LMFDB - Embedded newform 1148.2.n.e.141.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.3
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.e.57.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.325457 q^{3} +(0.538931 - 0.391556i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.89408 q^{9} +O(q^{10})$	\(q+0.325457 q^{3} +(0.538931 - 0.391556i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.89408 q^{9} +(-4.24816 - 3.08647i) q^{11} +(1.13089 + 3.48051i) q^{13} +(0.175399 - 0.127435i) q^{15} +(1.83222 + 1.33119i) q^{17} +(-2.09763 + 6.45584i) q^{19} +(-0.100572 + 0.309528i) q^{21} +(-2.80862 - 8.64404i) q^{23} +(-1.40795 + 4.33324i) q^{25} -1.91827 q^{27} +(-8.24886 + 5.99315i) q^{29} +(5.31581 + 3.86216i) q^{31} +(-1.38259 - 1.00451i) q^{33} +(0.205853 + 0.633552i) q^{35} +(-7.58977 + 5.51429i) q^{37} +(0.368055 + 1.13276i) q^{39} +(2.82568 - 5.74591i) q^{41} +(1.39909 + 4.30597i) q^{43} +(-1.55971 + 1.13319i) q^{45} +(-0.991640 - 3.05195i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.596310 + 0.433244i) q^{51} +(0.495136 - 0.359737i) q^{53} -3.49799 q^{55} +(-0.682688 + 2.10110i) q^{57} +(2.83322 + 8.71976i) q^{59} +(3.66183 - 11.2699i) q^{61} +(0.894319 - 2.75243i) q^{63} +(1.97229 + 1.43295i) q^{65} +(8.29526 - 6.02686i) q^{67} +(-0.914085 - 2.81326i) q^{69} +(-2.25805 - 1.64057i) q^{71} -12.6036 q^{73} +(-0.458229 + 1.41028i) q^{75} +(4.24816 - 3.08647i) q^{77} -7.25045 q^{79} +8.05792 q^{81} -5.91989 q^{83} +1.50868 q^{85} +(-2.68465 + 1.95051i) q^{87} +(-2.43556 + 7.49588i) q^{89} -3.65962 q^{91} +(1.73007 + 1.25697i) q^{93} +(1.39735 + 4.30059i) q^{95} +(-6.91856 + 5.02663i) q^{97} +(12.2945 + 8.93247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.325457			0.187903			0.0939514	−	0.995577i	$-0.470050\pi$
$3$	0.325457			0.187903			0.0939514	+	0.995577i	$0.470050\pi$
$4$		0			0
$5$	0.538931	−	0.391556i	0.241017	−	0.175109i	−0.460719	−	0.887546i	$-0.652408\pi$
$5$	0.538931	−	0.391556i	0.241017	−	0.175109i	0.701736	+	0.712437i	$0.252408\pi$
$6$		0			0
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$		0			0
$9$	−2.89408			−0.964693
$10$		0			0
$11$	−4.24816	−	3.08647i	−1.28087	−	0.930605i	−0.281289	−	0.959623i	$-0.590762\pi$
$11$	−4.24816	−	3.08647i	−1.28087	−	0.930605i	−0.999579	+	0.0290186i	$0.990762\pi$
$12$		0			0
$13$	1.13089	+	3.48051i	0.313651	+	0.965320i	0.976306	+	0.216395i	$0.0694297\pi$
$13$	1.13089	+	3.48051i	0.313651	+	0.965320i	−0.662655	+	0.748925i	$0.730570\pi$
$14$		0			0
$15$	0.175399	−	0.127435i	0.0452878	−	0.0329035i
$16$		0			0
$17$	1.83222	+	1.33119i	0.444379	+	0.322860i	0.787373	−	0.616477i	$-0.211441\pi$
$17$	1.83222	+	1.33119i	0.444379	+	0.322860i	−0.342993	+	0.939338i	$0.611441\pi$
$18$		0			0
$19$	−2.09763	+	6.45584i	−0.481229	+	1.48107i	0.356140	+	0.934432i	$0.384093\pi$
$19$	−2.09763	+	6.45584i	−0.481229	+	1.48107i	−0.837369	+	0.546638i	$0.815907\pi$
$20$		0			0
$21$	−0.100572	+	0.309528i	−0.0219466	+	0.0675446i
$22$		0			0
$23$	−2.80862	−	8.64404i	−0.585637	−	1.80241i	−0.596696	−	0.802467i	$-0.703520\pi$
$23$	−2.80862	−	8.64404i	−0.585637	−	1.80241i	0.0110586	−	0.999939i	$-0.496480\pi$
$24$		0			0
$25$	−1.40795	+	4.33324i	−0.281591	+	0.866648i
$26$		0			0
$27$	−1.91827			−0.369171
$28$		0			0
$29$	−8.24886	+	5.99315i	−1.53177	+	1.11290i	−0.576532	+	0.817075i	$0.695594\pi$
$29$	−8.24886	+	5.99315i	−1.53177	+	1.11290i	−0.955242	+	0.295825i	$0.904406\pi$
$30$		0			0
$31$	5.31581	+	3.86216i	0.954748	+	0.693665i	0.951925	−	0.306331i	$-0.0991014\pi$
$31$	5.31581	+	3.86216i	0.954748	+	0.693665i	0.00282296	+	0.999996i	$0.499101\pi$
$32$		0			0
$33$	−1.38259	−	1.00451i	−0.240679	−	0.174863i
$34$		0			0
$35$	0.205853	+	0.633552i	0.0347956	+	0.107090i
$36$		0			0
$37$	−7.58977	+	5.51429i	−1.24775	+	0.906544i	−0.998089	−	0.0617887i	$-0.980320\pi$
$37$	−7.58977	+	5.51429i	−1.24775	+	0.906544i	−0.249662	+	0.968333i	$0.580320\pi$
$38$		0			0
$39$	0.368055	+	1.13276i	0.0589360	+	0.181386i
$40$		0			0
$41$	2.82568	−	5.74591i	0.441298	−	0.897361i
$41$	2.82568	−	5.74591i	0.441298	−	0.897361i
$42$		0			0
$43$	1.39909	+	4.30597i	0.213360	+	0.656654i	0.999266	+	0.0383082i	$0.0121969\pi$
$43$	1.39909	+	4.30597i	0.213360	+	0.656654i	−0.785906	+	0.618346i	$0.787803\pi$
$44$		0			0
$45$	−1.55971	+	1.13319i	−0.232508	+	0.168927i
$46$		0			0
$47$	−0.991640	−	3.05195i	−0.144646	−	0.445173i	0.852320	−	0.523021i	$-0.175195\pi$
$47$	−0.991640	−	3.05195i	−0.144646	−	0.445173i	−0.996965	+	0.0778480i	$0.975195\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	0.596310	+	0.433244i	0.0835001	+	0.0606664i
$52$		0			0
$53$	0.495136	−	0.359737i	0.0680121	−	0.0494137i	−0.553260	−	0.833009i	$-0.686616\pi$
$53$	0.495136	−	0.359737i	0.0680121	−	0.0494137i	0.621272	+	0.783595i	$0.286616\pi$
$54$		0			0
$55$	−3.49799			−0.471669
$56$		0			0
$57$	−0.682688	+	2.10110i	−0.0904243	+	0.278297i
$58$		0			0
$59$	2.83322	+	8.71976i	0.368854	+	1.13522i	0.947532	+	0.319660i	$0.103569\pi$
$59$	2.83322	+	8.71976i	0.368854	+	1.13522i	−0.578678	+	0.815556i	$0.696431\pi$
$60$		0			0
$61$	3.66183	−	11.2699i	0.468849	−	1.44297i	−0.385228	−	0.922821i	$-0.625877\pi$
$61$	3.66183	−	11.2699i	0.468849	−	1.44297i	0.854077	−	0.520147i	$-0.174123\pi$
$62$		0			0
$63$	0.894319	−	2.75243i	0.112674	−	0.346774i
$64$		0			0
$65$	1.97229	+	1.43295i	0.244632	+	0.177735i
$66$		0			0
$67$	8.29526	−	6.02686i	1.01343	−	0.736298i	0.0485023	−	0.998823i	$-0.484555\pi$
$67$	8.29526	−	6.02686i	1.01343	−	0.736298i	0.964925	+	0.262525i	$0.0845552\pi$
$68$		0			0
$69$	−0.914085	−	2.81326i	−0.110043	−	0.338677i
$70$		0			0
$71$	−2.25805	−	1.64057i	−0.267981	−	0.194699i	0.445677	−	0.895194i	$-0.352963\pi$
$71$	−2.25805	−	1.64057i	−0.267981	−	0.194699i	−0.713658	+	0.700494i	$0.752963\pi$
$72$		0			0
$73$	−12.6036			−1.47514			−0.737569	−	0.675272i	$-0.764026\pi$
$73$	−12.6036			−1.47514			−0.737569	+	0.675272i	$0.764026\pi$
$74$		0			0
$75$	−0.458229	+	1.41028i	−0.0529117	+	0.162846i
$76$		0			0
$77$	4.24816	−	3.08647i	0.484122	−	0.351735i
$78$		0			0
$79$	−7.25045			−0.815740			−0.407870	−	0.913040i	$-0.633728\pi$
$79$	−7.25045			−0.815740			−0.407870	+	0.913040i	$0.633728\pi$
$80$		0			0
$81$	8.05792			0.895324
$82$		0			0
$83$	−5.91989			−0.649792			−0.324896	−	0.945750i	$-0.605329\pi$
$83$	−5.91989			−0.649792			−0.324896	+	0.945750i	$0.605329\pi$
$84$		0			0
$85$	1.50868			0.163639
$86$		0			0
$87$	−2.68465	+	1.95051i	−0.287825	+	0.209117i
$88$		0			0
$89$	−2.43556	+	7.49588i	−0.258169	+	0.794561i	0.735020	+	0.678045i	$0.237173\pi$
$89$	−2.43556	+	7.49588i	−0.258169	+	0.794561i	−0.993189	+	0.116516i	$0.962827\pi$
$90$		0			0
$91$	−3.65962			−0.383633
$92$		0			0
$93$	1.73007	+	1.25697i	0.179400	+	0.130342i
$94$		0			0
$95$	1.39735	+	4.30059i	0.143365	+	0.441231i
$96$		0			0
$97$	−6.91856	+	5.02663i	−0.702474	+	0.510377i	−0.880737	−	0.473606i	$-0.842952\pi$
$97$	−6.91856	+	5.02663i	−0.702474	+	0.510377i	0.178263	+	0.983983i	$0.442952\pi$
$98$		0			0
$99$	12.2945	+	8.93247i	1.23564	+	0.897747i
$100$		0			0
$101$	−5.39622	+	16.6079i	−0.536944	+	1.65254i	0.202467	+	0.979289i	$0.435104\pi$
$101$	−5.39622	+	16.6079i	−0.536944	+	1.65254i	−0.739411	+	0.673255i	$0.764896\pi$
$102$		0			0
$103$	−1.02265	+	3.14739i	−0.100765	+	0.310121i	−0.988713	−	0.149821i	$-0.952130\pi$
$103$	−1.02265	+	3.14739i	−0.100765	+	0.310121i	0.887949	+	0.459943i	$0.152130\pi$
$104$		0			0
$105$	0.0669965	+	0.206194i	0.00653819	+	0.0201225i
$106$		0			0
$107$	4.04265	−	12.4420i	0.390818	−	1.20281i	−0.541353	−	0.840796i	$-0.682088\pi$
$107$	4.04265	−	12.4420i	0.390818	−	1.20281i	0.932171	−	0.362019i	$-0.117912\pi$
$108$		0			0
$109$	−5.59041			−0.535464			−0.267732	−	0.963493i	$-0.586274\pi$
$109$	−5.59041			−0.535464			−0.267732	+	0.963493i	$0.586274\pi$
$110$		0			0
$111$	−2.47015	+	1.79467i	−0.234456	+	0.170342i
$112$		0			0
$113$	8.16453	+	5.93188i	0.768055	+	0.558024i	0.901370	−	0.433049i	$-0.142562\pi$
$113$	8.16453	+	5.93188i	0.768055	+	0.558024i	−0.133315	+	0.991074i	$0.542562\pi$
$114$		0			0
$115$	−4.89828	−	3.55881i	−0.456767	−	0.331861i
$116$		0			0
$117$	−3.27287	−	10.0729i	−0.302577	−	0.931237i
$118$		0			0
$119$	−1.83222	+	1.33119i	−0.167960	+	0.122030i
$120$		0			0
$121$	5.12137	+	15.7620i	0.465579	+	1.43291i
$122$		0			0
$123$	0.919639	−	1.87005i	0.0829210	−	0.168617i
$124$		0			0
$125$	1.96718	+	6.05437i	0.175950	+	0.541519i
$126$		0			0
$127$	0.787954	−	0.572482i	0.0699196	−	0.0507996i	−0.552276	−	0.833661i	$-0.686241\pi$
$127$	0.787954	−	0.572482i	0.0699196	−	0.0507996i	0.622196	+	0.782861i	$0.286241\pi$
$128$		0			0
$129$	0.455345	+	1.40141i	0.0400909	+	0.123387i
$130$		0			0
$131$	−6.73044	−	4.88995i	−0.588042	−	0.427237i	0.253573	−	0.967316i	$-0.418394\pi$
$131$	−6.73044	−	4.88995i	−0.588042	−	0.427237i	−0.841614	+	0.540079i	$0.818394\pi$
$132$		0			0
$133$	−5.49166	−	3.98993i	−0.476187	−	0.345970i
$134$		0			0
$135$	−1.03382	+	0.751111i	−0.0889767	+	0.0646453i
$136$		0			0
$137$	−17.7387			−1.51552			−0.757759	−	0.652535i	$-0.773706\pi$
$137$	−17.7387			−1.51552			−0.757759	+	0.652535i	$0.773706\pi$
$138$		0			0
$139$	5.75215	−	17.7033i	0.487891	−	1.50157i	−0.339859	−	0.940476i	$-0.610379\pi$
$139$	5.75215	−	17.7033i	0.487891	−	1.50157i	0.827750	−	0.561097i	$-0.189621\pi$
$140$		0			0
$141$	−0.322736	−	0.993280i	−0.0271793	−	0.0836493i
$142$		0			0
$143$	5.93829	−	18.2762i	0.496585	−	1.52833i
$144$		0			0
$145$	−2.09891	+	6.45979i	−0.174305	+	0.536456i
$146$		0			0
$147$	−0.263300	−	0.191299i	−0.0217167	−	0.0157781i
$148$		0			0
$149$	12.0184	−	8.73187i	0.984585	−	0.715343i	0.0258564	−	0.999666i	$-0.491769\pi$
$149$	12.0184	−	8.73187i	0.984585	−	0.715343i	0.958729	+	0.284323i	$0.0917687\pi$
$150$		0			0
$151$	−1.50768	−	4.64015i	−0.122693	−	0.377610i	0.870781	−	0.491671i	$-0.163614\pi$
$151$	−1.50768	−	4.64015i	−0.122693	−	0.377610i	−0.993474	+	0.114062i	$0.963614\pi$
$152$		0			0
$153$	−5.30259	−	3.85256i	−0.428689	−	0.311461i
$154$		0			0
$155$	4.37711			0.351578
$156$		0			0
$157$	0.338159	−	1.04075i	0.0269880	−	0.0830606i	−0.936655	−	0.350253i	$-0.886096\pi$
$157$	0.338159	−	1.04075i	0.0269880	−	0.0830606i	0.963643	+	0.267192i	$0.0860958\pi$
$158$		0			0
$159$	0.161145	−	0.117079i	0.0127797	−	0.00928497i
$160$		0			0
$161$	9.08888			0.716304
$162$		0			0
$163$	13.3161			1.04300			0.521498	−	0.853252i	$-0.325373\pi$
$163$	13.3161			1.04300			0.521498	+	0.853252i	$0.325373\pi$
$164$		0			0
$165$	−1.13845			−0.0886279
$166$		0			0
$167$	0.527389			0.0408106			0.0204053	−	0.999792i	$-0.493504\pi$
$167$	0.527389			0.0408106			0.0204053	+	0.999792i	$0.493504\pi$
$168$		0			0
$169$	−0.317821	+	0.230911i	−0.0244478	+	0.0177624i
$170$		0			0
$171$	6.07070	−	18.6837i	0.464238	−	1.42878i
$172$		0			0
$173$	4.24932			0.323070			0.161535	−	0.986867i	$-0.448356\pi$
$173$	4.24932			0.323070			0.161535	+	0.986867i	$0.448356\pi$
$174$		0			0
$175$	−3.68607	−	2.67809i	−0.278641	−	0.202444i
$176$		0			0
$177$	0.922092	+	2.83791i	0.0693087	+	0.213310i
$178$		0			0
$179$	−2.16036	+	1.56959i	−0.161473	+	0.117317i	−0.665587	−	0.746320i	$-0.731819\pi$
$179$	−2.16036	+	1.56959i	−0.161473	+	0.117317i	0.504115	+	0.863637i	$0.331819\pi$
$180$		0			0
$181$	5.10339	+	3.70783i	0.379332	+	0.275601i	0.761070	−	0.648670i	$-0.224674\pi$
$181$	5.10339	+	3.70783i	0.379332	+	0.275601i	−0.381738	+	0.924271i	$0.624674\pi$
$182$		0			0
$183$	1.19177	−	3.66788i	0.0880980	−	0.271138i
$184$		0			0
$185$	−1.93121	+	5.94365i	−0.141985	+	0.436986i
$186$		0			0
$187$	−3.67490	−	11.3102i	−0.268735	−	0.827083i
$188$		0			0
$189$	0.592778	−	1.82438i	0.0431183	−	0.132704i
$190$		0			0
$191$	1.98345			0.143518			0.0717588	−	0.997422i	$-0.477139\pi$
$191$	1.98345			0.143518			0.0717588	+	0.997422i	$0.477139\pi$
$192$		0			0
$193$	−2.45868	+	1.78634i	−0.176980	+	0.128583i	−0.672748	−	0.739871i	$-0.734886\pi$
$193$	−2.45868	+	1.78634i	−0.176980	+	0.128583i	0.495769	+	0.868455i	$0.334886\pi$
$194$		0			0
$195$	0.641895	+	0.466364i	0.0459670	+	0.0333970i
$196$		0			0
$197$	14.4089	+	10.4687i	1.02659	+	0.745864i	0.967624	−	0.252395i	$-0.0812184\pi$
$197$	14.4089	+	10.4687i	1.02659	+	0.745864i	0.0589700	+	0.998260i	$0.481218\pi$
$198$		0			0
$199$	3.90080	+	12.0054i	0.276521	+	0.851043i	0.988813	+	0.149160i	$0.0476569\pi$
$199$	3.90080	+	12.0054i	0.276521	+	0.851043i	−0.712293	+	0.701883i	$0.752343\pi$
$200$		0			0
$201$	2.69975	−	1.96149i	0.190426	−	0.138352i
$202$		0			0
$203$	−3.15078	−	9.69711i	−0.221142	−	0.680604i
$204$		0			0
$205$	−0.727000	−	4.20307i	−0.0507759	−	0.293555i
$206$		0			0
$207$	8.12836	+	25.0165i	0.564960	+	1.73877i
$208$		0			0
$209$	28.8368	−	20.9511i	1.99468	−	1.44922i
$210$		0			0
$211$	6.52009	+	20.0668i	0.448862	+	1.38145i	0.878193	+	0.478307i	$0.158749\pi$
$211$	6.52009	+	20.0668i	0.448862	+	1.38145i	−0.429331	+	0.903147i	$0.641251\pi$
$212$		0			0
$213$	−0.734898	−	0.533934i	−0.0503544	−	0.0365846i
$214$		0			0
$215$	2.44004	+	1.77280i	0.166410	+	0.120904i
$216$		0			0
$217$	−5.31581	+	3.86216i	−0.360861	+	0.262181i
$218$		0			0
$219$	−4.10193			−0.277182
$220$		0			0
$221$	−2.56118	+	7.88249i	−0.172283	+	0.530233i
$222$		0			0
$223$	−8.91413	−	27.4349i	−0.596934	−	1.83717i	−0.544852	−	0.838532i	$-0.683414\pi$
$223$	−8.91413	−	27.4349i	−0.596934	−	1.83717i	−0.0520819	−	0.998643i	$-0.516586\pi$
$224$		0			0
$225$	4.07473	−	12.5407i	0.271649	−	0.836049i
$226$		0			0
$227$	2.82138	−	8.68331i	0.187261	−	0.576331i	−0.812719	−	0.582656i	$-0.802013\pi$
$227$	2.82138	−	8.68331i	0.187261	−	0.576331i	0.999980	+	0.00632511i	$0.00201336\pi$
$228$		0			0
$229$	0.948868	+	0.689393i	0.0627030	+	0.0455564i	0.618695	−	0.785631i	$-0.287662\pi$
$229$	0.948868	+	0.689393i	0.0627030	+	0.0455564i	−0.555992	+	0.831187i	$0.687662\pi$
$230$		0			0
$231$	1.38259	−	1.00451i	0.0909679	−	0.0660921i
$232$		0			0
$233$	−0.567505	−	1.74660i	−0.0371785	−	0.114424i	0.930745	−	0.365669i	$-0.119160\pi$
$233$	−0.567505	−	1.74660i	−0.0371785	−	0.114424i	−0.967923	+	0.251246i	$0.919160\pi$
$234$		0			0
$235$	−1.72944	−	1.25651i	−0.112816	−	0.0819657i
$236$		0			0
$237$	−2.35971			−0.153280
$238$		0			0
$239$	−0.607947	+	1.87107i	−0.0393248	+	0.121029i	−0.968792	−	0.247876i	$-0.920267\pi$
$239$	−0.607947	+	1.87107i	−0.0393248	+	0.121029i	0.929467	+	0.368905i	$0.120267\pi$
$240$		0			0
$241$	22.1453	−	16.0895i	1.42651	−	1.03642i	0.435852	−	0.900018i	$-0.356447\pi$
$241$	22.1453	−	16.0895i	1.42651	−	1.03642i	0.990654	−	0.136399i	$-0.0435530\pi$
$242$		0			0
$243$	8.37732			0.537405
$244$		0			0
$245$	−0.666156			−0.0425591
$246$		0			0
$247$	−24.8418			−1.58064
$248$		0			0
$249$	−1.92667			−0.122098
$250$		0			0
$251$	−9.04562	+	6.57203i	−0.570954	+	0.414823i	−0.835452	−	0.549564i	$-0.814794\pi$
$251$	−9.04562	+	6.57203i	−0.570954	+	0.414823i	0.264497	+	0.964386i	$0.414794\pi$
$252$		0			0
$253$	−14.7481	+	45.3899i	−0.927204	+	2.85364i
$254$		0			0
$255$	0.491010			0.0307482
$256$		0			0
$257$	−20.7298	−	15.0611i	−1.29309	−	0.939483i	−0.293224	−	0.956044i	$-0.594728\pi$
$257$	−20.7298	−	15.0611i	−1.29309	−	0.939483i	−0.999863	+	0.0165611i	$0.994728\pi$
$258$		0			0
$259$	−2.89904	−	8.92231i	−0.180137	−	0.554406i
$260$		0			0
$261$	23.8728	−	17.3446i	1.47769	−	1.07361i
$262$		0			0
$263$	4.78545	+	3.47683i	0.295083	+	0.214391i	0.725470	−	0.688254i	$-0.241623\pi$
$263$	4.78545	+	3.47683i	0.295083	+	0.214391i	−0.430386	+	0.902645i	$0.641623\pi$
$264$		0			0
$265$	0.125987	−	0.387747i	0.00773930	−	0.0238191i
$266$		0			0
$267$	−0.792670	+	2.43959i	−0.0485106	+	0.149300i
$268$		0			0
$269$	9.71781	+	29.9083i	0.592505	+	1.82354i	0.566771	+	0.823875i	$0.308192\pi$
$269$	9.71781	+	29.9083i	0.592505	+	1.82354i	0.0257338	+	0.999669i	$0.491808\pi$
$270$		0			0
$271$	5.56247	−	17.1195i	0.337896	−	1.03994i	−0.627382	−	0.778712i	$-0.715873\pi$
$271$	5.56247	−	17.1195i	0.337896	−	1.03994i	0.965278	−	0.261226i	$-0.0841267\pi$
$272$		0			0
$273$	−1.19105			−0.0720857
$274$		0			0
$275$	19.3556	−	14.0627i	1.16719	−	0.848011i
$276$		0			0
$277$	13.1822	+	9.57740i	0.792040	+	0.575450i	0.908568	−	0.417737i	$-0.137177\pi$
$277$	13.1822	+	9.57740i	0.792040	+	0.575450i	−0.116528	+	0.993187i	$0.537177\pi$
$278$		0			0
$279$	−15.3844	−	11.1774i	−0.921038	−	0.669173i
$280$		0			0
$281$	−0.195604	−	0.602006i	−0.0116687	−	0.0359127i	0.945053	−	0.326918i	$-0.106010\pi$
$281$	−0.195604	−	0.602006i	−0.0116687	−	0.0359127i	−0.956721	+	0.291006i	$0.906010\pi$
$282$		0			0
$283$	4.05033	−	2.94274i	0.240767	−	0.174927i	−0.460858	−	0.887474i	$-0.652458\pi$
$283$	4.05033	−	2.94274i	0.240767	−	0.174927i	0.701625	+	0.712546i	$0.252458\pi$
$284$		0			0
$285$	0.454777	+	1.39966i	0.0269386	+	0.0829086i
$286$		0			0
$287$	4.59150	+	4.46297i	0.271028	+	0.263441i
$288$		0			0
$289$	−3.66831	−	11.2899i	−0.215783	−	0.664112i
$290$		0			0
$291$	−2.25170	+	1.63595i	−0.131997	+	0.0959013i
$292$		0			0
$293$	6.56220	+	20.1964i	0.383368	+	1.17988i	0.937657	+	0.347561i	$0.112990\pi$
$293$	6.56220	+	20.1964i	0.383368	+	1.17988i	−0.554290	+	0.832324i	$0.687010\pi$
$294$		0			0
$295$	4.94119	+	3.58998i	0.287687	+	0.209017i
$296$		0			0
$297$	8.14911	+	5.92068i	0.472859	+	0.343552i
$298$		0			0
$299$	26.9094	−	19.5508i	1.55621	−	1.13065i
$300$		0			0
$301$	−4.52756			−0.260964
$302$		0			0
$303$	−1.75624	+	5.40515i	−0.100893	+	0.310518i
$304$		0			0
$305$	−2.43935	−	7.50753i	−0.139677	−	0.429880i
$306$		0			0
$307$	−0.699876	+	2.15400i	−0.0399440	+	0.122935i	−0.969040	−	0.246903i	$-0.920587\pi$
$307$	−0.699876	+	2.15400i	−0.0399440	+	0.122935i	0.929096	+	0.369838i	$0.120587\pi$
$308$		0			0
$309$	−0.332828	+	1.02434i	−0.0189339	+	0.0582727i
$310$		0			0
$311$	−3.60844	−	2.62169i	−0.204616	−	0.148662i	0.480758	−	0.876853i	$-0.340361\pi$
$311$	−3.60844	−	2.62169i	−0.204616	−	0.148662i	−0.685374	+	0.728191i	$0.740361\pi$
$312$		0			0
$313$	0.479297	−	0.348230i	0.0270915	−	0.0196831i	−0.574157	−	0.818745i	$-0.694670\pi$
$313$	0.479297	−	0.348230i	0.0270915	−	0.0196831i	0.601249	+	0.799062i	$0.294670\pi$
$314$		0			0
$315$	−0.595756	−	1.83355i	−0.0335670	−	0.103309i
$316$		0			0
$317$	−17.5425	−	12.7454i	−0.985285	−	0.715851i	−0.0264013	−	0.999651i	$-0.508405\pi$
$317$	−17.5425	−	12.7454i	−0.985285	−	0.715851i	−0.958883	+	0.283800i	$0.908405\pi$
$318$		0			0
$319$	53.5401			2.99767
$320$		0			0
$321$	1.31571	−	4.04934i	0.0734358	−	0.226012i
$322$		0			0
$323$	−12.4372	+	9.03619i	−0.692027	+	0.502787i
$324$		0			0
$325$	−16.6741			−0.924913
$326$		0			0
$327$	−1.81944			−0.100615
$328$		0			0
$329$	3.20901			0.176919
$330$		0			0
$331$	−26.1708			−1.43848			−0.719240	−	0.694762i	$-0.755510\pi$
$331$	−26.1708			−1.43848			−0.719240	+	0.694762i	$0.755510\pi$
$332$		0			0
$333$	21.9654	−	15.9588i	1.20370	−	0.874537i
$334$		0			0
$335$	2.11072	−	6.49613i	0.115321	−	0.354921i
$336$		0			0
$337$	10.0739			0.548763			0.274381	−	0.961621i	$-0.411527\pi$
$337$	10.0739			0.548763			0.274381	+	0.961621i	$0.411527\pi$
$338$		0			0
$339$	2.65721	+	1.93057i	0.144320	+	0.104854i
$340$		0			0
$341$	−10.6620	−	32.8142i	−0.577378	−	1.77699i
$342$		0			0
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$		0			0
$345$	−1.59418	−	1.15824i	−0.0858278	−	0.0623575i
$346$		0			0
$347$	5.25485	−	16.1728i	0.282095	−	0.868200i	−0.705159	−	0.709049i	$-0.749124\pi$
$347$	5.25485	−	16.1728i	0.282095	−	0.868200i	0.987254	−	0.159151i	$-0.0508757\pi$
$348$		0			0
$349$	−0.300814	+	0.925809i	−0.0161022	+	0.0495574i	−0.958785	−	0.284133i	$-0.908294\pi$
$349$	−0.300814	+	0.925809i	−0.0161022	+	0.0495574i	0.942683	+	0.333691i	$0.108294\pi$
$350$		0			0
$351$	−2.16934	−	6.67656i	−0.115791	−	0.356368i
$352$		0			0
$353$	−0.308621	+	0.949837i	−0.0164262	+	0.0505547i	−0.958934	−	0.283630i	$-0.908461\pi$
$353$	−0.308621	+	0.949837i	−0.0164262	+	0.0505547i	0.942507	+	0.334185i	$0.108461\pi$
$354$		0			0
$355$	−1.85931			−0.0986817
$356$		0			0
$357$	−0.596310	+	0.433244i	−0.0315601	+	0.0229297i
$358$		0			0
$359$	−3.23584	−	2.35098i	−0.170781	−	0.124080i	0.499111	−	0.866538i	$-0.333660\pi$
$359$	−3.23584	−	2.35098i	−0.170781	−	0.124080i	−0.669893	+	0.742458i	$0.733660\pi$
$360$		0			0
$361$	−21.9064	−	15.9160i	−1.15297	−	0.837682i
$362$		0			0
$363$	1.66679	+	5.12984i	0.0874837	+	0.269247i
$364$		0			0
$365$	−6.79246	+	4.93501i	−0.355534	+	0.258310i
$366$		0			0
$367$	7.22453	+	22.2348i	0.377117	+	1.16065i	0.942039	+	0.335503i	$0.108906\pi$
$367$	7.22453	+	22.2348i	0.377117	+	1.16065i	−0.564922	+	0.825144i	$0.691094\pi$
$368$		0			0
$369$	−8.17775	+	16.6291i	−0.425716	+	0.865677i
$370$		0			0
$371$	0.189125	+	0.582067i	0.00981888	+	0.0302194i
$372$		0			0
$373$	−6.21759	+	4.51735i	−0.321935	+	0.233899i	−0.737001	−	0.675892i	$-0.763759\pi$
$373$	−6.21759	+	4.51735i	−0.321935	+	0.233899i	0.415066	+	0.909791i	$0.363759\pi$
$374$		0			0
$375$	0.640234	+	1.97044i	0.0330615	+	0.101753i
$376$		0			0
$377$	−30.1877	−	21.9327i	−1.55475	−	1.12959i
$378$		0			0
$379$	−7.77827	−	5.65124i	−0.399543	−	0.290285i	0.369812	−	0.929107i	$-0.379422\pi$
$379$	−7.77827	−	5.65124i	−0.399543	−	0.290285i	−0.769355	+	0.638822i	$0.779422\pi$
$380$		0			0
$381$	0.256445	−	0.186318i	0.0131381	−	0.00954539i
$382$		0			0
$383$	23.3506			1.19316			0.596580	−	0.802554i	$-0.296526\pi$
$383$	23.3506			1.19316			0.596580	+	0.802554i	$0.296526\pi$
$384$		0			0
$385$	1.08094	−	3.32679i	0.0550897	−	0.169549i
$386$		0			0
$387$	−4.04909	−	12.4618i	−0.205827	−	0.633469i
$388$		0			0
$389$	−5.25840	+	16.1837i	−0.266612	+	0.820546i	0.724706	+	0.689058i	$0.241976\pi$
$389$	−5.25840	+	16.1837i	−0.266612	+	0.820546i	−0.991318	+	0.131488i	$0.958024\pi$
$390$		0			0
$391$	6.36082	−	19.5766i	0.321681	−	0.990031i
$392$		0			0
$393$	−2.19047	−	1.59147i	−0.110495	−	0.0802791i
$394$		0			0
$395$	−3.90750	+	2.83896i	−0.196607	+	0.142844i
$396$		0			0
$397$	6.85695	+	21.1035i	0.344140	+	1.05916i	0.962042	+	0.272900i	$0.0879828\pi$
$397$	6.85695	+	21.1035i	0.344140	+	1.05916i	−0.617902	+	0.786255i	$0.712017\pi$
$398$		0			0
$399$	−1.78730	−	1.29855i	−0.0894770	−	0.0650088i
$400$		0			0
$401$	−34.4310			−1.71940			−0.859701	−	0.510798i	$-0.829350\pi$
$401$	−34.4310			−1.71940			−0.859701	+	0.510798i	$0.829350\pi$
$402$		0			0
$403$	−7.43072	+	22.8694i	−0.370150	+	1.13921i
$404$		0			0
$405$	4.34266	−	3.15513i	0.215789	−	0.156780i
$406$		0			0
$407$	49.2622			2.44184
$408$		0			0
$409$	−27.5815			−1.36382			−0.681908	−	0.731438i	$-0.738849\pi$
$409$	−27.5815			−1.36382			−0.681908	+	0.731438i	$0.738849\pi$
$410$		0			0
$411$	−5.77318			−0.284770
$412$		0			0
$413$	−9.16850			−0.451152
$414$		0			0
$415$	−3.19041	+	2.31797i	−0.156611	+	0.113785i
$416$		0			0
$417$	1.87208	−	5.76166i	0.0916761	−	0.282150i
$418$		0			0
$419$	18.9769			0.927083			0.463542	−	0.886075i	$-0.346578\pi$
$419$	18.9769			0.927083			0.463542	+	0.886075i	$0.346578\pi$
$420$		0			0
$421$	20.7214	+	15.0550i	1.00990	+	0.733736i	0.964188	−	0.265219i	$-0.0854441\pi$
$421$	20.7214	+	15.0550i	1.00990	+	0.733736i	0.0457127	+	0.998955i	$0.485444\pi$
$422$		0			0
$423$	2.86988	+	8.83259i	0.139538	+	0.429455i
$424$		0			0
$425$	−8.34804	+	6.06520i	−0.404939	+	0.294206i
$426$		0			0
$427$	9.58678	+	6.96521i	0.463937	+	0.337070i
$428$		0			0
$429$	1.93266	−	5.94812i	0.0933097	−	0.287178i
$430$		0			0
$431$	1.96184	−	6.03794i	0.0944987	−	0.290837i	−0.892624	−	0.450802i	$-0.851138\pi$
$431$	1.96184	−	6.03794i	0.0944987	−	0.290837i	0.987123	+	0.159965i	$0.0511381\pi$
$432$		0			0
$433$	8.25809	+	25.4158i	0.396858	+	1.22140i	0.927505	+	0.373811i	$0.121949\pi$
$433$	8.25809	+	25.4158i	0.396858	+	1.22140i	−0.530646	+	0.847593i	$0.678051\pi$
$434$		0			0
$435$	−0.683106	+	2.10238i	−0.0327524	+	0.100802i
$436$		0			0
$437$	61.6959			2.95132
$438$		0			0
$439$	2.00522	−	1.45688i	0.0957040	−	0.0695330i	−0.538904	−	0.842367i	$-0.681162\pi$
$439$	2.00522	−	1.45688i	0.0957040	−	0.0695330i	0.634608	+	0.772834i	$0.281162\pi$
$440$		0			0
$441$	2.34136	+	1.70110i	0.111493	+	0.0810046i
$442$		0			0
$443$	10.1509	+	7.37505i	0.482283	+	0.350399i	0.802209	−	0.597043i	$-0.203658\pi$
$443$	10.1509	+	7.37505i	0.482283	+	0.350399i	−0.319926	+	0.947443i	$0.603658\pi$
$444$		0			0
$445$	1.62246	+	4.99342i	0.0769120	+	0.236711i
$446$		0			0
$447$	3.91147	−	2.84185i	0.185006	−	0.134415i
$448$		0			0
$449$	3.35925	+	10.3387i	0.158533	+	0.487913i	0.998502	−	0.0547210i	$-0.0174269\pi$
$449$	3.35925	+	10.3387i	0.158533	+	0.487913i	−0.839969	+	0.542634i	$0.817427\pi$
$450$		0			0
$451$	−29.7385	+	15.6882i	−1.40033	+	0.738727i
$452$		0			0
$453$	−0.490684	−	1.51017i	−0.0230543	−	0.0709539i
$454$		0			0
$455$	−1.97229	+	1.43295i	−0.0924622	+	0.0671777i
$456$		0			0
$457$	1.78856	+	5.50463i	0.0836655	+	0.257496i	0.984134	−	0.177424i	$-0.0567765\pi$
$457$	1.78856	+	5.50463i	0.0836655	+	0.257496i	−0.900469	+	0.434920i	$0.856777\pi$
$458$		0			0
$459$	−3.51470	−	2.55358i	−0.164052	−	0.119191i
$460$		0			0
$461$	3.70075	+	2.68876i	0.172361	+	0.125228i	0.670621	−	0.741800i	$-0.266028\pi$
$461$	3.70075	+	2.68876i	0.172361	+	0.125228i	−0.498260	+	0.867028i	$0.666028\pi$
$462$		0			0
$463$	−17.3599	+	12.6127i	−0.806781	+	0.586161i	−0.912896	−	0.408193i	$-0.866159\pi$
$463$	−17.3599	+	12.6127i	−0.806781	+	0.586161i	0.106115	+	0.994354i	$0.466159\pi$
$464$		0			0
$465$	1.42456			0.0660625
$466$		0			0
$467$	−10.4747	+	32.2379i	−0.484713	+	1.49179i	0.347682	+	0.937612i	$0.386969\pi$
$467$	−10.4747	+	32.2379i	−0.484713	+	1.49179i	−0.832396	+	0.554182i	$0.813031\pi$
$468$		0			0
$469$	3.16851	+	9.75166i	0.146308	+	0.450290i
$470$		0			0
$471$	0.110056	−	0.338718i	0.00507112	−	0.0156073i
$472$		0			0
$473$	7.34666	−	22.6107i	0.337800	−	1.03964i
$474$		0			0
$475$	−25.0213	−	18.1790i	−1.14806	−	0.834112i
$476$		0			0
$477$	−1.43296	+	1.04111i	−0.0656108	+	0.0476690i
$478$		0			0
$479$	8.08292	+	24.8767i	0.369318	+	1.13664i	0.947233	+	0.320547i	$0.103867\pi$
$479$	8.08292	+	24.8767i	0.369318	+	1.13664i	−0.577914	+	0.816097i	$0.696133\pi$
$480$		0			0
$481$	−27.7757	−	20.1802i	−1.26646	−	0.920140i
$482$		0			0
$483$	2.95804			0.134596
$484$		0			0
$485$	−1.76042	+	5.41802i	−0.0799366	+	0.246019i
$486$		0			0
$487$	−25.3953	+	18.4508i	−1.15077	+	0.836084i	−0.988583	−	0.150676i	$-0.951855\pi$
$487$	−25.3953	+	18.4508i	−1.15077	+	0.836084i	−0.162188	+	0.986760i	$0.551855\pi$
$488$		0			0
$489$	4.33382			0.195982
$490$		0			0
$491$	−34.3875			−1.55188			−0.775942	−	0.630804i	$-0.782725\pi$
$491$	−34.3875			−1.55188			−0.775942	+	0.630804i	$0.782725\pi$
$492$		0			0
$493$	−23.0917			−1.04000
$494$		0			0
$495$	10.1235			0.455015
$496$		0			0
$497$	2.25805	−	1.64057i	0.101287	−	0.0735895i
$498$		0			0
$499$	5.71984	−	17.6039i	0.256055	−	0.788057i	−0.737565	−	0.675276i	$-0.764024\pi$
$499$	5.71984	−	17.6039i	0.256055	−	0.788057i	0.993620	−	0.112780i	$-0.0359757\pi$
$500$		0			0
$501$	0.171643			0.00766842
$502$		0			0
$503$	−6.85203	−	4.97829i	−0.305517	−	0.221971i	0.424454	−	0.905450i	$-0.360466\pi$
$503$	−6.85203	−	4.97829i	−0.305517	−	0.221971i	−0.729970	+	0.683479i	$0.760466\pi$
$504$		0			0
$505$	3.59472	+	11.0634i	0.159963	+	0.492316i
$506$		0			0
$507$	−0.103437	+	0.0751515i	−0.00459381	+	0.00333760i
$508$		0			0
$509$	−19.8183	−	14.3989i	−0.878432	−	0.638218i	0.0544041	−	0.998519i	$-0.482674\pi$
$509$	−19.8183	−	14.3989i	−0.878432	−	0.638218i	−0.932836	+	0.360301i	$0.882674\pi$
$510$		0			0
$511$	3.89472	−	11.9867i	0.172292	−	0.530261i
$512$		0			0
$513$	4.02382	−	12.3840i	0.177656	−	0.546769i
$514$		0			0
$515$	0.681243	+	2.09665i	0.0300192	+	0.0923895i
$516$		0			0
$517$	−5.20711	+	16.0258i	−0.229008	+	0.704816i
$518$		0			0
$519$	1.38297			0.0607057
$520$		0			0
$521$	31.9805	−	23.2352i	1.40109	−	1.01795i	0.406545	−	0.913631i	$-0.366733\pi$
$521$	31.9805	−	23.2352i	1.40109	−	1.01795i	0.994544	−	0.104320i	$-0.0332667\pi$
$522$		0			0
$523$	−34.4505	−	25.0298i	−1.50642	−	1.09448i	−0.967736	−	0.251966i	$-0.918923\pi$
$523$	−34.4505	−	25.0298i	−1.50642	−	1.09448i	−0.538681	−	0.842510i	$-0.681077\pi$
$524$		0			0
$525$	−1.19966	−	0.871603i	−0.0523574	−	0.0380399i
$526$		0			0
$527$	4.59849	+	14.1527i	0.200313	+	0.616501i
$528$		0			0
$529$	−48.2236	+	35.0365i	−2.09668	+	1.52333i
$530$		0			0
$531$	−8.19956	−	25.2357i	−0.355831	−	1.09513i
$532$		0			0
$533$	23.1942	+	3.33684i	1.00465	+	0.144535i
$534$		0			0
$535$	−2.69304	−	8.28832i	−0.116430	−	0.358335i
$536$		0			0
$537$	−0.703105	+	0.510836i	−0.0303412	+	0.0220442i
$538$		0			0
$539$	1.62265	+	4.99401i	0.0698925	+	0.215107i
$540$		0			0
$541$	13.3439	+	9.69493i	0.573700	+	0.416817i	0.836447	−	0.548047i	$-0.184629\pi$
$541$	13.3439	+	9.69493i	0.573700	+	0.416817i	−0.262747	+	0.964865i	$0.584629\pi$
$542$		0			0
$543$	1.66094	+	1.20674i	0.0712776	+	0.0517862i
$544$		0			0
$545$	−3.01284	+	2.18896i	−0.129056	+	0.0937647i
$546$		0			0
$547$	11.0987			0.474548			0.237274	−	0.971443i	$-0.423746\pi$
$547$	11.0987			0.474548			0.237274	+	0.971443i	$0.423746\pi$
$548$		0			0
$549$	−10.5976	+	32.6161i	−0.452295	+	1.39202i
$550$		0			0
$551$	−21.3877	−	65.8247i	−0.911148	−	2.80422i
$552$		0			0
$553$	2.24051	−	6.89559i	0.0952763	−	0.293230i
$554$		0			0
$555$	−0.628526	+	1.93440i	−0.0266794	+	0.0821109i
$556$		0			0
$557$	10.8372	+	7.87365i	0.459185	+	0.333617i	0.793211	−	0.608946i	$-0.208408\pi$
$557$	10.8372	+	7.87365i	0.459185	+	0.333617i	−0.334027	+	0.942564i	$0.608408\pi$
$558$		0			0
$559$	−13.4047	+	9.73912i	−0.566960	+	0.411921i
$560$		0			0
$561$	−1.19602	−	3.68098i	−0.0504961	−	0.155411i
$562$		0			0
$563$	−3.99480	−	2.90239i	−0.168361	−	0.122321i	0.500414	−	0.865786i	$-0.333181\pi$
$563$	−3.99480	−	2.90239i	−0.168361	−	0.122321i	−0.668775	+	0.743465i	$0.733181\pi$
$564$		0			0
$565$	6.72279			0.282830
$566$		0			0
$567$	−2.49003	+	7.66354i	−0.104572	+	0.321838i
$568$		0			0
$569$	12.4997	−	9.08157i	0.524015	−	0.380719i	−0.294099	−	0.955775i	$-0.595020\pi$
$569$	12.4997	−	9.08157i	0.524015	−	0.380719i	0.818114	+	0.575056i	$0.195020\pi$
$570$		0			0
$571$	−44.5530			−1.86448			−0.932242	−	0.361835i	$-0.882150\pi$
$571$	−44.5530			−1.86448			−0.932242	+	0.361835i	$0.882150\pi$
$572$		0			0
$573$	0.645529			0.0269674
$574$		0			0
$575$	41.4111			1.72696
$576$		0			0
$577$	34.9369			1.45444			0.727221	−	0.686404i	$-0.240812\pi$
$577$	34.9369			1.45444			0.727221	+	0.686404i	$0.240812\pi$
$578$		0			0
$579$	−0.800195	+	0.581376i	−0.0332550	+	0.0241611i
$580$		0			0
$581$	1.82935	−	5.63015i	0.0758941	−	0.233578i
$582$		0			0
$583$	−3.21373			−0.133099
$584$		0			0
$585$	−5.70795	−	4.14707i	−0.235995	−	0.171460i
$586$		0			0
$587$	5.67954	+	17.4798i	0.234420	+	0.721470i	0.997198	+	0.0748095i	$0.0238349\pi$
$587$	5.67954	+	17.4798i	0.234420	+	0.721470i	−0.762778	+	0.646660i	$0.776165\pi$
$588$		0			0
$589$	−36.0841	+	26.2166i	−1.48682	+	1.08024i
$590$		0			0
$591$	4.68949	+	3.40712i	0.192900	+	0.140150i
$592$		0			0
$593$	−2.48060	+	7.63450i	−0.101866	+	0.313511i	−0.988982	−	0.148035i	$-0.952705\pi$
$593$	−2.48060	+	7.63450i	−0.101866	+	0.313511i	0.887116	+	0.461546i	$0.152705\pi$
$594$		0			0
$595$	−0.466207	+	1.43484i	−0.0191126	+	0.0588226i
$596$		0			0
$597$	1.26954	+	3.90726i	0.0519590	+	0.159913i
$598$		0			0
$599$	4.53189	−	13.9477i	0.185168	−	0.569889i	−0.814783	−	0.579766i	$-0.803144\pi$
$599$	4.53189	−	13.9477i	0.185168	−	0.569889i	0.999951	+	0.00987721i	$0.00314407\pi$
$600$		0			0
$601$	−18.1543			−0.740531			−0.370265	−	0.928926i	$-0.620733\pi$
$601$	−18.1543			−0.740531			−0.370265	+	0.928926i	$0.620733\pi$
$602$		0			0
$603$	−24.0071	+	17.4422i	−0.977646	+	0.710301i
$604$		0			0
$605$	8.93177	+	6.48931i	0.363128	+	0.263828i
$606$		0			0
$607$	15.1307	+	10.9931i	0.614135	+	0.446195i	0.850868	−	0.525380i	$-0.176077\pi$
$607$	15.1307	+	10.9931i	0.614135	+	0.446195i	−0.236733	+	0.971575i	$0.576077\pi$
$608$		0			0
$609$	−1.02544	−	3.15600i	−0.0415531	−	0.127887i
$610$		0			0
$611$	9.50092	−	6.90282i	0.384366	−	0.279258i
$612$		0			0
$613$	8.52444	+	26.2355i	0.344299	+	1.05964i	0.961958	+	0.273197i	$0.0880811\pi$
$613$	8.52444	+	26.2355i	0.344299	+	1.05964i	−0.617659	+	0.786446i	$0.711919\pi$
$614$		0			0
$615$	−0.236608	−	1.36792i	−0.00954094	−	0.0551598i
$616$		0			0
$617$	4.96214	+	15.2719i	0.199768	+	0.614824i	0.999888	+	0.0149830i	$0.00476941\pi$
$617$	4.96214	+	15.2719i	0.199768	+	0.614824i	−0.800119	+	0.599841i	$0.795231\pi$
$618$		0			0
$619$	−29.6041	+	21.5086i	−1.18989	+	0.864505i	−0.993253	−	0.115971i	$-0.963002\pi$
$619$	−29.6041	+	21.5086i	−1.18989	+	0.864505i	−0.196637	+	0.980476i	$0.563002\pi$
$620$		0			0
$621$	5.38769	+	16.5816i	0.216200	+	0.665397i
$622$		0			0
$623$	−6.37637	−	4.63271i	−0.255464	−	0.185605i
$624$		0			0
$625$	−14.9996	−	10.8978i	−0.599982	−	0.435913i
$626$		0			0
$627$	9.38514	−	6.81870i	0.374806	−	0.272313i
$628$		0			0
$629$	−21.2467			−0.847162
$630$		0			0
$631$	−9.95879	+	30.6500i	−0.396453	+	1.22016i	0.531371	+	0.847139i	$0.321677\pi$
$631$	−9.95879	+	30.6500i	−0.396453	+	1.22016i	−0.927824	+	0.373018i	$0.878323\pi$
$632$		0			0
$633$	2.12201	+	6.53088i	0.0843424	+	0.259579i
$634$		0			0
$635$	0.200494	−	0.617057i	0.00795636	−	0.0244872i
$636$		0			0
$637$	1.13089	−	3.48051i	0.0448073	−	0.137903i
$638$		0			0
$639$	6.53496	+	4.74793i	0.258519	+	0.187825i
$640$		0			0
$641$	−13.9334	+	10.1232i	−0.550338	+	0.399844i	−0.827910	−	0.560861i	$-0.810470\pi$
$641$	−13.9334	+	10.1232i	−0.550338	+	0.399844i	0.277572	+	0.960705i	$0.410470\pi$
$642$		0			0
$643$	4.99168	+	15.3628i	0.196853	+	0.605850i	0.999950	+	0.0100021i	$0.00318382\pi$
$643$	4.99168	+	15.3628i	0.196853	+	0.605850i	−0.803097	+	0.595848i	$0.796816\pi$
$644$		0			0
$645$	0.794130	+	0.576969i	0.0312688	+	0.0227181i
$646$		0			0
$647$	−50.4766			−1.98444			−0.992220	−	0.124494i	$-0.960269\pi$
$647$	−50.4766			−1.98444			−0.992220	+	0.124494i	$0.960269\pi$
$648$		0			0
$649$	14.8773	−	45.7875i	0.583984	−	1.79732i
$650$		0			0
$651$	−1.73007	+	1.25697i	−0.0678068	+	0.0492645i
$652$		0			0
$653$	−24.3771			−0.953951			−0.476976	−	0.878917i	$-0.658267\pi$
$653$	−24.3771			−0.953951			−0.476976	+	0.878917i	$0.658267\pi$
$654$		0			0
$655$	−5.54194			−0.216541
$656$		0			0
$657$	36.4757			1.42305
$658$		0			0
$659$	−14.3693			−0.559748			−0.279874	−	0.960037i	$-0.590293\pi$
$659$	−14.3693			−0.559748			−0.279874	+	0.960037i	$0.590293\pi$
$660$		0			0
$661$	−7.69198	+	5.58855i	−0.299183	+	0.217370i	−0.727241	−	0.686382i	$-0.759198\pi$
$661$	−7.69198	+	5.58855i	−0.299183	+	0.217370i	0.428058	+	0.903751i	$0.359198\pi$
$662$		0			0
$663$	−0.833553	+	2.56541i	−0.0323725	+	0.0996324i
$664$		0			0
$665$	−4.52191			−0.175352
$666$		0			0
$667$	74.9729	+	54.4710i	2.90296	+	2.10912i
$668$		0			0
$669$	−2.90117	−	8.92888i	−0.112166	−	0.345210i
$670$		0			0
$671$	−50.3403	+	36.5744i	−1.94337	+	1.41194i
$672$		0			0
$673$	22.4859	+	16.3370i	0.866767	+	0.629743i	0.929718	−	0.368273i	$-0.120051\pi$
$673$	22.4859	+	16.3370i	0.866767	+	0.629743i	−0.0629502	+	0.998017i	$0.520051\pi$
$674$		0			0
$675$	2.70084	−	8.31232i	0.103955	−	0.319941i
$676$		0			0
$677$	2.95743	−	9.10204i	0.113663	−	0.349820i	−0.878003	−	0.478656i	$-0.841124\pi$
$677$	2.95743	−	9.10204i	0.113663	−	0.349820i	0.991666	+	0.128836i	$0.0411241\pi$
$678$		0			0
$679$	−2.64266	−	8.13326i	−0.101416	−	0.312126i
$680$		0			0
$681$	0.918237	−	2.82604i	0.0351869	−	0.108294i
$682$		0			0
$683$	4.69887			0.179797			0.0898987	−	0.995951i	$-0.471346\pi$
$683$	4.69887			0.179797			0.0898987	+	0.995951i	$0.471346\pi$
$684$		0			0
$685$	−9.55993	+	6.94569i	−0.365266	+	0.265381i
$686$		0			0
$687$	0.308816	+	0.224368i	0.0117821	+	0.00856017i
$688$		0			0
$689$	1.81201	+	1.31650i	0.0690321	+	0.0501547i
$690$		0			0
$691$	10.0561	+	30.9496i	0.382553	+	1.17738i	0.938240	+	0.345986i	$0.112456\pi$
$691$	10.0561	+	30.9496i	0.382553	+	1.17738i	−0.555686	+	0.831392i	$0.687544\pi$
$692$		0			0
$693$	−12.2945	+	8.93247i	−0.467029	+	0.339317i
$694$		0			0
$695$	−3.83183	−	11.7931i	−0.145349	−	0.447340i
$696$		0			0
$697$	12.8262	−	6.76628i	0.485826	−	0.256291i
$698$		0			0
$699$	−0.184699	−	0.568444i	−0.00698594	−	0.0215005i
$700$		0			0
$701$	15.1805	−	11.0292i	0.573358	−	0.416569i	−0.262966	−	0.964805i	$-0.584701\pi$
$701$	15.1805	−	11.0292i	0.573358	−	0.416569i	0.836323	+	0.548236i	$0.184701\pi$
$702$		0			0
$703$	−19.6789	−	60.5653i	−0.742202	−	2.28426i
$704$		0			0
$705$	−0.562858	−	0.408940i	−0.0211985	−	0.0154016i
$706$		0			0
$707$	−14.1275	−	10.2642i	−0.531319	−	0.386026i
$708$		0			0
$709$	−22.2694	+	16.1797i	−0.836346	+	0.607641i	−0.921348	−	0.388740i	$-0.872911\pi$
$709$	−22.2694	+	16.1797i	−0.836346	+	0.607641i	0.0850012	+	0.996381i	$0.472911\pi$
$710$		0			0
$711$	20.9834			0.786938
$712$		0			0
$713$	18.4546	−	56.7974i	0.691130	−	2.12708i
$714$		0			0
$715$	−3.95583	−	12.1748i	−0.147940	−	0.455311i
$716$		0			0
$717$	−0.197861	+	0.608953i	−0.00738924	+	0.0227418i
$718$		0			0
$719$	−10.5964	+	32.6122i	−0.395178	+	1.21623i	0.533646	+	0.845708i	$0.320822\pi$
$719$	−10.5964	+	32.6122i	−0.395178	+	1.21623i	−0.928823	+	0.370523i	$0.879178\pi$
$720$		0			0
$721$	−2.67733	−	1.94519i	−0.0997089	−	0.0724428i
$722$		0			0
$723$	7.20736	−	5.23645i	0.268045	−	0.194746i
$724$		0			0
$725$	−14.3557	−	44.1823i	−0.533158	−	1.64089i
$726$		0			0
$727$	26.1552	+	19.0028i	0.970041	+	0.704776i	0.955461	−	0.295117i	$-0.0953588\pi$
$727$	26.1552	+	19.0028i	0.970041	+	0.704776i	0.0145803	+	0.999894i	$0.495359\pi$
$728$		0			0
$729$	−21.4473			−0.794344
$730$		0			0
$731$	−3.16860	+	9.75195i	−0.117195	+	0.360689i
$732$		0			0
$733$	3.98533	−	2.89551i	0.147201	−	0.106948i	−0.511747	−	0.859136i	$-0.671002\pi$
$733$	3.98533	−	2.89551i	0.147201	−	0.106948i	0.658949	+	0.752188i	$0.271002\pi$
$734$		0			0
$735$	−0.216805			−0.00799698
$736$		0			0
$737$	−53.8413			−1.98327
$738$		0			0
$739$	25.8745			0.951810			0.475905	−	0.879497i	$-0.342121\pi$
$739$	25.8745			0.951810			0.475905	+	0.879497i	$0.342121\pi$
$740$		0			0
$741$	−8.08493			−0.297007
$742$		0			0
$743$	−20.8721	+	15.1644i	−0.765722	+	0.556329i	−0.900660	−	0.434525i	$-0.856916\pi$
$743$	−20.8721	+	15.1644i	−0.765722	+	0.556329i	0.134938	+	0.990854i	$0.456916\pi$
$744$		0			0
$745$	3.05807	−	9.41176i	0.112039	−	0.344820i
$746$		0			0
$747$	17.1326			0.626850
$748$		0			0
$749$	10.5838	+	7.68959i	0.386724	+	0.280971i
$750$		0			0
$751$	−5.93209	−	18.2571i	−0.216465	−	0.666211i	−0.999046	−	0.0436623i	$-0.986097\pi$
$751$	−5.93209	−	18.2571i	−0.216465	−	0.666211i	0.782581	−	0.622548i	$-0.213903\pi$
$752$		0			0
$753$	−2.94396	+	2.13891i	−0.107284	+	0.0779463i
$754$		0			0
$755$	−2.62941	−	1.91038i	−0.0956941	−	0.0695258i
$756$		0			0
$757$	4.40237	−	13.5491i	0.160007	−	0.492450i	−0.838627	−	0.544706i	$-0.816641\pi$
$757$	4.40237	−	13.5491i	0.160007	−	0.492450i	0.998634	+	0.0522559i	$0.0166411\pi$
$758$		0			0
$759$	−4.79987	+	14.7725i	−0.174224	+	0.536207i
$760$		0			0
$761$	−11.7771	−	36.2461i	−0.426918	−	1.31392i	−0.901145	−	0.433517i	$-0.857272\pi$
$761$	−11.7771	−	36.2461i	−0.426918	−	1.31392i	0.474227	−	0.880403i	$-0.342728\pi$
$762$		0			0
$763$	1.72753	−	5.31679i	0.0625408	−	0.192481i
$764$		0			0
$765$	−4.36623			−0.157861
$766$		0			0
$767$	−27.1452	+	19.7221i	−0.980155	+	0.712124i
$768$		0			0
$769$	−39.3236	−	28.5702i	−1.41804	−	1.03027i	−0.992091	−	0.125525i	$-0.959939\pi$
$769$	−39.3236	−	28.5702i	−1.41804	−	1.03027i	−0.425954	−	0.904745i	$-0.640061\pi$
$770$		0			0
$771$	−6.74665	−	4.90173i	−0.242975	−	0.176531i
$772$		0			0
$773$	−0.743810	−	2.28921i	−0.0267530	−	0.0823372i	0.936789	−	0.349896i	$-0.113783\pi$
$773$	−0.743810	−	2.28921i	−0.0267530	−	0.0823372i	−0.963542	+	0.267559i	$0.913783\pi$
$774$		0			0
$775$	−24.2201	+	17.5969i	−0.870012	+	0.632100i
$776$		0			0
$777$	−0.943512	−	2.90383i	−0.0338483	−	0.104174i
$778$		0			0
$779$	31.1674	+	30.2949i	1.11669	+	1.08543i
$780$		0			0
$781$	4.52898	+	13.9388i	0.162060	+	0.498768i
$782$		0			0
$783$	15.8235	−	11.4965i	0.565487	−	0.410850i
$784$		0			0
$785$	−0.225266	−	0.693299i	−0.00804010	−	0.0247449i
$786$		0			0
$787$	−15.7840	−	11.4677i	−0.562639	−	0.408781i	0.269785	−	0.962921i	$-0.413047\pi$
$787$	−15.7840	−	11.4677i	−0.562639	−	0.408781i	−0.832424	+	0.554140i	$0.813047\pi$
$788$		0			0
$789$	1.55746	+	1.13156i	0.0554470	+	0.0402846i
$790$		0			0
$791$	−8.16453	+	5.93188i	−0.290297	+	0.210913i
$792$		0			0
$793$	43.3662			1.53998
$794$		0			0
$795$	0.0410033	−	0.126195i	0.00145424	−	0.00447568i
$796$		0			0
$797$	4.93592	+	15.1912i	0.174839	+	0.538100i	0.999626	−	0.0273439i	$-0.00870493\pi$
$797$	4.93592	+	15.1912i	0.174839	+	0.538100i	−0.824787	+	0.565444i	$0.808705\pi$
$798$		0			0
$799$	2.24582	−	6.91191i	0.0794513	−	0.244526i
$800$		0			0
$801$	7.04869	−	21.6936i	0.249053	−	0.766507i
$802$		0			0
$803$	53.5420	+	38.9005i	1.88946	+	1.37277i
$804$		0			0
$805$	4.89828	−	3.55881i	0.172642	−	0.125432i
$806$		0			0
$807$	3.16273	+	9.73389i	0.111333	+	0.342649i
$808$		0			0
$809$	10.9082	+	7.92527i	0.383512	+	0.278637i	0.762792	−	0.646644i	$-0.223828\pi$
$809$	10.9082	+	7.92527i	0.383512	+	0.278637i	−0.379280	+	0.925282i	$0.623828\pi$
$810$		0			0
$811$	13.9233			0.488914			0.244457	−	0.969660i	$-0.421390\pi$
$811$	13.9233			0.488914			0.244457	+	0.969660i	$0.421390\pi$
$812$		0			0
$813$	1.81035	−	5.57168i	0.0634916	−	0.195407i
$814$		0			0
$815$	7.17646	−	5.21400i	0.251380	−	0.182638i
$816$		0			0
$817$	−30.7334			−1.07523
$818$		0			0
$819$	10.5912			0.370088
$820$		0			0
$821$	−27.8587			−0.972276			−0.486138	−	0.873882i	$-0.661595\pi$
$821$	−27.8587			−0.972276			−0.486138	+	0.873882i	$0.661595\pi$
$822$		0			0
$823$	−2.91228			−0.101516			−0.0507578	−	0.998711i	$-0.516164\pi$
$823$	−2.91228			−0.101516			−0.0507578	+	0.998711i	$0.516164\pi$
$824$		0			0
$825$	6.29942	−	4.57680i	0.219318	−	0.159344i
$826$		0			0
$827$	6.09908	−	18.7710i	0.212086	−	0.652733i	−0.787262	−	0.616619i	$-0.788502\pi$
$827$	6.09908	−	18.7710i	0.212086	−	0.652733i	0.999348	−	0.0361143i	$-0.0114980\pi$
$828$		0			0
$829$	−8.34109			−0.289698			−0.144849	−	0.989454i	$-0.546270\pi$
$829$	−8.34109			−0.289698			−0.144849	+	0.989454i	$0.546270\pi$
$830$		0			0
$831$	4.29023	+	3.11704i	0.148826	+	0.108129i
$832$		0			0
$833$	−0.699847	−	2.15391i	−0.0242482	−	0.0746284i
$834$		0			0
$835$	0.284226	−	0.206503i	0.00983606	−	0.00714631i
$836$		0			0
$837$	−10.1972	−	7.40867i	−0.352465	−	0.256081i
$838$		0			0
$839$	1.69668	−	5.22184i	0.0585759	−	0.180278i	−0.917487	−	0.397765i	$-0.869786\pi$
$839$	1.69668	−	5.22184i	0.0585759	−	0.180278i	0.976063	+	0.217487i	$0.0697860\pi$
$840$		0			0
$841$	23.1644	−	71.2926i	0.798771	−	2.45836i
$842$		0			0
$843$	−0.0636606	−	0.195927i	−0.00219259	−	0.00674809i
$844$		0			0
$845$	−0.0808692	+	0.248890i	−0.00278199	+	0.00856207i
$846$		0			0
$847$	−16.5731			−0.569459
$848$		0			0
$849$	1.31821	−	0.957735i	0.0452408	−	0.0328694i
$850$		0			0
$851$	68.9825	+	50.1187i	2.36469	+	1.71805i
$852$		0			0
$853$	29.0251	+	21.0880i	0.993801	+	0.722039i	0.960750	−	0.277415i	$-0.0894777\pi$
$853$	29.0251	+	21.0880i	0.993801	+	0.722039i	0.0330508	+	0.999454i	$0.489478\pi$
$854$		0			0
$855$	−4.04403	−	12.4462i	−0.138303	−	0.425653i
$856$		0			0
$857$	9.95566	−	7.23321i	0.340079	−	0.247082i	−0.404616	−	0.914487i	$-0.632595\pi$
$857$	9.95566	−	7.23321i	0.340079	−	0.247082i	0.744695	+	0.667405i	$0.232595\pi$
$858$		0			0
$859$	2.44486	+	7.52451i	0.0834175	+	0.256733i	0.984063	−	0.177823i	$-0.0569054\pi$
$859$	2.44486	+	7.52451i	0.0834175	+	0.256733i	−0.900645	+	0.434556i	$0.856905\pi$
$860$		0			0
$861$	1.49434	+	1.45251i	0.0509269	+	0.0495012i
$862$		0			0
$863$	9.17942	+	28.2513i	0.312471	+	0.961687i	0.976783	+	0.214231i	$0.0687247\pi$
$863$	9.17942	+	28.2513i	0.312471	+	0.961687i	−0.664312	+	0.747455i	$0.731275\pi$
$864$		0			0
$865$	2.29009	−	1.66385i	0.0778654	−	0.0565725i
$866$		0			0
$867$	−1.19388	−	3.67438i	−0.0405462	−	0.124788i
$868$		0			0
$869$	30.8011	+	22.3783i	1.04485	+	0.759131i
$870$		0			0
$871$	30.3575	+	22.0560i	1.02863	+	0.747341i
$872$		0			0
$873$	20.0229	−	14.5475i	0.677671	−	0.492357i
$874$		0			0
$875$	−6.36594			−0.215208
$876$		0			0
$877$	−5.14151	+	15.8239i	−0.173616	+	0.534336i	−0.999568	−	0.0294053i	$-0.990639\pi$
$877$	−5.14151	+	15.8239i	−0.173616	+	0.534336i	0.825951	+	0.563742i	$0.190639\pi$
$878$		0			0
$879$	2.13572	+	6.57306i	0.0720359	+	0.221704i
$880$		0			0
$881$	1.19118	−	3.66609i	0.0401320	−	0.123514i	−0.928983	−	0.370122i	$-0.879316\pi$
$881$	1.19118	−	3.66609i	0.0401320	−	0.123514i	0.969115	+	0.246608i	$0.0793160\pi$
$882$		0			0
$883$	−1.95612	+	6.02032i	−0.0658287	+	0.202600i	−0.978561	−	0.205959i	$-0.933969\pi$
$883$	−1.95612	+	6.02032i	−0.0658287	+	0.202600i	0.912732	+	0.408559i	$0.133969\pi$
$884$		0			0
$885$	1.60815	+	1.16839i	0.0540572	+	0.0392749i
$886$		0			0
$887$	−40.2690	+	29.2572i	−1.35210	+	0.982359i	−0.353198	+	0.935549i	$0.614906\pi$
$887$	−40.2690	+	29.2572i	−1.35210	+	0.982359i	−0.998904	+	0.0468105i	$0.985094\pi$
$888$		0			0
$889$	0.300972	+	0.926296i	0.0100943	+	0.0310670i
$890$		0			0
$891$	−34.2313	−	24.8705i	−1.14679	−	0.833193i
$892$		0			0
$893$	21.7830			0.728940
$894$		0			0
$895$	−0.549701	+	1.69181i	−0.0183745	+	0.0565508i
$896$		0			0
$897$	8.75787	−	6.36296i	0.292417	−	0.212453i
$898$		0			0
$899$	−66.9959			−2.23444
$900$		0			0
$901$	1.38608			0.0461769
$902$		0			0
$903$	−1.47353			−0.0490359
$904$		0			0
$905$	4.20220			0.139686
$906$		0			0
$907$	36.0248	−	26.1735i	1.19618	−	0.869078i	0.202279	−	0.979328i	$-0.435165\pi$
$907$	36.0248	−	26.1735i	1.19618	−	0.869078i	0.993904	+	0.110250i	$0.0351653\pi$
$908$		0			0
$909$	15.6171	−	48.0644i	0.517986	−	1.59420i
$910$		0			0
$911$	−16.5429			−0.548091			−0.274045	−	0.961717i	$-0.588362\pi$
$911$	−16.5429			−0.548091			−0.274045	+	0.961717i	$0.588362\pi$
$912$		0			0
$913$	25.1486	+	18.2715i	0.832298	+	0.604700i
$914$		0			0
$915$	−0.793902	−	2.44338i	−0.0262456	−	0.0807757i
$916$		0			0
$917$	6.73044	−	4.88995i	0.222259	−	0.161481i
$918$		0			0
$919$	5.05517	+	3.67279i	0.166755	+	0.121154i	0.668033	−	0.744132i	$-0.267137\pi$
$919$	5.05517	+	3.67279i	0.166755	+	0.121154i	−0.501278	+	0.865286i	$0.667137\pi$
$920$		0			0
$921$	−0.227780	+	0.701033i	−0.00750559	+	0.0230998i
$922$		0			0
$923$	3.15642	−	9.71445i	0.103895	−	0.319755i
$924$		0			0
$925$	−13.2087	−	40.6522i	−0.434299	−	1.33664i
$926$		0			0
$927$	2.95962	−	9.10879i	0.0972068	−	0.299172i
$928$		0			0
$929$	32.2468			1.05798			0.528991	−	0.848627i	$-0.322571\pi$
$929$	32.2468			1.05798			0.528991	+	0.848627i	$0.322571\pi$
$930$		0			0
$931$	5.49166	−	3.98993i	0.179982	−	0.130765i
$932$		0			0
$933$	−1.17439	−	0.853246i	−0.0384479	−	0.0279340i
$934$		0			0
$935$	−6.40909	−	4.65648i	−0.209600	−	0.152283i
$936$		0			0
$937$	3.96352	+	12.1985i	0.129483	+	0.398506i	0.994691	−	0.102906i	$-0.0328140\pi$
$937$	3.96352	+	12.1985i	0.129483	+	0.398506i	−0.865209	+	0.501412i	$0.832814\pi$
$938$		0			0
$939$	0.155991	−	0.113334i	0.00509056	−	0.00369851i
$940$		0			0
$941$	−2.63197	−	8.10036i	−0.0857997	−	0.264064i	0.898947	−	0.438057i	$-0.144333\pi$
$941$	−2.63197	−	8.10036i	−0.0857997	−	0.264064i	−0.984747	+	0.173993i	$0.944333\pi$
$942$		0			0
$943$	−57.6041	−	8.28723i	−1.87585	−	0.269869i
$944$		0			0
$945$	−0.394882	−	1.21532i	−0.0128455	−	0.0395345i
$946$		0			0
$947$	−6.70983	+	4.87498i	−0.218040	+	0.158415i	−0.691444	−	0.722430i	$-0.743025\pi$
$947$	−6.70983	+	4.87498i	−0.218040	+	0.158415i	0.473404	+	0.880845i	$0.343025\pi$
$948$		0			0
$949$	−14.2532	−	43.8669i	−0.462679	−	1.42398i
$950$		0			0
$951$	−5.70933	−	4.14807i	−0.185138	−	0.134510i
$952$		0			0
$953$	−3.89974	−	2.83333i	−0.126325	−	0.0917806i	0.522829	−	0.852438i	$-0.324877\pi$
$953$	−3.89974	−	2.83333i	−0.126325	−	0.0917806i	−0.649154	+	0.760657i	$0.724877\pi$
$954$		0			0
$955$	1.06894	−	0.776633i	0.0345902	−	0.0251313i
$956$		0			0
$957$	17.4250			0.563270
$958$		0			0
$959$	5.48155	−	16.8705i	0.177009	−	0.544776i
$960$		0			0
$961$	3.76202	+	11.5783i	0.121356	+	0.373494i
$962$		0			0
$963$	−11.6998	+	36.0081i	−0.377019	+	1.16035i
$964$		0			0
$965$	−0.625608	+	1.92542i	−0.0201390	+	0.0619816i
$966$		0			0
$967$	−4.57445	−	3.32353i	−0.147104	−	0.106878i	0.511799	−	0.859105i	$-0.328979\pi$
$967$	−4.57445	−	3.32353i	−0.147104	−	0.106878i	−0.658903	+	0.752228i	$0.728979\pi$
$968$		0			0
$969$	−4.04779	+	2.94089i	−0.130034	+	0.0944751i
$970$		0			0
$971$	9.00083	+	27.7017i	0.288850	+	0.888990i	0.985218	+	0.171305i	$0.0547983\pi$
$971$	9.00083	+	27.7017i	0.288850	+	0.888990i	−0.696368	+	0.717685i	$0.745202\pi$
$972$		0			0
$973$	15.0593	+	10.9412i	0.482780	+	0.350760i
$974$		0			0
$975$	−5.42671			−0.173794
$976$		0			0
$977$	−9.33223	+	28.7217i	−0.298565	+	0.918887i	0.683436	+	0.730010i	$0.260485\pi$
$977$	−9.33223	+	28.7217i	−0.298565	+	0.918887i	−0.982001	+	0.188877i	$0.939515\pi$
$978$		0			0
$979$	33.4824	−	24.3264i	1.07010	−	0.777475i
$980$		0			0
$981$	16.1791			0.516558
$982$		0			0
$983$	−13.5835			−0.433246			−0.216623	−	0.976255i	$-0.569504\pi$
$983$	−13.5835			−0.433246			−0.216623	+	0.976255i	$0.569504\pi$
$984$		0			0
$985$	11.8645			0.378035
$986$		0			0
$987$	1.04440			0.0332435
$988$		0			0
$989$	33.2914	−	24.1876i	1.05861	−	0.769122i
$990$		0			0
$991$	8.27646	−	25.4723i	0.262910	−	0.809155i	−0.729257	−	0.684240i	$-0.760134\pi$
$991$	8.27646	−	25.4723i	0.262910	−	0.809155i	0.992167	−	0.124915i	$-0.0398659\pi$
$992$		0			0
$993$	−8.51749			−0.270294
$994$		0			0
$995$	6.80307	+	4.94272i	0.215672	+	0.156695i
$996$		0			0
$997$	9.26423	+	28.5124i	0.293401	+	0.902995i	0.983754	+	0.179523i	$0.0574553\pi$
$997$	9.26423	+	28.5124i	0.293401	+	0.902995i	−0.690353	+	0.723473i	$0.742545\pi$
$998$		0			0
$999$	14.5592	−	10.5779i	0.460634	−	0.334670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.141.3	yes	24
41.16	even	5	inner	1148.2.n.e.57.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.57.3	✓	24	41.16	even	5	inner
1148.2.n.e.141.3	yes	24	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.325457 q^{3} +(0.538931 - 0.391556i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.89408 q^{9} +O(q^{10})\)	\(q+0.325457 q^{3} +(0.538931 - 0.391556i) q^{5} +(-0.309017 + 0.951057i) q^{7} -2.89408 q^{9} +(-4.24816 - 3.08647i) q^{11} +(1.13089 + 3.48051i) q^{13} +(0.175399 - 0.127435i) q^{15} +(1.83222 + 1.33119i) q^{17} +(-2.09763 + 6.45584i) q^{19} +(-0.100572 + 0.309528i) q^{21} +(-2.80862 - 8.64404i) q^{23} +(-1.40795 + 4.33324i) q^{25} -1.91827 q^{27} +(-8.24886 + 5.99315i) q^{29} +(5.31581 + 3.86216i) q^{31} +(-1.38259 - 1.00451i) q^{33} +(0.205853 + 0.633552i) q^{35} +(-7.58977 + 5.51429i) q^{37} +(0.368055 + 1.13276i) q^{39} +(2.82568 - 5.74591i) q^{41} +(1.39909 + 4.30597i) q^{43} +(-1.55971 + 1.13319i) q^{45} +(-0.991640 - 3.05195i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.596310 + 0.433244i) q^{51} +(0.495136 - 0.359737i) q^{53} -3.49799 q^{55} +(-0.682688 + 2.10110i) q^{57} +(2.83322 + 8.71976i) q^{59} +(3.66183 - 11.2699i) q^{61} +(0.894319 - 2.75243i) q^{63} +(1.97229 + 1.43295i) q^{65} +(8.29526 - 6.02686i) q^{67} +(-0.914085 - 2.81326i) q^{69} +(-2.25805 - 1.64057i) q^{71} -12.6036 q^{73} +(-0.458229 + 1.41028i) q^{75} +(4.24816 - 3.08647i) q^{77} -7.25045 q^{79} +8.05792 q^{81} -5.91989 q^{83} +1.50868 q^{85} +(-2.68465 + 1.95051i) q^{87} +(-2.43556 + 7.49588i) q^{89} -3.65962 q^{91} +(1.73007 + 1.25697i) q^{93} +(1.39735 + 4.30059i) q^{95} +(-6.91856 + 5.02663i) q^{97} +(12.2945 + 8.93247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more