q^{71} +(5.54088 + 11.8824i) q^{73} +(6.04294 + 7.88646i) q^{75} +(4.84108 - 4.84108i) q^{77} +(-16.5155 - 6.01117i) q^{79} +(1.90073 + 10.7796i) q^{81} +(13.1282 - 3.51769i) q^{83} +(-2.21872 + 2.31612i) q^{85} +(13.9454 + 3.73665i) q^{87} +(-4.65929 + 1.69584i) q^{89} +(-15.0075 - 2.64623i) q^{91} +(5.36321 + 0.469220i) q^{93} +(0.963270 + 9.69908i) q^{95} +(5.32688 + 0.466041i) q^{97} +(2.19090 + 0.386315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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