LMFDB - Embedded newform 819.2.o.c.568.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			568.2
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	819.568
Dual form			819.2.o.c.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 - 2.26728i) q^{2} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-0.500000 - 0.866025i) q^{7} -7.47214 q^{8} +O(q^{10})$	\(q+(1.30902 - 2.26728i) q^{2} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-0.500000 - 0.866025i) q^{7} -7.47214 q^{8} +(-3.42705 + 5.93583i) q^{10} +(0.927051 - 1.60570i) q^{11} +(-2.50000 + 2.59808i) q^{13} -2.61803 q^{14} +(-4.92705 + 8.53390i) q^{16} +(-0.736068 - 1.27491i) q^{17} +(0.927051 + 1.60570i) q^{19} +(6.35410 + 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} +(-2.23607 + 3.87298i) q^{23} +1.85410 q^{25} +(2.61803 + 9.06914i) q^{26} +(-2.42705 + 4.20378i) q^{28} +(3.54508 - 6.14027i) q^{29} -4.70820 q^{31} +(5.42705 + 9.39993i) q^{32} -3.85410 q^{34} +(1.30902 + 2.26728i) q^{35} +(-2.00000 + 3.46410i) q^{37} +4.85410 q^{38} +19.5623 q^{40} +(0.381966 - 0.661585i) q^{41} +(-6.28115 - 10.8793i) q^{43} -9.00000 q^{44} +(5.85410 + 10.1396i) q^{46} +2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.42705 - 4.20378i) q^{50} +(16.9894 + 4.20378i) q^{52} -3.76393 q^{53} +(-2.42705 + 4.20378i) q^{55} +(3.73607 + 6.47106i) q^{56} +(-9.28115 - 16.0754i) q^{58} +(-1.11803 - 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(6.54508 - 6.80185i) q^{65} +(6.35410 - 11.0056i) q^{67} +(-3.57295 + 6.18853i) q^{68} +6.85410 q^{70} +(-7.09017 - 12.2805i) q^{71} -2.00000 q^{73} +(5.23607 + 9.06914i) q^{74} +(4.50000 - 7.79423i) q^{76} -1.85410 q^{77} +4.00000 q^{79} +(12.8992 - 22.3420i) q^{80} +(-1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} -32.8885 q^{86} +(-6.92705 + 11.9980i) q^{88} +(2.45492 - 4.25204i) q^{89} +(3.50000 + 0.866025i) q^{91} +21.7082 q^{92} +(2.92705 - 5.06980i) q^{94} +(-2.42705 - 4.20378i) q^{95} +(-9.42705 - 16.3281i) q^{97} +(1.30902 + 2.26728i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8	$ 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8} - 7 q^{10} - 3 q^{11} - 10 q^{13} - 6 q^{14} - 13 q^{16} + 6 q^{17} - 3 q^{19} + 12 q^{20} - 3 q^{22} - 6 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 8 q^{31} + 15 q^{32} - 2 q^{34} + 3 q^{35} - 8 q^{37} + 6 q^{38} + 38 q^{40} + 6 q^{41} - 5 q^{43} - 36 q^{44} + 10 q^{46} - 2 q^{49} + 3 q^{50} + 21 q^{52} - 24 q^{53} - 3 q^{55} + 6 q^{56} - 17 q^{58} + 12 q^{61} - 9 q^{62} + 8 q^{64} + 15 q^{65} + 12 q^{67} - 21 q^{68} + 14 q^{70} - 6 q^{71} - 8 q^{73} + 12 q^{74} + 18 q^{76} + 6 q^{77} + 16 q^{79} + 27 q^{80} - 4 q^{82} + q^{85} - 60 q^{86} - 21 q^{88} + 21 q^{89} + 14 q^{91} + 60 q^{92} + 5 q^{94} - 3 q^{95} - 31 q^{97} + 3 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8 - 7 * q^10 - 3 * q^11 - 10 * q^13 - 6 * q^14 - 13 * q^16 + 6 * q^17 - 3 * q^19 + 12 * q^20 - 3 * q^22 - 6 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 8 * q^31 + 15 * q^32 - 2 * q^34 + 3 * q^35 - 8 * q^37 + 6 * q^38 + 38 * q^40 + 6 * q^41 - 5 * q^43 - 36 * q^44 + 10 * q^46 - 2 * q^49 + 3 * q^50 + 21 * q^52 - 24 * q^53 - 3 * q^55 + 6 * q^56 - 17 * q^58 + 12 * q^61 - 9 * q^62 + 8 * q^64 + 15 * q^65 + 12 * q^67 - 21 * q^68 + 14 * q^70 - 6 * q^71 - 8 * q^73 + 12 * q^74 + 18 * q^76 + 6 * q^77 + 16 * q^79 + 27 * q^80 - 4 * q^82 + q^85 - 60 * q^86 - 21 * q^88 + 21 * q^89 + 14 * q^91 + 60 * q^92 + 5 * q^94 - 3 * q^95 - 31 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.30902	−	2.26728i	0.925615	−	1.60321i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.30902	−	2.26728i	0.925615	−	1.60321i	0.790569	−	0.612372i	$-0.209785\pi$
$3$		0			0
$3$		0			0
$4$	−2.42705	−	4.20378i	−1.21353	−	2.10189i
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−7.47214			−2.64180
$9$		0			0
$10$	−3.42705	+	5.93583i	−1.08373	+	1.87707i
$11$	0.927051	−	1.60570i	0.279516	−	0.484137i	−0.691748	−	0.722139i	$-0.743159\pi$
$11$	0.927051	−	1.60570i	0.279516	−	0.484137i	0.971265	+	0.238002i	$0.0764925\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	−2.61803			−0.699699
$15$		0			0
$16$	−4.92705	+	8.53390i	−1.23176	+	2.13348i
$17$	−0.736068	−	1.27491i	−0.178523	−	0.309210i	0.762852	−	0.646573i	$-0.223798\pi$
$17$	−0.736068	−	1.27491i	−0.178523	−	0.309210i	−0.941375	+	0.337363i	$0.890465\pi$
$18$		0			0
$19$	0.927051	+	1.60570i	0.212680	+	0.368373i	0.952552	−	0.304375i	$-0.0984475\pi$
$19$	0.927051	+	1.60570i	0.212680	+	0.368373i	−0.739872	+	0.672747i	$0.765114\pi$
$20$	6.35410	+	11.0056i	1.42082	+	2.46093i
$21$		0			0
$22$	−2.42705	−	4.20378i	−0.517449	−	0.896248i
$23$	−2.23607	+	3.87298i	−0.466252	+	0.807573i	−0.999257	−	0.0385394i	$-0.987729\pi$
$23$	−2.23607	+	3.87298i	−0.466252	+	0.807573i	0.533005	+	0.846112i	$0.321063\pi$
$24$		0			0
$25$	1.85410			0.370820
$26$	2.61803	+	9.06914i	0.513439	+	1.77860i
$27$		0			0
$28$	−2.42705	+	4.20378i	−0.458670	+	0.794439i
$29$	3.54508	−	6.14027i	0.658306	−	1.14022i	−0.322748	−	0.946485i	$-0.604607\pi$
$29$	3.54508	−	6.14027i	0.658306	−	1.14022i	0.981054	−	0.193734i	$-0.0620599\pi$
$30$		0			0
$31$	−4.70820			−0.845618			−0.422809	−	0.906219i	$-0.638956\pi$
$31$	−4.70820			−0.845618			−0.422809	+	0.906219i	$0.638956\pi$
$32$	5.42705	+	9.39993i	0.959376	+	1.66169i
$33$		0			0
$34$	−3.85410			−0.660973
$35$	1.30902	+	2.26728i	0.221264	+	0.383241i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	4.85410			0.787439
$39$		0			0
$40$	19.5623			3.09307
$41$	0.381966	−	0.661585i	0.0596531	−	0.103322i	−0.834657	−	0.550771i	$-0.814334\pi$
$41$	0.381966	−	0.661585i	0.0596531	−	0.103322i	0.894310	+	0.447449i	$0.147667\pi$
$42$		0			0
$43$	−6.28115	−	10.8793i	−0.957867	−	1.65907i	−0.727667	−	0.685931i	$-0.759395\pi$
$43$	−6.28115	−	10.8793i	−0.957867	−	1.65907i	−0.230200	−	0.973143i	$-0.573938\pi$
$44$	−9.00000			−1.35680
$45$		0			0
$46$	5.85410	+	10.1396i	0.863140	+	1.49500i
$47$	2.23607			0.326164			0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607			0.326164			0.163082	+	0.986613i	$0.447856\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.42705	−	4.20378i	0.343237	−	0.594504i
$51$		0			0
$52$	16.9894	+	4.20378i	2.35600	+	0.582959i
$53$	−3.76393			−0.517016			−0.258508	−	0.966009i	$-0.583231\pi$
$53$	−3.76393			−0.517016			−0.258508	+	0.966009i	$0.583231\pi$
$54$		0			0
$55$	−2.42705	+	4.20378i	−0.327263	+	0.566837i
$56$	3.73607	+	6.47106i	0.499253	+	0.864732i
$57$		0			0
$58$	−9.28115	−	16.0754i	−1.21868	−	2.11081i
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	0.784024	−	0.620730i	$-0.213164\pi$
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	−0.929580	+	0.368620i	$0.879830\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−6.16312	+	10.6748i	−0.782717	+	1.35571i
$63$		0			0
$64$	8.70820			1.08853
$65$	6.54508	−	6.80185i	0.811818	−	0.843666i
$66$		0			0
$67$	6.35410	−	11.0056i	0.776277	−	1.34455i	−0.157797	−	0.987472i	$-0.550439\pi$
$67$	6.35410	−	11.0056i	0.776277	−	1.34455i	0.934074	−	0.357080i	$-0.116228\pi$
$68$	−3.57295	+	6.18853i	−0.433284	+	0.750469i
$69$		0			0
$70$	6.85410			0.819222
$71$	−7.09017	−	12.2805i	−0.841448	−	1.45743i	−0.888670	−	0.458547i	$-0.848370\pi$
$71$	−7.09017	−	12.2805i	−0.841448	−	1.45743i	0.0472218	−	0.998884i	$-0.484963\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	5.23607	+	9.06914i	0.608681	+	1.05427i
$75$		0			0
$76$	4.50000	−	7.79423i	0.516185	−	0.894059i
$77$	−1.85410			−0.211295
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	12.8992	−	22.3420i	1.44217	−	2.49792i
$81$		0			0
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	−6.70820			−0.736321			−0.368161	−	0.929762i	$-0.620012\pi$
$83$	−6.70820			−0.736321			−0.368161	+	0.929762i	$0.620012\pi$
$84$		0			0
$85$	1.92705	+	3.33775i	0.209018	+	0.362030i
$86$	−32.8885			−3.54646
$87$		0			0
$88$	−6.92705	+	11.9980i	−0.738426	+	1.27899i
$89$	2.45492	−	4.25204i	0.260220	−	0.450715i	−0.706080	−	0.708132i	$-0.749538\pi$
$89$	2.45492	−	4.25204i	0.260220	−	0.450715i	0.966300	+	0.257417i	$0.0828714\pi$
$90$		0			0
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$	21.7082			2.26324
$93$		0			0
$94$	2.92705	−	5.06980i	0.301902	−	0.522910i
$95$	−2.42705	−	4.20378i	−0.249010	−	0.431298i
$96$		0			0
$97$	−9.42705	−	16.3281i	−0.957172	−	1.65787i	−0.729318	−	0.684175i	$-0.760162\pi$
$97$	−9.42705	−	16.3281i	−0.957172	−	1.65787i	−0.227854	−	0.973695i	$-0.573171\pi$
$98$	1.30902	+	2.26728i	0.132231	+	0.229030i
$99$		0			0
$100$	−4.50000	−	7.79423i	−0.450000	−	0.779423i
$101$	−5.78115	+	10.0133i	−0.575246	+	0.996356i	0.420769	+	0.907168i	$0.361760\pi$
$101$	−5.78115	+	10.0133i	−0.575246	+	0.996356i	−0.996015	+	0.0891877i	$0.971573\pi$
$102$		0			0
$103$	−8.70820			−0.858045			−0.429022	−	0.903294i	$-0.641142\pi$
$103$	−8.70820			−0.858045			−0.429022	+	0.903294i	$0.641142\pi$
$104$	18.6803	−	19.4132i	1.83176	−	1.90362i
$105$		0			0
$106$	−4.92705	+	8.53390i	−0.478557	+	0.828886i
$107$	−1.69098	+	2.92887i	−0.163473	+	0.283144i	−0.936112	−	0.351702i	$-0.885603\pi$
$107$	−1.69098	+	2.92887i	−0.163473	+	0.283144i	0.772639	+	0.634846i	$0.218936\pi$
$108$		0			0
$109$	−2.70820			−0.259399			−0.129699	−	0.991553i	$-0.541401\pi$
$109$	−2.70820			−0.259399			−0.129699	+	0.991553i	$0.541401\pi$
$110$	6.35410	+	11.0056i	0.605840	+	1.04935i
$111$		0			0
$112$	9.85410			0.931125
$113$	0.736068	+	1.27491i	0.0692435	+	0.119933i	0.898568	−	0.438833i	$-0.144608\pi$
$113$	0.736068	+	1.27491i	0.0692435	+	0.119933i	−0.829325	+	0.558766i	$0.811275\pi$
$114$		0			0
$115$	5.85410	−	10.1396i	0.545898	−	0.945523i
$116$	−34.4164			−3.19548
$117$		0			0
$118$	−5.85410			−0.538914
$119$	−0.736068	+	1.27491i	−0.0674752	+	0.116871i
$120$		0			0
$121$	3.78115	+	6.54915i	0.343741	+	0.595377i
$122$	15.7082			1.42215
$123$		0			0
$124$	11.4271	+	19.7922i	1.02618	+	1.77739i
$125$	8.23607			0.736656
$126$		0			0
$127$	10.4271	−	18.0602i	0.925251	−	1.60258i	0.134094	−	0.990969i	$-0.457187\pi$
$127$	10.4271	−	18.0602i	0.925251	−	1.60258i	0.791157	−	0.611613i	$-0.209479\pi$
$128$	0.545085	−	0.944115i	0.0481792	−	0.0834488i
$129$		0			0
$130$	−6.85410	−	23.7433i	−0.601145	−	2.08243i
$131$	15.3262			1.33906			0.669530	−	0.742785i	$-0.266496\pi$
$131$	15.3262			1.33906			0.669530	+	0.742785i	$0.266496\pi$
$132$		0			0
$133$	0.927051	−	1.60570i	0.0803855	−	0.139232i
$134$	−16.6353	−	28.8131i	−1.43707	−	2.48907i
$135$		0			0
$136$	5.50000	+	9.52628i	0.471621	+	0.816872i
$137$	−1.30902	−	2.26728i	−0.111837	−	0.193707i	0.804674	−	0.593717i	$-0.202340\pi$
$137$	−1.30902	−	2.26728i	−0.111837	−	0.193707i	−0.916511	+	0.400010i	$0.869007\pi$
$138$		0			0
$139$	−2.28115	−	3.95107i	−0.193485	−	0.335126i	0.752918	−	0.658114i	$-0.228646\pi$
$139$	−2.28115	−	3.95107i	−0.193485	−	0.335126i	−0.946403	+	0.322989i	$0.895312\pi$
$140$	6.35410	−	11.0056i	0.537020	−	0.930145i
$141$		0			0
$142$	−37.1246			−3.11543
$143$	1.85410	+	6.42280i	0.155048	+	0.537101i
$144$		0			0
$145$	−9.28115	+	16.0754i	−0.770758	+	1.33499i
$146$	−2.61803	+	4.53457i	−0.216670	+	0.375284i
$147$		0			0
$148$	19.4164			1.59602
$149$	0.927051	+	1.60570i	0.0759470	+	0.131544i	0.901498	−	0.432784i	$-0.142469\pi$
$149$	0.927051	+	1.60570i	0.0759470	+	0.131544i	−0.825551	+	0.564328i	$0.809135\pi$
$150$		0			0
$151$	−1.29180			−0.105125			−0.0525624	−	0.998618i	$-0.516739\pi$
$151$	−1.29180			−0.105125			−0.0525624	+	0.998618i	$0.516739\pi$
$152$	−6.92705	−	11.9980i	−0.561858	−	0.973167i
$153$		0			0
$154$	−2.42705	+	4.20378i	−0.195577	+	0.338750i
$155$	12.3262			0.990067
$156$		0			0
$157$	14.8541			1.18549			0.592743	−	0.805392i	$-0.298045\pi$
$157$	14.8541			1.18549			0.592743	+	0.805392i	$0.298045\pi$
$158$	5.23607	−	9.06914i	0.416559	−	0.721502i
$159$		0			0
$160$	−14.2082	−	24.6093i	−1.12326	−	1.94554i
$161$	4.47214			0.352454
$162$		0			0
$163$	1.85410	+	3.21140i	0.145224	+	0.251536i	0.929457	−	0.368931i	$-0.120276\pi$
$163$	1.85410	+	3.21140i	0.145224	+	0.251536i	−0.784232	+	0.620467i	$0.786943\pi$
$164$	−3.70820			−0.289562
$165$		0			0
$166$	−8.78115	+	15.2094i	−0.681550	+	1.18048i
$167$	7.11803	−	12.3288i	0.550810	−	0.954031i	−0.447406	−	0.894331i	$-0.647652\pi$
$167$	7.11803	−	12.3288i	0.550810	−	0.954031i	0.998216	−	0.0597001i	$-0.0190144\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	10.0902			0.773881
$171$		0			0
$172$	−30.4894	+	52.8091i	−2.32479	+	4.02666i
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$	−0.927051	−	1.60570i	−0.0700785	−	0.121379i
$176$	9.13525	+	15.8227i	0.688596	+	1.19268i
$177$		0			0
$178$	−6.42705	−	11.1320i	−0.481728	−	0.834377i
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	9.70820			0.721605			0.360803	−	0.932642i	$-0.382503\pi$
$181$	9.70820			0.721605			0.360803	+	0.932642i	$0.382503\pi$
$182$	6.54508	−	6.80185i	0.485154	−	0.504187i
$183$		0			0
$184$	16.7082	−	28.9395i	1.23175	−	2.13345i
$185$	5.23607	−	9.06914i	0.384963	−	0.666776i
$186$		0			0
$187$	−2.72949			−0.199600
$188$	−5.42705	−	9.39993i	−0.395808	−	0.685560i
$189$		0			0
$190$	−12.7082			−0.921950
$191$	10.6910	+	18.5173i	0.773572	+	1.33987i	0.935593	+	0.353079i	$0.114865\pi$
$191$	10.6910	+	18.5173i	0.773572	+	1.33987i	−0.162021	+	0.986787i	$0.551801\pi$
$192$		0			0
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	−49.3607			−3.54389
$195$		0			0
$196$	4.85410			0.346722
$197$	−8.39919	+	14.5478i	−0.598417	+	1.03649i	0.394638	+	0.918837i	$0.370870\pi$
$197$	−8.39919	+	14.5478i	−0.598417	+	1.03649i	−0.993055	+	0.117652i	$0.962463\pi$
$198$		0			0
$199$	12.2082	+	21.1452i	0.865417	+	1.49895i	0.866633	+	0.498946i	$0.166280\pi$
$199$	12.2082	+	21.1452i	0.865417	+	1.49895i	−0.00121626	+	0.999999i	$0.500387\pi$
$200$	−13.8541			−0.979633
$201$		0			0
$202$	15.1353	+	26.2150i	1.06491	+	1.84448i
$203$	−7.09017			−0.497632
$204$		0			0
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	−11.3992	+	19.7440i	−0.794219	+	1.37563i
$207$		0			0
$208$	−9.85410	−	34.1356i	−0.683259	−	2.36688i
$209$	3.43769			0.237790
$210$		0			0
$211$	−2.35410	+	4.07742i	−0.162063	+	0.280701i	−0.935608	−	0.353039i	$-0.885148\pi$
$211$	−2.35410	+	4.07742i	−0.162063	+	0.280701i	0.773545	+	0.633741i	$0.218481\pi$
$212$	9.13525	+	15.8227i	0.627412	+	1.08671i
$213$		0			0
$214$	4.42705	+	7.66788i	0.302627	+	0.524165i
$215$	16.4443	+	28.4823i	1.12149	+	1.94248i
$216$		0			0
$217$	2.35410	+	4.07742i	0.159807	+	0.276794i
$218$	−3.54508	+	6.14027i	−0.240103	+	0.415871i
$219$		0			0
$220$	23.5623			1.58857
$221$	5.15248	+	1.27491i	0.346593	+	0.0857595i
$222$		0			0
$223$	−10.1353	+	17.5548i	−0.678707	+	1.17555i	0.296664	+	0.954982i	$0.404126\pi$
$223$	−10.1353	+	17.5548i	−0.678707	+	1.17555i	−0.975371	+	0.220573i	$0.929207\pi$
$224$	5.42705	−	9.39993i	0.362610	−	0.628059i
$225$		0			0
$226$	3.85410			0.256371
$227$	0.736068	+	1.27491i	0.0488545	+	0.0846186i	0.889419	−	0.457094i	$-0.151110\pi$
$227$	0.736068	+	1.27491i	0.0488545	+	0.0846186i	−0.840564	+	0.541712i	$0.817776\pi$
$228$		0			0
$229$	−13.1246			−0.867299			−0.433649	−	0.901082i	$-0.642774\pi$
$229$	−13.1246			−0.867299			−0.433649	+	0.901082i	$0.642774\pi$
$230$	−15.3262	−	26.5458i	−1.01058	−	1.75038i
$231$		0			0
$232$	−26.4894	+	45.8809i	−1.73911	+	3.01223i
$233$	−2.61803			−0.171513			−0.0857566	−	0.996316i	$-0.527331\pi$
$233$	−2.61803			−0.171513			−0.0857566	+	0.996316i	$0.527331\pi$
$234$		0			0
$235$	−5.85410			−0.381880
$236$	−5.42705	+	9.39993i	−0.353271	+	0.611883i
$237$		0			0
$238$	1.92705	+	3.33775i	0.124912	+	0.216354i
$239$	24.7082			1.59824			0.799120	−	0.601171i	$-0.205299\pi$
$239$	24.7082			1.59824			0.799120	+	0.601171i	$0.205299\pi$
$240$		0			0
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	−0.925287	−	0.379267i	$-0.876176\pi$
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	0.134189	−	0.990956i	$-0.457157\pi$
$242$	19.7984			1.27269
$243$		0			0
$244$	14.5623	−	25.2227i	0.932256	−	1.61471i
$245$	1.30902	−	2.26728i	0.0836300	−	0.144851i
$246$		0			0
$247$	−6.48936	−	1.60570i	−0.412908	−	0.102168i
$248$	35.1803			2.23395
$249$		0			0
$250$	10.7812	−	18.6735i	0.681860	−	1.18102i
$251$	0.381966	+	0.661585i	0.0241095	+	0.0417588i	0.877828	−	0.478975i	$-0.158992\pi$
$251$	0.381966	+	0.661585i	0.0241095	+	0.0417588i	−0.853719	+	0.520734i	$0.825658\pi$
$252$		0			0
$253$	4.14590	+	7.18091i	0.260650	+	0.451460i
$254$	−27.2984	−	47.2822i	−1.71285	−	2.96675i
$255$		0			0
$256$	7.28115	+	12.6113i	0.455072	+	0.788208i
$257$	8.37132	−	14.4996i	0.522189	−	0.904457i	−0.477478	−	0.878644i	$-0.658449\pi$
$257$	8.37132	−	14.4996i	0.522189	−	0.904457i	0.999667	−	0.0258138i	$-0.00821769\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$	−44.4787	−	11.0056i	−2.75845	−	0.682540i
$261$		0			0
$262$	20.0623	−	34.7489i	1.23945	−	2.14680i
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$	9.85410			0.605333
$266$	−2.42705	−	4.20378i	−0.148812	−	0.257750i
$267$		0			0
$268$	−61.6869			−3.76813
$269$	−14.3713	−	24.8919i	−0.876235	−	1.51768i	−0.855441	−	0.517900i	$-0.826714\pi$
$269$	−14.3713	−	24.8919i	−0.876235	−	1.51768i	−0.0207937	−	0.999784i	$-0.506619\pi$
$270$		0			0
$271$	4.20820	−	7.28882i	0.255630	−	0.442764i	−0.709436	−	0.704770i	$-0.751050\pi$
$271$	4.20820	−	7.28882i	0.255630	−	0.442764i	0.965066	+	0.262005i	$0.0843837\pi$
$272$	14.5066			0.879590
$273$		0			0
$274$	−6.85410			−0.414071
$275$	1.71885	−	2.97713i	0.103650	−	0.179528i
$276$		0			0
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−11.9443			−0.716370
$279$		0			0
$280$	−9.78115	−	16.9415i	−0.584536	−	1.01245i
$281$	−20.1803			−1.20386			−0.601929	−	0.798550i	$-0.705601\pi$
$281$	−20.1803			−1.20386			−0.601929	+	0.798550i	$0.705601\pi$
$282$		0			0
$283$	−6.70820	+	11.6190i	−0.398761	+	0.690675i	−0.993573	−	0.113190i	$-0.963893\pi$
$283$	−6.70820	+	11.6190i	−0.398761	+	0.690675i	0.594812	+	0.803865i	$0.297226\pi$
$284$	−34.4164	+	59.6110i	−2.04224	+	3.53726i
$285$		0			0
$286$	16.9894	+	4.20378i	1.00460	+	0.248574i
$287$	−0.763932			−0.0450935
$288$		0			0
$289$	7.41641	−	12.8456i	0.436259	−	0.755623i
$290$	24.2984	+	42.0860i	1.42685	+	2.47138i
$291$		0			0
$292$	4.85410	+	8.40755i	0.284065	+	0.492015i
$293$	−3.38197	−	5.85774i	−0.197577	−	0.342213i	0.750166	−	0.661250i	$-0.229974\pi$
$293$	−3.38197	−	5.85774i	−0.197577	−	0.342213i	−0.947742	+	0.319037i	$0.896640\pi$
$294$		0			0
$295$	2.92705	+	5.06980i	0.170419	+	0.295175i
$296$	14.9443	−	25.8842i	0.868618	−	1.50449i
$297$		0			0
$298$	4.85410			0.281191
$299$	−4.47214	−	15.4919i	−0.258630	−	0.895922i
$300$		0			0
$301$	−6.28115	+	10.8793i	−0.362040	+	0.627071i
$302$	−1.69098	+	2.92887i	−0.0973051	+	0.168537i
$303$		0			0
$304$	−18.2705			−1.04789
$305$	−7.85410	−	13.6037i	−0.449725	−	0.778946i
$306$		0			0
$307$	−4.85410			−0.277038			−0.138519	−	0.990360i	$-0.544234\pi$
$307$	−4.85410			−0.277038			−0.138519	+	0.990360i	$0.544234\pi$
$308$	4.50000	+	7.79423i	0.256411	+	0.444117i
$309$		0			0
$310$	16.1353	−	27.9471i	0.916421	−	1.58729i
$311$	−3.32624			−0.188614			−0.0943068	−	0.995543i	$-0.530063\pi$
$311$	−3.32624			−0.188614			−0.0943068	+	0.995543i	$0.530063\pi$
$312$		0			0
$313$	25.1246			1.42013			0.710064	−	0.704138i	$-0.248666\pi$
$313$	25.1246			1.42013			0.710064	+	0.704138i	$0.248666\pi$
$314$	19.4443	−	33.6785i	1.09730	−	1.90059i
$315$		0			0
$316$	−9.70820	−	16.8151i	−0.546129	−	0.945923i
$317$	−26.2361			−1.47356			−0.736782	−	0.676130i	$-0.763656\pi$
$317$	−26.2361			−1.47356			−0.736782	+	0.676130i	$0.763656\pi$
$318$		0			0
$319$	−6.57295	−	11.3847i	−0.368014	−	0.637420i
$320$	−22.7984			−1.27447
$321$		0			0
$322$	5.85410	−	10.1396i	0.326236	−	0.565058i
$323$	1.36475	−	2.36381i	0.0759364	−	0.131526i
$324$		0			0
$325$	−4.63525	+	4.81710i	−0.257118	+	0.267205i
$326$	9.70820			0.537688
$327$		0			0
$328$	−2.85410	+	4.94345i	−0.157591	+	0.272956i
$329$	−1.11803	−	1.93649i	−0.0616392	−	0.106762i
$330$		0			0
$331$	5.07295	+	8.78661i	0.278834	+	0.482956i	0.971095	−	0.238692i	$-0.0767186\pi$
$331$	5.07295	+	8.78661i	0.278834	+	0.482956i	−0.692261	+	0.721647i	$0.743385\pi$
$332$	16.2812	+	28.1998i	0.893544	+	1.54766i
$333$		0			0
$334$	−18.6353	−	32.2772i	−1.01968	−	1.76613i
$335$	−16.6353	+	28.8131i	−0.908881	+	1.57423i
$336$		0			0
$337$	−11.5623			−0.629839			−0.314919	−	0.949118i	$-0.601978\pi$
$337$	−11.5623			−0.629839			−0.314919	+	0.949118i	$0.601978\pi$
$338$	−30.1074	−	15.8710i	−1.63763	−	0.863268i
$339$		0			0
$340$	9.35410	−	16.2018i	0.507297	−	0.878665i
$341$	−4.36475	+	7.55996i	−0.236364	+	0.409395i
$342$		0			0
$343$	1.00000			0.0539949
$344$	46.9336	+	81.2914i	2.53049	+	4.38294i
$345$		0			0
$346$	−23.5623			−1.26672
$347$	15.3820	+	26.6423i	0.825747	+	1.43024i	0.901347	+	0.433098i	$0.142580\pi$
$347$	15.3820	+	26.6423i	0.825747	+	1.43024i	−0.0755997	+	0.997138i	$0.524087\pi$
$348$		0			0
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	0.443720	+	0.896166i	$0.353659\pi$
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	−0.997962	+	0.0638103i	$0.979675\pi$
$350$	−4.85410			−0.259463
$351$		0			0
$352$	20.1246			1.07265
$353$	11.0729	−	19.1789i	0.589354	−	1.02079i	−0.404964	−	0.914333i	$-0.632716\pi$
$353$	11.0729	−	19.1789i	0.589354	−	1.02079i	0.994317	−	0.106458i	$-0.0339508\pi$
$354$		0			0
$355$	18.5623	+	32.1509i	0.985185	+	1.70639i
$356$	−23.8328			−1.26314
$357$		0			0
$358$	11.7812	+	20.4056i	0.622653	+	1.07847i
$359$	22.0902			1.16587			0.582937	−	0.812517i	$-0.301903\pi$
$359$	22.0902			1.16587			0.582937	+	0.812517i	$0.301903\pi$
$360$		0			0
$361$	7.78115	−	13.4774i	0.409534	−	0.709334i
$362$	12.7082	−	22.0113i	0.667928	−	1.15689i
$363$		0			0
$364$	−4.85410	−	16.8151i	−0.254424	−	0.881351i
$365$	5.23607			0.274068
$366$		0			0
$367$	0.708204	−	1.22665i	0.0369679	−	0.0640304i	−0.846949	−	0.531673i	$-0.821563\pi$
$367$	0.708204	−	1.22665i	0.0369679	−	0.0640304i	0.883917	+	0.467643i	$0.154897\pi$
$368$	−22.0344	−	38.1648i	−1.14862	−	1.98948i
$369$		0			0
$370$	−13.7082	−	23.7433i	−0.712656	−	1.23436i
$371$	1.88197	+	3.25966i	0.0977068	+	0.169233i
$372$		0			0
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	0.999287	+	0.0377522i	$0.0120198\pi$
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	−0.466949	+	0.884284i	$0.654647\pi$
$374$	−3.57295	+	6.18853i	−0.184753	+	0.320001i
$375$		0			0
$376$	−16.7082			−0.861660
$377$	7.09017	+	24.5611i	0.365162	+	1.26496i
$378$		0			0
$379$	3.07295	−	5.32250i	0.157847	−	0.273399i	−0.776245	−	0.630431i	$-0.782878\pi$
$379$	3.07295	−	5.32250i	0.157847	−	0.273399i	0.934092	+	0.357032i	$0.116211\pi$
$380$	−11.7812	+	20.4056i	−0.604360	+	1.04678i
$381$		0			0
$382$	55.9787			2.86412
$383$	−10.9894	−	19.0341i	−0.561530	−	0.972598i	−0.997363	−	0.0725709i	$-0.976880\pi$
$383$	−10.9894	−	19.0341i	−0.561530	−	0.972598i	0.435833	−	0.900027i	$-0.356454\pi$
$384$		0			0
$385$	4.85410			0.247388
$386$	−7.85410	−	13.6037i	−0.399763	−	0.692410i
$387$		0			0
$388$	−45.7599	+	79.2584i	−2.32311	+	4.02374i
$389$	11.8885			0.602773			0.301387	−	0.953502i	$-0.402551\pi$
$389$	11.8885			0.602773			0.301387	+	0.953502i	$0.402551\pi$
$390$		0			0
$391$	6.58359			0.332947
$392$	3.73607	−	6.47106i	0.188700	−	0.326838i
$393$		0			0
$394$	21.9894	+	38.0867i	1.10781	+	1.91878i
$395$	−10.4721			−0.526910
$396$		0			0
$397$	−0.708204	−	1.22665i	−0.0355437	−	0.0615636i	0.847706	−	0.530466i	$-0.177983\pi$
$397$	−0.708204	−	1.22665i	−0.0355437	−	0.0615636i	−0.883250	+	0.468902i	$0.844650\pi$
$398$	63.9230			3.20417
$399$		0			0
$400$	−9.13525	+	15.8227i	−0.456763	+	0.791136i
$401$	17.7254	−	30.7013i	0.885165	−	1.53315i	0.0396416	−	0.999214i	$-0.487378\pi$
$401$	17.7254	−	30.7013i	0.885165	−	1.53315i	0.845524	−	0.533938i	$-0.179288\pi$
$402$		0			0
$403$	11.7705	−	12.2323i	0.586331	−	0.609333i
$404$	56.1246			2.79230
$405$		0			0
$406$	−9.28115	+	16.0754i	−0.460616	+	0.797810i
$407$	3.70820	+	6.42280i	0.183809	+	0.318366i
$408$		0			0
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	0.630500	−	0.776189i	$-0.282850\pi$
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	−0.987450	+	0.157935i	$0.949516\pi$
$410$	2.61803	+	4.53457i	0.129295	+	0.223946i
$411$		0			0
$412$	21.1353	+	36.6073i	1.04126	+	1.80351i
$413$	−1.11803	+	1.93649i	−0.0550149	+	0.0952885i
$414$		0			0
$415$	17.5623			0.862100
$416$	−37.9894	−	9.39993i	−1.86258	−	0.460869i
$417$		0			0
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	−5.97214	+	10.3440i	−0.291758	+	0.505340i	−0.974226	−	0.225576i	$-0.927574\pi$
$419$	−5.97214	+	10.3440i	−0.291758	+	0.505340i	0.682468	+	0.730916i	$0.260907\pi$
$420$		0			0
$421$	1.41641			0.0690315			0.0345157	−	0.999404i	$-0.489011\pi$
$421$	1.41641			0.0690315			0.0345157	+	0.999404i	$0.489011\pi$
$422$	6.16312	+	10.6748i	0.300016	+	0.519643i
$423$		0			0
$424$	28.1246			1.36585
$425$	−1.36475	−	2.36381i	−0.0661999	−	0.114662i
$426$		0			0
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$	16.4164			0.793517
$429$		0			0
$430$	86.1033			4.15227
$431$	3.89919	−	6.75359i	0.187817	−	0.325309i	−0.756705	−	0.653756i	$-0.773192\pi$
$431$	3.89919	−	6.75359i	0.187817	−	0.325309i	0.944522	+	0.328448i	$0.106525\pi$
$432$		0			0
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$	12.3262			0.591678
$435$		0			0
$436$	6.57295	+	11.3847i	0.314787	+	0.545227i
$437$	−8.29180			−0.396650
$438$		0			0
$439$	−7.42705	+	12.8640i	−0.354474	+	0.613967i	−0.987028	−	0.160550i	$-0.948673\pi$
$439$	−7.42705	+	12.8640i	−0.354474	+	0.613967i	0.632554	+	0.774516i	$0.282007\pi$
$440$	18.1353	−	31.4112i	0.864564	−	1.49747i
$441$		0			0
$442$	9.63525	−	10.0133i	0.458302	−	0.476282i
$443$	5.23607			0.248773			0.124387	−	0.992234i	$-0.460304\pi$
$443$	5.23607			0.248773			0.124387	+	0.992234i	$0.460304\pi$
$444$		0			0
$445$	−6.42705	+	11.1320i	−0.304671	+	0.527706i
$446$	26.5344	+	45.9590i	1.25644	+	2.17622i
$447$		0			0
$448$	−4.35410	−	7.54153i	−0.205712	−	0.356304i
$449$	9.76393	+	16.9116i	0.460788	+	0.798109i	0.999000	−	0.0447005i	$-0.0142334\pi$
$449$	9.76393	+	16.9116i	0.460788	+	0.798109i	−0.538212	+	0.842809i	$0.680900\pi$
$450$		0			0
$451$	−0.708204	−	1.22665i	−0.0333480	−	0.0577605i
$452$	3.57295	−	6.18853i	0.168057	−	0.291084i
$453$		0			0
$454$	3.85410			0.180882
$455$	−9.16312	−	2.26728i	−0.429574	−	0.106292i
$456$		0			0
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	−0.988055	−	0.154098i	$-0.950753\pi$
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	0.627481	+	0.778632i	$0.284086\pi$
$458$	−17.1803	+	29.7572i	−0.802785	+	1.39046i
$459$		0			0
$460$	−56.8328			−2.64984
$461$	−6.10739	−	10.5783i	−0.284450	−	0.492681i	0.688026	−	0.725686i	$-0.258477\pi$
$461$	−6.10739	−	10.5783i	−0.284450	−	0.492681i	−0.972476	+	0.233005i	$0.925144\pi$
$462$		0			0
$463$	6.70820			0.311757			0.155878	−	0.987776i	$-0.450179\pi$
$463$	6.70820			0.311757			0.155878	+	0.987776i	$0.450179\pi$
$464$	34.9336	+	60.5068i	1.62175	+	2.80896i
$465$		0			0
$466$	−3.42705	+	5.93583i	−0.158755	+	0.274972i
$467$	−2.34752			−0.108630			−0.0543152	−	0.998524i	$-0.517298\pi$
$467$	−2.34752			−0.108630			−0.0543152	+	0.998524i	$0.517298\pi$
$468$		0			0
$469$	−12.7082			−0.586810
$470$	−7.66312	+	13.2729i	−0.353473	+	0.612234i
$471$		0			0
$472$	8.35410	+	14.4697i	0.384529	+	0.666023i
$473$	−23.2918			−1.07096
$474$		0			0
$475$	1.71885	+	2.97713i	0.0788661	+	0.136600i
$476$	7.14590			0.327532
$477$		0			0
$478$	32.3435	−	56.0205i	1.47936	−	2.56232i
$479$	12.4894	−	21.6322i	0.570653	−	0.988400i	−0.425846	−	0.904796i	$-0.640023\pi$
$479$	12.4894	−	21.6322i	0.570653	−	0.988400i	0.996499	−	0.0836047i	$-0.0266433\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	−64.3050			−2.92901
$483$		0			0
$484$	18.3541	−	31.7902i	0.834277	−	1.44501i
$485$	24.6803	+	42.7476i	1.12068	+	1.94107i
$486$		0			0
$487$	−14.9894	−	25.9623i	−0.679233	−	1.17647i	−0.975212	−	0.221271i	$-0.928979\pi$
$487$	−14.9894	−	25.9623i	−0.679233	−	1.17647i	0.295980	−	0.955194i	$-0.404354\pi$
$488$	−22.4164	−	38.8264i	−1.01474	−	1.75759i
$489$		0			0
$490$	−3.42705	−	5.93583i	−0.154818	−	0.268153i
$491$	6.19098	−	10.7231i	0.279395	−	0.483927i	−0.691839	−	0.722051i	$-0.743199\pi$
$491$	6.19098	−	10.7231i	0.279395	−	0.483927i	0.971235	+	0.238125i	$0.0765327\pi$
$492$		0			0
$493$	−10.4377			−0.470090
$494$	−12.1353	+	12.6113i	−0.545991	+	0.567410i
$495$		0			0
$496$	23.1976	−	40.1794i	1.04160	−	1.80411i
$497$	−7.09017	+	12.2805i	−0.318038	+	0.550857i
$498$		0			0
$499$	14.8541			0.664961			0.332480	−	0.943110i	$-0.392114\pi$
$499$	14.8541			0.664961			0.332480	+	0.943110i	$0.392114\pi$
$500$	−19.9894	−	34.6226i	−0.893951	−	1.54837i
$501$		0			0
$502$	2.00000			0.0892644
$503$	13.3090	+	23.0519i	0.593420	+	1.02783i	0.993768	+	0.111470i	$0.0355559\pi$
$503$	13.3090	+	23.0519i	0.593420	+	1.02783i	−0.400348	+	0.916363i	$0.631111\pi$
$504$		0			0
$505$	15.1353	−	26.2150i	0.673510	−	1.16655i
$506$	21.7082			0.965047
$507$		0			0
$508$	−101.228			−4.49126
$509$	−9.29837	+	16.1053i	−0.412143	+	0.713853i	−0.995124	−	0.0986331i	$-0.968553\pi$
$509$	−9.29837	+	16.1053i	−0.412143	+	0.713853i	0.582981	+	0.812486i	$0.301886\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	40.3050			1.78124
$513$		0			0
$514$	−21.9164	−	37.9603i	−0.966691	−	1.67436i
$515$	22.7984			1.00462
$516$		0			0
$517$	2.07295	−	3.59045i	0.0911682	−	0.157908i
$518$	5.23607	−	9.06914i	0.230060	−	0.398475i
$519$		0			0
$520$	−48.9058	+	50.8244i	−2.14466	+	2.22880i
$521$	−18.6525			−0.817180			−0.408590	−	0.912718i	$-0.633979\pi$
$521$	−18.6525			−0.817180			−0.408590	+	0.912718i	$0.633979\pi$
$522$		0			0
$523$	−0.562306	+	0.973942i	−0.0245879	+	0.0425875i	−0.878058	−	0.478555i	$-0.841161\pi$
$523$	−0.562306	+	0.973942i	−0.0245879	+	0.0425875i	0.853470	+	0.521143i	$0.174494\pi$
$524$	−37.1976	−	64.4281i	−1.62498	−	2.81455i
$525$		0			0
$526$	−11.7812	−	20.4056i	−0.513683	−	0.889724i
$527$	3.46556	+	6.00252i	0.150962	+	0.261474i
$528$		0			0
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$	12.8992	−	22.3420i	0.560305	−	0.970477i
$531$		0			0
$532$	−9.00000			−0.390199
$533$	0.763932	+	2.64634i	0.0330896	+	0.114626i
$534$		0			0
$535$	4.42705	−	7.66788i	0.191398	−	0.331511i
$536$	−47.4787	+	82.2355i	−2.05077	+	3.55203i
$537$		0			0
$538$	−75.2492			−3.24422
$539$	0.927051	+	1.60570i	0.0399309	+	0.0691624i
$540$		0			0
$541$	35.2705			1.51640			0.758199	−	0.652023i	$-0.226080\pi$
$541$	35.2705			1.51640			0.758199	+	0.652023i	$0.226080\pi$
$542$	−11.0172	−	19.0824i	−0.473230	−	0.819659i
$543$		0			0
$544$	7.98936	−	13.8380i	0.342541	−	0.593298i
$545$	7.09017			0.303710
$546$		0			0
$547$	−3.00000			−0.128271			−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000			−0.128271			−0.0641354	+	0.997941i	$0.520429\pi$
$548$	−6.35410	+	11.0056i	−0.271434	+	0.470137i
$549$		0			0
$550$	−4.50000	−	7.79423i	−0.191881	−	0.332347i
$551$	13.1459			0.560034
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	13.0902			0.556148
$555$		0			0
$556$	−11.0729	+	19.1789i	−0.469598	+	0.813367i
$557$	−13.9894	+	24.2303i	−0.592748	+	1.02667i	0.401112	+	0.916029i	$0.368624\pi$
$557$	−13.9894	+	24.2303i	−0.592748	+	1.02667i	−0.993860	+	0.110641i	$0.964710\pi$
$558$		0			0
$559$	43.9681	+	10.8793i	1.85965	+	0.460144i
$560$	−25.7984			−1.09018
$561$		0			0
$562$	−26.4164	+	45.7546i	−1.11431	+	1.93004i
$563$	−10.5279	−	18.2348i	−0.443697	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$563$	−10.5279	−	18.2348i	−0.443697	−	0.768505i	−0.997960	+	0.0638360i	$0.979667\pi$
$564$		0			0
$565$	−1.92705	−	3.33775i	−0.0810716	−	0.140420i
$566$	17.5623	+	30.4188i	0.738199	+	1.27860i
$567$		0			0
$568$	52.9787	+	91.7618i	2.22294	+	3.85024i
$569$	7.47214	−	12.9421i	0.313248	−	0.542562i	−0.665815	−	0.746117i	$-0.731916\pi$
$569$	7.47214	−	12.9421i	0.313248	−	0.542562i	0.979064	+	0.203555i	$0.0652495\pi$
$570$		0			0
$571$	24.6869			1.03312			0.516558	−	0.856252i	$-0.327213\pi$
$571$	24.6869			1.03312			0.516558	+	0.856252i	$0.327213\pi$
$572$	22.5000	−	23.3827i	0.940772	−	0.977679i
$573$		0			0
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	−4.14590	+	7.18091i	−0.172896	+	0.299464i
$576$		0			0
$577$	−43.8328			−1.82478			−0.912392	−	0.409318i	$-0.865767\pi$
$577$	−43.8328			−1.82478			−0.912392	+	0.409318i	$0.865767\pi$
$578$	−19.4164	−	33.6302i	−0.807616	−	1.39883i
$579$		0			0
$580$	90.1033			3.74134
$581$	3.35410	+	5.80948i	0.139152	+	0.241018i
$582$		0			0
$583$	−3.48936	+	6.04374i	−0.144514	+	0.250306i
$584$	14.9443			0.618398
$585$		0			0
$586$	−17.7082			−0.731519
$587$	−9.95492	+	17.2424i	−0.410883	+	0.711671i	−0.994987	−	0.100009i	$-0.968113\pi$
$587$	−9.95492	+	17.2424i	−0.410883	+	0.711671i	0.584103	+	0.811679i	$0.301446\pi$
$588$		0			0
$589$	−4.36475	−	7.55996i	−0.179846	−	0.311503i
$590$	15.3262			0.630971
$591$		0			0
$592$	−19.7082	−	34.1356i	−0.810002	−	1.40296i
$593$	−43.7984			−1.79858			−0.899292	−	0.437349i	$-0.855917\pi$
$593$	−43.7984			−1.79858			−0.899292	+	0.437349i	$0.855917\pi$
$594$		0			0
$595$	1.92705	−	3.33775i	0.0790014	−	0.136834i
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$		0			0
$598$	−40.9787	−	10.1396i	−1.67574	−	0.414639i
$599$	−29.5066			−1.20561			−0.602803	−	0.797890i	$-0.705950\pi$
$599$	−29.5066			−1.20561			−0.602803	+	0.797890i	$0.705950\pi$
$600$		0			0
$601$	−20.1976	+	34.9832i	−0.823876	+	1.42699i	0.0788998	+	0.996883i	$0.474859\pi$
$601$	−20.1976	+	34.9832i	−0.823876	+	1.42699i	−0.902776	+	0.430112i	$0.858474\pi$
$602$	16.4443	+	28.4823i	0.670218	+	1.16085i
$603$		0			0
$604$	3.13525	+	5.43042i	0.127572	+	0.220961i
$605$	−9.89919	−	17.1459i	−0.402459	−	0.697080i
$606$		0			0
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$	−10.0623	+	17.4284i	−0.408080	+	0.706816i
$609$		0			0
$610$	−41.1246			−1.66509
$611$	−5.59017	+	5.80948i	−0.226154	+	0.235026i
$612$		0			0
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	0.271187	+	0.962527i	$0.412584\pi$
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	−0.969166	+	0.246409i	$0.920749\pi$
$614$	−6.35410	+	11.0056i	−0.256431	+	0.444151i
$615$		0			0
$616$	13.8541			0.558198
$617$	0.0278640	+	0.0482619i	0.00112176	+	0.00194295i	0.866586	−	0.499028i	$-0.166310\pi$
$617$	0.0278640	+	0.0482619i	0.00112176	+	0.00194295i	−0.865464	+	0.500971i	$0.832976\pi$
$618$		0			0
$619$	9.41641			0.378477			0.189239	−	0.981931i	$-0.439398\pi$
$619$	9.41641			0.378477			0.189239	+	0.981931i	$0.439398\pi$
$620$	−29.9164	−	51.8167i	−1.20147	−	2.08101i
$621$		0			0
$622$	−4.35410	+	7.54153i	−0.174584	+	0.302388i
$623$	−4.90983			−0.196708
$624$		0			0
$625$	−30.8328			−1.23331
$626$	32.8885	−	56.9646i	1.31449	−	2.27676i
$627$		0			0
$628$	−36.0517	−	62.4433i	−1.43862	−	2.49176i
$629$	5.88854			0.234792
$630$		0			0
$631$	−17.1976	−	29.7870i	−0.684624	−	1.18580i	−0.973555	−	0.228454i	$-0.926633\pi$
$631$	−17.1976	−	29.7870i	−0.684624	−	1.18580i	0.288931	−	0.957350i	$-0.406700\pi$
$632$	−29.8885			−1.18890
$633$		0			0
$634$	−34.3435	+	59.4846i	−1.36395	+	2.36244i
$635$	−27.2984	+	47.2822i	−1.08330	+	1.87634i
$636$		0			0
$637$	−1.00000	−	3.46410i	−0.0396214	−	0.137253i
$638$	−34.4164			−1.36256
$639$		0			0
$640$	−1.42705	+	2.47172i	−0.0564091	+	0.0977035i
$641$	−23.7533	−	41.1419i	−0.938199	−	1.62501i	−0.768829	−	0.639455i	$-0.779160\pi$
$641$	−23.7533	−	41.1419i	−0.938199	−	1.62501i	−0.169370	−	0.985553i	$-0.554173\pi$
$642$		0			0
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−10.8541	−	18.7999i	−0.427712	−	0.740818i
$645$		0			0
$646$	−3.57295	−	6.18853i	−0.140576	−	0.243484i
$647$	12.3820	−	21.4462i	0.486785	−	0.843137i	−0.513099	−	0.858329i	$-0.671503\pi$
$647$	12.3820	−	21.4462i	0.486785	−	0.843137i	0.999885	+	0.0151924i	$0.00483607\pi$
$648$		0			0
$649$	−4.14590			−0.162741
$650$	4.85410	+	16.8151i	0.190394	+	0.659543i
$651$		0			0
$652$	9.00000	−	15.5885i	0.352467	−	0.610491i
$653$	−0.190983	+	0.330792i	−0.00747374	+	0.0129449i	−0.869738	−	0.493514i	$-0.835712\pi$
$653$	−0.190983	+	0.330792i	−0.00747374	+	0.0129449i	0.862264	+	0.506458i	$0.169046\pi$
$654$		0			0
$655$	−40.1246			−1.56780
$656$	3.76393	+	6.51932i	0.146957	+	0.254537i
$657$		0			0
$658$	−5.85410			−0.228217
$659$	−11.9443	−	20.6881i	−0.465283	−	0.805893i	0.533931	−	0.845528i	$-0.320714\pi$
$659$	−11.9443	−	20.6881i	−0.465283	−	0.805893i	−0.999214	+	0.0396343i	$0.987381\pi$
$660$		0			0
$661$	24.2705	−	42.0378i	0.944013	−	1.63508i	0.186299	−	0.982493i	$-0.440351\pi$
$661$	24.2705	−	42.0378i	0.944013	−	1.63508i	0.757715	−	0.652586i	$-0.226316\pi$
$662$	26.5623			1.03237
$663$		0			0
$664$	50.1246			1.94521
$665$	−2.42705	+	4.20378i	−0.0941170	+	0.163015i
$666$		0			0
$667$	15.8541	+	27.4601i	0.613873	+	1.06326i
$668$	−69.1033			−2.67369
$669$		0			0
$670$	43.5517	+	75.4337i	1.68255	+	2.91426i
$671$	11.1246			0.429461
$672$		0			0
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	−0.188165	−	0.982137i	$-0.560254\pi$
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	0.944639	−	0.328113i	$-0.106413\pi$
$674$	−15.1353	+	26.2150i	−0.582988	+	1.00977i
$675$		0			0
$676$	−53.3951	+	33.6302i	−2.05366	+	1.29347i
$677$	−43.7426			−1.68117			−0.840583	−	0.541682i	$-0.817788\pi$
$677$	−43.7426			−1.68117			−0.840583	+	0.541682i	$0.817788\pi$
$678$		0			0
$679$	−9.42705	+	16.3281i	−0.361777	+	0.626616i
$680$	−14.3992	−	24.9401i	−0.552184	−	0.956410i
$681$		0			0
$682$	11.4271	+	19.7922i	0.437564	+	0.757884i
$683$	0.736068	+	1.27491i	0.0281649	+	0.0487830i	0.879764	−	0.475410i	$-0.157700\pi$
$683$	0.736068	+	1.27491i	0.0281649	+	0.0487830i	−0.851599	+	0.524193i	$0.824367\pi$
$684$		0			0
$685$	3.42705	+	5.93583i	0.130941	+	0.226796i
$686$	1.30902	−	2.26728i	0.0499785	−	0.0865653i
$687$		0			0
$688$	123.790			4.71946
$689$	9.40983	−	9.77898i	0.358486	−	0.372550i
$690$		0			0
$691$	2.92705	−	5.06980i	0.111350	−	0.192864i	−0.804965	−	0.593323i	$-0.797816\pi$
$691$	2.92705	−	5.06980i	0.111350	−	0.192864i	0.916315	+	0.400458i	$0.131149\pi$
$692$	−21.8435	+	37.8340i	−0.830364	+	1.43823i
$693$		0			0
$694$	80.5410			3.05730
$695$	5.97214	+	10.3440i	0.226536	+	0.392372i
$696$		0			0
$697$	−1.12461			−0.0425977
$698$	27.1074	+	46.9514i	1.02603	+	1.77714i
$699$		0			0
$700$	−4.50000	+	7.79423i	−0.170084	+	0.294594i
$701$	−11.2361			−0.424380			−0.212190	−	0.977228i	$-0.568060\pi$
$701$	−11.2361			−0.424380			−0.212190	+	0.977228i	$0.568060\pi$
$702$		0			0
$703$	−7.41641			−0.279715
$704$	8.07295	−	13.9828i	0.304261	−	0.526995i
$705$		0			0
$706$	−28.9894	−	50.2110i	−1.09103	−	1.88972i
$707$	11.5623			0.434845
$708$		0			0
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	0.555420	−	0.831570i	$-0.312557\pi$
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	−0.997871	+	0.0652231i	$0.979224\pi$
$710$	97.1935			3.64761
$711$		0			0
$712$	−18.3435	+	31.7718i	−0.687450	+	1.19070i
$713$	10.5279	−	18.2348i	0.394272	−	0.682898i
$714$		0			0
$715$	−4.85410	−	16.8151i	−0.181533	−	0.628849i
$716$	43.6869			1.63266
$717$		0			0
$718$	28.9164	−	50.0847i	1.07915	−	1.86914i
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	0.931779	−	0.363027i	$-0.118257\pi$
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	−0.780280	+	0.625430i	$0.784923\pi$
$720$		0			0
$721$	4.35410	+	7.54153i	0.162155	+	0.280861i
$722$	−20.3713	−	35.2842i	−0.758142	−	1.31314i
$723$		0			0
$724$	−23.5623	−	40.8111i	−0.875686	−	1.51673i
$725$	6.57295	−	11.3847i	0.244113	−	0.422816i
$726$		0			0
$727$	−30.7082			−1.13890			−0.569452	−	0.822025i	$-0.692845\pi$
$727$	−30.7082			−1.13890			−0.569452	+	0.822025i	$0.692845\pi$
$728$	−26.1525	−	6.47106i	−0.969275	−	0.239833i
$729$		0			0
$730$	6.85410	−	11.8717i	0.253682	−	0.439390i
$731$	−9.24671	+	16.0158i	−0.342002	+	0.592365i
$732$		0			0
$733$	−32.2705			−1.19194			−0.595969	−	0.803007i	$-0.703232\pi$
$733$	−32.2705			−1.19194			−0.595969	+	0.803007i	$0.703232\pi$
$734$	−1.85410	−	3.21140i	−0.0684362	−	0.118535i
$735$		0			0
$736$	−48.5410			−1.78925
$737$	−11.7812	−	20.4056i	−0.433964	−	0.751648i
$738$		0			0
$739$	3.43769	−	5.95426i	0.126458	−	0.219031i	−0.795844	−	0.605502i	$-0.792973\pi$
$739$	3.43769	−	5.95426i	0.126458	−	0.219031i	0.922302	+	0.386470i	$0.126306\pi$
$740$	−50.8328			−1.86865
$741$		0			0
$742$	9.85410			0.361755
$743$	19.6631	−	34.0575i	0.721370	−	1.24945i	−0.239081	−	0.971000i	$-0.576846\pi$
$743$	19.6631	−	34.0575i	0.721370	−	1.24945i	0.960451	−	0.278450i	$-0.0898205\pi$
$744$		0			0
$745$	−2.42705	−	4.20378i	−0.0889203	−	0.154014i
$746$	53.8328			1.97096
$747$		0			0
$748$	6.62461	+	11.4742i	0.242220	+	0.419537i
$749$	3.38197			0.123574
$750$		0			0
$751$	−11.3541	+	19.6659i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$751$	−11.3541	+	19.6659i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$752$	−11.0172	+	19.0824i	−0.401757	+	0.695863i
$753$		0			0
$754$	64.9681	+	16.0754i	2.36600	+	0.585433i
$755$	3.38197			0.123082
$756$		0			0
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$	−8.04508	−	13.9345i	−0.292211	−	0.506124i
$759$		0			0
$760$	18.1353	+	31.4112i	0.657835	+	1.13940i
$761$	−14.4271	−	24.9884i	−0.522980	−	0.905828i	−0.999642	−	0.0267417i	$-0.991487\pi$
$761$	−14.4271	−	24.9884i	−0.522980	−	0.905828i	0.476662	−	0.879087i	$-0.341846\pi$
$762$		0			0
$763$	1.35410	+	2.34537i	0.0490218	+	0.0849082i
$764$	51.8951	−	89.8850i	1.87750	−	3.25192i
$765$		0			0
$766$	−57.5410			−2.07904
$767$	7.82624	+	1.93649i	0.282589	+	0.0699227i
$768$		0			0
$769$	9.20820	−	15.9491i	0.332056	−	0.575138i	−0.650859	−	0.759199i	$-0.725591\pi$
$769$	9.20820	−	15.9491i	0.332056	−	0.575138i	0.982915	+	0.184061i	$0.0589243\pi$
$770$	6.35410	−	11.0056i	0.228986	−	0.396615i
$771$		0			0
$772$	−29.1246			−1.04822
$773$	12.6803	+	21.9630i	0.456080	+	0.789954i	0.998750	−	0.0499924i	$-0.0159197\pi$
$773$	12.6803	+	21.9630i	0.456080	+	0.789954i	−0.542669	+	0.839946i	$0.682586\pi$
$774$		0			0
$775$	−8.72949			−0.313573
$776$	70.4402	+	122.006i	2.52866	+	4.37976i
$777$		0			0
$778$	15.5623	−	26.9547i	0.557936	−	0.966373i
$779$	1.41641			0.0507481
$780$		0			0
$781$	−26.2918			−0.940794
$782$	8.61803	−	14.9269i	0.308180	−	0.533784i
$783$		0			0
$784$	−4.92705	−	8.53390i	−0.175966	−	0.304782i
$785$	−38.8885			−1.38799
$786$		0			0
$787$	−1.29180	−	2.23746i	−0.0460476	−	0.0797567i	0.842083	−	0.539348i	$-0.181329\pi$
$787$	−1.29180	−	2.23746i	−0.0460476	−	0.0797567i	−0.888131	+	0.459591i	$0.847996\pi$
$788$	81.5410			2.90478
$789$		0			0
$790$	−13.7082	+	23.7433i	−0.487716	+	0.844749i
$791$	0.736068	−	1.27491i	0.0261716	−	0.0453305i
$792$		0			0
$793$	−21.0000	−	5.19615i	−0.745732	−	0.184521i
$794$	−3.70820			−0.131599
$795$		0			0
$796$	59.2599	−	102.641i	2.10041	−	3.63802i
$797$	−4.09017	−	7.08438i	−0.144881	−	0.250942i	0.784447	−	0.620195i	$-0.212947\pi$
$797$	−4.09017	−	7.08438i	−0.144881	−	0.250942i	−0.929329	+	0.369254i	$0.879613\pi$
$798$		0			0
$799$	−1.64590	−	2.85078i	−0.0582277	−	0.100853i
$800$	10.0623	+	17.4284i	0.355756	+	0.616188i
$801$		0			0
$802$	−46.4058	−	80.3771i	−1.63864	−	2.83822i
$803$	−1.85410	+	3.21140i	−0.0654298	+	0.113328i
$804$		0			0
$805$	−11.7082			−0.412660
$806$	−12.3262	−	42.6993i	−0.434173	−	1.50402i
$807$		0			0
$808$	43.1976	−	74.8204i	1.51968	−	2.63217i
$809$	−2.20820	+	3.82472i	−0.0776363	+	0.134470i	−0.902230	−	0.431256i	$-0.858071\pi$
$809$	−2.20820	+	3.82472i	−0.0776363	+	0.134470i	0.824593	+	0.565726i	$0.191404\pi$
$810$		0			0
$811$	39.2705			1.37897			0.689487	−	0.724298i	$-0.257836\pi$
$811$	39.2705			1.37897			0.689487	+	0.724298i	$0.257836\pi$
$812$	17.2082	+	29.8055i	0.603890	+	1.04597i
$813$		0			0
$814$	19.4164			0.680545
$815$	−4.85410	−	8.40755i	−0.170032	−	0.294504i
$816$		0			0
$817$	11.6459	−	20.1713i	0.407438	−	0.705704i
$818$	−37.7984			−1.32159
$819$		0			0
$820$	9.70820			0.339025
$821$	−3.68034	+	6.37454i	−0.128445	+	0.222473i	−0.923074	−	0.384622i	$-0.874332\pi$
$821$	−3.68034	+	6.37454i	−0.128445	+	0.222473i	0.794629	+	0.607095i	$0.207665\pi$
$822$		0			0
$823$	19.2082	+	33.2696i	0.669556	+	1.15970i	0.978028	+	0.208472i	$0.0668489\pi$
$823$	19.2082	+	33.2696i	0.669556	+	1.15970i	−0.308473	+	0.951233i	$0.599818\pi$
$824$	65.0689			2.26678
$825$		0			0
$826$	2.92705	+	5.06980i	0.101845	+	0.176401i
$827$	−15.9787			−0.555634			−0.277817	−	0.960634i	$-0.589611\pi$
$827$	−15.9787			−0.555634			−0.277817	+	0.960634i	$0.589611\pi$
$828$		0			0
$829$	−3.78115	+	6.54915i	−0.131325	+	0.227461i	−0.924188	−	0.381939i	$-0.875256\pi$
$829$	−3.78115	+	6.54915i	−0.131325	+	0.227461i	0.792863	+	0.609400i	$0.208590\pi$
$830$	22.9894	−	39.8187i	0.797972	−	1.38213i
$831$		0			0
$832$	−21.7705	+	22.6246i	−0.754757	+	0.784366i
$833$	1.47214			0.0510065
$834$		0			0
$835$	−18.6353	+	32.2772i	−0.644900	+	1.11700i
$836$	−8.34346	−	14.4513i	−0.288565	−	0.499808i
$837$		0			0
$838$	15.6353	+	27.0811i	0.540111	+	0.935500i
$839$	6.87132	+	11.9015i	0.237224	+	0.410885i	0.959917	−	0.280285i	$-0.0904290\pi$
$839$	6.87132	+	11.9015i	0.237224	+	0.410885i	−0.722692	+	0.691170i	$0.757096\pi$
$840$		0			0
$841$	−10.6353	−	18.4208i	−0.366733	−	0.635200i
$842$	1.85410	−	3.21140i	0.0638966	−	0.110672i
$843$		0			0
$844$	22.8541			0.786671
$845$	1.30902	+	34.0093i	0.0450316	+	1.16995i
$846$		0			0
$847$	3.78115	−	6.54915i	0.129922	−	0.225031i
$848$	18.5451	−	32.1210i	0.636841	−	1.10304i
$849$		0			0
$850$	−7.14590			−0.245102
$851$	−8.94427	−	15.4919i	−0.306606	−	0.531057i
$852$		0			0
$853$	14.1246			0.483617			0.241809	−	0.970324i	$-0.422259\pi$
$853$	14.1246			0.483617			0.241809	+	0.970324i	$0.422259\pi$
$854$	−7.85410	−	13.6037i	−0.268762	−	0.465509i
$855$		0			0
$856$	12.6353	−	21.8849i	0.431864	−	0.748011i
$857$	26.4508			0.903544			0.451772	−	0.892133i	$-0.350792\pi$
$857$	26.4508			0.903544			0.451772	+	0.892133i	$0.350792\pi$
$858$		0			0
$859$	−44.2492			−1.50976			−0.754882	−	0.655861i	$-0.772306\pi$
$859$	−44.2492			−1.50976			−0.754882	+	0.655861i	$0.772306\pi$
$860$	79.8222	−	138.256i	2.72191	−	4.71449i
$861$		0			0
$862$	−10.2082	−	17.6811i	−0.347693	−	0.602222i
$863$	−11.8885			−0.404691			−0.202345	−	0.979314i	$-0.564856\pi$
$863$	−11.8885			−0.404691			−0.202345	+	0.979314i	$0.564856\pi$
$864$		0			0
$865$	11.7812	+	20.4056i	0.400571	+	0.693810i
$866$	−2.61803			−0.0889644
$867$		0			0
$868$	11.4271	−	19.7922i	0.387859	−	0.671792i
$869$	3.70820	−	6.42280i	0.125792	−	0.217878i
$870$		0			0
$871$	12.7082	+	44.0225i	0.430601	+	1.49165i
$872$	20.2361			0.685280
$873$		0			0
$874$	−10.8541	+	18.7999i	−0.367145	+	0.635915i
$875$	−4.11803	−	7.13264i	−0.139215	−	0.241127i
$876$		0			0
$877$	−0.354102	−	0.613323i	−0.0119572	−	0.0207104i	0.859985	−	0.510319i	$-0.170473\pi$
$877$	−0.354102	−	0.613323i	−0.0119572	−	0.0207104i	−0.871942	+	0.489609i	$0.837140\pi$
$878$	19.4443	+	33.6785i	0.656212	+	1.13659i
$879$		0			0
$880$	−23.9164	−	41.4244i	−0.806222	−	1.39642i
$881$	−18.2984	+	31.6937i	−0.616488	+	1.06779i	0.373634	+	0.927576i	$0.378112\pi$
$881$	−18.2984	+	31.6937i	−0.616488	+	1.06779i	−0.990122	+	0.140212i	$0.955222\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	−7.14590	−	24.7541i	−0.240343	−	0.832571i
$885$		0			0
$886$	6.85410	−	11.8717i	0.230268	−	0.398836i
$887$	27.3262	−	47.3304i	0.917525	−	1.58920i	0.114364	−	0.993439i	$-0.463517\pi$
$887$	27.3262	−	47.3304i	0.917525	−	1.58920i	0.803161	−	0.595761i	$-0.203150\pi$
$888$		0			0
$889$	−20.8541			−0.699424
$890$	16.8262	+	29.1439i	0.564017	+	0.976906i
$891$		0			0
$892$	98.3951			3.29451
$893$	2.07295	+	3.59045i	0.0693686	+	0.120150i
$894$		0			0
$895$	11.7812	−	20.4056i	0.393801	−	0.682082i
$896$	−1.09017			−0.0364200
$897$		0			0
$898$	51.1246			1.70605
$899$	−16.6910	+	28.9096i	−0.556675	+	0.964190i
$900$		0			0
$901$	2.77051	+	4.79866i	0.0922991	+	0.159867i
$902$	−3.70820			−0.123470
$903$		0			0
$904$	−5.50000	−	9.52628i	−0.182927	−	0.316839i
$905$	−25.4164			−0.844870
$906$		0			0
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	−0.595082	−	0.803665i	$-0.702880\pi$
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	0.993535	+	0.113523i	$0.0362137\pi$
$908$	3.57295	−	6.18853i	0.118572	−	0.205374i
$909$		0			0
$910$	−17.1353	+	17.8075i	−0.568028	+	0.590312i
$911$	22.6869			0.751651			0.375826	−	0.926690i	$-0.377359\pi$
$911$	22.6869			0.751651			0.375826	+	0.926690i	$0.377359\pi$
$912$		0			0
$913$	−6.21885	+	10.7714i	−0.205814	+	0.356480i
$914$	20.1803	+	34.9534i	0.667506	+	1.15615i
$915$		0			0
$916$	31.8541	+	55.1729i	1.05249	+	1.82296i
$917$	−7.66312	−	13.2729i	−0.253058	−	0.438310i
$918$		0			0
$919$	15.0000	+	25.9808i	0.494804	+	0.857026i	0.999982	−	0.00598907i	$-0.00190639\pi$
$919$	15.0000	+	25.9808i	0.494804	+	0.857026i	−0.505178	+	0.863015i	$0.668573\pi$
$920$	−43.7426	+	75.7645i	−1.44215	+	2.49788i
$921$		0			0
$922$	−31.9787			−1.05316
$923$	49.6312	+	12.2805i	1.63363	+	0.404219i
$924$		0			0
$925$	−3.70820	+	6.42280i	−0.121925	+	0.211180i
$926$	8.78115	−	15.2094i	0.288567	−	0.499812i
$927$		0			0
$928$	76.9574			2.52625
$929$	5.53444	+	9.58593i	0.181579	+	0.314504i	0.942418	−	0.334436i	$-0.108546\pi$
$929$	5.53444	+	9.58593i	0.181579	+	0.314504i	−0.760839	+	0.648940i	$0.775212\pi$
$930$		0			0
$931$	−1.85410			−0.0607657
$932$	6.35410	+	11.0056i	0.208136	+	0.360501i
$933$		0			0
$934$	−3.07295	+	5.32250i	−0.100550	+	0.174158i
$935$	7.14590			0.233696
$936$		0			0
$937$	−15.8754			−0.518626			−0.259313	−	0.965793i	$-0.583496\pi$
$937$	−15.8754			−0.518626			−0.259313	+	0.965793i	$0.583496\pi$
$938$	−16.6353	+	28.8131i	−0.543160	+	0.940781i
$939$		0			0
$940$	14.2082	+	24.6093i	0.463421	+	0.802668i
$941$	−20.3475			−0.663310			−0.331655	−	0.943401i	$-0.607607\pi$
$941$	−20.3475			−0.663310			−0.331655	+	0.943401i	$0.607607\pi$
$942$		0			0
$943$	1.70820	+	2.95870i	0.0556268	+	0.0963484i
$944$	22.0344			0.717160
$945$		0			0
$946$	−30.4894	+	52.8091i	−0.991294	+	1.71697i
$947$	−18.4336	+	31.9280i	−0.599012	+	1.03752i	0.393955	+	0.919130i	$0.371107\pi$
$947$	−18.4336	+	31.9280i	−0.599012	+	1.03752i	−0.992967	+	0.118390i	$0.962227\pi$
$948$		0			0
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$	9.00000			0.291999
$951$		0			0
$952$	5.50000	−	9.52628i	0.178256	−	0.308748i
$953$	13.3885	+	23.1896i	0.433697	+	0.751186i	0.997188	−	0.0749362i	$-0.0238753\pi$
$953$	13.3885	+	23.1896i	0.433697	+	0.751186i	−0.563491	+	0.826122i	$0.690542\pi$
$954$		0			0
$955$	−27.9894	−	48.4790i	−0.905714	−	1.56874i
$956$	−59.9681	−	103.868i	−1.93951	−	3.35932i
$957$		0			0
$958$	−32.6976	−	56.6338i	−1.05641	−	1.82976i
$959$	−1.30902	+	2.26728i	−0.0422704	+	0.0732144i
$960$		0			0
$961$	−8.83282			−0.284930
$962$	−36.6525	−	9.06914i	−1.18172	−	0.292401i
$963$		0			0
$964$	−59.6140	+	103.254i	−1.92004	+	3.32560i
$965$	−7.85410	+	13.6037i	−0.252832	+	0.437919i
$966$		0			0
$967$	−39.0000			−1.25416			−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000			−1.25416			−0.627078	+	0.778957i	$0.715749\pi$
$968$	−28.2533	−	48.9361i	−0.908095	−	1.57287i
$969$		0			0
$970$	129.228			4.14926
$971$	15.7918	+	27.3522i	0.506783	+	0.877774i	0.999969	+	0.00784995i	$0.00249874\pi$
$971$	15.7918	+	27.3522i	0.506783	+	0.877774i	−0.493186	+	0.869924i	$0.664168\pi$
$972$		0			0
$973$	−2.28115	+	3.95107i	−0.0731304	+	0.126666i
$974$	−78.4853			−2.51483
$975$		0			0
$976$	−59.1246			−1.89253
$977$	−11.2639	+	19.5097i	−0.360365	+	0.624171i	−0.988021	−	0.154320i	$-0.950681\pi$
$977$	−11.2639	+	19.5097i	−0.360365	+	0.624171i	0.627656	+	0.778491i	$0.284015\pi$
$978$		0			0
$979$	−4.55166	−	7.88371i	−0.145472	−	0.251965i
$980$	−12.7082			−0.405949
$981$		0			0
$982$	−16.2082	−	28.0734i	−0.517225	−	0.895859i
$983$	−18.3820			−0.586294			−0.293147	−	0.956067i	$-0.594702\pi$
$983$	−18.3820			−0.586294			−0.293147	+	0.956067i	$0.594702\pi$
$984$		0			0
$985$	21.9894	−	38.0867i	0.700639	−	1.21354i
$986$	−13.6631	+	23.6652i	−0.435122	+	0.753654i
$987$		0			0
$988$	9.00000	+	31.1769i	0.286328	+	0.991870i
$989$	56.1803			1.78643
$990$		0			0
$991$	8.07295	−	13.9828i	0.256446	−	0.444177i	−0.708842	−	0.705368i	$-0.750782\pi$
$991$	8.07295	−	13.9828i	0.256446	−	0.444177i	0.965287	+	0.261191i	$0.0841152\pi$
$992$	−25.5517	−	44.2568i	−0.811266	−	1.40515i
$993$		0			0
$994$	18.5623	+	32.1509i	0.588761	+	1.01976i
$995$	−31.9615	−	55.3589i	−1.01325	−	1.75500i
$996$		0			0
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	0.158352	−	0.987383i	$-0.449382\pi$
$998$	19.4443	−	33.6785i	0.615498	−	1.06607i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.c.568.2		4
3.2	odd	2		91.2.f.a.22.1	✓	4
12.11	even	2		1456.2.s.h.113.1		4
13.3	even	3	inner	819.2.o.c.757.2		4
21.2	odd	6		637.2.h.g.165.2		4
21.5	even	6		637.2.h.f.165.2		4
21.11	odd	6		637.2.g.b.373.1		4
21.17	even	6		637.2.g.c.373.1		4
21.20	even	2		637.2.f.c.295.1		4
39.17	odd	6		1183.2.a.c.1.1		2
39.20	even	12		1183.2.c.c.337.4		4
39.29	odd	6		91.2.f.a.29.1	yes	4
39.32	even	12		1183.2.c.c.337.1		4
39.35	odd	6		1183.2.a.g.1.2		2
156.107	even	6		1456.2.s.h.1121.1		4
273.68	even	6		637.2.g.c.263.1		4
273.107	odd	6		637.2.g.b.263.1		4
273.146	even	6		637.2.f.c.393.1		4
273.185	even	6		637.2.h.f.471.2		4
273.230	even	6		8281.2.a.bb.1.2		2
273.251	even	6		8281.2.a.n.1.1		2
273.263	odd	6		637.2.h.g.471.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.1	✓	4	3.2	odd	2
91.2.f.a.29.1	yes	4	39.29	odd	6
637.2.f.c.295.1		4	21.20	even	2
637.2.f.c.393.1		4	273.146	even	6
637.2.g.b.263.1		4	273.107	odd	6
637.2.g.b.373.1		4	21.11	odd	6
637.2.g.c.263.1		4	273.68	even	6
637.2.g.c.373.1		4	21.17	even	6
637.2.h.f.165.2		4	21.5	even	6
637.2.h.f.471.2		4	273.185	even	6
637.2.h.g.165.2		4	21.2	odd	6
637.2.h.g.471.2		4	273.263	odd	6
819.2.o.c.568.2		4	1.1	even	1	trivial
819.2.o.c.757.2		4	13.3	even	3	inner
1183.2.a.c.1.1		2	39.17	odd	6
1183.2.a.g.1.2		2	39.35	odd	6
1183.2.c.c.337.1		4	39.32	even	12
1183.2.c.c.337.4		4	39.20	even	12
1456.2.s.h.113.1		4	12.11	even	2
1456.2.s.h.1121.1		4	156.107	even	6
8281.2.a.n.1.1		2	273.251	even	6
8281.2.a.bb.1.2		2	273.230	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 - 2.26728i) q^{2} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-0.500000 - 0.866025i) q^{7} -7.47214 q^{8} +O(q^{10})\)	\(q+(1.30902 - 2.26728i) q^{2} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-0.500000 - 0.866025i) q^{7} -7.47214 q^{8} +(-3.42705 + 5.93583i) q^{10} +(0.927051 - 1.60570i) q^{11} +(-2.50000 + 2.59808i) q^{13} -2.61803 q^{14} +(-4.92705 + 8.53390i) q^{16} +(-0.736068 - 1.27491i) q^{17} +(0.927051 + 1.60570i) q^{19} +(6.35410 + 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} +(-2.23607 + 3.87298i) q^{23} +1.85410 q^{25} +(2.61803 + 9.06914i) q^{26} +(-2.42705 + 4.20378i) q^{28} +(3.54508 - 6.14027i) q^{29} -4.70820 q^{31} +(5.42705 + 9.39993i) q^{32} -3.85410 q^{34} +(1.30902 + 2.26728i) q^{35} +(-2.00000 + 3.46410i) q^{37} +4.85410 q^{38} +19.5623 q^{40} +(0.381966 - 0.661585i) q^{41} +(-6.28115 - 10.8793i) q^{43} -9.00000 q^{44} +(5.85410 + 10.1396i) q^{46} +2.23607 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.42705 - 4.20378i) q^{50} +(16.9894 + 4.20378i) q^{52} -3.76393 q^{53} +(-2.42705 + 4.20378i) q^{55} +(3.73607 + 6.47106i) q^{56} +(-9.28115 - 16.0754i) q^{58} +(-1.11803 - 1.93649i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(6.54508 - 6.80185i) q^{65} +(6.35410 - 11.0056i) q^{67} +(-3.57295 + 6.18853i) q^{68} +6.85410 q^{70} +(-7.09017 - 12.2805i) q^{71} -2.00000 q^{73} +(5.23607 + 9.06914i) q^{74} +(4.50000 - 7.79423i) q^{76} -1.85410 q^{77} +4.00000 q^{79} +(12.8992 - 22.3420i) q^{80} +(-1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} -32.8885 q^{86} +(-6.92705 + 11.9980i) q^{88} +(2.45492 - 4.25204i) q^{89} +(3.50000 + 0.866025i) q^{91} +21.7082 q^{92} +(2.92705 - 5.06980i) q^{94} +(-2.42705 - 4.20378i) q^{95} +(-9.42705 - 16.3281i) q^{97} +(1.30902 + 2.26728i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8	\( 4 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 2 q^{7} - 12 q^{8} - 7 q^{10} - 3 q^{11} - 10 q^{13} - 6 q^{14} - 13 q^{16} + 6 q^{17} - 3 q^{19} + 12 q^{20} - 3 q^{22} - 6 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 8 q^{31} + 15 q^{32} - 2 q^{34} + 3 q^{35} - 8 q^{37} + 6 q^{38} + 38 q^{40} + 6 q^{41} - 5 q^{43} - 36 q^{44} + 10 q^{46} - 2 q^{49} + 3 q^{50} + 21 q^{52} - 24 q^{53} - 3 q^{55} + 6 q^{56} - 17 q^{58} + 12 q^{61} - 9 q^{62} + 8 q^{64} + 15 q^{65} + 12 q^{67} - 21 q^{68} + 14 q^{70} - 6 q^{71} - 8 q^{73} + 12 q^{74} + 18 q^{76} + 6 q^{77} + 16 q^{79} + 27 q^{80} - 4 q^{82} + q^{85} - 60 q^{86} - 21 q^{88} + 21 q^{89} + 14 q^{91} + 60 q^{92} + 5 q^{94} - 3 q^{95} - 31 q^{97} + 3 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 2 * q^7 - 12 * q^8 - 7 * q^10 - 3 * q^11 - 10 * q^13 - 6 * q^14 - 13 * q^16 + 6 * q^17 - 3 * q^19 + 12 * q^20 - 3 * q^22 - 6 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 8 * q^31 + 15 * q^32 - 2 * q^34 + 3 * q^35 - 8 * q^37 + 6 * q^38 + 38 * q^40 + 6 * q^41 - 5 * q^43 - 36 * q^44 + 10 * q^46 - 2 * q^49 + 3 * q^50 + 21 * q^52 - 24 * q^53 - 3 * q^55 + 6 * q^56 - 17 * q^58 + 12 * q^61 - 9 * q^62 + 8 * q^64 + 15 * q^65 + 12 * q^67 - 21 * q^68 + 14 * q^70 - 6 * q^71 - 8 * q^73 + 12 * q^74 + 18 * q^76 + 6 * q^77 + 16 * q^79 + 27 * q^80 - 4 * q^82 + q^85 - 60 * q^86 - 21 * q^88 + 21 * q^89 + 14 * q^91 + 60 * q^92 + 5 * q^94 - 3 * q^95 - 31 * q^97 + 3 * q^98

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