LMFDB - Embedded newform 425.2.m.e.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	425.151
Dual form			425.2.m.e.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.176012 - 0.176012i) q^{2} +(-0.629010 - 1.51856i) q^{3} -1.93804i q^{4} +(-0.156572 + 0.377999i) q^{6} +(-1.32215 - 0.547653i) q^{7} +(-0.693142 + 0.693142i) q^{8} +(0.210935 - 0.210935i) q^{9} +O(q^{10})$	\(q+(-0.176012 - 0.176012i) q^{2} +(-0.629010 - 1.51856i) q^{3} -1.93804i q^{4} +(-0.156572 + 0.377999i) q^{6} +(-1.32215 - 0.547653i) q^{7} +(-0.693142 + 0.693142i) q^{8} +(0.210935 - 0.210935i) q^{9} +(1.03080 - 2.48857i) q^{11} +(-2.94304 + 1.21905i) q^{12} +0.174664i q^{13} +(0.136321 + 0.329108i) q^{14} -3.63208 q^{16} +(-3.44088 - 2.27165i) q^{17} -0.0742541 q^{18} +(2.69404 + 2.69404i) q^{19} +2.35225i q^{21} +(-0.619452 + 0.256585i) q^{22} +(-1.05544 + 2.54807i) q^{23} +(1.48857 + 0.616588i) q^{24} +(0.0307430 - 0.0307430i) q^{26} +(-5.00869 - 2.07467i) q^{27} +(-1.06137 + 2.56238i) q^{28} +(-5.94408 + 2.46212i) q^{29} +(-0.188417 - 0.454879i) q^{31} +(2.02557 + 2.02557i) q^{32} -4.42745 q^{33} +(0.205798 + 1.00547i) q^{34} +(-0.408800 - 0.408800i) q^{36} +(2.19772 + 5.30576i) q^{37} -0.948365i q^{38} +(0.265239 - 0.109866i) q^{39} +(5.54000 + 2.29474i) q^{41} +(0.414025 - 0.414025i) q^{42} +(8.00004 - 8.00004i) q^{43} +(-4.82296 - 1.99773i) q^{44} +(0.634261 - 0.262720i) q^{46} -2.65291i q^{47} +(2.28461 + 5.51554i) q^{48} +(-3.50159 - 3.50159i) q^{49} +(-1.28530 + 6.65408i) q^{51} +0.338506 q^{52} +(-8.73501 - 8.73501i) q^{53} +(0.516423 + 1.24676i) q^{54} +(1.29604 - 0.536837i) q^{56} +(2.39649 - 5.78565i) q^{57} +(1.47959 + 0.612867i) q^{58} +(5.72232 - 5.72232i) q^{59} +(-6.41902 - 2.65884i) q^{61} +(-0.0469005 + 0.113228i) q^{62} +(-0.394407 + 0.163369i) q^{63} +6.55110i q^{64} +(0.779283 + 0.779283i) q^{66} +12.3901 q^{67} +(-4.40254 + 6.66855i) q^{68} +4.53329 q^{69} +(-4.67878 - 11.2956i) q^{71} +0.292415i q^{72} +(14.4714 - 5.99425i) q^{73} +(0.547052 - 1.32070i) q^{74} +(5.22115 - 5.22115i) q^{76} +(-2.72575 + 2.72575i) q^{77} +(-0.0660229 - 0.0273476i) q^{78} +(4.94031 - 11.9270i) q^{79} +8.01609i q^{81} +(-0.571204 - 1.37901i) q^{82} +(6.06390 + 6.06390i) q^{83} +4.55876 q^{84} -2.81621 q^{86} +(7.47777 + 7.47777i) q^{87} +(1.01044 + 2.43943i) q^{88} +11.4907i q^{89} +(0.0956555 - 0.230933i) q^{91} +(4.93826 + 2.04549i) q^{92} +(-0.572247 + 0.572247i) q^{93} +(-0.466944 + 0.466944i) q^{94} +(1.80186 - 4.35007i) q^{96} +(-2.12392 + 0.879757i) q^{97} +1.23264i q^{98} +(-0.307495 - 0.742359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9}+O(q^{10}) $ 24 * q + 8 * q^9	$ 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56} + 48 q^{59} + 16 q^{61} - 96 q^{66} - 32 q^{69} + 16 q^{71} + 64 q^{74} - 24 q^{76} + 72 q^{79} + 96 q^{84} - 8 q^{91} + 40 q^{94} + 96 q^{96} + 80 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.176012	−	0.176012i	−0.124459	−	0.124459i	0.642134	−	0.766593i	$-0.278049\pi$
$2$	−0.176012	−	0.176012i	−0.124459	−	0.124459i	−0.766593	+	0.642134i	$0.778049\pi$
$3$	−0.629010	−	1.51856i	−0.363159	−	0.876744i	−0.994834	−	0.101511i	$-0.967632\pi$
$3$	−0.629010	−	1.51856i	−0.363159	−	0.876744i	0.631675	−	0.775233i	$-0.282368\pi$
$4$		−	1.93804i		−	0.969020i
$5$		0			0
$5$		0			0
$6$	−0.156572	+	0.377999i	−0.0639203	+	0.154317i
$7$	−1.32215	−	0.547653i	−0.499726	−	0.206993i	0.118559	−	0.992947i	$-0.462172\pi$
$7$	−1.32215	−	0.547653i	−0.499726	−	0.206993i	−0.618286	+	0.785954i	$0.712172\pi$
$8$	−0.693142	+	0.693142i	−0.245063	+	0.245063i
$9$	0.210935	−	0.210935i	0.0703116	−	0.0703116i
$10$		0			0
$11$	1.03080	−	2.48857i	0.310798	−	0.750333i	−0.688878	−	0.724878i	$-0.741896\pi$
$11$	1.03080	−	2.48857i	0.310798	−	0.750333i	0.999676	−	0.0254558i	$-0.00810370\pi$
$12$	−2.94304	+	1.21905i	−0.849582	+	0.351908i
$13$			0.174664i			0.0484432i	0.999707	+	0.0242216i	$0.00771073\pi$
$13$			0.174664i			0.0484432i	−0.999707	+	0.0242216i	$0.992289\pi$
$14$	0.136321	+	0.329108i	0.0364333	+	0.0879578i
$15$		0			0
$16$	−3.63208			−0.908019
$17$	−3.44088	−	2.27165i	−0.834535	−	0.550955i
$17$	−3.44088	−	2.27165i	−0.834535	−	0.550955i
$18$	−0.0742541			−0.0175019
$19$	2.69404	+	2.69404i	0.618055	+	0.618055i	0.945032	−	0.326978i	$-0.106030\pi$
$19$	2.69404	+	2.69404i	0.618055	+	0.618055i	−0.326978	+	0.945032i	$0.606030\pi$
$20$		0			0
$21$			2.35225i			0.513304i
$22$	−0.619452	+	0.256585i	−0.132068	+	0.0547042i
$23$	−1.05544	+	2.54807i	−0.220075	+	0.531309i	−0.994900	−	0.100867i	$-0.967838\pi$
$23$	−1.05544	+	2.54807i	−0.220075	+	0.531309i	0.774825	+	0.632176i	$0.217838\pi$
$24$	1.48857	+	0.616588i	0.303854	+	0.125860i
$25$		0			0
$26$	0.0307430	−	0.0307430i	0.00602920	−	0.00602920i
$27$	−5.00869	−	2.07467i	−0.963923	−	0.399270i
$28$	−1.06137	+	2.56238i	−0.200581	+	0.484245i
$29$	−5.94408	+	2.46212i	−1.10379	+	0.457204i	−0.858794	−	0.512321i	$-0.828786\pi$
$29$	−5.94408	+	2.46212i	−1.10379	+	0.457204i	−0.244994	+	0.969525i	$0.578786\pi$
$30$		0			0
$31$	−0.188417	−	0.454879i	−0.0338407	−	0.0816987i	0.906056	−	0.423159i	$-0.139079\pi$
$31$	−0.188417	−	0.454879i	−0.0338407	−	0.0816987i	−0.939896	+	0.341460i	$0.889079\pi$
$32$	2.02557	+	2.02557i	0.358074	+	0.358074i
$33$	−4.42745			−0.770719
$34$	0.205798	+	1.00547i	0.0352941	+	0.172437i
$35$		0			0
$36$	−0.408800	−	0.408800i	−0.0681333	−	0.0681333i
$37$	2.19772	+	5.30576i	0.361302	+	0.872261i	0.995110	+	0.0987704i	$0.0314910\pi$
$37$	2.19772	+	5.30576i	0.361302	+	0.872261i	−0.633808	+	0.773490i	$0.718509\pi$
$38$		−	0.948365i		−	0.153845i
$39$	0.265239	−	0.109866i	0.0424723	−	0.0175926i
$40$		0			0
$41$	5.54000	+	2.29474i	0.865203	+	0.358379i	0.770740	−	0.637150i	$-0.219887\pi$
$41$	5.54000	+	2.29474i	0.865203	+	0.358379i	0.0944627	+	0.995528i	$0.469887\pi$
$42$	0.414025	−	0.414025i	0.0638854	−	0.0638854i
$43$	8.00004	−	8.00004i	1.22000	−	1.22000i	0.252363	−	0.967633i	$-0.418792\pi$
$43$	8.00004	−	8.00004i	1.22000	−	1.22000i	0.967633	−	0.252363i	$-0.0812076\pi$
$44$	−4.82296	−	1.99773i	−0.727088	−	0.301170i
$45$		0			0
$46$	0.634261	−	0.262720i	0.0935167	−	0.0387359i
$47$		−	2.65291i		−	0.386967i	−0.981104	−	0.193483i	$-0.938021\pi$
$47$		−	2.65291i		−	0.386967i	0.981104	−	0.193483i	$-0.0619786\pi$
$48$	2.28461	+	5.51554i	0.329756	+	0.796100i
$49$	−3.50159	−	3.50159i	−0.500227	−	0.500227i
$50$		0			0
$51$	−1.28530	+	6.65408i	−0.179977	+	0.931758i
$52$	0.338506			0.0469424
$53$	−8.73501	−	8.73501i	−1.19985	−	1.19985i	−0.974212	−	0.225633i	$-0.927555\pi$
$53$	−8.73501	−	8.73501i	−1.19985	−	1.19985i	−0.225633	−	0.974212i	$-0.572445\pi$
$54$	0.516423	+	1.24676i	0.0702763	+	0.169662i
$55$		0			0
$56$	1.29604	−	0.536837i	0.173191	−	0.0717379i
$57$	2.39649	−	5.78565i	0.317423	−	0.766328i
$58$	1.47959	+	0.612867i	0.194280	+	0.0804733i
$59$	5.72232	−	5.72232i	0.744982	−	0.744982i	−0.228550	−	0.973532i	$-0.573398\pi$
$59$	5.72232	−	5.72232i	0.744982	−	0.744982i	0.973532	+	0.228550i	$0.0733984\pi$
$60$		0			0
$61$	−6.41902	−	2.65884i	−0.821871	−	0.340430i	−0.0681914	−	0.997672i	$-0.521723\pi$
$61$	−6.41902	−	2.65884i	−0.821871	−	0.340430i	−0.753679	+	0.657242i	$0.771723\pi$
$62$	−0.0469005	+	0.113228i	−0.00595637	+	0.0143799i
$63$	−0.394407	+	0.163369i	−0.0496906	+	0.0205825i
$64$			6.55110i			0.818888i
$65$		0			0
$66$	0.779283	+	0.779283i	0.0959231	+	0.0959231i
$67$	12.3901			1.51369			0.756845	−	0.653594i	$-0.226740\pi$
$67$	12.3901			1.51369			0.756845	+	0.653594i	$0.226740\pi$
$68$	−4.40254	+	6.66855i	−0.533886	+	0.808681i
$69$	4.53329			0.545744
$70$		0			0
$71$	−4.67878	−	11.2956i	−0.555269	−	1.34054i	−0.913474	−	0.406896i	$-0.866611\pi$
$71$	−4.67878	−	11.2956i	−0.555269	−	1.34054i	0.358205	−	0.933643i	$-0.383389\pi$
$72$			0.292415i			0.0344615i
$73$	14.4714	−	5.99425i	1.69375	−	0.701574i	0.693920	−	0.720052i	$-0.255882\pi$
$73$	14.4714	−	5.99425i	1.69375	−	0.701574i	0.999829	+	0.0184781i	$0.00588211\pi$
$74$	0.547052	−	1.32070i	0.0635935	−	0.153528i
$75$		0			0
$76$	5.22115	−	5.22115i	0.598907	−	0.598907i
$77$	−2.72575	+	2.72575i	−0.310628	+	0.310628i
$78$	−0.0660229	−	0.0273476i	−0.00747562	−	0.00309650i
$79$	4.94031	−	11.9270i	0.555828	−	1.34189i	−0.357214	−	0.934022i	$-0.616273\pi$
$79$	4.94031	−	11.9270i	0.555828	−	1.34189i	0.913042	−	0.407865i	$-0.133727\pi$
$80$		0			0
$81$			8.01609i			0.890677i
$82$	−0.571204	−	1.37901i	−0.0630789	−	0.152286i
$83$	6.06390	+	6.06390i	0.665600	+	0.665600i	0.956694	−	0.291094i	$-0.0940194\pi$
$83$	6.06390	+	6.06390i	0.665600	+	0.665600i	−0.291094	+	0.956694i	$0.594019\pi$
$84$	4.55876			0.497401
$85$		0			0
$86$	−2.81621			−0.303679
$87$	7.47777	+	7.47777i	0.801702	+	0.801702i
$88$	1.01044	+	2.43943i	0.107714	+	0.260044i
$89$			11.4907i			1.21801i	0.793165	+	0.609006i	$0.208432\pi$
$89$			11.4907i			1.21801i	−0.793165	+	0.609006i	$0.791568\pi$
$90$		0			0
$91$	0.0956555	−	0.230933i	0.0100274	−	0.0242083i
$92$	4.93826	+	2.04549i	0.514849	+	0.213257i
$93$	−0.572247	+	0.572247i	−0.0593393	+	0.0593393i
$94$	−0.466944	+	0.466944i	−0.0481616	+	0.0481616i
$95$		0			0
$96$	1.80186	−	4.35007i	0.183901	−	0.443977i
$97$	−2.12392	+	0.879757i	−0.215651	+	0.0893258i	−0.487894	−	0.872903i	$-0.662235\pi$
$97$	−2.12392	+	0.879757i	−0.215651	+	0.0893258i	0.272242	+	0.962229i	$0.412235\pi$
$98$			1.23264i			0.124516i
$99$	−0.307495	−	0.742359i	−0.0309044	−	0.0746099i
$100$		0			0
$101$	−0.890917			−0.0886495			−0.0443248	−	0.999017i	$-0.514114\pi$
$101$	−0.890917			−0.0886495			−0.0443248	+	0.999017i	$0.514114\pi$
$102$	1.39742	−	0.944970i	0.138366	−	0.0935660i
$103$	0.367137			0.0361751			0.0180875	−	0.999836i	$-0.494242\pi$
$103$	0.367137			0.0361751			0.0180875	+	0.999836i	$0.494242\pi$
$104$	−0.121067	−	0.121067i	−0.0118716	−	0.0118716i
$105$		0			0
$106$			3.07493i			0.298664i
$107$	6.14149	−	2.54389i	0.593720	−	0.245927i	−0.0655301	−	0.997851i	$-0.520874\pi$
$107$	6.14149	−	2.54389i	0.593720	−	0.245927i	0.659250	+	0.751924i	$0.270874\pi$
$108$	−4.02079	+	9.70705i	−0.386901	+	0.934061i
$109$	−8.16665	−	3.38274i	−0.782223	−	0.324007i	−0.0444107	−	0.999013i	$-0.514141\pi$
$109$	−8.16665	−	3.38274i	−0.782223	−	0.324007i	−0.737812	+	0.675006i	$0.764141\pi$
$110$		0			0
$111$	6.67475	−	6.67475i	0.633539	−	0.633539i
$112$	4.80216	+	1.98912i	0.453761	+	0.187954i
$113$	−2.18632	+	5.27825i	−0.205672	+	0.496536i	−0.992733	−	0.120339i	$-0.961602\pi$
$113$	−2.18632	+	5.27825i	−0.205672	+	0.496536i	0.787061	+	0.616875i	$0.211602\pi$
$114$	−1.44015	+	0.596531i	−0.134883	+	0.0558703i
$115$		0			0
$116$	4.77168	+	11.5199i	0.443040	+	1.06959i
$117$	0.0368428	+	0.0368428i	0.00340612	+	0.00340612i
$118$	−2.01439			−0.185440
$119$	3.30529	+	4.88787i	0.302995	+	0.448070i
$120$		0			0
$121$	2.64772	+	2.64772i	0.240702	+	0.240702i
$122$	0.661835	+	1.59781i	0.0599197	+	0.144659i
$123$		−	9.85627i		−	0.888710i
$124$	−0.881574	+	0.365160i	−0.0791676	+	0.0327923i
$125$		0			0
$126$	0.0981752	+	0.0406655i	0.00874614	+	0.00362277i
$127$	11.5590	−	11.5590i	1.02569	−	1.02569i	0.0260300	−	0.999661i	$-0.491713\pi$
$127$	11.5590	−	11.5590i	1.02569	−	1.02569i	0.999661	−	0.0260300i	$-0.00828653\pi$
$128$	5.20422	−	5.20422i	0.459992	−	0.459992i
$129$	−17.1807	−	7.11648i	−1.51268	−	0.626571i
$130$		0			0
$131$	−8.90518	+	3.68865i	−0.778049	+	0.322279i	−0.736128	−	0.676842i	$-0.763348\pi$
$131$	−8.90518	+	3.68865i	−0.778049	+	0.322279i	−0.0419214	+	0.999121i	$0.513348\pi$
$132$			8.58057i			0.746842i
$133$	−2.08653	−	5.03733i	−0.180925	−	0.436791i
$134$	−2.18080	−	2.18080i	−0.188393	−	0.188393i
$135$		0			0
$136$	3.95959	−	0.810442i	0.339532	−	0.0694949i
$137$	−6.60524			−0.564324			−0.282162	−	0.959367i	$-0.591052\pi$
$137$	−6.60524			−0.564324			−0.282162	+	0.959367i	$0.591052\pi$
$138$	−0.797913	−	0.797913i	−0.0679229	−	0.0679229i
$139$	1.75923	+	4.24715i	0.149216	+	0.360239i	0.980759	−	0.195221i	$-0.0625424\pi$
$139$	1.75923	+	4.24715i	0.149216	+	0.360239i	−0.831544	+	0.555459i	$0.812542\pi$
$140$		0			0
$141$	−4.02862	+	1.66871i	−0.339271	+	0.140531i
$142$	−1.16464	+	2.81168i	−0.0977340	+	0.235951i
$143$	0.434665	+	0.180044i	0.0363485	+	0.0150561i
$144$	−0.766131	+	0.766131i	−0.0638443	+	0.0638443i
$145$		0			0
$146$	−3.60220	−	1.49208i	−0.298120	−	0.123485i
$147$	−3.11485	+	7.51992i	−0.256909	+	0.620232i
$148$	10.2828	−	4.25926i	0.845238	−	0.350109i
$149$			11.6404i			0.953619i	0.879007	+	0.476810i	$0.158207\pi$
$149$			11.6404i			0.953619i	−0.879007	+	0.476810i	$0.841793\pi$
$150$		0			0
$151$	0.0974235	+	0.0974235i	0.00792821	+	0.00792821i	0.711060	−	0.703132i	$-0.248216\pi$
$151$	0.0974235	+	0.0974235i	0.00792821	+	0.00792821i	−0.703132	+	0.711060i	$0.748216\pi$
$152$	−3.73470			−0.302924
$153$	−1.20497	+	0.246631i	−0.0974160	+	0.0199390i
$154$	0.959530			0.0773211
$155$		0			0
$156$	−0.212924	−	0.514044i	−0.0170476	−	0.0411565i
$157$		−	9.66489i		−	0.771343i	−0.922636	−	0.385671i	$-0.873970\pi$
$157$		−	9.66489i		−	0.771343i	0.922636	−	0.385671i	$-0.126030\pi$
$158$	−2.96884	+	1.22973i	−0.236188	+	0.0978323i
$159$	−7.77027	+	18.7591i	−0.616222	+	1.48769i
$160$		0			0
$161$	2.79092	−	2.79092i	0.219955	−	0.219955i
$162$	1.41093	−	1.41093i	0.110853	−	0.110853i
$163$	−11.4699	−	4.75100i	−0.898394	−	0.372127i	−0.114792	−	0.993390i	$-0.536620\pi$
$163$	−11.4699	−	4.75100i	−0.898394	−	0.372127i	−0.783602	+	0.621263i	$0.786620\pi$
$164$	4.44730	−	10.7367i	0.347276	−	0.838399i
$165$		0			0
$166$		−	2.13464i		−	0.165680i
$167$	1.60248	+	3.86872i	0.124003	+	0.299371i	0.973675	−	0.227942i	$-0.0731997\pi$
$167$	1.60248	+	3.86872i	0.124003	+	0.299371i	−0.849671	+	0.527313i	$0.823200\pi$
$168$	−1.63045	−	1.63045i	−0.125792	−	0.125792i
$169$	12.9695			0.997653
$170$		0			0
$171$	1.13653			0.0869128
$172$	−15.5044	−	15.5044i	−1.18220	−	1.18220i
$173$	1.13080	+	2.73000i	0.0859733	+	0.207558i	0.961019	−	0.276483i	$-0.0891688\pi$
$173$	1.13080	+	2.73000i	0.0859733	+	0.207558i	−0.875046	+	0.484040i	$0.839169\pi$
$174$		−	2.63235i		−	0.199558i
$175$		0			0
$176$	−3.74395	+	9.03869i	−0.282211	+	0.681317i
$177$	−12.2891	−	5.09032i	−0.923706	−	0.382612i
$178$	2.02250	−	2.02250i	0.151593	−	0.151593i
$179$	16.4589	−	16.4589i	1.23019	−	1.23019i	0.266304	−	0.963889i	$-0.414197\pi$
$179$	16.4589	−	16.4589i	1.23019	−	1.23019i	0.963889	−	0.266304i	$-0.0858027\pi$
$180$		0			0
$181$	4.37037	−	10.5510i	0.324847	−	0.784250i	−0.674112	−	0.738629i	$-0.735474\pi$
$181$	4.37037	−	10.5510i	0.324847	−	0.784250i	0.998959	−	0.0456205i	$-0.0145265\pi$
$182$	−0.0574834	+	0.0238104i	−0.00426096	+	0.00176495i
$183$			11.4201i			0.844200i
$184$	−1.03460	−	2.49775i	−0.0762717	−	0.184136i
$185$		0			0
$186$	0.201445			0.0147706
$187$	−9.20002	+	6.22126i	−0.672772	+	0.454944i
$188$	−5.14145			−0.374978
$189$	5.48605	+	5.48605i	0.399052	+	0.399052i
$190$		0			0
$191$			3.08201i			0.223007i	0.993764	+	0.111503i	$0.0355666\pi$
$191$			3.08201i			0.223007i	−0.993764	+	0.111503i	$0.964433\pi$
$192$	9.94828	−	4.12071i	0.717955	−	0.297387i
$193$	6.11743	−	14.7688i	0.440343	−	1.06308i	−0.535486	−	0.844544i	$-0.679872\pi$
$193$	6.11743	−	14.7688i	0.440343	−	1.06308i	0.975829	−	0.218537i	$-0.0701284\pi$
$194$	0.528683	+	0.218988i	0.0379572	+	0.0157224i
$195$		0			0
$196$	−6.78621	+	6.78621i	−0.484729	+	0.484729i
$197$	−9.86109	−	4.08460i	−0.702573	−	0.291015i	0.00265412	−	0.999996i	$-0.499155\pi$
$197$	−9.86109	−	4.08460i	−0.702573	−	0.291015i	−0.705228	+	0.708981i	$0.749155\pi$
$198$	−0.0765412	+	0.184787i	−0.00543954	+	0.0131322i
$199$	−14.6337	+	6.06147i	−1.03735	+	0.429686i	−0.835362	−	0.549701i	$-0.814742\pi$
$199$	−14.6337	+	6.06147i	−1.03735	+	0.429686i	−0.201993	+	0.979387i	$0.564742\pi$
$200$		0			0
$201$	−7.79349	−	18.8152i	−0.549710	−	1.32712i
$202$	0.156812	+	0.156812i	0.0110333	+	0.0110333i
$203$	9.20737			0.646230
$204$	12.8959	+	2.49095i	0.902892	+	0.174402i
$205$		0			0
$206$	−0.0646205	−	0.0646205i	−0.00450232	−	0.00450232i
$207$	0.314846	+	0.760106i	0.0218833	+	0.0528310i
$208$		−	0.634394i		−	0.0439873i
$209$	9.48133	−	3.92729i	0.655837	−	0.271657i
$210$		0			0
$211$	−4.54512	−	1.88265i	−0.312899	−	0.129607i	0.220707	−	0.975340i	$-0.429164\pi$
$211$	−4.54512	−	1.88265i	−0.312899	−	0.129607i	−0.533606	+	0.845733i	$0.679164\pi$
$212$	−16.9288	+	16.9288i	−1.16267	+	1.16267i
$213$	−14.2101	+	14.2101i	−0.973658	+	0.973658i
$214$	−1.52873	−	0.633221i	−0.104502	−	0.0432861i
$215$		0			0
$216$	4.90977	−	2.03370i	0.334068	−	0.138375i
$217$			0.704606i			0.0478318i
$218$	0.842025	+	2.03283i	0.0570292	+	0.137681i
$219$	−18.2053	−	18.2053i	−1.23020	−	1.23020i
$220$		0			0
$221$	0.396776	−	0.600998i	0.0266900	−	0.0404275i
$222$	−2.34967			−0.157700
$223$	7.10210	+	7.10210i	0.475592	+	0.475592i	0.903719	−	0.428127i	$-0.140826\pi$
$223$	7.10210	+	7.10210i	0.475592	+	0.475592i	−0.428127	+	0.903719i	$0.640826\pi$
$224$	−1.56880	−	3.78743i	−0.104820	−	0.253058i
$225$		0			0
$226$	1.31385	−	0.544216i	0.0873963	−	0.0362007i
$227$	−1.71341	+	4.13654i	−0.113723	+	0.274552i	−0.970485	−	0.241160i	$-0.922472\pi$
$227$	−1.71341	+	4.13654i	−0.113723	+	0.274552i	0.856762	+	0.515711i	$0.172472\pi$
$228$	−11.2128	−	4.64450i	−0.742587	−	0.307589i
$229$	0.847088	−	0.847088i	0.0559771	−	0.0559771i	−0.678564	−	0.734541i	$-0.737397\pi$
$229$	0.847088	−	0.847088i	0.0559771	−	0.0559771i	0.734541	+	0.678564i	$0.237397\pi$
$230$		0			0
$231$	5.85376	+	2.42471i	0.385149	+	0.159534i
$232$	2.41349	−	5.82669i	0.158454	−	0.382541i
$233$	−23.5168	+	9.74096i	−1.54063	+	0.638152i	−0.981592	−	0.190987i	$-0.938831\pi$
$233$	−23.5168	+	9.74096i	−1.54063	+	0.638152i	−0.559042	+	0.829139i	$0.688831\pi$
$234$		−	0.0129695i		−	0.000847845i
$235$		0			0
$236$	−11.0901	−	11.0901i	−0.721903	−	0.721903i
$237$	−21.2194			−1.37835
$238$	0.278553	−	1.44209i	0.0180559	−	0.0934770i
$239$	−6.21407			−0.401955			−0.200977	−	0.979596i	$-0.564412\pi$
$239$	−6.21407			−0.401955			−0.200977	+	0.979596i	$0.564412\pi$
$240$		0			0
$241$	10.2576	+	24.7640i	0.660750	+	1.59519i	0.796631	+	0.604467i	$0.206614\pi$
$241$	10.2576	+	24.7640i	0.660750	+	1.59519i	−0.135880	+	0.990725i	$0.543386\pi$
$242$		−	0.932062i		−	0.0599152i
$243$	−2.85312	+	1.18180i	−0.183028	+	0.0758126i
$244$	−5.15294	+	12.4403i	−0.329883	+	0.796409i
$245$		0			0
$246$	−1.73482	+	1.73482i	−0.110608	+	0.110608i
$247$	−0.470552	+	0.470552i	−0.0299405	+	0.0299405i
$248$	0.445895	+	0.184696i	0.0283144	+	0.0117282i
$249$	5.39417	−	13.0227i	0.341842	−	0.825279i
$250$		0			0
$251$			10.6052i			0.669394i	0.942326	+	0.334697i	$0.108634\pi$
$251$			10.6052i			0.669394i	−0.942326	+	0.334697i	$0.891366\pi$
$252$	0.316615	+	0.764376i	0.0199449	+	0.0481512i
$253$	5.25310	+	5.25310i	0.330260	+	0.330260i
$254$	−4.06903			−0.255313
$255$		0			0
$256$	11.2702			0.704387
$257$	1.08911	+	1.08911i	0.0679369	+	0.0679369i	0.740259	−	0.672322i	$-0.234703\pi$
$257$	1.08911	+	1.08911i	0.0679369	+	0.0679369i	−0.672322	+	0.740259i	$0.734703\pi$
$258$	1.77142	+	4.27659i	0.110284	+	0.266249i
$259$		−	8.21860i		−	0.510679i
$260$		0			0
$261$	−0.734467	+	1.77316i	−0.0454624	+	0.109756i
$262$	2.21666	+	0.918172i	0.136946	+	0.0567249i
$263$	−0.301535	+	0.301535i	−0.0185935	+	0.0185935i	−0.716342	−	0.697749i	$-0.754185\pi$
$263$	−0.301535	+	0.301535i	−0.0185935	+	0.0185935i	0.697749	+	0.716342i	$0.254185\pi$
$264$	3.06885	−	3.06885i	0.188875	−	0.188875i
$265$		0			0
$266$	−0.519375	+	1.25388i	−0.0318449	+	0.0768805i
$267$	17.4494	−	7.22777i	1.06789	−	0.442333i
$268$		−	24.0125i		−	1.46680i
$269$	6.54570	+	15.8027i	0.399098	+	0.963508i	0.987880	+	0.155217i	$0.0496075\pi$
$269$	6.54570	+	15.8027i	0.399098	+	0.963508i	−0.588782	+	0.808292i	$0.700392\pi$
$270$		0			0
$271$	16.0704			0.976208			0.488104	−	0.872785i	$-0.337689\pi$
$271$	16.0704			0.976208			0.488104	+	0.872785i	$0.337689\pi$
$272$	12.4975	+	8.25079i	0.757774	+	0.500278i
$273$	−0.410855			−0.0248661
$274$	1.16260	+	1.16260i	0.0702353	+	0.0702353i
$275$		0			0
$276$		−	8.78570i		−	0.528837i
$277$	−15.4868	+	6.41483i	−0.930510	+	0.385430i	−0.795872	−	0.605465i	$-0.792987\pi$
$277$	−15.4868	+	6.41483i	−0.930510	+	0.385430i	−0.134638	+	0.990895i	$0.542987\pi$
$278$	0.437904	−	1.05719i	0.0262637	−	0.0634063i
$279$	−0.135694	−	0.0562061i	−0.00812376	−	0.00336497i
$280$		0			0
$281$	5.54254	−	5.54254i	0.330640	−	0.330640i	−0.522189	−	0.852830i	$-0.674885\pi$
$281$	5.54254	−	5.54254i	0.330640	−	0.330640i	0.852830	+	0.522189i	$0.174885\pi$
$282$	1.00280	+	0.415372i	0.0597157	+	0.0247350i
$283$	2.51826	−	6.07963i	0.149695	−	0.361396i	−0.831189	−	0.555991i	$-0.812339\pi$
$283$	2.51826	−	6.07963i	0.149695	−	0.361396i	0.980884	+	0.194594i	$0.0623390\pi$
$284$	−21.8913	+	9.06767i	−1.29901	+	0.538067i
$285$		0			0
$286$	−0.0448163	−	0.108196i	−0.00265004	−	0.00639777i
$287$	−6.06800	−	6.06800i	−0.358183	−	0.358183i
$288$	0.854527			0.0503535
$289$	6.67925	+	15.6329i	0.392897	+	0.919582i
$290$		0			0
$291$	2.67194	+	2.67194i	0.156632	+	0.156632i
$292$	−11.6171	−	28.0461i	−0.679839	−	1.64128i
$293$		−	3.15115i		−	0.184092i	−0.995755	−	0.0920461i	$-0.970659\pi$
$293$		−	3.15115i		−	0.184092i	0.995755	−	0.0920461i	$-0.0293407\pi$
$294$	1.87185	−	0.775344i	0.109168	−	0.0452190i
$295$		0			0
$296$	−5.20097	−	2.15431i	−0.302300	−	0.125217i
$297$	−10.3259	+	10.3259i	−0.599171	+	0.599171i
$298$	2.04885	−	2.04885i	0.118687	−	0.118687i
$299$	−0.445057	−	0.184348i	−0.0257383	−	0.0106611i
$300$		0			0
$301$	−14.9585	+	6.19602i	−0.862195	+	0.357133i
$302$		−	0.0342954i		−	0.00197348i
$303$	0.560396	+	1.35292i	0.0321939	+	0.0777229i
$304$	−9.78495	−	9.78495i	−0.561205	−	0.561205i
$305$		0			0
$306$	0.255499	+	0.168679i	0.0146059	+	0.00964273i
$307$	14.9905			0.855551			0.427775	−	0.903885i	$-0.359297\pi$
$307$	14.9905			0.855551			0.427775	+	0.903885i	$0.359297\pi$
$308$	5.28261	+	5.28261i	0.301005	+	0.301005i
$309$	−0.230933	−	0.557521i	−0.0131373	−	0.0317163i
$310$		0			0
$311$	9.26536	−	3.83784i	0.525390	−	0.217624i	−0.104193	−	0.994557i	$-0.533226\pi$
$311$	9.26536	−	3.83784i	0.525390	−	0.217624i	0.629583	+	0.776933i	$0.283226\pi$
$312$	−0.107696	+	0.260001i	−0.00609708	+	0.0147196i
$313$	3.27134	+	1.35503i	0.184907	+	0.0765910i	0.473216	−	0.880946i	$-0.343093\pi$
$313$	3.27134	+	1.35503i	0.184907	+	0.0765910i	−0.288309	+	0.957537i	$0.593093\pi$
$314$	−1.70114	+	1.70114i	−0.0960007	+	0.0960007i
$315$		0			0
$316$	−23.1149	−	9.57451i	−1.30032	−	0.538608i
$317$	4.67288	−	11.2813i	0.262455	−	0.633623i	−0.736634	−	0.676292i	$-0.763586\pi$
$317$	4.67288	−	11.2813i	0.262455	−	0.633623i	0.999089	+	0.0426686i	$0.0135860\pi$
$318$	4.66948	−	1.93416i	0.261851	−	0.108462i
$319$			17.3302i			0.970307i
$320$		0			0
$321$	−7.72612	−	7.72612i	−0.431230	−	0.431230i
$322$	−0.982469			−0.0547508
$323$	−3.14995	−	15.3897i	−0.175268	−	0.856308i
$324$	15.5355			0.863084
$325$		0			0
$326$	1.18261	+	2.85508i	0.0654988	+	0.158128i
$327$			14.5294i			0.803475i
$328$	−5.43059	+	2.24942i	−0.299854	+	0.124204i
$329$	−1.45288	+	3.50755i	−0.0800996	+	0.193378i
$330$		0			0
$331$	−13.0768	+	13.0768i	−0.718764	+	0.718764i	−0.968352	−	0.249588i	$-0.919705\pi$
$331$	−13.0768	+	13.0768i	−0.718764	+	0.718764i	0.249588	+	0.968352i	$0.419705\pi$
$332$	11.7521	−	11.7521i	0.644979	−	0.644979i
$333$	1.58274	+	0.655594i	0.0867338	+	0.0359263i
$334$	0.398886	−	0.962996i	0.0218261	−	0.0526928i
$335$		0			0
$336$		−	8.54356i		−	0.466090i
$337$	7.05727	+	17.0378i	0.384434	+	0.928106i	0.991096	+	0.133146i	$0.0425080\pi$
$337$	7.05727	+	17.0378i	0.384434	+	0.928106i	−0.606662	+	0.794960i	$0.707492\pi$
$338$	−2.28279	−	2.28279i	−0.124167	−	0.124167i
$339$	9.39059			0.510027
$340$		0			0
$341$	−1.32622			−0.0718189
$342$	−0.200043	−	0.200043i	−0.0108171	−	0.0108171i
$343$	6.54555	+	15.8023i	0.353426	+	0.853247i
$344$			11.0903i			0.597951i
$345$		0			0
$346$	0.281477	−	0.679547i	0.0151323	−	0.0365327i
$347$	4.68901	+	1.94225i	0.251719	+	0.104265i	0.504975	−	0.863134i	$-0.331502\pi$
$347$	4.68901	+	1.94225i	0.251719	+	0.104265i	−0.253256	+	0.967399i	$0.581502\pi$
$348$	14.4922	−	14.4922i	0.776865	−	0.776865i
$349$	17.2978	−	17.2978i	0.925928	−	0.925928i	−0.0715119	−	0.997440i	$-0.522782\pi$
$349$	17.2978	−	17.2978i	0.925928	−	0.925928i	0.997440	+	0.0715119i	$0.0227824\pi$
$350$		0			0
$351$	0.362371	−	0.874840i	0.0193419	−	0.0466955i
$352$	7.12875	−	2.95282i	0.379964	−	0.157386i
$353$			17.5325i			0.933161i	0.884479	+	0.466580i	$0.154514\pi$
$353$			17.5325i			0.933161i	−0.884479	+	0.466580i	$0.845486\pi$
$354$	1.26707	+	3.05899i	0.0673442	+	0.162583i
$355$		0			0
$356$	22.2695			1.18028
$357$	5.34349	−	8.09381i	0.282807	−	0.428370i
$358$	−5.79391			−0.306218
$359$	1.42687	+	1.42687i	0.0753076	+	0.0753076i	0.743757	−	0.668450i	$-0.233042\pi$
$359$	1.42687	+	1.42687i	0.0753076	+	0.0753076i	−0.668450	+	0.743757i	$0.733042\pi$
$360$		0			0
$361$		−	4.48433i		−	0.236017i
$362$	−2.62634	+	1.08786i	−0.138037	+	0.0571769i
$363$	2.35530	−	5.68619i	0.123621	−	0.298447i
$364$	−0.447557	−	0.185384i	−0.0234584	−	0.00971677i
$365$		0			0
$366$	2.01008	−	2.01008i	0.105069	−	0.105069i
$367$	29.9381	+	12.4008i	1.56276	+	0.647315i	0.985566	−	0.169294i	$-0.0541488\pi$
$367$	29.9381	+	12.4008i	1.56276	+	0.647315i	0.577191	+	0.816609i	$0.304149\pi$
$368$	3.83345	−	9.25478i	0.199833	−	0.482439i
$369$	1.65262	−	0.684538i	0.0860320	−	0.0356356i
$370$		0			0
$371$	6.76525	+	16.3328i	0.351234	+	0.847955i
$372$	1.10904	+	1.10904i	0.0575009	+	0.0575009i
$373$	20.6108			1.06719			0.533593	−	0.845741i	$-0.320841\pi$
$373$	20.6108			1.06719			0.533593	+	0.845741i	$0.320841\pi$
$374$	2.71433	+	0.524297i	0.140355	+	0.0271107i
$375$		0			0
$376$	1.83884	+	1.83884i	0.0948311	+	0.0948311i
$377$	−0.430044	−	1.03822i	−0.0221484	−	0.0534710i
$378$		−	1.93122i		−	0.0993313i
$379$	−15.3385	+	6.35343i	−0.787887	+	0.326354i	−0.740094	−	0.672504i	$-0.765219\pi$
$379$	−15.3385	+	6.35343i	−0.787887	+	0.326354i	−0.0477935	+	0.998857i	$0.515219\pi$
$380$		0			0
$381$	−24.8237	−	10.2823i	−1.27176	−	0.526779i
$382$	0.542471	−	0.542471i	0.0277552	−	0.0277552i
$383$	−16.4274	+	16.4274i	−0.839401	+	0.839401i	−0.988780	−	0.149379i	$-0.952273\pi$
$383$	−16.4274	+	16.4274i	−0.839401	+	0.839401i	0.149379	+	0.988780i	$0.452273\pi$
$384$	−11.1764	−	4.62944i	−0.570346	−	0.236245i
$385$		0			0
$386$	−3.67622	+	1.52274i	−0.187115	+	0.0775055i
$387$		−	3.37498i		−	0.171560i
$388$	1.70500	+	4.11624i	0.0865584	+	0.208971i
$389$	−25.9259	−	25.9259i	−1.31450	−	1.31450i	−0.918064	−	0.396433i	$-0.870248\pi$
$389$	−25.9259	−	25.9259i	−1.31450	−	1.31450i	−0.396433	−	0.918064i	$-0.629752\pi$
$390$		0			0
$391$	9.41996	−	6.36999i	0.476388	−	0.322144i
$392$	4.85419			0.245174
$393$	11.2029	+	11.2029i	0.565112	+	0.565112i
$394$	1.01673	+	2.45461i	0.0512222	+	0.123661i
$395$		0			0
$396$	−1.43872	+	0.595938i	−0.0722984	+	0.0299470i
$397$	−3.75494	+	9.06522i	−0.188455	+	0.454970i	−0.989662	−	0.143416i	$-0.954191\pi$
$397$	−3.75494	+	9.06522i	−0.188455	+	0.454970i	0.801208	+	0.598386i	$0.204191\pi$
$398$	3.64259	+	1.50881i	0.182587	+	0.0756299i
$399$	−6.33706	+	6.33706i	−0.317250	+	0.317250i
$400$		0			0
$401$	19.8539	+	8.22376i	0.991457	+	0.410675i	0.818657	−	0.574282i	$-0.194719\pi$
$401$	19.8539	+	8.22376i	0.991457	+	0.410675i	0.172799	+	0.984957i	$0.444719\pi$
$402$	−1.93994	+	4.68344i	−0.0967556	+	0.233589i
$403$	0.0794512	−	0.0329097i	0.00395774	−	0.00163935i
$404$			1.72663i			0.0859032i
$405$		0			0
$406$	−1.62061	−	1.62061i	−0.0804293	−	0.0804293i
$407$	15.4692			0.766779
$408$	−3.72133	−	5.50311i	−0.184233	−	0.272445i
$409$	31.2735			1.54638			0.773189	−	0.634176i	$-0.218661\pi$
$409$	31.2735			1.54638			0.773189	+	0.634176i	$0.218661\pi$
$410$		0			0
$411$	4.15476	+	10.0305i	0.204939	+	0.494767i
$412$		−	0.711526i		−	0.0350544i
$413$	−10.6996	+	4.43193i	−0.526494	+	0.218081i
$414$	0.0783710	−	0.189204i	0.00385173	−	0.00929889i
$415$		0			0
$416$	−0.353795	+	0.353795i	−0.0173462	+	0.0173462i
$417$	5.34300	−	5.34300i	0.261648	−	0.261648i
$418$	−2.36008	−	0.977576i	−0.115435	−	0.0478148i
$419$	7.78615	−	18.7974i	0.380378	−	0.918314i	−0.611514	−	0.791234i	$-0.709439\pi$
$419$	7.78615	−	18.7974i	0.380378	−	0.918314i	0.991892	−	0.127081i	$-0.0405608\pi$
$420$		0			0
$421$		−	1.80862i		−	0.0881467i	−0.999028	−	0.0440733i	$-0.985966\pi$
$421$		−	1.80862i		−	0.0881467i	0.999028	−	0.0440733i	$-0.0140335\pi$
$422$	0.468626	+	1.13136i	0.0228124	+	0.0550740i
$423$	−0.559591	−	0.559591i	−0.0272083	−	0.0272083i
$424$	12.1092			0.588075
$425$		0			0
$426$	5.00228			0.242361
$427$	7.03079	+	7.03079i	0.340244	+	0.340244i
$428$	−4.93016	−	11.9024i	−0.238308	−	0.575327i
$429$		−	0.773317i		−	0.0373361i
$430$		0			0
$431$	6.37695	−	15.3953i	0.307167	−	0.741566i	−0.692628	−	0.721295i	$-0.743547\pi$
$431$	6.37695	−	15.3953i	0.307167	−	0.741566i	0.999795	−	0.0202708i	$-0.00645283\pi$
$432$	18.1920	+	7.53536i	0.875261	+	0.362545i
$433$	−11.5388	+	11.5388i	−0.554519	+	0.554519i	−0.927742	−	0.373222i	$-0.878253\pi$
$433$	−11.5388	+	11.5388i	−0.554519	+	0.554519i	0.373222	+	0.927742i	$0.378253\pi$
$434$	0.124019	−	0.124019i	0.00595311	−	0.00595311i
$435$		0			0
$436$	−6.55588	+	15.8273i	−0.313970	+	0.757990i
$437$	−9.70800	+	4.02118i	−0.464396	+	0.192359i
$438$			6.40870i			0.306220i
$439$	−9.19489	−	22.1984i	−0.438848	−	1.05947i	−0.976347	−	0.216209i	$-0.930631\pi$
$439$	−9.19489	−	22.1984i	−0.438848	−	1.05947i	0.537499	−	0.843264i	$-0.319369\pi$
$440$		0			0
$441$	−1.47721			−0.0703434
$442$	−0.175620	+	0.0359457i	−0.00835340	+	0.00170976i
$443$	21.2757			1.01084			0.505419	−	0.862874i	$-0.331338\pi$
$443$	21.2757			1.01084			0.505419	+	0.862874i	$0.331338\pi$
$444$	−12.9359	−	12.9359i	−0.613912	−	0.613912i
$445$		0			0
$446$		−	2.50011i		−	0.118384i
$447$	17.6767	−	7.32193i	0.836080	−	0.346316i
$448$	3.58773	−	8.66156i	0.169504	−	0.409220i
$449$	−26.9783	−	11.1748i	−1.27318	−	0.527370i	−0.359253	−	0.933240i	$-0.616969\pi$
$449$	−26.9783	−	11.1748i	−1.27318	−	0.527370i	−0.913931	+	0.405870i	$0.866969\pi$
$450$		0			0
$451$	11.4213	−	11.4213i	0.537807	−	0.537807i
$452$	10.2295	+	4.23718i	0.481153	+	0.199300i
$453$	0.0866636	−	0.209224i	0.00407181	−	0.00983022i
$454$	1.02966	−	0.426500i	0.0483244	−	0.0200166i
$455$		0			0
$456$	2.34916	+	5.67138i	0.110010	+	0.265587i
$457$	−0.734055	−	0.734055i	−0.0343376	−	0.0343376i	0.689729	−	0.724067i	$-0.257729\pi$
$457$	−0.734055	−	0.734055i	−0.0343376	−	0.0343376i	−0.724067	+	0.689729i	$0.757729\pi$
$458$	−0.298195			−0.0139337
$459$	12.5214	+	18.5167i	0.584448	+	0.864283i
$460$		0			0
$461$	0.0496372	+	0.0496372i	0.00231183	+	0.00231183i	0.708262	−	0.705950i	$-0.249480\pi$
$461$	0.0496372	+	0.0496372i	0.00231183	+	0.00231183i	−0.705950	+	0.708262i	$0.749480\pi$
$462$	−0.603554	−	1.45711i	−0.0280799	−	0.0677908i
$463$			40.0649i			1.86197i	0.365051	+	0.930987i	$0.381051\pi$
$463$			40.0649i			1.86197i	−0.365051	+	0.930987i	$0.618949\pi$
$464$	21.5894	−	8.94260i	1.00226	−	0.415150i
$465$		0			0
$466$	5.85376	+	2.42471i	0.271170	+	0.112322i
$467$	16.0563	−	16.0563i	0.742997	−	0.742997i	−0.230156	−	0.973154i	$-0.573924\pi$
$467$	16.0563	−	16.0563i	0.742997	−	0.742997i	0.973154	+	0.230156i	$0.0739238\pi$
$468$	0.0714028	−	0.0714028i	0.00330059	−	0.00330059i
$469$	−16.3816	−	6.78547i	−0.756431	−	0.313324i
$470$		0			0
$471$	−14.6768	+	6.07932i	−0.676270	+	0.280120i
$472$			7.93276i			0.365135i
$473$	−11.6622	−	28.1552i	−0.536231	−	1.29458i
$474$	3.73486	+	3.73486i	0.171548	+	0.171548i
$475$		0			0
$476$	9.47288	−	6.40578i	0.434189	−	0.293608i
$477$	−3.68503			−0.168726
$478$	1.09375	+	1.09375i	0.0500270	+	0.0500270i
$479$	8.90144	+	21.4900i	0.406717	+	0.981902i	0.985995	+	0.166772i	$0.0533345\pi$
$479$	8.90144	+	21.4900i	0.406717	+	0.981902i	−0.579278	+	0.815130i	$0.696665\pi$
$480$		0			0
$481$	−0.926726	+	0.383863i	−0.0422551	+	0.0175026i
$482$	2.55331	−	6.16422i	0.116300	−	0.280773i
$483$	−5.99370	−	2.48267i	−0.272723	−	0.112965i
$484$	5.13139	−	5.13139i	0.233245	−	0.233245i
$485$		0			0
$486$	0.710195	+	0.294172i	0.0322151	+	0.0133439i
$487$	−6.47199	+	15.6248i	−0.293274	+	0.708026i	0.706726	+	0.707488i	$0.250171\pi$
$487$	−6.47199	+	15.6248i	−0.293274	+	0.708026i	−1.00000		0.000538564i	$0.999829\pi$
$488$	6.29224	−	2.60633i	0.284837	−	0.117983i
$489$			20.4063i			0.922803i
$490$		0			0
$491$	−14.8915	−	14.8915i	−0.672045	−	0.672045i	0.286142	−	0.958187i	$-0.407627\pi$
$491$	−14.8915	−	14.8915i	−0.672045	−	0.672045i	−0.958187	+	0.286142i	$0.907627\pi$
$492$	−19.1018			−0.861177
$493$	26.0459	+	5.03100i	1.17305	+	0.226585i
$494$	0.165646			0.00745275
$495$		0			0
$496$	0.684345	+	1.65216i	0.0307280	+	0.0741840i
$497$			17.4968i			0.784840i
$498$	−3.24159	+	1.34271i	−0.145259	+	0.0601682i
$499$	−8.62028	+	20.8112i	−0.385897	+	0.931637i	0.604903	+	0.796299i	$0.293212\pi$
$499$	−8.62028	+	20.8112i	−0.385897	+	0.931637i	−0.990800	+	0.135338i	$0.956788\pi$
$500$		0			0
$501$	4.86693	−	4.86693i	0.217438	−	0.217438i
$502$	1.86664	−	1.86664i	0.0833122	−	0.0833122i
$503$	26.8129	+	11.1063i	1.19553	+	0.495204i	0.889551	−	0.456835i	$-0.151017\pi$
$503$	26.8129	+	11.1063i	1.19553	+	0.495204i	0.305977	+	0.952039i	$0.401017\pi$
$504$	0.160142	−	0.386618i	0.00713330	−	0.0172213i
$505$		0			0
$506$		−	1.84922i		−	0.0822077i
$507$	−8.15794	−	19.6950i	−0.362307	−	0.874686i
$508$	−22.4017	−	22.4017i	−0.993915	−	0.993915i
$509$	4.38401			0.194318			0.0971589	−	0.995269i	$-0.469024\pi$
$509$	4.38401			0.194318			0.0971589	+	0.995269i	$0.469024\pi$
$510$		0			0
$511$	−22.4162			−0.991633
$512$	−12.3921	−	12.3921i	−0.547660	−	0.547660i
$513$	−7.90437	−	19.0828i	−0.348987	−	0.842528i
$514$		−	0.383393i		−	0.0169107i
$515$		0			0
$516$	−13.7920	+	33.2969i	−0.607160	+	1.46581i
$517$	−6.60196	−	2.73462i	−0.290354	−	0.120269i
$518$	−1.44657	+	1.44657i	−0.0635587	+	0.0635587i
$519$	3.43439	−	3.43439i	0.150753	−	0.150753i
$520$		0			0
$521$	−1.22242	+	2.95118i	−0.0535551	+	0.129294i	−0.948393	−	0.317099i	$-0.897291\pi$
$521$	−1.22242	+	2.95118i	−0.0535551	+	0.129294i	0.894837	+	0.446392i	$0.147291\pi$
$522$	0.441372	−	0.182822i	0.0193183	−	0.00800192i
$523$		−	34.0520i		−	1.48899i	−0.667629	−	0.744494i	$-0.732691\pi$
$523$		−	34.0520i		−	1.48899i	0.667629	−	0.744494i	$-0.267309\pi$
$524$	7.14875	+	17.2586i	0.312294	+	0.753945i
$525$		0			0
$526$	0.106148			0.00462825
$527$	−0.385004	+	1.99320i	−0.0167710	+	0.0868251i
$528$	16.0808			0.699828
$529$	10.8848	+	10.8848i	0.473251	+	0.473251i
$530$		0			0
$531$		−	2.41407i		−	0.104762i
$532$	−9.76254	+	4.04377i	−0.423260	+	0.175320i
$533$	−0.400810	+	0.967641i	−0.0173610	+	0.0419132i
$534$	−4.34347	−	1.79913i	−0.187961	−	0.0778558i
$535$		0			0
$536$	−8.58809	+	8.58809i	−0.370949	+	0.370949i
$537$	−35.3467	−	14.6411i	−1.52532	−	0.631808i
$538$	1.62934	−	3.93359i	0.0702460	−	0.169589i
$539$	−12.3234	+	5.10452i	−0.530806	+	0.219867i
$540$		0			0
$541$	−10.3587	−	25.0081i	−0.445355	−	1.07518i	−0.974042	−	0.226366i	$-0.927315\pi$
$541$	−10.3587	−	25.0081i	−0.445355	−	1.07518i	0.528687	−	0.848817i	$-0.322685\pi$
$542$	−2.82859	−	2.82859i	−0.121498	−	0.121498i
$543$	−18.7714			−0.805557
$544$	−2.36836	−	11.5711i	−0.101543	−	0.496108i
$545$		0			0
$546$	0.0723153	+	0.0723153i	0.00309481	+	0.00309481i
$547$	5.17849	+	12.5020i	0.221416	+	0.534546i	0.995083	−	0.0990470i	$-0.0315794\pi$
$547$	5.17849	+	12.5020i	0.221416	+	0.534546i	−0.773667	+	0.633593i	$0.781579\pi$
$548$			12.8012i			0.546841i
$549$	−1.91484	+	0.793151i	−0.0817232	+	0.0338509i
$550$		0			0
$551$	−22.6466	−	9.38053i	−0.964778	−	0.399624i
$552$	−3.14221	+	3.14221i	−0.133742	+	0.133742i
$553$	−13.0637	+	13.0637i	−0.555524	+	0.555524i
$554$	3.85494	+	1.59677i	0.163781	+	0.0678402i
$555$		0			0
$556$	8.23114	−	3.40945i	0.349078	−	0.144593i
$557$		−	30.5182i		−	1.29310i	−0.762873	−	0.646548i	$-0.776212\pi$
$557$		−	30.5182i		−	1.29310i	0.762873	−	0.646548i	$-0.223788\pi$
$558$	0.0139907	+	0.0337766i	0.000592275	+	0.00142988i
$559$	1.39732	+	1.39732i	0.0591005	+	0.0591005i
$560$		0			0
$561$	15.2343	+	10.0576i	0.643192	+	0.424632i
$562$	−1.95111			−0.0823024
$563$	5.73355	+	5.73355i	0.241640	+	0.241640i	0.817529	−	0.575888i	$-0.195344\pi$
$563$	5.73355	+	5.73355i	0.241640	+	0.241640i	−0.575888	+	0.817529i	$0.695344\pi$
$564$	3.23402	+	7.80762i	0.136177	+	0.328760i
$565$		0			0
$566$	−1.51333	+	0.626842i	−0.0636101	+	0.0263481i
$567$	4.39004	−	10.5985i	0.184364	−	0.445095i
$568$	11.0725	+	4.58638i	0.464592	+	0.192440i
$569$	2.71124	−	2.71124i	0.113661	−	0.113661i	−0.647989	−	0.761650i	$-0.724390\pi$
$569$	2.71124	−	2.71124i	0.113661	−	0.113661i	0.761650	+	0.647989i	$0.224390\pi$
$570$		0			0
$571$	6.06730	+	2.51316i	0.253909	+	0.105172i	0.506007	−	0.862529i	$-0.331121\pi$
$571$	6.06730	+	2.51316i	0.253909	+	0.105172i	−0.252099	+	0.967701i	$0.581121\pi$
$572$	0.348933	−	0.842398i	0.0145896	−	0.0352224i
$573$	4.68023	−	1.93862i	0.195520	−	0.0809869i
$574$			2.13608i			0.0891583i
$575$		0			0
$576$	1.38186	+	1.38186i	0.0575773	+	0.0575773i
$577$	23.2880			0.969493			0.484746	−	0.874655i	$-0.338912\pi$
$577$	23.2880			0.969493			0.484746	+	0.874655i	$0.338912\pi$
$578$	1.57595	−	3.92720i	0.0655508	−	0.163350i
$579$	−26.2753			−1.09196
$580$		0			0
$581$	−4.69649	−	11.3383i	−0.194843	−	0.470393i
$582$		−	0.940585i		−	0.0389885i
$583$	−30.7418	+	12.7337i	−1.27319	+	0.527374i
$584$	−5.87587	+	14.1856i	−0.243145	+	0.587004i
$585$		0			0
$586$	−0.554640	+	0.554640i	−0.0229120	+	0.0229120i
$587$	−26.0085	+	26.0085i	−1.07348	+	1.07348i	−0.0764077	+	0.997077i	$0.524345\pi$
$587$	−26.0085	+	26.0085i	−1.07348	+	1.07348i	−0.997077	+	0.0764077i	$0.975655\pi$
$588$	14.5739	+	6.03671i	0.601017	+	0.248950i
$589$	0.717858	−	1.73306i	0.0295788	−	0.0714096i
$590$		0			0
$591$			17.5440i			0.721662i
$592$	−7.98227	−	19.2709i	−0.328069	−	0.792030i
$593$	−19.1275	−	19.1275i	−0.785474	−	0.785474i	0.195275	−	0.980749i	$-0.437440\pi$
$593$	−19.1275	−	19.1275i	−0.785474	−	0.785474i	−0.980749	+	0.195275i	$0.937440\pi$
$594$	3.63497			0.149145
$595$		0			0
$596$	22.5596			0.924076
$597$	18.4095	+	18.4095i	0.753450	+	0.753450i
$598$	0.0458877	+	0.110783i	0.00187649	+	0.00453025i
$599$			12.2973i			0.502456i	0.967928	+	0.251228i	$0.0808344\pi$
$599$			12.2973i			0.502456i	−0.967928	+	0.251228i	$0.919166\pi$
$600$		0			0
$601$	−3.08883	+	7.45710i	−0.125996	+	0.304181i	−0.974273	−	0.225372i	$-0.927640\pi$
$601$	−3.08883	+	7.45710i	−0.125996	+	0.304181i	0.848277	+	0.529553i	$0.177640\pi$
$602$	3.72345	+	1.54230i	0.151757	+	0.0628596i
$603$	2.61350	−	2.61350i	0.106430	−	0.106430i
$604$	0.188811	−	0.188811i	0.00768260	−	0.00768260i
$605$		0			0
$606$	0.139493	−	0.336765i	0.00566651	−	0.0136802i
$607$	−22.2684	+	9.22388i	−0.903847	+	0.374386i	−0.785698	−	0.618610i	$-0.787696\pi$
$607$	−22.2684	+	9.22388i	−0.903847	+	0.374386i	−0.118149	+	0.992996i	$0.537696\pi$
$608$			10.9139i			0.442619i
$609$	−5.79153	−	13.9820i	−0.234685	−	0.566579i
$610$		0			0
$611$	0.463369			0.0187459
$612$	0.477981	+	2.33528i	0.0193212	+	0.0943980i
$613$	−39.8359			−1.60896			−0.804478	−	0.593983i	$-0.797555\pi$
$613$	−39.8359			−1.60896			−0.804478	+	0.593983i	$0.797555\pi$
$614$	−2.63850	−	2.63850i	−0.106481	−	0.106481i
$615$		0			0
$616$		−	3.77867i		−	0.152247i
$617$	−23.8320	+	9.87155i	−0.959442	+	0.397414i	−0.806772	−	0.590863i	$-0.798787\pi$
$617$	−23.8320	+	9.87155i	−0.959442	+	0.397414i	−0.152670	+	0.988277i	$0.548787\pi$
$618$	−0.0574834	+	0.138777i	−0.00231232	+	0.00558244i
$619$	3.48155	+	1.44210i	0.139935	+	0.0579630i	0.451552	−	0.892245i	$-0.350871\pi$
$619$	3.48155	+	1.44210i	0.139935	+	0.0579630i	−0.311617	+	0.950208i	$0.600871\pi$
$620$		0			0
$621$	10.5728	−	10.5728i	0.424272	−	0.424272i
$622$	−2.30632	−	0.955308i	−0.0924749	−	0.0383044i
$623$	6.29293	−	15.1925i	0.252121	−	0.608673i
$624$	−0.963369	+	0.399041i	−0.0385656	+	0.0159744i
$625$		0			0
$626$	−0.337293	−	0.814297i	−0.0134809	−	0.0325459i
$627$	−11.9277	−	11.9277i	−0.476347	−	0.476347i
$628$	−18.7309			−0.747446
$629$	4.49073	−	23.2489i	0.179057	−	0.926994i
$630$		0			0
$631$	13.6572	+	13.6572i	0.543685	+	0.543685i	0.924607	−	0.380922i	$-0.124393\pi$
$631$	13.6572	+	13.6572i	0.543685	+	0.543685i	−0.380922	+	0.924607i	$0.624393\pi$
$632$	4.84274	+	11.6914i	0.192634	+	0.465059i
$633$			8.08627i			0.321400i
$634$	−2.80813	+	1.16317i	−0.111525	+	0.0461952i
$635$		0			0
$636$	36.3558	+	15.0591i	1.44160	+	0.597131i
$637$	0.611602	−	0.611602i	0.0242326	−	0.0242326i
$638$	3.05033	−	3.05033i	0.120764	−	0.120764i
$639$	−3.36955	−	1.39571i	−0.133297	−	0.0552136i
$640$		0			0
$641$	19.0839	−	7.90483i	0.753770	−	0.312222i	0.0274914	−	0.999622i	$-0.491248\pi$
$641$	19.0839	−	7.90483i	0.753770	−	0.312222i	0.726279	+	0.687400i	$0.241248\pi$
$642$			2.71978i			0.107341i
$643$	11.1053	+	26.8106i	0.437951	+	1.05731i	0.976655	+	0.214813i	$0.0689141\pi$
$643$	11.1053	+	26.8106i	0.437951	+	1.05731i	−0.538704	+	0.842495i	$0.681086\pi$
$644$	−5.40890	−	5.40890i	−0.213141	−	0.213141i
$645$		0			0
$646$	−2.15435	+	3.26321i	−0.0847618	+	0.128389i
$647$	−41.2848			−1.62307			−0.811536	−	0.584302i	$-0.801368\pi$
$647$	−41.2848			−1.62307			−0.811536	+	0.584302i	$0.801368\pi$
$648$	−5.55629	−	5.55629i	−0.218272	−	0.218272i
$649$	−8.34184	−	20.1390i	−0.327446	−	0.790524i
$650$		0			0
$651$	1.06999	−	0.443205i	0.0419362	−	0.0173706i
$652$	−9.20763	+	22.2292i	−0.360598	+	0.870562i
$653$	22.6889	+	9.39804i	0.887884	+	0.367774i	0.779549	−	0.626341i	$-0.215448\pi$
$653$	22.6889	+	9.39804i	0.887884	+	0.367774i	0.108335	+	0.994114i	$0.465448\pi$
$654$	2.55734	−	2.55734i	0.0999999	−	0.0999999i
$655$		0			0
$656$	−20.1217	−	8.33468i	−0.785621	−	0.325415i
$657$	1.78813	−	4.31692i	0.0697614	−	0.168419i
$658$	0.873094	−	0.361647i	0.0340368	−	0.0140985i
$659$		−	17.7024i		−	0.689588i	−0.938678	−	0.344794i	$-0.887949\pi$
$659$		−	17.7024i		−	0.689588i	0.938678	−	0.344794i	$-0.112051\pi$
$660$		0			0
$661$	10.0305	+	10.0305i	0.390141	+	0.390141i	0.874738	−	0.484597i	$-0.161034\pi$
$661$	10.0305	+	10.0305i	0.390141	+	0.390141i	−0.484597	+	0.874738i	$0.661034\pi$
$662$	4.60333			0.178914
$663$	−1.16223	−	0.224495i	−0.0451373	−	0.00871867i
$664$	−8.40629			−0.326227
$665$		0			0
$666$	−0.163189	−	0.393974i	−0.00632346	−	0.0152662i
$667$		−	17.7445i		−	0.687072i
$668$	7.49773	−	3.10566i	0.290096	−	0.120162i
$669$	6.31771	−	15.2523i	0.244257	−	0.589688i
$670$		0			0
$671$	−13.2335	+	13.2335i	−0.510872	+	0.510872i
$672$	−4.76466	+	4.76466i	−0.183801	+	0.183801i
$673$	0.300312	+	0.124393i	0.0115762	+	0.00479501i	0.388464	−	0.921464i	$-0.373006\pi$
$673$	0.300312	+	0.124393i	0.0115762	+	0.00479501i	−0.376888	+	0.926259i	$0.623006\pi$
$674$	1.75668	−	4.24101i	0.0676650	−	0.163358i
$675$		0			0
$676$		−	25.1354i		−	0.966746i
$677$	−6.61933	−	15.9805i	−0.254402	−	0.614180i	0.744148	−	0.668014i	$-0.232856\pi$
$677$	−6.61933	−	15.9805i	−0.254402	−	0.614180i	−0.998550	+	0.0538347i	$0.982856\pi$
$678$	−1.65286	−	1.65286i	−0.0634775	−	0.0634775i
$679$	3.28995			0.126257
$680$		0			0
$681$	7.35936			0.282011
$682$	0.233431	+	0.233431i	0.00893852	+	0.00893852i
$683$	−13.1956	−	31.8570i	−0.504916	−	1.21898i	−0.946777	−	0.321891i	$-0.895681\pi$
$683$	−13.1956	−	31.8570i	−0.504916	−	1.21898i	0.441860	−	0.897084i	$-0.354319\pi$
$684$		−	2.20264i		−	0.0842202i
$685$		0			0
$686$	1.62931	−	3.93350i	0.0622072	−	0.150182i
$687$	−1.81919	−	0.753531i	−0.0694062	−	0.0287490i
$688$	−29.0568	+	29.0568i	−1.10778	+	1.10778i
$689$	1.52569	−	1.52569i	0.0581243	−	0.0581243i
$690$		0			0
$691$	16.1221	−	38.9223i	0.613315	−	1.48067i	−0.246022	−	0.969264i	$-0.579124\pi$
$691$	16.1221	−	38.9223i	0.613315	−	1.48067i	0.859337	−	0.511409i	$-0.170876\pi$
$692$	5.29084	−	2.19154i	0.201128	−	0.0833098i
$693$			1.14991i			0.0436815i
$694$	−0.483462	−	1.16718i	−0.0183520	−	0.0443056i
$695$		0			0
$696$	−10.3663			−0.392934
$697$	−13.8496	−	20.4808i	−0.524591	−	0.775767i
$698$	−6.08922			−0.230481
$699$	29.5846	+	29.5846i	1.11899	+	1.11899i
$700$		0			0
$701$			29.6266i			1.11898i	0.828836	+	0.559491i	$0.189003\pi$
$701$			29.6266i			1.11898i	−0.828836	+	0.559491i	$0.810997\pi$
$702$	−0.217764	+	0.0902007i	−0.00821897	+	0.00340441i
$703$	−8.37317	+	20.2146i	−0.315800	+	0.762409i
$704$	16.3029	+	6.75289i	0.614439	+	0.254509i
$705$		0			0
$706$	3.08593	−	3.08593i	0.116140	−	0.116140i
$707$	1.17793	+	0.487914i	0.0443005	+	0.0183499i
$708$	−9.86523	+	23.8168i	−0.370758	+	0.895089i
$709$	−15.0352	+	6.22777i	−0.564657	+	0.233889i	−0.646706	−	0.762740i	$-0.723854\pi$
$709$	−15.0352	+	6.22777i	−0.564657	+	0.233889i	0.0820483	+	0.996628i	$0.473854\pi$
$710$		0			0
$711$	−1.47373	−	3.55789i	−0.0552691	−	0.133431i
$712$	−7.96469	−	7.96469i	−0.298489	−	0.298489i
$713$	1.35793			0.0508547
$714$	−2.36512	+	0.484090i	−0.0885125	+	0.0181166i
$715$		0			0
$716$	−31.8979	−	31.8979i	−1.19208	−	1.19208i
$717$	3.90871	+	9.43647i	0.145974	+	0.352411i
$718$		−	0.502294i		−	0.0187454i
$719$	29.0292	−	12.0243i	1.08261	−	0.448430i	0.231184	−	0.972910i	$-0.425740\pi$
$719$	29.0292	−	12.0243i	1.08261	−	0.448430i	0.851423	+	0.524480i	$0.175740\pi$
$720$		0			0
$721$	−0.485411	−	0.201064i	−0.0180776	−	0.00748800i
$722$	−0.789295	+	0.789295i	−0.0293745	+	0.0293745i
$723$	31.1537	−	31.1537i	1.15862	−	1.15862i
$724$	−20.4483	−	8.46994i	−0.759953	−	0.314783i
$725$		0			0
$726$	−1.41540	+	0.586276i	−0.0525303	+	0.0217588i
$727$			21.6544i			0.803118i	0.915833	+	0.401559i	$0.131532\pi$
$727$			21.6544i			0.803118i	−0.915833	+	0.401559i	$0.868468\pi$
$728$	0.0937664	+	0.226372i	0.00347521	+	0.00838991i
$729$	20.5940	+	20.5940i	0.762740	+	0.762740i
$730$		0			0
$731$	−45.7004	+	9.35389i	−1.69029	+	0.345966i
$732$	22.1327			0.818047
$733$	−22.2422	−	22.2422i	−0.821534	−	0.821534i	0.164794	−	0.986328i	$-0.447304\pi$
$733$	−22.2422	−	22.2422i	−0.821534	−	0.821534i	−0.986328	+	0.164794i	$0.947304\pi$
$734$	−3.08678	−	7.45215i	−0.113935	−	0.275064i
$735$		0			0
$736$	−7.29917	+	3.02342i	−0.269051	+	0.111445i
$737$	12.7717	−	30.8337i	0.470452	−	1.13577i
$738$	−0.411368	−	0.170394i	−0.0151426	−	0.00627229i
$739$	9.68961	−	9.68961i	0.356438	−	0.356438i	−0.506060	−	0.862498i	$-0.668899\pi$
$739$	9.68961	−	9.68961i	0.356438	−	0.356438i	0.862498	+	0.506060i	$0.168899\pi$
$740$		0			0
$741$	1.01055	+	0.418582i	0.0371233	+	0.0153770i
$742$	1.68400	−	4.06552i	0.0618214	−	0.149250i
$743$	14.9867	−	6.20770i	0.549809	−	0.227738i	−0.0904453	−	0.995901i	$-0.528829\pi$
$743$	14.9867	−	6.20770i	0.549809	−	0.227738i	0.640254	+	0.768163i	$0.278829\pi$
$744$		−	0.793297i		−	0.0290837i
$745$		0			0
$746$	−3.62775	−	3.62775i	−0.132821	−	0.132821i
$747$	2.55818			0.0935988
$748$	12.0570	+	17.8300i	0.440849	+	0.651929i
$749$	−9.51315			−0.347603
$750$		0			0
$751$	−4.26568	−	10.2983i	−0.155657	−	0.375789i	0.826743	−	0.562580i	$-0.190191\pi$
$751$	−4.26568	−	10.2983i	−0.155657	−	0.375789i	−0.982400	+	0.186791i	$0.940191\pi$
$752$			9.63558i			0.351373i
$753$	16.1047	−	6.67077i	0.586887	−	0.243096i
$754$	−0.107046	+	0.258432i	−0.00389838	+	0.00941153i
$755$		0			0
$756$	10.6322	−	10.6322i	0.386689	−	0.386689i
$757$	−14.0667	+	14.0667i	−0.511262	+	0.511262i	−0.914913	−	0.403651i	$-0.867741\pi$
$757$	−14.0667	+	14.0667i	−0.511262	+	0.511262i	0.403651	+	0.914913i	$0.367741\pi$
$758$	3.81804	+	1.58149i	0.138678	+	0.0574421i
$759$	4.67292	−	11.2814i	0.169616	−	0.409490i
$760$		0			0
$761$			45.4255i			1.64667i	0.567553	+	0.823337i	$0.307890\pi$
$761$			45.4255i			1.64667i	−0.567553	+	0.823337i	$0.692110\pi$
$762$	2.55946	+	6.17908i	0.0927194	+	0.223844i
$763$	8.94498	+	8.94498i	0.323830	+	0.323830i
$764$	5.97306			0.216098
$765$		0			0
$766$	5.78284			0.208942
$767$	0.999485	+	0.999485i	0.0360893	+	0.0360893i
$768$	−7.08907	−	17.1145i	−0.255805	−	0.617567i
$769$		−	5.98158i		−	0.215701i	−0.994167	−	0.107851i	$-0.965603\pi$
$769$		−	5.98158i		−	0.215701i	0.994167	−	0.107851i	$-0.0343968\pi$
$770$		0			0
$771$	0.968824	−	2.33895i	0.0348913	−	0.0842352i
$772$	−28.6225	−	11.8558i	−1.03015	−	0.426701i
$773$	9.29889	−	9.29889i	0.334458	−	0.334458i	−0.519819	−	0.854277i	$-0.674001\pi$
$773$	9.29889	−	9.29889i	0.334458	−	0.334458i	0.854277	+	0.519819i	$0.174001\pi$
$774$	−0.594036	+	0.594036i	−0.0213522	+	0.0213522i
$775$		0			0
$776$	0.862382	−	2.08197i	0.0309577	−	0.0747385i
$777$	−12.4805	+	5.16958i	−0.447735	+	0.185458i
$778$			9.12654i			0.327202i
$779$	8.74284	+	21.1071i	0.313245	+	0.756240i
$780$		0			0
$781$	−32.9328			−1.17843
$782$	−2.77922	−	0.536831i	−0.0993847	−	0.0191970i
$783$	34.8802			1.24652
$784$	12.7180	+	12.7180i	0.454215	+	0.454215i
$785$		0			0
$786$		−	3.94369i		−	0.140667i
$787$	−23.7408	+	9.83375i	−0.846267	+	0.350535i	−0.763322	−	0.646019i	$-0.776433\pi$
$787$	−23.7408	+	9.83375i	−0.846267	+	0.350535i	−0.0829458	+	0.996554i	$0.526433\pi$
$788$	−7.91611	+	19.1112i	−0.282000	+	0.680808i
$789$	0.647570	+	0.268232i	0.0230541	+	0.00954932i
$790$		0			0
$791$	5.78130	−	5.78130i	0.205560	−	0.205560i
$792$	0.727698	+	0.301422i	0.0258576	+	0.0107106i
$793$	0.464405	−	1.12117i	0.0164915	−	0.0398140i
$794$	2.25650	−	0.934673i	0.0800802	−	0.0331703i
$795$		0			0
$796$	11.7474	+	28.3607i	0.416375	+	1.00522i
$797$	35.6691	+	35.6691i	1.26347	+	1.26347i	0.949402	+	0.314064i	$0.101691\pi$
$797$	35.6691	+	35.6691i	1.26347	+	1.26347i	0.314064	+	0.949402i	$0.398309\pi$
$798$	2.23080			0.0789693
$799$	−6.02647	+	9.12834i	−0.213201	+	0.322937i
$800$		0			0
$801$	2.42379	+	2.42379i	0.0856404	+	0.0856404i
$802$	−2.04704	−	4.94200i	−0.0722836	−	0.174508i
$803$		−	42.1920i		−	1.48892i
$804$	−36.4645	+	15.1041i	−1.28600	+	0.532680i
$805$		0			0
$806$	−0.0197769	−	0.00819184i	−0.000696610	−	0.000288545i
$807$	19.8801	−	19.8801i	0.699814	−	0.699814i
$808$	0.617532	−	0.617532i	0.0217247	−	0.0217247i
$809$	8.50125	+	3.52133i	0.298888	+	0.123803i	0.527088	−	0.849811i	$-0.323284\pi$
$809$	8.50125	+	3.52133i	0.298888	+	0.123803i	−0.228200	+	0.973614i	$0.573284\pi$
$810$		0			0
$811$	9.89831	−	4.10002i	0.347577	−	0.143971i	−0.202064	−	0.979372i	$-0.564765\pi$
$811$	9.89831	−	4.10002i	0.347577	−	0.143971i	0.549640	+	0.835401i	$0.314765\pi$
$812$		−	17.8442i		−	0.626210i
$813$	−10.1085	−	24.4040i	−0.354519	−	0.855885i
$814$	−2.72276	−	2.72276i	−0.0954327	−	0.0954327i
$815$		0			0
$816$	4.66829	−	24.1681i	0.163423	−	0.846054i
$817$	43.1048			1.50805
$818$	−5.50452	−	5.50452i	−0.192461	−	0.192461i
$819$	−0.0285347	−	0.0688888i	−0.000997083	−	0.00240717i
$820$		0			0
$821$	26.0334	−	10.7834i	0.908572	−	0.376343i	0.121062	−	0.992645i	$-0.461370\pi$
$821$	26.0334	−	10.7834i	0.908572	−	0.376343i	0.787510	+	0.616302i	$0.211370\pi$
$822$	1.03420	−	2.49677i	0.0360718	−	0.0870849i
$823$	−32.6522	−	13.5250i	−1.13819	−	0.471452i	−0.267630	−	0.963522i	$-0.586240\pi$
$823$	−32.6522	−	13.5250i	−1.13819	−	0.471452i	−0.870556	+	0.492070i	$0.836240\pi$
$824$	−0.254478	+	0.254478i	−0.00886516	+	0.00886516i
$825$		0			0
$826$	2.66333	+	1.10319i	0.0926692	+	0.0383848i
$827$	15.0178	−	36.2562i	0.522221	−	1.26075i	−0.414300	−	0.910140i	$-0.635974\pi$
$827$	15.0178	−	36.2562i	0.522221	−	1.26075i	0.936521	−	0.350612i	$-0.114026\pi$
$828$	1.47312	−	0.610184i	0.0511943	−	0.0212054i
$829$			17.4130i			0.604779i	0.953184	+	0.302389i	$0.0977843\pi$
$829$			17.4130i			0.604779i	−0.953184	+	0.302389i	$0.902216\pi$
$830$		0			0
$831$	19.4827	+	19.4827i	0.675846	+	0.675846i
$832$	−1.14424			−0.0396695
$833$	4.09416	+	20.0029i	0.141854	+	0.693059i
$834$	−1.88086			−0.0651290
$835$		0			0
$836$	−7.61125	−	18.3752i	−0.263241	−	0.635519i
$837$			2.66925i			0.0922629i
$838$	−4.67903	+	1.93812i	−0.161634	+	0.0669511i
$839$	10.2960	−	24.8566i	0.355456	−	0.858147i	−0.640471	−	0.767982i	$-0.721261\pi$
$839$	10.2960	−	24.8566i	0.355456	−	0.858147i	0.995927	−	0.0901643i	$-0.0287392\pi$
$840$		0			0
$841$	8.76397	−	8.76397i	0.302206	−	0.302206i
$842$	−0.318338	+	0.318338i	−0.0109707	+	0.0109707i
$843$	−11.9030	−	4.93039i	−0.409962	−	0.169812i
$844$	−3.64865	+	8.80862i	−0.125592	+	0.303205i
$845$		0			0
$846$			0.196989i			0.00677263i
$847$	−2.05066	−	4.95073i	−0.0704615	−	0.170109i
$848$	31.7262	+	31.7262i	1.08948	+	1.08948i
$849$	−10.8163			−0.371215
$850$		0			0
$851$	−15.8390			−0.542954
$852$	27.5397	+	27.5397i	0.943494	+	0.943494i
$853$	6.25540	+	15.1019i	0.214181	+	0.517078i	0.994058	−	0.108855i	$-0.0347184\pi$
$853$	6.25540	+	15.1019i	0.214181	+	0.517078i	−0.779877	+	0.625933i	$0.784718\pi$
$854$		−	2.47501i		−	0.0846930i
$855$		0			0
$856$	−2.49365	+	6.02020i	−0.0852311	+	0.205766i
$857$	3.57282	+	1.47991i	0.122045	+	0.0505527i	0.442870	−	0.896586i	$-0.353960\pi$
$857$	3.57282	+	1.47991i	0.122045	+	0.0505527i	−0.320825	+	0.947138i	$0.603960\pi$
$858$	−0.136113	+	0.136113i	−0.00464682	+	0.00464682i
$859$	−27.6000	+	27.6000i	−0.941701	+	0.941701i	−0.998392	−	0.0566905i	$-0.981945\pi$
$859$	−27.6000	+	27.6000i	−0.941701	+	0.941701i	0.0566905	+	0.998392i	$0.481945\pi$
$860$		0			0
$861$	−5.39782	+	13.0315i	−0.183957	+	0.444112i
$862$	−3.83218	+	1.58734i	−0.130524	+	0.0540650i
$863$		−	22.1279i		−	0.753243i	−0.926367	−	0.376621i	$-0.877086\pi$
$863$		−	22.1279i		−	0.753243i	0.926367	−	0.376621i	$-0.122914\pi$
$864$	−5.94308	−	14.3479i	−0.202188	−	0.488124i
$865$		0			0
$866$	4.06193			0.138030
$867$	19.5383	−	19.9761i	0.663554	−	0.678425i
$868$	1.36556			0.0463500
$869$	−24.5886	−	24.5886i	−0.834112	−	0.834112i
$870$		0			0
$871$			2.16411i			0.0733280i
$872$	8.00536	−	3.31593i	0.271096	−	0.112292i
$873$	−0.262437	+	0.633580i	−0.00888216	+	0.0214434i
$874$	2.41650	+	1.00095i	0.0817393	+	0.0338575i
$875$		0			0
$876$	−35.2826	+	35.2826i	−1.19209	+	1.19209i
$877$	18.2350	+	7.55317i	0.615751	+	0.255052i	0.668685	−	0.743546i	$-0.266857\pi$
$877$	18.2350	+	7.55317i	0.615751	+	0.255052i	−0.0529342	+	0.998598i	$0.516857\pi$
$878$	−2.28878	+	5.52560i	−0.0772425	+	0.186480i
$879$	−4.78523	+	1.98211i	−0.161402	+	0.0668548i
$880$		0			0
$881$	4.37489	+	10.5619i	0.147394	+	0.355840i	0.980283	−	0.197600i	$-0.0633147\pi$
$881$	4.37489	+	10.5619i	0.147394	+	0.355840i	−0.832889	+	0.553440i	$0.813315\pi$
$882$	0.260007	+	0.260007i	0.00875489	+	0.00875489i
$883$	−13.2658			−0.446431			−0.223216	−	0.974769i	$-0.571655\pi$
$883$	−13.2658			−0.446431			−0.223216	+	0.974769i	$0.571655\pi$
$884$	−1.16476	−	0.768967i	−0.0391751	−	0.0258631i
$885$		0			0
$886$	−3.74477	−	3.74477i	−0.125808	−	0.125808i
$887$	11.7128	+	28.2772i	0.393277	+	0.949455i	0.989221	+	0.146429i	$0.0467781\pi$
$887$	11.7128	+	28.2772i	0.393277	+	0.949455i	−0.595944	+	0.803026i	$0.703222\pi$
$888$			9.25310i			0.310514i
$889$	−21.6130	+	8.95239i	−0.724876	+	0.300254i
$890$		0			0
$891$	19.9486	+	8.26300i	0.668305	+	0.276821i
$892$	13.7642	−	13.7642i	0.460858	−	0.460858i
$893$	7.14704	−	7.14704i	0.239167	−	0.239167i
$894$	−4.40006	−	1.82256i	−0.147160	−	0.0609557i
$895$		0			0
$896$	−9.73087	+	4.03066i	−0.325086	+	0.134655i
$897$			0.791804i			0.0264376i
$898$	2.78161	+	6.71539i	0.0928234	+	0.224096i
$899$	2.23993	+	2.23993i	0.0747059	+	0.0747059i
$900$		0			0
$901$	10.2132	+	49.8989i	0.340252	+	1.66237i
$902$	−4.02056			−0.133870
$903$	18.8181	+	18.8181i	0.626228	+	0.626228i
$904$	−2.14315	−	5.17401i	−0.0712799	−	0.172085i
$905$		0			0
$906$	−0.0520798	+	0.0215722i	−0.00173024	+	0.000716687i
$907$	−0.293142	+	0.707707i	−0.00973362	+	0.0234990i	−0.928672	−	0.370903i	$-0.879048\pi$
$907$	−0.293142	+	0.707707i	−0.00973362	+	0.0234990i	0.918938	+	0.394402i	$0.129048\pi$
$908$	8.01678	+	3.32066i	0.266046	+	0.110200i
$909$	−0.187925	+	0.187925i	−0.00623309	+	0.00623309i
$910$		0			0
$911$	7.79323	+	3.22806i	0.258201	+	0.106951i	0.508029	−	0.861340i	$-0.330374\pi$
$911$	7.79323	+	3.22806i	0.258201	+	0.106951i	−0.249828	+	0.968290i	$0.580374\pi$
$912$	−8.70425	+	21.0139i	−0.288226	+	0.695840i
$913$	21.3412	−	8.83979i	0.706289	−	0.292555i
$914$			0.258405i			0.00854727i
$915$		0			0
$916$	−1.64169	−	1.64169i	−0.0542430	−	0.0542430i
$917$	13.7941			0.455522
$918$	1.05524	−	5.46306i	0.0348281	−	0.180308i
$919$	13.0143			0.429302			0.214651	−	0.976691i	$-0.431139\pi$
$919$	13.0143			0.429302			0.214651	+	0.976691i	$0.431139\pi$
$920$		0			0
$921$	−9.42915	−	22.7640i	−0.310701	−	0.750099i
$922$		−	0.0174735i		−	0.000575458i
$923$	1.97294	−	0.817217i	0.0649400	−	0.0268990i
$924$	4.69918	−	11.3448i	0.154592	−	0.373217i
$925$		0			0
$926$	7.05190	−	7.05190i	0.231740	−	0.231740i
$927$	0.0774419	−	0.0774419i	0.00254353	−	0.00254353i
$928$	−17.0274	−	7.05297i	−0.558951	−	0.231525i
$929$	−9.89198	+	23.8814i	−0.324545	+	0.783522i	0.674433	+	0.738336i	$0.264388\pi$
$929$	−9.89198	+	23.8814i	−0.324545	+	0.783522i	−0.998979	+	0.0451859i	$0.985612\pi$
$930$		0			0
$931$		−	18.8668i		−	0.618335i
$932$	18.8784	+	45.5764i	0.618382	+	1.49291i
$933$	−11.6560	−	11.6560i	−0.381601	−	0.381601i
$934$	−5.65220			−0.184946
$935$		0			0
$936$	−0.0510746			−0.00166942
$937$	−0.615699	−	0.615699i	−0.0201140	−	0.0201140i	0.696978	−	0.717092i	$-0.254527\pi$
$937$	−0.615699	−	0.615699i	−0.0201140	−	0.0201140i	−0.717092	+	0.696978i	$0.754527\pi$
$938$	1.68903	+	4.07768i	0.0551488	+	0.133141i
$939$		−	5.82007i		−	0.189931i
$940$		0			0
$941$	20.4139	−	49.2834i	0.665473	−	1.60659i	−0.123627	−	0.992329i	$-0.539453\pi$
$941$	20.4139	−	49.2834i	0.665473	−	1.60659i	0.789100	−	0.614265i	$-0.210547\pi$
$942$	3.65332	+	1.51325i	0.119032	+	0.0493045i
$943$	−11.6943	+	11.6943i	−0.380820	+	0.380820i
$944$	−20.7839	+	20.7839i	−0.676458	+	0.676458i
$945$		0			0
$946$	−2.90295	+	7.00834i	−0.0943830	+	0.227861i
$947$	12.6021	−	5.21997i	0.409514	−	0.169626i	−0.168409	−	0.985717i	$-0.553863\pi$
$947$	12.6021	−	5.21997i	0.409514	−	0.169626i	0.577924	+	0.816091i	$0.303863\pi$
$948$			41.1240i			1.33564i
$949$	1.04698	+	2.52764i	0.0339865	+	0.0820506i
$950$		0			0
$951$	−20.0707			−0.650838
$952$	−5.67902	−	1.09695i	−0.184058	−	0.0355525i
$953$	10.3660			0.335788			0.167894	−	0.985805i	$-0.446303\pi$
$953$	10.3660			0.335788			0.167894	+	0.985805i	$0.446303\pi$
$954$	0.648610	+	0.648610i	0.0209995	+	0.0209995i
$955$		0			0
$956$			12.0431i			0.389502i
$957$	26.3171	−	10.9009i	0.850711	−	0.352376i
$958$	2.21573	−	5.34925i	0.0715871	−	0.172827i
$959$	8.73313	+	3.61738i	0.282007	+	0.116811i
$960$		0			0
$961$	21.7489	−	21.7489i	0.701577	−	0.701577i
$962$	0.230679	+	0.0955505i	0.00743740	+	0.00308067i
$963$	0.758859	−	1.83205i	0.0244539	−	0.0590369i
$964$	47.9937	−	19.8796i	1.54577	−	0.640280i
$965$		0			0
$966$	0.617983	+	1.49194i	0.0198833	+	0.0480025i
$967$	10.1327	+	10.1327i	0.325847	+	0.325847i	0.851005	−	0.525158i	$-0.175994\pi$
$967$	10.1327	+	10.1327i	0.325847	+	0.325847i	−0.525158	+	0.851005i	$0.675994\pi$
$968$	−3.67050			−0.117974
$969$	−21.3890	+	14.4637i	−0.687113	+	0.464641i
$970$		0			0
$971$	21.0309	+	21.0309i	0.674913	+	0.674913i	0.958845	−	0.283931i	$-0.0916388\pi$
$971$	21.0309	+	21.0309i	0.674913	+	0.674913i	−0.283931	+	0.958845i	$0.591639\pi$
$972$	2.29038	+	5.52946i	0.0734639	+	0.177358i
$973$		−	6.57882i		−	0.210907i
$974$	3.88929	−	1.61100i	0.124621	−	0.0516197i
$975$		0			0
$976$	23.3144	+	9.65712i	0.746274	+	0.309117i
$977$	−26.2437	+	26.2437i	−0.839611	+	0.839611i	−0.988808	−	0.149196i	$-0.952331\pi$
$977$	−26.2437	+	26.2437i	−0.839611	+	0.839611i	0.149196	+	0.988808i	$0.452331\pi$
$978$	3.59174	−	3.59174i	0.114851	−	0.114851i
$979$	28.5955	+	11.8446i	0.913916	+	0.378556i
$980$		0			0
$981$	−2.43617	+	1.00909i	−0.0777808	+	0.0322179i
$982$			5.24217i			0.167284i
$983$	17.7804	+	42.9257i	0.567107	+	1.36912i	0.903983	+	0.427568i	$0.140629\pi$
$983$	17.7804	+	42.9257i	0.567107	+	1.36912i	−0.336877	+	0.941549i	$0.609371\pi$
$984$	6.83179	+	6.83179i	0.217790	+	0.217790i
$985$		0			0
$986$	−3.69887	−	5.46991i	−0.117796	−	0.174197i
$987$	6.24032			0.198631
$988$	0.911949	+	0.911949i	0.0290130	+	0.0290130i
$989$	11.9411	+	28.8283i	0.379703	+	0.916685i
$990$		0			0
$991$	−40.9290	+	16.9534i	−1.30015	+	0.538541i	−0.921996	−	0.387200i	$-0.873442\pi$
$991$	−40.9290	+	16.9534i	−1.30015	+	0.538541i	−0.378158	+	0.925741i	$0.623442\pi$
$992$	0.539738	−	1.30304i	0.0171367	−	0.0413717i
$993$	28.0833	+	11.6325i	0.891198	+	0.369146i
$994$	3.07965	−	3.07965i	0.0976806	−	0.0976806i
$995$		0			0
$996$	−25.2385	−	10.4541i	−0.799712	−	0.331252i
$997$	9.42589	−	22.7561i	0.298521	−	0.720693i	−0.701447	−	0.712721i	$-0.747462\pi$
$997$	9.42589	−	22.7561i	0.298521	−	0.720693i	0.999968	−	0.00797178i	$-0.00253752\pi$
$998$	5.18029	−	2.14575i	0.163979	−	0.0679224i
$999$		−	31.1344i		−	0.985050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.e.151.3		24
5.2	odd	4		85.2.m.a.49.4	yes	24
5.3	odd	4		85.2.m.a.49.3	✓	24
5.4	even	2	inner	425.2.m.e.151.4		24
15.2	even	4		765.2.bh.b.559.3		24
15.8	even	4		765.2.bh.b.559.4		24
17.5	odd	16		7225.2.a.by.1.14		24
17.8	even	8	inner	425.2.m.e.76.3		24
17.12	odd	16		7225.2.a.by.1.13		24
85.8	odd	8		85.2.m.a.59.4	yes	24
85.12	even	16		1445.2.b.i.579.14		24
85.22	even	16		1445.2.b.i.579.13		24
85.29	odd	16		7225.2.a.by.1.12		24
85.39	odd	16		7225.2.a.by.1.11		24
85.42	odd	8		85.2.m.a.59.3	yes	24
85.59	even	8	inner	425.2.m.e.76.4		24
85.63	even	16		1445.2.b.i.579.11		24
85.73	even	16		1445.2.b.i.579.12		24
255.8	even	8		765.2.bh.b.739.3		24
255.212	even	8		765.2.bh.b.739.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.49.3	✓	24	5.3	odd	4
85.2.m.a.49.4	yes	24	5.2	odd	4
85.2.m.a.59.3	yes	24	85.42	odd	8
85.2.m.a.59.4	yes	24	85.8	odd	8
425.2.m.e.76.3		24	17.8	even	8	inner
425.2.m.e.76.4		24	85.59	even	8	inner
425.2.m.e.151.3		24	1.1	even	1	trivial
425.2.m.e.151.4		24	5.4	even	2	inner
765.2.bh.b.559.3		24	15.2	even	4
765.2.bh.b.559.4		24	15.8	even	4
765.2.bh.b.739.3		24	255.8	even	8
765.2.bh.b.739.4		24	255.212	even	8
1445.2.b.i.579.11		24	85.63	even	16
1445.2.b.i.579.12		24	85.73	even	16
1445.2.b.i.579.13		24	85.22	even	16
1445.2.b.i.579.14		24	85.12	even	16
7225.2.a.by.1.11		24	85.39	odd	16
7225.2.a.by.1.12		24	85.29	odd	16
7225.2.a.by.1.13		24	17.12	odd	16
7225.2.a.by.1.14		24	17.5	odd	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.176012 - 0.176012i) q^{2} +(-0.629010 - 1.51856i) q^{3} -1.93804i q^{4} +(-0.156572 + 0.377999i) q^{6} +(-1.32215 - 0.547653i) q^{7} +(-0.693142 + 0.693142i) q^{8} +(0.210935 - 0.210935i) q^{9} +O(q^{10})\)	\(q+(-0.176012 - 0.176012i) q^{2} +(-0.629010 - 1.51856i) q^{3} -1.93804i q^{4} +(-0.156572 + 0.377999i) q^{6} +(-1.32215 - 0.547653i) q^{7} +(-0.693142 + 0.693142i) q^{8} +(0.210935 - 0.210935i) q^{9} +(1.03080 - 2.48857i) q^{11} +(-2.94304 + 1.21905i) q^{12} +0.174664i q^{13} +(0.136321 + 0.329108i) q^{14} -3.63208 q^{16} +(-3.44088 - 2.27165i) q^{17} -0.0742541 q^{18} +(2.69404 + 2.69404i) q^{19} +2.35225i q^{21} +(-0.619452 + 0.256585i) q^{22} +(-1.05544 + 2.54807i) q^{23} +(1.48857 + 0.616588i) q^{24} +(0.0307430 - 0.0307430i) q^{26} +(-5.00869 - 2.07467i) q^{27} +(-1.06137 + 2.56238i) q^{28} +(-5.94408 + 2.46212i) q^{29} +(-0.188417 - 0.454879i) q^{31} +(2.02557 + 2.02557i) q^{32} -4.42745 q^{33} +(0.205798 + 1.00547i) q^{34} +(-0.408800 - 0.408800i) q^{36} +(2.19772 + 5.30576i) q^{37} -0.948365i q^{38} +(0.265239 - 0.109866i) q^{39} +(5.54000 + 2.29474i) q^{41} +(0.414025 - 0.414025i) q^{42} +(8.00004 - 8.00004i) q^{43} +(-4.82296 - 1.99773i) q^{44} +(0.634261 - 0.262720i) q^{46} -2.65291i q^{47} +(2.28461 + 5.51554i) q^{48} +(-3.50159 - 3.50159i) q^{49} +(-1.28530 + 6.65408i) q^{51} +0.338506 q^{52} +(-8.73501 - 8.73501i) q^{53} +(0.516423 + 1.24676i) q^{54} +(1.29604 - 0.536837i) q^{56} +(2.39649 - 5.78565i) q^{57} +(1.47959 + 0.612867i) q^{58} +(5.72232 - 5.72232i) q^{59} +(-6.41902 - 2.65884i) q^{61} +(-0.0469005 + 0.113228i) q^{62} +(-0.394407 + 0.163369i) q^{63} +6.55110i q^{64} +(0.779283 + 0.779283i) q^{66} +12.3901 q^{67} +(-4.40254 + 6.66855i) q^{68} +4.53329 q^{69} +(-4.67878 - 11.2956i) q^{71} +0.292415i q^{72} +(14.4714 - 5.99425i) q^{73} +(0.547052 - 1.32070i) q^{74} +(5.22115 - 5.22115i) q^{76} +(-2.72575 + 2.72575i) q^{77} +(-0.0660229 - 0.0273476i) q^{78} +(4.94031 - 11.9270i) q^{79} +8.01609i q^{81} +(-0.571204 - 1.37901i) q^{82} +(6.06390 + 6.06390i) q^{83} +4.55876 q^{84} -2.81621 q^{86} +(7.47777 + 7.47777i) q^{87} +(1.01044 + 2.43943i) q^{88} +11.4907i q^{89} +(0.0956555 - 0.230933i) q^{91} +(4.93826 + 2.04549i) q^{92} +(-0.572247 + 0.572247i) q^{93} +(-0.466944 + 0.466944i) q^{94} +(1.80186 - 4.35007i) q^{96} +(-2.12392 + 0.879757i) q^{97} +1.23264i q^{98} +(-0.307495 - 0.742359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9}+O(q^{10}) \) 24 * q + 8 * q^9	\( 24 q + 8 q^{9} + 24 q^{14} + 8 q^{16} + 24 q^{19} - 32 q^{24} - 16 q^{26} - 24 q^{29} - 24 q^{31} - 8 q^{34} + 8 q^{36} + 24 q^{39} - 48 q^{41} - 72 q^{44} - 16 q^{46} - 48 q^{49} - 32 q^{54} + 24 q^{56} + 48 q^{59} + 16 q^{61} - 96 q^{66} - 32 q^{69} + 16 q^{71} + 64 q^{74} - 24 q^{76} + 72 q^{79} + 96 q^{84} - 8 q^{91} + 40 q^{94} + 96 q^{96} + 80 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 + 24 * q^14 + 8 * q^16 + 24 * q^19 - 32 * q^24 - 16 * q^26 - 24 * q^29 - 24 * q^31 - 8 * q^34 + 8 * q^36 + 24 * q^39 - 48 * q^41 - 72 * q^44 - 16 * q^46 - 48 * q^49 - 32 * q^54 + 24 * q^56 + 48 * q^59 + 16 * q^61 - 96 * q^66 - 32 * q^69 + 16 * q^71 + 64 * q^74 - 24 * q^76 + 72 * q^79 + 96 * q^84 - 8 * q^91 + 40 * q^94 + 96 * q^96 + 80 * q^99

Introduction

L-functions

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