LMFDB - Embedded newform 1960.2.q.x.961.2

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			961.2
Root			$1.09199 + 1.89138i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.x.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09199 - 1.89138i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.884883 + 1.53266i) q^{9} +O(q^{10})$	\(q+(-1.09199 - 1.89138i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.884883 + 1.53266i) q^{9} +(-1.79910 - 3.11613i) q^{11} +5.85838 q^{13} +2.18398 q^{15} +(3.18060 + 5.50897i) q^{17} +(-2.25141 + 3.89956i) q^{19} +(-1.31407 + 2.27604i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.68681 q^{27} +2.05866 q^{29} +(3.31407 + 5.74014i) q^{31} +(-3.92919 + 6.80556i) q^{33} +(2.95852 - 5.12431i) q^{37} +(-6.39729 - 11.0804i) q^{39} +7.22348 q^{41} -5.34880 q^{43} +(-0.884883 - 1.53266i) q^{45} +(-1.15942 + 2.00818i) q^{47} +(6.94637 - 12.0315i) q^{51} +(2.05389 + 3.55744i) q^{53} +3.59819 q^{55} +9.83408 q^{57} +(2.53553 + 4.39167i) q^{59} +(3.68681 - 6.38574i) q^{61} +(-2.92919 + 5.07351i) q^{65} +(-1.69833 - 2.94160i) q^{67} +5.73981 q^{69} +16.7224 q^{71} +(-7.35919 - 12.7465i) q^{73} +(-1.09199 + 1.89138i) q^{75} +(1.62752 - 2.81895i) q^{79} +(5.58861 + 9.67976i) q^{81} +10.6936 q^{83} -6.36121 q^{85} +(-2.24804 - 3.89371i) q^{87} +(-5.57701 + 9.65967i) q^{89} +(7.23787 - 12.5364i) q^{93} +(-2.25141 - 3.89956i) q^{95} +17.1896 q^{97} +6.36796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

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

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	−0.987458	−	0.157884i	$-0.949533\pi$
$3$	−1.09199	−	1.89138i	−0.630461	−	1.09199i	0.356997	−	0.934105i	$-0.383801\pi$
$4$		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	−0.998763	−	0.0497290i	$-0.984164\pi$
$11$	−1.79910	−	3.11613i	−0.542448	−	0.939547i	0.456315	−	0.889818i	$-0.349169\pi$
$12$		0			0
$13$	5.85838			1.62482			0.812411	−	0.583085i	$-0.198155\pi$
$13$	5.85838			1.62482			0.812411	+	0.583085i	$0.198155\pi$
$14$		0			0
$15$	2.18398			0.563901
$16$		0			0
$17$	3.18060	+	5.50897i	0.771410	+	1.33612i	0.936791	+	0.349891i	$0.113781\pi$
$17$	3.18060	+	5.50897i	0.771410	+	1.33612i	−0.165381	+	0.986230i	$0.552885\pi$
$18$		0			0
$19$	−2.25141	+	3.89956i	−0.516510	+	0.894621i	0.483307	+	0.875451i	$0.339436\pi$
$19$	−2.25141	+	3.89956i	−0.516510	+	0.894621i	−0.999816	+	0.0191698i	$0.993898\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.31407	+	2.27604i	−0.274003	+	0.474587i	−0.969883	−	0.243571i	$-0.921681\pi$
$23$	−1.31407	+	2.27604i	−0.274003	+	0.474587i	0.695880	+	0.718158i	$0.255015\pi$
$24$		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	0.993515	+	0.113700i	$0.0362704\pi$
$31$	3.31407	+	5.74014i	0.595225	+	1.03096i	−0.398290	+	0.917259i	$0.630396\pi$
$32$		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	−0.513500	−	0.858090i	$-0.671651\pi$
$37$	2.95852	−	5.12431i	0.486378	−	0.842431i	0.999877	+	0.0156589i	$0.00498458\pi$
$38$		0			0
$39$	−6.39729	−	11.0804i	−1.02439	−	1.77429i
$40$		0			0
$41$	7.22348			1.12812			0.564059	−	0.825734i	$-0.309239\pi$
$41$	7.22348			1.12812			0.564059	+	0.825734i	$0.309239\pi$
$42$		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	$-0.887426\pi$
$47$	−1.15942	+	2.00818i	−0.169119	+	0.292923i	0.768991	+	0.639259i	$0.220759\pi$
$48$		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	0.971907	−	0.235363i	$-0.0756280\pi$
$53$	2.05389	+	3.55744i	0.282123	+	0.488651i	−0.689784	+	0.724015i	$0.742295\pi$
$54$		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	$-0.0595847\pi$
$59$	2.53553	+	4.39167i	0.330098	+	0.571747i	−0.652432	+	0.757847i	$0.726251\pi$
$60$		0			0
$61$	3.68681	−	6.38574i	0.472047	−	0.817610i	−0.527441	−	0.849591i	$-0.676849\pi$
$61$	3.68681	−	6.38574i	0.472047	−	0.817610i	0.999488	+	0.0319818i	$0.0101819\pi$
$62$		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	0.743437	−	0.668806i	$-0.233194\pi$
$67$	−1.69833	−	2.94160i	−0.207485	−	0.359374i	−0.950921	+	0.309432i	$0.899861\pi$
$68$		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	−0.870648	−	0.491907i	$-0.836300\pi$
$73$	−7.35919	−	12.7465i	−0.861328	−	1.49186i	0.00932043	−	0.999957i	$-0.497033\pi$
$74$		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	−0.759828	−	0.650125i	$-0.774717\pi$
$79$	1.62752	−	2.81895i	0.183111	−	0.317157i	0.942938	+	0.332968i	$0.108050\pi$
$80$		0			0
$81$	5.58861	+	9.67976i	0.620957	+	1.07553i
$82$		0			0
$83$	10.6936			1.17377			0.586885	−	0.809670i	$-0.300354\pi$
$83$	10.6936			1.17377			0.586885	+	0.809670i	$0.300354\pi$
$84$		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	0.402914	+	0.915238i	$0.367997\pi$
$89$	−5.57701	+	9.65967i	−0.591162	+	1.02392i	−0.994076	+	0.108685i	$0.965336\pi$
$90$		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	$-0.162386\pi$
$97$	17.1896			1.74534			0.872671	+	0.488308i	$0.162386\pi$
$98$		0			0
$99$	6.36796			0.640004
$100$		0			0
$101$	−1.72065	−	2.98026i	−0.171212	−	0.296547i	0.767632	−	0.640891i	$-0.221435\pi$
$101$	−1.72065	−	2.98026i	−0.171212	−	0.296547i	−0.938844	+	0.344344i	$0.888101\pi$
$102$		0			0
$103$	5.98785	−	10.3713i	0.590000	−	1.02191i	−0.404231	−	0.914657i	$-0.632461\pi$
$103$	5.98785	−	10.3713i	0.590000	−	1.02191i	0.994232	−	0.107254i	$-0.0342058\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.33801	−	9.24570i	0.516045	−	0.893815i	−0.483782	−	0.875189i	$-0.660737\pi$
$107$	5.33801	−	9.24570i	0.516045	−	0.893815i	0.999827	−	0.0186269i	$-0.00592946\pi$
$108$		0			0
$109$	4.16706	+	7.21755i	0.399131	+	0.691316i	0.993619	−	0.112789i	$-0.0359784\pi$
$109$	4.16706	+	7.21755i	0.399131	+	0.691316i	−0.594487	+	0.804105i	$0.702645\pi$
$110$		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	$-0.902767\pi$
$131$	−2.47687	+	4.29007i	−0.216405	+	0.374825i	0.737301	+	0.675564i	$0.236100\pi$
$132$		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	0.999816	−	0.0191800i	$-0.00610555\pi$
$137$	5.65685	+	9.79796i	0.483298	+	0.837096i	−0.516518	+	0.856276i	$0.672772\pi$
$138$		0			0
$139$	8.70311			0.738188			0.369094	−	0.929392i	$-0.379668\pi$
$139$	8.70311			0.738188			0.369094	+	0.929392i	$0.379668\pi$
$140$		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	−0.703071	−	0.711119i	$-0.748189\pi$
$149$	3.22634	−	5.58818i	0.264312	−	0.457802i	0.967383	+	0.253318i	$0.0815218\pi$
$150$		0			0
$151$	2.01303	+	3.48667i	0.163818	+	0.283741i	0.936235	−	0.351375i	$-0.114286\pi$
$151$	2.01303	+	3.48667i	0.163818	+	0.283741i	−0.772417	+	0.635116i	$0.780952\pi$
$152$		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	−0.989567	−	0.144075i	$-0.953979\pi$
$157$	−7.76301	−	13.4459i	−0.619556	−	1.07310i	0.370011	−	0.929027i	$-0.379354\pi$
$158$		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	0.306294	−	0.951937i	$-0.400911\pi$
$163$	12.4805	−	21.6169i	0.977549	−	1.69316i	0.671254	−	0.741227i	$-0.265756\pi$
$164$		0			0
$165$	−3.92919	−	6.80556i	−0.305887	−	0.529812i
$166$		0			0
$167$	−16.0739			−1.24384			−0.621919	−	0.783082i	$-0.713647\pi$
$167$	−16.0739			−1.24384			−0.621919	+	0.783082i	$0.713647\pi$
$168$		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	$-0.832902\pi$
$173$	0.0178027	−	0.0308352i	0.00135351	−	0.00234436i	0.866701	+	0.498827i	$0.166236\pi$
$174$		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	0.937153	−	0.348918i	$-0.113451\pi$
$179$	2.22634	+	3.85613i	0.166404	+	0.288221i	−0.770749	+	0.637139i	$0.780118\pi$
$180$		0			0
$181$	−22.7377			−1.69008			−0.845039	−	0.534705i	$-0.820423\pi$
$181$	−22.7377			−1.69008			−0.845039	+	0.534705i	$0.820423\pi$
$182$		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	0.131985	−	0.991252i	$-0.457865\pi$
$191$	12.7760	−	22.1288i	0.924442	−	1.60118i	0.792456	−	0.609929i	$-0.208802\pi$
$192$		0			0
$193$	−10.5452	−	18.2648i	−0.759059	−	1.31473i	−0.943331	−	0.331854i	$-0.892326\pi$
$193$	−10.5452	−	18.2648i	−0.759059	−	1.31473i	0.184272	−	0.982875i	$-0.441007\pi$
$194$		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	0.800199	+	0.599734i	$0.204727\pi$
$199$	12.9709	+	22.4663i	0.919485	+	1.59259i	0.119285	+	0.992860i	$0.461940\pi$
$200$		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	$-0.456590\pi$
$223$	4.06042			0.271906			0.135953	+	0.990715i	$0.456590\pi$
$224$		0			0
$225$	1.76977			0.117984
$226$		0			0
$227$	5.98032	+	10.3582i	0.396928	+	0.687499i	0.993345	−	0.115175i	$-0.0367430\pi$
$227$	5.98032	+	10.3582i	0.396928	+	0.687499i	−0.596417	+	0.802674i	$0.703410\pi$
$228$		0			0
$229$	−5.65208	+	9.78969i	−0.373500	+	0.646921i	−0.990101	−	0.140355i	$-0.955176\pi$
$229$	−5.65208	+	9.78969i	−0.373500	+	0.646921i	0.616601	+	0.787276i	$0.288509\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.6530	+	18.4515i	−0.697898	+	1.20880i	0.271295	+	0.962496i	$0.412548\pi$
$233$	−10.6530	+	18.4515i	−0.697898	+	1.20880i	−0.969194	+	0.246299i	$0.920785\pi$
$234$		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	$-0.0308688\pi$
$241$	6.42386	+	11.1265i	0.413798	+	0.716718i	−0.581504	+	0.813544i	$0.697535\pi$
$242$		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	$-0.230485\pi$
$251$	23.7361			1.49821			0.749103	+	0.662453i	$0.230485\pi$
$252$		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	$-0.968549\pi$
$257$	−6.60697	+	11.4436i	−0.412131	+	0.713832i	0.582991	+	0.812478i	$0.301882\pi$
$258$		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	0.840368	+	0.542016i	$0.182339\pi$
$263$	14.4266	+	24.9876i	0.889584	+	1.54080i	0.0492151	+	0.998788i	$0.484328\pi$
$264$		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	$-0.191638\pi$
$269$	−1.28536	−	2.22631i	−0.0783700	−	0.135741i	−0.902547	+	0.430592i	$0.858305\pi$
$270$		0			0
$271$	−3.37361	+	5.84327i	−0.204932	+	0.354953i	−0.950111	−	0.311911i	$-0.899031\pi$
$271$	−3.37361	+	5.84327i	−0.204932	+	0.354953i	0.745179	+	0.666865i	$0.232364\pi$
$272$		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	0.910763	−	0.412931i	$-0.135495\pi$
$277$	1.62727	+	2.81851i	0.0977730	+	0.169348i	−0.812990	+	0.582278i	$0.802161\pi$
$278$		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	$-0.0453632\pi$
$283$	6.25681	+	10.8371i	0.371929	+	0.644199i	−0.617933	+	0.786230i	$0.712030\pi$
$284$		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	$-0.769687\pi$
$293$	−25.6574			−1.49892			−0.749460	+	0.662050i	$0.769687\pi$
$294$		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	$-0.610664\pi$
$307$	−11.9391			−0.681398			−0.340699	+	0.940172i	$0.610664\pi$
$308$		0			0
$309$	−26.1547			−1.48789
$310$		0			0
$311$	−4.24939	−	7.36017i	−0.240961	−	0.417357i	0.720027	−	0.693946i	$-0.244129\pi$
$311$	−4.24939	−	7.36017i	−0.240961	−	0.417357i	−0.960988	+	0.276589i	$0.910796\pi$
$312$		0			0
$313$	0.878058	−	1.52084i	0.0496308	−	0.0859631i	−0.840143	−	0.542365i	$-0.817529\pi$
$313$	0.878058	−	1.52084i	0.0496308	−	0.0859631i	0.889774	+	0.456402i	$0.150862\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.98245	+	5.16576i	−0.167511	+	0.290138i	−0.937544	−	0.347866i	$-0.886906\pi$
$317$	−2.98245	+	5.16576i	−0.167511	+	0.290138i	0.770033	+	0.638004i	$0.220240\pi$
$318$		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	−0.604519	−	0.796590i	$-0.706635\pi$
$331$	7.05191	−	12.2143i	0.387608	−	0.671357i	0.992127	+	0.125234i	$0.0399681\pi$
$332$		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	0.986509	+	0.163709i	$0.0523458\pi$
$347$	11.8293	+	20.4890i	0.635030	+	1.09990i	−0.351478	+	0.936196i	$0.614321\pi$
$348$		0			0
$349$	27.7912			1.48763			0.743814	−	0.668386i	$-0.233015\pi$
$349$	27.7912			1.48763			0.743814	+	0.668386i	$0.233015\pi$
$350$		0			0
$351$	−15.7403			−0.840157
$352$		0			0
$353$	−10.5840	−	18.3321i	−0.563331	−	0.975717i	−0.997203	−	0.0747430i	$-0.976186\pi$
$353$	−10.5840	−	18.3321i	−0.563331	−	0.975717i	0.433872	−	0.900974i	$-0.357147\pi$
$354$		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	−0.228977	+	0.973432i	$0.573538\pi$
$359$	−18.1421	+	31.4231i	−0.957505	+	1.65845i	−0.728528	+	0.685016i	$0.759795\pi$
$360$		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	0.910590	+	0.413310i	$0.135628\pi$
$367$	15.5793	+	26.9841i	0.813232	+	1.40856i	−0.0973579	+	0.995249i	$0.531039\pi$
$368$		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	−0.766629	−	0.642090i	$-0.778067\pi$
$373$	3.33639	−	5.77880i	0.172752	−	0.299215i	0.939381	+	0.342875i	$0.111401\pi$
$374$		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	$-0.862934\pi$
$383$	−1.81726	+	3.14759i	−0.0928578	+	0.160834i	0.815855	+	0.578257i	$0.196267\pi$
$384$		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	−0.997898	−	0.0647981i	$-0.979360\pi$
$389$	−10.9476	−	18.9618i	−0.555066	−	0.961403i	0.442832	−	0.896604i	$-0.353974\pi$
$390$		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	$-0.684370\pi$
$397$	8.98785	−	15.5674i	0.451087	−	0.781306i	0.998454	+	0.0555869i	$0.0177030\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.8172	+	23.9320i	−0.689996	+	1.19511i	0.281843	+	0.959461i	$0.409054\pi$
$401$	−13.8172	+	23.9320i	−0.689996	+	1.19511i	−0.971839	+	0.235647i	$0.924279\pi$
$402$		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	0.632164	+	0.774834i	$0.282167\pi$
$409$	19.9630	+	34.5770i	0.987108	+	1.70972i	0.354944	+	0.934887i	$0.384500\pi$
$410$		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	$-0.477481\pi$
$419$	2.89384			0.141373			0.0706867	+	0.997499i	$0.477481\pi$
$420$		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	0.862013	−	0.506885i	$-0.169203\pi$
$431$	−0.165441	−	0.286552i	−0.00796902	−	0.0138027i	−0.869982	+	0.493083i	$0.835870\pi$
$432$		0			0
$433$	−0.573752			−0.0275727			−0.0137864	−	0.999905i	$-0.504388\pi$
$433$	−0.573752			−0.0275727			−0.0137864	+	0.999905i	$0.504388\pi$
$434$		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	−0.324834	−	0.945771i	$-0.605308\pi$
$439$	13.7582	−	23.8300i	0.656645	−	1.13734i	0.981479	−	0.191571i	$-0.0613583\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.85838	−	17.0752i	0.468386	−	0.811268i	−0.530961	−	0.847396i	$-0.678169\pi$
$443$	9.85838	−	17.0752i	0.468386	−	0.811268i	0.999347	+	0.0361281i	$0.0115024\pi$
$444$		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	−0.906553	−	0.422091i	$-0.861296\pi$
$457$	−1.87556	+	3.24857i	−0.0877350	+	0.151962i	0.818818	+	0.574053i	$0.194630\pi$
$458$		0			0
$459$	−8.54566	−	14.8015i	−0.398877	−	0.690876i
$460$		0			0
$461$	8.77983			0.408917			0.204459	−	0.978875i	$-0.434457\pi$
$461$	8.77983			0.408917			0.204459	+	0.978875i	$0.434457\pi$
$462$		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	0.492801	+	0.870142i	$0.335973\pi$
$467$	−10.9599	+	18.9831i	−0.507165	+	0.878435i	−0.999966	+	0.00829277i	$0.997360\pi$
$468$		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	$-0.203755\pi$
$479$	−2.54431	−	4.40687i	−0.116252	−	0.201355i	−0.918280	+	0.395932i	$0.870421\pi$
$480$		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	0.760299	−	0.649574i	$-0.225053\pi$
$487$	−4.02518	−	6.97181i	−0.182398	−	0.315923i	−0.942697	+	0.333651i	$0.891719\pi$
$488$		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	−0.347198	−	0.937792i	$-0.612867\pi$
$499$	14.2642	−	24.7063i	0.638552	−	1.10601i	0.985751	−	0.168213i	$-0.0537997\pi$
$500$		0			0
$501$	17.5526	+	30.4019i	0.784191	+	1.35826i
$502$		0			0
$503$	−6.56948			−0.292919			−0.146459	−	0.989217i	$-0.546788\pi$
$503$	−6.56948			−0.292919			−0.146459	+	0.989217i	$0.546788\pi$
$504$		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	0.463766	+	0.885958i	$0.346498\pi$
$509$	−12.0787	+	20.9209i	−0.535379	+	0.927304i	−0.999145	+	0.0413458i	$0.986835\pi$
$510$		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	$-0.317747\pi$
$521$	−10.4315	−	18.0679i	−0.457012	−	0.791568i	−0.998801	+	0.0489461i	$0.984414\pi$
$522$		0			0
$523$	6.43539	−	11.1464i	0.281400	−	0.487399i	−0.690330	−	0.723495i	$-0.742535\pi$
$523$	6.43539	−	11.1464i	0.281400	−	0.487399i	0.971730	+	0.236096i	$0.0758679\pi$
$524$		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	−0.472043	−	0.881576i	$-0.656483\pi$
$541$	12.2681	−	21.2489i	0.527446	−	0.913563i	0.999488	−	0.0319870i	$-0.0101835\pi$
$542$		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	0.927451	−	0.373944i	$-0.121995\pi$
$557$	3.30130	+	5.71802i	0.139881	+	0.242280i	−0.787571	+	0.616224i	$0.788661\pi$
$558$		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	$-0.153418\pi$
$563$	0.987331	+	1.71011i	0.0416110	+	0.0720724i	−0.844470	+	0.535603i	$0.820084\pi$
$564$		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	−0.716532	−	0.697554i	$-0.754272\pi$
$569$	5.86403	−	10.1568i	0.245833	−	0.425795i	0.962365	+	0.271758i	$0.0876052\pi$
$570$		0			0
$571$	−2.84987	−	4.93612i	−0.119263	−	0.206570i	0.800213	−	0.599716i	$-0.204720\pi$
$571$	−2.84987	−	4.93612i	−0.119263	−	0.206570i	−0.919476	+	0.393146i	$0.871387\pi$
$572$		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	$-0.328105\pi$
$577$	−11.6671	−	20.2081i	−0.485709	−	0.841272i	−0.999865	+	0.0164241i	$0.994772\pi$
$578$		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	$-0.656287\pi$
$587$	−22.8470			−0.942997			−0.471498	+	0.881867i	$0.656287\pi$
$588$		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	$-0.737237\pi$
$593$	7.24051	−	12.5409i	0.297332	−	0.514994i	0.975525	+	0.219890i	$0.0705699\pi$
$594$		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	0.896273	−	0.443503i	$-0.146265\pi$
$599$	1.56762	+	2.71520i	0.0640512	+	0.110940i	−0.832222	+	0.554443i	$0.812931\pi$
$600$		0			0
$601$	32.2118			1.31395			0.656973	−	0.753914i	$-0.271836\pi$
$601$	32.2118			1.31395			0.656973	+	0.753914i	$0.271836\pi$
$602$		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	$-0.906047\pi$
$607$	−5.57929	+	9.66362i	−0.226456	+	0.392234i	0.730299	+	0.683128i	$0.239381\pi$
$608$		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	0.779830	−	0.625991i	$-0.215305\pi$
$613$	−3.76852	−	6.52727i	−0.152209	−	0.263634i	−0.932039	+	0.362357i	$0.881972\pi$
$614$		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	$-0.160495\pi$
$619$	0.482383	+	0.835512i	0.0193886	+	0.0335821i	−0.856168	+	0.516697i	$0.827161\pi$
$620$		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	0.886423	−	0.462877i	$-0.153183\pi$
$641$	1.07217	+	1.85705i	0.0423481	+	0.0733490i	−0.844074	+	0.536226i	$0.819849\pi$
$642$		0			0
$643$	−27.4980			−1.08441			−0.542207	−	0.840245i	$-0.682411\pi$
$643$	−27.4980			−1.08441			−0.542207	+	0.840245i	$0.682411\pi$
$644$		0			0
$645$	−11.6817			−0.459965
$646$		0			0
$647$	−15.4741	−	26.8020i	−0.608350	−	1.05369i	−0.991512	−	0.130013i	$-0.958498\pi$
$647$	−15.4741	−	26.8020i	−0.608350	−	1.05369i	0.383162	−	0.923681i	$-0.374835\pi$
$648$		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	−0.164779	−	0.986330i	$-0.552691\pi$
$653$	19.7224	−	34.1602i	0.771798	−	1.33679i	0.936577	−	0.350462i	$-0.113975\pi$
$654$		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	−0.998500	−	0.0547525i	$-0.982563\pi$
$661$	−14.0548	−	24.3436i	−0.546667	−	0.946855i	0.451833	−	0.892103i	$-0.350770\pi$
$662$		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	$-0.816739\pi$
$677$	1.35581	−	2.34833i	0.0521080	−	0.0902537i	0.890903	+	0.454194i	$0.150073\pi$
$678$		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	0.881164	−	0.472812i	$-0.156761\pi$
$683$	0.813164	+	1.40844i	0.0311149	+	0.0538925i	−0.850049	+	0.526704i	$0.823428\pi$
$684$		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	−0.265992	+	0.963975i	$0.585699\pi$
$691$	−25.4410	+	44.0652i	−0.967823	+	1.67632i	−0.701831	+	0.712343i	$0.747634\pi$
$692$		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	−0.982208	−	0.187798i	$-0.939865\pi$
$709$	−8.74609	+	15.1487i	−0.328466	+	0.568920i	0.653741	+	0.756718i	$0.273198\pi$
$710$		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	$-0.943102\pi$
$719$	−9.06468	+	15.7005i	−0.338055	+	0.585529i	0.646011	+	0.763328i	$0.276436\pi$
$720$		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	$-0.485679\pi$
$727$	2.42538			0.0899523			0.0449761	+	0.998988i	$0.485679\pi$
$728$		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	$-0.714391\pi$
$733$	9.88293	−	17.1177i	0.365035	−	0.632258i	0.988782	+	0.149368i	$0.0477238\pi$
$734$		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	−0.955164	−	0.296078i	$-0.904321\pi$
$739$	−19.9533	−	34.5601i	−0.733993	−	1.27131i	0.221171	−	0.975235i	$-0.429012\pi$
$740$		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	−0.795239	−	0.606296i	$-0.792654\pi$
$751$	3.49266	−	6.04946i	0.127449	−	0.220748i	0.922688	+	0.385549i	$0.125988\pi$
$752$		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	$-0.887803\pi$
$761$	−4.69756	+	8.13641i	−0.170286	+	0.294945i	0.768234	+	0.640170i	$0.221136\pi$
$762$		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	$-0.319997\pi$
$769$	29.7183			1.07167			0.535835	+	0.844323i	$0.319997\pi$
$770$		0			0
$771$	28.8590			1.03933
$772$		0			0
$773$	19.1054	+	33.0915i	0.687173	+	1.19022i	0.972749	+	0.231862i	$0.0744817\pi$
$773$	19.1054	+	33.0915i	0.687173	+	1.19022i	−0.285576	+	0.958356i	$0.592185\pi$
$774$		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	$-0.312474\pi$
$787$	−12.4057	−	21.4873i	−0.442215	−	0.765940i	−0.997854	+	0.0654847i	$0.979141\pi$
$788$		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	$-0.633113\pi$
$797$	−22.9296			−0.812210			−0.406105	+	0.913826i	$0.633113\pi$
$798$		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	0.992446	+	0.122683i	$0.0391499\pi$
$809$	17.1360	+	29.6804i	0.602470	+	1.04351i	−0.389976	+	0.920825i	$0.627517\pi$
$810$		0			0
$811$	−37.5925			−1.32005			−0.660025	−	0.751244i	$-0.729454\pi$
$811$	−37.5925			−1.32005			−0.660025	+	0.751244i	$0.729454\pi$
$812$		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	0.453006	+	0.891508i	$0.350352\pi$
$821$	−15.6321	+	27.0757i	−0.545565	+	0.944947i	−0.998571	+	0.0534393i	$0.982982\pi$
$822$		0			0
$823$	9.22260	+	15.9740i	0.321480	+	0.556819i	0.980794	−	0.195049i	$-0.0624865\pi$
$823$	9.22260	+	15.9740i	0.321480	+	0.556819i	−0.659314	+	0.751868i	$0.729153\pi$
$824$		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	$-0.234086\pi$
$829$	−6.05285	−	10.4838i	−0.210224	−	0.364119i	−0.951785	+	0.306767i	$0.900753\pi$
$830$		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	$-0.423299\pi$
$839$	13.8245			0.477276			0.238638	+	0.971109i	$0.423299\pi$
$840$		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	$-0.587136\pi$
$853$	−15.7912			−0.540680			−0.270340	+	0.962765i	$0.587136\pi$
$854$		0			0
$855$	7.96895			0.272532
$856$		0			0
$857$	6.74183	+	11.6772i	0.230297	+	0.398886i	0.957895	−	0.287117i	$-0.0926970\pi$
$857$	6.74183	+	11.6772i	0.230297	+	0.398886i	−0.727599	+	0.686003i	$0.759364\pi$
$858$		0			0
$859$	−11.9150	+	20.6374i	−0.406535	+	0.704140i	−0.994499	−	0.104748i	$-0.966596\pi$
$859$	−11.9150	+	20.6374i	−0.406535	+	0.704140i	0.587964	+	0.808887i	$0.299930\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.17796	+	2.04029i	−0.0400983	+	0.0694523i	−0.885378	−	0.464872i	$-0.846100\pi$
$863$	−1.17796	+	2.04029i	−0.0400983	+	0.0694523i	0.845280	+	0.534324i	$0.179434\pi$
$864$		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	−0.997972	−	0.0636515i	$-0.979725\pi$
$877$	−13.1446	+	22.7672i	−0.443862	+	0.768792i	0.554110	+	0.832444i	$0.313059\pi$
$878$		0			0
$879$	28.0176	+	48.5279i	0.945010	+	1.63680i
$880$		0			0
$881$	46.2476			1.55812			0.779061	−	0.626948i	$-0.215696\pi$
$881$	46.2476			1.55812			0.779061	+	0.626948i	$0.215696\pi$
$882$		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	0.448135	+	0.893966i	$0.352088\pi$
$887$	−16.3843	+	28.3784i	−0.550130	+	0.952853i	−0.998265	+	0.0588866i	$0.981245\pi$
$888$		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	0.816875	−	0.576814i	$-0.195704\pi$
$907$	−2.74355	−	4.75197i	−0.0910980	−	0.157786i	−0.907973	+	0.419028i	$0.862371\pi$
$908$		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	−0.349326	−	0.937001i	$-0.613589\pi$
$919$	19.3047	−	33.4368i	0.636804	−	1.10298i	0.986130	−	0.165976i	$-0.0530773\pi$
$920$		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	0.338894	+	0.940824i	$0.389947\pi$
$929$	−19.6694	+	34.0683i	−0.645331	+	1.11775i	−0.984225	+	0.176921i	$0.943386\pi$
$930$		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	$-0.597508\pi$
$937$	−18.4619			−0.603124			−0.301562	+	0.953447i	$0.597508\pi$
$938$		0			0
$939$	−3.83532			−0.125161
$940$		0			0
$941$	18.8002	+	32.5630i	0.612870	+	1.06152i	0.990754	+	0.135669i	$0.0433184\pi$
$941$	18.8002	+	32.5630i	0.612870	+	1.06152i	−0.377884	+	0.925853i	$0.623348\pi$
$942$		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	−0.344805	−	0.938674i	$-0.612055\pi$
$947$	19.7107	−	34.1400i	0.640513	−	1.10940i	0.985318	−	0.170727i	$-0.0546116\pi$
$948$		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	0.432895	+	0.901444i	$0.357492\pi$
$971$	−17.5818	+	30.4526i	−0.564226	+	0.977269i	−0.997121	+	0.0758244i	$0.975841\pi$
$972$		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	0.572543	−	0.819875i	$-0.305957\pi$
$977$	−13.2455	−	22.9419i	−0.423761	−	0.733976i	−0.996304	+	0.0858992i	$0.972624\pi$
$978$		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	$-0.310263\pi$
$983$	−13.6690	−	23.6754i	−0.435974	−	0.755128i	−0.997375	+	0.0724156i	$0.976929\pi$
$984$		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	−0.739274	−	0.673405i	$-0.764831\pi$
$991$	−29.9950	−	51.9529i	−0.952823	−	1.65034i	−0.213549	−	0.976932i	$-0.568502\pi$
$992$		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	$-0.0508993\pi$
$997$	11.2322	+	19.4548i	0.355729	+	0.616140i	−0.631514	+	0.775365i	$0.717566\pi$
$998$		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.x.961.2		8
7.2	even	3		1960.2.a.y.1.3	yes	4
7.3	odd	6		1960.2.q.y.361.3		8
7.4	even	3	inner	1960.2.q.x.361.2		8
7.5	odd	6		1960.2.a.x.1.2	✓	4
7.6	odd	2		1960.2.q.y.961.3		8
28.19	even	6		3920.2.a.ce.1.3		4
28.23	odd	6		3920.2.a.cd.1.2		4
35.9	even	6		9800.2.a.cl.1.2		4
35.19	odd	6		9800.2.a.cs.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.x.1.2	✓	4	7.5	odd	6
1960.2.a.y.1.3	yes	4	7.2	even	3
1960.2.q.x.361.2		8	7.4	even	3	inner
1960.2.q.x.961.2		8	1.1	even	1	trivial
1960.2.q.y.361.3		8	7.3	odd	6
1960.2.q.y.961.3		8	7.6	odd	2
3920.2.a.cd.1.2		4	28.23	odd	6
3920.2.a.ce.1.3		4	28.19	even	6
9800.2.a.cl.1.2		4	35.9	even	6
9800.2.a.cs.1.3		4	35.19	odd	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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