LMFDB - Embedded newform 1216.2.i.j.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.j.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} -2.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} -2.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +3.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(3.00000 - 5.19615i) q^{17} +(-3.50000 - 2.59808i) q^{19} +(-3.00000 + 5.19615i) q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} -8.00000 q^{31} +(4.50000 - 7.79423i) q^{33} +(-2.00000 + 3.46410i) q^{35} +8.00000 q^{37} +6.00000 q^{39} +(1.50000 - 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} -12.0000 q^{45} +(-5.00000 - 8.66025i) q^{47} -3.00000 q^{49} +(-9.00000 - 15.5885i) q^{51} +(1.00000 + 1.73205i) q^{53} +(3.00000 - 5.19615i) q^{55} +(-12.0000 + 5.19615i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(7.00000 + 12.1244i) q^{61} +(6.00000 + 10.3923i) q^{63} +4.00000 q^{65} +(3.50000 + 6.06218i) q^{67} +12.0000 q^{69} +(1.00000 - 1.73205i) q^{71} +(-5.50000 + 9.52628i) q^{73} +3.00000 q^{75} -6.00000 q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +15.0000 q^{83} +(-6.00000 - 10.3923i) q^{85} -18.0000 q^{87} +(9.00000 + 15.5885i) q^{89} +(-2.00000 - 3.46410i) q^{91} +(-12.0000 + 20.7846i) q^{93} +(-8.00000 + 3.46410i) q^{95} +(1.50000 - 2.59808i) q^{97} +(-9.00000 - 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 2 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 2 * q^5 - 4 * q^7 - 6 * q^9	$ 2 q + 3 q^{3} + 2 q^{5} - 4 q^{7} - 6 q^{9} + 6 q^{11} + 2 q^{13} - 6 q^{15} + 6 q^{17} - 7 q^{19} - 6 q^{21} + 4 q^{23} + q^{25} - 18 q^{27} - 6 q^{29} - 16 q^{31} + 9 q^{33} - 4 q^{35} + 16 q^{37} + 12 q^{39} + 3 q^{41} - 8 q^{43} - 24 q^{45} - 10 q^{47} - 6 q^{49} - 18 q^{51} + 2 q^{53} + 6 q^{55} - 24 q^{57} - 3 q^{59} + 14 q^{61} + 12 q^{63} + 8 q^{65} + 7 q^{67} + 24 q^{69} + 2 q^{71} - 11 q^{73} + 6 q^{75} - 12 q^{77} + 4 q^{79} - 9 q^{81} + 30 q^{83} - 12 q^{85} - 36 q^{87} + 18 q^{89} - 4 q^{91} - 24 q^{93} - 16 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 2 * q^5 - 4 * q^7 - 6 * q^9 + 6 * q^11 + 2 * q^13 - 6 * q^15 + 6 * q^17 - 7 * q^19 - 6 * q^21 + 4 * q^23 + q^25 - 18 * q^27 - 6 * q^29 - 16 * q^31 + 9 * q^33 - 4 * q^35 + 16 * q^37 + 12 * q^39 + 3 * q^41 - 8 * q^43 - 24 * q^45 - 10 * q^47 - 6 * q^49 - 18 * q^51 + 2 * q^53 + 6 * q^55 - 24 * q^57 - 3 * q^59 + 14 * q^61 + 12 * q^63 + 8 * q^65 + 7 * q^67 + 24 * q^69 + 2 * q^71 - 11 * q^73 + 6 * q^75 - 12 * q^77 + 4 * q^79 - 9 * q^81 + 30 * q^83 - 12 * q^85 - 36 * q^87 + 18 * q^89 - 4 * q^91 - 24 * q^93 - 16 * q^95 + 3 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$		0			0
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−3.00000	−	5.19615i	−0.774597	−	1.34164i
$16$		0			0
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$		0			0
$21$	−3.00000	+	5.19615i	−0.654654	+	1.13389i
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$		0			0
$33$	4.50000	−	7.79423i	0.783349	−	1.35680i
$34$		0			0
$35$	−2.00000	+	3.46410i	−0.338062	+	0.585540i
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$		0			0
$39$	6.00000			0.960769
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$	−12.0000			−1.78885
$46$		0			0
$47$	−5.00000	−	8.66025i	−0.729325	−	1.26323i	−0.957169	−	0.289530i	$-0.906501\pi$
$47$	−5.00000	−	8.66025i	−0.729325	−	1.26323i	0.227844	−	0.973698i	$-0.426832\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$		0			0
$51$	−9.00000	−	15.5885i	−1.26025	−	2.18282i
$52$		0			0
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$		0			0
$57$	−12.0000	+	5.19615i	−1.58944	+	0.688247i
$58$		0			0
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	6.00000	+	10.3923i	0.755929	+	1.30931i
$64$		0			0
$65$	4.00000			0.496139
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$		0			0
$69$	12.0000			1.44463
$70$		0			0
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	−0.800566	−	0.599245i	$-0.795468\pi$
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	0.919244	+	0.393688i	$0.128801\pi$
$72$		0			0
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$		0			0
$75$	3.00000			0.346410
$76$		0			0
$77$	−6.00000			−0.683763
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	15.0000			1.64646			0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000			1.64646			0.823232	+	0.567705i	$0.192169\pi$
$84$		0			0
$85$	−6.00000	−	10.3923i	−0.650791	−	1.12720i
$86$		0			0
$87$	−18.0000			−1.92980
$88$		0			0
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.736644	+	0.676280i	$0.236409\pi$
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.217354	+	0.976093i	$0.430258\pi$
$90$		0			0
$91$	−2.00000	−	3.46410i	−0.209657	−	0.363137i
$92$		0			0
$93$	−12.0000	+	20.7846i	−1.24434	+	2.15526i
$94$		0			0
$95$	−8.00000	+	3.46410i	−0.820783	+	0.355409i
$96$		0			0
$97$	1.50000	−	2.59808i	0.152302	−	0.263795i	−0.779771	−	0.626064i	$-0.784665\pi$
$97$	1.50000	−	2.59808i	0.152302	−	0.263795i	0.932073	+	0.362270i	$0.117998\pi$
$98$		0			0
$99$	−9.00000	−	15.5885i	−0.904534	−	1.56670i
$100$		0			0
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$		0			0
$105$	6.00000	+	10.3923i	0.585540	+	1.01419i
$106$		0			0
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$		0			0
$111$	12.0000	−	20.7846i	1.13899	−	1.97279i
$112$		0			0
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$		0			0
$115$	8.00000			0.746004
$116$		0			0
$117$	6.00000	−	10.3923i	0.554700	−	0.960769i
$118$		0			0
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$		0			0
$129$	12.0000	+	20.7846i	1.05654	+	1.82998i
$130$		0			0
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	7.00000	+	5.19615i	0.606977	+	0.450564i
$134$		0			0
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$		0			0
$137$	−8.50000	−	14.7224i	−0.726204	−	1.25782i	−0.958477	−	0.285171i	$-0.907949\pi$
$137$	−8.50000	−	14.7224i	−0.726204	−	1.25782i	0.232273	−	0.972651i	$-0.425384\pi$
$138$		0			0
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	−3.50000	−	6.06218i	−0.296866	−	0.514187i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$	−30.0000			−2.52646
$142$		0			0
$143$	3.00000	+	5.19615i	0.250873	+	0.434524i
$144$		0			0
$145$	−12.0000			−0.996546
$146$		0			0
$147$	−4.50000	+	7.79423i	−0.371154	+	0.642857i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	−36.0000			−2.91043
$154$		0			0
$155$	−8.00000	+	13.8564i	−0.642575	+	1.11297i
$156$		0			0
$157$	10.0000	−	17.3205i	0.798087	−	1.38233i	−0.122774	−	0.992435i	$-0.539179\pi$
$157$	10.0000	−	17.3205i	0.798087	−	1.38233i	0.920860	−	0.389892i	$-0.127488\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	−4.00000	−	6.92820i	−0.315244	−	0.546019i
$162$		0			0
$163$	17.0000			1.33154			0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000			1.33154			0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$	−9.00000	−	15.5885i	−0.700649	−	1.21356i
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−3.00000	+	25.9808i	−0.229416	+	1.98680i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$		0			0
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$		0			0
$179$	−19.0000			−1.42013			−0.710063	−	0.704138i	$-0.751334\pi$
$179$	−19.0000			−1.42013			−0.710063	+	0.704138i	$0.751334\pi$
$180$		0			0
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	0.552143	−	0.833749i	$-0.313810\pi$
$181$	−6.00000	−	10.3923i	−0.445976	−	0.772454i	−0.998120	+	0.0612954i	$0.980477\pi$
$182$		0			0
$183$	42.0000			3.10473
$184$		0			0
$185$	8.00000	−	13.8564i	0.588172	−	1.01874i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$		0			0
$189$	18.0000			1.30931
$190$		0			0
$191$	20.0000			1.44715			0.723575	−	0.690246i	$-0.242498\pi$
$191$	20.0000			1.44715			0.723575	+	0.690246i	$0.242498\pi$
$192$		0			0
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$		0			0
$195$	6.00000	−	10.3923i	0.429669	−	0.744208i
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$		0			0
$201$	21.0000			1.48123
$202$		0			0
$203$	6.00000	+	10.3923i	0.421117	+	0.729397i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$		0			0
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$		0			0
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$		0			0
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$		0			0
$215$	8.00000	+	13.8564i	0.545595	+	0.944999i
$216$		0			0
$217$	16.0000			1.08615
$218$		0			0
$219$	16.5000	+	28.5788i	1.11497	+	1.93118i
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$		0			0
$225$	3.00000	−	5.19615i	0.200000	−	0.346410i
$226$		0			0
$227$	11.0000			0.730096			0.365048	−	0.930989i	$-0.381053\pi$
$227$	11.0000			0.730096			0.365048	+	0.930989i	$0.381053\pi$
$228$		0			0
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$		0			0
$231$	−9.00000	+	15.5885i	−0.592157	+	1.02565i
$232$		0			0
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	−0.957599	−	0.288106i	$-0.906975\pi$
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	0.728306	+	0.685252i	$0.240308\pi$
$234$		0			0
$235$	−20.0000			−1.30466
$236$		0			0
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	1.00000	−	8.66025i	0.0636285	−	0.551039i
$248$		0			0
$249$	22.5000	−	38.9711i	1.42588	−	2.46970i
$250$		0			0
$251$	−0.500000	−	0.866025i	−0.0315597	−	0.0546630i	0.849814	−	0.527082i	$-0.176714\pi$
$251$	−0.500000	−	0.866025i	−0.0315597	−	0.0546630i	−0.881374	+	0.472419i	$0.843381\pi$
$252$		0			0
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$		0			0
$255$	−36.0000			−2.25441
$256$		0			0
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	0.735972	−	0.677012i	$-0.236726\pi$
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	−0.954296	+	0.298864i	$0.903392\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−18.0000	+	31.1769i	−1.11417	+	1.92980i
$262$		0			0
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	0.116939	+	0.993139i	$0.462692\pi$
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	−0.918553	+	0.395298i	$0.870641\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	54.0000			3.30475
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−15.0000	+	25.9808i	−0.911185	+	1.57822i	−0.0987925	+	0.995108i	$0.531498\pi$
$271$	−15.0000	+	25.9808i	−0.911185	+	1.57822i	−0.812393	+	0.583111i	$0.801835\pi$
$272$		0			0
$273$	−12.0000			−0.726273
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	18.0000			1.08152			0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000			1.08152			0.540758	+	0.841178i	$0.318138\pi$
$278$		0			0
$279$	24.0000	+	41.5692i	1.43684	+	2.48868i
$280$		0			0
$281$	8.50000	+	14.7224i	0.507067	+	0.878267i	0.999967	+	0.00818015i	$0.00260385\pi$
$281$	8.50000	+	14.7224i	0.507067	+	0.878267i	−0.492899	+	0.870087i	$0.664063\pi$
$282$		0			0
$283$	−4.50000	+	7.79423i	−0.267497	+	0.463319i	−0.968215	−	0.250120i	$-0.919530\pi$
$283$	−4.50000	+	7.79423i	−0.267497	+	0.463319i	0.700718	+	0.713439i	$0.252863\pi$
$284$		0			0
$285$	−3.00000	+	25.9808i	−0.177705	+	1.53897i
$286$		0			0
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	−4.50000	−	7.79423i	−0.263795	−	0.456906i
$292$		0			0
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$		0			0
$297$	−27.0000			−1.56670
$298$		0			0
$299$	−4.00000	+	6.92820i	−0.231326	+	0.400668i
$300$		0			0
$301$	8.00000	−	13.8564i	0.461112	−	0.798670i
$302$		0			0
$303$	6.00000			0.344691
$304$		0			0
$305$	28.0000			1.60328
$306$		0			0
$307$	−4.50000	+	7.79423i	−0.256829	+	0.444840i	−0.965391	−	0.260808i	$-0.916011\pi$
$307$	−4.50000	+	7.79423i	−0.256829	+	0.444840i	0.708562	+	0.705649i	$0.249344\pi$
$308$		0			0
$309$	−15.0000	+	25.9808i	−0.853320	+	1.47799i
$310$		0			0
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$		0			0
$315$	24.0000			1.35225
$316$		0			0
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	0.956818	+	0.290689i	$0.0938844\pi$
$317$	13.0000	+	22.5167i	0.730153	+	1.26466i	−0.226665	+	0.973973i	$0.572782\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	6.00000	−	10.3923i	0.334887	−	0.580042i
$322$		0			0
$323$	−24.0000	+	10.3923i	−1.33540	+	0.578243i
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$		0			0
$327$	−24.0000	−	41.5692i	−1.32720	−	2.29878i
$328$		0			0
$329$	10.0000	+	17.3205i	0.551318	+	0.954911i
$330$		0			0
$331$	25.0000			1.37412			0.687062	−	0.726599i	$-0.258900\pi$
$331$	25.0000			1.37412			0.687062	+	0.726599i	$0.258900\pi$
$332$		0			0
$333$	−24.0000	−	41.5692i	−1.31519	−	2.27798i
$334$		0			0
$335$	14.0000			0.764902
$336$		0			0
$337$	−15.5000	+	26.8468i	−0.844339	+	1.46244i	0.0418554	+	0.999124i	$0.486673\pi$
$337$	−15.5000	+	26.8468i	−0.844339	+	1.46244i	−0.886194	+	0.463314i	$0.846660\pi$
$338$		0			0
$339$	22.5000	−	38.9711i	1.22203	−	2.11662i
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$	12.0000	−	20.7846i	0.646058	−	1.11901i
$346$		0			0
$347$	−3.50000	+	6.06218i	−0.187890	+	0.325435i	−0.944547	−	0.328378i	$-0.893498\pi$
$347$	−3.50000	+	6.06218i	−0.187890	+	0.325435i	0.756657	+	0.653812i	$0.226831\pi$
$348$		0			0
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$		0			0
$351$	−9.00000	−	15.5885i	−0.480384	−	0.832050i
$352$		0			0
$353$	−25.0000			−1.33062			−0.665308	−	0.746569i	$-0.731700\pi$
$353$	−25.0000			−1.33062			−0.665308	+	0.746569i	$0.731700\pi$
$354$		0			0
$355$	−2.00000	−	3.46410i	−0.106149	−	0.183855i
$356$		0			0
$357$	18.0000	+	31.1769i	0.952661	+	1.65006i
$358$		0			0
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$		0			0
$363$	−3.00000	+	5.19615i	−0.157459	+	0.272727i
$364$		0			0
$365$	11.0000	+	19.0526i	0.575766	+	0.997257i
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$	−18.0000			−0.937043
$370$		0			0
$371$	−2.00000	−	3.46410i	−0.103835	−	0.179847i
$372$		0			0
$373$	−24.0000			−1.24267			−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000			−1.24267			−0.621336	+	0.783544i	$0.713410\pi$
$374$		0			0
$375$	18.0000	−	31.1769i	0.929516	−	1.60997i
$376$		0			0
$377$	6.00000	−	10.3923i	0.309016	−	0.535231i
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$		0			0
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$		0			0
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$		0			0
$387$	48.0000			2.43998
$388$		0			0
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	0.994393	−	0.105748i	$-0.0337237\pi$
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	−0.588777	+	0.808296i	$0.700390\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$		0			0
$393$	1.50000	+	2.59808i	0.0756650	+	0.131056i
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$		0			0
$399$	24.0000	−	10.3923i	1.20150	−	0.520266i
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$		0			0
$405$	9.00000	+	15.5885i	0.447214	+	0.774597i
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	−51.0000			−2.51564
$412$		0			0
$413$	3.00000	−	5.19615i	0.147620	−	0.255686i
$414$		0			0
$415$	15.0000	−	25.9808i	0.736321	−	1.27535i
$416$		0			0
$417$	−21.0000			−1.02837
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−6.00000	+	10.3923i	−0.292422	+	0.506490i	−0.974382	−	0.224900i	$-0.927795\pi$
$421$	−6.00000	+	10.3923i	−0.292422	+	0.506490i	0.681960	+	0.731390i	$0.261128\pi$
$422$		0			0
$423$	−30.0000	+	51.9615i	−1.45865	+	2.52646i
$424$		0			0
$425$	6.00000			0.291043
$426$		0			0
$427$	−14.0000	−	24.2487i	−0.677507	−	1.17348i
$428$		0			0
$429$	18.0000			0.869048
$430$		0			0
$431$	13.0000	+	22.5167i	0.626188	+	1.08459i	0.988310	+	0.152459i	$0.0487191\pi$
$431$	13.0000	+	22.5167i	0.626188	+	1.08459i	−0.362122	+	0.932131i	$0.617948\pi$
$432$		0			0
$433$	−7.00000	−	12.1244i	−0.336399	−	0.582659i	0.647354	−	0.762190i	$-0.275876\pi$
$433$	−7.00000	−	12.1244i	−0.336399	−	0.582659i	−0.983752	+	0.179530i	$0.942542\pi$
$434$		0			0
$435$	−18.0000	+	31.1769i	−0.863034	+	1.49482i
$436$		0			0
$437$	2.00000	−	17.3205i	0.0956730	−	0.828552i
$438$		0			0
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$		0			0
$441$	9.00000	+	15.5885i	0.428571	+	0.742307i
$442$		0			0
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	0.899457	−	0.437009i	$-0.143962\pi$
$443$	1.50000	+	2.59808i	0.0712672	+	0.123438i	−0.828190	+	0.560448i	$0.810629\pi$
$444$		0			0
$445$	36.0000			1.70656
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.0000			0.991051			0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000			0.991051			0.495526	+	0.868593i	$0.334975\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.00000			−0.375046
$456$		0			0
$457$	−7.00000			−0.327446			−0.163723	−	0.986506i	$-0.552350\pi$
$457$	−7.00000			−0.327446			−0.163723	+	0.986506i	$0.552350\pi$
$458$		0			0
$459$	−27.0000	+	46.7654i	−1.26025	+	2.18282i
$460$		0			0
$461$	−9.00000	+	15.5885i	−0.419172	+	0.726027i	−0.995856	−	0.0909401i	$-0.971013\pi$
$461$	−9.00000	+	15.5885i	−0.419172	+	0.726027i	0.576685	+	0.816967i	$0.304346\pi$
$462$		0			0
$463$	10.0000			0.464739			0.232370	−	0.972628i	$-0.425352\pi$
$463$	10.0000			0.464739			0.232370	+	0.972628i	$0.425352\pi$
$464$		0			0
$465$	24.0000	+	41.5692i	1.11297	+	1.92773i
$466$		0			0
$467$	21.0000			0.971764			0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000			0.971764			0.485882	+	0.874024i	$0.338498\pi$
$468$		0			0
$469$	−7.00000	−	12.1244i	−0.323230	−	0.559851i
$470$		0			0
$471$	−30.0000	−	51.9615i	−1.38233	−	2.39426i
$472$		0			0
$473$	−12.0000	+	20.7846i	−0.551761	+	0.955677i
$474$		0			0
$475$	0.500000	−	4.33013i	0.0229416	−	0.198680i
$476$		0			0
$477$	6.00000	−	10.3923i	0.274721	−	0.475831i
$478$		0			0
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	0.985504	+	0.169654i	$0.0542649\pi$
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	−0.345827	+	0.938298i	$0.612402\pi$
$480$		0			0
$481$	8.00000	+	13.8564i	0.364769	+	0.631798i
$482$		0			0
$483$	−24.0000			−1.09204
$484$		0			0
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$		0			0
$489$	25.5000	−	44.1673i	1.15315	−	1.99731i
$490$		0			0
$491$	−14.0000	+	24.2487i	−0.631811	+	1.09433i	0.355370	+	0.934726i	$0.384355\pi$
$491$	−14.0000	+	24.2487i	−0.631811	+	1.09433i	−0.987181	+	0.159603i	$0.948978\pi$
$492$		0			0
$493$	−36.0000			−1.62136
$494$		0			0
$495$	−36.0000			−1.61808
$496$		0			0
$497$	−2.00000	+	3.46410i	−0.0897123	+	0.155386i
$498$		0			0
$499$	0.500000	−	0.866025i	0.0223831	−	0.0387686i	−0.854617	−	0.519259i	$-0.826208\pi$
$499$	0.500000	−	0.866025i	0.0223831	−	0.0387686i	0.877000	+	0.480490i	$0.159541\pi$
$500$		0			0
$501$	−36.0000			−1.60836
$502$		0			0
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	−0.917912	−	0.396783i	$-0.870127\pi$
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	0.115332	−	0.993327i	$-0.463207\pi$
$504$		0			0
$505$	4.00000			0.177998
$506$		0			0
$507$	−13.5000	−	23.3827i	−0.599556	−	1.03846i
$508$		0			0
$509$	−10.0000	−	17.3205i	−0.443242	−	0.767718i	0.554686	−	0.832060i	$-0.312839\pi$
$509$	−10.0000	−	17.3205i	−0.443242	−	0.767718i	−0.997928	+	0.0643419i	$0.979505\pi$
$510$		0			0
$511$	11.0000	−	19.0526i	0.486611	−	0.842836i
$512$		0			0
$513$	31.5000	+	23.3827i	1.39076	+	1.03237i
$514$		0			0
$515$	−10.0000	+	17.3205i	−0.440653	+	0.763233i
$516$		0			0
$517$	−15.0000	−	25.9808i	−0.659699	−	1.14263i
$518$		0			0
$519$	−9.00000	−	15.5885i	−0.395056	−	0.684257i
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	0.636401	−	0.771358i	$-0.280422\pi$
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	−0.986216	+	0.165460i	$0.947089\pi$
$524$		0			0
$525$	−6.00000			−0.261861
$526$		0			0
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$	6.00000			0.259889
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$		0			0
$537$	−28.5000	+	49.3634i	−1.22987	+	2.13019i
$538$		0			0
$539$	−9.00000			−0.387657
$540$		0			0
$541$	20.0000	+	34.6410i	0.859867	+	1.48933i	0.872055	+	0.489408i	$0.162787\pi$
$541$	20.0000	+	34.6410i	0.859867	+	1.48933i	−0.0121878	+	0.999926i	$0.503880\pi$
$542$		0			0
$543$	−36.0000			−1.54491
$544$		0			0
$545$	−16.0000	−	27.7128i	−0.685365	−	1.18709i
$546$		0			0
$547$	−16.0000	−	27.7128i	−0.684111	−	1.18491i	−0.973715	−	0.227768i	$-0.926857\pi$
$547$	−16.0000	−	27.7128i	−0.684111	−	1.18491i	0.289605	−	0.957146i	$-0.406476\pi$
$548$		0			0
$549$	42.0000	−	72.7461i	1.79252	−	3.10473i
$550$		0			0
$551$	−3.00000	+	25.9808i	−0.127804	+	1.10682i
$552$		0			0
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$		0			0
$555$	−24.0000	−	41.5692i	−1.01874	−	1.76452i
$556$		0			0
$557$	−8.00000	−	13.8564i	−0.338971	−	0.587115i	0.645269	−	0.763956i	$-0.276745\pi$
$557$	−8.00000	−	13.8564i	−0.338971	−	0.587115i	−0.984239	+	0.176841i	$0.943412\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$	−27.0000	−	46.7654i	−1.13994	−	1.97444i
$562$		0			0
$563$	19.0000			0.800755			0.400377	−	0.916350i	$-0.368879\pi$
$563$	19.0000			0.800755			0.400377	+	0.916350i	$0.368879\pi$
$564$		0			0
$565$	15.0000	−	25.9808i	0.631055	−	1.09302i
$566$		0			0
$567$	9.00000	−	15.5885i	0.377964	−	0.654654i
$568$		0			0
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	13.0000			0.544033			0.272017	−	0.962293i	$-0.412309\pi$
$571$	13.0000			0.544033			0.272017	+	0.962293i	$0.412309\pi$
$572$		0			0
$573$	30.0000	−	51.9615i	1.25327	−	2.17072i
$574$		0			0
$575$	−2.00000	+	3.46410i	−0.0834058	+	0.144463i
$576$		0			0
$577$	−45.0000			−1.87337			−0.936687	−	0.350167i	$-0.886125\pi$
$577$	−45.0000			−1.87337			−0.936687	+	0.350167i	$0.886125\pi$
$578$		0			0
$579$	15.0000	+	25.9808i	0.623379	+	1.07972i
$580$		0			0
$581$	−30.0000			−1.24461
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$		0			0
$585$	−12.0000	−	20.7846i	−0.496139	−	0.859338i
$586$		0			0
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	−0.999985	−	0.00542667i	$-0.998273\pi$
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	0.504692	+	0.863299i	$0.331606\pi$
$588$		0			0
$589$	28.0000	+	20.7846i	1.15372	+	0.856415i
$590$		0			0
$591$	−18.0000	+	31.1769i	−0.740421	+	1.28245i
$592$		0			0
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	0.943507	−	0.331353i	$-0.107505\pi$
$593$	4.50000	+	7.79423i	0.184793	+	0.320071i	−0.758714	+	0.651424i	$0.774172\pi$
$594$		0			0
$595$	12.0000	+	20.7846i	0.491952	+	0.852086i
$596$		0			0
$597$	30.0000			1.22782
$598$		0			0
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$		0			0
$603$	21.0000	−	36.3731i	0.855186	−	1.48123i
$604$		0			0
$605$	−2.00000	+	3.46410i	−0.0813116	+	0.140836i
$606$		0			0
$607$	−14.0000			−0.568242			−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000			−0.568242			−0.284121	+	0.958788i	$0.591702\pi$
$608$		0			0
$609$	36.0000			1.45879
$610$		0			0
$611$	10.0000	−	17.3205i	0.404557	−	0.700713i
$612$		0			0
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	0.0346469	+	0.999400i	$0.488969\pi$
$613$	−21.0000	+	36.3731i	−0.848182	+	1.46909i	−0.882829	+	0.469695i	$0.844364\pi$
$614$		0			0
$615$	−18.0000			−0.725830
$616$		0			0
$617$	4.50000	+	7.79423i	0.181163	+	0.313784i	0.942277	−	0.334835i	$-0.108680\pi$
$617$	4.50000	+	7.79423i	0.181163	+	0.313784i	−0.761114	+	0.648618i	$0.775347\pi$
$618$		0			0
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−18.0000	−	31.1769i	−0.722315	−	1.25109i
$622$		0			0
$623$	−18.0000	−	31.1769i	−0.721155	−	1.24908i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$	−36.0000	+	15.5885i	−1.43770	+	0.622543i
$628$		0			0
$629$	24.0000	−	41.5692i	0.956943	−	1.65747i
$630$		0			0
$631$	1.00000	+	1.73205i	0.0398094	+	0.0689519i	0.885244	−	0.465128i	$-0.153992\pi$
$631$	1.00000	+	1.73205i	0.0398094	+	0.0689519i	−0.845434	+	0.534080i	$0.820658\pi$
$632$		0			0
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$		0			0
$635$	−4.00000			−0.158735
$636$		0			0
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$		0			0
$639$	−12.0000			−0.474713
$640$		0			0
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	0.225876	+	0.974156i	$0.427476\pi$
$641$	−18.5000	+	32.0429i	−0.730706	+	1.26562i	−0.956582	+	0.291464i	$0.905858\pi$
$642$		0			0
$643$	−0.500000	+	0.866025i	−0.0197181	+	0.0341527i	−0.875716	−	0.482826i	$-0.839610\pi$
$643$	−0.500000	+	0.866025i	−0.0197181	+	0.0341527i	0.855998	+	0.516979i	$0.172944\pi$
$644$		0			0
$645$	48.0000			1.89000
$646$		0			0
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$		0			0
$651$	24.0000	−	41.5692i	0.940634	−	1.62923i
$652$		0			0
$653$	−4.00000			−0.156532			−0.0782660	−	0.996933i	$-0.524938\pi$
$653$	−4.00000			−0.156532			−0.0782660	+	0.996933i	$0.524938\pi$
$654$		0			0
$655$	1.00000	+	1.73205i	0.0390732	+	0.0676768i
$656$		0			0
$657$	66.0000			2.57491
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	−3.00000	−	5.19615i	−0.116686	−	0.202107i	0.801766	−	0.597638i	$-0.203894\pi$
$661$	−3.00000	−	5.19615i	−0.116686	−	0.202107i	−0.918453	+	0.395531i	$0.870561\pi$
$662$		0			0
$663$	18.0000	−	31.1769i	0.699062	−	1.21081i
$664$		0			0
$665$	16.0000	−	6.92820i	0.620453	−	0.268664i
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$		0			0
$669$	−24.0000	−	41.5692i	−0.927894	−	1.60716i
$670$		0			0
$671$	21.0000	+	36.3731i	0.810696	+	1.40417i
$672$		0			0
$673$	−22.0000			−0.848038			−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000			−0.848038			−0.424019	+	0.905653i	$0.639381\pi$
$674$		0			0
$675$	−4.50000	−	7.79423i	−0.173205	−	0.300000i
$676$		0			0
$677$	−26.0000			−0.999261			−0.499631	−	0.866239i	$-0.666531\pi$
$677$	−26.0000			−0.999261			−0.499631	+	0.866239i	$0.666531\pi$
$678$		0			0
$679$	−3.00000	+	5.19615i	−0.115129	+	0.199410i
$680$		0			0
$681$	16.5000	−	28.5788i	0.632281	−	1.09514i
$682$		0			0
$683$	−44.0000			−1.68361			−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000			−1.68361			−0.841807	+	0.539779i	$0.818508\pi$
$684$		0			0
$685$	−34.0000			−1.29907
$686$		0			0
$687$	30.0000	−	51.9615i	1.14457	−	1.98246i
$688$		0			0
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$		0			0
$693$	18.0000	+	31.1769i	0.683763	+	1.18431i
$694$		0			0
$695$	−14.0000			−0.531050
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$	10.5000	+	18.1865i	0.397146	+	0.687878i
$700$		0			0
$701$	−7.00000	+	12.1244i	−0.264386	+	0.457931i	−0.967403	−	0.253243i	$-0.918503\pi$
$701$	−7.00000	+	12.1244i	−0.264386	+	0.457931i	0.703016	+	0.711174i	$0.251836\pi$
$702$		0			0
$703$	−28.0000	−	20.7846i	−1.05604	−	0.783906i
$704$		0			0
$705$	−30.0000	+	51.9615i	−1.12987	+	1.95698i
$706$		0			0
$707$	−2.00000	−	3.46410i	−0.0752177	−	0.130281i
$708$		0			0
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	0.901135	−	0.433539i	$-0.142735\pi$
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	−0.826023	+	0.563636i	$0.809402\pi$
$710$		0			0
$711$	−24.0000			−0.900070
$712$		0			0
$713$	−16.0000	−	27.7128i	−0.599205	−	1.03785i
$714$		0			0
$715$	12.0000			0.448775
$716$		0			0
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$		0			0
$719$	23.0000	−	39.8372i	0.857755	−	1.48568i	−0.0163099	−	0.999867i	$-0.505192\pi$
$719$	23.0000	−	39.8372i	0.857755	−	1.48568i	0.874065	−	0.485809i	$-0.161475\pi$
$720$		0			0
$721$	20.0000			0.744839
$722$		0			0
$723$	−39.0000			−1.45043
$724$		0			0
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	22.0000	−	38.1051i	0.815935	−	1.41324i	−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	22.0000	−	38.1051i	0.815935	−	1.41324i	0.908655	−	0.417548i	$-0.137111\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$		0			0
$733$	−36.0000			−1.32969			−0.664845	−	0.746981i	$-0.731502\pi$
$733$	−36.0000			−1.32969			−0.664845	+	0.746981i	$0.731502\pi$
$734$		0			0
$735$	9.00000	+	15.5885i	0.331970	+	0.574989i
$736$		0			0
$737$	10.5000	+	18.1865i	0.386772	+	0.669910i
$738$		0			0
$739$	6.50000	−	11.2583i	0.239106	−	0.414144i	−0.721352	−	0.692569i	$-0.756479\pi$
$739$	6.50000	−	11.2583i	0.239106	−	0.414144i	0.960458	+	0.278425i	$0.0898122\pi$
$740$		0			0
$741$	−21.0000	−	15.5885i	−0.771454	−	0.572656i
$742$		0			0
$743$	12.0000	−	20.7846i	0.440237	−	0.762513i	−0.557470	−	0.830197i	$-0.688228\pi$
$743$	12.0000	−	20.7846i	0.440237	−	0.762513i	0.997707	+	0.0676840i	$0.0215610\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−45.0000	−	77.9423i	−1.64646	−	2.85176i
$748$		0			0
$749$	−8.00000			−0.292314
$750$		0			0
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	0.993895	−	0.110333i	$-0.0351919\pi$
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	−0.592499	+	0.805571i	$0.701859\pi$
$752$		0			0
$753$	−3.00000			−0.109326
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.00000	+	12.1244i	−0.254419	+	0.440667i	−0.964738	−	0.263213i	$-0.915218\pi$
$757$	−7.00000	+	12.1244i	−0.254419	+	0.440667i	0.710318	+	0.703881i	$0.248551\pi$
$758$		0			0
$759$	36.0000			1.30672
$760$		0			0
$761$	21.0000			0.761249			0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000			0.761249			0.380625	+	0.924730i	$0.375709\pi$
$762$		0			0
$763$	−16.0000	+	27.7128i	−0.579239	+	1.00327i
$764$		0			0
$765$	−36.0000	+	62.3538i	−1.30158	+	2.25441i
$766$		0			0
$767$	−6.00000			−0.216647
$768$		0			0
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	0.883493	−	0.468445i	$-0.155186\pi$
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	−0.847432	+	0.530904i	$0.821852\pi$
$770$		0			0
$771$	−21.0000			−0.756297
$772$		0			0
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$773$	7.00000	+	12.1244i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$		0			0
$777$	−24.0000	+	41.5692i	−0.860995	+	1.49129i
$778$		0			0
$779$	−12.0000	+	5.19615i	−0.429945	+	0.186171i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$		0			0
$783$	27.0000	+	46.7654i	0.964901	+	1.67126i
$784$		0			0
$785$	−20.0000	−	34.6410i	−0.713831	−	1.23639i
$786$		0			0
$787$	−35.0000			−1.24762			−0.623808	−	0.781578i	$-0.714415\pi$
$787$	−35.0000			−1.24762			−0.623808	+	0.781578i	$0.714415\pi$
$788$		0			0
$789$	39.0000	+	67.5500i	1.38844	+	2.40484i
$790$		0			0
$791$	−30.0000			−1.06668
$792$		0			0
$793$	−14.0000	+	24.2487i	−0.497155	+	0.861097i
$794$		0			0
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$		0			0
$797$	4.00000			0.141687			0.0708436	−	0.997487i	$-0.477431\pi$
$797$	4.00000			0.141687			0.0708436	+	0.997487i	$0.477431\pi$
$798$		0			0
$799$	−60.0000			−2.12265
$800$		0			0
$801$	54.0000	−	93.5307i	1.90800	−	3.30475i
$802$		0			0
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$		0			0
$805$	−16.0000			−0.563926
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.0000			−0.386739			−0.193370	−	0.981126i	$-0.561942\pi$
$809$	−11.0000			−0.386739			−0.193370	+	0.981126i	$0.561942\pi$
$810$		0			0
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	0.986451	−	0.164057i	$-0.0524582\pi$
$811$	10.0000	+	17.3205i	0.351147	+	0.608205i	−0.635303	+	0.772263i	$0.719125\pi$
$812$		0			0
$813$	45.0000	+	77.9423i	1.57822	+	2.73356i
$814$		0			0
$815$	17.0000	−	29.4449i	0.595484	−	1.03141i
$816$		0			0
$817$	32.0000	−	13.8564i	1.11954	−	0.484774i
$818$		0			0
$819$	−12.0000	+	20.7846i	−0.419314	+	0.726273i
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	−3.00000	−	5.19615i	−0.104573	−	0.181126i	0.808990	−	0.587822i	$-0.200014\pi$
$823$	−3.00000	−	5.19615i	−0.104573	−	0.181126i	−0.913564	+	0.406695i	$0.866681\pi$
$824$		0			0
$825$	9.00000			0.313340
$826$		0			0
$827$	7.50000	+	12.9904i	0.260801	+	0.451720i	0.966455	−	0.256836i	$-0.0826802\pi$
$827$	7.50000	+	12.9904i	0.260801	+	0.451720i	−0.705654	+	0.708556i	$0.749347\pi$
$828$		0			0
$829$	−32.0000			−1.11141			−0.555703	−	0.831381i	$-0.687551\pi$
$829$	−32.0000			−1.11141			−0.555703	+	0.831381i	$0.687551\pi$
$830$		0			0
$831$	27.0000	−	46.7654i	0.936620	−	1.62227i
$832$		0			0
$833$	−9.00000	+	15.5885i	−0.311832	+	0.540108i
$834$		0			0
$835$	−24.0000			−0.830554
$836$		0			0
$837$	72.0000			2.48868
$838$		0			0
$839$	−13.0000	+	22.5167i	−0.448810	+	0.777361i	−0.998309	−	0.0581329i	$-0.981485\pi$
$839$	−13.0000	+	22.5167i	−0.448810	+	0.777361i	0.549499	+	0.835494i	$0.314819\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	51.0000			1.75653
$844$		0			0
$845$	−9.00000	−	15.5885i	−0.309609	−	0.536259i
$846$		0			0
$847$	4.00000			0.137442
$848$		0			0
$849$	13.5000	+	23.3827i	0.463319	+	0.802492i
$850$		0			0
$851$	16.0000	+	27.7128i	0.548473	+	0.949983i
$852$		0			0
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	−0.552948	−	0.833215i	$-0.686497\pi$
$853$	13.0000	−	22.5167i	0.445112	−	0.770956i	0.998060	+	0.0622597i	$0.0198307\pi$
$854$		0			0
$855$	42.0000	+	31.1769i	1.43637	+	1.06623i
$856$		0			0
$857$	−6.50000	+	11.2583i	−0.222036	+	0.384577i	−0.955426	−	0.295231i	$-0.904604\pi$
$857$	−6.50000	+	11.2583i	−0.222036	+	0.384577i	0.733390	+	0.679808i	$0.237937\pi$
$858$		0			0
$859$	−0.500000	−	0.866025i	−0.0170598	−	0.0295484i	0.857369	−	0.514701i	$-0.172097\pi$
$859$	−0.500000	−	0.866025i	−0.0170598	−	0.0295484i	−0.874429	+	0.485153i	$0.838764\pi$
$860$		0			0
$861$	9.00000	+	15.5885i	0.306719	+	0.531253i
$862$		0			0
$863$	−8.00000			−0.272323			−0.136162	−	0.990687i	$-0.543477\pi$
$863$	−8.00000			−0.272323			−0.136162	+	0.990687i	$0.543477\pi$
$864$		0			0
$865$	−6.00000	−	10.3923i	−0.204006	−	0.353349i
$866$		0			0
$867$	−57.0000			−1.93582
$868$		0			0
$869$	6.00000	−	10.3923i	0.203536	−	0.352535i
$870$		0			0
$871$	−7.00000	+	12.1244i	−0.237186	+	0.410818i
$872$		0			0
$873$	−18.0000			−0.609208
$874$		0			0
$875$	−24.0000			−0.811348
$876$		0			0
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	0.157205	+	0.987566i	$0.449752\pi$
$877$	−23.0000	+	39.8372i	−0.776655	+	1.34521i	−0.933860	+	0.357640i	$0.883582\pi$
$878$		0			0
$879$	−21.0000	+	36.3731i	−0.708312	+	1.22683i
$880$		0			0
$881$	−37.0000			−1.24656			−0.623281	−	0.781998i	$-0.714201\pi$
$881$	−37.0000			−1.24656			−0.623281	+	0.781998i	$0.714201\pi$
$882$		0			0
$883$	5.50000	+	9.52628i	0.185090	+	0.320585i	0.943607	−	0.331068i	$-0.107409\pi$
$883$	5.50000	+	9.52628i	0.185090	+	0.320585i	−0.758517	+	0.651653i	$0.774076\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$		0			0
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$	2.00000	+	3.46410i	0.0670778	+	0.116182i
$890$		0			0
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		0			0
$893$	−5.00000	+	43.3013i	−0.167319	+	1.44902i
$894$		0			0
$895$	−19.0000	+	32.9090i	−0.635100	+	1.10003i
$896$		0			0
$897$	12.0000	+	20.7846i	0.400668	+	0.693978i
$898$		0			0
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$	−24.0000	−	41.5692i	−0.798670	−	1.38334i
$904$		0			0
$905$	−24.0000			−0.797787
$906$		0			0
$907$	1.50000	−	2.59808i	0.0498067	−	0.0862677i	−0.840047	−	0.542513i	$-0.817473\pi$
$907$	1.50000	−	2.59808i	0.0498067	−	0.0862677i	0.889854	+	0.456246i	$0.150806\pi$
$908$		0			0
$909$	6.00000	−	10.3923i	0.199007	−	0.344691i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	45.0000			1.48928
$914$		0			0
$915$	42.0000	−	72.7461i	1.38848	−	2.40491i
$916$		0			0
$917$	1.00000	−	1.73205i	0.0330229	−	0.0571974i
$918$		0			0
$919$	−14.0000			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$920$		0			0
$921$	13.5000	+	23.3827i	0.444840	+	0.770486i
$922$		0			0
$923$	4.00000			0.131662
$924$		0			0
$925$	4.00000	+	6.92820i	0.131519	+	0.227798i
$926$		0			0
$927$	30.0000	+	51.9615i	0.985329	+	1.70664i
$928$		0			0
$929$	−2.50000	+	4.33013i	−0.0820223	+	0.142067i	−0.904118	−	0.427282i	$-0.859471\pi$
$929$	−2.50000	+	4.33013i	−0.0820223	+	0.142067i	0.822096	+	0.569349i	$0.192805\pi$
$930$		0			0
$931$	10.5000	+	7.79423i	0.344124	+	0.255446i
$932$		0			0
$933$	−18.0000	+	31.1769i	−0.589294	+	1.02069i
$934$		0			0
$935$	−18.0000	−	31.1769i	−0.588663	−	1.01959i
$936$		0			0
$937$	−3.50000	−	6.06218i	−0.114340	−	0.198043i	0.803176	−	0.595742i	$-0.203142\pi$
$937$	−3.50000	−	6.06218i	−0.114340	−	0.198043i	−0.917516	+	0.397699i	$0.869809\pi$
$938$		0			0
$939$	−3.00000			−0.0979013
$940$		0			0
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		0			0
$943$	12.0000			0.390774
$944$		0			0
$945$	18.0000	−	31.1769i	0.585540	−	1.01419i
$946$		0			0
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	−0.543746	−	0.839250i	$-0.682994\pi$
$947$	14.0000	−	24.2487i	0.454939	−	0.787977i	0.998685	+	0.0512727i	$0.0163278\pi$
$948$		0			0
$949$	−22.0000			−0.714150
$950$		0			0
$951$	78.0000			2.52932
$952$		0			0
$953$	1.50000	−	2.59808i	0.0485898	−	0.0841599i	−0.840708	−	0.541489i	$-0.817861\pi$
$953$	1.50000	−	2.59808i	0.0485898	−	0.0841599i	0.889297	+	0.457329i	$0.151194\pi$
$954$		0			0
$955$	20.0000	−	34.6410i	0.647185	−	1.12096i
$956$		0			0
$957$	−54.0000			−1.74557
$958$		0			0
$959$	17.0000	+	29.4449i	0.548959	+	0.950824i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	−12.0000	−	20.7846i	−0.386695	−	0.669775i
$964$		0			0
$965$	10.0000	+	17.3205i	0.321911	+	0.557567i
$966$		0			0
$967$	−7.00000	+	12.1244i	−0.225105	+	0.389893i	−0.956351	−	0.292221i	$-0.905606\pi$
$967$	−7.00000	+	12.1244i	−0.225105	+	0.389893i	0.731246	+	0.682114i	$0.238939\pi$
$968$		0			0
$969$	−9.00000	+	77.9423i	−0.289122	+	2.50387i
$970$		0			0
$971$	27.5000	−	47.6314i	0.882517	−	1.52856i	0.0339836	−	0.999422i	$-0.489181\pi$
$971$	27.5000	−	47.6314i	0.882517	−	1.52856i	0.848533	−	0.529142i	$-0.177486\pi$
$972$		0			0
$973$	7.00000	+	12.1244i	0.224410	+	0.388689i
$974$		0			0
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$		0			0
$977$	−59.0000			−1.88758			−0.943789	−	0.330550i	$-0.892766\pi$
$977$	−59.0000			−1.88758			−0.943789	+	0.330550i	$0.892766\pi$
$978$		0			0
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$		0			0
$981$	−96.0000			−3.06504
$982$		0			0
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	−0.945705	−	0.325027i	$-0.894626\pi$
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	0.754334	+	0.656490i	$0.227960\pi$
$984$		0			0
$985$	−12.0000	+	20.7846i	−0.382352	+	0.662253i
$986$		0			0
$987$	60.0000			1.90982
$988$		0			0
$989$	−32.0000			−1.01754
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$		0			0
$993$	37.5000	−	64.9519i	1.19003	−	2.06119i
$994$		0			0
$995$	20.0000			0.634043
$996$		0			0
$997$	17.0000	+	29.4449i	0.538395	+	0.932528i	0.998991	+	0.0449179i	$0.0143026\pi$
$997$	17.0000	+	29.4449i	0.538395	+	0.932528i	−0.460595	+	0.887610i	$0.652364\pi$
$998$		0			0
$999$	−72.0000			−2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.j.961.1		2
4.3	odd	2		1216.2.i.a.961.1		2
8.3	odd	2		608.2.i.b.353.1	yes	2
8.5	even	2		608.2.i.a.353.1	✓	2
19.7	even	3	inner	1216.2.i.j.577.1		2
76.7	odd	6		1216.2.i.a.577.1		2
152.45	even	6		608.2.i.a.577.1	yes	2
152.83	odd	6		608.2.i.b.577.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.a.353.1	✓	2	8.5	even	2
608.2.i.a.577.1	yes	2	152.45	even	6
608.2.i.b.353.1	yes	2	8.3	odd	2
608.2.i.b.577.1	yes	2	152.83	odd	6
1216.2.i.a.577.1		2	76.7	odd	6
1216.2.i.a.961.1		2	4.3	odd	2
1216.2.i.j.577.1		2	19.7	even	3	inner
1216.2.i.j.961.1		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} -2.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(1.00000 - 1.73205i) q^{5} -2.00000 q^{7} +(-3.00000 - 5.19615i) q^{9} +3.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(3.00000 - 5.19615i) q^{17} +(-3.50000 - 2.59808i) q^{19} +(-3.00000 + 5.19615i) q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +(-3.00000 - 5.19615i) q^{29} -8.00000 q^{31} +(4.50000 - 7.79423i) q^{33} +(-2.00000 + 3.46410i) q^{35} +8.00000 q^{37} +6.00000 q^{39} +(1.50000 - 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} -12.0000 q^{45} +(-5.00000 - 8.66025i) q^{47} -3.00000 q^{49} +(-9.00000 - 15.5885i) q^{51} +(1.00000 + 1.73205i) q^{53} +(3.00000 - 5.19615i) q^{55} +(-12.0000 + 5.19615i) q^{57} +(-1.50000 + 2.59808i) q^{59} +(7.00000 + 12.1244i) q^{61} +(6.00000 + 10.3923i) q^{63} +4.00000 q^{65} +(3.50000 + 6.06218i) q^{67} +12.0000 q^{69} +(1.00000 - 1.73205i) q^{71} +(-5.50000 + 9.52628i) q^{73} +3.00000 q^{75} -6.00000 q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +15.0000 q^{83} +(-6.00000 - 10.3923i) q^{85} -18.0000 q^{87} +(9.00000 + 15.5885i) q^{89} +(-2.00000 - 3.46410i) q^{91} +(-12.0000 + 20.7846i) q^{93} +(-8.00000 + 3.46410i) q^{95} +(1.50000 - 2.59808i) q^{97} +(-9.00000 - 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 2 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 2 * q^5 - 4 * q^7 - 6 * q^9	\( 2 q + 3 q^{3} + 2 q^{5} - 4 q^{7} - 6 q^{9} + 6 q^{11} + 2 q^{13} - 6 q^{15} + 6 q^{17} - 7 q^{19} - 6 q^{21} + 4 q^{23} + q^{25} - 18 q^{27} - 6 q^{29} - 16 q^{31} + 9 q^{33} - 4 q^{35} + 16 q^{37} + 12 q^{39} + 3 q^{41} - 8 q^{43} - 24 q^{45} - 10 q^{47} - 6 q^{49} - 18 q^{51} + 2 q^{53} + 6 q^{55} - 24 q^{57} - 3 q^{59} + 14 q^{61} + 12 q^{63} + 8 q^{65} + 7 q^{67} + 24 q^{69} + 2 q^{71} - 11 q^{73} + 6 q^{75} - 12 q^{77} + 4 q^{79} - 9 q^{81} + 30 q^{83} - 12 q^{85} - 36 q^{87} + 18 q^{89} - 4 q^{91} - 24 q^{93} - 16 q^{95} + 3 q^{97} - 18 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 2 * q^5 - 4 * q^7 - 6 * q^9 + 6 * q^11 + 2 * q^13 - 6 * q^15 + 6 * q^17 - 7 * q^19 - 6 * q^21 + 4 * q^23 + q^25 - 18 * q^27 - 6 * q^29 - 16 * q^31 + 9 * q^33 - 4 * q^35 + 16 * q^37 + 12 * q^39 + 3 * q^41 - 8 * q^43 - 24 * q^45 - 10 * q^47 - 6 * q^49 - 18 * q^51 + 2 * q^53 + 6 * q^55 - 24 * q^57 - 3 * q^59 + 14 * q^61 + 12 * q^63 + 8 * q^65 + 7 * q^67 + 24 * q^69 + 2 * q^71 - 11 * q^73 + 6 * q^75 - 12 * q^77 + 4 * q^79 - 9 * q^81 + 30 * q^83 - 12 * q^85 - 36 * q^87 + 18 * q^89 - 4 * q^91 - 24 * q^93 - 16 * q^95 + 3 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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