LMFDB - Embedded newform 768.2.o.b.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			95.5
Character	$\chi$	$=$	768.95
Dual form			768.2.o.b.671.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.988287 - 1.42242i) q^{3} +(-2.70066 + 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(-1.04658 + 2.81152i) q^{9} +O(q^{10})$	\(q+(-0.988287 - 1.42242i) q^{3} +(-2.70066 + 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(-1.04658 + 2.81152i) q^{9} +(0.276697 - 0.114612i) q^{11} +(0.155281 - 0.374881i) q^{13} +(4.26022 + 2.73593i) q^{15} +1.41723 q^{17} +(2.51972 + 1.04370i) q^{19} +(-1.42485 + 7.91204i) q^{21} +(3.30034 + 3.30034i) q^{23} +(2.50664 - 2.50664i) q^{25} +(5.03350 - 1.28991i) q^{27} +(-0.650676 + 1.57087i) q^{29} +4.16702i q^{31} +(-0.436482 - 0.280311i) q^{33} +(12.5351 + 5.19221i) q^{35} +(2.82757 + 6.82635i) q^{37} +(-0.686701 + 0.149615i) q^{39} +(-3.81949 + 3.81949i) q^{41} +(-2.07136 - 5.00071i) q^{43} +(-0.318658 - 8.76372i) q^{45} -5.44085i q^{47} +14.5435i q^{49} +(-1.40063 - 2.01590i) q^{51} +(-1.85159 - 4.47012i) q^{53} +(-0.619053 + 0.619053i) q^{55} +(-1.00562 - 4.61558i) q^{57} +(-1.37699 - 3.32434i) q^{59} +(10.9629 + 4.54098i) q^{61} +(12.6624 - 5.79262i) q^{63} +1.18613i q^{65} +(-4.19888 + 10.1370i) q^{67} +(1.43280 - 7.95617i) q^{69} +(-3.77857 + 3.77857i) q^{71} +(-3.89137 - 3.89137i) q^{73} +(-6.04279 - 1.08823i) q^{75} +(-1.28429 - 0.531970i) q^{77} +4.81995 q^{79} +(-6.80935 - 5.88497i) q^{81} +(-3.60399 + 8.70081i) q^{83} +(-3.82744 + 1.58538i) q^{85} +(2.87750 - 0.626933i) q^{87} +(3.69926 + 3.69926i) q^{89} +(-1.74001 + 0.720735i) q^{91} +(5.92727 - 4.11821i) q^{93} -7.97242 q^{95} +10.9958 q^{97} +(0.0326483 + 0.897890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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			0
$2$		0			0
$3$	−0.988287	−	1.42242i	−0.570588	−	0.821237i
$3$	−0.988287	−	1.42242i	−0.570588	−	0.821237i
$4$		0			0
$5$	−2.70066	+	1.11865i	−1.20777	+	0.500275i	−0.893502	−	0.449059i	$-0.851759\pi$
$5$	−2.70066	+	1.11865i	−1.20777	+	0.500275i	−0.314269	+	0.949334i	$0.601759\pi$
$6$		0			0
$7$	−3.28204	−	3.28204i	−1.24049	−	1.24049i	−0.959797	−	0.280697i	$-0.909435\pi$
$7$	−3.28204	−	3.28204i	−1.24049	−	1.24049i	−0.280697	−	0.959797i	$-0.590565\pi$
$8$		0			0
$9$	−1.04658	+	2.81152i	−0.348860	+	0.937175i
$10$		0			0
$11$	0.276697	−	0.114612i	0.0834272	−	0.0345567i	−0.340580	−	0.940216i	$-0.610623\pi$
$11$	0.276697	−	0.114612i	0.0834272	−	0.0345567i	0.424007	+	0.905659i	$0.360623\pi$
$12$		0			0
$13$	0.155281	−	0.374881i	0.0430671	−	0.103973i	−0.900882	−	0.434064i	$-0.857079\pi$
$13$	0.155281	−	0.374881i	0.0430671	−	0.103973i	0.943949	+	0.330091i	$0.107079\pi$
$14$		0			0
$15$	4.26022	+	2.73593i	1.09998	+	0.706415i
$16$		0			0
$17$	1.41723			0.343728			0.171864	−	0.985121i	$-0.445021\pi$
$17$	1.41723			0.343728			0.171864	+	0.985121i	$0.445021\pi$
$18$		0			0
$19$	2.51972	+	1.04370i	0.578062	+	0.239441i	0.652506	−	0.757784i	$-0.273718\pi$
$19$	2.51972	+	1.04370i	0.578062	+	0.239441i	−0.0744431	+	0.997225i	$0.523718\pi$
$20$		0			0
$21$	−1.42485	+	7.91204i	−0.310929	+	1.72655i
$22$		0			0
$23$	3.30034	+	3.30034i	0.688169	+	0.688169i	0.961827	−	0.273658i	$-0.0882337\pi$
$23$	3.30034	+	3.30034i	0.688169	+	0.688169i	−0.273658	+	0.961827i	$0.588234\pi$
$24$		0			0
$25$	2.50664	−	2.50664i	0.501328	−	0.501328i
$26$		0			0
$27$	5.03350	−	1.28991i	0.968698	−	0.248244i
$28$		0			0
$29$	−0.650676	+	1.57087i	−0.120827	+	0.291703i	−0.972708	−	0.232033i	$-0.925462\pi$
$29$	−0.650676	+	1.57087i	−0.120827	+	0.291703i	0.851880	+	0.523736i	$0.175462\pi$
$30$		0			0
$31$			4.16702i			0.748419i	0.927344	+	0.374209i	$0.122086\pi$
$31$			4.16702i			0.748419i	−0.927344	+	0.374209i	$0.877914\pi$
$32$		0			0
$33$	−0.436482	−	0.280311i	−0.0759817	−	0.0487959i
$34$		0			0
$35$	12.5351	+	5.19221i	2.11882	+	0.877644i
$36$		0			0
$37$	2.82757	+	6.82635i	0.464849	+	1.12225i	0.966383	+	0.257107i	$0.0827693\pi$
$37$	2.82757	+	6.82635i	0.464849	+	1.12225i	−0.501534	+	0.865138i	$0.667231\pi$
$38$		0			0
$39$	−0.686701	+	0.149615i	−0.109960	+	0.0239575i
$40$		0			0
$41$	−3.81949	+	3.81949i	−0.596504	+	0.596504i	−0.939380	−	0.342877i	$-0.888599\pi$
$41$	−3.81949	+	3.81949i	−0.596504	+	0.596504i	0.342877	+	0.939380i	$0.388599\pi$
$42$		0			0
$43$	−2.07136	−	5.00071i	−0.315880	−	0.762602i	−0.999464	−	0.0327301i	$-0.989580\pi$
$43$	−2.07136	−	5.00071i	−0.315880	−	0.762602i	0.683584	−	0.729872i	$-0.260420\pi$
$44$		0			0
$45$	−0.318658	−	8.76372i	−0.0475028	−	1.30642i
$46$		0			0
$47$		−	5.44085i		−	0.793629i	−0.917899	−	0.396815i	$-0.870116\pi$
$47$		−	5.44085i		−	0.793629i	0.917899	−	0.396815i	$-0.129884\pi$
$48$		0			0
$49$			14.5435i			2.07765i
$50$		0			0
$51$	−1.40063	−	2.01590i	−0.196127	−	0.282282i
$52$		0			0
$53$	−1.85159	−	4.47012i	−0.254335	−	0.614019i	0.744210	−	0.667946i	$-0.232826\pi$
$53$	−1.85159	−	4.47012i	−0.254335	−	0.614019i	−0.998545	+	0.0539269i	$0.982826\pi$
$54$		0			0
$55$	−0.619053	+	0.619053i	−0.0834731	+	0.0834731i
$56$		0			0
$57$	−1.00562	−	4.61558i	−0.133197	−	0.611348i
$58$		0			0
$59$	−1.37699	−	3.32434i	−0.179268	−	0.432792i	0.808545	−	0.588434i	$-0.200255\pi$
$59$	−1.37699	−	3.32434i	−0.179268	−	0.432792i	−0.987814	+	0.155642i	$0.950255\pi$
$60$		0			0
$61$	10.9629	+	4.54098i	1.40366	+	0.581413i	0.950698	−	0.310119i	$-0.100369\pi$
$61$	10.9629	+	4.54098i	1.40366	+	0.581413i	0.452958	+	0.891532i	$0.350369\pi$
$62$		0			0
$63$	12.6624	−	5.79262i	1.59532	−	0.729801i
$64$		0			0
$65$			1.18613i			0.147121i
$66$		0			0
$67$	−4.19888	+	10.1370i	−0.512974	+	1.23843i	0.429170	+	0.903224i	$0.358806\pi$
$67$	−4.19888	+	10.1370i	−0.512974	+	1.23843i	−0.942145	+	0.335206i	$0.891194\pi$
$68$		0			0
$69$	1.43280	−	7.95617i	0.172489	−	0.957810i
$70$		0			0
$71$	−3.77857	+	3.77857i	−0.448434	+	0.448434i	−0.894834	−	0.446400i	$-0.852706\pi$
$71$	−3.77857	+	3.77857i	−0.448434	+	0.448434i	0.446400	+	0.894834i	$0.352706\pi$
$72$		0			0
$73$	−3.89137	−	3.89137i	−0.455450	−	0.455450i	0.441708	−	0.897159i	$-0.354373\pi$
$73$	−3.89137	−	3.89137i	−0.455450	−	0.455450i	−0.897159	+	0.441708i	$0.854373\pi$
$74$		0			0
$75$	−6.04279	−	1.08823i	−0.697761	−	0.125657i
$76$		0			0
$77$	−1.28429	−	0.531970i	−0.146358	−	0.0606236i
$78$		0			0
$79$	4.81995			0.542287			0.271143	−	0.962539i	$-0.412598\pi$
$79$	4.81995			0.542287			0.271143	+	0.962539i	$0.412598\pi$
$80$		0			0
$81$	−6.80935	−	5.88497i	−0.756594	−	0.653885i
$82$		0			0
$83$	−3.60399	+	8.70081i	−0.395590	+	0.955038i	0.593109	+	0.805122i	$0.297900\pi$
$83$	−3.60399	+	8.70081i	−0.395590	+	0.955038i	−0.988699	+	0.149916i	$0.952100\pi$
$84$		0			0
$85$	−3.82744	+	1.58538i	−0.415145	+	0.171959i
$86$		0			0
$87$	2.87750	−	0.626933i	0.308500	−	0.0672143i
$88$		0			0
$89$	3.69926	+	3.69926i	0.392121	+	0.392121i	0.875443	−	0.483322i	$-0.160570\pi$
$89$	3.69926	+	3.69926i	0.392121	+	0.392121i	−0.483322	+	0.875443i	$0.660570\pi$
$90$		0			0
$91$	−1.74001	+	0.720735i	−0.182402	+	0.0755536i
$92$		0			0
$93$	5.92727	−	4.11821i	0.614629	−	0.427039i
$94$		0			0
$95$	−7.97242			−0.817953
$96$		0			0
$97$	10.9958			1.11646			0.558229	−	0.829687i	$-0.311481\pi$
$97$	10.9958			1.11646			0.558229	+	0.829687i	$0.311481\pi$
$98$		0			0
$99$	0.0326483	+	0.897890i	0.00328127	+	0.0902413i
$100$		0			0
$101$	−2.51499	+	1.04174i	−0.250251	+	0.103657i	−0.504283	−	0.863538i	$-0.668243\pi$
$101$	−2.51499	+	1.04174i	−0.250251	+	0.103657i	0.254032	+	0.967196i	$0.418243\pi$
$102$		0			0
$103$	−0.332885	−	0.332885i	−0.0328001	−	0.0328001i	0.690517	−	0.723317i	$-0.257383\pi$
$103$	−0.332885	−	0.332885i	−0.0328001	−	0.0328001i	−0.723317	+	0.690517i	$0.757383\pi$
$104$		0			0
$105$	−5.00275	−	22.9616i	−0.488219	−	2.24082i
$106$		0			0
$107$	0.394269	−	0.163312i	0.0381154	−	0.0157879i	−0.363544	−	0.931577i	$-0.618433\pi$
$107$	0.394269	−	0.163312i	0.0381154	−	0.0157879i	0.401660	+	0.915789i	$0.368433\pi$
$108$		0			0
$109$	−1.81782	+	4.38860i	−0.174115	+	0.420352i	−0.986713	−	0.162474i	$-0.948053\pi$
$109$	−1.81782	+	4.38860i	−0.174115	+	0.420352i	0.812598	+	0.582825i	$0.198053\pi$
$110$		0			0
$111$	6.91552	−	10.7684i	0.656392	−	1.02209i
$112$		0			0
$113$	18.5323			1.74337			0.871687	−	0.490063i	$-0.163026\pi$
$113$	18.5323			1.74337			0.871687	+	0.490063i	$0.163026\pi$
$114$		0			0
$115$	−12.6050	−	5.22117i	−1.17542	−	0.486876i
$116$		0			0
$117$	0.891473	+	0.828917i	0.0824167	+	0.0766334i
$118$		0			0
$119$	−4.65139	−	4.65139i	−0.426392	−	0.426392i
$120$		0			0
$121$	−7.71475	+	7.71475i	−0.701341	+	0.701341i
$122$		0			0
$123$	9.20768	+	1.65818i	0.830229	+	0.149513i
$124$		0			0
$125$	1.62772	−	3.92966i	0.145587	−	0.351479i
$126$		0			0
$127$			4.80013i			0.425943i	0.977058	+	0.212971i	$0.0683141\pi$
$127$			4.80013i			0.425943i	−0.977058	+	0.212971i	$0.931686\pi$
$128$		0			0
$129$	−5.06603	+	7.88850i	−0.446039	+	0.694543i
$130$		0			0
$131$	−20.2118	−	8.37202i	−1.76592	−	0.731467i	−0.995589	−	0.0938185i	$-0.970093\pi$
$131$	−20.2118	−	8.37202i	−1.76592	−	0.731467i	−0.770328	−	0.637648i	$-0.779907\pi$
$132$		0			0
$133$	−4.84434	−	11.6953i	−0.420057	−	1.01411i
$134$		0			0
$135$	−12.1508	+	9.11434i	−1.04577	+	0.784437i
$136$		0			0
$137$	−12.7302	+	12.7302i	−1.08762	+	1.08762i	−0.0918436	+	0.995773i	$0.529276\pi$
$137$	−12.7302	+	12.7302i	−1.08762	+	1.08762i	−0.995773	+	0.0918436i	$0.970724\pi$
$138$		0			0
$139$	−0.193431	−	0.466984i	−0.0164066	−	0.0396091i	0.915464	−	0.402400i	$-0.131824\pi$
$139$	−0.193431	−	0.466984i	−0.0164066	−	0.0396091i	−0.931871	+	0.362791i	$0.881824\pi$
$140$		0			0
$141$	−7.73919	+	5.37712i	−0.651758	+	0.452835i
$142$		0			0
$143$		−	0.121525i		−	0.0101624i
$144$		0			0
$145$		−	4.97026i		−	0.412758i
$146$		0			0
$147$	20.6871	−	14.3732i	1.70624	−	1.18548i
$148$		0			0
$149$	4.31949	+	10.4282i	0.353866	+	0.854308i	0.996136	+	0.0878294i	$0.0279930\pi$
$149$	4.31949	+	10.4282i	0.353866	+	0.854308i	−0.642269	+	0.766479i	$0.722007\pi$
$150$		0			0
$151$	−13.7687	+	13.7687i	−1.12048	+	1.12048i	−0.128814	+	0.991669i	$0.541117\pi$
$151$	−13.7687	+	13.7687i	−1.12048	+	1.12048i	−0.991669	+	0.128814i	$0.958883\pi$
$152$		0			0
$153$	−1.48324	+	3.98457i	−0.119913	+	0.322133i
$154$		0			0
$155$	−4.66143	−	11.2537i	−0.374415	−	0.903918i
$156$		0			0
$157$	−7.94660	−	3.29159i	−0.634208	−	0.262697i	0.0423321	−	0.999104i	$-0.486521\pi$
$157$	−7.94660	−	3.29159i	−0.634208	−	0.262697i	−0.676540	+	0.736406i	$0.736521\pi$
$158$		0			0
$159$	−4.52851	+	7.05151i	−0.359135	+	0.559221i
$160$		0			0
$161$		−	21.6637i		−	1.70734i
$162$		0			0
$163$	−4.77631	+	11.5310i	−0.374110	+	0.903181i	0.618935	+	0.785442i	$0.287565\pi$
$163$	−4.77631	+	11.5310i	−0.374110	+	0.903181i	−0.993045	+	0.117739i	$0.962435\pi$
$164$		0			0
$165$	1.49236	+	0.268754i	0.116180	+	0.0209225i
$166$		0			0
$167$	14.7585	−	14.7585i	1.14205	−	1.14205i	0.153970	−	0.988076i	$-0.450794\pi$
$167$	14.7585	−	14.7585i	1.14205	−	1.14205i	0.988076	−	0.153970i	$-0.0492059\pi$
$168$		0			0
$169$	9.07596	+	9.07596i	0.698151	+	0.698151i
$170$		0			0
$171$	−5.57147	+	5.99193i	−0.426061	+	0.458214i
$172$		0			0
$173$	7.60827	+	3.15145i	0.578446	+	0.239600i	0.652671	−	0.757641i	$-0.273648\pi$
$173$	7.60827	+	3.15145i	0.578446	+	0.239600i	−0.0742253	+	0.997241i	$0.523648\pi$
$174$		0			0
$175$	−16.4538			−1.24379
$176$		0			0
$177$	−3.36776	+	5.24406i	−0.253136	+	0.394167i
$178$		0			0
$179$	−1.38731	+	3.34926i	−0.103692	+	0.250335i	−0.967208	−	0.253987i	$-0.918258\pi$
$179$	−1.38731	+	3.34926i	−0.103692	+	0.250335i	0.863515	+	0.504323i	$0.168258\pi$
$180$		0			0
$181$	−6.51464	+	2.69845i	−0.484229	+	0.200574i	−0.611424	−	0.791303i	$-0.709403\pi$
$181$	−6.51464	+	2.69845i	−0.484229	+	0.200574i	0.127194	+	0.991878i	$0.459403\pi$
$182$		0			0
$183$	−4.37529	−	20.0817i	−0.323431	−	1.48448i
$184$		0			0
$185$	−15.2726	−	15.2726i	−1.12286	−	1.12286i
$186$		0			0
$187$	0.392142	−	0.162431i	0.0286763	−	0.0118781i
$188$		0			0
$189$	−20.7537	−	12.2866i	−1.50961	−	0.893718i
$190$		0			0
$191$	−18.8097			−1.36102			−0.680511	−	0.732737i	$-0.738242\pi$
$191$	−18.8097			−1.36102			−0.680511	+	0.732737i	$0.738242\pi$
$192$		0			0
$193$	−11.1498			−0.802582			−0.401291	−	0.915951i	$-0.631438\pi$
$193$	−11.1498			−0.802582			−0.401291	+	0.915951i	$0.631438\pi$
$194$		0			0
$195$	1.68718	−	1.17224i	0.120821	−	0.0839455i
$196$		0			0
$197$	14.7643	−	6.11558i	1.05191	−	0.435717i	0.211340	−	0.977413i	$-0.432217\pi$
$197$	14.7643	−	6.11558i	1.05191	−	0.435717i	0.840575	+	0.541696i	$0.182217\pi$
$198$		0			0
$199$	0.686194	+	0.686194i	0.0486430	+	0.0486430i	0.731010	−	0.682367i	$-0.239049\pi$
$199$	0.686194	+	0.686194i	0.0486430	+	0.0486430i	−0.682367	+	0.731010i	$0.739049\pi$
$200$		0			0
$201$	18.5688	−	4.04566i	1.30974	−	0.285359i
$202$		0			0
$203$	7.29119	−	3.02011i	0.511742	−	0.211970i
$204$		0			0
$205$	6.04246	−	14.5878i	0.422024	−	1.01886i
$206$		0			0
$207$	−12.7331	+	5.82492i	−0.885009	+	0.404860i
$208$		0			0
$209$	0.816817			0.0565004
$210$		0			0
$211$	−2.25868	−	0.935575i	−0.155494	−	0.0644076i	0.303579	−	0.952806i	$-0.401818\pi$
$211$	−2.25868	−	0.935575i	−0.155494	−	0.0644076i	−0.459073	+	0.888399i	$0.651818\pi$
$212$		0			0
$213$	9.10904	+	1.64042i	0.624141	+	0.112400i
$214$		0			0
$215$	11.1881	+	11.1881i	0.763021	+	0.763021i
$216$		0			0
$217$	13.6763	−	13.6763i	0.928409	−	0.928409i
$218$		0			0
$219$	−1.68939	+	9.38096i	−0.114158	+	0.633907i
$220$		0			0
$221$	0.220068	−	0.531291i	0.0148034	−	0.0357385i
$222$		0			0
$223$		−	10.3472i		−	0.692900i	−0.938068	−	0.346450i	$-0.887387\pi$
$223$		−	10.3472i		−	0.692900i	0.938068	−	0.346450i	$-0.112613\pi$
$224$		0			0
$225$	4.42409	+	9.67088i	0.294939	+	0.644725i
$226$		0			0
$227$	10.4804	+	4.34114i	0.695611	+	0.288131i	0.702336	−	0.711846i	$-0.252141\pi$
$227$	10.4804	+	4.34114i	0.695611	+	0.288131i	−0.00672494	+	0.999977i	$0.502141\pi$
$228$		0			0
$229$	7.39471	+	17.8524i	0.488656	+	1.17972i	0.955396	+	0.295326i	$0.0954284\pi$
$229$	7.39471	+	17.8524i	0.488656	+	1.17972i	−0.466740	+	0.884395i	$0.654572\pi$
$230$		0			0
$231$	0.512559	+	2.35254i	0.0337239	+	0.154786i
$232$		0			0
$233$	15.9703	−	15.9703i	1.04625	−	1.04625i	0.0473714	−	0.998877i	$-0.484916\pi$
$233$	15.9703	−	15.9703i	1.04625	−	1.04625i	0.998877	−	0.0473714i	$-0.0150844\pi$
$234$		0			0
$235$	6.08640	+	14.6939i	0.397033	+	0.958522i
$236$		0			0
$237$	−4.76349	−	6.85601i	−0.309422	−	0.445346i
$238$		0			0
$239$			22.5155i			1.45641i	0.685361	+	0.728204i	$0.259645\pi$
$239$			22.5155i			1.45641i	−0.685361	+	0.728204i	$0.740355\pi$
$240$		0			0
$241$		−	21.7886i		−	1.40353i	−0.712409	−	0.701765i	$-0.752396\pi$
$241$		−	21.7886i		−	1.40353i	0.712409	−	0.701765i	$-0.247604\pi$
$242$		0			0
$243$	−1.64133	+	15.5018i	−0.105291	+	0.994441i
$244$		0			0
$245$	−16.2691	−	39.2771i	−1.03939	−	2.50932i
$246$		0			0
$247$	0.782526	−	0.782526i	0.0497909	−	0.0497909i
$248$		0			0
$249$	15.9380	−	3.47249i	1.01003	−	0.220060i
$250$		0			0
$251$	−5.96821	−	14.4085i	−0.376710	−	0.909458i	−0.992578	−	0.121609i	$-0.961195\pi$
$251$	−5.96821	−	14.4085i	−0.376710	−	0.909458i	0.615868	−	0.787849i	$-0.288805\pi$
$252$		0			0
$253$	1.29145	+	0.534937i	0.0811928	+	0.0336312i
$254$		0			0
$255$	6.03769	+	3.87744i	0.378095	+	0.242815i
$256$		0			0
$257$		−	11.8781i		−	0.740934i	−0.928846	−	0.370467i	$-0.879198\pi$
$257$		−	11.8781i		−	0.740934i	0.928846	−	0.370467i	$-0.120802\pi$
$258$		0			0
$259$	13.1242	−	31.6845i	0.815495	−	1.96878i
$260$		0			0
$261$	−3.73556	−	3.47343i	−0.231225	−	0.215000i
$262$		0			0
$263$	3.29543	−	3.29543i	0.203205	−	0.203205i	−0.598167	−	0.801372i	$-0.704104\pi$
$263$	3.29543	−	3.29543i	0.203205	−	0.203205i	0.801372	+	0.598167i	$0.204104\pi$
$264$		0			0
$265$	10.0010	+	10.0010i	0.614357	+	0.614357i
$266$		0			0
$267$	1.60599	−	8.91786i	0.0982849	−	0.545764i
$268$		0			0
$269$	26.9975	+	11.1827i	1.64607	+	0.681824i	0.996890	−	0.0788107i	$-0.0251123\pi$
$269$	26.9975	+	11.1827i	1.64607	+	0.681824i	0.649180	+	0.760635i	$0.275112\pi$
$270$		0			0
$271$	3.49827			0.212505			0.106252	−	0.994339i	$-0.466115\pi$
$271$	3.49827			0.212505			0.106252	+	0.994339i	$0.466115\pi$
$272$		0			0
$273$	2.74482	+	1.76274i	0.166124	+	0.106686i
$274$		0			0
$275$	0.406289	−	0.980869i	0.0245002	−	0.0591486i
$276$		0			0
$277$	10.1905	−	4.22105i	0.612289	−	0.253619i	−0.0549177	−	0.998491i	$-0.517490\pi$
$277$	10.1905	−	4.22105i	0.612289	−	0.253619i	0.667207	+	0.744872i	$0.267490\pi$
$278$		0			0
$279$	−11.7157	−	4.36112i	−0.701399	−	0.261093i
$280$		0			0
$281$	14.1081	+	14.1081i	0.841616	+	0.841616i	0.989069	−	0.147453i	$-0.0471074\pi$
$281$	14.1081	+	14.1081i	0.841616	+	0.841616i	−0.147453	+	0.989069i	$0.547107\pi$
$282$		0			0
$283$	−17.2200	+	7.13275i	−1.02362	+	0.423998i	−0.830406	−	0.557159i	$-0.811892\pi$
$283$	−17.2200	+	7.13275i	−1.02362	+	0.423998i	−0.193215	+	0.981156i	$0.561892\pi$
$284$		0			0
$285$	7.87904	+	11.3402i	0.466714	+	0.671733i
$286$		0			0
$287$	25.0714			1.47992
$288$		0			0
$289$	−14.9915			−0.881851
$290$		0			0
$291$	−10.8670	−	15.6407i	−0.637037	−	0.916877i
$292$		0			0
$293$	−21.6538	+	8.96928i	−1.26503	+	0.523991i	−0.911448	−	0.411414i	$-0.865035\pi$
$293$	−21.6538	+	8.96928i	−1.26503	+	0.523991i	−0.353577	+	0.935405i	$0.615035\pi$
$294$		0			0
$295$	7.43753	+	7.43753i	0.433030	+	0.433030i
$296$		0			0
$297$	1.24491	−	0.933812i	0.0722372	−	0.0541853i
$298$		0			0
$299$	1.74971	−	0.724755i	0.101189	−	0.0419137i
$300$		0			0
$301$	−9.61423	+	23.2108i	−0.554155	+	1.33785i
$302$		0			0
$303$	3.96733	+	2.54784i	0.227917	+	0.146370i
$304$		0			0
$305$	−34.6868			−1.98616
$306$		0			0
$307$	19.7154	+	8.16639i	1.12522	+	0.466081i	0.866153	−	0.499779i	$-0.166585\pi$
$307$	19.7154	+	8.16639i	1.12522	+	0.466081i	0.259065	+	0.965860i	$0.416585\pi$
$308$		0			0
$309$	−0.144518	+	0.802489i	−0.00822132	+	0.0456520i
$310$		0			0
$311$	10.5699	+	10.5699i	0.599365	+	0.599365i	0.940144	−	0.340779i	$-0.110691\pi$
$311$	10.5699	+	10.5699i	0.599365	+	0.599365i	−0.340779	+	0.940144i	$0.610691\pi$
$312$		0			0
$313$	−24.0589	+	24.0589i	−1.35989	+	1.35989i	−0.485846	+	0.874044i	$0.661489\pi$
$313$	−24.0589	+	24.0589i	−1.35989	+	1.35989i	−0.874044	+	0.485846i	$0.838511\pi$
$314$		0			0
$315$	−27.7170	+	29.8087i	−1.56168	+	1.67953i
$316$		0			0
$317$	−8.93517	+	21.5714i	−0.501849	+	1.21157i	0.446626	+	0.894721i	$0.352625\pi$
$317$	−8.93517	+	21.5714i	−0.501849	+	1.21157i	−0.948475	+	0.316851i	$0.897375\pi$
$318$		0			0
$319$			0.509230i			0.0285114i
$320$		0			0
$321$	−0.621949	−	0.399419i	−0.0347138	−	0.0222934i
$322$		0			0
$323$	3.57101	+	1.47916i	0.198696	+	0.0823027i
$324$		0			0
$325$	−0.550458	−	1.32892i	−0.0305339	−	0.0737154i
$326$		0			0
$327$	8.03897	−	1.75149i	0.444556	−	0.0968575i
$328$		0			0
$329$	−17.8571	+	17.8571i	−0.984492	+	0.984492i
$330$		0			0
$331$	10.6785	+	25.7802i	0.586943	+	1.41701i	0.886411	+	0.462900i	$0.153191\pi$
$331$	10.6785	+	25.7802i	0.586943	+	1.41701i	−0.299467	+	0.954107i	$0.596809\pi$
$332$		0			0
$333$	−22.1517	+	0.805461i	−1.21391	+	0.0441390i
$334$		0			0
$335$		−	32.0736i		−	1.75237i
$336$		0			0
$337$			7.72298i			0.420698i	0.977626	+	0.210349i	$0.0674600\pi$
$337$			7.72298i			0.420698i	−0.977626	+	0.210349i	$0.932540\pi$
$338$		0			0
$339$	−18.3152	−	26.3608i	−0.994747	−	1.43172i
$340$		0			0
$341$	0.477589	+	1.15300i	0.0258629	+	0.0624385i
$342$		0			0
$343$	24.7581	−	24.7581i	1.33681	−	1.33681i
$344$		0			0
$345$	5.03065	+	23.0897i	0.270841	+	1.24311i
$346$		0			0
$347$	2.88801	+	6.97227i	0.155037	+	0.374291i	0.982245	−	0.187604i	$-0.0600723\pi$
$347$	2.88801	+	6.97227i	0.155037	+	0.374291i	−0.827208	+	0.561896i	$0.810072\pi$
$348$		0			0
$349$	−3.70439	−	1.53441i	−0.198292	−	0.0821351i	0.281328	−	0.959612i	$-0.409225\pi$
$349$	−3.70439	−	1.53441i	−0.198292	−	0.0821351i	−0.479619	+	0.877477i	$0.659225\pi$
$350$		0			0
$351$	0.298041	−	2.08726i	0.0159083	−	0.111410i
$352$		0			0
$353$			33.0427i			1.75869i	0.476189	+	0.879343i	$0.342018\pi$
$353$			33.0427i			1.75869i	−0.476189	+	0.879343i	$0.657982\pi$
$354$		0			0
$355$	5.97773	−	14.4315i	0.317265	−	0.765945i
$356$		0			0
$357$	−2.01934	+	11.2132i	−0.106875	+	0.593463i
$358$		0			0
$359$	1.02805	−	1.02805i	0.0542584	−	0.0542584i	−0.679457	−	0.733715i	$-0.737785\pi$
$359$	1.02805	−	1.02805i	0.0542584	−	0.0542584i	0.733715	+	0.679457i	$0.237785\pi$
$360$		0			0
$361$	−8.17537	−	8.17537i	−0.430283	−	0.430283i
$362$		0			0
$363$	18.5980	+	3.34926i	0.976143	+	0.175791i
$364$		0			0
$365$	14.8623	+	6.15618i	0.777930	+	0.322229i
$366$		0			0
$367$	11.6801			0.609694			0.304847	−	0.952401i	$-0.401395\pi$
$367$	11.6801			0.609694			0.304847	+	0.952401i	$0.401395\pi$
$368$		0			0
$369$	−6.74119	−	14.7360i	−0.350932	−	0.767125i
$370$		0			0
$371$	−8.59414	+	20.7481i	−0.446185	+	1.07719i
$372$		0			0
$373$	11.6155	−	4.81129i	0.601427	−	0.249119i	−0.0611312	−	0.998130i	$-0.519471\pi$
$373$	11.6155	−	4.81129i	0.601427	−	0.249119i	0.662558	+	0.749011i	$0.269471\pi$
$374$		0			0
$375$	−7.19829	+	1.56832i	−0.371718	+	0.0809879i
$376$		0			0
$377$	0.487851	+	0.487851i	0.0251256	+	0.0251256i
$378$		0			0
$379$	15.2623	−	6.32186i	0.783972	−	0.324732i	0.0454550	−	0.998966i	$-0.485526\pi$
$379$	15.2623	−	6.32186i	0.783972	−	0.324732i	0.738517	+	0.674234i	$0.235526\pi$
$380$		0			0
$381$	6.82782	−	4.74390i	0.349800	−	0.243038i
$382$		0			0
$383$	−28.9536			−1.47946			−0.739729	−	0.672905i	$-0.765046\pi$
$383$	−28.9536			−1.47946			−0.739729	+	0.672905i	$0.765046\pi$
$384$		0			0
$385$	4.06351			0.207096
$386$		0			0
$387$	16.2275	−	0.590049i	0.824889	−	0.0299939i
$388$		0			0
$389$	6.31149	−	2.61431i	0.320005	−	0.132551i	−0.216898	−	0.976194i	$-0.569594\pi$
$389$	6.31149	−	2.61431i	0.320005	−	0.132551i	0.536903	+	0.843644i	$0.319594\pi$
$390$		0			0
$391$	4.67733	+	4.67733i	0.236543	+	0.236543i
$392$		0			0
$393$	8.06654	+	37.0238i	0.406903	+	1.86760i
$394$		0			0
$395$	−13.0170	+	5.39183i	−0.654958	+	0.271293i
$396$		0			0
$397$	1.66407	−	4.01741i	0.0835171	−	0.201628i	−0.876604	−	0.481212i	$-0.840197\pi$
$397$	1.66407	−	4.01741i	0.0835171	−	0.201628i	0.960121	+	0.279584i	$0.0901966\pi$
$398$		0			0
$399$	−11.8480	+	18.4490i	−0.593143	+	0.923604i
$400$		0			0
$401$	3.93840			0.196674			0.0983371	−	0.995153i	$-0.468648\pi$
$401$	3.93840			0.196674			0.0983371	+	0.995153i	$0.468648\pi$
$402$		0			0
$403$	1.56214	+	0.647058i	0.0778155	+	0.0322322i
$404$		0			0
$405$	24.9729	+	8.27601i	1.24091	+	0.411238i
$406$		0			0
$407$	1.56476	+	1.56476i	0.0775621	+	0.0775621i
$408$		0			0
$409$	12.8960	−	12.8960i	0.637664	−	0.637664i	−0.312314	−	0.949979i	$-0.601104\pi$
$409$	12.8960	−	12.8960i	0.637664	−	0.637664i	0.949979	+	0.312314i	$0.101104\pi$
$410$		0			0
$411$	30.6889	+	5.52667i	1.51377	+	0.272610i
$412$		0			0
$413$	−6.39128	+	15.4299i	−0.314494	+	0.759256i
$414$		0			0
$415$		−	27.5295i		−	1.35137i
$416$		0			0
$417$	−0.473084	+	0.736656i	−0.0231670	+	0.0360742i
$418$		0			0
$419$	−5.81232	−	2.40754i	−0.283951	−	0.117616i	0.236163	−	0.971714i	$-0.424110\pi$
$419$	−5.81232	−	2.40754i	−0.283951	−	0.117616i	−0.520113	+	0.854097i	$0.674110\pi$
$420$		0			0
$421$	−7.88620	−	19.0390i	−0.384350	−	0.927903i	−0.991113	−	0.133020i	$-0.957532\pi$
$421$	−7.88620	−	19.0390i	−0.384350	−	0.927903i	0.606763	−	0.794883i	$-0.292468\pi$
$422$		0			0
$423$	15.2971	+	5.69428i	0.743770	+	0.276865i
$424$		0			0
$425$	3.55248	−	3.55248i	0.172321	−	0.172321i
$426$		0			0
$427$	−21.0770	−	50.8843i	−1.01999	−	2.46246i
$428$		0			0
$429$	−0.172860	+	0.120102i	−0.00834578	+	0.00579857i
$430$		0			0
$431$			33.6809i			1.62235i	0.584801	+	0.811177i	$0.301173\pi$
$431$			33.6809i			1.62235i	−0.584801	+	0.811177i	$0.698827\pi$
$432$		0			0
$433$		−	20.3471i		−	0.977819i	−0.872335	−	0.488909i	$-0.837395\pi$
$433$		−	20.3471i		−	0.977819i	0.872335	−	0.488909i	$-0.162605\pi$
$434$		0			0
$435$	−7.06982	+	4.91204i	−0.338972	+	0.235514i
$436$		0			0
$437$	4.87135	+	11.7605i	0.233028	+	0.562580i
$438$		0			0
$439$	12.4753	−	12.4753i	0.595414	−	0.595414i	−0.343675	−	0.939089i	$-0.611672\pi$
$439$	12.4753	−	12.4753i	0.595414	−	0.595414i	0.939089	+	0.343675i	$0.111672\pi$
$440$		0			0
$441$	−40.8895	−	15.2209i	−1.94712	−	0.724807i
$442$		0			0
$443$	10.7190	+	25.8778i	0.509273	+	1.22949i	0.944303	+	0.329077i	$0.106738\pi$
$443$	10.7190	+	25.8778i	0.509273	+	1.22949i	−0.435030	+	0.900416i	$0.643262\pi$
$444$		0			0
$445$	−14.1286	−	5.85227i	−0.669761	−	0.277424i
$446$		0			0
$447$	10.5644	−	16.4502i	0.499678	−	0.778066i
$448$		0			0
$449$			16.2439i			0.766596i	0.923625	+	0.383298i	$0.125212\pi$
$449$			16.2439i			0.766596i	−0.923625	+	0.383298i	$0.874788\pi$
$450$		0			0
$451$	−0.619083	+	1.49460i	−0.0291515	+	0.0703779i
$452$		0			0
$453$	33.1924	+	5.97751i	1.55952	+	0.280848i
$454$		0			0
$455$	3.89292	−	3.89292i	0.182503	−	0.182503i
$456$		0			0
$457$	−2.84177	−	2.84177i	−0.132932	−	0.132932i	0.637510	−	0.770442i	$-0.279965\pi$
$457$	−2.84177	−	2.84177i	−0.132932	−	0.132932i	−0.770442	+	0.637510i	$0.779965\pi$
$458$		0			0
$459$	7.13361	−	1.82810i	0.332968	−	0.0853284i
$460$		0			0
$461$	−20.8642	−	8.64224i	−0.971743	−	0.402509i	−0.160382	−	0.987055i	$-0.551273\pi$
$461$	−20.8642	−	8.64224i	−0.971743	−	0.402509i	−0.811361	+	0.584546i	$0.801273\pi$
$462$		0			0
$463$	−22.3599			−1.03915			−0.519576	−	0.854424i	$-0.673910\pi$
$463$	−22.3599			−1.03915			−0.519576	+	0.854424i	$0.673910\pi$
$464$		0			0
$465$	−11.4007	+	17.7524i	−0.528694	+	0.823248i
$466$		0			0
$467$	3.58346	−	8.65124i	0.165823	−	0.400332i	−0.819024	−	0.573760i	$-0.805484\pi$
$467$	3.58346	−	8.65124i	0.165823	−	0.400332i	0.984847	+	0.173428i	$0.0554844\pi$
$468$		0			0
$469$	47.0508	−	19.4891i	2.17260	−	0.899922i
$470$		0			0
$471$	3.17148	+	14.5565i	0.146134	+	0.670726i
$472$		0			0
$473$	−1.14628	−	1.14628i	−0.0527060	−	0.0527060i
$474$		0			0
$475$	8.93220	−	3.69984i	0.409838	−	0.169760i
$476$		0			0
$477$	14.5057	−	0.527443i	0.664170	−	0.0241500i
$478$		0			0
$479$	1.51545			0.0692426			0.0346213	−	0.999401i	$-0.488977\pi$
$479$	1.51545			0.0692426			0.0346213	+	0.999401i	$0.488977\pi$
$480$		0			0
$481$	2.99813			0.136703
$482$		0			0
$483$	−30.8149	+	21.4099i	−1.40213	+	0.974185i
$484$		0			0
$485$	−29.6960	+	12.3005i	−1.34843	+	0.558536i
$486$		0			0
$487$	10.7114	+	10.7114i	0.485378	+	0.485378i	0.906844	−	0.421466i	$-0.138484\pi$
$487$	10.7114	+	10.7114i	0.485378	+	0.485378i	−0.421466	+	0.906844i	$0.638484\pi$
$488$		0			0
$489$	21.1224	−	4.60203i	0.955188	−	0.208111i
$490$		0			0
$491$	20.2550	−	8.38989i	0.914095	−	0.378630i	0.124472	−	0.992223i	$-0.460276\pi$
$491$	20.2550	−	8.38989i	0.914095	−	0.378630i	0.789623	+	0.613593i	$0.210276\pi$
$492$		0			0
$493$	−0.922155	+	2.22628i	−0.0415318	+	0.100267i
$494$		0			0
$495$	−1.09260	−	2.38837i	−0.0491085	−	0.107349i
$496$		0			0
$497$	24.8028			1.11256
$498$		0			0
$499$	−10.2527	−	4.24681i	−0.458974	−	0.190113i	0.141203	−	0.989981i	$-0.454903\pi$
$499$	−10.2527	−	4.24681i	−0.458974	−	0.190113i	−0.600177	+	0.799867i	$0.704903\pi$
$500$		0			0
$501$	−35.5784	−	6.40720i	−1.58953	−	0.286253i
$502$		0			0
$503$	−14.9291	−	14.9291i	−0.665655	−	0.665655i	0.291052	−	0.956707i	$-0.405995\pi$
$503$	−14.9291	−	14.9291i	−0.665655	−	0.665655i	−0.956707	+	0.291052i	$0.905995\pi$
$504$		0			0
$505$	5.62678	−	5.62678i	0.250389	−	0.250389i
$506$		0			0
$507$	3.94021	−	21.8795i	0.174991	−	0.971704i
$508$		0			0
$509$	0.540947	−	1.30596i	0.0239770	−	0.0578857i	−0.911438	−	0.411438i	$-0.865027\pi$
$509$	0.540947	−	1.30596i	0.0239770	−	0.0578857i	0.935415	+	0.353553i	$0.115027\pi$
$510$		0			0
$511$			25.5432i			1.12997i
$512$		0			0
$513$	14.0293	+	2.00325i	0.619407	+	0.0884456i
$514$		0			0
$515$	1.27139	+	0.526627i	0.0560241	+	0.0232059i
$516$		0			0
$517$	−0.623584	−	1.50547i	−0.0274252	−	0.0662103i
$518$		0			0
$519$	−3.03645	−	13.9367i	−0.133286	−	0.611754i
$520$		0			0
$521$	4.02013	−	4.02013i	0.176125	−	0.176125i	−0.613539	−	0.789664i	$-0.710255\pi$
$521$	4.02013	−	4.02013i	0.176125	−	0.176125i	0.789664	+	0.613539i	$0.210255\pi$
$522$		0			0
$523$	−2.35502	−	5.68552i	−0.102978	−	0.248610i	0.863990	−	0.503509i	$-0.167958\pi$
$523$	−2.35502	−	5.68552i	−0.102978	−	0.248610i	−0.966968	+	0.254899i	$0.917958\pi$
$524$		0			0
$525$	16.2610	+	23.4042i	0.709690	+	1.02144i
$526$		0			0
$527$			5.90561i			0.257253i
$528$		0			0
$529$		−	1.21549i		−	0.0528475i
$530$		0			0
$531$	10.7876	−	0.392248i	0.468141	−	0.0170221i
$532$		0			0
$533$	0.838760	+	2.02495i	0.0363307	+	0.0877101i
$534$		0			0
$535$	−0.882097	+	0.882097i	−0.0381364	+	0.0381364i
$536$		0			0
$537$	6.13513	−	1.33669i	0.264750	−	0.0576823i
$538$		0			0
$539$	1.66686	+	4.02415i	0.0717966	+	0.173332i
$540$		0			0
$541$	−27.0891	−	11.2207i	−1.16465	−	0.482414i	−0.285230	−	0.958459i	$-0.592070\pi$
$541$	−27.0891	−	11.2207i	−1.16465	−	0.482414i	−0.879421	+	0.476045i	$0.842070\pi$
$542$		0			0
$543$	10.2767	+	6.59973i	0.441014	+	0.283222i
$544$		0			0
$545$		−	13.8856i		−	0.594794i
$546$		0			0
$547$	−2.18960	+	5.28616i	−0.0936205	+	0.226020i	−0.963752	−	0.266800i	$-0.914034\pi$
$547$	−2.18960	+	5.28616i	−0.0936205	+	0.226020i	0.870132	+	0.492820i	$0.164034\pi$
$548$		0			0
$549$	−24.2406	+	26.0700i	−1.03456	+	1.11264i
$550$		0			0
$551$	−3.27904	+	3.27904i	−0.139692	+	0.139692i
$552$		0			0
$553$	−15.8193	−	15.8193i	−0.672703	−	0.672703i
$554$		0			0
$555$	−6.63039	+	36.8178i	−0.281445	+	1.56283i
$556$		0			0
$557$	−33.6235	−	13.9273i	−1.42467	−	0.590119i	−0.468644	−	0.883387i	$-0.655257\pi$
$557$	−33.6235	−	13.9273i	−1.42467	−	0.590119i	−0.956030	+	0.293268i	$0.905257\pi$
$558$		0			0
$559$	−2.19631			−0.0928941
$560$		0			0
$561$	−0.618594	−	0.397264i	−0.0261171	−	0.0167725i
$562$		0			0
$563$	10.2970	−	24.8591i	0.433965	−	1.04768i	−0.544031	−	0.839065i	$-0.683103\pi$
$563$	10.2970	−	24.8591i	0.433965	−	1.04768i	0.977997	−	0.208620i	$-0.0668972\pi$
$564$		0			0
$565$	−50.0494	+	20.7312i	−2.10560	+	0.872166i
$566$		0			0
$567$	3.03385	+	41.6632i	0.127410	+	1.74969i
$568$		0			0
$569$	−5.01618	−	5.01618i	−0.210289	−	0.210289i	0.594101	−	0.804390i	$-0.297508\pi$
$569$	−5.01618	−	5.01618i	−0.210289	−	0.210289i	−0.804390	+	0.594101i	$0.797508\pi$
$570$		0			0
$571$	8.20928	−	3.40040i	0.343548	−	0.142302i	−0.204237	−	0.978921i	$-0.565471\pi$
$571$	8.20928	−	3.40040i	0.343548	−	0.142302i	0.547785	+	0.836619i	$0.315471\pi$
$572$		0			0
$573$	18.5894	+	26.7554i	0.776583	+	1.11772i
$574$		0			0
$575$	16.5455			0.689997
$576$		0			0
$577$	36.7704			1.53077			0.765386	−	0.643571i	$-0.222548\pi$
$577$	36.7704			1.53077			0.765386	+	0.643571i	$0.222548\pi$
$578$		0			0
$579$	11.0192	+	15.8598i	0.457943	+	0.659109i
$580$		0			0
$581$	40.3848	−	16.7279i	1.67544	−	0.693992i
$582$		0			0
$583$	−1.02466	−	1.02466i	−0.0424369	−	0.0424369i
$584$		0			0
$585$	−3.33483	−	1.24138i	−0.137878	−	0.0513246i
$586$		0			0
$587$	22.3129	−	9.24233i	0.920954	−	0.381472i	0.128714	−	0.991682i	$-0.458915\pi$
$587$	22.3129	−	9.24233i	0.920954	−	0.381472i	0.792240	+	0.610210i	$0.208915\pi$
$588$		0			0
$589$	−4.34912	+	10.4997i	−0.179202	+	0.432633i
$590$		0			0
$591$	−23.2903	−	14.9572i	−0.958036	−	0.615256i
$592$		0			0
$593$	2.15691			0.0885737			0.0442868	−	0.999019i	$-0.485898\pi$
$593$	2.15691			0.0885737			0.0442868	+	0.999019i	$0.485898\pi$
$594$		0			0
$595$	17.7651	+	7.35854i	0.728297	+	0.301671i
$596$		0			0
$597$	0.297902	−	1.65421i	0.0121923	−	0.0677025i
$598$		0			0
$599$	−4.80949	−	4.80949i	−0.196511	−	0.196511i	0.601992	−	0.798502i	$-0.294374\pi$
$599$	−4.80949	−	4.80949i	−0.196511	−	0.196511i	−0.798502	+	0.601992i	$0.794374\pi$
$600$		0			0
$601$	5.18282	−	5.18282i	0.211411	−	0.211411i	−0.593455	−	0.804867i	$-0.702237\pi$
$601$	5.18282	−	5.18282i	0.211411	−	0.211411i	0.804867	+	0.593455i	$0.202237\pi$
$602$		0			0
$603$	−24.1059	−	22.4144i	−0.981669	−	0.912785i
$604$		0			0
$605$	12.2048	−	29.4650i	0.496196	−	1.19792i
$606$		0			0
$607$		−	5.19779i		−	0.210972i	−0.994421	−	0.105486i	$-0.966360\pi$
$607$		−	5.19779i		−	0.210972i	0.994421	−	0.105486i	$-0.0336398\pi$
$608$		0			0
$609$	−11.5017	−	7.38643i	−0.466071	−	0.299313i
$610$		0			0
$611$	−2.03967	−	0.844859i	−0.0825162	−	0.0341793i
$612$		0			0
$613$	−12.1586	−	29.3536i	−0.491083	−	1.18558i	−0.954170	−	0.299266i	$-0.903258\pi$
$613$	−12.1586	−	29.3536i	−0.491083	−	1.18558i	0.463087	−	0.886313i	$-0.346742\pi$
$614$		0			0
$615$	−26.7217	+	5.82198i	−1.07752	+	0.234765i
$616$		0			0
$617$	10.7968	−	10.7968i	0.434663	−	0.434663i	−0.455548	−	0.890211i	$-0.650557\pi$
$617$	10.7968	−	10.7968i	0.434663	−	0.434663i	0.890211	+	0.455548i	$0.150557\pi$
$618$		0			0
$619$	11.7667	+	28.4074i	0.472944	+	1.14179i	0.962856	+	0.270016i	$0.0870290\pi$
$619$	11.7667	+	28.4074i	0.472944	+	1.14179i	−0.489912	+	0.871772i	$0.662971\pi$
$620$		0			0
$621$	20.8694	+	12.3551i	0.837461	+	0.495794i
$622$		0			0
$623$		−	24.2822i		−	0.972848i
$624$		0			0
$625$			30.1581i			1.20633i
$626$		0			0
$627$	−0.807250	−	1.16186i	−0.0322384	−	0.0464002i
$628$		0			0
$629$	4.00730	+	9.67449i	0.159782	+	0.385747i
$630$		0			0
$631$	−5.17311	+	5.17311i	−0.205938	+	0.205938i	−0.802539	−	0.596600i	$-0.796518\pi$
$631$	−5.17311	+	5.17311i	−0.205938	+	0.205938i	0.596600	+	0.802539i	$0.296518\pi$
$632$		0			0
$633$	0.901437	+	4.13741i	0.0358289	+	0.164447i
$634$		0			0
$635$	−5.36966	−	12.9635i	−0.213088	−	0.514441i
$636$		0			0
$637$	5.45209	+	2.25833i	0.216020	+	0.0894782i
$638$		0			0
$639$	−6.66897	−	14.5781i	−0.263820	−	0.576701i
$640$		0			0
$641$		−	35.5298i		−	1.40334i	−0.712500	−	0.701672i	$-0.752437\pi$
$641$		−	35.5298i		−	1.40334i	0.712500	−	0.701672i	$-0.247563\pi$
$642$		0			0
$643$	−3.04889	+	7.36067i	−0.120237	+	0.290277i	−0.972526	−	0.232793i	$-0.925213\pi$
$643$	−3.04889	+	7.36067i	−0.120237	+	0.290277i	0.852290	+	0.523070i	$0.175213\pi$
$644$		0			0
$645$	4.85716	−	26.9712i	0.191251	−	1.06199i
$646$		0			0
$647$	−9.34579	+	9.34579i	−0.367421	+	0.367421i	−0.866536	−	0.499115i	$-0.833659\pi$
$647$	−9.34579	+	9.34579i	−0.367421	+	0.367421i	0.499115	+	0.866536i	$0.333659\pi$
$648$		0			0
$649$	−0.762015	−	0.762015i	−0.0299117	−	0.0299117i
$650$		0			0
$651$	−32.9696	−	5.93739i	−1.29218	−	0.232705i
$652$		0			0
$653$	−3.13779	−	1.29972i	−0.122791	−	0.0508618i	0.320442	−	0.947268i	$-0.396169\pi$
$653$	−3.13779	−	1.29972i	−0.122791	−	0.0508618i	−0.443233	+	0.896406i	$0.646169\pi$
$654$		0			0
$655$	63.9506			2.49876
$656$		0			0
$657$	15.0133	−	6.86805i	0.585725	−	0.267948i
$658$		0			0
$659$	−12.0747	+	29.1508i	−0.470362	+	1.13555i	0.493642	+	0.869665i	$0.335665\pi$
$659$	−12.0747	+	29.1508i	−0.470362	+	1.13555i	−0.964004	+	0.265889i	$0.914335\pi$
$660$		0			0
$661$	−21.5134	+	8.91114i	−0.836774	+	0.346603i	−0.759581	−	0.650413i	$-0.774596\pi$
$661$	−21.5134	+	8.91114i	−0.836774	+	0.346603i	−0.0771932	+	0.997016i	$0.524596\pi$
$662$		0			0
$663$	−0.973211	+	0.212038i	−0.0377964	+	0.00823487i
$664$		0			0
$665$	26.1658	+	26.1658i	1.01467	+	1.01467i
$666$		0			0
$667$	−7.33186	+	3.03696i	−0.283891	+	0.117591i
$668$		0			0
$669$	−14.7181	+	10.2260i	−0.569035	+	0.395360i
$670$		0			0
$671$	3.55385			0.137195
$672$		0			0
$673$	−27.9251			−1.07643			−0.538216	−	0.842807i	$-0.680902\pi$
$673$	−27.9251			−1.07643			−0.538216	+	0.842807i	$0.680902\pi$
$674$		0			0
$675$	9.38383	−	15.8505i	0.361184	−	0.610087i
$676$		0			0
$677$	6.25960	−	2.59281i	0.240576	−	0.0996498i	−0.259138	−	0.965840i	$-0.583438\pi$
$677$	6.25960	−	2.59281i	0.240576	−	0.0996498i	0.499714	+	0.866191i	$0.333438\pi$
$678$		0			0
$679$	−36.0887	−	36.0887i	−1.38496	−	1.38496i
$680$		0			0
$681$	−4.18273	−	19.1979i	−0.160283	−	0.735665i
$682$		0			0
$683$	−26.2767	+	10.8842i	−1.00545	+	0.416471i	−0.823793	−	0.566891i	$-0.808146\pi$
$683$	−26.2767	+	10.8842i	−1.00545	+	0.416471i	−0.181657	+	0.983362i	$0.558146\pi$
$684$		0			0
$685$	20.1393	−	48.6207i	0.769484	−	1.85770i
$686$		0			0
$687$	18.0856	−	28.1617i	0.690009	−	1.07444i
$688$		0			0
$689$	−1.96328			−0.0747950
$690$		0			0
$691$	26.2910	+	10.8901i	1.00016	+	0.414279i	0.821855	−	0.569697i	$-0.192939\pi$
$691$	26.2910	+	10.8901i	1.00016	+	0.414279i	0.178303	+	0.983976i	$0.442939\pi$
$692$		0			0
$693$	2.83975	−	3.05406i	0.107873	−	0.116014i
$694$		0			0
$695$	1.04478	+	1.04478i	0.0396309	+	0.0396309i
$696$		0			0
$697$	−5.41308	+	5.41308i	−0.205035	+	0.205035i
$698$		0			0
$699$	−38.4998	−	6.93330i	−1.45619	−	0.262241i
$700$		0			0
$701$	15.7331	−	37.9830i	0.594230	−	1.43460i	−0.285153	−	0.958482i	$-0.592044\pi$
$701$	15.7331	−	37.9830i	0.594230	−	1.43460i	0.879383	−	0.476116i	$-0.157956\pi$
$702$		0			0
$703$			20.1516i			0.760032i
$704$		0			0
$705$	14.8858	−	23.1792i	0.560632	−	0.872979i
$706$		0			0
$707$	11.6733	+	4.83525i	0.439021	+	0.181848i
$708$		0			0
$709$	−3.26185	−	7.87481i	−0.122501	−	0.295745i	0.850718	−	0.525622i	$-0.176167\pi$
$709$	−3.26185	−	7.87481i	−0.122501	−	0.295745i	−0.973220	+	0.229877i	$0.926167\pi$
$710$		0			0
$711$	−5.04446	+	13.5514i	−0.189182	+	0.508218i
$712$		0			0
$713$	−13.7526	+	13.7526i	−0.515039	+	0.515039i
$714$		0			0
$715$	0.135944	+	0.328198i	0.00508402	+	0.0122739i
$716$		0			0
$717$	32.0266	−	22.2518i	1.19606	−	0.831008i
$718$		0			0
$719$		−	6.72495i		−	0.250798i	−0.992106	−	0.125399i	$-0.959979\pi$
$719$		−	6.72495i		−	0.250798i	0.992106	−	0.125399i	$-0.0400211\pi$
$720$		0			0
$721$			2.18508i			0.0813766i
$722$		0			0
$723$	−30.9927	+	21.5334i	−1.15263	+	0.800836i
$724$		0			0
$725$	2.30660	+	5.56862i	0.0856649	+	0.206813i
$726$		0			0
$727$	−11.8994	+	11.8994i	−0.441326	+	0.441326i	−0.892457	−	0.451132i	$-0.851021\pi$
$727$	−11.8994	+	11.8994i	−0.441326	+	0.441326i	0.451132	+	0.892457i	$0.351021\pi$
$728$		0			0
$729$	23.6722	−	12.9856i	0.876750	−	0.480947i
$730$		0			0
$731$	−2.93559	−	7.08715i	−0.108577	−	0.262128i
$732$		0			0
$733$	27.8224	+	11.5244i	1.02764	+	0.425664i	0.831861	−	0.554984i	$-0.187276\pi$
$733$	27.8224	+	11.5244i	1.02764	+	0.425664i	0.195782	+	0.980647i	$0.437276\pi$
$734$		0			0
$735$	−39.7901	+	61.9586i	−1.46768	+	2.28538i
$736$		0			0
$737$			3.28611i			0.121045i
$738$		0			0
$739$	9.46555	−	22.8519i	0.348196	−	0.840619i	−0.648637	−	0.761098i	$-0.724661\pi$
$739$	9.46555	−	22.8519i	0.348196	−	0.840619i	0.996833	−	0.0795214i	$-0.0253392\pi$
$740$		0			0
$741$	−1.88644	−	0.339724i	−0.0693002	−	0.0124801i
$742$		0			0
$743$	−34.0574	+	34.0574i	−1.24944	+	1.24944i	−0.293479	+	0.955966i	$0.594813\pi$
$743$	−34.0574	+	34.0574i	−1.24944	+	1.24944i	−0.955966	+	0.293479i	$0.905187\pi$
$744$		0			0
$745$	−23.3309	−	23.3309i	−0.854778	−	0.854778i
$746$		0			0
$747$	−20.6907	−	19.2388i	−0.757033	−	0.703911i
$748$		0			0
$749$	−1.83000	−	0.758011i	−0.0668667	−	0.0276971i
$750$		0			0
$751$	−28.4849			−1.03943			−0.519714	−	0.854341i	$-0.673961\pi$
$751$	−28.4849			−1.03943			−0.519714	+	0.854341i	$0.673961\pi$
$752$		0			0
$753$	−14.5967	+	22.7291i	−0.531935	+	0.828294i
$754$		0			0
$755$	21.7822	−	52.5870i	0.792737	−	1.91384i
$756$		0			0
$757$	−25.6728	+	10.6340i	−0.933093	+	0.386500i	−0.796851	−	0.604176i	$-0.793502\pi$
$757$	−25.6728	+	10.6340i	−0.933093	+	0.386500i	−0.136242	+	0.990676i	$0.543502\pi$
$758$		0			0
$759$	−0.515417	−	2.36566i	−0.0187085	−	0.0858681i
$760$		0			0
$761$	−29.3477	−	29.3477i	−1.06385	−	1.06385i	−0.997817	−	0.0660371i	$-0.978964\pi$
$761$	−29.3477	−	29.3477i	−1.06385	−	1.06385i	−0.0660371	−	0.997817i	$-0.521036\pi$
$762$		0			0
$763$	20.3697	−	8.43740i	0.737432	−	0.305454i
$764$		0			0
$765$	−0.451611	−	12.4202i	−0.0163280	−	0.449053i
$766$		0			0
$767$	−1.46005			−0.0527193
$768$		0			0
$769$	−32.2426			−1.16270			−0.581349	−	0.813654i	$-0.697475\pi$
$769$	−32.2426			−1.16270			−0.581349	+	0.813654i	$0.697475\pi$
$770$		0			0
$771$	−16.8957	+	11.7389i	−0.608482	+	0.422768i
$772$		0			0
$773$	−12.3588	+	5.11920i	−0.444517	+	0.184125i	−0.593703	−	0.804684i	$-0.702335\pi$
$773$	−12.3588	+	5.11920i	−0.444517	+	0.184125i	0.149186	+	0.988809i	$0.452335\pi$
$774$		0			0
$775$	10.4452	+	10.4452i	0.375203	+	0.375203i
$776$		0			0
$777$	−58.0392	+	12.6453i	−2.08215	+	0.453647i
$778$		0			0
$779$	−13.6104	+	5.63762i	−0.487644	+	0.201989i
$780$		0			0
$781$	−0.612450	+	1.47859i	−0.0219152	+	0.0529079i
$782$		0			0
$783$	−1.24889	+	8.74629i	−0.0446316	+	0.312567i
$784$		0			0
$785$	25.1432			0.897398
$786$		0			0
$787$	−38.0948	−	15.7794i	−1.35793	−	0.562475i	−0.419444	−	0.907781i	$-0.637775\pi$
$787$	−38.0948	−	15.7794i	−1.35793	−	0.562475i	−0.938490	+	0.345307i	$0.887775\pi$
$788$		0			0
$789$	−7.94432	−	1.43067i	−0.282825	−	0.0509331i
$790$		0			0
$791$	−60.8237	−	60.8237i	−2.16264	−	2.16264i
$792$		0			0
$793$	3.40465	−	3.40465i	0.120903	−	0.120903i
$794$		0			0
$795$	4.34181	−	24.1095i	0.153988	−	0.855076i
$796$		0			0
$797$	−5.35573	+	12.9299i	−0.189710	+	0.458000i	−0.989904	−	0.141742i	$-0.954730\pi$
$797$	−5.35573	+	12.9299i	−0.189710	+	0.458000i	0.800194	+	0.599741i	$0.204730\pi$
$798$		0			0
$799$		−	7.71092i		−	0.272793i
$800$		0			0
$801$	−14.2721	+	6.52900i	−0.504282	+	0.230691i
$802$		0			0
$803$	−1.52272	−	0.630733i	−0.0537358	−	0.0222581i
$804$		0			0
$805$	24.2341	+	58.5062i	0.854138	+	2.06207i
$806$		0			0
$807$	−10.7747	−	49.4537i	−0.379288	−	1.74085i
$808$		0			0
$809$	20.7156	−	20.7156i	0.728323	−	0.728323i	−0.241963	−	0.970286i	$-0.577791\pi$
$809$	20.7156	−	20.7156i	0.728323	−	0.728323i	0.970286	+	0.241963i	$0.0777911\pi$
$810$		0			0
$811$	−11.3246	−	27.3401i	−0.397662	−	0.960040i	−0.988219	−	0.153045i	$-0.951092\pi$
$811$	−11.3246	−	27.3401i	−0.397662	−	0.960040i	0.590557	−	0.806996i	$-0.298908\pi$
$812$		0			0
$813$	−3.45730	−	4.97603i	−0.121253	−	0.174517i
$814$		0			0
$815$		−	36.4844i		−	1.27799i
$816$		0			0
$817$		−	14.7623i		−	0.516466i
$818$		0			0
$819$	−0.205309	−	5.64638i	−0.00717407	−	0.197301i
$820$		0			0
$821$	−7.72933	−	18.6602i	−0.269755	−	0.651247i	0.729716	−	0.683750i	$-0.239652\pi$
$821$	−7.72933	−	18.6602i	−0.269755	−	0.651247i	−0.999472	+	0.0325031i	$0.989652\pi$
$822$		0			0
$823$	−9.01439	+	9.01439i	−0.314222	+	0.314222i	−0.846543	−	0.532321i	$-0.821320\pi$
$823$	−9.01439	+	9.01439i	−0.314222	+	0.314222i	0.532321	+	0.846543i	$0.321320\pi$
$824$		0			0
$825$	−1.79674	+	0.391464i	−0.0625545	+	0.0136290i
$826$		0			0
$827$	2.63867	+	6.37031i	0.0917555	+	0.221517i	0.963094	−	0.269165i	$-0.0867476\pi$
$827$	2.63867	+	6.37031i	0.0917555	+	0.221517i	−0.871339	+	0.490682i	$0.836748\pi$
$828$		0			0
$829$	13.8454	+	5.73494i	0.480870	+	0.199183i	0.609932	−	0.792454i	$-0.291197\pi$
$829$	13.8454	+	5.73494i	0.480870	+	0.199183i	−0.129062	+	0.991636i	$0.541197\pi$
$830$		0			0
$831$	−16.0753	−	10.3236i	−0.557645	−	0.358123i
$832$		0			0
$833$			20.6115i			0.714145i
$834$		0			0
$835$	−23.3480	+	56.3672i	−0.807992	+	1.95067i
$836$		0			0
$837$	5.37510	+	20.9747i	0.185791	+	0.724992i
$838$		0			0
$839$	26.1199	−	26.1199i	0.901760	−	0.901760i	−0.0938284	−	0.995588i	$-0.529911\pi$
$839$	26.1199	−	26.1199i	0.901760	−	0.901760i	0.995588	+	0.0938284i	$0.0299105\pi$
$840$		0			0
$841$	18.4618	+	18.4618i	0.636615	+	0.636615i
$842$		0			0
$843$	6.12483	−	34.0105i	0.210950	−	1.17138i
$844$		0			0
$845$	−34.6639	−	14.3583i	−1.19247	−	0.493939i
$846$		0			0
$847$	50.6402			1.74002
$848$		0			0
$849$	27.1641	+	17.4449i	0.932268	+	0.598708i
$850$		0			0
$851$	−13.1974	+	31.8612i	−0.452399	+	1.09219i
$852$		0			0
$853$	1.69735	−	0.703064i	0.0581161	−	0.0240725i	−0.353436	−	0.935459i	$-0.614987\pi$
$853$	1.69735	−	0.703064i	0.0581161	−	0.0240725i	0.411552	+	0.911386i	$0.364987\pi$
$854$		0			0
$855$	8.34377	−	22.4147i	0.285351	−	0.766565i
$856$		0			0
$857$	0.0113831	+	0.0113831i	0.000388840	+	0.000388840i	0.707301	−	0.706912i	$-0.249912\pi$
$857$	0.0113831	+	0.0113831i	0.000388840	+	0.000388840i	−0.706912	+	0.707301i	$0.749912\pi$
$858$		0			0
$859$	−24.9835	+	10.3485i	−0.852428	+	0.353087i	−0.765741	−	0.643149i	$-0.777628\pi$
$859$	−24.9835	+	10.3485i	−0.852428	+	0.353087i	−0.0866863	+	0.996236i	$0.527628\pi$
$860$		0			0
$861$	−24.7777	−	35.6622i	−0.844423	−	1.21536i
$862$		0			0
$863$	−16.4680			−0.560576			−0.280288	−	0.959916i	$-0.590430\pi$
$863$	−16.4680			−0.560576			−0.280288	+	0.959916i	$0.590430\pi$
$864$		0			0
$865$	−24.0727			−0.818496
$866$		0			0
$867$	14.8159	+	21.3242i	0.503173	+	0.724209i
$868$		0			0
$869$	1.33366	−	0.552422i	0.0452415	−	0.0187396i
$870$		0			0
$871$	3.14815	+	3.14815i	0.106671	+	0.106671i
$872$		0			0
$873$	−11.5080	+	30.9151i	−0.389487	+	1.04632i
$874$		0			0
$875$	−18.2395	+	7.55505i	−0.616608	+	0.255407i
$876$		0			0
$877$	11.7332	−	28.3264i	0.396202	−	0.956515i	−0.592357	−	0.805676i	$-0.701802\pi$
$877$	11.7332	−	28.3264i	0.396202	−	0.956515i	0.988558	−	0.150840i	$-0.0481977\pi$
$878$		0			0
$879$	34.1582	+	21.9366i	1.15213	+	0.739903i
$880$		0			0
$881$	−16.3847			−0.552015			−0.276008	−	0.961155i	$-0.589012\pi$
$881$	−16.3847			−0.552015			−0.276008	+	0.961155i	$0.589012\pi$
$882$		0			0
$883$	−22.3631	−	9.26309i	−0.752577	−	0.311728i	−0.0267846	−	0.999641i	$-0.508527\pi$
$883$	−22.3631	−	9.26309i	−0.752577	−	0.311728i	−0.725793	+	0.687914i	$0.758527\pi$
$884$		0			0
$885$	3.22891	−	17.9297i	0.108539	−	0.602702i
$886$		0			0
$887$	30.9346	+	30.9346i	1.03868	+	1.03868i	0.999221	+	0.0394616i	$0.0125643\pi$
$887$	30.9346	+	30.9346i	1.03868	+	1.03868i	0.0394616	+	0.999221i	$0.487436\pi$
$888$		0			0
$889$	15.7542	−	15.7542i	0.528379	−	0.528379i
$890$		0			0
$891$	−2.55861	−	0.847921i	−0.0857166	−	0.0284064i
$892$		0			0
$893$	5.67862	−	13.7094i	0.190028	−	0.458767i
$894$		0			0
$895$		−	10.5971i		−	0.354222i
$896$		0			0
$897$	−2.76013	−	1.77257i	−0.0921579	−	0.0591843i
$898$		0			0
$899$	−6.54585	−	2.71138i	−0.218316	−	0.0904295i
$900$		0			0
$901$	−2.62412	−	6.33518i	−0.0874220	−	0.211055i
$902$		0			0
$903$	42.5172	−	9.26342i	1.41488	−	0.308267i
$904$		0			0
$905$	14.5752	−	14.5752i	0.484496	−	0.484496i
$906$		0			0
$907$	5.03654	+	12.1593i	0.167235	+	0.403742i	0.985173	−	0.171565i	$-0.0548825\pi$
$907$	5.03654	+	12.1593i	0.167235	+	0.403742i	−0.817937	+	0.575307i	$0.804882\pi$
$908$		0			0
$909$	−0.296751	−	8.16122i	−0.00984261	−	0.270691i
$910$		0			0
$911$			32.5810i			1.07946i	0.841840	+	0.539728i	$0.181473\pi$
$911$			32.5810i			1.07946i	−0.841840	+	0.539728i	$0.818527\pi$
$912$		0			0
$913$			2.82055i			0.0933464i
$914$		0			0
$915$	34.2805	+	49.3393i	1.13328	+	1.63111i
$916$		0			0
$917$	38.8587	+	93.8133i	1.28323	+	3.09799i
$918$		0			0
$919$	−8.42914	+	8.42914i	−0.278052	+	0.278052i	−0.832331	−	0.554279i	$-0.812994\pi$
$919$	−8.42914	+	8.42914i	−0.278052	+	0.278052i	0.554279	+	0.832331i	$0.312994\pi$
$920$		0			0
$921$	−7.86841	−	36.1144i	−0.259273	−	1.19001i
$922$		0			0
$923$	0.829774	+	2.00325i	0.0273123	+	0.0659378i
$924$		0			0
$925$	24.1989	+	10.0235i	0.795655	+	0.329571i
$926$		0			0
$927$	1.28430	−	0.587524i	0.0421821	−	0.0192968i
$928$		0			0
$929$			28.0122i			0.919051i	0.888165	+	0.459525i	$0.151981\pi$
$929$			28.0122i			0.919051i	−0.888165	+	0.459525i	$0.848019\pi$
$930$		0			0
$931$	−15.1791	+	36.6456i	−0.497474	+	1.20101i
$932$		0			0
$933$	4.58879	−	25.4810i	0.150230	−	0.834211i
$934$		0			0
$935$	−0.877339	+	0.877339i	−0.0286920	+	0.0286920i
$936$		0			0
$937$	−16.3178	−	16.3178i	−0.533079	−	0.533079i	0.388408	−	0.921487i	$-0.373025\pi$
$937$	−16.3178	−	16.3178i	−0.533079	−	0.533079i	−0.921487	+	0.388408i	$0.873025\pi$
$938$		0			0
$939$	57.9991	+	10.4449i	1.89273	+	0.340855i
$940$		0			0
$941$	10.7582	+	4.45619i	0.350707	+	0.145268i	0.551081	−	0.834452i	$-0.314216\pi$
$941$	10.7582	+	4.45619i	0.350707	+	0.145268i	−0.200374	+	0.979720i	$0.564216\pi$
$942$		0			0
$943$	−25.2112			−0.820991
$944$		0			0
$945$	69.7929	+	9.96578i	2.27036	+	0.324187i
$946$		0			0
$947$	9.56768	−	23.0984i	0.310908	−	0.750598i	−0.688764	−	0.724985i	$-0.741847\pi$
$947$	9.56768	−	23.0984i	0.310908	−	0.750598i	0.999672	−	0.0256122i	$-0.00815350\pi$
$948$		0			0
$949$	−2.06305	+	0.854544i	−0.0669695	+	0.0277397i
$950$		0			0
$951$	39.5142	−	8.60914i	1.28134	−	0.279170i
$952$		0			0
$953$	3.73365	+	3.73365i	0.120945	+	0.120945i	0.764989	−	0.644044i	$-0.222745\pi$
$953$	3.73365	+	3.73365i	0.120945	+	0.120945i	−0.644044	+	0.764989i	$0.722745\pi$
$954$		0			0
$955$	50.7986	−	21.0415i	1.64380	−	0.680886i
$956$		0			0
$957$	0.724340	−	0.503265i	0.0234146	−	0.0162682i
$958$		0			0
$959$	83.5622			2.69836
$960$		0			0
$961$	13.6359			0.439869
$962$		0			0
$963$	0.0465209	+	1.27942i	0.00149912	+	0.0412286i
$964$		0			0
$965$	30.1118	−	12.4727i	0.969334	−	0.401511i
$966$		0			0
$967$	−32.6431	−	32.6431i	−1.04973	−	1.04973i	−0.998697	−	0.0510357i	$-0.983748\pi$
$967$	−32.6431	−	32.6431i	−1.04973	−	1.04973i	−0.0510357	−	0.998697i	$-0.516252\pi$
$968$		0			0
$969$	−1.42519	−	6.54132i	−0.0457836	−	0.210138i
$970$		0			0
$971$	−51.2848	+	21.2429i	−1.64581	+	0.681716i	−0.996865	−	0.0791224i	$-0.974788\pi$
$971$	−51.2848	+	21.2429i	−1.64581	+	0.681716i	−0.648942	+	0.760838i	$0.724788\pi$
$972$		0			0
$973$	−0.897811	+	2.16751i	−0.0287825	+	0.0694871i
$974$		0			0
$975$	−1.34628	+	2.09634i	−0.0431155	+	0.0671367i
$976$		0			0
$977$	−25.6955			−0.822072			−0.411036	−	0.911619i	$-0.634833\pi$
$977$	−25.6955			−0.822072			−0.411036	+	0.911619i	$0.634833\pi$
$978$		0			0
$979$	1.44755	+	0.599596i	0.0462640	+	0.0191632i
$980$		0			0
$981$	−10.4362	−	9.70386i	−0.333201	−	0.309820i
$982$		0			0
$983$	40.5980	+	40.5980i	1.29487	+	1.29487i	0.931735	+	0.363140i	$0.118295\pi$
$983$	40.5980	+	40.5980i	1.29487	+	1.29487i	0.363140	+	0.931735i	$0.381705\pi$
$984$		0			0
$985$	−33.0322	+	33.0322i	−1.05249	+	1.05249i
$986$		0			0
$987$	43.0482	+	7.75242i	1.37024	+	0.246762i
$988$		0			0
$989$	9.66786	−	23.3403i	0.307420	−	0.742177i
$990$		0			0
$991$			31.4960i			1.00050i	0.865880	+	0.500251i	$0.166759\pi$
$991$			31.4960i			1.00050i	−0.865880	+	0.500251i	$0.833241\pi$
$992$		0			0
$993$	26.1169	−	40.6676i	0.828795	−	1.29055i
$994$		0			0
$995$	−2.62078	−	1.08556i	−0.0830844	−	0.0344147i
$996$		0			0
$997$	7.47755	+	18.0524i	0.236816	+	0.571726i	0.996950	−	0.0780412i	$-0.0248666\pi$
$997$	7.47755	+	18.0524i	0.236816	+	0.571726i	−0.760134	+	0.649767i	$0.774867\pi$
$998$		0			0
$999$	23.0380	+	30.7131i	0.728889	+	0.971720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.95.5		56
3.2	odd	2	inner	768.2.o.b.95.14		56
4.3	odd	2		768.2.o.a.95.10		56
8.3	odd	2		384.2.o.a.47.5		56
8.5	even	2		96.2.o.a.35.8	yes	56
12.11	even	2		768.2.o.a.95.1		56
24.5	odd	2		96.2.o.a.35.7	yes	56
24.11	even	2		384.2.o.a.47.14		56
32.5	even	8		384.2.o.a.335.14		56
32.11	odd	8	inner	768.2.o.b.671.14		56
32.21	even	8		768.2.o.a.671.1		56
32.27	odd	8		96.2.o.a.11.7	✓	56
96.5	odd	8		384.2.o.a.335.5		56
96.11	even	8	inner	768.2.o.b.671.5		56
96.53	odd	8		768.2.o.a.671.10		56
96.59	even	8		96.2.o.a.11.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.7	✓	56	32.27	odd	8
96.2.o.a.11.8	yes	56	96.59	even	8
96.2.o.a.35.7	yes	56	24.5	odd	2
96.2.o.a.35.8	yes	56	8.5	even	2
384.2.o.a.47.5		56	8.3	odd	2
384.2.o.a.47.14		56	24.11	even	2
384.2.o.a.335.5		56	96.5	odd	8
384.2.o.a.335.14		56	32.5	even	8
768.2.o.a.95.1		56	12.11	even	2
768.2.o.a.95.10		56	4.3	odd	2
768.2.o.a.671.1		56	32.21	even	8
768.2.o.a.671.10		56	96.53	odd	8
768.2.o.b.95.5		56	1.1	even	1	trivial
768.2.o.b.95.14		56	3.2	odd	2	inner
768.2.o.b.671.5		56	96.11	even	8	inner
768.2.o.b.671.14		56	32.11	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.988287 - 1.42242i) q^{3} +(-2.70066 + 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(-1.04658 + 2.81152i) q^{9} +O(q^{10})\)	\(q+(-0.988287 - 1.42242i) q^{3} +(-2.70066 + 1.11865i) q^{5} +(-3.28204 - 3.28204i) q^{7} +(-1.04658 + 2.81152i) q^{9} +(0.276697 - 0.114612i) q^{11} +(0.155281 - 0.374881i) q^{13} +(4.26022 + 2.73593i) q^{15} +1.41723 q^{17} +(2.51972 + 1.04370i) q^{19} +(-1.42485 + 7.91204i) q^{21} +(3.30034 + 3.30034i) q^{23} +(2.50664 - 2.50664i) q^{25} +(5.03350 - 1.28991i) q^{27} +(-0.650676 + 1.57087i) q^{29} +4.16702i q^{31} +(-0.436482 - 0.280311i) q^{33} +(12.5351 + 5.19221i) q^{35} +(2.82757 + 6.82635i) q^{37} +(-0.686701 + 0.149615i) q^{39} +(-3.81949 + 3.81949i) q^{41} +(-2.07136 - 5.00071i) q^{43} +(-0.318658 - 8.76372i) q^{45} -5.44085i q^{47} +14.5435i q^{49} +(-1.40063 - 2.01590i) q^{51} +(-1.85159 - 4.47012i) q^{53} +(-0.619053 + 0.619053i) q^{55} +(-1.00562 - 4.61558i) q^{57} +(-1.37699 - 3.32434i) q^{59} +(10.9629 + 4.54098i) q^{61} +(12.6624 - 5.79262i) q^{63} +1.18613i q^{65} +(-4.19888 + 10.1370i) q^{67} +(1.43280 - 7.95617i) q^{69} +(-3.77857 + 3.77857i) q^{71} +(-3.89137 - 3.89137i) q^{73} +(-6.04279 - 1.08823i) q^{75} +(-1.28429 - 0.531970i) q^{77} +4.81995 q^{79} +(-6.80935 - 5.88497i) q^{81} +(-3.60399 + 8.70081i) q^{83} +(-3.82744 + 1.58538i) q^{85} +(2.87750 - 0.626933i) q^{87} +(3.69926 + 3.69926i) q^{89} +(-1.74001 + 0.720735i) q^{91} +(5.92727 - 4.11821i) q^{93} -7.97242 q^{95} +10.9958 q^{97} +(0.0326483 + 0.897890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

L-functions

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