LMFDB - Embedded newform 380.2.bh.a.33.3

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			33.3
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02333 - 1.46147i) q^{3} +(0.710865 + 2.12006i) q^{5} +(-2.65380 - 0.711084i) q^{7} +(-0.0626300 + 0.172074i) q^{9} +O(q^{10})$	\(q+(-1.02333 - 1.46147i) q^{3} +(0.710865 + 2.12006i) q^{5} +(-2.65380 - 0.711084i) q^{7} +(-0.0626300 + 0.172074i) q^{9} +(2.84045 - 4.91980i) q^{11} +(-1.87803 - 1.31501i) q^{13} +(2.37096 - 3.20844i) q^{15} +(1.57974 - 3.38777i) q^{17} +(-3.00247 - 3.15994i) q^{19} +(1.67650 + 4.60614i) q^{21} +(-3.36528 - 0.294424i) q^{23} +(-3.98934 + 3.01416i) q^{25} +(-4.85444 + 1.30074i) q^{27} +(-1.09210 - 0.397492i) q^{29} +(7.63721 - 4.40934i) q^{31} +(-10.0969 + 0.883363i) q^{33} +(-0.378951 - 6.13172i) q^{35} +(3.85089 + 3.85089i) q^{37} +4.09038i q^{39} +(-2.15157 - 0.379380i) q^{41} +(-0.126691 - 1.44809i) q^{43} +(-0.409330 - 0.0104579i) q^{45} +(0.0279851 - 0.0130497i) q^{47} +(0.474851 + 0.274156i) q^{49} +(-6.56773 + 1.15807i) q^{51} +(0.107930 - 1.23364i) q^{53} +(12.4495 + 2.52462i) q^{55} +(-1.54564 + 7.62170i) q^{57} +(6.00753 - 2.18656i) q^{59} +(8.16469 - 6.85099i) q^{61} +(0.288567 - 0.412116i) q^{63} +(1.45288 - 4.91633i) q^{65} +(5.85638 + 12.5590i) q^{67} +(3.01352 + 5.21957i) q^{69} +(-7.74802 + 9.23373i) q^{71} +(10.1192 - 7.08552i) q^{73} +(8.48754 + 2.74583i) q^{75} +(-11.0364 + 11.0364i) q^{77} +(-2.15191 + 12.2041i) q^{79} +(7.28954 + 6.11665i) q^{81} +(3.01260 - 11.2432i) q^{83} +(8.30526 + 0.940909i) q^{85} +(0.536661 + 2.00284i) q^{87} +(1.92434 + 10.9135i) q^{89} +(4.04883 + 4.82520i) q^{91} +(-14.2596 - 6.64934i) q^{93} +(4.56492 - 8.61171i) q^{95} +(-10.5280 - 4.90928i) q^{97} +(0.668674 + 0.796895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.02333	−	1.46147i	−0.590823	−	0.843782i	0.406741	−	0.913543i	$-0.366665\pi$
$3$	−1.02333	−	1.46147i	−0.590823	−	0.843782i	−0.997564	+	0.0697615i	$0.977776\pi$
$4$		0			0
$5$	0.710865	+	2.12006i	0.317908	+	0.948121i
$5$	0.710865	+	2.12006i	0.317908	+	0.948121i
$6$		0			0
$7$	−2.65380	−	0.711084i	−1.00304	−	0.268765i	−0.280323	−	0.959906i	$-0.590442\pi$
$7$	−2.65380	−	0.711084i	−1.00304	−	0.268765i	−0.722720	+	0.691141i	$0.757108\pi$
$8$		0			0
$9$	−0.0626300	+	0.172074i	−0.0208767	+	0.0573581i
$10$		0			0
$11$	2.84045	−	4.91980i	0.856427	−	1.48337i	−0.0188880	−	0.999822i	$-0.506013\pi$
$11$	2.84045	−	4.91980i	0.856427	−	1.48337i	0.875315	−	0.483553i	$-0.160654\pi$
$12$		0			0
$13$	−1.87803	−	1.31501i	−0.520870	−	0.364717i	0.283380	−	0.959008i	$-0.408544\pi$
$13$	−1.87803	−	1.31501i	−0.520870	−	0.364717i	−0.804251	+	0.594290i	$0.797433\pi$
$14$		0			0
$15$	2.37096	−	3.20844i	0.612180	−	0.828417i
$16$		0			0
$17$	1.57974	−	3.38777i	0.383144	−	0.821654i	−0.616274	−	0.787532i	$-0.711359\pi$
$17$	1.57974	−	3.38777i	0.383144	−	0.821654i	0.999418	−	0.0341223i	$-0.0108636\pi$
$18$		0			0
$19$	−3.00247	−	3.15994i	−0.688813	−	0.724939i
$19$	−3.00247	−	3.15994i	−0.688813	−	0.724939i
$20$		0			0
$21$	1.67650	+	4.60614i	0.365842	+	1.00514i
$22$		0			0
$23$	−3.36528	−	0.294424i	−0.701710	−	0.0613917i	−0.269284	−	0.963061i	$-0.586787\pi$
$23$	−3.36528	−	0.294424i	−0.701710	−	0.0613917i	−0.432426	+	0.901669i	$0.642342\pi$
$24$		0			0
$25$	−3.98934	+	3.01416i	−0.797869	+	0.602832i
$26$		0			0
$27$	−4.85444	+	1.30074i	−0.934237	+	0.250328i
$28$		0			0
$29$	−1.09210	−	0.397492i	−0.202798	−	0.0738125i	0.238624	−	0.971112i	$-0.423304\pi$
$29$	−1.09210	−	0.397492i	−0.202798	−	0.0738125i	−0.441422	+	0.897300i	$0.645526\pi$
$30$		0			0
$31$	7.63721	−	4.40934i	1.37168	−	0.791942i	0.380543	−	0.924763i	$-0.375737\pi$
$31$	7.63721	−	4.40934i	1.37168	−	0.791942i	0.991140	+	0.132822i	$0.0424037\pi$
$32$		0			0
$33$	−10.0969	+	0.883363i	−1.75764	+	0.153774i
$34$		0			0
$35$	−0.378951	−	6.13172i	−0.0640544	−	1.03645i
$36$		0			0
$37$	3.85089	+	3.85089i	0.633083	+	0.633083i	0.948840	−	0.315757i	$-0.102258\pi$
$37$	3.85089	+	3.85089i	0.633083	+	0.633083i	−0.315757	+	0.948840i	$0.602258\pi$
$38$		0			0
$39$			4.09038i			0.654984i
$40$		0			0
$41$	−2.15157	−	0.379380i	−0.336019	−	0.0592491i	0.00309324	−	0.999995i	$-0.499015\pi$
$41$	−2.15157	−	0.379380i	−0.336019	−	0.0592491i	−0.339112	+	0.940746i	$0.610127\pi$
$42$		0			0
$43$	−0.126691	−	1.44809i	−0.0193203	−	0.220832i	−0.999717	−	0.0237970i	$-0.992424\pi$
$43$	−0.126691	−	1.44809i	−0.0193203	−	0.220832i	0.980397	−	0.197035i	$-0.0631311\pi$
$44$		0			0
$45$	−0.409330	−	0.0104579i	−0.0610193	−	0.00155897i
$46$		0			0
$47$	0.0279851	−	0.0130497i	0.00408204	−	0.00190349i	−0.420576	−	0.907257i	$-0.638172\pi$
$47$	0.0279851	−	0.0130497i	0.00408204	−	0.00190349i	0.424658	+	0.905354i	$0.360394\pi$
$48$		0			0
$49$	0.474851	+	0.274156i	0.0678359	+	0.0391651i
$50$		0			0
$51$	−6.56773	+	1.15807i	−0.919667	+	0.162162i
$52$		0			0
$53$	0.107930	−	1.23364i	0.0148253	−	0.169454i	−0.985172	−	0.171567i	$-0.945117\pi$
$53$	0.107930	−	1.23364i	0.0148253	−	0.169454i	0.999998	+	0.00211296i	$0.000672577\pi$
$54$		0			0
$55$	12.4495	+	2.52462i	1.67868	+	0.340419i
$56$		0			0
$57$	−1.54564	+	7.62170i	−0.204724	+	1.00952i
$58$		0			0
$59$	6.00753	−	2.18656i	0.782114	−	0.284666i	0.0800600	−	0.996790i	$-0.474489\pi$
$59$	6.00753	−	2.18656i	0.782114	−	0.284666i	0.702054	+	0.712124i	$0.252267\pi$
$60$		0			0
$61$	8.16469	−	6.85099i	1.04538	−	0.877179i	0.0527806	−	0.998606i	$-0.483192\pi$
$61$	8.16469	−	6.85099i	1.04538	−	0.877179i	0.992600	+	0.121427i	$0.0387472\pi$
$62$		0			0
$63$	0.288567	−	0.412116i	0.0363560	−	0.0519218i
$64$		0			0
$65$	1.45288	−	4.91633i	0.180207	−	0.609795i
$66$		0			0
$67$	5.85638	+	12.5590i	0.715471	+	1.53433i	0.840281	+	0.542151i	$0.182390\pi$
$67$	5.85638	+	12.5590i	0.715471	+	1.53433i	−0.124810	+	0.992181i	$0.539832\pi$
$68$		0			0
$69$	3.01352	+	5.21957i	0.362785	+	0.628362i
$70$		0			0
$71$	−7.74802	+	9.23373i	−0.919521	+	1.09584i	0.0755958	+	0.997139i	$0.475914\pi$
$71$	−7.74802	+	9.23373i	−0.919521	+	1.09584i	−0.995117	+	0.0987040i	$0.968530\pi$
$72$		0			0
$73$	10.1192	−	7.08552i	1.18436	−	0.829298i	0.195877	−	0.980629i	$-0.437245\pi$
$73$	10.1192	−	7.08552i	1.18436	−	0.829298i	0.988483	+	0.151331i	$0.0483559\pi$
$74$		0			0
$75$	8.48754	+	2.74583i	0.980057	+	0.317061i
$76$		0			0
$77$	−11.0364	+	11.0364i	−1.25771	+	1.25771i
$78$		0			0
$79$	−2.15191	+	12.2041i	−0.242109	+	1.37307i	0.585002	+	0.811032i	$0.301094\pi$
$79$	−2.15191	+	12.2041i	−0.242109	+	1.37307i	−0.827111	+	0.562038i	$0.810017\pi$
$80$		0			0
$81$	7.28954	+	6.11665i	0.809949	+	0.679628i
$82$		0			0
$83$	3.01260	−	11.2432i	0.330676	−	1.23410i	−0.577806	−	0.816174i	$-0.696091\pi$
$83$	3.01260	−	11.2432i	0.330676	−	1.23410i	0.908482	−	0.417925i	$-0.137242\pi$
$84$		0			0
$85$	8.30526	+	0.940909i	0.900832	+	0.102056i
$86$		0			0
$87$	0.536661	+	2.00284i	0.0575361	+	0.214727i
$88$		0			0
$89$	1.92434	+	10.9135i	0.203980	+	1.15683i	0.899037	+	0.437874i	$0.144268\pi$
$89$	1.92434	+	10.9135i	0.203980	+	1.15683i	−0.695056	+	0.718955i	$0.744621\pi$
$90$		0			0
$91$	4.04883	+	4.82520i	0.424432	+	0.505819i
$92$		0			0
$93$	−14.2596	−	6.64934i	−1.47865	−	0.689505i
$94$		0			0
$95$	4.56492	−	8.61171i	0.468351	−	0.883543i
$96$		0			0
$97$	−10.5280	−	4.90928i	−1.06896	−	0.498462i	−0.193171	−	0.981165i	$-0.561877\pi$
$97$	−10.5280	−	4.90928i	−1.06896	−	0.498462i	−0.875784	+	0.482703i	$0.839655\pi$
$98$		0			0
$99$	0.668674	+	0.796895i	0.0672043	+	0.0800910i
$100$		0			0
$101$	1.92926	+	10.9414i	0.191969	+	1.08871i	0.916670	+	0.399645i	$0.130867\pi$
$101$	1.92926	+	10.9414i	0.191969	+	1.08871i	−0.724701	+	0.689063i	$0.758022\pi$
$102$		0			0
$103$	−0.809577	−	3.02138i	−0.0797700	−	0.297706i	0.914502	−	0.404580i	$-0.132582\pi$
$103$	−0.809577	−	3.02138i	−0.0797700	−	0.297706i	−0.994273	+	0.106874i	$0.965916\pi$
$104$		0			0
$105$	−8.57355	+	6.82862i	−0.836693	+	0.666405i
$106$		0			0
$107$	3.04373	−	11.3593i	0.294248	−	1.09815i	−0.647564	−	0.762011i	$-0.724212\pi$
$107$	3.04373	−	11.3593i	0.294248	−	1.09815i	0.941812	−	0.336139i	$-0.109121\pi$
$108$		0			0
$109$	3.34279	+	2.80494i	0.320181	+	0.268664i	0.788685	−	0.614797i	$-0.210762\pi$
$109$	3.34279	+	2.80494i	0.320181	+	0.268664i	−0.468504	+	0.883462i	$0.655207\pi$
$110$		0			0
$111$	1.68723	−	9.56873i	0.160144	−	0.908224i
$112$		0			0
$113$	−9.74527	+	9.74527i	−0.916758	+	0.916758i	−0.996792	−	0.0800343i	$-0.974497\pi$
$113$	−9.74527	+	9.74527i	−0.916758	+	0.916758i	0.0800343	+	0.996792i	$0.474497\pi$
$114$		0			0
$115$	−1.76806	−	7.34391i	−0.164873	−	0.684823i
$116$		0			0
$117$	0.343900	−	0.240801i	0.0317935	−	0.0222621i
$118$		0			0
$119$	−6.60131	+	7.86713i	−0.605141	+	0.721179i
$120$		0			0
$121$	−10.6363	−	18.4226i	−0.966934	−	1.67478i
$122$		0			0
$123$	1.64732	+	3.53269i	0.148534	+	0.318532i
$124$		0			0
$125$	−9.22609	−	6.31500i	−0.825207	−	0.564831i
$126$		0			0
$127$	0.178067	−	0.254306i	0.0158009	−	0.0225660i	−0.811174	−	0.584805i	$-0.801171\pi$
$127$	0.178067	−	0.254306i	0.0158009	−	0.0225660i	0.826975	+	0.562239i	$0.190060\pi$
$128$		0			0
$129$	−1.98670	+	1.66704i	−0.174919	+	0.146774i
$130$		0			0
$131$	−16.1924	+	5.89355i	−1.41474	+	0.514922i	−0.932516	−	0.361128i	$-0.882392\pi$
$131$	−16.1924	+	5.89355i	−1.41474	+	0.514922i	−0.482220	+	0.876050i	$0.660169\pi$
$132$		0			0
$133$	5.72097	+	10.5209i	0.496071	+	0.912274i
$134$		0			0
$135$	−6.20850	−	9.36706i	−0.534343	−	0.806189i
$136$		0			0
$137$	−0.00193160	+	0.0220783i	−0.000165028	+	0.00188627i	−0.996277	−	0.0862126i	$-0.972524\pi$
$137$	−0.00193160	+	0.0220783i	−0.000165028	+	0.00188627i	0.996112	+	0.0880988i	$0.0280791\pi$
$138$		0			0
$139$	12.8861	−	2.27216i	1.09298	−	0.192722i	0.402033	−	0.915625i	$-0.368304\pi$
$139$	12.8861	−	2.27216i	1.09298	−	0.192722i	0.690950	+	0.722903i	$0.257193\pi$
$140$		0			0
$141$	−0.0477098	−	0.0275453i	−0.00401789	−	0.00231973i
$142$		0			0
$143$	−11.8040	+	5.50430i	−0.987100	+	0.460292i
$144$		0			0
$145$	0.0663729	−	2.59789i	0.00551197	−	0.215743i
$146$		0			0
$147$	−0.0852608	−	0.974536i	−0.00703219	−	0.0803783i
$148$		0			0
$149$	6.76916	+	1.19359i	0.554551	+	0.0977824i	0.443899	−	0.896077i	$-0.353595\pi$
$149$	6.76916	+	1.19359i	0.554551	+	0.0977824i	0.110652	+	0.993859i	$0.464706\pi$
$150$		0			0
$151$			2.79979i			0.227843i	0.993490	+	0.113922i	$0.0363413\pi$
$151$			2.79979i			0.227843i	−0.993490	+	0.113922i	$0.963659\pi$
$152$		0			0
$153$	0.484009	+	0.484009i	0.0391298	+	0.0391298i
$154$		0			0
$155$	14.7771	+	13.0569i	1.18693	+	1.04876i
$156$		0			0
$157$	16.9240	−	1.48066i	1.35068	−	0.118169i	0.611270	−	0.791422i	$-0.290659\pi$
$157$	16.9240	−	1.48066i	1.35068	−	0.118169i	0.739413	+	0.673252i	$0.235103\pi$
$158$		0			0
$159$	−1.91339	+	1.10469i	−0.151741	+	0.0876079i
$160$		0			0
$161$	8.72144	+	3.17434i	0.687346	+	0.250173i
$162$		0			0
$163$	14.0503	−	3.76477i	1.10051	−	0.294880i	0.337536	−	0.941313i	$-0.390407\pi$
$163$	14.0503	−	3.76477i	1.10051	−	0.294880i	0.762971	+	0.646433i	$0.223740\pi$
$164$		0			0
$165$	−9.05030	−	20.7781i	−0.704565	−	1.61757i
$166$		0			0
$167$	6.53860	+	0.572054i	0.505972	+	0.0442668i	0.337285	−	0.941403i	$-0.390492\pi$
$167$	6.53860	+	0.572054i	0.505972	+	0.0442668i	0.168688	+	0.985670i	$0.446047\pi$
$168$		0			0
$169$	−2.64853	−	7.27677i	−0.203733	−	0.559752i
$170$		0			0
$171$	0.731789	−	0.318741i	0.0559613	−	0.0243747i
$172$		0			0
$173$	4.25616	−	9.12737i	0.323590	−	0.693941i	−0.675466	−	0.737391i	$-0.736057\pi$
$173$	4.25616	−	9.12737i	0.323590	−	0.693941i	0.999056	+	0.0434507i	$0.0138351\pi$
$174$		0			0
$175$	12.7302	−	5.16222i	0.962316	−	0.390227i
$176$		0			0
$177$	−9.34331	−	6.54226i	−0.702287	−	0.491746i
$178$		0			0
$179$	6.91141	−	11.9709i	0.516583	−	0.894748i	−0.483232	−	0.875492i	$-0.660537\pi$
$179$	6.91141	−	11.9709i	0.516583	−	0.894748i	0.999815	−	0.0192552i	$-0.00612949\pi$
$180$		0			0
$181$	3.84634	−	10.5677i	0.285896	−	0.785494i	−0.710733	−	0.703462i	$-0.751637\pi$
$181$	3.84634	−	10.5677i	0.285896	−	0.785494i	0.996630	−	0.0820324i	$-0.0261411\pi$
$182$		0			0
$183$	−18.3677	−	4.92162i	−1.35778	−	0.363817i
$184$		0			0
$185$	−5.42668	+	10.9016i	−0.398977	+	0.801502i
$186$		0			0
$187$	−12.1800	−	17.3948i	−0.890686	−	1.27203i
$188$		0			0
$189$	13.8077			1.00436
$190$		0			0
$191$	−21.1537			−1.53063			−0.765314	−	0.643657i	$-0.777416\pi$
$191$	−21.1537			−1.53063			−0.765314	+	0.643657i	$0.777416\pi$
$192$		0			0
$193$	10.7544	+	15.3589i	0.774120	+	1.10556i	0.991581	+	0.129489i	$0.0413336\pi$
$193$	10.7544	+	15.3589i	0.774120	+	1.10556i	−0.217461	+	0.976069i	$0.569778\pi$
$194$		0			0
$195$	−8.67186	+	2.90770i	−0.621005	+	0.208225i
$196$		0			0
$197$	14.8907	+	3.98996i	1.06092	+	0.284273i	0.746757	−	0.665096i	$-0.231610\pi$
$197$	14.8907	+	3.98996i	1.06092	+	0.284273i	0.314163	+	0.949369i	$0.398276\pi$
$198$		0			0
$199$	−3.54943	+	9.75197i	−0.251612	+	0.691299i	0.748007	+	0.663691i	$0.231011\pi$
$199$	−3.54943	+	9.75197i	−0.251612	+	0.691299i	−0.999619	+	0.0276076i	$0.991211\pi$
$200$		0			0
$201$	12.3617	−	21.4110i	0.871925	−	1.51022i
$202$		0			0
$203$	2.61557	+	1.83144i	0.183577	+	0.128542i
$204$		0			0
$205$	−0.725165	−	4.83115i	−0.0506477	−	0.337422i
$206$		0			0
$207$	0.261430	−	0.560639i	0.0181707	−	0.0389671i
$208$		0			0
$209$	−24.0746	+	5.79589i	−1.66527	+	0.400910i
$210$		0			0
$211$	4.84503	+	13.3116i	0.333546	+	0.916410i	0.987182	+	0.159601i	$0.0510206\pi$
$211$	4.84503	+	13.3116i	0.333546	+	0.916410i	−0.653636	+	0.756809i	$0.726757\pi$
$212$		0			0
$213$	21.4237	+	1.87433i	1.46793	+	0.128427i
$214$		0			0
$215$	2.97998	−	1.29799i	0.203233	−	0.0885222i
$216$		0			0
$217$	−23.4031	+	6.27083i	−1.58870	+	0.425692i
$218$		0			0
$219$	−20.7106	−	7.53804i	−1.39949	−	0.509374i
$220$		0			0
$221$	−7.42173	+	4.28494i	−0.499240	+	0.288236i
$222$		0			0
$223$	−20.5867	+	1.80110i	−1.37859	+	0.120611i	−0.752217	−	0.658915i	$-0.771016\pi$
$223$	−20.5867	+	1.80110i	−1.37859	+	0.120611i	−0.626370	+	0.779526i	$0.715460\pi$
$224$		0			0
$225$	−0.268807	−	0.875240i	−0.0179205	−	0.0583494i
$226$		0			0
$227$	−18.5286	−	18.5286i	−1.22979	−	1.22979i	−0.964044	−	0.265744i	$-0.914382\pi$
$227$	−18.5286	−	18.5286i	−1.22979	−	1.22979i	−0.265744	−	0.964044i	$-0.585618\pi$
$228$		0			0
$229$		−	14.2947i		−	0.944617i	−0.881433	−	0.472309i	$-0.843421\pi$
$229$		−	14.2947i		−	0.944617i	0.881433	−	0.472309i	$-0.156579\pi$
$230$		0			0
$231$	27.4233	+	4.83546i	1.80432	+	0.318150i
$232$		0			0
$233$	−1.96193	−	22.4250i	−0.128530	−	1.46911i	−0.737195	−	0.675680i	$-0.763850\pi$
$233$	−1.96193	−	22.4250i	−0.128530	−	1.46911i	0.608665	−	0.793427i	$-0.291705\pi$
$234$		0			0
$235$	0.0475597	+	0.0500536i	0.00310245	+	0.00326514i
$236$		0			0
$237$	20.0381	−	9.34392i	1.30162	−	0.606953i
$238$		0			0
$239$	1.70353	+	0.983534i	0.110192	+	0.0636195i	0.554083	−	0.832461i	$-0.313069\pi$
$239$	1.70353	+	0.983534i	0.110192	+	0.0636195i	−0.443891	+	0.896081i	$0.646402\pi$
$240$		0			0
$241$	2.56008	−	0.451411i	0.164909	−	0.0290779i	−0.0905839	−	0.995889i	$-0.528873\pi$
$241$	2.56008	−	0.451411i	0.164909	−	0.0290779i	0.255493	+	0.966811i	$0.417762\pi$
$242$		0			0
$243$	0.165632	−	1.89318i	0.0106253	−	0.121447i
$244$		0			0
$245$	−0.243672	+	1.20160i	−0.0155676	+	0.0767676i
$246$		0			0
$247$	1.48337	+	9.88270i	0.0943843	+	0.628821i
$248$		0			0
$249$	−19.5145	+	7.10270i	−1.23668	+	0.450115i
$250$		0			0
$251$	−9.97102	+	8.36668i	−0.629365	+	0.528100i	−0.900732	−	0.434376i	$-0.856969\pi$
$251$	−9.97102	+	8.36668i	−0.629365	+	0.528100i	0.271366	+	0.962476i	$0.412524\pi$
$252$		0			0
$253$	−11.0074	+	15.7202i	−0.692030	+	0.988322i
$254$		0			0
$255$	−7.12395	−	13.1008i	−0.446119	−	0.820403i
$256$		0			0
$257$	7.63436	+	16.3719i	0.476219	+	1.02125i	0.986878	+	0.161471i	$0.0516237\pi$
$257$	7.63436	+	16.3719i	0.476219	+	1.02125i	−0.510659	+	0.859783i	$0.670599\pi$
$258$		0			0
$259$	−7.48120	−	12.9578i	−0.464859	−	0.805160i
$260$		0			0
$261$	0.136797	−	0.163028i	0.00846749	−	0.0100912i
$262$		0			0
$263$	−0.911418	+	0.638182i	−0.0562004	+	0.0393520i	−0.601339	−	0.798994i	$-0.705366\pi$
$263$	−0.911418	+	0.638182i	−0.0562004	+	0.0393520i	0.545139	+	0.838346i	$0.316477\pi$
$264$		0			0
$265$	2.69213	−	0.648136i	0.165376	−	0.0398147i
$266$		0			0
$267$	13.9805	−	13.9805i	0.855595	−	0.855595i
$268$		0			0
$269$	5.13598	−	29.1276i	0.313146	−	1.77594i	−0.269285	−	0.963060i	$-0.586787\pi$
$269$	5.13598	−	29.1276i	0.313146	−	1.77594i	0.582432	−	0.812880i	$-0.302101\pi$
$270$		0			0
$271$	7.93153	+	6.65534i	0.481806	+	0.404283i	0.851079	−	0.525038i	$-0.175949\pi$
$271$	7.93153	+	6.65534i	0.481806	+	0.404283i	−0.369273	+	0.929321i	$0.620393\pi$
$272$		0			0
$273$	2.90860	−	10.8551i	0.176037	−	0.656978i
$274$		0			0
$275$	3.49753	+	28.1883i	0.210909	+	1.69982i
$276$		0			0
$277$	0.0312037	+	0.116454i	0.00187485	+	0.00699703i	0.966857	−	0.255319i	$-0.0821804\pi$
$277$	0.0312037	+	0.116454i	0.00187485	+	0.00699703i	−0.964982	+	0.262316i	$0.915514\pi$
$278$		0			0
$279$	0.280417	+	1.59033i	0.0167881	+	0.0952103i
$280$		0			0
$281$	−3.48479	−	4.15301i	−0.207885	−	0.247748i	0.652020	−	0.758202i	$-0.273922\pi$
$281$	−3.48479	−	4.15301i	−0.207885	−	0.247748i	−0.859905	+	0.510454i	$0.829477\pi$
$282$		0			0
$283$	10.6117	+	4.94832i	0.630801	+	0.294147i	0.711602	−	0.702583i	$-0.247970\pi$
$283$	10.6117	+	4.94832i	0.630801	+	0.294147i	−0.0808011	+	0.996730i	$0.525748\pi$
$284$		0			0
$285$	−17.2572	+	2.14115i	−1.02223	+	0.126831i
$286$		0			0
$287$	5.44007	+	2.53675i	0.321117	+	0.149739i
$288$		0			0
$289$	1.94601	+	2.31917i	0.114471	+	0.136422i
$290$		0			0
$291$	3.59887	+	20.4102i	0.210970	+	1.19647i
$292$		0			0
$293$	−3.80846	−	14.2134i	−0.222493	−	0.830355i	−0.983393	−	0.181486i	$-0.941909\pi$
$293$	−3.80846	−	14.2134i	−0.222493	−	0.830355i	0.760901	−	0.648868i	$-0.224757\pi$
$294$		0			0
$295$	8.90619	+	11.1820i	0.518539	+	0.651041i
$296$		0			0
$297$	−7.38938	+	27.5775i	−0.428775	+	1.60021i
$298$		0			0
$299$	5.93292	+	4.97831i	0.343109	+	0.287903i
$300$		0			0
$301$	−0.693500	+	3.93303i	−0.0399727	+	0.226696i
$302$		0			0
$303$	14.0163	−	14.0163i	0.805213	−	0.805213i
$304$		0			0
$305$	20.3285	+	12.4395i	1.16401	+	0.712286i
$306$		0			0
$307$	−11.3508	+	7.94793i	−0.647826	+	0.453613i	−0.850742	−	0.525584i	$-0.823847\pi$
$307$	−11.3508	+	7.94793i	−0.647826	+	0.453613i	0.202916	+	0.979196i	$0.434958\pi$
$308$		0			0
$309$	−3.58720	+	4.27506i	−0.204069	+	0.243200i
$310$		0			0
$311$	−11.6592	−	20.1944i	−0.661134	−	1.14512i	−0.980318	−	0.197425i	$-0.936742\pi$
$311$	−11.6592	−	20.1944i	−0.661134	−	1.14512i	0.319184	−	0.947693i	$-0.396591\pi$
$312$		0			0
$313$	8.79109	+	18.8525i	0.496902	+	1.06561i	0.981604	+	0.190930i	$0.0611503\pi$
$313$	8.79109	+	18.8525i	0.496902	+	1.06561i	−0.484702	+	0.874679i	$0.661072\pi$
$314$		0			0
$315$	1.07885	+	0.318821i	0.0607860	+	0.0179636i
$316$		0			0
$317$	−1.63352	+	2.33291i	−0.0917476	+	0.131029i	−0.862402	−	0.506224i	$-0.831041\pi$
$317$	−1.63352	+	2.33291i	−0.0917476	+	0.131029i	0.770654	+	0.637254i	$0.219930\pi$
$318$		0			0
$319$	−5.05764	+	4.24386i	−0.283173	+	0.237611i
$320$		0			0
$321$	−19.7161	+	7.17609i	−1.10045	+	0.400530i
$322$		0			0
$323$	−15.4482	+	5.17977i	−0.859563	+	0.288210i
$324$		0			0
$325$	11.4557	−	0.414649i	0.635449	−	0.0230006i
$326$		0			0
$327$	0.678544	−	7.75579i	0.0375235	−	0.428896i
$328$		0			0
$329$	−0.0835463	+	0.0147315i	−0.00460606	+	0.000812172i
$330$		0			0
$331$	−2.29460	−	1.32479i	−0.126123	−	0.0728170i	0.435611	−	0.900135i	$-0.356532\pi$
$331$	−2.29460	−	1.32479i	−0.126123	−	0.0728170i	−0.561734	+	0.827318i	$0.689866\pi$
$332$		0			0
$333$	−0.903822	+	0.421459i	−0.0495291	+	0.0230958i
$334$		0			0
$335$	−22.4629	+	21.3437i	−1.22728	+	1.16613i
$336$		0			0
$337$	−1.06777	−	12.2047i	−0.0581653	−	0.664833i	−0.968180	−	0.250256i	$-0.919485\pi$
$337$	−1.06777	−	12.2047i	−0.0581653	−	0.664833i	0.910014	−	0.414577i	$-0.136070\pi$
$338$		0			0
$339$	24.2151	+	4.26978i	1.31518	+	0.231903i
$340$		0			0
$341$		−	50.0980i		−	2.71296i
$342$		0			0
$343$	12.5338	+	12.5338i	0.676762	+	0.676762i
$344$		0			0
$345$	−8.92361	+	10.0993i	−0.480431	+	0.543726i
$346$		0			0
$347$	11.2471	−	0.983997i	0.603778	−	0.0528237i	0.218832	−	0.975763i	$-0.429775\pi$
$347$	11.2471	−	0.983997i	0.603778	−	0.0528237i	0.384946	+	0.922939i	$0.374220\pi$
$348$		0			0
$349$	17.6910	−	10.2139i	0.946977	−	0.546738i	0.0548367	−	0.998495i	$-0.482536\pi$
$349$	17.6910	−	10.2139i	0.946977	−	0.546738i	0.892141	+	0.451758i	$0.149203\pi$
$350$		0			0
$351$	10.8272	+	3.94079i	0.577915	+	0.210344i
$352$		0			0
$353$	29.4599	−	7.89375i	1.56799	−	0.420142i	0.632809	−	0.774308i	$-0.281902\pi$
$353$	29.4599	−	7.89375i	1.56799	−	0.420142i	0.935183	+	0.354166i	$0.115235\pi$
$354$		0			0
$355$	−25.0839	−	9.86237i	−1.33132	−	0.523440i
$356$		0			0
$357$	18.2530	+	1.59693i	0.966049	+	0.0845183i
$358$		0			0
$359$	−6.97374	−	19.1602i	−0.368060	−	1.01124i	−0.976099	−	0.217329i	$-0.930266\pi$
$359$	−6.97374	−	19.1602i	−0.368060	−	1.01124i	0.608039	−	0.793907i	$-0.291957\pi$
$360$		0			0
$361$	−0.970398	+	18.9752i	−0.0510736	+	0.998695i
$362$		0			0
$363$	−16.0396	+	34.3971i	−0.841862	+	1.80538i
$364$		0			0
$365$	22.2151	+	16.4164i	1.16279	+	0.859276i
$366$		0			0
$367$	3.10737	+	2.17580i	0.162203	+	0.113576i	0.651860	−	0.758339i	$-0.273989\pi$
$367$	3.10737	+	2.17580i	0.162203	+	0.113576i	−0.489657	+	0.871915i	$0.662878\pi$
$368$		0			0
$369$	0.200034	−	0.346469i	0.0104134	−	0.0180365i
$370$		0			0
$371$	−1.16365	+	3.19710i	−0.0604137	+	0.165985i
$372$		0			0
$373$	15.8778	+	4.25444i	0.822121	+	0.220287i	0.645274	−	0.763952i	$-0.276743\pi$
$373$	15.8778	+	4.25444i	0.822121	+	0.220287i	0.176848	+	0.984238i	$0.443410\pi$
$374$		0			0
$375$	0.212169	+	19.9460i	0.0109564	+	1.03001i
$376$		0			0
$377$	1.52829	+	2.18262i	0.0787109	+	0.112411i
$378$		0			0
$379$	23.7092			1.21786			0.608929	−	0.793224i	$-0.291599\pi$
$379$	23.7092			1.21786			0.608929	+	0.793224i	$0.291599\pi$
$380$		0			0
$381$	−0.553884			−0.0283764
$382$		0			0
$383$	13.7396	+	19.6221i	0.702059	+	1.00264i	0.998861	+	0.0477050i	$0.0151907\pi$
$383$	13.7396	+	19.6221i	0.702059	+	1.00264i	−0.296803	+	0.954939i	$0.595920\pi$
$384$		0			0
$385$	−31.2432	−	15.5525i	−1.59230	−	0.792626i
$386$		0			0
$387$	0.257114	+	0.0688934i	0.0130698	+	0.00350205i
$388$		0			0
$389$	3.49249	−	9.59555i	0.177076	−	0.486514i	−0.819123	−	0.573618i	$-0.805539\pi$
$389$	3.49249	−	9.59555i	0.177076	−	0.486514i	0.996199	+	0.0871047i	$0.0277615\pi$
$390$		0			0
$391$	−6.31372	+	10.9357i	−0.319298	+	0.553041i
$392$		0			0
$393$	25.1835	+	17.6337i	1.27034	+	0.889501i
$394$		0			0
$395$	−27.4032	+	4.11328i	−1.37881	+	0.206961i
$396$		0			0
$397$	−11.8354	+	25.3810i	−0.594001	+	1.27384i	0.347769	+	0.937580i	$0.386939\pi$
$397$	−11.8354	+	25.3810i	−0.594001	+	1.27384i	−0.941770	+	0.336258i	$0.890839\pi$
$398$		0			0
$399$	9.52148	−	19.1274i	0.476670	−	0.957568i
$400$		0			0
$401$	−1.14417	−	3.14359i	−0.0571373	−	0.156983i	0.907840	−	0.419317i	$-0.137730\pi$
$401$	−1.14417	−	3.14359i	−0.0571373	−	0.156983i	−0.964977	+	0.262333i	$0.915508\pi$
$402$		0			0
$403$	−20.1412	−	1.76213i	−1.00330	−	0.0877777i
$404$		0			0
$405$	−7.78581	+	19.8024i	−0.386880	+	0.983990i
$406$		0			0
$407$	29.8839	−	8.00736i	1.48129	−	0.396910i
$408$		0			0
$409$	−18.0291	−	6.56207i	−0.891484	−	0.324474i	−0.144649	−	0.989483i	$-0.546205\pi$
$409$	−18.0291	−	6.56207i	−0.891484	−	0.324474i	−0.746835	+	0.665009i	$0.768427\pi$
$410$		0			0
$411$	0.0342435	−	0.0197705i	0.00168911	−	0.000975206i
$412$		0			0
$413$	−17.4976	+	1.53084i	−0.861002	+	0.0753279i
$414$		0			0
$415$	25.9778	−	1.60547i	1.27520	−	0.0788096i
$416$		0			0
$417$	−16.5075	−	16.5075i	−0.808375	−	0.808375i
$418$		0			0
$419$			24.3569i			1.18991i	0.803758	+	0.594957i	$0.202831\pi$
$419$			24.3569i			1.18991i	−0.803758	+	0.594957i	$0.797169\pi$
$420$		0			0
$421$	27.1726	+	4.79125i	1.32431	+	0.233511i	0.790692	−	0.612214i	$-0.209721\pi$
$421$	27.1726	+	4.79125i	1.32431	+	0.233511i	0.533618	+	0.845726i	$0.320832\pi$
$422$		0			0
$423$	0.000492807		0.00563281i	2.39611e−5		0.000273877i
$424$		0			0
$425$	3.90913	+	18.2765i	0.189621	+	0.886543i
$426$		0			0
$427$	−26.5391	+	12.3754i	−1.28432	+	0.598887i
$428$		0			0
$429$	20.1238	+	11.6185i	0.971587	+	0.560946i
$430$		0			0
$431$	5.98962	−	1.05613i	0.288510	−	0.0508721i	−0.0275201	−	0.999621i	$-0.508761\pi$
$431$	5.98962	−	1.05613i	0.288510	−	0.0508721i	0.316030	+	0.948749i	$0.397650\pi$
$432$		0			0
$433$	3.42395	−	39.1360i	0.164545	−	1.88075i	−0.246504	−	0.969142i	$-0.579282\pi$
$433$	3.42395	−	39.1360i	0.164545	−	1.88075i	0.411049	−	0.911613i	$-0.365162\pi$
$434$		0			0
$435$	−3.86467	+	2.56151i	−0.185297	+	0.122815i
$436$		0			0
$437$	9.17379	+	11.5181i	0.438842	+	0.550984i
$438$		0			0
$439$	18.1422	−	6.60324i	0.865882	−	0.315155i	0.129384	−	0.991595i	$-0.458700\pi$
$439$	18.1422	−	6.60324i	0.865882	−	0.315155i	0.736498	+	0.676439i	$0.236478\pi$
$440$		0			0
$441$	−0.0769151	+	0.0645394i	−0.00366262	+	0.00307331i
$442$		0			0
$443$	−0.0221234	+	0.0315954i	−0.00105111	+	0.00150114i	−0.819677	−	0.572826i	$-0.805847\pi$
$443$	−0.0221234	+	0.0315954i	−0.00105111	+	0.00150114i	0.818626	+	0.574327i	$0.194736\pi$
$444$		0			0
$445$	−21.7694	+	11.8378i	−1.03197	+	0.561164i
$446$		0			0
$447$	−5.18272	−	11.1144i	−0.245134	−	0.525692i
$448$		0			0
$449$	7.47665	+	12.9499i	0.352845	+	0.611146i	0.986747	−	0.162268i	$-0.0518809\pi$
$449$	7.47665	+	12.9499i	0.352845	+	0.611146i	−0.633902	+	0.773414i	$0.718548\pi$
$450$		0			0
$451$	−7.97789	+	9.50768i	−0.375664	+	0.447699i
$452$		0			0
$453$	4.09181	−	2.86512i	0.192250	−	0.134615i
$454$		0			0
$455$	−7.35157	+	12.0138i	−0.344647	+	0.563218i
$456$		0			0
$457$	20.9679	−	20.9679i	0.980839	−	0.980839i	−0.0189806	−	0.999820i	$-0.506042\pi$
$457$	20.9679	−	20.9679i	0.980839	−	0.980839i	0.999820	+	0.0189806i	$0.00604208\pi$
$458$		0			0
$459$	−3.26214	+	18.5005i	−0.152264	+	0.863531i
$460$		0			0
$461$	1.98495	+	1.66557i	0.0924483	+	0.0775733i	0.687840	−	0.725862i	$-0.258559\pi$
$461$	1.98495	+	1.66557i	0.0924483	+	0.0775733i	−0.595392	+	0.803435i	$0.703003\pi$
$462$		0			0
$463$	−1.20336	+	4.49100i	−0.0559249	+	0.208714i	−0.988234	−	0.152947i	$-0.951124\pi$
$463$	−1.20336	+	4.49100i	−0.0559249	+	0.208714i	0.932310	+	0.361661i	$0.117790\pi$
$464$		0			0
$465$	3.96041	−	34.9580i	0.183660	−	1.62114i
$466$		0			0
$467$	−5.07446	−	18.9382i	−0.234818	−	0.876353i	−0.978231	−	0.207520i	$-0.933461\pi$
$467$	−5.07446	−	18.9382i	−0.234818	−	0.876353i	0.743413	−	0.668833i	$-0.233206\pi$
$468$		0			0
$469$	−6.61114	−	37.4936i	−0.305274	−	1.73129i
$470$		0			0
$471$	−19.4829	−	23.2188i	−0.897723	−	1.06987i
$472$		0			0
$473$	−7.48417	−	3.48992i	−0.344122	−	0.160467i
$474$		0			0
$475$	21.5024	+	3.55616i	0.986598	+	0.163168i
$476$		0			0
$477$	0.205519	+	0.0958350i	0.00941006	+	0.00438798i
$478$		0			0
$479$	−25.2430	−	30.0835i	−1.15338	−	1.37455i	−0.915037	−	0.403369i	$-0.867839\pi$
$479$	−25.2430	−	30.0835i	−1.15338	−	1.37455i	−0.238347	−	0.971180i	$-0.576605\pi$
$480$		0			0
$481$	−2.16812	−	12.2960i	−0.0988579	−	0.560651i
$482$		0			0
$483$	−4.28573	−	15.9946i	−0.195007	−	0.727778i
$484$		0			0
$485$	2.92401	−	25.8098i	0.132773	−	1.17196i
$486$		0			0
$487$	4.90989	−	18.3239i	0.222488	−	0.830337i	−0.760907	−	0.648861i	$-0.775246\pi$
$487$	4.90989	−	18.3239i	0.222488	−	0.830337i	0.983395	−	0.181476i	$-0.0580876\pi$
$488$		0			0
$489$	−19.8803	−	16.6816i	−0.899018	−	0.754366i
$490$		0			0
$491$	−1.98596	+	11.2629i	−0.0896249	+	0.508288i	0.906638	+	0.421910i	$0.138640\pi$
$491$	−1.98596	+	11.2629i	−0.0896249	+	0.508288i	−0.996262	+	0.0863778i	$0.972471\pi$
$492$		0			0
$493$	−3.07185	+	3.07185i	−0.138349	+	0.138349i
$494$		0			0
$495$	−1.21413	+	1.98412i	−0.0545711	+	0.0891794i
$496$		0			0
$497$	27.1277	−	18.9950i	1.21684	−	0.852043i
$498$		0			0
$499$	−14.6658	+	17.4781i	−0.656533	+	0.782426i	−0.986884	−	0.161432i	$-0.948389\pi$
$499$	−14.6658	+	17.4781i	−0.656533	+	0.782426i	0.330350	+	0.943858i	$0.392833\pi$
$500$		0			0
$501$	−5.85514	−	10.1414i	−0.261588	−	0.453084i
$502$		0			0
$503$	16.6699	+	35.7487i	0.743273	+	1.59395i	0.803170	+	0.595750i	$0.203145\pi$
$503$	16.6699	+	35.7487i	0.743273	+	1.59395i	−0.0598966	+	0.998205i	$0.519077\pi$
$504$		0			0
$505$	−21.8250	+	11.8680i	−0.971200	+	0.528119i
$506$		0			0
$507$	−7.92448	+	11.3173i	−0.351938	+	0.502620i
$508$		0			0
$509$	−19.9020	+	16.6998i	−0.882142	+	0.740205i	−0.966618	−	0.256221i	$-0.917523\pi$
$509$	−19.9020	+	16.6998i	−0.882142	+	0.740205i	0.0844766	+	0.996425i	$0.473078\pi$
$510$		0			0
$511$	−31.8927	+	11.6080i	−1.41085	+	0.513507i
$512$		0			0
$513$	18.6855	+	11.4343i	0.824987	+	0.504836i
$514$		0			0
$515$	5.83003	−	3.86415i	0.256902	−	0.170275i
$516$		0			0
$517$	0.0152884	−	0.174748i	0.000672385	−	0.00768540i
$518$		0			0
$519$	−17.6949	+	3.12008i	−0.776719	+	0.136956i
$520$		0			0
$521$	−2.55912	−	1.47751i	−0.112117	−	0.0647308i	0.442893	−	0.896575i	$-0.353952\pi$
$521$	−2.55912	−	1.47751i	−0.112117	−	0.0647308i	−0.555010	+	0.831844i	$0.687286\pi$
$522$		0			0
$523$	18.7610	−	8.74839i	0.820361	−	0.382540i	0.0333223	−	0.999445i	$-0.489391\pi$
$523$	18.7610	−	8.74839i	0.820361	−	0.382540i	0.787038	+	0.616904i	$0.211613\pi$
$524$		0			0
$525$	−20.5718	−	13.3222i	−0.897825	−	0.581430i
$526$		0			0
$527$	−2.87301	−	32.8387i	−0.125150	−	1.43048i
$528$		0			0
$529$	−11.4121	−	2.01227i	−0.496180	−	0.0874899i
$530$		0			0
$531$			1.17069i			0.0508035i
$532$		0			0
$533$	3.54181	+	3.54181i	0.153413	+	0.153413i
$534$		0			0
$535$	26.2462	−	1.62206i	1.13472	−	0.0701279i
$536$		0			0
$537$	−24.5678	+	2.14941i	−1.06018	+	0.0927538i
$538$		0			0
$539$	2.69758	−	1.55745i	0.116193	−	0.0670841i
$540$		0			0
$541$	−2.93852	−	1.06953i	−0.126337	−	0.0459829i	0.278078	−	0.960558i	$-0.410303\pi$
$541$	−2.93852	−	1.06953i	−0.126337	−	0.0459829i	−0.404415	+	0.914576i	$0.632525\pi$
$542$		0			0
$543$	−19.3806	+	5.19301i	−0.831700	+	0.222853i
$544$		0			0
$545$	−3.57037	+	9.08086i	−0.152938	+	0.388981i
$546$		0			0
$547$	12.1728	+	1.06499i	0.520473	+	0.0455355i	0.344366	−	0.938836i	$-0.388094\pi$
$547$	12.1728	+	1.06499i	0.520473	+	0.0455355i	0.176107	+	0.984371i	$0.443649\pi$
$548$		0			0
$549$	0.667525	+	1.83401i	0.0284893	+	0.0782737i
$550$		0			0
$551$	2.02295	+	4.64443i	0.0861804	+	0.197859i
$552$		0			0
$553$	14.3889	−	30.8571i	0.611879	−	1.31218i
$554$		0			0
$555$	21.4857	−	3.22505i	0.912018	−	0.136896i
$556$		0			0
$557$	9.72579	+	6.81007i	0.412095	+	0.288552i	0.761182	−	0.648538i	$-0.224619\pi$
$557$	9.72579	+	6.81007i	0.412095	+	0.288552i	−0.349087	+	0.937090i	$0.613508\pi$
$558$		0			0
$559$	−1.66632	+	2.88615i	−0.0704778	+	0.122071i
$560$		0			0
$561$	−12.9578	+	35.6014i	−0.547080	+	1.50309i
$562$		0			0
$563$	−0.850762	−	0.227961i	−0.0358553	−	0.00960741i	0.240847	−	0.970563i	$-0.422575\pi$
$563$	−0.850762	−	0.227961i	−0.0358553	−	0.00960741i	−0.276702	+	0.960956i	$0.589242\pi$
$564$		0			0
$565$	−27.5882	−	13.7330i	−1.16064	−	0.577753i
$566$		0			0
$567$	−14.9956	−	21.4159i	−0.629754	−	0.899382i
$568$		0			0
$569$	−10.6163			−0.445058			−0.222529	−	0.974926i	$-0.571431\pi$
$569$	−10.6163			−0.445058			−0.222529	+	0.974926i	$0.571431\pi$
$570$		0			0
$571$	10.9851			0.459712			0.229856	−	0.973225i	$-0.426174\pi$
$571$	10.9851			0.459712			0.229856	+	0.973225i	$0.426174\pi$
$572$		0			0
$573$	21.6473	+	30.9156i	0.904330	+	1.29152i
$574$		0			0
$575$	14.3127	−	8.96894i	0.596881	−	0.374030i
$576$		0			0
$577$	−22.7300	−	6.09047i	−0.946260	−	0.253550i	−0.247486	−	0.968892i	$-0.579604\pi$
$577$	−22.7300	−	6.09047i	−0.946260	−	0.253550i	−0.698775	+	0.715342i	$0.746271\pi$
$578$		0			0
$579$	11.4413	−	31.4346i	0.475482	−	1.30638i
$580$		0			0
$581$	−15.9897	+	27.6950i	−0.663364	+	1.14898i
$582$		0			0
$583$	−5.76271	−	4.03509i	−0.238667	−	0.167116i
$584$		0			0
$585$	0.754980	+	0.557912i	0.0312146	+	0.0230668i
$586$		0			0
$587$	9.08538	−	19.4837i	0.374994	−	0.804177i	−0.624734	−	0.780838i	$-0.714792\pi$
$587$	9.08538	−	19.4837i	0.374994	−	0.804177i	0.999728	−	0.0233392i	$-0.00742976\pi$
$588$		0			0
$589$	−36.8637	−	10.8942i	−1.51894	−	0.448887i
$590$		0			0
$591$	−9.40698	−	25.8455i	−0.386951	−	1.06314i
$592$		0			0
$593$	2.06256	+	0.180451i	0.0846994	+	0.00741023i	0.129427	−	0.991589i	$-0.458686\pi$
$593$	2.06256	+	0.180451i	0.0846994	+	0.00741023i	−0.0447273	+	0.998999i	$0.514242\pi$
$594$		0			0
$595$	−21.3715	−	8.40273i	−0.876145	−	0.344478i
$596$		0			0
$597$	17.8845	−	4.79214i	0.731964	−	0.196129i
$598$		0			0
$599$	2.94753	+	1.07281i	0.120433	+	0.0438339i	0.401534	−	0.915844i	$-0.368477\pi$
$599$	2.94753	+	1.07281i	0.120433	+	0.0438339i	−0.281101	+	0.959678i	$0.590700\pi$
$600$		0			0
$601$	8.11532	−	4.68538i	0.331031	−	0.191121i	−0.325268	−	0.945622i	$-0.605454\pi$
$601$	8.11532	−	4.68538i	0.331031	−	0.191121i	0.656299	+	0.754501i	$0.272121\pi$
$602$		0			0
$603$	−2.52788	+	0.221160i	−0.102943	+	0.00900635i
$604$		0			0
$605$	31.4961	−	35.6455i	1.28050	−	1.44920i
$606$		0			0
$607$	2.43479	+	2.43479i	0.0988249	+	0.0988249i	0.754791	−	0.655966i	$-0.227738\pi$
$607$	2.43479	+	2.43479i	0.0988249	+	0.0988249i	−0.655966	+	0.754791i	$0.727738\pi$
$608$		0			0
$609$		−	5.69677i		−	0.230845i
$610$		0			0
$611$	−0.0697171	−	0.0122930i	−0.00282045	−	0.000497322i
$612$		0			0
$613$	4.06839	+	46.5019i	0.164321	+	1.87820i	0.414575	+	0.910015i	$0.363930\pi$
$613$	4.06839	+	46.5019i	0.164321	+	1.87820i	−0.250254	+	0.968180i	$0.580514\pi$
$614$		0			0
$615$	−6.31851	+	6.00369i	−0.254787	+	0.242092i
$616$		0			0
$617$	−30.9987	+	14.4549i	−1.24796	+	0.581934i	−0.930484	−	0.366332i	$-0.880613\pi$
$617$	−30.9987	+	14.4549i	−1.24796	+	0.581934i	−0.317477	+	0.948266i	$0.602836\pi$
$618$		0			0
$619$	19.4213	+	11.2129i	0.780608	+	0.450684i	0.836646	−	0.547744i	$-0.184513\pi$
$619$	19.4213	+	11.2129i	0.780608	+	0.450684i	−0.0560377	+	0.998429i	$0.517847\pi$
$620$		0			0
$621$	16.7195	−	2.94810i	0.670931	−	0.118303i
$622$		0			0
$623$	2.65359	−	30.3307i	0.106314	−	1.21517i
$624$		0			0
$625$	6.82971	−	24.0490i	0.273188	−	0.961961i
$626$		0			0
$627$	33.1069	+	29.2532i	1.32216	+	1.16826i
$628$		0			0
$629$	19.1293	−	6.96251i	0.762737	−	0.277614i
$630$		0			0
$631$	−9.76730	+	8.19574i	−0.388830	+	0.326267i	−0.816157	−	0.577830i	$-0.803900\pi$
$631$	−9.76730	+	8.19574i	−0.388830	+	0.326267i	0.427327	+	0.904097i	$0.359455\pi$
$632$		0			0
$633$	14.4965	−	20.7031i	0.576184	−	0.822875i
$634$		0			0
$635$	0.665728	+	0.196737i	0.0264186	+	0.00780725i
$636$		0			0
$637$	−0.531266	−	1.13930i	−0.0210495	−	0.0451409i
$638$		0			0
$639$	−1.10363	−	1.91154i	−0.0436590	−	0.0756195i
$640$		0			0
$641$	5.18255	−	6.17633i	0.204699	−	0.243950i	−0.653922	−	0.756562i	$-0.726878\pi$
$641$	5.18255	−	6.17633i	0.204699	−	0.243950i	0.858620	+	0.512612i	$0.171322\pi$
$642$		0			0
$643$	−3.88525	+	2.72048i	−0.153219	+	0.107285i	−0.647672	−	0.761919i	$-0.724257\pi$
$643$	−3.88525	+	2.72048i	−0.153219	+	0.107285i	0.494453	+	0.869204i	$0.335368\pi$
$644$		0			0
$645$	−4.94650	−	3.02689i	−0.194768	−	0.119184i
$646$		0			0
$647$	24.8376	−	24.8376i	0.976466	−	0.976466i	−0.0232633	−	0.999729i	$-0.507406\pi$
$647$	24.8376	−	24.8376i	0.976466	−	0.976466i	0.999729	+	0.0232633i	$0.00740561\pi$
$648$		0			0
$649$	6.30662	−	35.7666i	0.247557	−	1.40396i
$650$		0			0
$651$	33.1138	+	27.7858i	1.29783	+	1.08901i
$652$		0			0
$653$	4.54172	−	16.9499i	0.177731	−	0.663302i	−0.818339	−	0.574736i	$-0.805105\pi$
$653$	4.54172	−	16.9499i	0.177731	−	0.663302i	0.996070	−	0.0885660i	$-0.0282284\pi$
$654$		0			0
$655$	−24.0053	−	30.1394i	−0.937965	−	1.17764i
$656$		0			0
$657$	0.585474	+	2.18502i	0.0228415	+	0.0852456i
$658$		0			0
$659$	6.62510	+	37.5728i	0.258077	+	1.46363i	0.788048	+	0.615614i	$0.211092\pi$
$659$	6.62510	+	37.5728i	0.258077	+	1.46363i	−0.529971	+	0.848016i	$0.677797\pi$
$660$		0			0
$661$	−19.2093	−	22.8928i	−0.747156	−	0.890426i	0.249807	−	0.968296i	$-0.419633\pi$
$661$	−19.2093	−	22.8928i	−0.747156	−	0.890426i	−0.996964	+	0.0778694i	$0.975188\pi$
$662$		0			0
$663$	13.8572	+	6.46174i	0.538171	+	0.250953i
$664$		0			0
$665$	−18.2380	+	19.6077i	−0.707241	+	0.760355i
$666$		0			0
$667$	3.55820	+	1.65922i	0.137774	+	0.0642451i
$668$		0			0
$669$	23.6993	+	28.2438i	0.916270	+	1.09197i
$670$		0			0
$671$	−10.5141	−	59.6285i	−0.405893	−	2.30193i
$672$		0			0
$673$	9.02654	+	33.6875i	0.347948	+	1.29856i	0.889131	+	0.457653i	$0.151310\pi$
$673$	9.02654	+	33.6875i	0.347948	+	1.29856i	−0.541183	+	0.840905i	$0.682023\pi$
$674$		0			0
$675$	15.4454	−	19.8211i	0.594492	−	0.762916i
$676$		0			0
$677$	−11.2754	+	42.0802i	−0.433347	+	1.61727i	0.311645	+	0.950199i	$0.399120\pi$
$677$	−11.2754	+	42.0802i	−0.433347	+	1.61727i	−0.744991	+	0.667074i	$0.767546\pi$
$678$		0			0
$679$	24.4483	+	20.5146i	0.938239	+	0.787276i
$680$		0			0
$681$	−8.11810	+	46.0401i	−0.311086	+	1.76426i
$682$		0			0
$683$	−7.44272	+	7.44272i	−0.284788	+	0.284788i	−0.835015	−	0.550227i	$-0.814541\pi$
$683$	−7.44272	+	7.44272i	−0.284788	+	0.284788i	0.550227	+	0.835015i	$0.314541\pi$
$684$		0			0
$685$	−0.0481805	+	0.0115996i	−0.00184088	+	0.000443196i
$686$		0			0
$687$	−20.8913	+	14.6282i	−0.797051	+	0.558101i
$688$		0			0
$689$	−1.82495	+	2.17488i	−0.0695249	+	0.0828565i
$690$		0			0
$691$	−22.6643	−	39.2558i	−0.862192	−	1.49336i	−0.869808	−	0.493390i	$-0.835758\pi$
$691$	−22.6643	−	39.2558i	−0.862192	−	1.49336i	0.00761621	−	0.999971i	$-0.497576\pi$
$692$		0			0
$693$	−1.20787	−	2.59029i	−0.0458832	−	0.0983968i
$694$		0			0
$695$	13.9774	+	25.7041i	0.530193	+	0.975013i
$696$		0			0
$697$	−4.68417	+	6.68969i	−0.177426	+	0.253390i
$698$		0			0
$699$	−30.7658	+	25.8155i	−1.16367	+	0.976433i
$700$		0			0
$701$	−0.370000	+	0.134669i	−0.0139747	+	0.00508637i	−0.348998	−	0.937123i	$-0.613478\pi$
$701$	−0.370000	+	0.134669i	−0.0139747	+	0.00508637i	0.335023	+	0.942210i	$0.391256\pi$
$702$		0			0
$703$	0.606403	−	23.7308i	0.0228709	−	0.895023i
$704$		0			0
$705$	0.0244825	−	0.120729i	0.000922065	−	0.00454691i
$706$		0			0
$707$	2.66037	−	30.4082i	0.100053	−	1.14362i
$708$		0			0
$709$	−4.52952	+	0.798677i	−0.170110	+	0.0299950i	−0.258054	−	0.966130i	$-0.583081\pi$
$709$	−4.52952	+	0.798677i	−0.170110	+	0.0299950i	0.0879444	+	0.996125i	$0.471970\pi$
$710$		0			0
$711$	−1.96524	−	1.13463i	−0.0737023	−	0.0425520i
$712$		0			0
$713$	−26.9996	+	12.5901i	−1.01114	+	0.471503i
$714$		0			0
$715$	−20.0605	−	21.1124i	−0.750220	−	0.789560i
$716$		0			0
$717$	−0.305873	−	3.49615i	−0.0114231	−	0.130566i
$718$		0			0
$719$	15.5955	+	2.74990i	0.581612	+	0.102554i	0.456711	−	0.889615i	$-0.349027\pi$
$719$	15.5955	+	2.74990i	0.581612	+	0.102554i	0.124901	+	0.992169i	$0.460139\pi$
$720$		0			0
$721$			8.59384i			0.320051i
$722$		0			0
$723$	−3.27954	−	3.27954i	−0.121967	−	0.121967i
$724$		0			0
$725$	5.55487	−	1.70603i	0.206303	−	0.0633604i
$726$		0			0
$727$	20.8448	−	1.82368i	0.773089	−	0.0676365i	0.306217	−	0.951962i	$-0.400937\pi$
$727$	20.8448	−	1.82368i	0.773089	−	0.0676365i	0.466872	+	0.884325i	$0.345381\pi$
$728$		0			0
$729$	21.7865	−	12.5784i	0.806908	−	0.465868i
$730$		0			0
$731$	−5.10593	−	1.85841i	−0.188850	−	0.0687356i
$732$		0			0
$733$	−48.1439	+	12.9001i	−1.77824	+	0.476477i	−0.990260	−	0.139229i	$-0.955538\pi$
$733$	−48.1439	+	12.9001i	−1.77824	+	0.476477i	−0.787976	+	0.615706i	$0.788871\pi$
$734$		0			0
$735$	2.00547	−	0.873521i	0.0739728	−	0.0322203i
$736$		0			0
$737$	78.4227	+	6.86110i	2.88874	+	0.252732i
$738$		0			0
$739$	−12.8479	−	35.2994i	−0.472618	−	1.29851i	−0.915641	−	0.401998i	$-0.868316\pi$
$739$	−12.8479	−	35.2994i	−0.472618	−	1.29851i	0.443022	−	0.896511i	$-0.353906\pi$
$740$		0			0
$741$	12.9253	−	12.2812i	0.474824	−	0.451162i
$742$		0			0
$743$	−10.5360	+	22.5945i	−0.386528	+	0.828912i	0.612726	+	0.790295i	$0.290073\pi$
$743$	−10.5360	+	22.5945i	−0.386528	+	0.828912i	−0.999254	+	0.0386165i	$0.987705\pi$
$744$		0			0
$745$	2.28148	+	15.1995i	0.0835870	+	0.556868i
$746$		0			0
$747$	1.74598	+	1.22255i	0.0638822	+	0.0447308i
$748$		0			0
$749$	−16.1549	+	27.9811i	−0.590288	+	1.02241i
$750$		0			0
$751$	−14.9816	+	41.1616i	−0.546686	+	1.50201i	0.291472	+	0.956579i	$0.405855\pi$
$751$	−14.9816	+	41.1616i	−0.546686	+	1.50201i	−0.838158	+	0.545427i	$0.816367\pi$
$752$		0			0
$753$	22.4314	+	6.01047i	0.817444	+	0.219034i
$754$		0			0
$755$	−5.93573	+	1.99027i	−0.216023	+	0.0724333i
$756$		0			0
$757$	−11.1589	−	15.9366i	−0.405578	−	0.579225i	0.563458	−	0.826144i	$-0.309471\pi$
$757$	−11.1589	−	15.9366i	−0.405578	−	0.579225i	−0.969036	+	0.246920i	$0.920582\pi$
$758$		0			0
$759$	34.2389			1.24279
$760$		0			0
$761$	9.23827			0.334887			0.167443	−	0.985882i	$-0.446449\pi$
$761$	9.23827			0.334887			0.167443	+	0.985882i	$0.446449\pi$
$762$		0			0
$763$	−6.87656	−	9.82075i	−0.248948	−	0.355535i
$764$		0			0
$765$	−0.682065	+	1.37019i	−0.0246601	+	0.0495395i
$766$		0			0
$767$	−14.1576	−	3.79353i	−0.511203	−	0.136976i
$768$		0			0
$769$	−7.91335	+	21.7418i	−0.285363	+	0.784028i	0.711337	+	0.702851i	$0.248090\pi$
$769$	−7.91335	+	21.7418i	−0.285363	+	0.784028i	−0.996700	+	0.0811767i	$0.974132\pi$
$770$		0			0
$771$	16.1147	−	27.9114i	0.580355	−	1.00520i
$772$		0			0
$773$	−27.6334	−	19.3491i	−0.993903	−	0.695939i	−0.0409831	−	0.999160i	$-0.513049\pi$
$773$	−27.6334	−	19.3491i	−0.993903	−	0.695939i	−0.952920	+	0.303221i	$0.901938\pi$
$774$		0			0
$775$	−17.1770	+	40.6101i	−0.617015	+	1.45876i
$776$		0			0
$777$	−11.2817	+	24.1938i	−0.404730	+	0.867947i
$778$		0			0
$779$	5.26120	+	7.93789i	0.188502	+	0.284405i
$780$		0			0
$781$	23.4203	+	64.3466i	0.838043	+	2.30250i
$782$		0			0
$783$	5.81857	+	0.509059i	0.207939	+	0.0181923i
$784$		0			0
$785$	15.1698	+	34.8274i	0.541433	+	1.24304i
$786$		0			0
$787$	−37.3660	+	10.0122i	−1.33195	+	0.356896i	−0.853443	−	0.521186i	$-0.825490\pi$
$787$	−37.3660	+	10.0122i	−1.33195	+	0.356896i	−0.478510	+	0.878082i	$0.658823\pi$
$788$		0			0
$789$	1.86537	+	0.678940i	0.0664090	+	0.0241709i
$790$		0			0
$791$	32.7917	−	18.9323i	1.16594	−	0.673156i
$792$		0			0
$793$	−24.3426	+	2.12970i	−0.864430	+	0.0756279i
$794$		0			0
$795$	−3.70218	−	3.27121i	−0.131303	−	0.116018i
$796$		0			0
$797$	−1.43819	−	1.43819i	−0.0509431	−	0.0509431i	0.681176	−	0.732119i	$-0.261469\pi$
$797$	−1.43819	−	1.43819i	−0.0509431	−	0.0509431i	−0.732119	+	0.681176i	$0.761469\pi$
$798$		0			0
$799$		−	0.115422i		−	0.00408334i
$800$		0			0
$801$	−1.99846	−	0.352382i	−0.0706120	−	0.0124508i
$802$		0			0
$803$	−6.11636	−	69.9103i	−0.215842	−	2.46708i
$804$		0			0
$805$	−0.530049	+	20.7465i	−0.0186818	+	0.731219i
$806$		0			0
$807$	−47.8250	+	22.3012i	−1.68352	+	0.785038i
$808$		0			0
$809$	−20.6097	−	11.8990i	−0.724597	−	0.418346i	0.0918451	−	0.995773i	$-0.470724\pi$
$809$	−20.6097	−	11.8990i	−0.724597	−	0.418346i	−0.816442	+	0.577427i	$0.804057\pi$
$810$		0			0
$811$	19.7211	−	3.47737i	0.692502	−	0.122107i	0.183690	−	0.982984i	$-0.441196\pi$
$811$	19.7211	−	3.47737i	0.692502	−	0.122107i	0.508812	+	0.860877i	$0.330085\pi$
$812$		0			0
$813$	1.61000	−	18.4024i	0.0564651	−	0.645399i
$814$		0			0
$815$	17.9694	+	27.1114i	0.629442	+	0.949669i
$816$		0			0
$817$	−4.19548	+	4.74818i	−0.146781	+	0.166118i
$818$		0			0
$819$	−1.08387	+	0.394497i	−0.0378736	+	0.0137848i
$820$		0			0
$821$	−23.8177	+	19.9854i	−0.831244	+	0.697497i	−0.955576	−	0.294744i	$-0.904766\pi$
$821$	−23.8177	+	19.9854i	−0.831244	+	0.697497i	0.124332	+	0.992241i	$0.460321\pi$
$822$		0			0
$823$	6.58423	−	9.40325i	0.229512	−	0.327777i	−0.687834	−	0.725868i	$-0.741438\pi$
$823$	6.58423	−	9.40325i	0.229512	−	0.327777i	0.917346	+	0.398091i	$0.130327\pi$
$824$		0			0
$825$	37.6173	−	33.9576i	1.30967	−	1.18225i
$826$		0			0
$827$	−19.2139	−	41.2043i	−0.668132	−	1.43281i	−0.889183	−	0.457552i	$-0.848727\pi$
$827$	−19.2139	−	41.2043i	−0.668132	−	1.43281i	0.221051	−	0.975262i	$-0.429051\pi$
$828$		0			0
$829$	2.73550	+	4.73802i	0.0950078	+	0.164558i	0.909612	−	0.415459i	$-0.136379\pi$
$829$	2.73550	+	4.73802i	0.0950078	+	0.164558i	−0.814604	+	0.580017i	$0.803046\pi$
$830$		0			0
$831$	0.138262	−	0.164775i	0.00479627	−	0.00571597i
$832$		0			0
$833$	1.67892	−	1.17559i	0.0581710	−	0.0407318i
$834$		0			0
$835$	3.43527	+	14.2689i	0.118883	+	0.493796i
$836$		0			0
$837$	−31.3389	+	31.3389i	−1.08323	+	1.08323i
$838$		0			0
$839$	−2.99863	+	17.0061i	−0.103524	+	0.587115i	0.888275	+	0.459311i	$0.151904\pi$
$839$	−2.99863	+	17.0061i	−0.103524	+	0.587115i	−0.991800	+	0.127803i	$0.959207\pi$
$840$		0			0
$841$	−21.1806	−	17.7726i	−0.730366	−	0.612850i
$842$		0			0
$843$	−2.50341	+	9.34284i	−0.0862219	+	0.321784i
$844$		0			0
$845$	13.5445	−	10.7878i	0.465944	−	0.371113i
$846$		0			0
$847$	15.1266	+	56.4532i	0.519755	+	1.93975i
$848$		0			0
$849$	−3.62749	−	20.5725i	−0.124495	−	0.706047i
$850$		0			0
$851$	−11.8256	−	14.0931i	−0.405375	−	0.483107i
$852$		0			0
$853$	−5.20290	−	2.42615i	−0.178144	−	0.0830698i	0.331500	−	0.943455i	$-0.392445\pi$
$853$	−5.20290	−	2.42615i	−0.178144	−	0.0830698i	−0.509644	+	0.860385i	$0.670223\pi$
$854$		0			0
$855$	1.19595	+	1.32486i	0.0409008	+	0.0453091i
$856$		0			0
$857$	−22.9878	−	10.7194i	−0.785247	−	0.366167i	−0.0117209	−	0.999931i	$-0.503731\pi$
$857$	−22.9878	−	10.7194i	−0.785247	−	0.366167i	−0.773526	+	0.633765i	$0.781509\pi$
$858$		0			0
$859$	17.4834	+	20.8359i	0.596526	+	0.710913i	0.976846	−	0.213942i	$-0.0686305\pi$
$859$	17.4834	+	20.8359i	0.596526	+	0.710913i	−0.380320	+	0.924855i	$0.624186\pi$
$860$		0			0
$861$	−1.85962	−	10.5465i	−0.0633758	−	0.359422i
$862$		0			0
$863$	−2.71456	−	10.1309i	−0.0924048	−	0.344859i	0.904208	−	0.427092i	$-0.140462\pi$
$863$	−2.71456	−	10.1309i	−0.0924048	−	0.344859i	−0.996613	+	0.0822321i	$0.973795\pi$
$864$		0			0
$865$	22.3762	+	2.53501i	0.760812	+	0.0861929i
$866$		0			0
$867$	1.39798	−	5.21733i	0.0474778	−	0.177190i
$868$		0			0
$869$	53.9294	+	45.2521i	1.82943	+	1.53507i
$870$		0			0
$871$	5.51681	−	31.2874i	0.186930	−	1.06013i
$872$		0			0
$873$	1.50413	−	1.50413i	0.0509071	−	0.0509071i
$874$		0			0
$875$	19.9937	+	23.3193i	0.675911	+	0.788336i
$876$		0			0
$877$	−36.4781	+	25.5423i	−1.23178	+	0.862501i	−0.994060	−	0.108833i	$-0.965288\pi$
$877$	−36.4781	+	25.5423i	−1.23178	+	0.862501i	−0.237719	+	0.971334i	$0.576400\pi$
$878$		0			0
$879$	−16.8751	+	20.1110i	−0.569185	+	0.678328i
$880$		0			0
$881$	22.6394	+	39.2125i	0.762740	+	1.32110i	0.941433	+	0.337199i	$0.109480\pi$
$881$	22.6394	+	39.2125i	0.762740	+	1.32110i	−0.178693	+	0.983905i	$0.557187\pi$
$882$		0			0
$883$	−4.35986	−	9.34974i	−0.146721	−	0.314644i	0.819189	−	0.573524i	$-0.194424\pi$
$883$	−4.35986	−	9.34974i	−0.146721	−	0.314644i	−0.965909	+	0.258880i	$0.916646\pi$
$884$		0			0
$885$	7.22818	−	24.4591i	0.242972	−	0.822183i
$886$		0			0
$887$	−17.1974	+	24.5605i	−0.577433	+	0.824660i	−0.996526	−	0.0832835i	$-0.973459\pi$
$887$	−17.1974	+	24.5605i	−0.577433	+	0.824660i	0.419093	+	0.907943i	$0.362348\pi$
$888$		0			0
$889$	−0.653389	+	0.548258i	−0.0219140	+	0.0183880i
$890$		0			0
$891$	50.7982	−	18.4890i	1.70181	−	0.619406i
$892$		0			0
$893$	−0.125260	−	0.0492499i	−0.00419168	−	0.00164809i
$894$		0			0
$895$	30.2922	+	6.14293i	1.01256	+	0.205335i
$896$		0			0
$897$	1.20431	−	13.7653i	0.0402106	−	0.459609i
$898$		0			0
$899$	−10.0933	+	1.77972i	−0.336630	+	0.0593569i
$900$		0			0
$901$	−4.00879	−	2.31448i	−0.133552	−	0.0771065i
$902$		0			0
$903$	6.45770	−	3.01128i	0.214899	−	0.100209i
$904$		0			0
$905$	25.1385	+	0.642259i	0.835633	+	0.0213494i
$906$		0			0
$907$	3.38879	+	38.7341i	0.112523	+	1.28614i	0.817092	+	0.576507i	$0.195585\pi$
$907$	3.38879	+	38.7341i	0.112523	+	1.28614i	−0.704569	+	0.709636i	$0.748860\pi$
$908$		0			0
$909$	−2.00356	−	0.353282i	−0.0664540	−	0.0117176i
$910$		0			0
$911$			41.3662i			1.37052i	0.728296	+	0.685262i	$0.240312\pi$
$911$			41.3662i			1.37052i	−0.728296	+	0.685262i	$0.759688\pi$
$912$		0			0
$913$	−46.7570	−	46.7570i	−1.54743	−	1.54743i
$914$		0			0
$915$	−2.62283	−	42.4394i	−0.0867080	−	1.40300i
$916$		0			0
$917$	47.1622	−	4.12616i	1.55743	−	0.136258i
$918$		0			0
$919$	10.5077	−	6.06662i	0.346617	−	0.200119i	−0.316577	−	0.948567i	$-0.602534\pi$
$919$	10.5077	−	6.06662i	0.346617	−	0.200119i	0.663194	+	0.748447i	$0.269200\pi$
$920$		0			0
$921$	23.2314	+	8.45553i	0.765500	+	0.278619i
$922$		0			0
$923$	26.6934	−	7.15248i	0.878624	−	0.235427i
$924$		0			0
$925$	−26.9697	−	3.75533i	−0.886760	−	0.123475i
$926$		0			0
$927$	0.570607	+	0.0499216i	0.0187412	+	0.00163964i
$928$		0			0
$929$	14.1541	+	38.8882i	0.464382	+	1.27588i	0.922158	+	0.386813i	$0.126424\pi$
$929$	14.1541	+	38.8882i	0.464382	+	1.27588i	−0.457776	+	0.889068i	$0.651354\pi$
$930$		0			0
$931$	−0.559411	−	2.32364i	−0.0183340	−	0.0761543i
$932$		0			0
$933$	−17.5822	+	37.7052i	−0.575617	+	1.23441i
$934$		0			0
$935$	28.2197	−	38.1876i	0.922884	−	1.24887i
$936$		0			0
$937$	32.1751	+	22.5292i	1.05111	+	0.735998i	0.965519	−	0.260332i	$-0.0838319\pi$
$937$	32.1751	+	22.5292i	1.05111	+	0.735998i	0.0855953	+	0.996330i	$0.472721\pi$
$938$		0			0
$939$	18.5563	−	32.1404i	0.605561	−	1.04886i
$940$		0			0
$941$	9.04734	−	24.8574i	0.294935	−	0.810327i	−0.700391	−	0.713759i	$-0.746991\pi$
$941$	9.04734	−	24.8574i	0.294935	−	0.810327i	0.995326	−	0.0965681i	$-0.0307866\pi$
$942$		0			0
$943$	7.12894	+	1.91019i	0.232150	+	0.0622045i
$944$		0			0
$945$	9.81538	+	29.2731i	0.319294	+	0.952254i
$946$		0			0
$947$	16.2883	+	23.2621i	0.529298	+	0.755916i	0.991394	−	0.130914i	$-0.0417912\pi$
$947$	16.2883	+	23.2621i	0.529298	+	0.755916i	−0.462096	+	0.886830i	$0.652902\pi$
$948$		0			0
$949$	−28.3216			−0.919357
$950$		0			0
$951$	5.08112			0.164767
$952$		0			0
$953$	−17.8244	−	25.4559i	−0.577389	−	0.824597i	0.419133	−	0.907925i	$-0.362334\pi$
$953$	−17.8244	−	25.4559i	−0.577389	−	0.824597i	−0.996522	+	0.0833276i	$0.973445\pi$
$954$		0			0
$955$	−15.0374	−	44.8472i	−0.486600	−	1.45122i
$956$		0			0
$957$	11.3779	+	3.04871i	0.367797	+	0.0985509i
$958$		0			0
$959$	0.0208256	−	0.0572179i	0.000672494	−	0.00184766i
$960$		0			0
$961$	23.3846	−	40.5034i	0.754343	−	1.30656i
$962$		0			0
$963$	1.76402	+	1.23518i	0.0568449	+	0.0398032i
$964$		0			0
$965$	−24.9169	+	33.7182i	−0.802104	+	1.08543i
$966$		0			0
$967$	3.45278	−	7.40451i	0.111034	−	0.238113i	−0.842937	−	0.538012i	$-0.819175\pi$
$967$	3.45278	−	7.40451i	0.111034	−	0.238113i	0.953971	+	0.299899i	$0.0969531\pi$
$968$		0			0
$969$	23.3788	+	17.2766i	0.751036	+	0.555003i
$970$		0			0
$971$	4.80854	+	13.2114i	0.154313	+	0.423973i	0.992626	−	0.121217i	$-0.0386797\pi$
$971$	4.80854	+	13.2114i	0.154313	+	0.423973i	−0.838313	+	0.545190i	$0.816458\pi$
$972$		0			0
$973$	−35.8128	−	3.13322i	−1.14811	−	0.100446i
$974$		0			0
$975$	−12.3290	−	16.3179i	−0.394845	−	0.522591i
$976$		0			0
$977$	3.17719	−	0.851326i	0.101647	−	0.0272363i	−0.207637	−	0.978206i	$-0.566577\pi$
$977$	3.17719	−	0.851326i	0.101647	−	0.0272363i	0.309284	+	0.950970i	$0.399911\pi$
$978$		0			0
$979$	59.1582	+	21.5318i	1.89071	+	0.688160i
$980$		0			0
$981$	−0.692016	+	0.399536i	−0.0220944	+	0.0127562i
$982$		0			0
$983$	41.3963	−	3.62171i	1.32034	−	0.115515i	0.594899	−	0.803801i	$-0.297192\pi$
$983$	41.3963	−	3.62171i	1.32034	−	0.115515i	0.725439	+	0.688286i	$0.241637\pi$
$984$		0			0
$985$	2.12633	+	34.4056i	0.0677504	+	1.09625i
$986$		0			0
$987$	0.107025	+	0.107025i	0.00340666	+	0.00340666i
$988$		0			0
$989$			4.91053i			0.156146i
$990$		0			0
$991$	−43.2554	−	7.62709i	−1.37405	−	0.242283i	−0.562614	−	0.826720i	$-0.690204\pi$
$991$	−43.2554	−	7.62709i	−1.37405	−	0.242283i	−0.811439	+	0.584437i	$0.801315\pi$
$992$		0			0
$993$	0.412002	+	4.70920i	0.0130745	+	0.149442i
$994$		0			0
$995$	−23.1980	−	0.592680i	−0.735425	−	0.0187892i
$996$		0			0
$997$	1.42108	−	0.662659i	0.0450059	−	0.0209866i	−0.399985	−	0.916522i	$-0.630985\pi$
$997$	1.42108	−	0.662659i	0.0450059	−	0.0209866i	0.444991	+	0.895535i	$0.353207\pi$
$998$		0			0
$999$	−23.7029	−	13.6849i	−0.749928	−	0.432971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.33.3	✓	120
5.2	odd	4	inner	380.2.bh.a.337.3	yes	120
19.15	odd	18	inner	380.2.bh.a.53.3	yes	120
95.72	even	36	inner	380.2.bh.a.357.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.3	✓	120	1.1	even	1	trivial
380.2.bh.a.53.3	yes	120	19.15	odd	18	inner
380.2.bh.a.337.3	yes	120	5.2	odd	4	inner
380.2.bh.a.357.3	yes	120	95.72	even	36	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)

\(f(q)\)	\(=\)	\(q+(-1.02333 - 1.46147i) q^{3} +(0.710865 + 2.12006i) q^{5} +(-2.65380 - 0.711084i) q^{7} +(-0.0626300 + 0.172074i) q^{9} +O(q^{10})\)	\(q+(-1.02333 - 1.46147i) q^{3} +(0.710865 + 2.12006i) q^{5} +(-2.65380 - 0.711084i) q^{7} +(-0.0626300 + 0.172074i) q^{9} +(2.84045 - 4.91980i) q^{11} +(-1.87803 - 1.31501i) q^{13} +(2.37096 - 3.20844i) q^{15} +(1.57974 - 3.38777i) q^{17} +(-3.00247 - 3.15994i) q^{19} +(1.67650 + 4.60614i) q^{21} +(-3.36528 - 0.294424i) q^{23} +(-3.98934 + 3.01416i) q^{25} +(-4.85444 + 1.30074i) q^{27} +(-1.09210 - 0.397492i) q^{29} +(7.63721 - 4.40934i) q^{31} +(-10.0969 + 0.883363i) q^{33} +(-0.378951 - 6.13172i) q^{35} +(3.85089 + 3.85089i) q^{37} +4.09038i q^{39} +(-2.15157 - 0.379380i) q^{41} +(-0.126691 - 1.44809i) q^{43} +(-0.409330 - 0.0104579i) q^{45} +(0.0279851 - 0.0130497i) q^{47} +(0.474851 + 0.274156i) q^{49} +(-6.56773 + 1.15807i) q^{51} +(0.107930 - 1.23364i) q^{53} +(12.4495 + 2.52462i) q^{55} +(-1.54564 + 7.62170i) q^{57} +(6.00753 - 2.18656i) q^{59} +(8.16469 - 6.85099i) q^{61} +(0.288567 - 0.412116i) q^{63} +(1.45288 - 4.91633i) q^{65} +(5.85638 + 12.5590i) q^{67} +(3.01352 + 5.21957i) q^{69} +(-7.74802 + 9.23373i) q^{71} +(10.1192 - 7.08552i) q^{73} +(8.48754 + 2.74583i) q^{75} +(-11.0364 + 11.0364i) q^{77} +(-2.15191 + 12.2041i) q^{79} +(7.28954 + 6.11665i) q^{81} +(3.01260 - 11.2432i) q^{83} +(8.30526 + 0.940909i) q^{85} +(0.536661 + 2.00284i) q^{87} +(1.92434 + 10.9135i) q^{89} +(4.04883 + 4.82520i) q^{91} +(-14.2596 - 6.64934i) q^{93} +(4.56492 - 8.61171i) q^{95} +(-10.5280 - 4.90928i) q^{97} +(0.668674 + 0.796895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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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