LMFDB - Embedded newform 380.2.bh.a.357.3

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			357.3
Character	$\chi$	$=$	380.357
Dual form			380.2.bh.a.33.3

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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	−0.997564	−	0.0697615i	$-0.977776\pi$
$3$	−1.02333	+	1.46147i	−0.590823	+	0.843782i	0.406741	+	0.913543i	$0.366665\pi$
$4$		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	−0.722720	−	0.691141i	$-0.757108\pi$
$7$	−2.65380	+	0.711084i	−1.00304	+	0.268765i	−0.280323	+	0.959906i	$0.590442\pi$
$8$		0			0
$9$	−0.0626300	−	0.172074i	−0.0208767	−	0.0573581i
$10$		0			0
$11$	2.84045	+	4.91980i	0.856427	+	1.48337i	0.875315	+	0.483553i	$0.160654\pi$
$11$	2.84045	+	4.91980i	0.856427	+	1.48337i	−0.0188880	+	0.999822i	$0.506013\pi$
$12$		0			0
$13$	−1.87803	+	1.31501i	−0.520870	+	0.364717i	−0.804251	−	0.594290i	$-0.797433\pi$
$13$	−1.87803	+	1.31501i	−0.520870	+	0.364717i	0.283380	+	0.959008i	$0.408544\pi$
$14$		0			0
$15$	2.37096	+	3.20844i	0.612180	+	0.828417i
$16$		0			0
$17$	1.57974	+	3.38777i	0.383144	+	0.821654i	0.999418	+	0.0341223i	$0.0108636\pi$
$17$	1.57974	+	3.38777i	0.383144	+	0.821654i	−0.616274	+	0.787532i	$0.711359\pi$
$18$		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	−0.432426	−	0.901669i	$-0.642342\pi$
$23$	−3.36528	+	0.294424i	−0.701710	+	0.0613917i	−0.269284	+	0.963061i	$0.586787\pi$
$24$		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	−0.441422	−	0.897300i	$-0.645526\pi$
$29$	−1.09210	+	0.397492i	−0.202798	+	0.0738125i	0.238624	+	0.971112i	$0.423304\pi$
$30$		0			0
$31$	7.63721	+	4.40934i	1.37168	+	0.791942i	0.991140	−	0.132822i	$-0.0424037\pi$
$31$	7.63721	+	4.40934i	1.37168	+	0.791942i	0.380543	+	0.924763i	$0.375737\pi$
$32$		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	−0.315757	−	0.948840i	$-0.602258\pi$
$37$	3.85089	−	3.85089i	0.633083	−	0.633083i	0.948840	+	0.315757i	$0.102258\pi$
$38$		0			0
$39$		−	4.09038i		−	0.654984i
$40$		0			0
$41$	−2.15157	+	0.379380i	−0.336019	+	0.0592491i	−0.339112	−	0.940746i	$-0.610127\pi$
$41$	−2.15157	+	0.379380i	−0.336019	+	0.0592491i	0.00309324	+	0.999995i	$0.499015\pi$
$42$		0			0
$43$	−0.126691	+	1.44809i	−0.0193203	+	0.220832i	0.980397	+	0.197035i	$0.0631311\pi$
$43$	−0.126691	+	1.44809i	−0.0193203	+	0.220832i	−0.999717	+	0.0237970i	$0.992424\pi$
$44$		0			0
$45$	−0.409330	+	0.0104579i	−0.0610193	+	0.00155897i
$46$		0			0
$47$	0.0279851	+	0.0130497i	0.00408204	+	0.00190349i	0.424658	−	0.905354i	$-0.360394\pi$
$47$	0.0279851	+	0.0130497i	0.00408204	+	0.00190349i	−0.420576	+	0.907257i	$0.638172\pi$
$48$		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	0.999998	−	0.00211296i	$-0.000672577\pi$
$53$	0.107930	+	1.23364i	0.0148253	+	0.169454i	−0.985172	+	0.171567i	$0.945117\pi$
$54$		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	0.702054	−	0.712124i	$-0.252267\pi$
$59$	6.00753	+	2.18656i	0.782114	+	0.284666i	0.0800600	+	0.996790i	$0.474489\pi$
$60$		0			0
$61$	8.16469	+	6.85099i	1.04538	+	0.877179i	0.992600	−	0.121427i	$-0.0387472\pi$
$61$	8.16469	+	6.85099i	1.04538	+	0.877179i	0.0527806	+	0.998606i	$0.483192\pi$
$62$		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	−0.124810	−	0.992181i	$-0.539832\pi$
$67$	5.85638	−	12.5590i	0.715471	−	1.53433i	0.840281	−	0.542151i	$-0.182390\pi$
$68$		0			0
$69$	3.01352	−	5.21957i	0.362785	−	0.628362i
$70$		0			0
$71$	−7.74802	−	9.23373i	−0.919521	−	1.09584i	−0.995117	−	0.0987040i	$-0.968530\pi$
$71$	−7.74802	−	9.23373i	−0.919521	−	1.09584i	0.0755958	−	0.997139i	$-0.475914\pi$
$72$		0			0
$73$	10.1192	+	7.08552i	1.18436	+	0.829298i	0.988483	−	0.151331i	$-0.0483559\pi$
$73$	10.1192	+	7.08552i	1.18436	+	0.829298i	0.195877	+	0.980629i	$0.437245\pi$
$74$		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	−0.827111	−	0.562038i	$-0.810017\pi$
$79$	−2.15191	−	12.2041i	−0.242109	−	1.37307i	0.585002	−	0.811032i	$-0.301094\pi$
$80$		0			0
$81$	7.28954	−	6.11665i	0.809949	−	0.679628i
$82$		0			0
$83$	3.01260	+	11.2432i	0.330676	+	1.23410i	0.908482	+	0.417925i	$0.137242\pi$
$83$	3.01260	+	11.2432i	0.330676	+	1.23410i	−0.577806	+	0.816174i	$0.696091\pi$
$84$		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	−0.695056	−	0.718955i	$-0.744621\pi$
$89$	1.92434	−	10.9135i	0.203980	−	1.15683i	0.899037	−	0.437874i	$-0.144268\pi$
$90$		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	−0.875784	−	0.482703i	$-0.839655\pi$
$97$	−10.5280	+	4.90928i	−1.06896	+	0.498462i	−0.193171	+	0.981165i	$0.561877\pi$
$98$		0			0
$99$	0.668674	−	0.796895i	0.0672043	−	0.0800910i
$100$		0			0
$101$	1.92926	−	10.9414i	0.191969	−	1.08871i	−0.724701	−	0.689063i	$-0.758022\pi$
$101$	1.92926	−	10.9414i	0.191969	−	1.08871i	0.916670	−	0.399645i	$-0.130867\pi$
$102$		0			0
$103$	−0.809577	+	3.02138i	−0.0797700	+	0.297706i	−0.994273	−	0.106874i	$-0.965916\pi$
$103$	−0.809577	+	3.02138i	−0.0797700	+	0.297706i	0.914502	+	0.404580i	$0.132582\pi$
$104$		0			0
$105$	−8.57355	−	6.82862i	−0.836693	−	0.666405i
$106$		0			0
$107$	3.04373	+	11.3593i	0.294248	+	1.09815i	0.941812	+	0.336139i	$0.109121\pi$
$107$	3.04373	+	11.3593i	0.294248	+	1.09815i	−0.647564	+	0.762011i	$0.724212\pi$
$108$		0			0
$109$	3.34279	−	2.80494i	0.320181	−	0.268664i	−0.468504	−	0.883462i	$-0.655207\pi$
$109$	3.34279	−	2.80494i	0.320181	−	0.268664i	0.788685	+	0.614797i	$0.210762\pi$
$110$		0			0
$111$	1.68723	+	9.56873i	0.160144	+	0.908224i
$112$		0			0
$113$	−9.74527	−	9.74527i	−0.916758	−	0.916758i	0.0800343	−	0.996792i	$-0.474497\pi$
$113$	−9.74527	−	9.74527i	−0.916758	−	0.916758i	−0.996792	+	0.0800343i	$0.974497\pi$
$114$		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	0.826975	−	0.562239i	$-0.190060\pi$
$127$	0.178067	+	0.254306i	0.0158009	+	0.0225660i	−0.811174	+	0.584805i	$0.801171\pi$
$128$		0			0
$129$	−1.98670	−	1.66704i	−0.174919	−	0.146774i
$130$		0			0
$131$	−16.1924	−	5.89355i	−1.41474	−	0.514922i	−0.482220	−	0.876050i	$-0.660169\pi$
$131$	−16.1924	−	5.89355i	−1.41474	−	0.514922i	−0.932516	+	0.361128i	$0.882392\pi$
$132$		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	0.996112	−	0.0880988i	$-0.0280791\pi$
$137$	−0.00193160	−	0.0220783i	−0.000165028	−	0.00188627i	−0.996277	+	0.0862126i	$0.972524\pi$
$138$		0			0
$139$	12.8861	+	2.27216i	1.09298	+	0.192722i	0.690950	−	0.722903i	$-0.257193\pi$
$139$	12.8861	+	2.27216i	1.09298	+	0.192722i	0.402033	+	0.915625i	$0.368304\pi$
$140$		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	0.110652	−	0.993859i	$-0.464706\pi$
$149$	6.76916	−	1.19359i	0.554551	−	0.0977824i	0.443899	+	0.896077i	$0.353595\pi$
$150$		0			0
$151$		−	2.79979i		−	0.227843i	−0.993490	−	0.113922i	$-0.963659\pi$
$151$		−	2.79979i		−	0.227843i	0.993490	−	0.113922i	$-0.0363413\pi$
$152$		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	0.739413	−	0.673252i	$-0.235103\pi$
$157$	16.9240	+	1.48066i	1.35068	+	0.118169i	0.611270	+	0.791422i	$0.290659\pi$
$158$		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	0.762971	−	0.646433i	$-0.223740\pi$
$163$	14.0503	+	3.76477i	1.10051	+	0.294880i	0.337536	+	0.941313i	$0.390407\pi$
$164$		0			0
$165$	−9.05030	+	20.7781i	−0.704565	+	1.61757i
$166$		0			0
$167$	6.53860	−	0.572054i	0.505972	−	0.0442668i	0.168688	−	0.985670i	$-0.446047\pi$
$167$	6.53860	−	0.572054i	0.505972	−	0.0442668i	0.337285	+	0.941403i	$0.390492\pi$
$168$		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	0.999056	−	0.0434507i	$-0.0138351\pi$
$173$	4.25616	+	9.12737i	0.323590	+	0.693941i	−0.675466	+	0.737391i	$0.736057\pi$
$174$		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	0.999815	+	0.0192552i	$0.00612949\pi$
$179$	6.91141	+	11.9709i	0.516583	+	0.894748i	−0.483232	+	0.875492i	$0.660537\pi$
$180$		0			0
$181$	3.84634	+	10.5677i	0.285896	+	0.785494i	0.996630	+	0.0820324i	$0.0261411\pi$
$181$	3.84634	+	10.5677i	0.285896	+	0.785494i	−0.710733	+	0.703462i	$0.751637\pi$
$182$		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	−0.217461	−	0.976069i	$-0.569778\pi$
$193$	10.7544	−	15.3589i	0.774120	−	1.10556i	0.991581	−	0.129489i	$-0.0413336\pi$
$194$		0			0
$195$	−8.67186	−	2.90770i	−0.621005	−	0.208225i
$196$		0			0
$197$	14.8907	−	3.98996i	1.06092	−	0.284273i	0.314163	−	0.949369i	$-0.398276\pi$
$197$	14.8907	−	3.98996i	1.06092	−	0.284273i	0.746757	+	0.665096i	$0.231610\pi$
$198$		0			0
$199$	−3.54943	−	9.75197i	−0.251612	−	0.691299i	−0.999619	−	0.0276076i	$-0.991211\pi$
$199$	−3.54943	−	9.75197i	−0.251612	−	0.691299i	0.748007	−	0.663691i	$-0.231011\pi$
$200$		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	−0.653636	−	0.756809i	$-0.726757\pi$
$211$	4.84503	−	13.3116i	0.333546	−	0.916410i	0.987182	−	0.159601i	$-0.0510206\pi$
$212$		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	−0.626370	−	0.779526i	$-0.715460\pi$
$223$	−20.5867	−	1.80110i	−1.37859	−	0.120611i	−0.752217	+	0.658915i	$0.771016\pi$
$224$		0			0
$225$	−0.268807	+	0.875240i	−0.0179205	+	0.0583494i
$226$		0			0
$227$	−18.5286	+	18.5286i	−1.22979	+	1.22979i	−0.265744	+	0.964044i	$0.585618\pi$
$227$	−18.5286	+	18.5286i	−1.22979	+	1.22979i	−0.964044	+	0.265744i	$0.914382\pi$
$228$		0			0
$229$			14.2947i			0.944617i	0.881433	+	0.472309i	$0.156579\pi$
$229$			14.2947i			0.944617i	−0.881433	+	0.472309i	$0.843421\pi$
$230$		0			0
$231$	27.4233	−	4.83546i	1.80432	−	0.318150i
$232$		0			0
$233$	−1.96193	+	22.4250i	−0.128530	+	1.46911i	0.608665	+	0.793427i	$0.291705\pi$
$233$	−1.96193	+	22.4250i	−0.128530	+	1.46911i	−0.737195	+	0.675680i	$0.763850\pi$
$234$		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	−0.443891	−	0.896081i	$-0.646402\pi$
$239$	1.70353	−	0.983534i	0.110192	−	0.0636195i	0.554083	+	0.832461i	$0.313069\pi$
$240$		0			0
$241$	2.56008	+	0.451411i	0.164909	+	0.0290779i	0.255493	−	0.966811i	$-0.417762\pi$
$241$	2.56008	+	0.451411i	0.164909	+	0.0290779i	−0.0905839	+	0.995889i	$0.528873\pi$
$242$		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	0.271366	−	0.962476i	$-0.412524\pi$
$251$	−9.97102	−	8.36668i	−0.629365	−	0.528100i	−0.900732	+	0.434376i	$0.856969\pi$
$252$		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	−0.510659	−	0.859783i	$-0.670599\pi$
$257$	7.63436	−	16.3719i	0.476219	−	1.02125i	0.986878	−	0.161471i	$-0.0516237\pi$
$258$		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	0.545139	−	0.838346i	$-0.316477\pi$
$263$	−0.911418	−	0.638182i	−0.0562004	−	0.0393520i	−0.601339	+	0.798994i	$0.705366\pi$
$264$		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	0.582432	+	0.812880i	$0.302101\pi$
$269$	5.13598	+	29.1276i	0.313146	+	1.77594i	−0.269285	+	0.963060i	$0.586787\pi$
$270$		0			0
$271$	7.93153	−	6.65534i	0.481806	−	0.404283i	−0.369273	−	0.929321i	$-0.620393\pi$
$271$	7.93153	−	6.65534i	0.481806	−	0.404283i	0.851079	+	0.525038i	$0.175949\pi$
$272$		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	−0.964982	−	0.262316i	$-0.915514\pi$
$277$	0.0312037	−	0.116454i	0.00187485	−	0.00699703i	0.966857	+	0.255319i	$0.0821804\pi$
$278$		0			0
$279$	0.280417	−	1.59033i	0.0167881	−	0.0952103i
$280$		0			0
$281$	−3.48479	+	4.15301i	−0.207885	+	0.247748i	−0.859905	−	0.510454i	$-0.829477\pi$
$281$	−3.48479	+	4.15301i	−0.207885	+	0.247748i	0.652020	+	0.758202i	$0.273922\pi$
$282$		0			0
$283$	10.6117	−	4.94832i	0.630801	−	0.294147i	−0.0808011	−	0.996730i	$-0.525748\pi$
$283$	10.6117	−	4.94832i	0.630801	−	0.294147i	0.711602	+	0.702583i	$0.247970\pi$
$284$		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	0.760901	+	0.648868i	$0.224757\pi$
$293$	−3.80846	+	14.2134i	−0.222493	+	0.830355i	−0.983393	+	0.181486i	$0.941909\pi$
$294$		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	0.202916	−	0.979196i	$-0.434958\pi$
$307$	−11.3508	−	7.94793i	−0.647826	−	0.453613i	−0.850742	+	0.525584i	$0.823847\pi$
$308$		0			0
$309$	−3.58720	−	4.27506i	−0.204069	−	0.243200i
$310$		0			0
$311$	−11.6592	+	20.1944i	−0.661134	+	1.14512i	0.319184	+	0.947693i	$0.396591\pi$
$311$	−11.6592	+	20.1944i	−0.661134	+	1.14512i	−0.980318	+	0.197425i	$0.936742\pi$
$312$		0			0
$313$	8.79109	−	18.8525i	0.496902	−	1.06561i	−0.484702	−	0.874679i	$-0.661072\pi$
$313$	8.79109	−	18.8525i	0.496902	−	1.06561i	0.981604	−	0.190930i	$-0.0611503\pi$
$314$		0			0
$315$	1.07885	−	0.318821i	0.0607860	−	0.0179636i
$316$		0			0
$317$	−1.63352	−	2.33291i	−0.0917476	−	0.131029i	0.770654	−	0.637254i	$-0.219930\pi$
$317$	−1.63352	−	2.33291i	−0.0917476	−	0.131029i	−0.862402	+	0.506224i	$0.831041\pi$
$318$		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	−0.561734	−	0.827318i	$-0.689866\pi$
$331$	−2.29460	+	1.32479i	−0.126123	+	0.0728170i	0.435611	+	0.900135i	$0.356532\pi$
$332$		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	0.910014	+	0.414577i	$0.136070\pi$
$337$	−1.06777	+	12.2047i	−0.0581653	+	0.664833i	−0.968180	+	0.250256i	$0.919485\pi$
$338$		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	0.384946	−	0.922939i	$-0.374220\pi$
$347$	11.2471	+	0.983997i	0.603778	+	0.0528237i	0.218832	+	0.975763i	$0.429775\pi$
$348$		0			0
$349$	17.6910	+	10.2139i	0.946977	+	0.546738i	0.892141	−	0.451758i	$-0.149203\pi$
$349$	17.6910	+	10.2139i	0.946977	+	0.546738i	0.0548367	+	0.998495i	$0.482536\pi$
$350$		0			0
$351$	10.8272	−	3.94079i	0.577915	−	0.210344i
$352$		0			0
$353$	29.4599	+	7.89375i	1.56799	+	0.420142i	0.935183	−	0.354166i	$-0.115235\pi$
$353$	29.4599	+	7.89375i	1.56799	+	0.420142i	0.632809	+	0.774308i	$0.281902\pi$
$354$		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	0.608039	+	0.793907i	$0.291957\pi$
$359$	−6.97374	+	19.1602i	−0.368060	+	1.01124i	−0.976099	+	0.217329i	$0.930266\pi$
$360$		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	−0.489657	−	0.871915i	$-0.662878\pi$
$367$	3.10737	−	2.17580i	0.162203	−	0.113576i	0.651860	+	0.758339i	$0.273989\pi$
$368$		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	0.176848	−	0.984238i	$-0.443410\pi$
$373$	15.8778	−	4.25444i	0.822121	−	0.220287i	0.645274	+	0.763952i	$0.276743\pi$
$374$		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	−0.296803	−	0.954939i	$-0.595920\pi$
$383$	13.7396	−	19.6221i	0.702059	−	1.00264i	0.998861	−	0.0477050i	$-0.0151907\pi$
$384$		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	0.996199	−	0.0871047i	$-0.0277615\pi$
$389$	3.49249	+	9.59555i	0.177076	+	0.486514i	−0.819123	+	0.573618i	$0.805539\pi$
$390$		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	−0.941770	−	0.336258i	$-0.890839\pi$
$397$	−11.8354	−	25.3810i	−0.594001	−	1.27384i	0.347769	−	0.937580i	$-0.386939\pi$
$398$		0			0
$399$	9.52148	+	19.1274i	0.476670	+	0.957568i
$400$		0			0
$401$	−1.14417	+	3.14359i	−0.0571373	+	0.156983i	−0.964977	−	0.262333i	$-0.915508\pi$
$401$	−1.14417	+	3.14359i	−0.0571373	+	0.156983i	0.907840	+	0.419317i	$0.137730\pi$
$402$		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	−0.746835	−	0.665009i	$-0.768427\pi$
$409$	−18.0291	+	6.56207i	−0.891484	+	0.324474i	−0.144649	+	0.989483i	$0.546205\pi$
$410$		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	$-0.797169\pi$
$419$		−	24.3569i		−	1.18991i	0.803758	−	0.594957i	$-0.202831\pi$
$420$		0			0
$421$	27.1726	−	4.79125i	1.32431	−	0.233511i	0.533618	−	0.845726i	$-0.320832\pi$
$421$	27.1726	−	4.79125i	1.32431	−	0.233511i	0.790692	+	0.612214i	$0.209721\pi$
$422$		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	0.316030	−	0.948749i	$-0.397650\pi$
$431$	5.98962	+	1.05613i	0.288510	+	0.0508721i	−0.0275201	+	0.999621i	$0.508761\pi$
$432$		0			0
$433$	3.42395	+	39.1360i	0.164545	+	1.88075i	0.411049	+	0.911613i	$0.365162\pi$
$433$	3.42395	+	39.1360i	0.164545	+	1.88075i	−0.246504	+	0.969142i	$0.579282\pi$
$434$		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	0.736498	−	0.676439i	$-0.236478\pi$
$439$	18.1422	+	6.60324i	0.865882	+	0.315155i	0.129384	+	0.991595i	$0.458700\pi$
$440$		0			0
$441$	−0.0769151	−	0.0645394i	−0.00366262	−	0.00307331i
$442$		0			0
$443$	−0.0221234	−	0.0315954i	−0.00105111	−	0.00150114i	0.818626	−	0.574327i	$-0.194736\pi$
$443$	−0.0221234	−	0.0315954i	−0.00105111	−	0.00150114i	−0.819677	+	0.572826i	$0.805847\pi$
$444$		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	−0.633902	−	0.773414i	$-0.718548\pi$
$449$	7.47665	−	12.9499i	0.352845	−	0.611146i	0.986747	+	0.162268i	$0.0518809\pi$
$450$		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	0.999820	−	0.0189806i	$-0.00604208\pi$
$457$	20.9679	+	20.9679i	0.980839	+	0.980839i	−0.0189806	+	0.999820i	$0.506042\pi$
$458$		0			0
$459$	−3.26214	−	18.5005i	−0.152264	−	0.863531i
$460$		0			0
$461$	1.98495	−	1.66557i	0.0924483	−	0.0775733i	−0.595392	−	0.803435i	$-0.703003\pi$
$461$	1.98495	−	1.66557i	0.0924483	−	0.0775733i	0.687840	+	0.725862i	$0.258559\pi$
$462$		0			0
$463$	−1.20336	−	4.49100i	−0.0559249	−	0.208714i	0.932310	−	0.361661i	$-0.117790\pi$
$463$	−1.20336	−	4.49100i	−0.0559249	−	0.208714i	−0.988234	+	0.152947i	$0.951124\pi$
$464$		0			0
$465$	3.96041	+	34.9580i	0.183660	+	1.62114i
$466$		0			0
$467$	−5.07446	+	18.9382i	−0.234818	+	0.876353i	0.743413	+	0.668833i	$0.233206\pi$
$467$	−5.07446	+	18.9382i	−0.234818	+	0.876353i	−0.978231	+	0.207520i	$0.933461\pi$
$468$		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	−0.238347	+	0.971180i	$0.576605\pi$
$479$	−25.2430	+	30.0835i	−1.15338	+	1.37455i	−0.915037	+	0.403369i	$0.867839\pi$
$480$		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	0.983395	+	0.181476i	$0.0580876\pi$
$487$	4.90989	+	18.3239i	0.222488	+	0.830337i	−0.760907	+	0.648861i	$0.775246\pi$
$488$		0			0
$489$	−19.8803	+	16.6816i	−0.899018	+	0.754366i
$490$		0			0
$491$	−1.98596	−	11.2629i	−0.0896249	−	0.508288i	−0.996262	−	0.0863778i	$-0.972471\pi$
$491$	−1.98596	−	11.2629i	−0.0896249	−	0.508288i	0.906638	−	0.421910i	$-0.138640\pi$
$492$		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	0.330350	−	0.943858i	$-0.392833\pi$
$499$	−14.6658	−	17.4781i	−0.656533	−	0.782426i	−0.986884	+	0.161432i	$0.948389\pi$
$500$		0			0
$501$	−5.85514	+	10.1414i	−0.261588	+	0.453084i
$502$		0			0
$503$	16.6699	−	35.7487i	0.743273	−	1.59395i	−0.0598966	−	0.998205i	$-0.519077\pi$
$503$	16.6699	−	35.7487i	0.743273	−	1.59395i	0.803170	−	0.595750i	$-0.203145\pi$
$504$		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	0.0844766	−	0.996425i	$-0.473078\pi$
$509$	−19.9020	−	16.6998i	−0.882142	−	0.740205i	−0.966618	+	0.256221i	$0.917523\pi$
$510$		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	−0.555010	−	0.831844i	$-0.687286\pi$
$521$	−2.55912	+	1.47751i	−0.112117	+	0.0647308i	0.442893	+	0.896575i	$0.353952\pi$
$522$		0			0
$523$	18.7610	+	8.74839i	0.820361	+	0.382540i	0.787038	−	0.616904i	$-0.211613\pi$
$523$	18.7610	+	8.74839i	0.820361	+	0.382540i	0.0333223	+	0.999445i	$0.489391\pi$
$524$		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	−0.404415	−	0.914576i	$-0.632525\pi$
$541$	−2.93852	+	1.06953i	−0.126337	+	0.0459829i	0.278078	+	0.960558i	$0.410303\pi$
$542$		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	0.176107	−	0.984371i	$-0.443649\pi$
$547$	12.1728	−	1.06499i	0.520473	−	0.0455355i	0.344366	+	0.938836i	$0.388094\pi$
$548$		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	−0.349087	−	0.937090i	$-0.613508\pi$
$557$	9.72579	−	6.81007i	0.412095	−	0.288552i	0.761182	+	0.648538i	$0.224619\pi$
$558$		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	−0.276702	−	0.960956i	$-0.589242\pi$
$563$	−0.850762	+	0.227961i	−0.0358553	+	0.00960741i	0.240847	+	0.970563i	$0.422575\pi$
$564$		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	−0.698775	−	0.715342i	$-0.746271\pi$
$577$	−22.7300	+	6.09047i	−0.946260	+	0.253550i	−0.247486	+	0.968892i	$0.579604\pi$
$578$		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	0.999728	+	0.0233392i	$0.00742976\pi$
$587$	9.08538	+	19.4837i	0.374994	+	0.804177i	−0.624734	+	0.780838i	$0.714792\pi$
$588$		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	−0.0447273	−	0.998999i	$-0.514242\pi$
$593$	2.06256	−	0.180451i	0.0846994	−	0.00741023i	0.129427	+	0.991589i	$0.458686\pi$
$594$		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	−0.281101	−	0.959678i	$-0.590700\pi$
$599$	2.94753	−	1.07281i	0.120433	−	0.0438339i	0.401534	+	0.915844i	$0.368477\pi$
$600$		0			0
$601$	8.11532	+	4.68538i	0.331031	+	0.191121i	0.656299	−	0.754501i	$-0.272121\pi$
$601$	8.11532	+	4.68538i	0.331031	+	0.191121i	−0.325268	+	0.945622i	$0.605454\pi$
$602$		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	−0.655966	−	0.754791i	$-0.727738\pi$
$607$	2.43479	−	2.43479i	0.0988249	−	0.0988249i	0.754791	+	0.655966i	$0.227738\pi$
$608$		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	−0.250254	−	0.968180i	$-0.580514\pi$
$613$	4.06839	−	46.5019i	0.164321	−	1.87820i	0.414575	−	0.910015i	$-0.363930\pi$
$614$		0			0
$615$	−6.31851	−	6.00369i	−0.254787	−	0.242092i
$616$		0			0
$617$	−30.9987	−	14.4549i	−1.24796	−	0.581934i	−0.317477	−	0.948266i	$-0.602836\pi$
$617$	−30.9987	−	14.4549i	−1.24796	−	0.581934i	−0.930484	+	0.366332i	$0.880613\pi$
$618$		0			0
$619$	19.4213	−	11.2129i	0.780608	−	0.450684i	−0.0560377	−	0.998429i	$-0.517847\pi$
$619$	19.4213	−	11.2129i	0.780608	−	0.450684i	0.836646	+	0.547744i	$0.184513\pi$
$620$		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	0.427327	−	0.904097i	$-0.359455\pi$
$631$	−9.76730	−	8.19574i	−0.388830	−	0.326267i	−0.816157	+	0.577830i	$0.803900\pi$
$632$		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	0.858620	−	0.512612i	$-0.171322\pi$
$641$	5.18255	+	6.17633i	0.204699	+	0.243950i	−0.653922	+	0.756562i	$0.726878\pi$
$642$		0			0
$643$	−3.88525	−	2.72048i	−0.153219	−	0.107285i	0.494453	−	0.869204i	$-0.335368\pi$
$643$	−3.88525	−	2.72048i	−0.153219	−	0.107285i	−0.647672	+	0.761919i	$0.724257\pi$
$644$		0			0
$645$	−4.94650	+	3.02689i	−0.194768	+	0.119184i
$646$		0			0
$647$	24.8376	+	24.8376i	0.976466	+	0.976466i	0.999729	−	0.0232633i	$-0.00740561\pi$
$647$	24.8376	+	24.8376i	0.976466	+	0.976466i	−0.0232633	+	0.999729i	$0.507406\pi$
$648$		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	0.996070	+	0.0885660i	$0.0282284\pi$
$653$	4.54172	+	16.9499i	0.177731	+	0.663302i	−0.818339	+	0.574736i	$0.805105\pi$
$654$		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	−0.529971	−	0.848016i	$-0.677797\pi$
$659$	6.62510	−	37.5728i	0.258077	−	1.46363i	0.788048	−	0.615614i	$-0.211092\pi$
$660$		0			0
$661$	−19.2093	+	22.8928i	−0.747156	+	0.890426i	−0.996964	−	0.0778694i	$-0.975188\pi$
$661$	−19.2093	+	22.8928i	−0.747156	+	0.890426i	0.249807	+	0.968296i	$0.419633\pi$
$662$		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	−0.541183	−	0.840905i	$-0.682023\pi$
$673$	9.02654	−	33.6875i	0.347948	−	1.29856i	0.889131	−	0.457653i	$-0.151310\pi$
$674$		0			0
$675$	15.4454	+	19.8211i	0.594492	+	0.762916i
$676$		0			0
$677$	−11.2754	−	42.0802i	−0.433347	−	1.61727i	−0.744991	−	0.667074i	$-0.767546\pi$
$677$	−11.2754	−	42.0802i	−0.433347	−	1.61727i	0.311645	−	0.950199i	$-0.399120\pi$
$678$		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	0.550227	−	0.835015i	$-0.314541\pi$
$683$	−7.44272	−	7.44272i	−0.284788	−	0.284788i	−0.835015	+	0.550227i	$0.814541\pi$
$684$		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	0.00761621	+	0.999971i	$0.497576\pi$
$691$	−22.6643	+	39.2558i	−0.862192	+	1.49336i	−0.869808	+	0.493390i	$0.835758\pi$
$692$		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	0.335023	−	0.942210i	$-0.391256\pi$
$701$	−0.370000	−	0.134669i	−0.0139747	−	0.00508637i	−0.348998	+	0.937123i	$0.613478\pi$
$702$		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	0.0879444	−	0.996125i	$-0.471970\pi$
$709$	−4.52952	−	0.798677i	−0.170110	−	0.0299950i	−0.258054	+	0.966130i	$0.583081\pi$
$710$		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	0.124901	−	0.992169i	$-0.460139\pi$
$719$	15.5955	−	2.74990i	0.581612	−	0.102554i	0.456711	+	0.889615i	$0.349027\pi$
$720$		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	0.466872	−	0.884325i	$-0.345381\pi$
$727$	20.8448	+	1.82368i	0.773089	+	0.0676365i	0.306217	+	0.951962i	$0.400937\pi$
$728$		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	−0.787976	−	0.615706i	$-0.788871\pi$
$733$	−48.1439	−	12.9001i	−1.77824	−	0.476477i	−0.990260	+	0.139229i	$0.955538\pi$
$734$		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	0.443022	+	0.896511i	$0.353906\pi$
$739$	−12.8479	+	35.2994i	−0.472618	+	1.29851i	−0.915641	+	0.401998i	$0.868316\pi$
$740$		0			0
$741$	12.9253	+	12.2812i	0.474824	+	0.451162i
$742$		0			0
$743$	−10.5360	−	22.5945i	−0.386528	−	0.828912i	−0.999254	−	0.0386165i	$-0.987705\pi$
$743$	−10.5360	−	22.5945i	−0.386528	−	0.828912i	0.612726	−	0.790295i	$-0.290073\pi$
$744$		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	−0.838158	−	0.545427i	$-0.816367\pi$
$751$	−14.9816	−	41.1616i	−0.546686	−	1.50201i	0.291472	−	0.956579i	$-0.405855\pi$
$752$		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	−0.969036	−	0.246920i	$-0.920582\pi$
$757$	−11.1589	+	15.9366i	−0.405578	+	0.579225i	0.563458	+	0.826144i	$0.309471\pi$
$758$		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	−0.996700	−	0.0811767i	$-0.974132\pi$
$769$	−7.91335	−	21.7418i	−0.285363	−	0.784028i	0.711337	−	0.702851i	$-0.248090\pi$
$770$		0			0
$771$	16.1147	+	27.9114i	0.580355	+	1.00520i
$772$		0			0
$773$	−27.6334	+	19.3491i	−0.993903	+	0.695939i	−0.952920	−	0.303221i	$-0.901938\pi$
$773$	−27.6334	+	19.3491i	−0.993903	+	0.695939i	−0.0409831	+	0.999160i	$0.513049\pi$
$774$		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	−0.478510	−	0.878082i	$-0.658823\pi$
$787$	−37.3660	−	10.0122i	−1.33195	−	0.356896i	−0.853443	+	0.521186i	$0.825490\pi$
$788$		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	−0.732119	−	0.681176i	$-0.761469\pi$
$797$	−1.43819	+	1.43819i	−0.0509431	+	0.0509431i	0.681176	+	0.732119i	$0.261469\pi$
$798$		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	−0.816442	−	0.577427i	$-0.804057\pi$
$809$	−20.6097	+	11.8990i	−0.724597	+	0.418346i	0.0918451	+	0.995773i	$0.470724\pi$
$810$		0			0
$811$	19.7211	+	3.47737i	0.692502	+	0.122107i	0.508812	−	0.860877i	$-0.330085\pi$
$811$	19.7211	+	3.47737i	0.692502	+	0.122107i	0.183690	+	0.982984i	$0.441196\pi$
$812$		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	0.124332	−	0.992241i	$-0.460321\pi$
$821$	−23.8177	−	19.9854i	−0.831244	−	0.697497i	−0.955576	+	0.294744i	$0.904766\pi$
$822$		0			0
$823$	6.58423	+	9.40325i	0.229512	+	0.327777i	0.917346	−	0.398091i	$-0.130327\pi$
$823$	6.58423	+	9.40325i	0.229512	+	0.327777i	−0.687834	+	0.725868i	$0.741438\pi$
$824$		0			0
$825$	37.6173	+	33.9576i	1.30967	+	1.18225i
$826$		0			0
$827$	−19.2139	+	41.2043i	−0.668132	+	1.43281i	0.221051	+	0.975262i	$0.429051\pi$
$827$	−19.2139	+	41.2043i	−0.668132	+	1.43281i	−0.889183	+	0.457552i	$0.848727\pi$
$828$		0			0
$829$	2.73550	−	4.73802i	0.0950078	−	0.164558i	−0.814604	−	0.580017i	$-0.803046\pi$
$829$	2.73550	−	4.73802i	0.0950078	−	0.164558i	0.909612	+	0.415459i	$0.136379\pi$
$830$		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	−0.991800	−	0.127803i	$-0.959207\pi$
$839$	−2.99863	−	17.0061i	−0.103524	−	0.587115i	0.888275	−	0.459311i	$-0.151904\pi$
$840$		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	−0.509644	−	0.860385i	$-0.670223\pi$
$853$	−5.20290	+	2.42615i	−0.178144	+	0.0830698i	0.331500	+	0.943455i	$0.392445\pi$
$854$		0			0
$855$	1.19595	−	1.32486i	0.0409008	−	0.0453091i
$856$		0			0
$857$	−22.9878	+	10.7194i	−0.785247	+	0.366167i	−0.773526	−	0.633765i	$-0.781509\pi$
$857$	−22.9878	+	10.7194i	−0.785247	+	0.366167i	−0.0117209	+	0.999931i	$0.503731\pi$
$858$		0			0
$859$	17.4834	−	20.8359i	0.596526	−	0.710913i	−0.380320	−	0.924855i	$-0.624186\pi$
$859$	17.4834	−	20.8359i	0.596526	−	0.710913i	0.976846	+	0.213942i	$0.0686305\pi$
$860$		0			0
$861$	−1.85962	+	10.5465i	−0.0633758	+	0.359422i
$862$		0			0
$863$	−2.71456	+	10.1309i	−0.0924048	+	0.344859i	−0.996613	−	0.0822321i	$-0.973795\pi$
$863$	−2.71456	+	10.1309i	−0.0924048	+	0.344859i	0.904208	+	0.427092i	$0.140462\pi$
$864$		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	−0.237719	−	0.971334i	$-0.576400\pi$
$877$	−36.4781	−	25.5423i	−1.23178	−	0.862501i	−0.994060	+	0.108833i	$0.965288\pi$
$878$		0			0
$879$	−16.8751	−	20.1110i	−0.569185	−	0.678328i
$880$		0			0
$881$	22.6394	−	39.2125i	0.762740	−	1.32110i	−0.178693	−	0.983905i	$-0.557187\pi$
$881$	22.6394	−	39.2125i	0.762740	−	1.32110i	0.941433	−	0.337199i	$-0.109480\pi$
$882$		0			0
$883$	−4.35986	+	9.34974i	−0.146721	+	0.314644i	−0.965909	−	0.258880i	$-0.916646\pi$
$883$	−4.35986	+	9.34974i	−0.146721	+	0.314644i	0.819189	+	0.573524i	$0.194424\pi$
$884$		0			0
$885$	7.22818	+	24.4591i	0.242972	+	0.822183i
$886$		0			0
$887$	−17.1974	−	24.5605i	−0.577433	−	0.824660i	0.419093	−	0.907943i	$-0.362348\pi$
$887$	−17.1974	−	24.5605i	−0.577433	−	0.824660i	−0.996526	+	0.0832835i	$0.973459\pi$
$888$		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	−0.704569	−	0.709636i	$-0.748860\pi$
$907$	3.38879	−	38.7341i	0.112523	−	1.28614i	0.817092	−	0.576507i	$-0.195585\pi$
$908$		0			0
$909$	−2.00356	+	0.353282i	−0.0664540	+	0.0117176i
$910$		0			0
$911$		−	41.3662i		−	1.37052i	−0.728296	−	0.685262i	$-0.759688\pi$
$911$		−	41.3662i		−	1.37052i	0.728296	−	0.685262i	$-0.240312\pi$
$912$		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	0.663194	−	0.748447i	$-0.269200\pi$
$919$	10.5077	+	6.06662i	0.346617	+	0.200119i	−0.316577	+	0.948567i	$0.602534\pi$
$920$		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	−0.457776	−	0.889068i	$-0.651354\pi$
$929$	14.1541	−	38.8882i	0.464382	−	1.27588i	0.922158	−	0.386813i	$-0.126424\pi$
$930$		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	0.0855953	−	0.996330i	$-0.472721\pi$
$937$	32.1751	−	22.5292i	1.05111	−	0.735998i	0.965519	+	0.260332i	$0.0838319\pi$
$938$		0			0
$939$	18.5563	+	32.1404i	0.605561	+	1.04886i
$940$		0			0
$941$	9.04734	+	24.8574i	0.294935	+	0.810327i	0.995326	+	0.0965681i	$0.0307866\pi$
$941$	9.04734	+	24.8574i	0.294935	+	0.810327i	−0.700391	+	0.713759i	$0.746991\pi$
$942$		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	−0.462096	−	0.886830i	$-0.652902\pi$
$947$	16.2883	−	23.2621i	0.529298	−	0.755916i	0.991394	+	0.130914i	$0.0417912\pi$
$948$		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	−0.996522	−	0.0833276i	$-0.973445\pi$
$953$	−17.8244	+	25.4559i	−0.577389	+	0.824597i	0.419133	+	0.907925i	$0.362334\pi$
$954$		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	0.953971	−	0.299899i	$-0.0969531\pi$
$967$	3.45278	+	7.40451i	0.111034	+	0.238113i	−0.842937	+	0.538012i	$0.819175\pi$
$968$		0			0
$969$	23.3788	−	17.2766i	0.751036	−	0.555003i
$970$		0			0
$971$	4.80854	−	13.2114i	0.154313	−	0.423973i	−0.838313	−	0.545190i	$-0.816458\pi$
$971$	4.80854	−	13.2114i	0.154313	−	0.423973i	0.992626	+	0.121217i	$0.0386797\pi$
$972$		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	0.309284	−	0.950970i	$-0.399911\pi$
$977$	3.17719	+	0.851326i	0.101647	+	0.0272363i	−0.207637	+	0.978206i	$0.566577\pi$
$978$		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	0.725439	−	0.688286i	$-0.241637\pi$
$983$	41.3963	+	3.62171i	1.32034	+	0.115515i	0.594899	+	0.803801i	$0.297192\pi$
$984$		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	−0.811439	−	0.584437i	$-0.801315\pi$
$991$	−43.2554	+	7.62709i	−1.37405	+	0.242283i	−0.562614	+	0.826720i	$0.690204\pi$
$992$		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	0.444991	−	0.895535i	$-0.353207\pi$
$997$	1.42108	+	0.662659i	0.0450059	+	0.0209866i	−0.399985	+	0.916522i	$0.630985\pi$
$998$		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.357.3	yes	120
5.3	odd	4	inner	380.2.bh.a.53.3	yes	120
19.14	odd	18	inner	380.2.bh.a.337.3	yes	120
95.33	even	36	inner	380.2.bh.a.33.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.3	✓	120	95.33	even	36	inner
380.2.bh.a.53.3	yes	120	5.3	odd	4	inner
380.2.bh.a.337.3	yes	120	19.14	odd	18	inner
380.2.bh.a.357.3	yes	120	1.1	even	1	trivial

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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