LMFDB - Embedded newform 912.2.q.l.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(49,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, 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("912.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.2
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	912.49
Dual form			912.2.q.l.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-0.675970 + 1.17081i) q^{5} -0.351939 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-0.675970 + 1.17081i) q^{5} -0.351939 q^{7} +(-0.500000 - 0.866025i) q^{9} -5.52420 q^{11} +(2.58613 + 4.47931i) q^{13} +(0.675970 + 1.17081i) q^{15} +(2.43807 + 3.61328i) q^{19} +(-0.175970 + 0.304788i) q^{21} +(4.41016 + 7.63862i) q^{23} +(1.58613 + 2.74726i) q^{25} -1.00000 q^{27} +(-1.35194 - 2.34163i) q^{29} +0.524200 q^{31} +(-2.76210 + 4.78410i) q^{33} +(0.237900 - 0.412055i) q^{35} -1.00000 q^{37} +5.17226 q^{39} +(1.35194 - 2.34163i) q^{41} +(-3.26210 + 5.65012i) q^{43} +1.35194 q^{45} +(-3.00000 - 5.19615i) q^{47} -6.87614 q^{49} +(2.02791 + 3.51244i) q^{53} +(3.73419 - 6.46781i) q^{55} +(4.34823 - 0.304788i) q^{57} +(-2.76210 + 4.78410i) q^{59} +(0.938069 + 1.62478i) q^{61} +(0.175970 + 0.304788i) q^{63} -6.99258 q^{65} +(5.99629 + 10.3859i) q^{67} +8.82032 q^{69} +(2.52420 - 4.37204i) q^{71} +(-3.85194 + 6.67175i) q^{73} +3.17226 q^{75} +1.94418 q^{77} +(3.91016 - 6.77260i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.34452 q^{83} -2.70388 q^{87} +(2.32403 + 4.02534i) q^{89} +(-0.910161 - 1.57644i) q^{91} +(0.262100 - 0.453970i) q^{93} +(-5.87854 + 0.412055i) q^{95} +(6.90645 - 11.9623i) q^{97} +(2.76210 + 4.78410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9 + q^13 + 2 * q^15 - 4 * q^19 + q^21 + 14 * q^23 - 5 * q^25 - 6 * q^27 - 4 * q^29 - 30 * q^31 + 18 * q^35 - 6 * q^37 + 2 * q^39 + 4 * q^41 - 3 * q^43 + 4 * q^45 - 18 * q^47 - 4 * q^49 + 6 * q^53 + 12 * q^55 - 5 * q^57 - 13 * q^61 - q^63 + 12 * q^65 + 9 * q^67 + 28 * q^69 - 18 * q^71 - 19 * q^73 - 10 * q^75 + 24 * q^77 + 11 * q^79 - 3 * q^81 + 8 * q^83 - 8 * q^87 + 16 * q^89 + 7 * q^91 - 15 * q^93 - 2 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−0.675970	+	1.17081i	−0.302303	+	0.523604i	−0.976657	−	0.214804i	$-0.931089\pi$
$5$	−0.675970	+	1.17081i	−0.302303	+	0.523604i	0.674354	+	0.738408i	$0.264422\pi$
$6$		0			0
$7$	−0.351939			−0.133021			−0.0665103	−	0.997786i	$-0.521187\pi$
$7$	−0.351939			−0.133021			−0.0665103	+	0.997786i	$0.521187\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−5.52420			−1.66561			−0.832804	−	0.553567i	$-0.813266\pi$
$11$	−5.52420			−1.66561			−0.832804	+	0.553567i	$0.813266\pi$
$12$		0			0
$13$	2.58613	+	4.47931i	0.717263	+	1.24234i	0.962080	+	0.272767i	$0.0879389\pi$
$13$	2.58613	+	4.47931i	0.717263	+	1.24234i	−0.244817	+	0.969569i	$0.578728\pi$
$14$		0			0
$15$	0.675970	+	1.17081i	0.174535	+	0.302303i
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	2.43807	+	3.61328i	0.559331	+	0.828944i
$19$	2.43807	+	3.61328i	0.559331	+	0.828944i
$20$		0			0
$21$	−0.175970	+	0.304788i	−0.0383997	+	0.0665103i
$22$		0			0
$23$	4.41016	+	7.63862i	0.919582	+	1.59276i	0.800051	+	0.599932i	$0.204806\pi$
$23$	4.41016	+	7.63862i	0.919582	+	1.59276i	0.119531	+	0.992830i	$0.461861\pi$
$24$		0			0
$25$	1.58613	+	2.74726i	0.317226	+	0.549452i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.35194	−	2.34163i	−0.251049	−	0.434829i	0.712766	−	0.701402i	$-0.247442\pi$
$29$	−1.35194	−	2.34163i	−0.251049	−	0.434829i	−0.963815	+	0.266573i	$0.914109\pi$
$30$		0			0
$31$	0.524200			0.0941490			0.0470745	−	0.998891i	$-0.485010\pi$
$31$	0.524200			0.0941490			0.0470745	+	0.998891i	$0.485010\pi$
$32$		0			0
$33$	−2.76210	+	4.78410i	−0.480820	+	0.832804i
$34$		0			0
$35$	0.237900	−	0.412055i	0.0402125	−	0.0696500i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$	5.17226			0.828225
$40$		0			0
$41$	1.35194	−	2.34163i	0.211137	−	0.365701i	−0.740933	−	0.671579i	$-0.765617\pi$
$41$	1.35194	−	2.34163i	0.211137	−	0.365701i	0.952071	+	0.305878i	$0.0989499\pi$
$42$		0			0
$43$	−3.26210	+	5.65012i	−0.497466	+	0.861636i	−0.999996	−	0.00292406i	$-0.999069\pi$
$43$	−3.26210	+	5.65012i	−0.497466	+	0.861636i	0.502530	+	0.864560i	$0.332403\pi$
$44$		0			0
$45$	1.35194			0.201535
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−6.87614			−0.982306
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.02791	+	3.51244i	0.278555	+	0.482471i	0.971026	−	0.238975i	$-0.0768113\pi$
$53$	2.02791	+	3.51244i	0.278555	+	0.482471i	−0.692471	+	0.721446i	$0.743478\pi$
$54$		0			0
$55$	3.73419	−	6.46781i	0.503518	−	0.872119i
$56$		0			0
$57$	4.34823	−	0.304788i	0.575937	−	0.0403702i
$58$		0			0
$59$	−2.76210	+	4.78410i	−0.359595	+	0.622836i	−0.987893	−	0.155136i	$-0.950418\pi$
$59$	−2.76210	+	4.78410i	−0.359595	+	0.622836i	0.628298	+	0.777972i	$0.283752\pi$
$60$		0			0
$61$	0.938069	+	1.62478i	0.120107	+	0.208032i	0.919810	−	0.392364i	$-0.128343\pi$
$61$	0.938069	+	1.62478i	0.120107	+	0.208032i	−0.799702	+	0.600397i	$0.795009\pi$
$62$		0			0
$63$	0.175970	+	0.304788i	0.0221701	+	0.0383997i
$64$		0			0
$65$	−6.99258			−0.867323
$66$		0			0
$67$	5.99629	+	10.3859i	0.732564	+	1.26884i	0.955784	+	0.294069i	$0.0950096\pi$
$67$	5.99629	+	10.3859i	0.732564	+	1.26884i	−0.223221	+	0.974768i	$0.571657\pi$
$68$		0			0
$69$	8.82032			1.06184
$70$		0			0
$71$	2.52420	−	4.37204i	0.299567	−	0.518866i	−0.676470	−	0.736471i	$-0.736491\pi$
$71$	2.52420	−	4.37204i	0.299567	−	0.518866i	0.976037	+	0.217605i	$0.0698243\pi$
$72$		0			0
$73$	−3.85194	+	6.67175i	−0.450835	+	0.780870i	−0.998438	−	0.0558687i	$-0.982207\pi$
$73$	−3.85194	+	6.67175i	−0.450835	+	0.780870i	0.547603	+	0.836738i	$0.315541\pi$
$74$		0			0
$75$	3.17226			0.366301
$76$		0			0
$77$	1.94418			0.221560
$78$		0			0
$79$	3.91016	−	6.77260i	0.439927	−	0.761977i	−0.557756	−	0.830005i	$-0.688337\pi$
$79$	3.91016	−	6.77260i	0.439927	−	0.761977i	0.997683	+	0.0680283i	$0.0216708\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−8.34452			−0.915930			−0.457965	−	0.888970i	$-0.651422\pi$
$83$	−8.34452			−0.915930			−0.457965	+	0.888970i	$0.651422\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.70388			−0.289886
$88$		0			0
$89$	2.32403	+	4.02534i	0.246347	+	0.426685i	0.962509	−	0.271248i	$-0.0874365\pi$
$89$	2.32403	+	4.02534i	0.246347	+	0.426685i	−0.716163	+	0.697933i	$0.754103\pi$
$90$		0			0
$91$	−0.910161	−	1.57644i	−0.0954108	−	0.165256i
$92$		0			0
$93$	0.262100	−	0.453970i	0.0271785	−	0.0470745i
$94$		0			0
$95$	−5.87854	+	0.412055i	−0.603126	+	0.0422760i
$96$		0			0
$97$	6.90645	−	11.9623i	0.701244	−	1.21459i	−0.266786	−	0.963756i	$-0.585962\pi$
$97$	6.90645	−	11.9623i	0.701244	−	1.21459i	0.968030	−	0.250834i	$-0.0807049\pi$
$98$		0			0
$99$	2.76210	+	4.78410i	0.277601	+	0.480820i
$100$		0			0
$101$	1.17226	+	2.03041i	0.116644	+	0.202034i	0.918436	−	0.395570i	$-0.129453\pi$
$101$	1.17226	+	2.03041i	0.116644	+	0.202034i	−0.801792	+	0.597604i	$0.796120\pi$
$102$		0			0
$103$	16.1042			1.58680			0.793398	−	0.608703i	$-0.208310\pi$
$103$	16.1042			1.58680			0.793398	+	0.608703i	$0.208310\pi$
$104$		0			0
$105$	−0.237900	−	0.412055i	−0.0232167	−	0.0402125i
$106$		0			0
$107$	0.592243			0.0572543			0.0286272	−	0.999590i	$-0.490886\pi$
$107$	0.592243			0.0572543			0.0286272	+	0.999590i	$0.490886\pi$
$108$		0			0
$109$	6.79001	−	11.7606i	0.650365	−	1.12647i	−0.332669	−	0.943043i	$-0.607949\pi$
$109$	6.79001	−	11.7606i	0.650365	−	1.12647i	0.983034	−	0.183422i	$-0.0587173\pi$
$110$		0			0
$111$	−0.500000	+	0.866025i	−0.0474579	+	0.0821995i
$112$		0			0
$113$	−12.9926			−1.22224			−0.611120	−	0.791538i	$-0.709281\pi$
$113$	−12.9926			−1.22224			−0.611120	+	0.791538i	$0.709281\pi$
$114$		0			0
$115$	−11.9245			−1.11197
$116$		0			0
$117$	2.58613	−	4.47931i	0.239088	−	0.414112i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	19.5168			1.77425
$122$		0			0
$123$	−1.35194	−	2.34163i	−0.121900	−	0.211137i
$124$		0			0
$125$	−11.0484			−0.988199
$126$		0			0
$127$	5.35194	+	9.26983i	0.474908	+	0.822564i	0.999587	−	0.0287355i	$-0.00914807\pi$
$127$	5.35194	+	9.26983i	0.474908	+	0.822564i	−0.524679	+	0.851300i	$0.675815\pi$
$128$		0			0
$129$	3.26210	+	5.65012i	0.287212	+	0.497466i
$130$		0			0
$131$	−1.64806	+	2.85453i	−0.143992	+	0.249401i	−0.928996	−	0.370089i	$-0.879327\pi$
$131$	−1.64806	+	2.85453i	−0.143992	+	0.249401i	0.785005	+	0.619490i	$0.212661\pi$
$132$		0			0
$133$	−0.858052	−	1.27166i	−0.0744026	−	0.110267i
$134$		0			0
$135$	0.675970	−	1.17081i	0.0581782	−	0.100768i
$136$		0			0
$137$	−8.52420	−	14.7643i	−0.728272	−	1.26140i	−0.957613	−	0.288057i	$-0.906991\pi$
$137$	−8.52420	−	14.7643i	−0.728272	−	1.26140i	0.229342	−	0.973346i	$-0.426343\pi$
$138$		0			0
$139$	−8.96598	−	15.5295i	−0.760484	−	1.31720i	−0.942601	−	0.333921i	$-0.891628\pi$
$139$	−8.96598	−	15.5295i	−0.760484	−	1.31720i	0.182117	−	0.983277i	$-0.441705\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−14.2863	−	24.7446i	−1.19468	−	2.06925i
$144$		0			0
$145$	3.65548			0.303571
$146$		0			0
$147$	−3.43807	+	5.95491i	−0.283567	+	0.491153i
$148$		0			0
$149$	−0.972091	+	1.68371i	−0.0796368	+	0.137935i	−0.903093	−	0.429444i	$-0.858709\pi$
$149$	−0.972091	+	1.68371i	−0.0796368	+	0.137935i	0.823456	+	0.567379i	$0.192043\pi$
$150$		0			0
$151$	−13.6406			−1.11006			−0.555030	−	0.831830i	$-0.687293\pi$
$151$	−13.6406			−1.11006			−0.555030	+	0.831830i	$0.687293\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.354343	+	0.613740i	−0.0284615	+	0.0492968i
$156$		0			0
$157$	−8.32032	+	14.4112i	−0.664034	+	1.15014i	0.315512	+	0.948921i	$0.397824\pi$
$157$	−8.32032	+	14.4112i	−0.664034	+	1.15014i	−0.979546	+	0.201219i	$0.935510\pi$
$158$		0			0
$159$	4.05582			0.321647
$160$		0			0
$161$	−1.55211	−	2.68833i	−0.122323	−	0.211870i
$162$		0			0
$163$	1.99258			0.156071			0.0780355	−	0.996951i	$-0.475135\pi$
$163$	1.99258			0.156071			0.0780355	+	0.996951i	$0.475135\pi$
$164$		0			0
$165$	−3.73419	−	6.46781i	−0.290706	−	0.503518i
$166$		0			0
$167$	1.29372	+	2.24078i	0.100111	+	0.173397i	0.911730	−	0.410790i	$-0.134747\pi$
$167$	1.29372	+	2.24078i	0.100111	+	0.173397i	−0.811619	+	0.584187i	$0.801414\pi$
$168$		0			0
$169$	−6.87614	+	11.9098i	−0.528934	+	0.916140i
$170$		0			0
$171$	1.91016	−	3.91807i	0.146074	−	0.299622i
$172$		0			0
$173$	−8.82032	+	15.2772i	−0.670597	+	1.16151i	0.307139	+	0.951665i	$0.400628\pi$
$173$	−8.82032	+	15.2772i	−0.670597	+	1.16151i	−0.977735	+	0.209843i	$0.932705\pi$
$174$		0			0
$175$	−0.558221	−	0.966868i	−0.0421976	−	0.0730883i
$176$		0			0
$177$	2.76210	+	4.78410i	0.207612	+	0.359595i
$178$		0			0
$179$	−2.22808			−0.166534			−0.0832672	−	0.996527i	$-0.526535\pi$
$179$	−2.22808			−0.166534			−0.0832672	+	0.996527i	$0.526535\pi$
$180$		0			0
$181$	−4.73419	−	8.19986i	−0.351890	−	0.609491i	0.634691	−	0.772766i	$-0.281127\pi$
$181$	−4.73419	−	8.19986i	−0.351890	−	0.609491i	−0.986581	+	0.163275i	$0.947794\pi$
$182$		0			0
$183$	1.87614			0.138688
$184$		0			0
$185$	0.675970	−	1.17081i	0.0496983	−	0.0860799i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.351939			0.0255998
$190$		0			0
$191$	22.5726			1.63330			0.816648	−	0.577136i	$-0.195830\pi$
$191$	22.5726			1.63330			0.816648	+	0.577136i	$0.195830\pi$
$192$		0			0
$193$	6.93807	−	12.0171i	0.499413	−	0.865009i	−0.500587	−	0.865686i	$-0.666882\pi$
$193$	6.93807	−	12.0171i	0.499413	−	0.865009i	1.00000		0.000677488i	$0.000215651\pi$
$194$		0			0
$195$	−3.49629	+	6.05575i	−0.250375	+	0.433662i
$196$		0			0
$197$	8.30354			0.591603			0.295801	−	0.955249i	$-0.404413\pi$
$197$	8.30354			0.591603			0.295801	+	0.955249i	$0.404413\pi$
$198$		0			0
$199$	−3.44178	−	5.96134i	−0.243981	−	0.422588i	0.717863	−	0.696184i	$-0.245120\pi$
$199$	−3.44178	−	5.96134i	−0.243981	−	0.422588i	−0.961845	+	0.273596i	$0.911787\pi$
$200$		0			0
$201$	11.9926			0.845891
$202$		0			0
$203$	0.475800	+	0.824110i	0.0333946	+	0.0578412i
$204$		0			0
$205$	1.82774	+	3.16574i	0.127655	+	0.221105i
$206$		0			0
$207$	4.41016	−	7.63862i	0.306527	−	0.530921i
$208$		0			0
$209$	−13.4684	−	19.9605i	−0.931627	−	1.38070i
$210$		0			0
$211$	−4.31792	+	7.47885i	−0.297258	+	0.514865i	−0.975508	−	0.219966i	$-0.929405\pi$
$211$	−4.31792	+	7.47885i	−0.297258	+	0.514865i	0.678250	+	0.734831i	$0.262739\pi$
$212$		0			0
$213$	−2.52420	−	4.37204i	−0.172955	−	0.299567i
$214$		0			0
$215$	−4.41016	−	7.63862i	−0.300770	−	0.520950i
$216$		0			0
$217$	−0.184486			−0.0125238
$218$		0			0
$219$	3.85194	+	6.67175i	0.260290	+	0.450835i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	6.13824	−	10.6317i	0.411047	−	0.711954i	−0.583958	−	0.811784i	$-0.698497\pi$
$223$	6.13824	−	10.6317i	0.411047	−	0.711954i	0.995004	+	0.0998301i	$0.0318299\pi$
$224$		0			0
$225$	1.58613	−	2.74726i	0.105742	−	0.183151i
$226$		0			0
$227$	−0.475800			−0.0315800			−0.0157900	−	0.999875i	$-0.505026\pi$
$227$	−0.475800			−0.0315800			−0.0157900	+	0.999875i	$0.505026\pi$
$228$		0			0
$229$	−5.17226			−0.341793			−0.170896	−	0.985289i	$-0.554666\pi$
$229$	−5.17226			−0.341793			−0.170896	+	0.985289i	$0.554666\pi$
$230$		0			0
$231$	0.972091	−	1.68371i	0.0639589	−	0.110780i
$232$		0			0
$233$	5.34452	−	9.25698i	0.350131	−	0.606445i	−0.636141	−	0.771573i	$-0.719470\pi$
$233$	5.34452	−	9.25698i	0.350131	−	0.606445i	0.986272	+	0.165128i	$0.0528037\pi$
$234$		0			0
$235$	8.11164			0.529145
$236$		0			0
$237$	−3.91016	−	6.77260i	−0.253992	−	0.439927i
$238$		0			0
$239$	0.475800			0.0307770			0.0153885	−	0.999882i	$-0.495101\pi$
$239$	0.475800			0.0307770			0.0153885	+	0.999882i	$0.495101\pi$
$240$		0			0
$241$	0.320321	+	0.554813i	0.0206337	+	0.0357386i	0.876158	−	0.482024i	$-0.160098\pi$
$241$	0.320321	+	0.554813i	0.0206337	+	0.0357386i	−0.855524	+	0.517763i	$0.826765\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	4.64806	−	8.05068i	0.296954	−	0.514339i
$246$		0			0
$247$	−9.87985	+	20.2653i	−0.628640	+	1.28945i
$248$		0			0
$249$	−4.17226	+	7.22657i	−0.264406	+	0.457965i
$250$		0			0
$251$	−2.52420	−	4.37204i	−0.159326	−	0.275961i	0.775300	−	0.631593i	$-0.217599\pi$
$251$	−2.52420	−	4.37204i	−0.159326	−	0.275961i	−0.934626	+	0.355633i	$0.884265\pi$
$252$		0			0
$253$	−24.3626	−	42.1973i	−1.53166	−	2.65292i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.3724	−	17.9656i	−0.647014	−	1.12066i	−0.983832	−	0.179092i	$-0.942684\pi$
$257$	−10.3724	−	17.9656i	−0.647014	−	1.12066i	0.336818	−	0.941570i	$-0.390649\pi$
$258$		0			0
$259$	0.351939			0.0218684
$260$		0			0
$261$	−1.35194	+	2.34163i	−0.0836829	+	0.144943i
$262$		0			0
$263$	8.52420	−	14.7643i	0.525625	−	0.910409i	−0.473930	−	0.880563i	$-0.657165\pi$
$263$	8.52420	−	14.7643i	0.525625	−	0.910409i	0.999555	−	0.0298460i	$-0.00950169\pi$
$264$		0			0
$265$	−5.48322			−0.336831
$266$		0			0
$267$	4.64806			0.284457
$268$		0			0
$269$	−4.55211	+	7.88448i	−0.277547	+	0.480725i	−0.970775	−	0.239993i	$-0.922855\pi$
$269$	−4.55211	+	7.88448i	−0.277547	+	0.480725i	0.693228	+	0.720719i	$0.256188\pi$
$270$		0			0
$271$	13.2207	−	22.8989i	0.803098	−	1.39101i	−0.114470	−	0.993427i	$-0.536517\pi$
$271$	13.2207	−	22.8989i	0.803098	−	1.39101i	0.917568	−	0.397580i	$-0.130150\pi$
$272$		0			0
$273$	−1.82032			−0.110171
$274$		0			0
$275$	−8.76210	−	15.1764i	−0.528374	−	0.915171i
$276$		0			0
$277$	26.1574			1.57165			0.785824	−	0.618451i	$-0.212239\pi$
$277$	26.1574			1.57165			0.785824	+	0.618451i	$0.212239\pi$
$278$		0			0
$279$	−0.262100	−	0.453970i	−0.0156915	−	0.0271785i
$280$		0			0
$281$	12.2002	+	21.1313i	0.727801	+	1.26059i	0.957811	+	0.287400i	$0.0927909\pi$
$281$	12.2002	+	21.1313i	0.727801	+	1.26059i	−0.230010	+	0.973188i	$0.573876\pi$
$282$		0			0
$283$	−0.172260	+	0.298364i	−0.0102398	+	0.0177359i	−0.871100	−	0.491106i	$-0.836593\pi$
$283$	−0.172260	+	0.298364i	−0.0102398	+	0.0177359i	0.860860	+	0.508842i	$0.169926\pi$
$284$		0			0
$285$	−2.58242	+	5.29699i	−0.152969	+	0.313767i
$286$		0			0
$287$	−0.475800	+	0.824110i	−0.0280856	+	0.0486457i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	−6.90645	−	11.9623i	−0.404863	−	0.701244i
$292$		0			0
$293$	17.2813			1.00958			0.504792	−	0.863241i	$-0.331569\pi$
$293$	17.2813			1.00958			0.504792	+	0.863241i	$0.331569\pi$
$294$		0			0
$295$	−3.73419	−	6.46781i	−0.217413	−	0.376570i
$296$		0			0
$297$	5.52420			0.320547
$298$		0			0
$299$	−22.8105	+	39.5089i	−1.31917	+	2.28486i
$300$		0			0
$301$	1.14806	−	1.98850i	0.0661731	−	0.114615i
$302$		0			0
$303$	2.34452			0.134689
$304$		0			0
$305$	−2.53643			−0.145235
$306$		0			0
$307$	4.43807	−	7.68696i	0.253294	−	0.438718i	−0.711137	−	0.703054i	$-0.751819\pi$
$307$	4.43807	−	7.68696i	0.253294	−	0.438718i	0.964431	+	0.264336i	$0.0851527\pi$
$308$		0			0
$309$	8.05211	−	13.9467i	0.458068	−	0.793398i
$310$		0			0
$311$	11.1648			0.633100			0.316550	−	0.948576i	$-0.397475\pi$
$311$	11.1648			0.633100			0.316550	+	0.948576i	$0.397475\pi$
$312$		0			0
$313$	2.25839	+	3.91165i	0.127652	+	0.221099i	0.922766	−	0.385360i	$-0.125923\pi$
$313$	2.25839	+	3.91165i	0.127652	+	0.221099i	−0.795115	+	0.606459i	$0.792589\pi$
$314$		0			0
$315$	−0.475800			−0.0268083
$316$		0			0
$317$	2.50371	+	4.33655i	0.140622	+	0.243565i	0.927731	−	0.373249i	$-0.121756\pi$
$317$	2.50371	+	4.33655i	0.140622	+	0.243565i	−0.787109	+	0.616814i	$0.788423\pi$
$318$		0			0
$319$	7.46838	+	12.9356i	0.418149	+	0.724256i
$320$		0			0
$321$	0.296122	−	0.512898i	0.0165279	−	0.0286272i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−8.20388	+	14.2095i	−0.455069	+	0.788203i
$326$		0			0
$327$	−6.79001	−	11.7606i	−0.375488	−	0.650365i
$328$		0			0
$329$	1.05582	+	1.82873i	0.0582091	+	0.100821i
$330$		0			0
$331$	10.1797			0.559526			0.279763	−	0.960069i	$-0.409744\pi$
$331$	10.1797			0.559526			0.279763	+	0.960069i	$0.409744\pi$
$332$		0			0
$333$	0.500000	+	0.866025i	0.0273998	+	0.0474579i
$334$		0			0
$335$	−16.2132			−0.885824
$336$		0			0
$337$	−11.7584	+	20.3661i	−0.640520	+	1.10941i	0.344796	+	0.938677i	$0.387948\pi$
$337$	−11.7584	+	20.3661i	−0.640520	+	1.10941i	−0.985317	+	0.170736i	$0.945385\pi$
$338$		0			0
$339$	−6.49629	+	11.2519i	−0.352830	+	0.611120i
$340$		0			0
$341$	−2.89578			−0.156815
$342$		0			0
$343$	4.88356			0.263687
$344$		0			0
$345$	−5.96227	+	10.3270i	−0.320998	+	0.555984i
$346$		0			0
$347$	6.23790	−	10.8044i	0.334868	−	0.580008i	−0.648591	−	0.761137i	$-0.724642\pi$
$347$	6.23790	−	10.8044i	0.334868	−	0.580008i	0.983459	+	0.181128i	$0.0579749\pi$
$348$		0			0
$349$	6.23550			0.333778			0.166889	−	0.985976i	$-0.446628\pi$
$349$	6.23550			0.333778			0.166889	+	0.985976i	$0.446628\pi$
$350$		0			0
$351$	−2.58613	−	4.47931i	−0.138037	−	0.239088i
$352$		0			0
$353$	29.8081			1.58652			0.793262	−	0.608880i	$-0.208381\pi$
$353$	29.8081			1.58652			0.793262	+	0.608880i	$0.208381\pi$
$354$		0			0
$355$	3.41256	+	5.91073i	0.181120	+	0.313709i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.87614	+	11.9098i	−0.362909	+	0.628576i	−0.988438	−	0.151624i	$-0.951550\pi$
$359$	−6.87614	+	11.9098i	−0.362909	+	0.628576i	0.625529	+	0.780201i	$0.284883\pi$
$360$		0			0
$361$	−7.11164	+	17.6189i	−0.374297	+	0.927309i
$362$		0			0
$363$	9.75839	−	16.9020i	0.512183	−	0.887126i
$364$		0			0
$365$	−5.20759	−	9.01981i	−0.272578	−	0.472118i
$366$		0			0
$367$	9.25468	+	16.0296i	0.483090	+	0.836737i	0.999811	−	0.0194166i	$-0.00618090\pi$
$367$	9.25468	+	16.0296i	0.483090	+	0.836737i	−0.516721	+	0.856154i	$0.672848\pi$
$368$		0			0
$369$	−2.70388			−0.140758
$370$		0			0
$371$	−0.713701	−	1.23617i	−0.0370535	−	0.0641785i
$372$		0			0
$373$	6.53162			0.338194			0.169097	−	0.985599i	$-0.445915\pi$
$373$	6.53162			0.338194			0.169097	+	0.985599i	$0.445915\pi$
$374$		0			0
$375$	−5.52420	+	9.56819i	−0.285268	+	0.494099i
$376$		0			0
$377$	6.99258	−	12.1115i	0.360136	−	0.623774i
$378$		0			0
$379$	−24.8687			−1.27742			−0.638710	−	0.769447i	$-0.720532\pi$
$379$	−24.8687			−1.27742			−0.638710	+	0.769447i	$0.720532\pi$
$380$		0			0
$381$	10.7039			0.548376
$382$		0			0
$383$	−4.99018	+	8.64324i	−0.254986	+	0.441649i	−0.964892	−	0.262648i	$-0.915404\pi$
$383$	−4.99018	+	8.64324i	−0.254986	+	0.441649i	0.709906	+	0.704297i	$0.248738\pi$
$384$		0			0
$385$	−1.31421	+	2.27628i	−0.0669783	+	0.116010i
$386$		0			0
$387$	6.52420			0.331644
$388$		0			0
$389$	8.54469	+	14.7998i	0.433233	+	0.750382i	0.997150	−	0.0754502i	$-0.0240394\pi$
$389$	8.54469	+	14.7998i	0.433233	+	0.750382i	−0.563917	+	0.825832i	$0.690706\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	1.64806	+	2.85453i	0.0831337	+	0.143992i
$394$		0			0
$395$	5.28630	+	9.15614i	0.265983	+	0.460695i
$396$		0			0
$397$	0.821627	−	1.42310i	0.0412363	−	0.0714233i	−0.844671	−	0.535286i	$-0.820204\pi$
$397$	0.821627	−	1.42310i	0.0412363	−	0.0714233i	0.885907	+	0.463863i	$0.153537\pi$
$398$		0			0
$399$	−1.53031	+	0.107267i	−0.0766115	+	0.00537006i
$400$		0			0
$401$	3.67597	−	6.36697i	0.183569	−	0.317951i	−0.759524	−	0.650479i	$-0.774568\pi$
$401$	3.67597	−	6.36697i	0.183569	−	0.317951i	0.943093	+	0.332528i	$0.107902\pi$
$402$		0			0
$403$	1.35565	+	2.34805i	0.0675297	+	0.116965i
$404$		0			0
$405$	−0.675970	−	1.17081i	−0.0335892	−	0.0581782i
$406$		0			0
$407$	5.52420			0.273824
$408$		0			0
$409$	−1.03773	−	1.79740i	−0.0513125	−	0.0888758i	0.839228	−	0.543779i	$-0.183007\pi$
$409$	−1.03773	−	1.79740i	−0.0513125	−	0.0888758i	−0.890541	+	0.454903i	$0.849674\pi$
$410$		0			0
$411$	−17.0484			−0.840936
$412$		0			0
$413$	0.972091	−	1.68371i	0.0478335	−	0.0828500i
$414$		0			0
$415$	5.64064	−	9.76988i	0.276888	−	0.479585i
$416$		0			0
$417$	−17.9320			−0.878132
$418$		0			0
$419$	−8.22808			−0.401968			−0.200984	−	0.979595i	$-0.564414\pi$
$419$	−8.22808			−0.401968			−0.200984	+	0.979595i	$0.564414\pi$
$420$		0			0
$421$	−2.79001	+	4.83244i	−0.135977	+	0.235519i	−0.925970	−	0.377597i	$-0.876751\pi$
$421$	−2.79001	+	4.83244i	−0.135977	+	0.235519i	0.789993	+	0.613115i	$0.210084\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.330143	−	0.571825i	−0.0159768	−	0.0276726i
$428$		0			0
$429$	−28.5726			−1.37950
$430$		0			0
$431$	14.0484	+	24.3325i	0.676688	+	1.17206i	0.975973	+	0.217893i	$0.0699185\pi$
$431$	14.0484	+	24.3325i	0.676688	+	1.17206i	−0.299285	+	0.954164i	$0.596748\pi$
$432$		0			0
$433$	−14.1661	−	24.5365i	−0.680782	−	1.17915i	−0.974743	−	0.223331i	$-0.928307\pi$
$433$	−14.1661	−	24.5365i	−0.680782	−	1.17915i	0.293961	−	0.955817i	$-0.405026\pi$
$434$		0			0
$435$	1.82774	−	3.16574i	0.0876334	−	0.151786i
$436$		0			0
$437$	−16.8482	+	34.5587i	−0.805960	+	1.65316i
$438$		0			0
$439$	−5.16855	+	8.95219i	−0.246681	+	0.427265i	−0.962603	−	0.270916i	$-0.912673\pi$
$439$	−5.16855	+	8.95219i	−0.246681	+	0.427265i	0.715922	+	0.698181i	$0.246007\pi$
$440$		0			0
$441$	3.43807	+	5.95491i	0.163718	+	0.283567i
$442$		0			0
$443$	−0.475800	−	0.824110i	−0.0226060	−	0.0391547i	0.854501	−	0.519450i	$-0.173863\pi$
$443$	−0.475800	−	0.824110i	−0.0226060	−	0.0391547i	−0.877107	+	0.480295i	$0.840530\pi$
$444$		0			0
$445$	−6.28390			−0.297885
$446$		0			0
$447$	0.972091	+	1.68371i	0.0459783	+	0.0796368i
$448$		0			0
$449$	−21.8639			−1.03182			−0.515911	−	0.856642i	$-0.672546\pi$
$449$	−21.8639			−1.03182			−0.515911	+	0.856642i	$0.672546\pi$
$450$		0			0
$451$	−7.46838	+	12.9356i	−0.351672	+	0.609114i
$452$		0			0
$453$	−6.82032	+	11.8131i	−0.320447	+	0.555030i
$454$		0			0
$455$	2.46096			0.115372
$456$		0			0
$457$	21.7645			1.01810			0.509050	−	0.860737i	$-0.329997\pi$
$457$	21.7645			1.01810			0.509050	+	0.860737i	$0.329997\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.5521	+	18.2768i	−0.491461	+	0.851235i	−0.999952	−	0.00983244i	$-0.996870\pi$
$461$	−10.5521	+	18.2768i	−0.491461	+	0.851235i	0.508491	+	0.861067i	$0.330204\pi$
$462$		0			0
$463$	−5.16745			−0.240152			−0.120076	−	0.992765i	$-0.538314\pi$
$463$	−5.16745			−0.240152			−0.120076	+	0.992765i	$0.538314\pi$
$464$		0			0
$465$	0.354343	+	0.613740i	0.0164323	+	0.0284615i
$466$		0			0
$467$	36.8007			1.70293			0.851466	−	0.524410i	$-0.175714\pi$
$467$	36.8007			1.70293			0.851466	+	0.524410i	$0.175714\pi$
$468$		0			0
$469$	−2.11033	−	3.65520i	−0.0974460	−	0.168781i
$470$		0			0
$471$	8.32032	+	14.4112i	0.383380	+	0.664034i
$472$		0			0
$473$	18.0205	−	31.2124i	0.828583	−	1.43515i
$474$		0			0
$475$	−6.05953	+	12.4291i	−0.278030	+	0.570288i
$476$		0			0
$477$	2.02791	−	3.51244i	0.0928516	−	0.160824i
$478$		0			0
$479$	7.28870	+	12.6244i	0.333029	+	0.576824i	0.983104	−	0.183046i	$-0.0585958\pi$
$479$	7.28870	+	12.6244i	0.333029	+	0.576824i	−0.650075	+	0.759870i	$0.725263\pi$
$480$		0			0
$481$	−2.58613	−	4.47931i	−0.117917	−	0.204239i
$482$		0			0
$483$	−3.10422			−0.141247
$484$		0			0
$485$	9.33710	+	16.1723i	0.423976	+	0.734348i
$486$		0			0
$487$	−7.04840			−0.319393			−0.159697	−	0.987166i	$-0.551052\pi$
$487$	−7.04840			−0.319393			−0.159697	+	0.987166i	$0.551052\pi$
$488$		0			0
$489$	0.996291	−	1.72563i	0.0450538	−	0.0780355i
$490$		0			0
$491$	5.22808	−	9.05530i	0.235940	−	0.408660i	−0.723606	−	0.690214i	$-0.757516\pi$
$491$	5.22808	−	9.05530i	0.235940	−	0.408660i	0.959545	+	0.281554i	$0.0908498\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−7.46838			−0.335679
$496$		0			0
$497$	−0.888365	+	1.53869i	−0.0398486	+	0.0690198i
$498$		0			0
$499$	2.23659	−	3.87390i	0.100124	−	0.173419i	−0.811612	−	0.584197i	$-0.801409\pi$
$499$	2.23659	−	3.87390i	0.100124	−	0.173419i	0.911735	+	0.410778i	$0.134743\pi$
$500$		0			0
$501$	2.58744			0.115598
$502$		0			0
$503$	11.5242	+	19.9605i	0.513839	+	0.889995i	0.999871	+	0.0160539i	$0.00511034\pi$
$503$	11.5242	+	19.9605i	0.513839	+	0.889995i	−0.486032	+	0.873941i	$0.661556\pi$
$504$		0			0
$505$	−3.16965			−0.141048
$506$		0			0
$507$	6.87614	+	11.9098i	0.305380	+	0.528934i
$508$		0			0
$509$	13.1723	+	22.8150i	0.583850	+	1.01126i	0.995018	+	0.0996984i	$0.0317878\pi$
$509$	13.1723	+	22.8150i	0.583850	+	1.01126i	−0.411168	+	0.911560i	$0.634879\pi$
$510$		0			0
$511$	1.35565	−	2.34805i	0.0599704	−	0.103872i
$512$		0			0
$513$	−2.43807	−	3.61328i	−0.107643	−	0.159530i
$514$		0			0
$515$	−10.8860	+	18.8550i	−0.479693	+	0.830852i
$516$		0			0
$517$	16.5726	+	28.7046i	0.728862	+	1.26243i
$518$		0			0
$519$	8.82032	+	15.2772i	0.387169	+	0.670597i
$520$		0			0
$521$	42.6332			1.86780			0.933898	−	0.357540i	$-0.116385\pi$
$521$	42.6332			1.86780			0.933898	+	0.357540i	$0.116385\pi$
$522$		0			0
$523$	−5.94047	−	10.2892i	−0.259759	−	0.449915i	0.706418	−	0.707794i	$-0.250310\pi$
$523$	−5.94047	−	10.2892i	−0.259759	−	0.449915i	−0.966177	+	0.257879i	$0.916976\pi$
$524$		0			0
$525$	−1.11644			−0.0487256
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−27.3990	+	47.4565i	−1.19126	+	2.06333i
$530$		0			0
$531$	5.52420			0.239730
$532$		0			0
$533$	13.9852			0.605765
$534$		0			0
$535$	−0.400338	+	0.693406i	−0.0173081	+	0.0299786i
$536$		0			0
$537$	−1.11404	+	1.92957i	−0.0480743	+	0.0832672i
$538$		0			0
$539$	37.9852			1.63614
$540$		0			0
$541$	−16.9610	−	29.3773i	−0.729209	−	1.26303i	−0.957218	−	0.289368i	$-0.906555\pi$
$541$	−16.9610	−	29.3773i	−0.729209	−	1.26303i	0.228009	−	0.973659i	$-0.426778\pi$
$542$		0			0
$543$	−9.46838			−0.406327
$544$		0			0
$545$	9.17968	+	15.8997i	0.393214	+	0.681067i
$546$		0			0
$547$	−4.49760	−	7.79007i	−0.192303	−	0.333079i	0.753710	−	0.657207i	$-0.228262\pi$
$547$	−4.49760	−	7.79007i	−0.192303	−	0.333079i	−0.946013	+	0.324128i	$0.894929\pi$
$548$		0			0
$549$	0.938069	−	1.62478i	0.0400358	−	0.0693441i
$550$		0			0
$551$	5.16484	−	10.5940i	0.220030	−	0.451319i
$552$		0			0
$553$	−1.37614	+	2.38354i	−0.0585194	+	0.101359i
$554$		0			0
$555$	−0.675970	−	1.17081i	−0.0286933	−	0.0496983i
$556$		0			0
$557$	−4.94418	−	8.56358i	−0.209492	−	0.362850i	0.742063	−	0.670330i	$-0.233848\pi$
$557$	−4.94418	−	8.56358i	−0.209492	−	0.362850i	−0.951555	+	0.307480i	$0.900514\pi$
$558$		0			0
$559$	−33.7449			−1.42726
$560$		0			0
$561$		0			0
$562$		0			0
$563$	36.4413			1.53582			0.767909	−	0.640559i	$-0.221297\pi$
$563$	36.4413			1.53582			0.767909	+	0.640559i	$0.221297\pi$
$564$		0			0
$565$	8.78259	−	15.2119i	0.369486	−	0.639969i
$566$		0			0
$567$	0.175970	−	0.304788i	0.00739003	−	0.0127999i
$568$		0			0
$569$	−27.2717			−1.14329			−0.571644	−	0.820502i	$-0.693694\pi$
$569$	−27.2717			−1.14329			−0.571644	+	0.820502i	$0.693694\pi$
$570$		0			0
$571$	16.1042			0.673940			0.336970	−	0.941515i	$-0.390598\pi$
$571$	16.1042			0.673940			0.336970	+	0.941515i	$0.390598\pi$
$572$		0			0
$573$	11.2863	−	19.5484i	0.471492	−	0.816648i
$574$		0			0
$575$	−13.9902	+	24.2317i	−0.583431	+	1.01053i
$576$		0			0
$577$	−27.3323			−1.13786			−0.568929	−	0.822387i	$-0.692642\pi$
$577$	−27.3323			−1.13786			−0.568929	+	0.822387i	$0.692642\pi$
$578$		0			0
$579$	−6.93807	−	12.0171i	−0.288336	−	0.499413i
$580$		0			0
$581$	2.93676			0.121838
$582$		0			0
$583$	−11.2026	−	19.4034i	−0.463963	−	0.803608i
$584$		0			0
$585$	3.49629	+	6.05575i	0.144554	+	0.250375i
$586$		0			0
$587$	13.0508	−	22.6047i	0.538664	−	0.932994i	−0.460312	−	0.887757i	$-0.652262\pi$
$587$	13.0508	−	22.6047i	0.538664	−	0.932994i	0.998976	−	0.0452367i	$-0.0144042\pi$
$588$		0			0
$589$	1.27803	+	1.89408i	0.0526605	+	0.0780443i
$590$		0			0
$591$	4.15177	−	7.19108i	0.170781	−	0.295801i
$592$		0			0
$593$	4.55211	+	7.88448i	0.186933	+	0.323777i	0.944226	−	0.329298i	$-0.106812\pi$
$593$	4.55211	+	7.88448i	0.186933	+	0.323777i	−0.757293	+	0.653075i	$0.773479\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.88356			−0.281725
$598$		0			0
$599$	−13.2937	−	23.0254i	−0.543167	−	0.940792i	−0.998720	−	0.0505836i	$-0.983892\pi$
$599$	−13.2937	−	23.0254i	−0.543167	−	0.940792i	0.455553	−	0.890209i	$-0.349441\pi$
$600$		0			0
$601$	31.2691			1.27549			0.637746	−	0.770247i	$-0.279867\pi$
$601$	31.2691			1.27549			0.637746	+	0.770247i	$0.279867\pi$
$602$		0			0
$603$	5.99629	−	10.3859i	0.244188	−	0.422946i
$604$		0			0
$605$	−13.1928	+	22.8505i	−0.536362	+	0.929006i
$606$		0			0
$607$	−18.8687			−0.765858			−0.382929	−	0.923778i	$-0.625085\pi$
$607$	−18.8687			−0.765858			−0.382929	+	0.923778i	$0.625085\pi$
$608$		0			0
$609$	0.951601			0.0385608
$610$		0			0
$611$	15.5168	−	26.8759i	0.627742	−	1.08728i
$612$		0			0
$613$	9.61033	−	16.6456i	0.388158	−	0.672309i	−0.604044	−	0.796951i	$-0.706445\pi$
$613$	9.61033	−	16.6456i	0.388158	−	0.672309i	0.992202	+	0.124642i	$0.0397783\pi$
$614$		0			0
$615$	3.65548			0.147403
$616$		0			0
$617$	−11.2608	−	19.5043i	−0.453343	−	0.785212i	0.545249	−	0.838274i	$-0.316435\pi$
$617$	−11.2608	−	19.5043i	−0.453343	−	0.785212i	−0.998591	+	0.0530621i	$0.983102\pi$
$618$		0			0
$619$	−5.99258			−0.240862			−0.120431	−	0.992722i	$-0.538428\pi$
$619$	−5.99258			−0.240862			−0.120431	+	0.992722i	$0.538428\pi$
$620$		0			0
$621$	−4.41016	−	7.63862i	−0.176974	−	0.306527i
$622$		0			0
$623$	−0.817917	−	1.41667i	−0.0327692	−	0.0567579i
$624$		0			0
$625$	−0.462269	+	0.800673i	−0.0184908	+	0.0320269i
$626$		0			0
$627$	−24.0205	+	1.68371i	−0.959286	+	0.0672410i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.700169	−	1.21273i	−0.0278733	−	0.0482780i	0.851752	−	0.523945i	$-0.175540\pi$
$631$	−0.700169	−	1.21273i	−0.0278733	−	0.0482780i	−0.879626	+	0.475667i	$0.842207\pi$
$632$		0			0
$633$	4.31792	+	7.47885i	0.171622	+	0.297258i
$634$		0			0
$635$	−14.4710			−0.574264
$636$		0			0
$637$	−17.7826	−	30.8003i	−0.704572	−	1.22035i
$638$		0			0
$639$	−5.04840			−0.199712
$640$		0			0
$641$	−5.30354	+	9.18600i	−0.209477	+	0.362825i	−0.951550	−	0.307494i	$-0.900510\pi$
$641$	−5.30354	+	9.18600i	−0.209477	+	0.362825i	0.742073	+	0.670319i	$0.233843\pi$
$642$		0			0
$643$	−21.9963	+	38.0987i	−0.867449	+	1.50247i	−0.00285431	+	0.999996i	$0.500909\pi$
$643$	−21.9963	+	38.0987i	−0.867449	+	1.50247i	−0.864595	+	0.502470i	$0.832425\pi$
$644$		0			0
$645$	−8.82032			−0.347300
$646$		0			0
$647$	8.11164			0.318901			0.159451	−	0.987206i	$-0.449028\pi$
$647$	8.11164			0.318901			0.159451	+	0.987206i	$0.449028\pi$
$648$		0			0
$649$	15.2584	−	26.4283i	0.598944	−	1.03740i
$650$		0			0
$651$	−0.0922432	+	0.159770i	−0.00361530	+	0.00626188i
$652$		0			0
$653$	34.6890			1.35749			0.678744	−	0.734375i	$-0.262525\pi$
$653$	34.6890			1.35749			0.678744	+	0.734375i	$0.262525\pi$
$654$		0			0
$655$	−2.22808	−	3.85914i	−0.0870582	−	0.150789i
$656$		0			0
$657$	7.70388			0.300557
$658$		0			0
$659$	15.5218	+	26.8845i	0.604643	+	1.04727i	0.992108	+	0.125388i	$0.0400177\pi$
$659$	15.5218	+	26.8845i	0.604643	+	1.04727i	−0.387464	+	0.921885i	$0.626649\pi$
$660$		0			0
$661$	7.34452	+	12.7211i	0.285669	+	0.494793i	0.972771	−	0.231768i	$-0.0744510\pi$
$661$	7.34452	+	12.7211i	0.285669	+	0.494793i	−0.687102	+	0.726561i	$0.741118\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.06889	−	0.145018i	0.0802281	−	0.00562357i
$666$		0			0
$667$	11.9245	−	20.6539i	0.461720	−	0.799722i
$668$		0			0
$669$	−6.13824	−	10.6317i	−0.237318	−	0.411047i
$670$		0			0
$671$	−5.18208	−	8.97563i	−0.200052	−	0.346500i
$672$		0			0
$673$	−12.3567			−0.476318			−0.238159	−	0.971226i	$-0.576544\pi$
$673$	−12.3567			−0.476318			−0.238159	+	0.971226i	$0.576544\pi$
$674$		0			0
$675$	−1.58613	−	2.74726i	−0.0610502	−	0.105742i
$676$		0			0
$677$	32.7858			1.26006			0.630031	−	0.776570i	$-0.283042\pi$
$677$	32.7858			1.26006			0.630031	+	0.776570i	$0.283042\pi$
$678$		0			0
$679$	−2.43065	+	4.21001i	−0.0932798	+	0.161565i
$680$		0			0
$681$	−0.237900	+	0.412055i	−0.00911636	+	0.0157900i
$682$		0			0
$683$	−41.3977			−1.58404			−0.792020	−	0.610495i	$-0.790970\pi$
$683$	−41.3977			−1.58404			−0.792020	+	0.610495i	$0.790970\pi$
$684$		0			0
$685$	23.0484			0.880634
$686$		0			0
$687$	−2.58613	+	4.47931i	−0.0986670	+	0.170896i
$688$		0			0
$689$	−10.4889	+	18.1673i	−0.399594	+	0.692117i
$690$		0			0
$691$	42.9368			1.63339			0.816696	−	0.577069i	$-0.195803\pi$
$691$	42.9368			1.63339			0.816696	+	0.577069i	$0.195803\pi$
$692$		0			0
$693$	−0.972091	−	1.68371i	−0.0369267	−	0.0639589i
$694$		0			0
$695$	24.2429			0.919586
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−5.34452	−	9.25698i	−0.202148	−	0.350131i
$700$		0			0
$701$	1.03533	−	1.79324i	0.0391038	−	0.0677297i	−0.845811	−	0.533482i	$-0.820883\pi$
$701$	1.03533	−	1.79324i	0.0391038	−	0.0677297i	0.884915	+	0.465753i	$0.154216\pi$
$702$		0			0
$703$	−2.43807	−	3.61328i	−0.0919535	−	0.136278i
$704$		0			0
$705$	4.05582	−	7.02488i	0.152751	−	0.264572i
$706$		0			0
$707$	−0.412564	−	0.714582i	−0.0155161	−	0.0268746i
$708$		0			0
$709$	6.28259	+	10.8818i	0.235948	+	0.408673i	0.959548	−	0.281546i	$-0.0908473\pi$
$709$	6.28259	+	10.8818i	0.235948	+	0.408673i	−0.723600	+	0.690220i	$0.757514\pi$
$710$		0			0
$711$	−7.82032			−0.293285
$712$		0			0
$713$	2.31180	+	4.00416i	0.0865778	+	0.149957i
$714$		0			0
$715$	38.6284			1.44462
$716$		0			0
$717$	0.237900	−	0.412055i	0.00888455	−	0.0153885i
$718$		0			0
$719$	−25.1550	+	43.5698i	−0.938124	+	1.62488i	−0.169158	+	0.985589i	$0.554105\pi$
$719$	−25.1550	+	43.5698i	−0.938124	+	1.62488i	−0.768966	+	0.639289i	$0.779229\pi$
$720$		0			0
$721$	−5.66771			−0.211076
$722$		0			0
$723$	0.640642			0.0238257
$724$		0			0
$725$	4.28870	−	7.42825i	0.159278	−	0.275878i
$726$		0			0
$727$	−16.6672	+	28.8685i	−0.618154	+	1.07067i	0.371668	+	0.928366i	$0.378786\pi$
$727$	−16.6672	+	28.8685i	−0.618154	+	1.07067i	−0.989822	+	0.142308i	$0.954548\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−25.8129			−0.953421			−0.476711	−	0.879060i	$-0.658171\pi$
$733$	−25.8129			−0.953421			−0.476711	+	0.879060i	$0.658171\pi$
$734$		0			0
$735$	−4.64806	−	8.05068i	−0.171446	−	0.296954i
$736$		0			0
$737$	−33.1247	−	57.3737i	−1.22016	−	2.11339i
$738$		0			0
$739$	24.2802	−	42.0545i	0.893161	−	1.54700i	0.0570970	−	0.998369i	$-0.481816\pi$
$739$	24.2802	−	42.0545i	0.893161	−	1.54700i	0.836064	−	0.548632i	$-0.184851\pi$
$740$		0			0
$741$	12.6103	+	18.6888i	0.463252	+	0.686552i
$742$		0			0
$743$	7.33470	−	12.7041i	0.269084	−	0.466067i	−0.699542	−	0.714592i	$-0.746612\pi$
$743$	7.33470	−	12.7041i	0.269084	−	0.466067i	0.968626	+	0.248525i	$0.0799457\pi$
$744$		0			0
$745$	−1.31421	−	2.27628i	−0.0481489	−	0.0833963i
$746$		0			0
$747$	4.17226	+	7.22657i	0.152655	+	0.264406i
$748$		0			0
$749$	−0.208434			−0.00761600
$750$		0			0
$751$	3.87243	+	6.70724i	0.141307	+	0.244751i	0.927989	−	0.372607i	$-0.121536\pi$
$751$	3.87243	+	6.70724i	0.141307	+	0.244751i	−0.786682	+	0.617358i	$0.788203\pi$
$752$		0			0
$753$	−5.04840			−0.183974
$754$		0			0
$755$	9.22066	−	15.9707i	0.335574	−	0.581231i
$756$		0			0
$757$	15.8626	−	27.4748i	0.576536	−	0.998590i	−0.419337	−	0.907831i	$-0.637737\pi$
$757$	15.8626	−	27.4748i	0.576536	−	0.998590i	0.995873	−	0.0907593i	$-0.0289294\pi$
$758$		0			0
$759$	−48.7252			−1.76861
$760$		0			0
$761$	−37.2255			−1.34942			−0.674711	−	0.738082i	$-0.735732\pi$
$761$	−37.2255			−1.34942			−0.674711	+	0.738082i	$0.735732\pi$
$762$		0			0
$763$	−2.38967	+	4.13903i	−0.0865119	+	0.149843i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−28.5726			−1.03170
$768$		0			0
$769$	11.2645	+	19.5107i	0.406208	+	0.703574i	0.994461	−	0.105103i	$-0.0335174\pi$
$769$	11.2645	+	19.5107i	0.406208	+	0.703574i	−0.588253	+	0.808677i	$0.700184\pi$
$770$		0			0
$771$	−20.7449			−0.747108
$772$		0			0
$773$	25.5726	+	44.2930i	0.919782	+	1.59311i	0.799744	+	0.600341i	$0.204968\pi$
$773$	25.5726	+	44.2930i	0.919782	+	1.59311i	0.120038	+	0.992769i	$0.461698\pi$
$774$		0			0
$775$	0.831449	+	1.44011i	0.0298665	+	0.0517303i
$776$		0			0
$777$	0.175970	−	0.304788i	0.00631287	−	0.0109342i
$778$		0			0
$779$	11.7571	−	0.824110i	0.421241	−	0.0295268i
$780$		0			0
$781$	−13.9442	+	24.1520i	−0.498962	+	0.864228i
$782$		0			0
$783$	1.35194	+	2.34163i	0.0483144	+	0.0836829i
$784$		0			0
$785$	−11.2486	−	19.4831i	−0.401479	−	0.695381i
$786$		0			0
$787$	1.16745			0.0416152			0.0208076	−	0.999783i	$-0.493376\pi$
$787$	1.16745			0.0416152			0.0208076	+	0.999783i	$0.493376\pi$
$788$		0			0
$789$	−8.52420	−	14.7643i	−0.303470	−	0.525625i
$790$		0			0
$791$	4.57260			0.162583
$792$		0			0
$793$	−4.85194	+	8.40381i	−0.172297	+	0.298428i
$794$		0			0
$795$	−2.74161	+	4.74861i	−0.0972349	+	0.168416i
$796$		0			0
$797$	37.1600			1.31628			0.658138	−	0.752897i	$-0.271344\pi$
$797$	37.1600			1.31628			0.658138	+	0.752897i	$0.271344\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	2.32403	−	4.02534i	0.0821156	−	0.142228i
$802$		0			0
$803$	21.2789	−	36.8561i	0.750915	−	1.30062i
$804$		0			0
$805$	4.19671			0.147915
$806$		0			0
$807$	4.55211	+	7.88448i	0.160242	+	0.277547i
$808$		0			0
$809$	30.7597			1.08145			0.540727	−	0.841198i	$-0.318149\pi$
$809$	30.7597			1.08145			0.540727	+	0.841198i	$0.318149\pi$
$810$		0			0
$811$	−17.1042	−	29.6254i	−0.600610	−	1.04029i	−0.992729	−	0.120373i	$-0.961591\pi$
$811$	−17.1042	−	29.6254i	−0.600610	−	1.04029i	0.392118	−	0.919915i	$-0.371742\pi$
$812$		0			0
$813$	−13.2207	−	22.8989i	−0.463669	−	0.803098i
$814$		0			0
$815$	−1.34692	+	2.33294i	−0.0471807	+	0.0817194i
$816$		0			0
$817$	−28.3687	+	1.98850i	−0.992496	+	0.0695688i
$818$		0			0
$819$	−0.910161	+	1.57644i	−0.0318036	+	0.0550854i
$820$		0			0
$821$	−14.4610	−	25.0471i	−0.504691	−	0.874151i	−0.999985	−	0.00542532i	$-0.998273\pi$
$821$	−14.4610	−	25.0471i	−0.504691	−	0.874151i	0.495294	−	0.868725i	$-0.335060\pi$
$822$		0			0
$823$	3.24030	+	5.61237i	0.112950	+	0.195635i	0.916958	−	0.398983i	$-0.130637\pi$
$823$	3.24030	+	5.61237i	0.112950	+	0.195635i	−0.804008	+	0.594618i	$0.797303\pi$
$824$		0			0
$825$	−17.5242			−0.610114
$826$		0			0
$827$	−20.2281	−	35.0361i	−0.703399	−	1.21832i	−0.967266	−	0.253764i	$-0.918331\pi$
$827$	−20.2281	−	35.0361i	−0.703399	−	1.21832i	0.263867	−	0.964559i	$-0.415002\pi$
$828$		0			0
$829$	−51.5019			−1.78874			−0.894368	−	0.447331i	$-0.852374\pi$
$829$	−51.5019			−1.78874			−0.894368	+	0.447331i	$0.852374\pi$
$830$		0			0
$831$	13.0787	−	22.6530i	0.453695	−	0.785824i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−3.49806			−0.121055
$836$		0			0
$837$	−0.524200			−0.0181190
$838$		0			0
$839$	16.8105	−	29.1166i	0.580363	−	1.00522i	−0.415073	−	0.909788i	$-0.636244\pi$
$839$	16.8105	−	29.1166i	0.580363	−	1.00522i	0.995436	−	0.0954300i	$-0.0304226\pi$
$840$		0			0
$841$	10.8445	−	18.7833i	0.373949	−	0.647699i
$842$		0			0
$843$	24.4003			0.840392
$844$		0			0
$845$	−9.29612	−	16.1014i	−0.319796	−	0.553903i
$846$		0			0
$847$	−6.86872			−0.236012
$848$		0			0
$849$	0.172260	+	0.298364i	0.00591196	+	0.0102398i
$850$		0			0
$851$	−4.41016	−	7.63862i	−0.151178	−	0.261849i
$852$		0			0
$853$	25.3007	−	43.8221i	0.866279	−	1.50044i	0.000506763	−	1.00000i	$-0.499839\pi$
$853$	25.3007	−	43.8221i	0.866279	−	1.50044i	0.865772	−	0.500439i	$-0.166828\pi$
$854$		0			0
$855$	3.29612	+	4.88494i	0.112725	+	0.167061i
$856$		0			0
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$		0			0
$859$	11.0447	+	19.1300i	0.376840	+	0.652706i	0.990601	−	0.136786i	$-0.0436773\pi$
$859$	11.0447	+	19.1300i	0.376840	+	0.652706i	−0.613761	+	0.789492i	$0.710344\pi$
$860$		0			0
$861$	0.475800	+	0.824110i	0.0162152	+	0.0280856i
$862$		0			0
$863$	−10.6890			−0.363859			−0.181930	−	0.983312i	$-0.558234\pi$
$863$	−10.6890			−0.363859			−0.181930	+	0.983312i	$0.558234\pi$
$864$		0			0
$865$	−11.9245	−	20.6539i	−0.405446	−	0.702254i
$866$		0			0
$867$	17.0000			0.577350
$868$		0			0
$869$	−21.6005	+	37.4132i	−0.732747	+	1.26916i
$870$		0			0
$871$	−31.0144	+	53.7185i	−1.05088	+	1.82018i
$872$		0			0
$873$	−13.8129			−0.467496
$874$		0			0
$875$	3.88836			0.131451
$876$		0			0
$877$	−15.5968	+	27.0144i	−0.526666	+	0.912213i	0.472851	+	0.881143i	$0.343225\pi$
$877$	−15.5968	+	27.0144i	−0.526666	+	0.912213i	−0.999517	+	0.0310705i	$0.990108\pi$
$878$		0			0
$879$	8.64064	−	14.9660i	0.291442	−	0.504792i
$880$		0			0
$881$	−9.69646			−0.326682			−0.163341	−	0.986570i	$-0.552227\pi$
$881$	−9.69646			−0.326682			−0.163341	+	0.986570i	$0.552227\pi$
$882$		0			0
$883$	−19.0750	−	33.0389i	−0.641925	−	1.11185i	−0.985003	−	0.172540i	$-0.944803\pi$
$883$	−19.0750	−	33.0389i	−0.641925	−	1.11185i	0.343078	−	0.939307i	$-0.388531\pi$
$884$		0			0
$885$	−7.46838			−0.251047
$886$		0			0
$887$	−4.99018	−	8.64324i	−0.167554	−	0.290212i	0.770005	−	0.638037i	$-0.220253\pi$
$887$	−4.99018	−	8.64324i	−0.167554	−	0.290212i	−0.937559	+	0.347826i	$0.886920\pi$
$888$		0			0
$889$	−1.88356	−	3.26242i	−0.0631725	−	0.109418i
$890$		0			0
$891$	2.76210	−	4.78410i	0.0925338	−	0.160273i
$892$		0			0
$893$	11.4610	−	23.5084i	0.383527	−	0.786680i
$894$		0			0
$895$	1.50611	−	2.60866i	0.0503438	−	0.0871980i
$896$		0			0
$897$	22.8105	+	39.5089i	0.761620	+	1.31917i
$898$		0			0
$899$	−0.708686	−	1.22748i	−0.0236360	−	0.0409388i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−1.14806	−	1.98850i	−0.0382051	−	0.0661731i
$904$		0			0
$905$	12.8007			0.425509
$906$		0			0
$907$	10.2329	−	17.7239i	0.339777	−	0.588512i	−0.644613	−	0.764509i	$-0.722982\pi$
$907$	10.2329	−	17.7239i	0.339777	−	0.588512i	0.984391	+	0.175997i	$0.0563149\pi$
$908$		0			0
$909$	1.17226	−	2.03041i	0.0388814	−	0.0673446i
$910$		0			0
$911$	27.1696			0.900171			0.450085	−	0.892986i	$-0.351394\pi$
$911$	27.1696			0.900171			0.450085	+	0.892986i	$0.351394\pi$
$912$		0			0
$913$	46.0968			1.52558
$914$		0			0
$915$	−1.26821	+	2.19661i	−0.0419258	+	0.0726177i
$916$		0			0
$917$	0.580017	−	1.00462i	0.0191539	−	0.0331755i
$918$		0			0
$919$	−33.1378			−1.09311			−0.546557	−	0.837422i	$-0.684062\pi$
$919$	−33.1378			−1.09311			−0.546557	+	0.837422i	$0.684062\pi$
$920$		0			0
$921$	−4.43807	−	7.68696i	−0.146239	−	0.253294i
$922$		0			0
$923$	26.1116			0.859475
$924$		0			0
$925$	−1.58613	−	2.74726i	−0.0521516	−	0.0903293i
$926$		0			0
$927$	−8.05211	−	13.9467i	−0.264466	−	0.458068i
$928$		0			0
$929$	24.3166	−	42.1176i	0.797802	−	1.38183i	−0.123242	−	0.992377i	$-0.539329\pi$
$929$	24.3166	−	42.1176i	0.797802	−	1.38183i	0.921045	−	0.389457i	$-0.127337\pi$
$930$		0			0
$931$	−16.7645	−	24.8454i	−0.549434	−	0.814276i
$932$		0			0
$933$	5.58242	−	9.66904i	0.182760	−	0.316550i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	24.8626	+	43.0633i	0.812226	+	1.40682i	0.911303	+	0.411737i	$0.135078\pi$
$937$	24.8626	+	43.0633i	0.812226	+	1.40682i	−0.0990768	+	0.995080i	$0.531589\pi$
$938$		0			0
$939$	4.51678			0.147400
$940$		0			0
$941$	−23.9245	−	41.4385i	−0.779918	−	1.35086i	−0.931989	−	0.362487i	$-0.881928\pi$
$941$	−23.9245	−	41.4385i	−0.779918	−	1.35086i	0.152071	−	0.988370i	$-0.451406\pi$
$942$		0			0
$943$	23.8491			0.776633
$944$		0			0
$945$	−0.237900	+	0.412055i	−0.00773889	+	0.0134042i
$946$		0			0
$947$	6.69646	−	11.5986i	0.217606	−	0.376904i	−0.736470	−	0.676470i	$-0.763509\pi$
$947$	6.69646	−	11.5986i	0.217606	−	0.376904i	0.954075	+	0.299566i	$0.0968420\pi$
$948$		0			0
$949$	−39.8465			−1.29347
$950$		0			0
$951$	5.00742			0.162377
$952$		0			0
$953$	2.72437	−	4.71875i	0.0882510	−	0.152855i	−0.818521	−	0.574477i	$-0.805206\pi$
$953$	2.72437	−	4.71875i	0.0882510	−	0.152855i	0.906772	+	0.421622i	$0.138539\pi$
$954$		0			0
$955$	−15.2584	+	26.4283i	−0.493750	+	0.855200i
$956$		0			0
$957$	14.9368			0.482837
$958$		0			0
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$		0			0
$961$	−30.7252			−0.991136
$962$		0			0
$963$	−0.296122	−	0.512898i	−0.00954239	−	0.0165279i
$964$		0			0
$965$	9.37985	+	16.2464i	0.301948	+	0.522989i
$966$		0			0
$967$	16.6066	−	28.7635i	0.534033	−	0.924972i	−0.465177	−	0.885218i	$-0.654009\pi$
$967$	16.6066	−	28.7635i	0.534033	−	0.924972i	0.999209	−	0.0397542i	$-0.0126575\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−26.5652	+	46.0122i	−0.852517	+	1.47660i	0.0264121	+	0.999651i	$0.491592\pi$
$971$	−26.5652	+	46.0122i	−0.852517	+	1.47660i	−0.878929	+	0.476952i	$0.841742\pi$
$972$		0			0
$973$	3.15548	+	5.46545i	0.101160	+	0.175214i
$974$		0			0
$975$	8.20388	+	14.2095i	0.262734	+	0.455069i
$976$		0			0
$977$	−10.9219			−0.349423			−0.174712	−	0.984620i	$-0.555899\pi$
$977$	−10.9219			−0.349423			−0.174712	+	0.984620i	$0.555899\pi$
$978$		0			0
$979$	−12.8384	−	22.2368i	−0.410317	−	0.710690i
$980$		0			0
$981$	−13.5800			−0.433577
$982$		0			0
$983$	−19.6941	+	34.1111i	−0.628143	+	1.08798i	0.359781	+	0.933037i	$0.382851\pi$
$983$	−19.6941	+	34.1111i	−0.628143	+	1.08798i	−0.987924	+	0.154939i	$0.950482\pi$
$984$		0			0
$985$	−5.61294	+	9.72190i	−0.178843	+	0.309765i
$986$		0			0
$987$	2.11164			0.0672141
$988$		0			0
$989$	−57.5455			−1.82984
$990$		0			0
$991$	7.19406	−	12.4605i	0.228527	−	0.395820i	−0.728845	−	0.684679i	$-0.759943\pi$
$991$	7.19406	−	12.4605i	0.228527	−	0.395820i	0.957372	+	0.288859i	$0.0932758\pi$
$992$		0			0
$993$	5.08984	−	8.81586i	0.161521	−	0.279763i
$994$		0			0
$995$	9.30615			0.295025
$996$		0			0
$997$	−17.9758	−	31.1350i	−0.569299	−	0.986055i	−0.996635	−	0.0819625i	$-0.973881\pi$
$997$	−17.9758	−	31.1350i	−0.569299	−	0.986055i	0.427336	−	0.904093i	$-0.359452\pi$
$998$		0			0
$999$	1.00000			0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.q.l.49.2		6
3.2	odd	2		2736.2.s.z.1873.2		6
4.3	odd	2		57.2.e.b.49.1	yes	6
12.11	even	2		171.2.f.b.163.3		6
19.7	even	3	inner	912.2.q.l.577.2		6
57.26	odd	6		2736.2.s.z.577.2		6
76.7	odd	6		57.2.e.b.7.1	✓	6
76.11	odd	6		1083.2.a.l.1.3		3
76.27	even	6		1083.2.a.o.1.1		3
228.11	even	6		3249.2.a.y.1.1		3
228.83	even	6		171.2.f.b.64.3		6
228.179	odd	6		3249.2.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.b.7.1	✓	6	76.7	odd	6
57.2.e.b.49.1	yes	6	4.3	odd	2
171.2.f.b.64.3		6	228.83	even	6
171.2.f.b.163.3		6	12.11	even	2
912.2.q.l.49.2		6	1.1	even	1	trivial
912.2.q.l.577.2		6	19.7	even	3	inner
1083.2.a.l.1.3		3	76.11	odd	6
1083.2.a.o.1.1		3	76.27	even	6
2736.2.s.z.577.2		6	57.26	odd	6
2736.2.s.z.1873.2		6	3.2	odd	2
3249.2.a.t.1.3		3	228.179	odd	6
3249.2.a.y.1.1		3	228.11	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.675970 + 1.17081i) q^{5} -0.351939 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.675970 + 1.17081i) q^{5} -0.351939 q^{7} +(-0.500000 - 0.866025i) q^{9} -5.52420 q^{11} +(2.58613 + 4.47931i) q^{13} +(0.675970 + 1.17081i) q^{15} +(2.43807 + 3.61328i) q^{19} +(-0.175970 + 0.304788i) q^{21} +(4.41016 + 7.63862i) q^{23} +(1.58613 + 2.74726i) q^{25} -1.00000 q^{27} +(-1.35194 - 2.34163i) q^{29} +0.524200 q^{31} +(-2.76210 + 4.78410i) q^{33} +(0.237900 - 0.412055i) q^{35} -1.00000 q^{37} +5.17226 q^{39} +(1.35194 - 2.34163i) q^{41} +(-3.26210 + 5.65012i) q^{43} +1.35194 q^{45} +(-3.00000 - 5.19615i) q^{47} -6.87614 q^{49} +(2.02791 + 3.51244i) q^{53} +(3.73419 - 6.46781i) q^{55} +(4.34823 - 0.304788i) q^{57} +(-2.76210 + 4.78410i) q^{59} +(0.938069 + 1.62478i) q^{61} +(0.175970 + 0.304788i) q^{63} -6.99258 q^{65} +(5.99629 + 10.3859i) q^{67} +8.82032 q^{69} +(2.52420 - 4.37204i) q^{71} +(-3.85194 + 6.67175i) q^{73} +3.17226 q^{75} +1.94418 q^{77} +(3.91016 - 6.77260i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.34452 q^{83} -2.70388 q^{87} +(2.32403 + 4.02534i) q^{89} +(-0.910161 - 1.57644i) q^{91} +(0.262100 - 0.453970i) q^{93} +(-5.87854 + 0.412055i) q^{95} +(6.90645 - 11.9623i) q^{97} +(2.76210 + 4.78410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9 + q^13 + 2 * q^15 - 4 * q^19 + q^21 + 14 * q^23 - 5 * q^25 - 6 * q^27 - 4 * q^29 - 30 * q^31 + 18 * q^35 - 6 * q^37 + 2 * q^39 + 4 * q^41 - 3 * q^43 + 4 * q^45 - 18 * q^47 - 4 * q^49 + 6 * q^53 + 12 * q^55 - 5 * q^57 - 13 * q^61 - q^63 + 12 * q^65 + 9 * q^67 + 28 * q^69 - 18 * q^71 - 19 * q^73 - 10 * q^75 + 24 * q^77 + 11 * q^79 - 3 * q^81 + 8 * q^83 - 8 * q^87 + 16 * q^89 + 7 * q^91 - 15 * q^93 - 2 * q^95 + 2 * q^97

Introduction

L-functions

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