LMFDB - Embedded newform 1960.2.q.y.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.21913473024.16
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 $ x^8 - 2x^7 + 11x^6 - 2x^5 + 51x^4 + 162x^2 + 112x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.3
Root			$1.09199 - 1.89138i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.y.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09199 - 1.89138i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.884883 - 1.53266i) q^{9} +O(q^{10})$	\(q+(1.09199 - 1.89138i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.884883 - 1.53266i) q^{9} +(-1.79910 + 3.11613i) q^{11} -5.85838 q^{13} +2.18398 q^{15} +(-3.18060 + 5.50897i) q^{17} +(2.25141 + 3.89956i) q^{19} +(-1.31407 - 2.27604i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.68681 q^{27} +2.05866 q^{29} +(-3.31407 + 5.74014i) q^{31} +(3.92919 + 6.80556i) q^{33} +(2.95852 + 5.12431i) q^{37} +(-6.39729 + 11.0804i) q^{39} -7.22348 q^{41} -5.34880 q^{43} +(0.884883 - 1.53266i) q^{45} +(1.15942 + 2.00818i) q^{47} +(6.94637 + 12.0315i) q^{51} +(2.05389 - 3.55744i) q^{53} -3.59819 q^{55} +9.83408 q^{57} +(-2.53553 + 4.39167i) q^{59} +(-3.68681 - 6.38574i) q^{61} +(-2.92919 - 5.07351i) q^{65} +(-1.69833 + 2.94160i) q^{67} -5.73981 q^{69} +16.7224 q^{71} +(7.35919 - 12.7465i) q^{73} +(1.09199 + 1.89138i) q^{75} +(1.62752 + 2.81895i) q^{79} +(5.58861 - 9.67976i) q^{81} -10.6936 q^{83} -6.36121 q^{85} +(2.24804 - 3.89371i) q^{87} +(5.57701 + 9.65967i) q^{89} +(7.23787 + 12.5364i) q^{93} +(-2.25141 + 3.89956i) q^{95} -17.1896 q^{97} +6.36796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9	$ 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9} - 2 q^{11} - 20 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{23} - 4 q^{25} - 28 q^{27} - 4 q^{29} - 12 q^{31} + 18 q^{33} - 14 q^{39} - 24 q^{41} - 16 q^{43} + 6 q^{45} - 2 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 20 q^{61} - 10 q^{65} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 16 q^{73} + 2 q^{75} - 22 q^{79} + 20 q^{81} - 72 q^{83} + 12 q^{85} - 18 q^{87} + 40 q^{89} + 32 q^{93} - 52 q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9 - 2 * q^11 - 20 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^23 - 4 * q^25 - 28 * q^27 - 4 * q^29 - 12 * q^31 + 18 * q^33 - 14 * q^39 - 24 * q^41 - 16 * q^43 + 6 * q^45 - 2 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 - 16 * q^57 + 8 * q^59 + 20 * q^61 - 10 * q^65 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 16 * q^73 + 2 * q^75 - 22 * q^79 + 20 * q^81 - 72 * q^83 + 12 * q^85 - 18 * q^87 + 40 * q^89 + 32 * q^93 - 52 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.09199	−	1.89138i	0.630461	−	1.09199i	−0.356997	−	0.934105i	$-0.616199\pi$
$3$	1.09199	−	1.89138i	0.630461	−	1.09199i	0.987458	−	0.157884i	$-0.0504673\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.884883	−	1.53266i	−0.294961	−	0.510887i
$10$		0			0
$11$	−1.79910	+	3.11613i	−0.542448	+	0.939547i	0.456315	+	0.889818i	$0.349169\pi$
$11$	−1.79910	+	3.11613i	−0.542448	+	0.939547i	−0.998763	+	0.0497290i	$0.984164\pi$
$12$		0			0
$13$	−5.85838			−1.62482			−0.812411	−	0.583085i	$-0.801845\pi$
$13$	−5.85838			−1.62482			−0.812411	+	0.583085i	$0.801845\pi$
$14$		0			0
$15$	2.18398			0.563901
$16$		0			0
$17$	−3.18060	+	5.50897i	−0.771410	+	1.33612i	0.165381	+	0.986230i	$0.447115\pi$
$17$	−3.18060	+	5.50897i	−0.771410	+	1.33612i	−0.936791	+	0.349891i	$0.886219\pi$
$18$		0			0
$19$	2.25141	+	3.89956i	0.516510	+	0.894621i	0.999816	+	0.0191698i	$0.00610231\pi$
$19$	2.25141	+	3.89956i	0.516510	+	0.894621i	−0.483307	+	0.875451i	$0.660564\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.31407	−	2.27604i	−0.274003	−	0.474587i	0.695880	−	0.718158i	$-0.255015\pi$
$23$	−1.31407	−	2.27604i	−0.274003	−	0.474587i	−0.969883	+	0.243571i	$0.921681\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.68681			0.517076
$28$		0			0
$29$	2.05866			0.382284			0.191142	−	0.981562i	$-0.438781\pi$
$29$	2.05866			0.382284			0.191142	+	0.981562i	$0.438781\pi$
$30$		0			0
$31$	−3.31407	+	5.74014i	−0.595225	+	1.03096i	0.398290	+	0.917259i	$0.369604\pi$
$31$	−3.31407	+	5.74014i	−0.595225	+	1.03096i	−0.993515	+	0.113700i	$0.963730\pi$
$32$		0			0
$33$	3.92919	+	6.80556i	0.683984	+	1.18470i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.95852	+	5.12431i	0.486378	+	0.842431i	0.999877	−	0.0156589i	$-0.00498458\pi$
$37$	2.95852	+	5.12431i	0.486378	+	0.842431i	−0.513500	+	0.858090i	$0.671651\pi$
$38$		0			0
$39$	−6.39729	+	11.0804i	−1.02439	+	1.77429i
$40$		0			0
$41$	−7.22348			−1.12812			−0.564059	−	0.825734i	$-0.690761\pi$
$41$	−7.22348			−1.12812			−0.564059	+	0.825734i	$0.690761\pi$
$42$		0			0
$43$	−5.34880			−0.815684			−0.407842	−	0.913052i	$-0.633719\pi$
$43$	−5.34880			−0.815684			−0.407842	+	0.913052i	$0.633719\pi$
$44$		0			0
$45$	0.884883	−	1.53266i	0.131911	−	0.228476i
$46$		0			0
$47$	1.15942	+	2.00818i	0.169119	+	0.292923i	0.938110	−	0.346336i	$-0.112574\pi$
$47$	1.15942	+	2.00818i	0.169119	+	0.292923i	−0.768991	+	0.639259i	$0.779241\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	6.94637	+	12.0315i	0.972686	+	1.68474i
$52$		0			0
$53$	2.05389	−	3.55744i	0.282123	−	0.488651i	−0.689784	−	0.724015i	$-0.742295\pi$
$53$	2.05389	−	3.55744i	0.282123	−	0.488651i	0.971907	+	0.235363i	$0.0756280\pi$
$54$		0			0
$55$	−3.59819			−0.485180
$56$		0			0
$57$	9.83408			1.30256
$58$		0			0
$59$	−2.53553	+	4.39167i	−0.330098	+	0.571747i	−0.982531	−	0.186100i	$-0.940415\pi$
$59$	−2.53553	+	4.39167i	−0.330098	+	0.571747i	0.652432	+	0.757847i	$0.273749\pi$
$60$		0			0
$61$	−3.68681	−	6.38574i	−0.472047	−	0.817610i	0.527441	−	0.849591i	$-0.323151\pi$
$61$	−3.68681	−	6.38574i	−0.472047	−	0.817610i	−0.999488	+	0.0319818i	$0.989818\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.92919	−	5.07351i	−0.363321	−	0.629291i
$66$		0			0
$67$	−1.69833	+	2.94160i	−0.207485	+	0.359374i	−0.950921	−	0.309432i	$-0.899861\pi$
$67$	−1.69833	+	2.94160i	−0.207485	+	0.359374i	0.743437	+	0.668806i	$0.233194\pi$
$68$		0			0
$69$	−5.73981			−0.690992
$70$		0			0
$71$	16.7224			1.98459			0.992293	−	0.123917i	$-0.0395457\pi$
$71$	16.7224			1.98459			0.992293	+	0.123917i	$0.0395457\pi$
$72$		0			0
$73$	7.35919	−	12.7465i	0.861328	−	1.49186i	−0.00932043	−	0.999957i	$-0.502967\pi$
$73$	7.35919	−	12.7465i	0.861328	−	1.49186i	0.870648	−	0.491907i	$-0.163700\pi$
$74$		0			0
$75$	1.09199	+	1.89138i	0.126092	+	0.218398i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.62752	+	2.81895i	0.183111	+	0.317157i	0.942938	−	0.332968i	$-0.108050\pi$
$79$	1.62752	+	2.81895i	0.183111	+	0.317157i	−0.759828	+	0.650125i	$0.774717\pi$
$80$		0			0
$81$	5.58861	−	9.67976i	0.620957	−	1.07553i
$82$		0			0
$83$	−10.6936			−1.17377			−0.586885	−	0.809670i	$-0.699646\pi$
$83$	−10.6936			−1.17377			−0.586885	+	0.809670i	$0.699646\pi$
$84$		0			0
$85$	−6.36121			−0.689970
$86$		0			0
$87$	2.24804	−	3.89371i	0.241015	−	0.417450i
$88$		0			0
$89$	5.57701	+	9.65967i	0.591162	+	1.02392i	0.994076	+	0.108685i	$0.0346641\pi$
$89$	5.57701	+	9.65967i	0.591162	+	1.02392i	−0.402914	+	0.915238i	$0.632003\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	7.23787	+	12.5364i	0.750532	+	1.29996i
$94$		0			0
$95$	−2.25141	+	3.89956i	−0.230990	+	0.400087i
$96$		0			0
$97$	−17.1896			−1.74534			−0.872671	−	0.488308i	$-0.837614\pi$
$97$	−17.1896			−1.74534			−0.872671	+	0.488308i	$0.837614\pi$
$98$		0			0
$99$	6.36796			0.640004
$100$		0			0
$101$	1.72065	−	2.98026i	0.171212	−	0.296547i	−0.767632	−	0.640891i	$-0.778565\pi$
$101$	1.72065	−	2.98026i	0.171212	−	0.296547i	0.938844	+	0.344344i	$0.111899\pi$
$102$		0			0
$103$	−5.98785	−	10.3713i	−0.590000	−	1.02191i	−0.994232	−	0.107254i	$-0.965794\pi$
$103$	−5.98785	−	10.3713i	−0.590000	−	1.02191i	0.404231	−	0.914657i	$-0.367539\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.33801	+	9.24570i	0.516045	+	0.893815i	0.999827	+	0.0186269i	$0.00592946\pi$
$107$	5.33801	+	9.24570i	0.516045	+	0.893815i	−0.483782	+	0.875189i	$0.660737\pi$
$108$		0			0
$109$	4.16706	−	7.21755i	0.399131	−	0.691316i	−0.594487	−	0.804105i	$-0.702645\pi$
$109$	4.16706	−	7.21755i	0.399131	−	0.691316i	0.993619	+	0.112789i	$0.0359784\pi$
$110$		0			0
$111$	12.9227			1.22657
$112$		0			0
$113$	−12.1542			−1.14337			−0.571684	−	0.820474i	$-0.693710\pi$
$113$	−12.1542			−1.14337			−0.571684	+	0.820474i	$0.693710\pi$
$114$		0			0
$115$	1.31407	−	2.27604i	0.122538	−	0.212242i
$116$		0			0
$117$	5.18398	+	8.97892i	0.479259	+	0.830101i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.973496	−	1.68614i	−0.0884996	−	0.153286i
$122$		0			0
$123$	−7.88797	+	13.6624i	−0.711234	+	1.23189i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−9.82453			−0.871786			−0.435893	−	0.899998i	$-0.643567\pi$
$127$	−9.82453			−0.871786			−0.435893	+	0.899998i	$0.643567\pi$
$128$		0			0
$129$	−5.84083	+	10.1166i	−0.514257	+	0.890719i
$130$		0			0
$131$	2.47687	+	4.29007i	0.216405	+	0.374825i	0.953706	−	0.300739i	$-0.0972334\pi$
$131$	2.47687	+	4.29007i	0.216405	+	0.374825i	−0.737301	+	0.675564i	$0.763900\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.34340	+	2.32684i	0.115622	+	0.200263i
$136$		0			0
$137$	5.65685	−	9.79796i	0.483298	−	0.837096i	−0.516518	−	0.856276i	$-0.672772\pi$
$137$	5.65685	−	9.79796i	0.483298	−	0.837096i	0.999816	+	0.0191800i	$0.00610555\pi$
$138$		0			0
$139$	−8.70311			−0.738188			−0.369094	−	0.929392i	$-0.620332\pi$
$139$	−8.70311			−0.738188			−0.369094	+	0.929392i	$0.620332\pi$
$140$		0			0
$141$	5.06431			0.426492
$142$		0			0
$143$	10.5398	−	18.2554i	0.881381	−	1.52660i
$144$		0			0
$145$	1.02933	+	1.78285i	0.0854813	+	0.148058i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.22634	+	5.58818i	0.264312	+	0.457802i	0.967383	−	0.253318i	$-0.0815218\pi$
$149$	3.22634	+	5.58818i	0.264312	+	0.457802i	−0.703071	+	0.711119i	$0.748189\pi$
$150$		0			0
$151$	2.01303	−	3.48667i	0.163818	−	0.283741i	−0.772417	−	0.635116i	$-0.780952\pi$
$151$	2.01303	−	3.48667i	0.163818	−	0.283741i	0.936235	+	0.351375i	$0.114286\pi$
$152$		0			0
$153$	11.2578			0.910143
$154$		0			0
$155$	−6.62814			−0.532385
$156$		0			0
$157$	7.76301	−	13.4459i	0.619556	−	1.07310i	−0.370011	−	0.929027i	$-0.620646\pi$
$157$	7.76301	−	13.4459i	0.619556	−	1.07310i	0.989567	−	0.144075i	$-0.0460206\pi$
$158$		0			0
$159$	−4.48565	−	7.76937i	−0.355735	−	0.616151i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	12.4805	+	21.6169i	0.977549	+	1.69316i	0.671254	+	0.741227i	$0.265756\pi$
$163$	12.4805	+	21.6169i	0.977549	+	1.69316i	0.306294	+	0.951937i	$0.400911\pi$
$164$		0			0
$165$	−3.92919	+	6.80556i	−0.305887	+	0.529812i
$166$		0			0
$167$	16.0739			1.24384			0.621919	−	0.783082i	$-0.286353\pi$
$167$	16.0739			1.24384			0.621919	+	0.783082i	$0.286353\pi$
$168$		0			0
$169$	21.3206			1.64005
$170$		0			0
$171$	3.98447	−	6.90131i	0.304700	−	0.527757i
$172$		0			0
$173$	−0.0178027	−	0.0308352i	−0.00135351	−	0.00234436i	0.865348	−	0.501172i	$-0.167098\pi$
$173$	−0.0178027	−	0.0308352i	−0.00135351	−	0.00234436i	−0.866701	+	0.498827i	$0.833764\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.53755	+	9.59132i	0.416228	+	0.720928i
$178$		0			0
$179$	2.22634	−	3.85613i	0.166404	−	0.288221i	−0.770749	−	0.637139i	$-0.780118\pi$
$179$	2.22634	−	3.85613i	0.166404	−	0.288221i	0.937153	+	0.348918i	$0.113451\pi$
$180$		0			0
$181$	22.7377			1.69008			0.845039	−	0.534705i	$-0.179577\pi$
$181$	22.7377			1.69008			0.845039	+	0.534705i	$0.179577\pi$
$182$		0			0
$183$	−16.1038			−1.19043
$184$		0			0
$185$	−2.95852	+	5.12431i	−0.217515	+	0.376747i
$186$		0			0
$187$	−11.4444	−	19.8223i	−0.836899	−	1.44955i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.7760	+	22.1288i	0.924442	+	1.60118i	0.792456	+	0.609929i	$0.208802\pi$
$191$	12.7760	+	22.1288i	0.924442	+	1.60118i	0.131985	+	0.991252i	$0.457865\pi$
$192$		0			0
$193$	−10.5452	+	18.2648i	−0.759059	+	1.31473i	0.184272	+	0.982875i	$0.441007\pi$
$193$	−10.5452	+	18.2648i	−0.759059	+	1.31473i	−0.943331	+	0.331854i	$0.892326\pi$
$194$		0			0
$195$	−12.7946			−0.916239
$196$		0			0
$197$	16.4622			1.17288			0.586442	−	0.809991i	$-0.300528\pi$
$197$	16.4622			1.17288			0.586442	+	0.809991i	$0.300528\pi$
$198$		0			0
$199$	−12.9709	+	22.4663i	−0.919485	+	1.59259i	−0.119285	+	0.992860i	$0.538060\pi$
$199$	−12.9709	+	22.4663i	−0.919485	+	1.59259i	−0.800199	+	0.599734i	$0.795273\pi$
$200$		0			0
$201$	3.70913	+	6.42440i	0.261622	+	0.453142i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.61174	−	6.25572i	−0.252255	−	0.436918i
$206$		0			0
$207$	−2.32560	+	4.02806i	−0.161640	+	0.279969i
$208$		0			0
$209$	−16.2020			−1.12072
$210$		0			0
$211$	8.84877			0.609174			0.304587	−	0.952484i	$-0.401481\pi$
$211$	8.84877			0.609174			0.304587	+	0.952484i	$0.401481\pi$
$212$		0			0
$213$	18.2607	−	31.6285i	1.25120	−	2.16715i
$214$		0			0
$215$	−2.67440	−	4.63220i	−0.182393	−	0.315913i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−16.0723	−	27.8381i	−1.08607	−	1.88112i
$220$		0			0
$221$	18.6332	−	32.2736i	1.25340	−	2.17096i
$222$		0			0
$223$	−4.06042			−0.271906			−0.135953	−	0.990715i	$-0.543410\pi$
$223$	−4.06042			−0.271906			−0.135953	+	0.990715i	$0.543410\pi$
$224$		0			0
$225$	1.76977			0.117984
$226$		0			0
$227$	−5.98032	+	10.3582i	−0.396928	+	0.687499i	−0.993345	−	0.115175i	$-0.963257\pi$
$227$	−5.98032	+	10.3582i	−0.396928	+	0.687499i	0.596417	+	0.802674i	$0.296590\pi$
$228$		0			0
$229$	5.65208	+	9.78969i	0.373500	+	0.646921i	0.990101	−	0.140355i	$-0.0448243\pi$
$229$	5.65208	+	9.78969i	0.373500	+	0.646921i	−0.616601	+	0.787276i	$0.711491\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.6530	−	18.4515i	−0.697898	−	1.20880i	−0.969194	−	0.246299i	$-0.920785\pi$
$233$	−10.6530	−	18.4515i	−0.697898	−	1.20880i	0.271295	−	0.962496i	$-0.412548\pi$
$234$		0			0
$235$	−1.15942	+	2.00818i	−0.0756325	+	0.130999i
$236$		0			0
$237$	7.10896			0.461776
$238$		0			0
$239$	−22.5361			−1.45774			−0.728871	−	0.684651i	$-0.759955\pi$
$239$	−22.5361			−1.45774			−0.728871	+	0.684651i	$0.759955\pi$
$240$		0			0
$241$	−6.42386	+	11.1265i	−0.413798	+	0.716718i	−0.995301	−	0.0968253i	$-0.969131\pi$
$241$	−6.42386	+	11.1265i	−0.413798	+	0.716718i	0.581504	+	0.813544i	$0.302465\pi$
$242$		0			0
$243$	−8.17521	−	14.1599i	−0.524440	−	0.908356i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.1896	−	22.8451i	−0.839236	−	1.45360i
$248$		0			0
$249$	−11.6773	+	20.2256i	−0.740016	+	1.28175i
$250$		0			0
$251$	−23.7361			−1.49821			−0.749103	−	0.662453i	$-0.769515\pi$
$251$	−23.7361			−1.49821			−0.749103	+	0.662453i	$0.769515\pi$
$252$		0			0
$253$	9.45657			0.594530
$254$		0			0
$255$	−6.94637	+	12.0315i	−0.434999	+	0.753440i
$256$		0			0
$257$	6.60697	+	11.4436i	0.412131	+	0.713832i	0.995123	−	0.0986462i	$-0.0314512\pi$
$257$	6.60697	+	11.4436i	0.412131	+	0.713832i	−0.582991	+	0.812478i	$0.698118\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.82167	−	3.15523i	−0.112759	−	0.195304i
$262$		0			0
$263$	14.4266	−	24.9876i	0.889584	−	1.54080i	0.0492151	−	0.998788i	$-0.484328\pi$
$263$	14.4266	−	24.9876i	0.889584	−	1.54080i	0.840368	−	0.542016i	$-0.182339\pi$
$264$		0			0
$265$	4.10777			0.252338
$266$		0			0
$267$	24.3602			1.49082
$268$		0			0
$269$	1.28536	−	2.22631i	0.0783700	−	0.135741i	−0.824177	−	0.566333i	$-0.808362\pi$
$269$	1.28536	−	2.22631i	0.0783700	−	0.135741i	0.902547	+	0.430592i	$0.141695\pi$
$270$		0			0
$271$	3.37361	+	5.84327i	0.204932	+	0.354953i	0.950111	−	0.311911i	$-0.100969\pi$
$271$	3.37361	+	5.84327i	0.204932	+	0.354953i	−0.745179	+	0.666865i	$0.767636\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.79910	−	3.11613i	−0.108490	−	0.187909i
$276$		0			0
$277$	1.62727	−	2.81851i	0.0977730	−	0.169348i	−0.812990	−	0.582278i	$-0.802161\pi$
$277$	1.62727	−	2.81851i	0.0977730	−	0.169348i	0.910763	+	0.412931i	$0.135495\pi$
$278$		0			0
$279$	11.7303			0.702273
$280$		0			0
$281$	−2.55422			−0.152372			−0.0761860	−	0.997094i	$-0.524274\pi$
$281$	−2.55422			−0.152372			−0.0761860	+	0.997094i	$0.524274\pi$
$282$		0			0
$283$	−6.25681	+	10.8371i	−0.371929	+	0.644199i	−0.989862	−	0.142031i	$-0.954637\pi$
$283$	−6.25681	+	10.8371i	−0.371929	+	0.644199i	0.617933	+	0.786230i	$0.287970\pi$
$284$		0			0
$285$	4.91704	+	8.51656i	0.291260	+	0.504478i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−11.7325	−	20.3212i	−0.690145	−	1.19537i
$290$		0			0
$291$	−18.7709	+	32.5122i	−1.10037	+	1.90590i
$292$		0			0
$293$	25.6574			1.49892			0.749460	−	0.662050i	$-0.230313\pi$
$293$	25.6574			1.49892			0.749460	+	0.662050i	$0.230313\pi$
$294$		0			0
$295$	−5.07107			−0.295249
$296$		0			0
$297$	−4.83382	+	8.37243i	−0.280487	+	0.485818i
$298$		0			0
$299$	7.69833	+	13.3339i	0.445206	+	0.771120i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.75787	−	6.50883i	−0.215884	−	0.373922i
$304$		0			0
$305$	3.68681	−	6.38574i	0.211106	−	0.365646i
$306$		0			0
$307$	11.9391			0.681398			0.340699	−	0.940172i	$-0.389336\pi$
$307$	11.9391			0.681398			0.340699	+	0.940172i	$0.389336\pi$
$308$		0			0
$309$	−26.1547			−1.48789
$310$		0			0
$311$	4.24939	−	7.36017i	0.240961	−	0.417357i	−0.720027	−	0.693946i	$-0.755871\pi$
$311$	4.24939	−	7.36017i	0.240961	−	0.417357i	0.960988	+	0.276589i	$0.0892041\pi$
$312$		0			0
$313$	−0.878058	−	1.52084i	−0.0496308	−	0.0859631i	0.840143	−	0.542365i	$-0.182471\pi$
$313$	−0.878058	−	1.52084i	−0.0496308	−	0.0859631i	−0.889774	+	0.456402i	$0.849138\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.98245	−	5.16576i	−0.167511	−	0.290138i	0.770033	−	0.638004i	$-0.220240\pi$
$317$	−2.98245	−	5.16576i	−0.167511	−	0.290138i	−0.937544	+	0.347866i	$0.886906\pi$
$318$		0			0
$319$	−3.70373	+	6.41505i	−0.207369	+	0.359174i
$320$		0			0
$321$	23.3162			1.30138
$322$		0			0
$323$	−28.6434			−1.59376
$324$		0			0
$325$	2.92919	−	5.07351i	0.162482	−	0.281427i
$326$		0			0
$327$	−9.10076	−	15.7630i	−0.503273	−	0.871695i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.05191	+	12.2143i	0.387608	+	0.671357i	0.992127	−	0.125234i	$-0.0399681\pi$
$331$	7.05191	+	12.2143i	0.387608	+	0.671357i	−0.604519	+	0.796590i	$0.706635\pi$
$332$		0			0
$333$	5.23589	−	9.06882i	0.286925	−	0.496968i
$334$		0			0
$335$	−3.39667			−0.185580
$336$		0			0
$337$	−22.8876			−1.24677			−0.623384	−	0.781916i	$-0.714242\pi$
$337$	−22.8876			−1.24677			−0.623384	+	0.781916i	$0.714242\pi$
$338$		0			0
$339$	−13.2722	+	22.9882i	−0.720849	+	1.24855i
$340$		0			0
$341$	−11.9247	−	20.6541i	−0.645757	−	1.11848i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.86991	−	4.97082i	−0.154511	−	0.267620i
$346$		0			0
$347$	11.8293	−	20.4890i	0.635030	−	1.09990i	−0.351478	−	0.936196i	$-0.614321\pi$
$347$	11.8293	−	20.4890i	0.635030	−	1.09990i	0.986509	−	0.163709i	$-0.0523458\pi$
$348$		0			0
$349$	−27.7912			−1.48763			−0.743814	−	0.668386i	$-0.766985\pi$
$349$	−27.7912			−1.48763			−0.743814	+	0.668386i	$0.766985\pi$
$350$		0			0
$351$	−15.7403			−0.840157
$352$		0			0
$353$	10.5840	−	18.3321i	0.563331	−	0.975717i	−0.433872	−	0.900974i	$-0.642853\pi$
$353$	10.5840	−	18.3321i	0.563331	−	0.975717i	0.997203	−	0.0747430i	$-0.0238136\pi$
$354$		0			0
$355$	8.36121	+	14.4820i	0.443767	+	0.768627i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.1421	−	31.4231i	−0.957505	−	1.65845i	−0.728528	−	0.685016i	$-0.759795\pi$
$359$	−18.1421	−	31.4231i	−0.957505	−	1.65845i	−0.228977	−	0.973432i	$-0.573538\pi$
$360$		0			0
$361$	−0.637724	+	1.10457i	−0.0335644	+	0.0581353i
$362$		0			0
$363$	−4.25219			−0.223182
$364$		0			0
$365$	14.7184			0.770395
$366$		0			0
$367$	−15.5793	+	26.9841i	−0.813232	+	1.40856i	0.0973579	+	0.995249i	$0.468961\pi$
$367$	−15.5793	+	26.9841i	−0.813232	+	1.40856i	−0.910590	+	0.413310i	$0.864372\pi$
$368$		0			0
$369$	6.39194	+	11.0712i	0.332751	+	0.576341i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	3.33639	+	5.77880i	0.172752	+	0.299215i	0.939381	−	0.342875i	$-0.111401\pi$
$373$	3.33639	+	5.77880i	0.172752	+	0.299215i	−0.766629	+	0.642090i	$0.778067\pi$
$374$		0			0
$375$	−1.09199	+	1.89138i	−0.0563901	+	0.0976705i
$376$		0			0
$377$	−12.0604			−0.621143
$378$		0			0
$379$	21.3984			1.09916			0.549582	−	0.835440i	$-0.314787\pi$
$379$	21.3984			1.09916			0.549582	+	0.835440i	$0.314787\pi$
$380$		0			0
$381$	−10.7283	+	18.5819i	−0.549627	+	0.951981i
$382$		0			0
$383$	1.81726	+	3.14759i	0.0928578	+	0.160834i	0.908713	−	0.417422i	$-0.137066\pi$
$383$	1.81726	+	3.14759i	0.0928578	+	0.160834i	−0.815855	+	0.578257i	$0.803733\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.73306	+	8.19790i	0.240595	+	0.416723i
$388$		0			0
$389$	−10.9476	+	18.9618i	−0.555066	+	0.961403i	0.442832	+	0.896604i	$0.353974\pi$
$389$	−10.9476	+	18.9618i	−0.555066	+	0.961403i	−0.997898	+	0.0647981i	$0.979360\pi$
$390$		0			0
$391$	16.7182			0.845474
$392$		0			0
$393$	10.8189			0.545740
$394$		0			0
$395$	−1.62752	+	2.81895i	−0.0818896	+	0.141837i
$396$		0			0
$397$	−8.98785	−	15.5674i	−0.451087	−	0.781306i	0.547367	−	0.836893i	$-0.315630\pi$
$397$	−8.98785	−	15.5674i	−0.451087	−	0.781306i	−0.998454	+	0.0555869i	$0.982297\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.8172	−	23.9320i	−0.689996	−	1.19511i	−0.971839	−	0.235647i	$-0.924279\pi$
$401$	−13.8172	−	23.9320i	−0.689996	−	1.19511i	0.281843	−	0.959461i	$-0.409054\pi$
$402$		0			0
$403$	19.4151	−	33.6279i	0.967135	−	1.67513i
$404$		0			0
$405$	11.1772			0.555401
$406$		0			0
$407$	−21.2907			−1.05534
$408$		0			0
$409$	−19.9630	+	34.5770i	−0.987108	+	1.70972i	−0.354944	+	0.934887i	$0.615500\pi$
$409$	−19.9630	+	34.5770i	−0.987108	+	1.70972i	−0.632164	+	0.774834i	$0.717833\pi$
$410$		0			0
$411$	−12.3545	−	21.3985i	−0.609400	−	1.05551i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−5.34678	−	9.26089i	−0.262463	−	0.454599i
$416$		0			0
$417$	−9.50371	+	16.4609i	−0.465398	+	0.806094i
$418$		0			0
$419$	−2.89384			−0.141373			−0.0706867	−	0.997499i	$-0.522519\pi$
$419$	−2.89384			−0.141373			−0.0706867	+	0.997499i	$0.522519\pi$
$420$		0			0
$421$	−33.5744			−1.63632			−0.818158	−	0.574993i	$-0.805005\pi$
$421$	−33.5744			−1.63632			−0.818158	+	0.574993i	$0.805005\pi$
$422$		0			0
$423$	2.05191	−	3.55401i	0.0997672	−	0.172802i
$424$		0			0
$425$	−3.18060	−	5.50897i	−0.154282	−	0.267224i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−23.0187	−	39.8695i	−1.11135	−	1.92492i
$430$		0			0
$431$	−0.165441	+	0.286552i	−0.00796902	+	0.0138027i	−0.869982	−	0.493083i	$-0.835870\pi$
$431$	−0.165441	+	0.286552i	−0.00796902	+	0.0138027i	0.862013	+	0.506885i	$0.169203\pi$
$432$		0			0
$433$	0.573752			0.0275727			0.0137864	−	0.999905i	$-0.495612\pi$
$433$	0.573752			0.0275727			0.0137864	+	0.999905i	$0.495612\pi$
$434$		0			0
$435$	4.49607			0.215570
$436$		0			0
$437$	5.91704	−	10.2486i	0.283050	−	0.490258i
$438$		0			0
$439$	−13.7582	−	23.8300i	−0.656645	−	1.13734i	−0.981479	−	0.191571i	$-0.938642\pi$
$439$	−13.7582	−	23.8300i	−0.656645	−	1.13734i	0.324834	−	0.945771i	$-0.394692\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.85838	+	17.0752i	0.468386	+	0.811268i	0.999347	−	0.0361281i	$-0.0115024\pi$
$443$	9.85838	+	17.0752i	0.468386	+	0.811268i	−0.530961	+	0.847396i	$0.678169\pi$
$444$		0			0
$445$	−5.57701	+	9.65967i	−0.264376	+	0.457912i
$446$		0			0
$447$	14.0925			0.666553
$448$		0			0
$449$	32.6751			1.54203			0.771016	−	0.636816i	$-0.219749\pi$
$449$	32.6751			1.54203			0.771016	+	0.636816i	$0.219749\pi$
$450$		0			0
$451$	12.9957	−	22.5093i	0.611945	−	1.05992i
$452$		0			0
$453$	−4.39641	−	7.61481i	−0.206561	−	0.357775i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.87556	−	3.24857i	−0.0877350	−	0.151962i	0.818818	−	0.574053i	$-0.194630\pi$
$457$	−1.87556	−	3.24857i	−0.0877350	−	0.151962i	−0.906553	+	0.422091i	$0.861296\pi$
$458$		0			0
$459$	−8.54566	+	14.8015i	−0.398877	+	0.690876i
$460$		0			0
$461$	−8.77983			−0.408917			−0.204459	−	0.978875i	$-0.565543\pi$
$461$	−8.77983			−0.408917			−0.204459	+	0.978875i	$0.565543\pi$
$462$		0			0
$463$	−4.78203			−0.222240			−0.111120	−	0.993807i	$-0.535444\pi$
$463$	−4.78203			−0.222240			−0.111120	+	0.993807i	$0.535444\pi$
$464$		0			0
$465$	−7.23787	+	12.5364i	−0.335648	+	0.581359i
$466$		0			0
$467$	10.9599	+	18.9831i	0.507165	+	0.878435i	0.999966	+	0.00829277i	$0.00263970\pi$
$467$	10.9599	+	18.9831i	0.507165	+	0.878435i	−0.492801	+	0.870142i	$0.664027\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−16.9543	−	29.3656i	−0.781211	−	1.35310i
$472$		0			0
$473$	9.62301	−	16.6675i	0.442466	−	0.766374i
$474$		0			0
$475$	−4.50283			−0.206604
$476$		0			0
$477$	−7.26980			−0.332861
$478$		0			0
$479$	2.54431	−	4.40687i	0.116252	−	0.201355i	−0.802027	−	0.597287i	$-0.796245\pi$
$479$	2.54431	−	4.40687i	0.116252	−	0.201355i	0.918280	+	0.395932i	$0.129579\pi$
$480$		0			0
$481$	−17.3321	−	30.0201i	−0.790277	−	1.36880i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.59482	−	14.8867i	−0.390271	−	0.675968i
$486$		0			0
$487$	−4.02518	+	6.97181i	−0.182398	+	0.315923i	−0.942697	−	0.333651i	$-0.891719\pi$
$487$	−4.02518	+	6.97181i	−0.182398	+	0.315923i	0.760299	+	0.649574i	$0.225053\pi$
$488$		0			0
$489$	54.5143			2.46522
$490$		0			0
$491$	12.8081			0.578021			0.289010	−	0.957326i	$-0.406674\pi$
$491$	12.8081			0.578021			0.289010	+	0.957326i	$0.406674\pi$
$492$		0			0
$493$	−6.54778	+	11.3411i	−0.294897	+	0.510777i
$494$		0			0
$495$	3.18398	+	5.51481i	0.143109	+	0.247872i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.2642	+	24.7063i	0.638552	+	1.10601i	0.985751	+	0.168213i	$0.0537997\pi$
$499$	14.2642	+	24.7063i	0.638552	+	1.10601i	−0.347198	+	0.937792i	$0.612867\pi$
$500$		0			0
$501$	17.5526	−	30.4019i	0.784191	−	1.35826i
$502$		0			0
$503$	6.56948			0.292919			0.146459	−	0.989217i	$-0.453212\pi$
$503$	6.56948			0.292919			0.146459	+	0.989217i	$0.453212\pi$
$504$		0			0
$505$	3.44131			0.153136
$506$		0			0
$507$	23.2819	−	40.3254i	1.03398	−	1.79091i
$508$		0			0
$509$	12.0787	+	20.9209i	0.535379	+	0.927304i	0.999145	+	0.0413458i	$0.0131645\pi$
$509$	12.0787	+	20.9209i	0.535379	+	0.927304i	−0.463766	+	0.885958i	$0.653502\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	6.04911	+	10.4774i	0.267075	+	0.462587i
$514$		0			0
$515$	5.98785	−	10.3713i	0.263856	−	0.457012i
$516$		0			0
$517$	−8.34366			−0.366954
$518$		0			0
$519$	−0.0777615			−0.00341335
$520$		0			0
$521$	10.4315	−	18.0679i	0.457012	−	0.791568i	−0.541789	−	0.840514i	$-0.682253\pi$
$521$	10.4315	−	18.0679i	0.457012	−	0.791568i	0.998801	+	0.0489461i	$0.0155863\pi$
$522$		0			0
$523$	−6.43539	−	11.1464i	−0.281400	−	0.487399i	0.690330	−	0.723495i	$-0.257465\pi$
$523$	−6.43539	−	11.1464i	−0.281400	−	0.487399i	−0.971730	+	0.236096i	$0.924132\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.0815	−	36.5142i	−0.918324	−	1.59058i
$528$		0			0
$529$	8.04643	−	13.9368i	0.349845	−	0.605949i
$530$		0			0
$531$	8.97460			0.389465
$532$		0			0
$533$	42.3179			1.83299
$534$		0			0
$535$	−5.33801	+	9.24570i	−0.230782	+	0.399726i
$536$		0			0
$537$	−4.86228	−	8.42171i	−0.209823	−	0.363424i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.2681	+	21.2489i	0.527446	+	0.913563i	0.999488	+	0.0319870i	$0.0101835\pi$
$541$	12.2681	+	21.2489i	0.527446	+	0.913563i	−0.472043	+	0.881576i	$0.656483\pi$
$542$		0			0
$543$	24.8293	−	43.0056i	1.06553	−	1.84555i
$544$		0			0
$545$	8.33411			0.356994
$546$		0			0
$547$	−27.5781			−1.17916			−0.589578	−	0.807711i	$-0.700706\pi$
$547$	−27.5781			−1.17916			−0.589578	+	0.807711i	$0.700706\pi$
$548$		0			0
$549$	−6.52478	+	11.3013i	−0.278471	+	0.482326i
$550$		0			0
$551$	4.63490	+	8.02788i	0.197453	+	0.341999i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	6.46135	+	11.1914i	0.274269	+	0.475048i
$556$		0			0
$557$	3.30130	−	5.71802i	0.139881	−	0.242280i	−0.787571	−	0.616224i	$-0.788661\pi$
$557$	3.30130	−	5.71802i	0.139881	−	0.242280i	0.927451	+	0.373944i	$0.121995\pi$
$558$		0			0
$559$	31.3353			1.32534
$560$		0			0
$561$	−49.9888			−2.11053
$562$		0			0
$563$	−0.987331	+	1.71011i	−0.0416110	+	0.0720724i	−0.886081	−	0.463531i	$-0.846582\pi$
$563$	−0.987331	+	1.71011i	−0.0416110	+	0.0720724i	0.844470	+	0.535603i	$0.179916\pi$
$564$		0			0
$565$	−6.07709	−	10.5258i	−0.255665	−	0.442825i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.86403	+	10.1568i	0.245833	+	0.425795i	0.962365	−	0.271758i	$-0.0876052\pi$
$569$	5.86403	+	10.1568i	0.245833	+	0.425795i	−0.716532	+	0.697554i	$0.754272\pi$
$570$		0			0
$571$	−2.84987	+	4.93612i	−0.119263	+	0.206570i	−0.919476	−	0.393146i	$-0.871387\pi$
$571$	−2.84987	+	4.93612i	−0.119263	+	0.206570i	0.800213	+	0.599716i	$0.204720\pi$
$572$		0			0
$573$	55.8052			2.33130
$574$		0			0
$575$	2.62814			0.109601
$576$		0			0
$577$	11.6671	−	20.2081i	0.485709	−	0.841272i	−0.514156	−	0.857697i	$-0.671895\pi$
$577$	11.6671	−	20.2081i	0.485709	−	0.841272i	0.999865	+	0.0164241i	$0.00522820\pi$
$578$		0			0
$579$	23.0305	+	39.8899i	0.957114	+	1.65777i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7.39028	+	12.8003i	0.306074	+	0.530136i
$584$		0			0
$585$	−5.18398	+	8.97892i	−0.214331	+	0.371232i
$586$		0			0
$587$	22.8470			0.942997			0.471498	−	0.881867i	$-0.343713\pi$
$587$	22.8470			0.942997			0.471498	+	0.881867i	$0.343713\pi$
$588$		0			0
$589$	−29.8454			−1.22976
$590$		0			0
$591$	17.9766	−	31.1364i	0.739458	−	1.28078i
$592$		0			0
$593$	−7.24051	−	12.5409i	−0.297332	−	0.514994i	0.678193	−	0.734884i	$-0.262763\pi$
$593$	−7.24051	−	12.5409i	−0.297332	−	0.514994i	−0.975525	+	0.219890i	$0.929430\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	28.3282	+	49.0659i	1.15940	+	2.00814i
$598$		0			0
$599$	1.56762	−	2.71520i	0.0640512	−	0.110940i	−0.832222	−	0.554443i	$-0.812931\pi$
$599$	1.56762	−	2.71520i	0.0640512	−	0.110940i	0.896273	+	0.443503i	$0.146265\pi$
$600$		0			0
$601$	−32.2118			−1.31395			−0.656973	−	0.753914i	$-0.728164\pi$
$601$	−32.2118			−1.31395			−0.656973	+	0.753914i	$0.728164\pi$
$602$		0			0
$603$	6.01131			0.244799
$604$		0			0
$605$	0.973496	−	1.68614i	0.0395782	−	0.0685515i
$606$		0			0
$607$	5.57929	+	9.66362i	0.226456	+	0.392234i	0.956755	−	0.290894i	$-0.0939526\pi$
$607$	5.57929	+	9.66362i	0.226456	+	0.392234i	−0.730299	+	0.683128i	$0.760619\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.79234	−	11.7647i	−0.274789	−	0.475948i
$612$		0			0
$613$	−3.76852	+	6.52727i	−0.152209	+	0.263634i	−0.932039	−	0.362357i	$-0.881972\pi$
$613$	−3.76852	+	6.52727i	−0.152209	+	0.263634i	0.779830	+	0.625991i	$0.215305\pi$
$614$		0			0
$615$	−15.7759			−0.636147
$616$		0			0
$617$	−22.7728			−0.916797			−0.458399	−	0.888747i	$-0.651577\pi$
$617$	−22.7728			−0.916797			−0.458399	+	0.888747i	$0.651577\pi$
$618$		0			0
$619$	−0.482383	+	0.835512i	−0.0193886	+	0.0335821i	−0.875557	−	0.483115i	$-0.839505\pi$
$619$	−0.482383	+	0.835512i	−0.0193886	+	0.0335821i	0.856168	+	0.516697i	$0.172839\pi$
$620$		0			0
$621$	−3.53066	−	6.11528i	−0.141680	−	0.245398i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−17.6925	+	30.6442i	−0.706569	+	1.22381i
$628$		0			0
$629$	−37.6395			−1.50079
$630$		0			0
$631$	6.90059			0.274708			0.137354	−	0.990522i	$-0.456140\pi$
$631$	6.90059			0.274708			0.137354	+	0.990522i	$0.456140\pi$
$632$		0			0
$633$	9.66277	−	16.7364i	0.384060	−	0.665212i
$634$		0			0
$635$	−4.91227	−	8.50829i	−0.194937	−	0.337641i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−14.7974	−	25.6298i	−0.585375	−	1.01390i
$640$		0			0
$641$	1.07217	−	1.85705i	0.0423481	−	0.0733490i	−0.844074	−	0.536226i	$-0.819849\pi$
$641$	1.07217	−	1.85705i	0.0423481	−	0.0733490i	0.886423	+	0.462877i	$0.153183\pi$
$642$		0			0
$643$	27.4980			1.08441			0.542207	−	0.840245i	$-0.317589\pi$
$643$	27.4980			1.08441			0.542207	+	0.840245i	$0.317589\pi$
$644$		0			0
$645$	−11.6817			−0.459965
$646$		0			0
$647$	15.4741	−	26.8020i	0.608350	−	1.05369i	−0.383162	−	0.923681i	$-0.625165\pi$
$647$	15.4741	−	26.8020i	0.608350	−	1.05369i	0.991512	−	0.130013i	$-0.0415018\pi$
$648$		0			0
$649$	−9.12334	−	15.8021i	−0.358122	−	0.620286i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.7224	+	34.1602i	0.771798	+	1.33679i	0.936577	+	0.350462i	$0.113975\pi$
$653$	19.7224	+	34.1602i	0.771798	+	1.33679i	−0.164779	+	0.986330i	$0.552691\pi$
$654$		0			0
$655$	−2.47687	+	4.29007i	−0.0967794	+	0.167627i
$656$		0			0
$657$	−26.0481			−1.01623
$658$		0			0
$659$	8.80237			0.342892			0.171446	−	0.985194i	$-0.445156\pi$
$659$	8.80237			0.342892			0.171446	+	0.985194i	$0.445156\pi$
$660$		0			0
$661$	14.0548	−	24.3436i	0.546667	−	0.946855i	−0.451833	−	0.892103i	$-0.649230\pi$
$661$	14.0548	−	24.3436i	0.546667	−	0.946855i	0.998500	−	0.0547525i	$-0.0174370\pi$
$662$		0			0
$663$	−40.6945	−	70.4849i	−1.58044	−	2.73741i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.70523	−	4.68560i	−0.104747	−	0.181427i
$668$		0			0
$669$	−4.43393	+	7.67980i	−0.171426	+	0.296918i
$670$		0			0
$671$	26.5317			1.02424
$672$		0			0
$673$	−14.7933			−0.570241			−0.285121	−	0.958492i	$-0.592034\pi$
$673$	−14.7933			−0.570241			−0.285121	+	0.958492i	$0.592034\pi$
$674$		0			0
$675$	−1.34340	+	2.32684i	−0.0517076	+	0.0895602i
$676$		0			0
$677$	−1.35581	−	2.34833i	−0.0521080	−	0.0902537i	0.838795	−	0.544448i	$-0.183261\pi$
$677$	−1.35581	−	2.34833i	−0.0521080	−	0.0902537i	−0.890903	+	0.454194i	$0.849927\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	13.0609	+	22.6221i	0.500495	+	0.866882i
$682$		0			0
$683$	0.813164	−	1.40844i	0.0311149	−	0.0538925i	−0.850049	−	0.526704i	$-0.823428\pi$
$683$	0.813164	−	1.40844i	0.0311149	−	0.0538925i	0.881164	+	0.472812i	$0.156761\pi$
$684$		0			0
$685$	11.3137			0.432275
$686$		0			0
$687$	24.6880			0.941908
$688$		0			0
$689$	−12.0324	+	20.8408i	−0.458400	+	0.793971i
$690$		0			0
$691$	25.4410	+	44.0652i	0.967823	+	1.67632i	0.701831	+	0.712343i	$0.252366\pi$
$691$	25.4410	+	44.0652i	0.967823	+	1.67632i	0.265992	+	0.963975i	$0.414301\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.35155	−	7.53711i	−0.165064	−	0.285899i
$696$		0			0
$697$	22.9750	−	39.7939i	0.870241	−	1.50730i
$698$		0			0
$699$	−46.5317			−1.75999
$700$		0			0
$701$	7.93106			0.299552			0.149776	−	0.988720i	$-0.452145\pi$
$701$	7.93106			0.299552			0.149776	+	0.988720i	$0.452145\pi$
$702$		0			0
$703$	−13.3217	+	23.0739i	−0.502438	+	0.870247i
$704$		0			0
$705$	2.53216	+	4.38583i	0.0953666	+	0.165180i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.74609	−	15.1487i	−0.328466	−	0.568920i	0.653741	−	0.756718i	$-0.273198\pi$
$709$	−8.74609	−	15.1487i	−0.328466	−	0.568920i	−0.982208	+	0.187798i	$0.939865\pi$
$710$		0			0
$711$	2.88034	−	4.98889i	0.108021	−	0.187098i
$712$		0			0
$713$	17.4197			0.652374
$714$		0			0
$715$	21.0796			0.788332
$716$		0			0
$717$	−24.6092	+	42.6245i	−0.919049	+	1.59184i
$718$		0			0
$719$	9.06468	+	15.7005i	0.338055	+	0.585529i	0.984067	−	0.177798i	$-0.0568975\pi$
$719$	9.06468	+	15.7005i	0.338055	+	0.585529i	−0.646011	+	0.763328i	$0.723564\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	14.0296	+	24.3000i	0.521766	+	0.903725i
$724$		0			0
$725$	−1.02933	+	1.78285i	−0.0382284	+	0.0662135i
$726$		0			0
$727$	−2.42538			−0.0899523			−0.0449761	−	0.998988i	$-0.514321\pi$
$727$	−2.42538			−0.0899523			−0.0449761	+	0.998988i	$0.514321\pi$
$728$		0			0
$729$	−2.17729			−0.0806402
$730$		0			0
$731$	17.0124	−	29.4664i	0.629227	−	1.08985i
$732$		0			0
$733$	−9.88293	−	17.1177i	−0.365035	−	0.632258i	0.623747	−	0.781626i	$-0.285609\pi$
$733$	−9.88293	−	17.1177i	−0.365035	−	0.632258i	−0.988782	+	0.149368i	$0.952276\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.11093	−	10.5844i	−0.225099	−	0.389883i
$738$		0			0
$739$	−19.9533	+	34.5601i	−0.733993	+	1.27131i	0.221171	+	0.975235i	$0.429012\pi$
$739$	−19.9533	+	34.5601i	−0.733993	+	1.27131i	−0.955164	+	0.296078i	$0.904321\pi$
$740$		0			0
$741$	−57.6118			−2.11642
$742$		0			0
$743$	33.0921			1.21403			0.607016	−	0.794689i	$-0.292366\pi$
$743$	33.0921			1.21403			0.607016	+	0.794689i	$0.292366\pi$
$744$		0			0
$745$	−3.22634	+	5.58818i	−0.118204	+	0.204735i
$746$		0			0
$747$	9.46255	+	16.3896i	0.346217	+	0.599665i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	3.49266	+	6.04946i	0.127449	+	0.220748i	0.922688	−	0.385549i	$-0.125988\pi$
$751$	3.49266	+	6.04946i	0.127449	+	0.220748i	−0.795239	+	0.606296i	$0.792654\pi$
$752$		0			0
$753$	−25.9195	+	44.8939i	−0.944560	+	1.63603i
$754$		0			0
$755$	4.02606			0.146523
$756$		0			0
$757$	−24.4796			−0.889725			−0.444863	−	0.895599i	$-0.646747\pi$
$757$	−24.4796			−0.889725			−0.444863	+	0.895599i	$0.646747\pi$
$758$		0			0
$759$	10.3265	−	17.8860i	0.374827	−	0.649220i
$760$		0			0
$761$	4.69756	+	8.13641i	0.170286	+	0.294945i	0.938520	−	0.345225i	$-0.112197\pi$
$761$	4.69756	+	8.13641i	0.170286	+	0.294945i	−0.768234	+	0.640170i	$0.778864\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.62892	+	9.74958i	0.203514	+	0.352497i
$766$		0			0
$767$	14.8541	−	25.7281i	0.536351	−	0.928987i
$768$		0			0
$769$	−29.7183			−1.07167			−0.535835	−	0.844323i	$-0.680003\pi$
$769$	−29.7183			−1.07167			−0.535835	+	0.844323i	$0.680003\pi$
$770$		0			0
$771$	28.8590			1.03933
$772$		0			0
$773$	−19.1054	+	33.0915i	−0.687173	+	1.19022i	0.285576	+	0.958356i	$0.407815\pi$
$773$	−19.1054	+	33.0915i	−0.687173	+	1.19022i	−0.972749	+	0.231862i	$0.925518\pi$
$774$		0			0
$775$	−3.31407	−	5.74014i	−0.119045	−	0.206192i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16.2630	−	28.1684i	−0.582684	−	1.00924i
$780$		0			0
$781$	−30.0852	+	52.1091i	−1.07653	+	1.86461i
$782$		0			0
$783$	5.53122			0.197670
$784$		0			0
$785$	15.5260			0.554148
$786$		0			0
$787$	12.4057	−	21.4873i	0.442215	−	0.765940i	−0.555638	−	0.831424i	$-0.687526\pi$
$787$	12.4057	−	21.4873i	0.442215	−	0.765940i	0.997854	+	0.0654847i	$0.0208594\pi$
$788$		0			0
$789$	−31.5074	−	54.5725i	−1.12169	−	1.94283i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	21.5987	+	37.4101i	0.766993	+	1.32847i
$794$		0			0
$795$	4.48565	−	7.76937i	0.159089	−	0.275551i
$796$		0			0
$797$	22.9296			0.812210			0.406105	−	0.913826i	$-0.366887\pi$
$797$	22.9296			0.812210			0.406105	+	0.913826i	$0.366887\pi$
$798$		0			0
$799$	−14.7507			−0.521841
$800$		0			0
$801$	9.87001	−	17.0954i	0.348740	−	0.604035i
$802$		0			0
$803$	26.4798	+	45.8643i	0.934451	+	1.61852i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.80721	−	4.86222i	−0.0988183	−	0.171158i
$808$		0			0
$809$	17.1360	−	29.6804i	0.602470	−	1.04351i	−0.389976	−	0.920825i	$-0.627517\pi$
$809$	17.1360	−	29.6804i	0.602470	−	1.04351i	0.992446	−	0.122683i	$-0.0391499\pi$
$810$		0			0
$811$	37.5925			1.32005			0.660025	−	0.751244i	$-0.270546\pi$
$811$	37.5925			1.32005			0.660025	+	0.751244i	$0.270546\pi$
$812$		0			0
$813$	14.7358			0.516807
$814$		0			0
$815$	−12.4805	+	21.6169i	−0.437173	+	0.757206i
$816$		0			0
$817$	−12.0424	−	20.8580i	−0.421309	−	0.729728i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.6321	−	27.0757i	−0.545565	−	0.944947i	−0.998571	−	0.0534393i	$-0.982982\pi$
$821$	−15.6321	−	27.0757i	−0.545565	−	0.944947i	0.453006	−	0.891508i	$-0.350352\pi$
$822$		0			0
$823$	9.22260	−	15.9740i	0.321480	−	0.556819i	−0.659314	−	0.751868i	$-0.729153\pi$
$823$	9.22260	−	15.9740i	0.321480	−	0.556819i	0.980794	+	0.195049i	$0.0624865\pi$
$824$		0			0
$825$	−7.85838			−0.273594
$826$		0			0
$827$	14.5931			0.507450			0.253725	−	0.967276i	$-0.418344\pi$
$827$	14.5931			0.507450			0.253725	+	0.967276i	$0.418344\pi$
$828$		0			0
$829$	6.05285	−	10.4838i	0.210224	−	0.364119i	−0.741561	−	0.670886i	$-0.765914\pi$
$829$	6.05285	−	10.4838i	0.210224	−	0.364119i	0.951785	+	0.306767i	$0.0992473\pi$
$830$		0			0
$831$	−3.55392	−	6.15556i	−0.123284	−	0.213534i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.03696	+	13.9204i	0.278131	+	0.481736i
$836$		0			0
$837$	−8.90427	+	15.4226i	−0.307777	+	0.533085i
$838$		0			0
$839$	−13.8245			−0.477276			−0.238638	−	0.971109i	$-0.576701\pi$
$839$	−13.8245			−0.477276			−0.238638	+	0.971109i	$0.576701\pi$
$840$		0			0
$841$	−24.7619			−0.853859
$842$		0			0
$843$	−2.78918	+	4.83101i	−0.0960645	+	0.166389i
$844$		0			0
$845$	10.6603	+	18.4642i	0.366726	+	0.635187i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	13.6647	+	23.6680i	0.468973	+	0.812285i
$850$		0			0
$851$	7.77542	−	13.4674i	0.266538	−	0.461657i
$852$		0			0
$853$	15.7912			0.540680			0.270340	−	0.962765i	$-0.412864\pi$
$853$	15.7912			0.540680			0.270340	+	0.962765i	$0.412864\pi$
$854$		0			0
$855$	7.96895			0.272532
$856$		0			0
$857$	−6.74183	+	11.6772i	−0.230297	+	0.398886i	−0.957895	−	0.287117i	$-0.907303\pi$
$857$	−6.74183	+	11.6772i	−0.230297	+	0.398886i	0.727599	+	0.686003i	$0.240636\pi$
$858$		0			0
$859$	11.9150	+	20.6374i	0.406535	+	0.704140i	0.994499	−	0.104748i	$-0.0334035\pi$
$859$	11.9150	+	20.6374i	0.406535	+	0.704140i	−0.587964	+	0.808887i	$0.700070\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.17796	−	2.04029i	−0.0400983	−	0.0694523i	0.845280	−	0.534324i	$-0.179434\pi$
$863$	−1.17796	−	2.04029i	−0.0400983	−	0.0694523i	−0.885378	+	0.464872i	$0.846100\pi$
$864$		0			0
$865$	0.0178027	−	0.0308352i	0.000605310	−	0.00104843i
$866$		0			0
$867$	−51.2469			−1.74044
$868$		0			0
$869$	−11.7123			−0.397312
$870$		0			0
$871$	9.94948	−	17.2330i	0.337125	−	0.583918i
$872$		0			0
$873$	15.2108	+	26.3459i	0.514808	+	0.891674i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.1446	−	22.7672i	−0.443862	−	0.768792i	0.554110	−	0.832444i	$-0.313059\pi$
$877$	−13.1446	−	22.7672i	−0.443862	−	0.768792i	−0.997972	+	0.0636515i	$0.979725\pi$
$878$		0			0
$879$	28.0176	−	48.5279i	0.945010	−	1.63680i
$880$		0			0
$881$	−46.2476			−1.55812			−0.779061	−	0.626948i	$-0.784304\pi$
$881$	−46.2476			−1.55812			−0.779061	+	0.626948i	$0.784304\pi$
$882$		0			0
$883$	40.1184			1.35009			0.675045	−	0.737777i	$-0.264124\pi$
$883$	40.1184			1.35009			0.675045	+	0.737777i	$0.264124\pi$
$884$		0			0
$885$	−5.53755	+	9.59132i	−0.186143	+	0.322409i
$886$		0			0
$887$	16.3843	+	28.3784i	0.550130	+	0.952853i	0.998265	+	0.0588866i	$0.0187551\pi$
$887$	16.3843	+	28.3784i	0.550130	+	0.952853i	−0.448135	+	0.893966i	$0.647912\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	20.1089	+	34.8297i	0.673674	+	1.16684i
$892$		0			0
$893$	−5.22068	+	9.04249i	−0.174704	+	0.302595i
$894$		0			0
$895$	4.45268			0.148837
$896$		0			0
$897$	33.6260			1.12274
$898$		0			0
$899$	−6.82255	+	11.8170i	−0.227545	+	0.394119i
$900$		0			0
$901$	13.0652	+	22.6296i	0.435265	+	0.753901i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.3688	+	19.6914i	0.377913	+	0.654564i
$906$		0			0
$907$	−2.74355	+	4.75197i	−0.0910980	+	0.157786i	−0.907973	−	0.419028i	$-0.862371\pi$
$907$	−2.74355	+	4.75197i	−0.0910980	+	0.157786i	0.816875	+	0.576814i	$0.195704\pi$
$908$		0			0
$909$	−6.09031			−0.202003
$910$		0			0
$911$	−38.3276			−1.26985			−0.634924	−	0.772574i	$-0.718969\pi$
$911$	−38.3276			−1.26985			−0.634924	+	0.772574i	$0.718969\pi$
$912$		0			0
$913$	19.2387	−	33.3225i	0.636710	−	1.10281i
$914$		0			0
$915$	−8.05191	−	13.9463i	−0.266188	−	0.461051i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	19.3047	+	33.4368i	0.636804	+	1.10298i	0.986130	+	0.165976i	$0.0530773\pi$
$919$	19.3047	+	33.4368i	0.636804	+	1.10298i	−0.349326	+	0.937001i	$0.613589\pi$
$920$		0			0
$921$	13.0373	−	22.5813i	0.429594	−	0.744079i
$922$		0			0
$923$	−97.9662			−3.22460
$924$		0			0
$925$	−5.91704			−0.194551
$926$		0			0
$927$	−10.5971	+	18.3547i	−0.348054	+	0.602848i
$928$		0			0
$929$	19.6694	+	34.0683i	0.645331	+	1.11775i	0.984225	+	0.176921i	$0.0566138\pi$
$929$	19.6694	+	34.0683i	0.645331	+	1.11775i	−0.338894	+	0.940824i	$0.610053\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−9.28059	−	16.0744i	−0.303833	−	0.526254i
$934$		0			0
$935$	11.4444	−	19.8223i	0.374273	−	0.648259i
$936$		0			0
$937$	18.4619			0.603124			0.301562	−	0.953447i	$-0.402492\pi$
$937$	18.4619			0.603124			0.301562	+	0.953447i	$0.402492\pi$
$938$		0			0
$939$	−3.83532			−0.125161
$940$		0			0
$941$	−18.8002	+	32.5630i	−0.612870	+	1.06152i	0.377884	+	0.925853i	$0.376652\pi$
$941$	−18.8002	+	32.5630i	−0.612870	+	1.06152i	−0.990754	+	0.135669i	$0.956682\pi$
$942$		0			0
$943$	9.49218	+	16.4409i	0.309108	+	0.535390i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.7107	+	34.1400i	0.640513	+	1.10940i	0.985318	+	0.170727i	$0.0546116\pi$
$947$	19.7107	+	34.1400i	0.640513	+	1.10940i	−0.344805	+	0.938674i	$0.612055\pi$
$948$		0			0
$949$	−43.1129	+	74.6737i	−1.39950	+	2.42401i
$950$		0			0
$951$	−13.0272			−0.422437
$952$		0			0
$953$	24.4541			0.792148			0.396074	−	0.918219i	$-0.370372\pi$
$953$	24.4541			0.792148			0.396074	+	0.918219i	$0.370372\pi$
$954$		0			0
$955$	−12.7760	+	22.1288i	−0.413423	+	0.716070i
$956$		0			0
$957$	8.08887	+	14.0103i	0.261476	+	0.452890i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−6.46615	−	11.1997i	−0.208586	−	0.361281i
$962$		0			0
$963$	9.44702	−	16.3627i	0.304426	−	0.527281i
$964$		0			0
$965$	−21.0904			−0.678923
$966$		0			0
$967$	22.5757			0.725986			0.362993	−	0.931792i	$-0.381755\pi$
$967$	22.5757			0.725986			0.362993	+	0.931792i	$0.381755\pi$
$968$		0			0
$969$	−31.2783	+	54.1756i	−1.00480	+	1.74037i
$970$		0			0
$971$	17.5818	+	30.4526i	0.564226	+	0.977269i	0.997121	+	0.0758244i	$0.0241588\pi$
$971$	17.5818	+	30.4526i	0.564226	+	0.977269i	−0.432895	+	0.901444i	$0.642508\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−6.39729	−	11.0804i	−0.204877	−	0.354858i
$976$		0			0
$977$	−13.2455	+	22.9419i	−0.423761	+	0.733976i	−0.996304	−	0.0858992i	$-0.972624\pi$
$977$	−13.2455	+	22.9419i	−0.423761	+	0.733976i	0.572543	+	0.819875i	$0.305957\pi$
$978$		0			0
$979$	−40.1343			−1.28270
$980$		0			0
$981$	−14.7494			−0.470913
$982$		0			0
$983$	13.6690	−	23.6754i	0.435974	−	0.755128i	−0.561401	−	0.827544i	$-0.689737\pi$
$983$	13.6690	−	23.6754i	0.435974	−	0.755128i	0.997375	+	0.0724156i	$0.0230708\pi$
$984$		0			0
$985$	8.23111	+	14.2567i	0.262265	+	0.454256i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.02871	+	12.1741i	0.223500	+	0.387113i
$990$		0			0
$991$	−29.9950	+	51.9529i	−0.952823	+	1.65034i	−0.213549	+	0.976932i	$0.568502\pi$
$991$	−29.9950	+	51.9529i	−0.952823	+	1.65034i	−0.739274	+	0.673405i	$0.764831\pi$
$992$		0			0
$993$	30.8024			0.977486
$994$		0			0
$995$	−25.9419			−0.822412
$996$		0			0
$997$	−11.2322	+	19.4548i	−0.355729	+	0.616140i	−0.987242	−	0.159224i	$-0.949101\pi$
$997$	−11.2322	+	19.4548i	−0.355729	+	0.616140i	0.631514	+	0.775365i	$0.282434\pi$
$998$		0			0
$999$	7.94897	+	13.7680i	0.251494	+	0.435601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.y.361.3		8
7.2	even	3	inner	1960.2.q.y.961.3		8
7.3	odd	6		1960.2.a.y.1.3	yes	4
7.4	even	3		1960.2.a.x.1.2	✓	4
7.5	odd	6		1960.2.q.x.961.2		8
7.6	odd	2		1960.2.q.x.361.2		8
28.3	even	6		3920.2.a.cd.1.2		4
28.11	odd	6		3920.2.a.ce.1.3		4
35.4	even	6		9800.2.a.cs.1.3		4
35.24	odd	6		9800.2.a.cl.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.x.1.2	✓	4	7.4	even	3
1960.2.a.y.1.3	yes	4	7.3	odd	6
1960.2.q.x.361.2		8	7.6	odd	2
1960.2.q.x.961.2		8	7.5	odd	6
1960.2.q.y.361.3		8	1.1	even	1	trivial
1960.2.q.y.961.3		8	7.2	even	3	inner
3920.2.a.cd.1.2		4	28.3	even	6
3920.2.a.ce.1.3		4	28.11	odd	6
9800.2.a.cl.1.2		4	35.24	odd	6
9800.2.a.cs.1.3		4	35.4	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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09199 - 1.89138i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.884883 - 1.53266i) q^{9} +O(q^{10})\)	\(q+(1.09199 - 1.89138i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.884883 - 1.53266i) q^{9} +(-1.79910 + 3.11613i) q^{11} -5.85838 q^{13} +2.18398 q^{15} +(-3.18060 + 5.50897i) q^{17} +(2.25141 + 3.89956i) q^{19} +(-1.31407 - 2.27604i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.68681 q^{27} +2.05866 q^{29} +(-3.31407 + 5.74014i) q^{31} +(3.92919 + 6.80556i) q^{33} +(2.95852 + 5.12431i) q^{37} +(-6.39729 + 11.0804i) q^{39} -7.22348 q^{41} -5.34880 q^{43} +(0.884883 - 1.53266i) q^{45} +(1.15942 + 2.00818i) q^{47} +(6.94637 + 12.0315i) q^{51} +(2.05389 - 3.55744i) q^{53} -3.59819 q^{55} +9.83408 q^{57} +(-2.53553 + 4.39167i) q^{59} +(-3.68681 - 6.38574i) q^{61} +(-2.92919 - 5.07351i) q^{65} +(-1.69833 + 2.94160i) q^{67} -5.73981 q^{69} +16.7224 q^{71} +(7.35919 - 12.7465i) q^{73} +(1.09199 + 1.89138i) q^{75} +(1.62752 + 2.81895i) q^{79} +(5.58861 - 9.67976i) q^{81} -10.6936 q^{83} -6.36121 q^{85} +(2.24804 - 3.89371i) q^{87} +(5.57701 + 9.65967i) q^{89} +(7.23787 + 12.5364i) q^{93} +(-2.25141 + 3.89956i) q^{95} -17.1896 q^{97} +6.36796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9	\( 8 q + 2 q^{3} + 4 q^{5} - 6 q^{9} - 2 q^{11} - 20 q^{13} + 4 q^{15} + 6 q^{17} + 4 q^{23} - 4 q^{25} - 28 q^{27} - 4 q^{29} - 12 q^{31} + 18 q^{33} - 14 q^{39} - 24 q^{41} - 16 q^{43} + 6 q^{45} - 2 q^{47} - 2 q^{51} + 4 q^{53} - 4 q^{55} - 16 q^{57} + 8 q^{59} + 20 q^{61} - 10 q^{65} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 16 q^{73} + 2 q^{75} - 22 q^{79} + 20 q^{81} - 72 q^{83} + 12 q^{85} - 18 q^{87} + 40 q^{89} + 32 q^{93} - 52 q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^5 - 6 * q^9 - 2 * q^11 - 20 * q^13 + 4 * q^15 + 6 * q^17 + 4 * q^23 - 4 * q^25 - 28 * q^27 - 4 * q^29 - 12 * q^31 + 18 * q^33 - 14 * q^39 - 24 * q^41 - 16 * q^43 + 6 * q^45 - 2 * q^47 - 2 * q^51 + 4 * q^53 - 4 * q^55 - 16 * q^57 + 8 * q^59 + 20 * q^61 - 10 * q^65 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 16 * q^73 + 2 * q^75 - 22 * q^79 + 20 * q^81 - 72 * q^83 + 12 * q^85 - 18 * q^87 + 40 * q^89 + 32 * q^93 - 52 * q^97 + 24 * q^99

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