LMFDB - Embedded newform 560.2.q.l.401.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			401.3
Root			$-0.391571i$ of defining polynomial
Character	$\chi$	$=$	560.401
Dual form			560.2.q.l.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29211 + 2.23800i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +O(q^{10})$	\(q+(1.29211 + 2.23800i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +(0.839111 + 1.45338i) q^{11} -4.84667 q^{13} -2.58423 q^{15} +(-1.00000 - 1.73205i) q^{17} +(3.42334 - 5.92939i) q^{19} +(-5.50756 + 4.05146i) q^{21} +(-1.13122 + 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.75268 q^{27} +3.32178 q^{29} +(4.58423 + 7.94011i) q^{31} +(-2.16845 + 3.75587i) q^{33} +(-2.42334 - 1.06181i) q^{35} +(1.42334 - 2.46529i) q^{37} +(-6.26245 - 10.8469i) q^{39} +9.52489 q^{41} -6.58423 q^{43} +(-1.83911 - 3.18543i) q^{45} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(2.58423 - 4.47601i) q^{51} +(-3.74511 - 6.48673i) q^{53} -1.67822 q^{55} +17.6933 q^{57} +(4.00000 + 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-8.91357 - 3.90558i) q^{63} +(2.42334 - 4.19734i) q^{65} +(-2.87634 - 4.98196i) q^{67} -5.84667 q^{69} +(5.84667 + 10.1267i) q^{73} +(1.29211 - 2.23800i) q^{75} +(-3.57666 + 2.63106i) q^{77} +(2.84667 - 4.93058i) q^{79} +(3.25268 + 5.63380i) q^{81} +12.5842 q^{83} +2.00000 q^{85} +(4.29211 + 7.43416i) q^{87} +(2.92334 - 5.06337i) q^{89} +(-1.41577 - 12.7447i) q^{91} +(-11.8467 + 20.5190i) q^{93} +(3.42334 + 5.92939i) q^{95} -2.00000 q^{97} -6.17287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9	$ 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43} - 9 q^{45} - 15 q^{47} - 12 q^{49} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} + 6 q^{61} - 9 q^{63} - 3 q^{65} + 6 q^{67} - 39 q^{77} - 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 24 q^{91} - 36 q^{93} + 3 q^{95} - 12 q^{97} - 126 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9 + 3 * q^11 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 + 18 * q^33 + 3 * q^35 - 9 * q^37 - 18 * q^39 + 18 * q^41 - 24 * q^43 - 9 * q^45 - 15 * q^47 - 12 * q^49 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 + 6 * q^61 - 9 * q^63 - 3 * q^65 + 6 * q^67 - 39 * q^77 - 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 24 * q^91 - 36 * q^93 + 3 * q^95 - 12 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.29211	+	2.23800i	0.746002	+	1.29211i	0.949725	+	0.313084i	$0.101362\pi$
$3$	1.29211	+	2.23800i	0.746002	+	1.29211i	−0.203724	+	0.979028i	$0.565304\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	0.292113	+	2.62958i	0.110408	+	0.993886i
$7$	0.292113	+	2.62958i	0.110408	+	0.993886i
$8$		0			0
$9$	−1.83911	+	3.18543i	−0.613037	+	1.06181i
$10$		0			0
$11$	0.839111	+	1.45338i	0.253001	+	0.438211i	0.964351	−	0.264627i	$-0.0852490\pi$
$11$	0.839111	+	1.45338i	0.253001	+	0.438211i	−0.711349	+	0.702839i	$0.751916\pi$
$12$		0			0
$13$	−4.84667			−1.34422			−0.672112	−	0.740449i	$-0.734613\pi$
$13$	−4.84667			−1.34422			−0.672112	+	0.740449i	$0.734613\pi$
$14$		0			0
$15$	−2.58423			−0.667244
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	3.42334	−	5.92939i	0.785367	−	1.36030i	−0.143412	−	0.989663i	$-0.545808\pi$
$19$	3.42334	−	5.92939i	0.785367	−	1.36030i	0.928779	−	0.370633i	$-0.120859\pi$
$20$		0			0
$21$	−5.50756	+	4.05146i	−1.20185	+	0.884101i
$22$		0			0
$23$	−1.13122	+	1.95934i	−0.235876	+	0.408550i	−0.959527	−	0.281617i	$-0.909129\pi$
$23$	−1.13122	+	1.95934i	−0.235876	+	0.408550i	0.723651	+	0.690166i	$0.242463\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.75268			−0.337303
$28$		0			0
$29$	3.32178			0.616839			0.308419	−	0.951250i	$-0.400200\pi$
$29$	3.32178			0.616839			0.308419	+	0.951250i	$0.400200\pi$
$30$		0			0
$31$	4.58423	+	7.94011i	0.823351	+	1.42609i	0.903173	+	0.429277i	$0.141232\pi$
$31$	4.58423	+	7.94011i	0.823351	+	1.42609i	−0.0798217	+	0.996809i	$0.525435\pi$
$32$		0			0
$33$	−2.16845	+	3.75587i	−0.377479	+	0.653813i
$34$		0			0
$35$	−2.42334	−	1.06181i	−0.409619	−	0.179479i
$36$		0			0
$37$	1.42334	−	2.46529i	0.233995	−	0.405291i	−0.724985	−	0.688765i	$-0.758153\pi$
$37$	1.42334	−	2.46529i	0.233995	−	0.405291i	0.958980	+	0.283473i	$0.0914867\pi$
$38$		0			0
$39$	−6.26245	−	10.8469i	−1.00279	−	1.73689i
$40$		0			0
$41$	9.52489			1.48754			0.743769	−	0.668437i	$-0.233036\pi$
$41$	9.52489			1.48754			0.743769	+	0.668437i	$0.233036\pi$
$42$		0			0
$43$	−6.58423			−1.00408			−0.502042	−	0.864843i	$-0.667418\pi$
$43$	−6.58423			−1.00408			−0.502042	+	0.864843i	$0.667418\pi$
$44$		0			0
$45$	−1.83911	−	3.18543i	−0.274158	−	0.474856i
$46$		0			0
$47$	−6.10156	+	10.5682i	−0.890004	+	1.54153i	−0.0501344	+	0.998742i	$0.515965\pi$
$47$	−6.10156	+	10.5682i	−0.890004	+	1.54153i	−0.839869	+	0.542789i	$0.817368\pi$
$48$		0			0
$49$	−6.82934	+	1.53627i	−0.975620	+	0.219466i
$50$		0			0
$51$	2.58423	−	4.47601i	0.361864	−	0.626767i
$52$		0			0
$53$	−3.74511	−	6.48673i	−0.514431	−	0.891021i	−0.999860	−	0.0167445i	$-0.994670\pi$
$53$	−3.74511	−	6.48673i	−0.514431	−	0.891021i	0.485429	−	0.874276i	$-0.338664\pi$
$54$		0			0
$55$	−1.67822			−0.226291
$56$		0			0
$57$	17.6933			2.34354
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	3.24511	−	5.62070i	0.415494	−	0.719657i	−0.579986	−	0.814627i	$-0.696942\pi$
$61$	3.24511	−	5.62070i	0.415494	−	0.719657i	0.995480	+	0.0949692i	$0.0302753\pi$
$62$		0			0
$63$	−8.91357	−	3.90558i	−1.12300	−	0.492056i
$64$		0			0
$65$	2.42334	−	4.19734i	0.300578	−	0.520616i
$66$		0			0
$67$	−2.87634	−	4.98196i	−0.351401	−	0.608644i	0.635094	−	0.772434i	$-0.280961\pi$
$67$	−2.87634	−	4.98196i	−0.351401	−	0.608644i	−0.986495	+	0.163791i	$0.947628\pi$
$68$		0			0
$69$	−5.84667			−0.703857
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	5.84667	+	10.1267i	0.684301	+	1.18524i	0.973656	+	0.228022i	$0.0732260\pi$
$73$	5.84667	+	10.1267i	0.684301	+	1.18524i	−0.289355	+	0.957222i	$0.593441\pi$
$74$		0			0
$75$	1.29211	−	2.23800i	0.149200	−	0.258423i
$76$		0			0
$77$	−3.57666	+	2.63106i	−0.407599	+	0.299837i
$78$		0			0
$79$	2.84667	−	4.93058i	0.320276	−	0.554734i	−0.660269	−	0.751029i	$-0.729558\pi$
$79$	2.84667	−	4.93058i	0.320276	−	0.554734i	0.980545	+	0.196295i	$0.0628911\pi$
$80$		0			0
$81$	3.25268	+	5.63380i	0.361408	+	0.625978i
$82$		0			0
$83$	12.5842			1.38130			0.690649	−	0.723190i	$-0.257325\pi$
$83$	12.5842			1.38130			0.690649	+	0.723190i	$0.257325\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	4.29211	+	7.43416i	0.460163	+	0.797025i
$88$		0			0
$89$	2.92334	−	5.06337i	0.309873	−	0.536716i	−0.668461	−	0.743747i	$-0.733047\pi$
$89$	2.92334	−	5.06337i	0.309873	−	0.536716i	0.978334	+	0.207031i	$0.0663801\pi$
$90$		0			0
$91$	−1.41577	−	12.7447i	−0.148414	−	1.33601i
$92$		0			0
$93$	−11.8467	+	20.5190i	−1.22844	+	2.12773i
$94$		0			0
$95$	3.42334	+	5.92939i	0.351227	+	0.608343i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−6.17287			−0.620397
$100$		0			0
$101$	8.50756	+	14.7355i	0.846534	+	1.46624i	0.884282	+	0.466953i	$0.154648\pi$
$101$	8.50756	+	14.7355i	0.846534	+	1.46624i	−0.0377483	+	0.999287i	$0.512019\pi$
$102$		0			0
$103$	3.55456	−	6.15668i	0.350241	−	0.606635i	−0.636050	−	0.771648i	$-0.719433\pi$
$103$	3.55456	−	6.15668i	0.350241	−	0.606635i	0.986292	+	0.165012i	$0.0527663\pi$
$104$		0			0
$105$	−0.754885	−	6.79542i	−0.0736692	−	0.663165i
$106$		0			0
$107$	−0.876338	+	1.51786i	−0.0847188	+	0.146737i	−0.905271	−	0.424834i	$-0.860333\pi$
$107$	−0.876338	+	1.51786i	−0.0847188	+	0.146737i	0.820553	+	0.571571i	$0.193666\pi$
$108$		0			0
$109$	−9.77001	−	16.9222i	−0.935797	−	1.62085i	−0.773206	−	0.634154i	$-0.781348\pi$
$109$	−9.77001	−	16.9222i	−0.935797	−	1.62085i	−0.162591	−	0.986694i	$-0.551985\pi$
$110$		0			0
$111$	7.35644			0.698243
$112$		0			0
$113$	10.3369			0.972414			0.486207	−	0.873844i	$-0.338380\pi$
$113$	10.3369			0.972414			0.486207	+	0.873844i	$0.338380\pi$
$114$		0			0
$115$	−1.13122	−	1.95934i	−0.105487	−	0.182709i
$116$		0			0
$117$	8.91357	−	15.4387i	0.824059	−	1.42731i
$118$		0			0
$119$	4.26245	−	3.13553i	0.390738	−	0.287434i
$120$		0			0
$121$	4.09179	−	7.08718i	0.371981	−	0.644289i
$122$		0			0
$123$	12.3072	+	21.3168i	1.10971	+	1.92207i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	19.1836			1.70227			0.851133	−	0.524949i	$-0.175916\pi$
$127$	19.1836			1.70227			0.851133	+	0.524949i	$0.175916\pi$
$128$		0			0
$129$	−8.50756	−	14.7355i	−0.749049	−	1.29739i
$130$		0			0
$131$	−8.91357	+	15.4387i	−0.778782	+	1.34889i	0.153862	+	0.988092i	$0.450829\pi$
$131$	−8.91357	+	15.4387i	−0.778782	+	1.34889i	−0.932644	+	0.360797i	$0.882505\pi$
$132$		0			0
$133$	16.5918	+	7.26987i	1.43869	+	0.630378i
$134$		0			0
$135$	0.876338	−	1.51786i	0.0754232	−	0.130637i
$136$		0			0
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$		0			0
$139$	5.16845			0.438382			0.219191	−	0.975682i	$-0.429658\pi$
$139$	5.16845			0.438382			0.219191	+	0.975682i	$0.429658\pi$
$140$		0			0
$141$	−31.5356			−2.65578
$142$		0			0
$143$	−4.06689	−	7.04407i	−0.340091	−	0.589054i
$144$		0			0
$145$	−1.66089	+	2.87674i	−0.137929	+	0.238901i
$146$		0			0
$147$	−12.2624	−	13.2991i	−1.01139	−	1.09689i
$148$		0			0
$149$	−0.398443	+	0.690123i	−0.0326417	+	0.0565371i	−0.881885	−	0.471465i	$-0.843725\pi$
$149$	−0.398443	+	0.690123i	−0.0326417	+	0.0565371i	0.849243	+	0.528002i	$0.177059\pi$
$150$		0			0
$151$	−8.26245	−	14.3110i	−0.672388	−	1.16461i	−0.977225	−	0.212206i	$-0.931935\pi$
$151$	−8.26245	−	14.3110i	−0.672388	−	1.16461i	0.304837	−	0.952405i	$-0.401398\pi$
$152$		0			0
$153$	7.35644			0.594733
$154$		0			0
$155$	−9.16845			−0.736428
$156$		0			0
$157$	−4.10156	−	7.10411i	−0.327340	−	0.566969i	0.654643	−	0.755938i	$-0.272819\pi$
$157$	−4.10156	−	7.10411i	−0.327340	−	0.566969i	−0.981983	+	0.188969i	$0.939486\pi$
$158$		0			0
$159$	9.67822	−	16.7632i	0.767533	−	1.32941i
$160$		0			0
$161$	−5.48267	−	2.40229i	−0.432095	−	0.189327i
$162$		0			0
$163$	1.84667	−	3.19853i	0.144643	−	0.250528i	−0.784597	−	0.620006i	$-0.787130\pi$
$163$	1.84667	−	3.19853i	0.144643	−	0.250528i	0.929240	+	0.369478i	$0.120463\pi$
$164$		0			0
$165$	−2.16845	−	3.75587i	−0.168814	−	0.292394i
$166$		0			0
$167$	0.262447			0.0203087			0.0101544	−	0.999948i	$-0.496768\pi$
$167$	0.262447			0.0203087			0.0101544	+	0.999948i	$0.496768\pi$
$168$		0			0
$169$	10.4902			0.806941
$170$		0			0
$171$	12.5918	+	21.8096i	0.962918	+	1.66782i
$172$		0			0
$173$	9.42334	−	16.3217i	0.716443	−	1.24092i	−0.245957	−	0.969281i	$-0.579102\pi$
$173$	9.42334	−	16.3217i	0.716443	−	1.24092i	0.962400	−	0.271635i	$-0.0875643\pi$
$174$		0			0
$175$	2.13122	−	1.56777i	0.161105	−	0.118512i
$176$		0			0
$177$	−10.3369	+	17.9040i	−0.776969	+	1.34575i
$178$		0			0
$179$	−6.00756	−	10.4054i	−0.449026	−	0.777736i	0.549297	−	0.835627i	$-0.314896\pi$
$179$	−6.00756	−	10.4054i	−0.449026	−	0.777736i	−0.998323	+	0.0578912i	$0.981562\pi$
$180$		0			0
$181$	−6.03466			−0.448553			−0.224276	−	0.974526i	$-0.572002\pi$
$181$	−6.03466			−0.448553			−0.224276	+	0.974526i	$0.572002\pi$
$182$		0			0
$183$	16.7722			1.23984
$184$		0			0
$185$	1.42334	+	2.46529i	0.104646	+	0.181252i
$186$		0			0
$187$	1.67822	−	2.90676i	0.122724	−	0.212564i
$188$		0			0
$189$	−0.511979	−	4.60880i	−0.0372410	−	0.335241i
$190$		0			0
$191$	1.41577	−	2.45219i	0.102442	−	0.177434i	−0.810248	−	0.586087i	$-0.800668\pi$
$191$	1.41577	−	2.45219i	0.102442	−	0.177434i	0.912690	+	0.408652i	$0.134001\pi$
$192$		0			0
$193$	−6.49023	−	11.2414i	−0.467177	−	0.809174i	0.532120	−	0.846669i	$-0.321396\pi$
$193$	−6.49023	−	11.2414i	−0.467177	−	0.809174i	−0.999297	+	0.0374948i	$0.988062\pi$
$194$		0			0
$195$	12.5249			0.896926
$196$		0			0
$197$	−4.84667			−0.345311			−0.172656	−	0.984982i	$-0.555235\pi$
$197$	−4.84667			−0.345311			−0.172656	+	0.984982i	$0.555235\pi$
$198$		0			0
$199$	−7.69334	−	13.3253i	−0.545367	−	0.944603i	−0.998584	−	0.0532026i	$-0.983057\pi$
$199$	−7.69334	−	13.3253i	−0.545367	−	0.944603i	0.453217	−	0.891400i	$-0.350276\pi$
$200$		0			0
$201$	7.43311	−	12.8745i	0.524291	−	0.908098i
$202$		0			0
$203$	0.970334	+	8.73487i	0.0681041	+	0.613068i
$204$		0			0
$205$	−4.76245	+	8.24880i	−0.332624	+	0.576121i
$206$		0			0
$207$	−4.16089	−	7.20687i	−0.289202	−	0.500912i
$208$		0			0
$209$	11.4902			0.794796
$210$		0			0
$211$	−9.18357			−0.632223			−0.316112	−	0.948722i	$-0.602377\pi$
$211$	−9.18357			−0.632223			−0.316112	+	0.948722i	$0.602377\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.29211	−	5.70211i	0.224520	−	0.388880i
$216$		0			0
$217$	−19.5400	+	14.3740i	−1.32646	+	0.975769i
$218$		0			0
$219$	−15.1091	+	26.1698i	−1.02098	+	1.76839i
$220$		0			0
$221$	4.84667	+	8.39468i	0.326022	+	0.564687i
$222$		0			0
$223$	12.9805			0.869236			0.434618	−	0.900615i	$-0.356883\pi$
$223$	12.9805			0.869236			0.434618	+	0.900615i	$0.356883\pi$
$224$		0			0
$225$	3.67822			0.245215
$226$		0			0
$227$	−11.0151	−	19.0788i	−0.731099	−	1.26630i	−0.956414	−	0.292015i	$-0.905674\pi$
$227$	−11.0151	−	19.0788i	−0.731099	−	1.26630i	0.225314	−	0.974286i	$-0.427659\pi$
$228$		0			0
$229$	−2.15333	+	3.72967i	−0.142296	+	0.246464i	−0.928361	−	0.371680i	$-0.878782\pi$
$229$	−2.15333	+	3.72967i	−0.142296	+	0.246464i	0.786065	+	0.618144i	$0.212115\pi$
$230$		0			0
$231$	−10.5098	−	4.60497i	−0.691492	−	0.302985i
$232$		0			0
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	−0.994283	+	0.106773i	$0.965948\pi$
$234$		0			0
$235$	−6.10156	−	10.5682i	−0.398022	−	0.689394i
$236$		0			0
$237$	14.7129			0.955705
$238$		0			0
$239$	−10.8618			−0.702591			−0.351296	−	0.936265i	$-0.614259\pi$
$239$	−10.8618			−0.702591			−0.351296	+	0.936265i	$0.614259\pi$
$240$		0			0
$241$	−0.101557	−	0.175902i	−0.00654187	−	0.0113309i	0.862736	−	0.505655i	$-0.168749\pi$
$241$	−0.101557	−	0.175902i	−0.00654187	−	0.0113309i	−0.869278	+	0.494324i	$0.835416\pi$
$242$		0			0
$243$	−11.0347	+	19.1126i	−0.707874	+	1.22607i
$244$		0			0
$245$	2.08423	−	6.68251i	0.133156	−	0.426930i
$246$		0			0
$247$	−16.5918	+	28.7378i	−1.05571	+	1.82854i
$248$		0			0
$249$	16.2602	+	28.1636i	1.03045	+	1.78479i
$250$		0			0
$251$	−5.03466			−0.317785			−0.158893	−	0.987296i	$-0.550792\pi$
$251$	−5.03466			−0.317785			−0.158893	+	0.987296i	$0.550792\pi$
$252$		0			0
$253$	−3.79689			−0.238708
$254$		0			0
$255$	2.58423	+	4.47601i	0.161830	+	0.280299i
$256$		0			0
$257$	−11.6933	+	20.2535i	−0.729411	+	1.26338i	0.227722	+	0.973726i	$0.426872\pi$
$257$	−11.6933	+	20.2535i	−0.729411	+	1.26338i	−0.957133	+	0.289650i	$0.906461\pi$
$258$		0			0
$259$	6.89844	+	3.02263i	0.428648	+	0.187817i
$260$		0			0
$261$	−6.10912	+	10.5813i	−0.378145	+	0.654966i
$262$		0			0
$263$	13.5546	+	23.4772i	0.835810	+	1.44767i	0.893369	+	0.449323i	$0.148335\pi$
$263$	13.5546	+	23.4772i	0.835810	+	1.44767i	−0.0575594	+	0.998342i	$0.518332\pi$
$264$		0			0
$265$	7.49023			0.460121
$266$		0			0
$267$	15.1091			0.924663
$268$		0			0
$269$	−3.24511	−	5.62070i	−0.197858	−	0.342700i	0.749976	−	0.661466i	$-0.230065\pi$
$269$	−3.24511	−	5.62070i	−0.197858	−	0.342700i	−0.947834	+	0.318765i	$0.896732\pi$
$270$		0			0
$271$	−11.6933	+	20.2535i	−0.710320	+	1.23031i	0.254417	+	0.967095i	$0.418116\pi$
$271$	−11.6933	+	20.2535i	−0.710320	+	1.23031i	−0.964737	+	0.263216i	$0.915217\pi$
$272$		0			0
$273$	26.6933	−	19.6361i	1.61555	−	1.18843i
$274$		0			0
$275$	0.839111	−	1.45338i	0.0506003	−	0.0876422i
$276$		0			0
$277$	−1.83155	−	3.17234i	−0.110047	−	0.190607i	0.805742	−	0.592267i	$-0.201767\pi$
$277$	−1.83155	−	3.17234i	−0.110047	−	0.190607i	−0.915789	+	0.401660i	$0.868434\pi$
$278$		0			0
$279$	−33.7236			−2.01898
$280$		0			0
$281$	13.8965			0.828993			0.414497	−	0.910051i	$-0.363958\pi$
$281$	13.8965			0.828993			0.414497	+	0.910051i	$0.363958\pi$
$282$		0			0
$283$	−10.1685	−	17.6123i	−0.604452	−	1.04694i	−0.992138	−	0.125150i	$-0.960059\pi$
$283$	−10.1685	−	17.6123i	−0.604452	−	1.04694i	0.387686	−	0.921791i	$-0.373274\pi$
$284$		0			0
$285$	−8.84667	+	15.3229i	−0.524032	+	0.907649i
$286$		0			0
$287$	2.78234	+	25.0464i	0.164236	+	1.47844i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−2.58423	−	4.47601i	−0.151490	−	0.262388i
$292$		0			0
$293$	18.8467			1.10103			0.550517	−	0.834824i	$-0.314431\pi$
$293$	18.8467			1.10103			0.550517	+	0.834824i	$0.314431\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−1.47069	−	2.54731i	−0.0853380	−	0.147810i
$298$		0			0
$299$	5.48267	−	9.49626i	0.317071	−	0.549183i
$300$		0			0
$301$	−1.92334	−	17.3137i	−0.110859	−	0.997946i
$302$		0			0
$303$	−21.9855	+	38.0799i	−1.26303	+	2.18763i
$304$		0			0
$305$	3.24511	+	5.62070i	0.185815	+	0.321841i
$306$		0			0
$307$	2.39623			0.136760			0.0683802	−	0.997659i	$-0.478217\pi$
$307$	2.39623			0.136760			0.0683802	+	0.997659i	$0.478217\pi$
$308$		0			0
$309$	18.3716			1.04512
$310$		0			0
$311$	−2.83155	−	4.90439i	−0.160562	−	0.278102i	0.774508	−	0.632564i	$-0.217997\pi$
$311$	−2.83155	−	4.90439i	−0.160562	−	0.278102i	−0.935071	+	0.354462i	$0.884664\pi$
$312$		0			0
$313$	−14.8618	+	25.7414i	−0.840038	+	1.45499i	0.0498231	+	0.998758i	$0.484134\pi$
$313$	−14.8618	+	25.7414i	−0.840038	+	1.45499i	−0.889861	+	0.456231i	$0.849199\pi$
$314$		0			0
$315$	7.83911	−	5.76659i	0.441684	−	0.324910i
$316$		0			0
$317$	−9.52489	+	16.4976i	−0.534971	+	0.926597i	0.464193	+	0.885734i	$0.346344\pi$
$317$	−9.52489	+	16.4976i	−0.534971	+	0.926597i	−0.999165	+	0.0408636i	$0.986989\pi$
$318$		0			0
$319$	2.78734	+	4.82781i	0.156061	+	0.270306i
$320$		0			0
$321$	−4.52931			−0.252801
$322$		0			0
$323$	−13.6933			−0.761918
$324$		0			0
$325$	2.42334	+	4.19734i	0.134422	+	0.232827i
$326$		0			0
$327$	25.2479	−	43.7307i	1.39621	−	2.41831i
$328$		0			0
$329$	−29.5722	−	12.9574i	−1.63037	−	0.714365i
$330$		0			0
$331$	1.16089	−	2.01072i	0.0638083	−	0.110519i	−0.832356	−	0.554241i	$-0.813009\pi$
$331$	1.16089	−	2.01072i	0.0638083	−	0.110519i	0.896165	+	0.443722i	$0.146342\pi$
$332$		0			0
$333$	5.23534	+	9.06788i	0.286895	+	0.496917i
$334$		0			0
$335$	5.75268			0.314302
$336$		0			0
$337$	−16.4062			−0.893704			−0.446852	−	0.894608i	$-0.647455\pi$
$337$	−16.4062			−0.893704			−0.446852	+	0.894608i	$0.647455\pi$
$338$		0			0
$339$	13.3564	+	23.1340i	0.725422	+	1.25647i
$340$		0			0
$341$	−7.69334	+	13.3253i	−0.416618	+	0.721603i
$342$		0			0
$343$	−6.03466	−	17.5095i	−0.325841	−	0.945425i
$344$		0			0
$345$	2.92334	−	5.06337i	0.157387	−	0.272602i
$346$		0			0
$347$	2.29211	+	3.97006i	0.123047	+	0.213124i	0.920968	−	0.389639i	$-0.127400\pi$
$347$	2.29211	+	3.97006i	0.123047	+	0.213124i	−0.797921	+	0.602762i	$0.794067\pi$
$348$		0			0
$349$	12.3716			0.662235			0.331117	−	0.943590i	$-0.392574\pi$
$349$	12.3716			0.662235			0.331117	+	0.943590i	$0.392574\pi$
$350$		0			0
$351$	8.49465			0.453411
$352$		0			0
$353$	−9.69334	−	16.7894i	−0.515925	−	0.893608i	−0.999829	−	0.0184869i	$-0.994115\pi$
$353$	−9.69334	−	16.7894i	−0.515925	−	0.893608i	0.483904	−	0.875121i	$-0.339218\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	12.5249	+	5.48792i	0.662888	+	0.290451i
$358$		0			0
$359$	−4.90600	+	8.49745i	−0.258929	+	0.448478i	−0.965955	−	0.258709i	$-0.916703\pi$
$359$	−4.90600	+	8.49745i	−0.258929	+	0.448478i	0.707026	+	0.707187i	$0.250036\pi$
$360$		0			0
$361$	−13.9385	−	24.1421i	−0.733603	−	1.27064i
$362$		0			0
$363$	21.1482			1.10999
$364$		0			0
$365$	−11.6933			−0.612058
$366$		0			0
$367$	−6.35901	−	11.0141i	−0.331937	−	0.574933i	0.650954	−	0.759117i	$-0.274369\pi$
$367$	−6.35901	−	11.0141i	−0.331937	−	0.574933i	−0.982892	+	0.184184i	$0.941036\pi$
$368$		0			0
$369$	−17.5173	+	30.3409i	−0.911916	+	1.57948i
$370$		0			0
$371$	15.9634	−	11.7429i	0.828776	−	0.609662i
$372$		0			0
$373$	8.20311	−	14.2082i	0.424741	−	0.735673i	−0.571655	−	0.820494i	$-0.693698\pi$
$373$	8.20311	−	14.2082i	0.424741	−	0.735673i	0.996396	+	0.0848208i	$0.0270318\pi$
$374$		0			0
$375$	1.29211	+	2.23800i	0.0667244	+	0.115570i
$376$		0			0
$377$	−16.0996			−0.829170
$378$		0			0
$379$	−14.4707			−0.743309			−0.371655	−	0.928371i	$-0.621209\pi$
$379$	−14.4707			−0.743309			−0.371655	+	0.928371i	$0.621209\pi$
$380$		0			0
$381$	24.7873	+	42.9329i	1.26989	+	2.19952i
$382$		0			0
$383$	−1.77478	+	3.07401i	−0.0906871	+	0.157075i	−0.907800	−	0.419402i	$-0.862240\pi$
$383$	−1.77478	+	3.07401i	−0.0906871	+	0.157075i	0.817113	+	0.576477i	$0.195573\pi$
$384$		0			0
$385$	−0.490230	−	4.41301i	−0.0249844	−	0.224908i
$386$		0			0
$387$	12.1091	−	20.9736i	0.615541	−	1.06615i
$388$		0			0
$389$	−4.49023	−	7.77731i	−0.227664	−	0.394325i	0.729452	−	0.684032i	$-0.239775\pi$
$389$	−4.49023	−	7.77731i	−0.227664	−	0.394325i	−0.957115	+	0.289707i	$0.906442\pi$
$390$		0			0
$391$	4.52489			0.228834
$392$		0			0
$393$	−46.0693			−2.32389
$394$		0			0
$395$	2.84667	+	4.93058i	0.143232	+	0.248084i
$396$		0			0
$397$	14.0498	−	24.3349i	0.705139	−	1.22134i	−0.261503	−	0.965203i	$-0.584218\pi$
$397$	14.0498	−	24.3349i	0.705139	−	1.22134i	0.966642	−	0.256133i	$-0.0824486\pi$
$398$		0			0
$399$	5.16845	+	46.5260i	0.258746	+	2.32921i
$400$		0			0
$401$	13.3467	−	23.1171i	0.666501	−	1.15441i	−0.312375	−	0.949959i	$-0.601125\pi$
$401$	13.3467	−	23.1171i	0.666501	−	1.15441i	0.978876	−	0.204455i	$-0.0655421\pi$
$402$		0			0
$403$	−22.2182	−	38.4831i	−1.10677	−	1.91698i
$404$		0			0
$405$	−6.50535			−0.323254
$406$		0			0
$407$	4.77735			0.236804
$408$		0			0
$409$	−14.0325	−	24.3049i	−0.693860	−	1.20180i	−0.970563	−	0.240846i	$-0.922575\pi$
$409$	−14.0325	−	24.3049i	−0.693860	−	1.20180i	0.276703	−	0.960955i	$-0.410758\pi$
$410$		0			0
$411$	5.16845	−	8.95202i	0.254941	−	0.441571i
$412$		0			0
$413$	−17.0498	+	12.5421i	−0.838965	+	0.617157i
$414$		0			0
$415$	−6.29211	+	10.8983i	−0.308868	+	0.534974i
$416$		0			0
$417$	6.67822	+	11.5670i	0.327034	+	0.566439i
$418$		0			0
$419$	18.8769			0.922198			0.461099	−	0.887349i	$-0.347455\pi$
$419$	18.8769			0.922198			0.461099	+	0.887349i	$0.347455\pi$
$420$		0			0
$421$	−28.1836			−1.37358			−0.686792	−	0.726854i	$-0.740982\pi$
$421$	−28.1836			−1.37358			−0.686792	+	0.726854i	$0.740982\pi$
$422$		0			0
$423$	−22.4429	−	38.8722i	−1.09121	−	1.89003i
$424$		0			0
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$	15.7280	+	6.89140i	0.761132	+	0.333498i
$428$		0			0
$429$	10.5098	−	18.2035i	0.507416	−	0.878871i
$430$		0			0
$431$	1.41577	+	2.45219i	0.0681955	+	0.118118i	0.898107	−	0.439777i	$-0.144943\pi$
$431$	1.41577	+	2.45219i	0.0681955	+	0.118118i	−0.829912	+	0.557895i	$0.811609\pi$
$432$		0			0
$433$	−2.33690			−0.112304			−0.0561522	−	0.998422i	$-0.517883\pi$
$433$	−2.33690			−0.112304			−0.0561522	+	0.998422i	$0.517883\pi$
$434$		0			0
$435$	−8.58423			−0.411582
$436$		0			0
$437$	7.74511	+	13.4149i	0.370499	+	0.641723i
$438$		0			0
$439$	−3.03466	+	5.25619i	−0.144837	+	0.250864i	−0.929312	−	0.369296i	$-0.879599\pi$
$439$	−3.03466	+	5.25619i	−0.144837	+	0.250864i	0.784475	+	0.620160i	$0.212932\pi$
$440$		0			0
$441$	7.66624	−	24.5798i	0.365059	−	1.17047i
$442$		0			0
$443$	5.80188	−	10.0492i	0.275656	−	0.477450i	−0.694645	−	0.719353i	$-0.744438\pi$
$443$	5.80188	−	10.0492i	0.275656	−	0.477450i	0.970300	+	0.241903i	$0.0777717\pi$
$444$		0			0
$445$	2.92334	+	5.06337i	0.138579	+	0.240027i
$446$		0			0
$447$	−2.05933			−0.0974031
$448$		0			0
$449$	4.13821			0.195294			0.0976470	−	0.995221i	$-0.468868\pi$
$449$	4.13821			0.195294			0.0976470	+	0.995221i	$0.468868\pi$
$450$		0			0
$451$	7.99244	+	13.8433i	0.376349	+	0.651856i
$452$		0			0
$453$	21.3520	−	36.9828i	1.00321	−	1.73760i
$454$		0			0
$455$	11.7451	+	5.14625i	0.550619	+	0.241260i
$456$		0			0
$457$	6.32178	−	10.9496i	0.295720	−	0.512203i	−0.679432	−	0.733739i	$-0.737774\pi$
$457$	6.32178	−	10.9496i	0.295720	−	0.512203i	0.975152	+	0.221536i	$0.0711070\pi$
$458$		0			0
$459$	1.75268	+	3.03572i	0.0818079	+	0.141695i
$460$		0			0
$461$	20.7129			0.964695			0.482348	−	0.875980i	$-0.339784\pi$
$461$	20.7129			0.964695			0.482348	+	0.875980i	$0.339784\pi$
$462$		0			0
$463$	16.3811			0.761295			0.380647	−	0.924720i	$-0.375701\pi$
$463$	16.3811			0.761295			0.380647	+	0.924720i	$0.375701\pi$
$464$		0			0
$465$	−11.8467	−	20.5190i	−0.549376	−	0.951548i
$466$		0			0
$467$	−0.861215	+	1.49167i	−0.0398523	+	0.0690262i	−0.885264	−	0.465090i	$-0.846022\pi$
$467$	−0.861215	+	1.49167i	−0.0398523	+	0.0690262i	0.845411	+	0.534116i	$0.179355\pi$
$468$		0			0
$469$	12.2602	−	9.01884i	0.566125	−	0.416452i
$470$		0			0
$471$	10.5993	−	18.3586i	0.488392	−	0.845920i
$472$		0			0
$473$	−5.52489	−	9.56940i	−0.254035	−	0.440001i
$474$		0			0
$475$	−6.84667			−0.314147
$476$		0			0
$477$	27.5507			1.26146
$478$		0			0
$479$	−0.890881	−	1.54305i	−0.0407054	−	0.0705038i	0.844955	−	0.534838i	$-0.179627\pi$
$479$	−0.890881	−	1.54305i	−0.0407054	−	0.0705038i	−0.885660	+	0.464334i	$0.846294\pi$
$480$		0			0
$481$	−6.89844	+	11.9485i	−0.314542	+	0.544803i
$482$		0			0
$483$	−1.70789	−	15.3743i	−0.0777116	−	0.699553i
$484$		0			0
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	−5.50977	−	9.54320i	−0.249672	−	0.432444i	0.713763	−	0.700387i	$-0.246989\pi$
$487$	−5.50977	−	9.54320i	−0.249672	−	0.432444i	−0.963435	+	0.267943i	$0.913656\pi$
$488$		0			0
$489$	9.54443			0.431614
$490$		0			0
$491$	20.9311			0.944608			0.472304	−	0.881436i	$-0.343422\pi$
$491$	20.9311			0.944608			0.472304	+	0.881436i	$0.343422\pi$
$492$		0			0
$493$	−3.32178	−	5.75349i	−0.149605	−	0.259124i
$494$		0			0
$495$	3.08643	−	5.34586i	0.138725	−	0.240279i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.75268	+	6.49983i	−0.167993	+	0.290972i	−0.937714	−	0.347408i	$-0.887062\pi$
$499$	−3.75268	+	6.49983i	−0.167993	+	0.290972i	0.769721	+	0.638380i	$0.220395\pi$
$500$		0			0
$501$	0.339111	+	0.587357i	0.0151503	+	0.0262412i
$502$		0			0
$503$	−20.5842			−0.917805			−0.458903	−	0.888487i	$-0.651757\pi$
$503$	−20.5842			−0.917805			−0.458903	+	0.888487i	$0.651757\pi$
$504$		0			0
$505$	−17.0151			−0.757163
$506$		0			0
$507$	13.5546	+	23.4772i	0.601979	+	1.04266i
$508$		0			0
$509$	−6.82934	+	11.8288i	−0.302705	+	0.524301i	−0.976748	−	0.214392i	$-0.931223\pi$
$509$	−6.82934	+	11.8288i	−0.302705	+	0.524301i	0.674043	+	0.738693i	$0.264556\pi$
$510$		0			0
$511$	−24.9211	+	18.3324i	−1.10245	+	0.810978i
$512$		0			0
$513$	−6.00000	+	10.3923i	−0.264906	+	0.458831i
$514$		0			0
$515$	3.55456	+	6.15668i	0.156633	+	0.271296i
$516$		0			0
$517$	−20.4795			−0.900688
$518$		0			0
$519$	48.7040			2.13787
$520$		0			0
$521$	21.0820	+	36.5151i	0.923620	+	1.59976i	0.793766	+	0.608224i	$0.208118\pi$
$521$	21.0820	+	36.5151i	0.923620	+	1.59976i	0.129854	+	0.991533i	$0.458549\pi$
$522$		0			0
$523$	−15.3218	+	26.5381i	−0.669975	+	1.16043i	0.307936	+	0.951407i	$0.400362\pi$
$523$	−15.3218	+	26.5381i	−0.669975	+	1.16043i	−0.977911	+	0.209023i	$0.932972\pi$
$524$		0			0
$525$	6.26245	+	2.74396i	0.273316	+	0.119756i
$526$		0			0
$527$	9.16845	−	15.8802i	0.399384	−	0.691753i
$528$		0			0
$529$	8.94067	+	15.4857i	0.388725	+	0.673291i
$530$		0			0
$531$	−29.4258			−1.27697
$532$		0			0
$533$	−46.1640			−1.99959
$534$		0			0
$535$	−0.876338	−	1.51786i	−0.0378874	−	0.0656229i
$536$		0			0
$537$	15.5249	−	26.8899i	0.669949	−	1.16038i
$538$		0			0
$539$	−7.96335	−	8.63654i	−0.343006	−	0.372002i
$540$		0			0
$541$	16.8445	−	29.1755i	0.724200	−	1.25435i	−0.235102	−	0.971971i	$-0.575543\pi$
$541$	16.8445	−	29.1755i	0.724200	−	1.25435i	0.959302	−	0.282381i	$-0.0911241\pi$
$542$		0			0
$543$	−7.79747	−	13.5056i	−0.334621	−	0.579581i
$544$		0			0
$545$	19.5400			0.837002
$546$		0			0
$547$	3.03979			0.129972			0.0649861	−	0.997886i	$-0.479300\pi$
$547$	3.03979			0.129972			0.0649861	+	0.997886i	$0.479300\pi$
$548$		0			0
$549$	11.9363	+	20.6742i	0.509427	+	0.882353i
$550$		0			0
$551$	11.3716	−	19.6961i	0.484445	−	0.839083i
$552$		0			0
$553$	13.7969	+	6.04526i	0.586703	+	0.257070i
$554$		0			0
$555$	−3.67822	+	6.37087i	−0.156132	+	0.270428i
$556$		0			0
$557$	−9.08202	−	15.7305i	−0.384817	−	0.666523i	0.606926	−	0.794758i	$-0.292402\pi$
$557$	−9.08202	−	15.7305i	−0.384817	−	0.666523i	−0.991744	+	0.128235i	$0.959069\pi$
$558$		0			0
$559$	31.9116			1.34972
$560$		0			0
$561$	8.67380			0.366208
$562$		0			0
$563$	−18.4952	−	32.0347i	−0.779481	−	1.35010i	−0.932241	−	0.361837i	$-0.882150\pi$
$563$	−18.4952	−	32.0347i	−0.779481	−	1.35010i	0.152760	−	0.988263i	$-0.451184\pi$
$564$		0			0
$565$	−5.16845	+	8.95202i	−0.217438	+	0.376614i
$566$		0			0
$567$	−13.8644	+	10.1989i	−0.582248	+	0.428312i
$568$		0			0
$569$	−16.3047	+	28.2405i	−0.683527	+	1.18390i	0.290370	+	0.956915i	$0.406222\pi$
$569$	−16.3047	+	28.2405i	−0.683527	+	1.18390i	−0.973897	+	0.226990i	$0.927112\pi$
$570$		0			0
$571$	20.2182	+	35.0190i	0.846107	+	1.46550i	0.884656	+	0.466243i	$0.154393\pi$
$571$	20.2182	+	35.0190i	0.846107	+	1.46550i	−0.0385496	+	0.999257i	$0.512274\pi$
$572$		0			0
$573$	7.31736			0.305687
$574$		0			0
$575$	2.26245			0.0943505
$576$		0			0
$577$	19.0151	+	32.9352i	0.791610	+	1.37111i	0.924970	+	0.380041i	$0.124090\pi$
$577$	19.0151	+	32.9352i	0.791610	+	1.37111i	−0.133360	+	0.991068i	$0.542577\pi$
$578$		0			0
$579$	16.7722	−	29.0503i	0.697030	−	1.20729i
$580$		0			0
$581$	3.67601	+	33.0912i	0.152507	+	1.37285i
$582$		0			0
$583$	6.28513	−	10.8862i	0.260304	−	0.450859i
$584$		0			0
$585$	8.91357	+	15.4387i	0.368531	+	0.638314i
$586$		0			0
$587$	−34.0302			−1.40458			−0.702289	−	0.711892i	$-0.747839\pi$
$587$	−34.0302			−1.40458			−0.702289	+	0.711892i	$0.747839\pi$
$588$		0			0
$589$	62.7734			2.58653
$590$		0			0
$591$	−6.26245	−	10.8469i	−0.257603	−	0.446181i
$592$		0			0
$593$	16.8618	−	29.2055i	0.692431	−	1.19933i	−0.278608	−	0.960405i	$-0.589873\pi$
$593$	16.8618	−	29.2055i	0.692431	−	1.19933i	0.971039	−	0.238921i	$-0.0767936\pi$
$594$		0			0
$595$	0.584225	+	5.25915i	0.0239509	+	0.215604i
$596$		0			0
$597$	19.8813	−	34.4355i	0.813689	−	1.40935i
$598$		0			0
$599$	3.15333	+	5.46172i	0.128841	+	0.223160i	0.923228	−	0.384253i	$-0.125541\pi$
$599$	3.15333	+	5.46172i	0.128841	+	0.223160i	−0.794387	+	0.607413i	$0.792207\pi$
$600$		0			0
$601$	−11.2871			−0.460411			−0.230206	−	0.973142i	$-0.573940\pi$
$601$	−11.2871			−0.460411			−0.230206	+	0.973142i	$0.573940\pi$
$602$		0			0
$603$	21.1596			0.861686
$604$		0			0
$605$	4.09179	+	7.08718i	0.166355	+	0.288135i
$606$		0			0
$607$	−7.73057	+	13.3897i	−0.313774	+	0.543473i	−0.979176	−	0.203012i	$-0.934927\pi$
$607$	−7.73057	+	13.3897i	−0.313774	+	0.543473i	0.665402	+	0.746485i	$0.268260\pi$
$608$		0			0
$609$	−18.2949	+	13.4580i	−0.741347	+	0.545348i
$610$		0			0
$611$	29.5722	−	51.2206i	1.19637	−	2.07217i
$612$		0			0
$613$	11.0820	+	19.1946i	0.447598	+	0.775263i	0.998229	−	0.0594857i	$-0.0189461\pi$
$613$	11.0820	+	19.1946i	0.447598	+	0.775263i	−0.550631	+	0.834749i	$0.685613\pi$
$614$		0			0
$615$	−24.6145			−0.992551
$616$		0			0
$617$	−14.9805			−0.603091			−0.301545	−	0.953452i	$-0.597502\pi$
$617$	−14.9805			−0.603091			−0.301545	+	0.953452i	$0.597502\pi$
$618$		0			0
$619$	11.8196	+	20.4721i	0.475069	+	0.822843i	0.999592	−	0.0285529i	$-0.00908990\pi$
$619$	11.8196	+	20.4721i	0.475069	+	0.822843i	−0.524524	+	0.851396i	$0.675757\pi$
$620$		0			0
$621$	1.98267	−	3.43408i	0.0795617	−	0.137805i
$622$		0			0
$623$	14.1685	+	6.20806i	0.567647	+	0.248721i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	14.8467	+	25.7152i	0.592919	+	1.02697i
$628$		0			0
$629$	−5.69334			−0.227008
$630$		0			0
$631$	13.7818			0.548643			0.274322	−	0.961638i	$-0.411547\pi$
$631$	13.7818			0.548643			0.274322	+	0.961638i	$0.411547\pi$
$632$		0			0
$633$	−11.8662	−	20.5529i	−0.471640	−	0.816904i
$634$		0			0
$635$	−9.59179	+	16.6135i	−0.380638	+	0.659285i
$636$		0			0
$637$	33.0996	−	7.44577i	1.31145	−	0.295012i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.9309	−	37.9854i	−0.866218	−	1.50033i	−0.865832	−	0.500334i	$-0.833210\pi$
$641$	−21.9309	−	37.9854i	−0.866218	−	1.50033i	−0.000386062	−	1.00000i	$-0.500123\pi$
$642$		0			0
$643$	−7.04979			−0.278016			−0.139008	−	0.990291i	$-0.544391\pi$
$643$	−7.04979			−0.278016			−0.139008	+	0.990291i	$0.544391\pi$
$644$		0			0
$645$	17.0151			0.669970
$646$		0			0
$647$	−12.2403	−	21.2009i	−0.481217	−	0.833493i	0.518550	−	0.855047i	$-0.326472\pi$
$647$	−12.2403	−	21.2009i	−0.481217	−	0.833493i	−0.999768	+	0.0215540i	$0.993139\pi$
$648$		0			0
$649$	−6.71288	+	11.6271i	−0.263504	+	0.456402i
$650$		0			0
$651$	−57.4169	−	25.1579i	−2.25035	−	0.986014i
$652$		0			0
$653$	−0.408213	+	0.707046i	−0.0159746	+	0.0276688i	−0.873902	−	0.486102i	$-0.838418\pi$
$653$	−0.408213	+	0.707046i	−0.0159746	+	0.0276688i	0.857928	+	0.513771i	$0.171752\pi$
$654$		0			0
$655$	−8.91357	−	15.4387i	−0.348282	−	0.603242i
$656$		0			0
$657$	−43.0107			−1.67801
$658$		0			0
$659$	−21.2871			−0.829228			−0.414614	−	0.909997i	$-0.636083\pi$
$659$	−21.2871			−0.829228			−0.414614	+	0.909997i	$0.636083\pi$
$660$		0			0
$661$	−12.9731	−	22.4701i	−0.504596	−	0.873986i	−0.999986	−	0.00531513i	$-0.998308\pi$
$661$	−12.9731	−	22.4701i	−0.504596	−	0.873986i	0.495390	−	0.868671i	$-0.335025\pi$
$662$		0			0
$663$	−12.5249	+	21.6938i	−0.486427	+	0.842515i
$664$		0			0
$665$	−14.5918	+	10.7340i	−0.565845	+	0.416246i
$666$		0			0
$667$	−3.75767	+	6.50848i	−0.145498	+	0.252009i
$668$		0			0
$669$	16.7722	+	29.0503i	0.648451	+	1.12315i
$670$		0			0
$671$	10.8920			0.420483
$672$		0			0
$673$	22.0693			0.850710			0.425355	−	0.905027i	$-0.360149\pi$
$673$	22.0693			0.850710			0.425355	+	0.905027i	$0.360149\pi$
$674$		0			0
$675$	0.876338	+	1.51786i	0.0337303	+	0.0584225i
$676$		0			0
$677$	−2.74511	+	4.75468i	−0.105503	+	0.182737i	−0.913944	−	0.405841i	$-0.866979\pi$
$677$	−2.74511	+	4.75468i	−0.105503	+	0.182737i	0.808440	+	0.588578i	$0.200312\pi$
$678$		0			0
$679$	−0.584225	−	5.25915i	−0.0224205	−	0.201828i
$680$		0			0
$681$	28.4656	−	49.3038i	1.09080	−	1.88933i
$682$		0			0
$683$	9.61389	+	16.6517i	0.367865	+	0.637161i	0.989232	−	0.146359i	$-0.0467554\pi$
$683$	9.61389	+	16.6517i	0.367865	+	0.637161i	−0.621366	+	0.783520i	$0.713422\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	−11.1294			−0.424612
$688$		0			0
$689$	18.1513	+	31.4390i	0.691511	+	1.19773i
$690$		0			0
$691$	7.10912	−	12.3134i	0.270444	−	0.468422i	−0.698532	−	0.715579i	$-0.746163\pi$
$691$	7.10912	−	12.3134i	0.270444	−	0.468422i	0.968975	+	0.247157i	$0.0794963\pi$
$692$		0			0
$693$	−1.80317	−	16.2320i	−0.0684969	−	0.616604i
$694$		0			0
$695$	−2.58423	+	4.47601i	−0.0980253	+	0.169785i
$696$		0			0
$697$	−9.52489	−	16.4976i	−0.360781	−	0.624891i
$698$		0			0
$699$	−46.5161			−1.75940
$700$		0			0
$701$	14.1533			0.534564			0.267282	−	0.963618i	$-0.413875\pi$
$701$	14.1533			0.534564			0.267282	+	0.963618i	$0.413875\pi$
$702$		0			0
$703$	−9.74511	−	16.8790i	−0.367544	−	0.636605i
$704$		0			0
$705$	15.7678	−	27.3106i	0.593850	−	1.02858i
$706$		0			0
$707$	−36.2630	+	26.6757i	−1.36381	+	1.00324i
$708$		0			0
$709$	−8.52268	+	14.7617i	−0.320076	+	0.554388i	−0.980503	−	0.196502i	$-0.937042\pi$
$709$	−8.52268	+	14.7617i	−0.320076	+	0.554388i	0.660427	+	0.750890i	$0.270375\pi$
$710$		0			0
$711$	10.4707	+	18.1358i	0.392682	+	0.680144i
$712$		0			0
$713$	−20.7431			−0.776836
$714$		0			0
$715$	8.13379			0.304186
$716$		0			0
$717$	−14.0347	−	24.3088i	−0.524134	−	0.907827i
$718$		0			0
$719$	−5.75268	+	9.96393i	−0.214539	+	0.371592i	−0.953130	−	0.302562i	$-0.902158\pi$
$719$	−5.75268	+	9.96393i	−0.214539	+	0.371592i	0.738591	+	0.674154i	$0.235491\pi$
$720$		0			0
$721$	17.2278	+	7.54854i	0.641596	+	0.281122i
$722$		0			0
$723$	0.262447	−	0.454571i	0.00976049	−	0.0169057i
$724$		0			0
$725$	−1.66089	−	2.87674i	−0.0616839	−	0.106840i
$726$		0			0
$727$	−16.4114			−0.608664			−0.304332	−	0.952566i	$-0.598433\pi$
$727$	−16.4114			−0.608664			−0.304332	+	0.952566i	$0.598433\pi$
$728$		0			0
$729$	−37.5161			−1.38948
$730$		0			0
$731$	6.58423	+	11.4042i	0.243526	+	0.421800i
$732$		0			0
$733$	4.55712	−	7.89317i	0.168321	−	0.291541i	−0.769509	−	0.638637i	$-0.779499\pi$
$733$	4.55712	−	7.89317i	0.168321	−	0.291541i	0.937830	+	0.347096i	$0.112832\pi$
$734$		0			0
$735$	17.6486	−	3.97006i	0.650977	−	0.146438i
$736$		0			0
$737$	4.82713	−	8.36084i	0.177810	−	0.307975i
$738$		0			0
$739$	−17.4978	−	30.3071i	−0.643667	−	1.11486i	−0.984608	−	0.174779i	$-0.944079\pi$
$739$	−17.4978	−	30.3071i	−0.643667	−	1.11486i	0.340941	−	0.940085i	$-0.389254\pi$
$740$		0			0
$741$	−85.7538			−3.15025
$742$		0			0
$743$	43.5305			1.59698			0.798489	−	0.602009i	$-0.205633\pi$
$743$	43.5305			1.59698			0.798489	+	0.602009i	$0.205633\pi$
$744$		0			0
$745$	−0.398443	−	0.690123i	−0.0145978	−	0.0252842i
$746$		0			0
$747$	−23.1438	+	40.0862i	−0.846787	+	1.46668i
$748$		0			0
$749$	−4.24732	−	1.86101i	−0.155194	−	0.0679999i
$750$		0			0
$751$	3.15333	−	5.46172i	0.115067	−	0.199301i	−0.802740	−	0.596329i	$-0.796625\pi$
$751$	3.15333	−	5.46172i	0.115067	−	0.199301i	0.917806	+	0.397028i	$0.129959\pi$
$752$		0			0
$753$	−6.50535	−	11.2676i	−0.237068	−	0.410614i
$754$		0			0
$755$	16.5249			0.601402
$756$		0			0
$757$	24.3369			0.884540			0.442270	−	0.896882i	$-0.354173\pi$
$757$	24.3369			0.884540			0.442270	+	0.896882i	$0.354173\pi$
$758$		0			0
$759$	−4.90600	−	8.49745i	−0.178077	−	0.308438i
$760$		0			0
$761$	14.1016	−	24.4246i	0.511181	−	0.885392i	−0.488735	−	0.872432i	$-0.662541\pi$
$761$	14.1016	−	24.4246i	0.511181	−	0.885392i	0.999916	−	0.0129592i	$-0.00412517\pi$
$762$		0			0
$763$	41.6441	−	30.6342i	1.50762	−	1.10903i
$764$		0			0
$765$	−3.67822	+	6.37087i	−0.132986	+	0.230339i
$766$		0			0
$767$	−19.3867	−	33.5787i	−0.700013	−	1.21246i
$768$		0			0
$769$	−41.8965			−1.51082			−0.755412	−	0.655250i	$-0.772563\pi$
$769$	−41.8965			−1.51082			−0.755412	+	0.655250i	$0.772563\pi$
$770$		0			0
$771$	−60.4365			−2.17657
$772$		0			0
$773$	−19.9287	−	34.5175i	−0.716785	−	1.24151i	−0.962267	−	0.272107i	$-0.912280\pi$
$773$	−19.9287	−	34.5175i	−0.716785	−	1.24151i	0.245482	−	0.969401i	$-0.421054\pi$
$774$		0			0
$775$	4.58423	−	7.94011i	0.164670	−	0.285217i
$776$		0			0
$777$	2.14891	+	19.3443i	0.0770917	+	0.693974i
$778$		0			0
$779$	32.6069	−	56.4768i	1.16826	−	2.02349i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−5.82200			−0.208061
$784$		0			0
$785$	8.20311			0.292782
$786$		0			0
$787$	17.6637	+	30.5944i	0.629642	+	1.09057i	0.987623	+	0.156843i	$0.0501318\pi$
$787$	17.6637	+	30.5944i	0.629642	+	1.09057i	−0.357981	+	0.933729i	$0.616535\pi$
$788$		0			0
$789$	−35.0280	+	60.6703i	−1.24703	+	2.15992i
$790$		0			0
$791$	3.01954	+	27.1817i	0.107363	+	0.966469i
$792$		0			0
$793$	−15.7280	+	27.2417i	−0.558518	+	0.967381i
$794$		0			0
$795$	9.67822	+	16.7632i	0.343251	+	0.594528i
$796$		0			0
$797$	29.6933			1.05179			0.525896	−	0.850549i	$-0.323730\pi$
$797$	29.6933			1.05179			0.525896	+	0.850549i	$0.323730\pi$
$798$		0			0
$799$	24.4062			0.863430
$800$		0			0
$801$	10.7527	+	18.6242i	0.379927	+	0.658053i
$802$		0			0
$803$	−9.81201	+	16.9949i	−0.346258	+	0.599737i
$804$		0			0
$805$	4.82178	−	3.54698i	0.169945	−	0.125015i
$806$		0			0
$807$	8.38611	−	14.5252i	0.295205	−	0.511310i
$808$		0			0
$809$	9.82178	+	17.0118i	0.345315	+	0.598104i	0.985411	−	0.170191i	$-0.0544386\pi$
$809$	9.82178	+	17.0118i	0.345315	+	0.598104i	−0.640096	+	0.768295i	$0.721105\pi$
$810$		0			0
$811$	−0.252452			−0.00886479			−0.00443239	−	0.999990i	$-0.501411\pi$
$811$	−0.252452			−0.00886479			−0.00443239	+	0.999990i	$0.501411\pi$
$812$		0			0
$813$	−60.4365			−2.11960
$814$		0			0
$815$	1.84667	+	3.19853i	0.0646861	+	0.112040i
$816$		0			0
$817$	−22.5400	+	39.0405i	−0.788575	+	1.36585i
$818$		0			0
$819$	43.2011	+	18.9290i	1.50957	+	0.661434i
$820$		0			0
$821$	−22.3867	+	38.7749i	−0.781301	+	1.35325i	0.149883	+	0.988704i	$0.452110\pi$
$821$	−22.3867	+	38.7749i	−0.781301	+	1.35325i	−0.931184	+	0.364549i	$0.881223\pi$
$822$		0			0
$823$	1.64856	+	2.85538i	0.0574650	+	0.0995323i	0.893327	−	0.449408i	$-0.148365\pi$
$823$	1.64856	+	2.85538i	0.0574650	+	0.0995323i	−0.835862	+	0.548940i	$0.815032\pi$
$824$		0			0
$825$	4.33690			0.150992
$826$		0			0
$827$	−9.41577			−0.327419			−0.163709	−	0.986509i	$-0.552346\pi$
$827$	−9.41577			−0.327419			−0.163709	+	0.986509i	$0.552346\pi$
$828$		0			0
$829$	2.35644	+	4.08148i	0.0818426	+	0.141756i	0.904041	−	0.427445i	$-0.140586\pi$
$829$	2.35644	+	4.08148i	0.0818426	+	0.141756i	−0.822199	+	0.569200i	$0.807253\pi$
$830$		0			0
$831$	4.73314	−	8.19803i	0.164191	−	0.284387i
$832$		0			0
$833$	9.49023	+	10.2925i	0.328817	+	0.356614i
$834$		0			0
$835$	−0.131223	+	0.227285i	−0.00454117	+	0.00786554i
$836$		0			0
$837$	−8.03466	−	13.9164i	−0.277719	−	0.481023i
$838$		0			0
$839$	−22.1880			−0.766015			−0.383007	−	0.923745i	$-0.625112\pi$
$839$	−22.1880			−0.766015			−0.383007	+	0.923745i	$0.625112\pi$
$840$		0			0
$841$	−17.9658			−0.619510
$842$		0			0
$843$	17.9558	+	31.1003i	0.618430	+	1.07115i
$844$		0			0
$845$	−5.24511	+	9.08481i	−0.180437	+	0.312527i
$846$		0			0
$847$	19.8315	+	8.68941i	0.681420	+	0.298572i
$848$		0			0
$849$	26.2776	−	45.5141i	0.901844	−	1.56204i
$850$		0			0
$851$	3.22022	+	5.57759i	0.110388	+	0.191197i
$852$		0			0
$853$	39.9267			1.36706			0.683532	−	0.729920i	$-0.260443\pi$
$853$	39.9267			1.36706			0.683532	+	0.729920i	$0.260443\pi$
$854$		0			0
$855$	−25.1836			−0.861260
$856$		0			0
$857$	0.812009	+	1.40644i	0.0277377	+	0.0480431i	0.879561	−	0.475786i	$-0.157836\pi$
$857$	0.812009	+	1.40644i	0.0277377	+	0.0480431i	−0.851823	+	0.523829i	$0.824503\pi$
$858$		0			0
$859$	4.00000	−	6.92820i	0.136478	−	0.236387i	−0.789683	−	0.613515i	$-0.789755\pi$
$859$	4.00000	−	6.92820i	0.136478	−	0.236387i	0.926161	+	0.377128i	$0.123088\pi$
$860$		0			0
$861$	−52.4589	+	38.5897i	−1.78780	+	1.31513i
$862$		0			0
$863$	9.11168	−	15.7819i	0.310165	−	0.537222i	−0.668233	−	0.743952i	$-0.732949\pi$
$863$	9.11168	−	15.7819i	0.310165	−	0.537222i	0.978398	+	0.206730i	$0.0662823\pi$
$864$		0			0
$865$	9.42334	+	16.3217i	0.320403	+	0.554954i
$866$		0			0
$867$	33.5949			1.14094
$868$		0			0
$869$	9.55469			0.324121
$870$		0			0
$871$	13.9407	+	24.1459i	0.472362	+	0.818154i
$872$		0			0
$873$	3.67822	−	6.37087i	0.124489	−	0.215621i
$874$		0			0
$875$	0.292113	+	2.62958i	0.00987521	+	0.0888959i
$876$		0			0
$877$	25.4385	−	44.0607i	0.858996	−	1.48782i	−0.0138922	−	0.999903i	$-0.504422\pi$
$877$	25.4385	−	44.0607i	0.858996	−	1.48782i	0.872888	−	0.487921i	$-0.162244\pi$
$878$		0			0
$879$	24.3520	+	42.1789i	0.821373	+	1.42266i
$880$		0			0
$881$	−19.1187			−0.644124			−0.322062	−	0.946719i	$-0.604376\pi$
$881$	−19.1187			−0.644124			−0.322062	+	0.946719i	$0.604376\pi$
$882$		0			0
$883$	−39.3174			−1.32313			−0.661567	−	0.749886i	$-0.730108\pi$
$883$	−39.3174			−1.32313			−0.661567	+	0.749886i	$0.730108\pi$
$884$		0			0
$885$	−10.3369	−	17.9040i	−0.347471	−	0.601838i
$886$		0			0
$887$	13.5199	−	23.4171i	0.453954	−	0.786271i	−0.544674	−	0.838648i	$-0.683346\pi$
$887$	13.5199	−	23.4171i	0.453954	−	0.786271i	0.998627	+	0.0523772i	$0.0166798\pi$
$888$		0			0
$889$	5.60377	+	50.4447i	0.187944	+	1.69186i
$890$		0			0
$891$	−5.45871	+	9.45476i	−0.182874	+	0.316746i
$892$		0			0
$893$	41.7754	+	72.3570i	1.39796	+	2.42134i
$894$		0			0
$895$	12.0151			0.401621
$896$		0			0
$897$	28.3369			0.946142
$898$		0			0
$899$	15.2278	+	26.3753i	0.507875	+	0.879665i
$900$		0			0
$901$	−7.49023	+	12.9735i	−0.249536	+	0.432209i
$902$		0			0
$903$	36.2630	−	26.6757i	1.20676	−	0.887712i
$904$		0			0
$905$	3.01733	−	5.22617i	0.100299	−	0.173724i
$906$		0			0
$907$	16.4012	+	28.4078i	0.544594	+	0.943264i	0.998632	+	0.0522823i	$0.0166496\pi$
$907$	16.4012	+	28.4078i	0.544594	+	0.943264i	−0.454038	+	0.890982i	$0.650017\pi$
$908$		0			0
$909$	−62.5854			−2.07583
$910$		0			0
$911$	−6.18799			−0.205017			−0.102509	−	0.994732i	$-0.532687\pi$
$911$	−6.18799			−0.205017			−0.102509	+	0.994732i	$0.532687\pi$
$912$		0			0
$913$	10.5596	+	18.2897i	0.349470	+	0.605300i
$914$		0			0
$915$	−8.38611	+	14.5252i	−0.277236	+	0.480187i
$916$		0			0
$917$	−43.2011	−	18.9290i	−1.42663	−	0.625092i
$918$		0			0
$919$	−23.8965	+	41.3899i	−0.788271	+	1.36533i	0.138754	+	0.990327i	$0.455690\pi$
$919$	−23.8965	+	41.3899i	−0.788271	+	1.36533i	−0.927025	+	0.374999i	$0.877643\pi$
$920$		0			0
$921$	3.09620	+	5.36278i	0.102023	+	0.176710i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−2.84667			−0.0935980
$926$		0			0
$927$	13.0745	+	22.6456i	0.429421	+	0.743780i
$928$		0			0
$929$	19.9309	−	34.5213i	0.653912	−	1.13261i	−0.328254	−	0.944590i	$-0.606460\pi$
$929$	19.9309	−	34.5213i	0.653912	−	1.13261i	0.982165	−	0.188018i	$-0.0602065\pi$
$930$		0			0
$931$	−14.2700	+	45.7530i	−0.467681	+	1.49949i
$932$		0			0
$933$	7.31736	−	12.6740i	0.239560	−	0.414929i
$934$		0			0
$935$	1.67822	+	2.90676i	0.0548837	+	0.0950614i
$936$		0			0
$937$	0.406229			0.0132709			0.00663546	−	0.999978i	$-0.497888\pi$
$937$	0.406229			0.0132709			0.00663546	+	0.999978i	$0.497888\pi$
$938$		0			0
$939$	−76.8125			−2.50668
$940$		0			0
$941$	−16.8271	−	29.1454i	−0.548549	−	0.950114i	−0.998374	−	0.0569979i	$-0.981847\pi$
$941$	−16.8271	−	29.1454i	−0.548549	−	0.950114i	0.449825	−	0.893116i	$-0.351486\pi$
$942$		0			0
$943$	−10.7748	+	18.6625i	−0.350875	+	0.607734i
$944$		0			0
$945$	4.24732	+	1.86101i	0.138165	+	0.0605387i
$946$		0			0
$947$	2.92055	−	5.05854i	0.0949050	−	0.164380i	−0.814664	−	0.579933i	$-0.803079\pi$
$947$	2.92055	−	5.05854i	0.0949050	−	0.164380i	0.909569	+	0.415553i	$0.136412\pi$
$948$		0			0
$949$	−28.3369	−	49.0810i	−0.919855	−	1.59324i
$950$		0			0
$951$	−49.2289			−1.59636
$952$		0			0
$953$	32.0605			1.03854			0.519271	−	0.854610i	$-0.326204\pi$
$953$	32.0605			1.03854			0.519271	+	0.854610i	$0.326204\pi$
$954$		0			0
$955$	1.41577	+	2.45219i	0.0458134	+	0.0793511i
$956$		0			0
$957$	−7.20311	+	12.4762i	−0.232844	+	0.403297i
$958$		0			0
$959$	8.52489	−	6.27106i	0.275283	−	0.202503i
$960$		0			0
$961$	−26.5302	+	45.9517i	−0.855814	+	1.48231i
$962$		0			0
$963$	−3.22337	−	5.58303i	−0.103872	−	0.179911i
$964$		0			0
$965$	12.9805			0.417856
$966$		0			0
$967$	−24.0896			−0.774669			−0.387334	−	0.921939i	$-0.626604\pi$
$967$	−24.0896			−0.774669			−0.387334	+	0.921939i	$0.626604\pi$
$968$		0			0
$969$	−17.6933	−	30.6458i	−0.568392	−	0.984484i
$970$		0			0
$971$	9.23534	−	15.9961i	0.296376	−	0.513339i	−0.678928	−	0.734205i	$-0.737555\pi$
$971$	9.23534	−	15.9961i	0.296376	−	0.513339i	0.975304	+	0.220866i	$0.0708884\pi$
$972$		0			0
$973$	1.50977	+	13.5908i	0.0484010	+	0.435702i
$974$		0			0
$975$	−6.26245	+	10.8469i	−0.200559	+	0.347378i
$976$		0			0
$977$	−12.1685	−	21.0764i	−0.389303	−	0.674293i	0.603053	−	0.797701i	$-0.293951\pi$
$977$	−12.1685	−	21.0764i	−0.389303	−	0.674293i	−0.992356	+	0.123408i	$0.960618\pi$
$978$		0			0
$979$	9.81201			0.313593
$980$		0			0
$981$	71.8725			2.29471
$982$		0			0
$983$	4.33434	+	7.50729i	0.138244	+	0.239445i	0.926832	−	0.375476i	$-0.122521\pi$
$983$	4.33434	+	7.50729i	0.138244	+	0.239445i	−0.788588	+	0.614922i	$0.789188\pi$
$984$		0			0
$985$	2.42334	−	4.19734i	0.0772139	−	0.133738i
$986$		0			0
$987$	−9.21195	−	82.9253i	−0.293220	−	2.63954i
$988$		0			0
$989$	7.44823	−	12.9007i	0.236840	−	0.410219i
$990$		0			0
$991$	−27.7527	−	48.0690i	−0.881593	−	1.52696i	−0.849570	−	0.527476i	$-0.823138\pi$
$991$	−27.7527	−	48.0690i	−0.881593	−	1.52696i	−0.0320231	−	0.999487i	$-0.510195\pi$
$992$		0			0
$993$	6.00000			0.190404
$994$		0			0
$995$	15.3867			0.487791
$996$		0			0
$997$	17.5596	+	30.4140i	0.556117	+	0.963222i	0.997816	+	0.0660591i	$0.0210426\pi$
$997$	17.5596	+	30.4140i	0.556117	+	0.963222i	−0.441699	+	0.897163i	$0.645624\pi$
$998$		0			0
$999$	−2.49465	+	4.32086i	−0.0789271	+	0.136706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.l.401.3		6
4.3	odd	2		280.2.q.e.121.1	yes	6
7.2	even	3		3920.2.a.cc.1.1		3
7.4	even	3	inner	560.2.q.l.81.3		6
7.5	odd	6		3920.2.a.cb.1.3		3
12.11	even	2		2520.2.bi.q.1801.1		6
20.3	even	4		1400.2.bh.i.849.5		12
20.7	even	4		1400.2.bh.i.849.2		12
20.19	odd	2		1400.2.q.j.401.3		6
28.3	even	6		1960.2.q.w.361.3		6
28.11	odd	6		280.2.q.e.81.1	✓	6
28.19	even	6		1960.2.a.v.1.1		3
28.23	odd	6		1960.2.a.w.1.3		3
28.27	even	2		1960.2.q.w.961.3		6
84.11	even	6		2520.2.bi.q.361.1		6
140.19	even	6		9800.2.a.cf.1.3		3
140.39	odd	6		1400.2.q.j.1201.3		6
140.67	even	12		1400.2.bh.i.249.5		12
140.79	odd	6		9800.2.a.ce.1.1		3
140.123	even	12		1400.2.bh.i.249.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.1	✓	6	28.11	odd	6
280.2.q.e.121.1	yes	6	4.3	odd	2
560.2.q.l.81.3		6	7.4	even	3	inner
560.2.q.l.401.3		6	1.1	even	1	trivial
1400.2.q.j.401.3		6	20.19	odd	2
1400.2.q.j.1201.3		6	140.39	odd	6
1400.2.bh.i.249.2		12	140.123	even	12
1400.2.bh.i.249.5		12	140.67	even	12
1400.2.bh.i.849.2		12	20.7	even	4
1400.2.bh.i.849.5		12	20.3	even	4
1960.2.a.v.1.1		3	28.19	even	6
1960.2.a.w.1.3		3	28.23	odd	6
1960.2.q.w.361.3		6	28.3	even	6
1960.2.q.w.961.3		6	28.27	even	2
2520.2.bi.q.361.1		6	84.11	even	6
2520.2.bi.q.1801.1		6	12.11	even	2
3920.2.a.cb.1.3		3	7.5	odd	6
3920.2.a.cc.1.1		3	7.2	even	3
9800.2.a.ce.1.1		3	140.79	odd	6
9800.2.a.cf.1.3		3	140.19	even	6

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29211 + 2.23800i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +O(q^{10})\)	\(q+(1.29211 + 2.23800i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +(0.839111 + 1.45338i) q^{11} -4.84667 q^{13} -2.58423 q^{15} +(-1.00000 - 1.73205i) q^{17} +(3.42334 - 5.92939i) q^{19} +(-5.50756 + 4.05146i) q^{21} +(-1.13122 + 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.75268 q^{27} +3.32178 q^{29} +(4.58423 + 7.94011i) q^{31} +(-2.16845 + 3.75587i) q^{33} +(-2.42334 - 1.06181i) q^{35} +(1.42334 - 2.46529i) q^{37} +(-6.26245 - 10.8469i) q^{39} +9.52489 q^{41} -6.58423 q^{43} +(-1.83911 - 3.18543i) q^{45} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(2.58423 - 4.47601i) q^{51} +(-3.74511 - 6.48673i) q^{53} -1.67822 q^{55} +17.6933 q^{57} +(4.00000 + 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-8.91357 - 3.90558i) q^{63} +(2.42334 - 4.19734i) q^{65} +(-2.87634 - 4.98196i) q^{67} -5.84667 q^{69} +(5.84667 + 10.1267i) q^{73} +(1.29211 - 2.23800i) q^{75} +(-3.57666 + 2.63106i) q^{77} +(2.84667 - 4.93058i) q^{79} +(3.25268 + 5.63380i) q^{81} +12.5842 q^{83} +2.00000 q^{85} +(4.29211 + 7.43416i) q^{87} +(2.92334 - 5.06337i) q^{89} +(-1.41577 - 12.7447i) q^{91} +(-11.8467 + 20.5190i) q^{93} +(3.42334 + 5.92939i) q^{95} -2.00000 q^{97} -6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9	\( 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43} - 9 q^{45} - 15 q^{47} - 12 q^{49} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} + 6 q^{61} - 9 q^{63} - 3 q^{65} + 6 q^{67} - 39 q^{77} - 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 24 q^{91} - 36 q^{93} + 3 q^{95} - 12 q^{97} - 126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9 + 3 * q^11 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 + 18 * q^33 + 3 * q^35 - 9 * q^37 - 18 * q^39 + 18 * q^41 - 24 * q^43 - 9 * q^45 - 15 * q^47 - 12 * q^49 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 + 6 * q^61 - 9 * q^63 - 3 * q^65 + 6 * q^67 - 39 * q^77 - 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 24 * q^91 - 36 * q^93 + 3 * q^95 - 12 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

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