LMFDB - Embedded newform 3150.2.m.g.1457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.1457
Dual form			3150.2.m.g.2843.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.41421i q^{11} +(-2.02494 + 2.02494i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(4.37101 - 4.37101i) q^{17} -4.87832i q^{19} +(-2.41421 - 2.41421i) q^{22} +(3.74238 + 3.74238i) q^{23} -2.86370i q^{26} +(0.707107 - 0.707107i) q^{28} +5.21682 q^{29} -4.93942 q^{31} +(0.707107 - 0.707107i) q^{32} +6.18154i q^{34} +(6.87832 + 6.87832i) q^{37} +(3.44949 + 3.44949i) q^{38} -8.77729i q^{41} +(0.174857 - 0.174857i) q^{43} +3.41421 q^{44} -5.29253 q^{46} +(-3.42883 + 3.42883i) q^{47} +1.00000i q^{49} +(2.02494 + 2.02494i) q^{52} +(6.43916 + 6.43916i) q^{53} +1.00000i q^{56} +(-3.68885 + 3.68885i) q^{58} +2.22803 q^{59} -15.2526 q^{61} +(3.49269 - 3.49269i) q^{62} +1.00000i q^{64} +(-3.81382 - 3.81382i) q^{67} +(-4.37101 - 4.37101i) q^{68} +10.9282i q^{71} +(2.51059 - 2.51059i) q^{73} -9.72741 q^{74} -4.87832 q^{76} +(-2.41421 + 2.41421i) q^{77} -9.98414i q^{79} +(6.20648 + 6.20648i) q^{82} +(2.35640 + 2.35640i) q^{83} +0.247285i q^{86} +(-2.41421 + 2.41421i) q^{88} +4.07055 q^{89} -2.86370 q^{91} +(3.74238 - 3.74238i) q^{92} -4.84909i q^{94} +(5.64564 + 5.64564i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 8 q^{13} - 8 q^{14} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 16 q^{37} + 8 q^{38} + 8 q^{43} + 16 q^{44} + 8 q^{46} - 8 q^{47} + 8 q^{52} + 32 q^{53} + 8 q^{58} - 8 q^{59} - 32 q^{61} + 32 q^{62} - 16 q^{67} - 16 q^{74} - 8 q^{77} + 8 q^{82} - 8 q^{83} - 8 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^13 - 8 * q^14 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 16 * q^37 + 8 * q^38 + 8 * q^43 + 16 * q^44 + 8 * q^46 - 8 * q^47 + 8 * q^52 + 32 * q^53 + 8 * q^58 - 8 * q^59 - 32 * q^61 + 32 * q^62 - 16 * q^67 - 16 * q^74 - 8 * q^77 + 8 * q^82 - 8 * q^83 - 8 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$			3.41421i			1.02942i	0.857363	+	0.514712i	$0.172101\pi$
$11$			3.41421i			1.02942i	−0.857363	+	0.514712i	$0.827899\pi$
$12$		0			0
$13$	−2.02494	+	2.02494i	−0.561618	+	0.561618i	−0.929767	−	0.368149i	$-0.879992\pi$
$13$	−2.02494	+	2.02494i	−0.561618	+	0.561618i	0.368149	+	0.929767i	$0.379992\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.37101	−	4.37101i	1.06013	−	1.06013i	0.0620526	−	0.998073i	$-0.480235\pi$
$17$	4.37101	−	4.37101i	1.06013	−	1.06013i	0.998073	−	0.0620526i	$-0.0197646\pi$
$18$		0			0
$19$		−	4.87832i		−	1.11916i	−0.828776	−	0.559581i	$-0.810962\pi$
$19$		−	4.87832i		−	1.11916i	0.828776	−	0.559581i	$-0.189038\pi$
$20$		0			0
$21$		0			0
$22$	−2.41421	−	2.41421i	−0.514712	−	0.514712i
$23$	3.74238	+	3.74238i	0.780341	+	0.780341i	0.979888	−	0.199547i	$-0.0639472\pi$
$23$	3.74238	+	3.74238i	0.780341	+	0.780341i	−0.199547	+	0.979888i	$0.563947\pi$
$24$		0			0
$25$		0			0
$26$		−	2.86370i		−	0.561618i
$27$		0			0
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	5.21682			0.968739			0.484369	−	0.874864i	$-0.339049\pi$
$29$	5.21682			0.968739			0.484369	+	0.874864i	$0.339049\pi$
$30$		0			0
$31$	−4.93942			−0.887145			−0.443573	−	0.896238i	$-0.646289\pi$
$31$	−4.93942			−0.887145			−0.443573	+	0.896238i	$0.646289\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			6.18154i			1.06013i
$35$		0			0
$36$		0			0
$37$	6.87832	+	6.87832i	1.13079	+	1.13079i	0.990046	+	0.140742i	$0.0449487\pi$
$37$	6.87832	+	6.87832i	1.13079	+	1.13079i	0.140742	+	0.990046i	$0.455051\pi$
$38$	3.44949	+	3.44949i	0.559581	+	0.559581i
$39$		0			0
$40$		0			0
$41$		−	8.77729i		−	1.37078i	−0.728175	−	0.685392i	$-0.759631\pi$
$41$		−	8.77729i		−	1.37078i	0.728175	−	0.685392i	$-0.240369\pi$
$42$		0			0
$43$	0.174857	−	0.174857i	0.0266654	−	0.0266654i	−0.693648	−	0.720314i	$-0.743998\pi$
$43$	0.174857	−	0.174857i	0.0266654	−	0.0266654i	0.720314	+	0.693648i	$0.243998\pi$
$44$	3.41421			0.514712
$45$		0			0
$46$	−5.29253			−0.780341
$47$	−3.42883	+	3.42883i	−0.500146	+	0.500146i	−0.911483	−	0.411338i	$-0.865062\pi$
$47$	−3.42883	+	3.42883i	−0.500146	+	0.500146i	0.411338	+	0.911483i	$0.365062\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	2.02494	+	2.02494i	0.280809	+	0.280809i
$53$	6.43916	+	6.43916i	0.884486	+	0.884486i	0.993987	−	0.109500i	$-0.0349251\pi$
$53$	6.43916	+	6.43916i	0.884486	+	0.884486i	−0.109500	+	0.993987i	$0.534925\pi$
$54$		0			0
$55$		0			0
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−3.68885	+	3.68885i	−0.484369	+	0.484369i
$59$	2.22803			0.290065			0.145032	−	0.989427i	$-0.453671\pi$
$59$	2.22803			0.290065			0.145032	+	0.989427i	$0.453671\pi$
$60$		0			0
$61$	−15.2526			−1.95290			−0.976448	−	0.215752i	$-0.930780\pi$
$61$	−15.2526			−1.95290			−0.976448	+	0.215752i	$0.930780\pi$
$62$	3.49269	−	3.49269i	0.443573	−	0.443573i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−3.81382	−	3.81382i	−0.465932	−	0.465932i	0.434662	−	0.900594i	$-0.356868\pi$
$67$	−3.81382	−	3.81382i	−0.465932	−	0.465932i	−0.900594	+	0.434662i	$0.856868\pi$
$68$	−4.37101	−	4.37101i	−0.530063	−	0.530063i
$69$		0			0
$70$		0			0
$71$			10.9282i			1.29694i	0.761241	+	0.648470i	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$		0			0
$73$	2.51059	−	2.51059i	0.293842	−	0.293842i	−0.544754	−	0.838596i	$-0.683377\pi$
$73$	2.51059	−	2.51059i	0.293842	−	0.293842i	0.838596	+	0.544754i	$0.183377\pi$
$74$	−9.72741			−1.13079
$75$		0			0
$76$	−4.87832			−0.559581
$77$	−2.41421	+	2.41421i	−0.275125	+	0.275125i
$78$		0			0
$79$		−	9.98414i		−	1.12330i	−0.827374	−	0.561652i	$-0.810166\pi$
$79$		−	9.98414i		−	1.12330i	0.827374	−	0.561652i	$-0.189834\pi$
$80$		0			0
$81$		0			0
$82$	6.20648	+	6.20648i	0.685392	+	0.685392i
$83$	2.35640	+	2.35640i	0.258648	+	0.258648i	0.824504	−	0.565856i	$-0.191454\pi$
$83$	2.35640	+	2.35640i	0.258648	+	0.258648i	−0.565856	+	0.824504i	$0.691454\pi$
$84$		0			0
$85$		0			0
$86$			0.247285i			0.0266654i
$87$		0			0
$88$	−2.41421	+	2.41421i	−0.257356	+	0.257356i
$89$	4.07055			0.431478			0.215739	−	0.976451i	$-0.430784\pi$
$89$	4.07055			0.431478			0.215739	+	0.976451i	$0.430784\pi$
$90$		0			0
$91$	−2.86370			−0.300198
$92$	3.74238	−	3.74238i	0.390170	−	0.390170i
$93$		0			0
$94$		−	4.84909i		−	0.500146i
$95$		0			0
$96$		0			0
$97$	5.64564	+	5.64564i	0.573228	+	0.573228i	0.933029	−	0.359801i	$-0.117155\pi$
$97$	5.64564	+	5.64564i	0.573228	+	0.573228i	−0.359801	+	0.933029i	$0.617155\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$		0			0
$100$		0			0
$101$			4.91484i			0.489044i	0.969644	+	0.244522i	$0.0786311\pi$
$101$			4.91484i			0.489044i	−0.969644	+	0.244522i	$0.921369\pi$
$102$		0			0
$103$	−8.07019	+	8.07019i	−0.795179	+	0.795179i	−0.982331	−	0.187152i	$-0.940074\pi$
$103$	−8.07019	+	8.07019i	−0.795179	+	0.795179i	0.187152	+	0.982331i	$0.440074\pi$
$104$	−2.86370			−0.280809
$105$		0			0
$106$	−9.10634			−0.884486
$107$	5.77729	−	5.77729i	0.558512	−	0.558512i	−0.370372	−	0.928884i	$-0.620770\pi$
$107$	5.77729	−	5.77729i	0.558512	−	0.558512i	0.928884	+	0.370372i	$0.120770\pi$
$108$		0			0
$109$			6.07712i			0.582083i	0.956710	+	0.291041i	$0.0940017\pi$
$109$			6.07712i			0.582083i	−0.956710	+	0.291041i	$0.905998\pi$
$110$		0			0
$111$		0			0
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	6.76733	+	6.76733i	0.636617	+	0.636617i	0.949719	−	0.313103i	$-0.101368\pi$
$113$	6.76733	+	6.76733i	0.636617	+	0.636617i	−0.313103	+	0.949719i	$0.601368\pi$
$114$		0			0
$115$		0			0
$116$		−	5.21682i		−	0.484369i
$117$		0			0
$118$	−1.57545	+	1.57545i	−0.145032	+	0.145032i
$119$	6.18154			0.566661
$120$		0			0
$121$	−0.656854			−0.0597140
$122$	10.7852	−	10.7852i	0.976448	−	0.976448i
$123$		0			0
$124$			4.93942i			0.443573i
$125$		0			0
$126$		0			0
$127$	11.0345	+	11.0345i	0.979158	+	0.979158i	0.999787	−	0.0206295i	$-0.00656703\pi$
$127$	11.0345	+	11.0345i	0.979158	+	0.979158i	−0.0206295	+	0.999787i	$0.506567\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$		0			0
$131$			2.41370i			0.210886i	0.994425	+	0.105443i	$0.0336260\pi$
$131$			2.41370i			0.210886i	−0.994425	+	0.105443i	$0.966374\pi$
$132$		0			0
$133$	3.44949	−	3.44949i	0.299109	−	0.299109i
$134$	5.39355			0.465932
$135$		0			0
$136$	6.18154			0.530063
$137$	9.39836	−	9.39836i	0.802956	−	0.802956i	−0.180601	−	0.983557i	$-0.557804\pi$
$137$	9.39836	−	9.39836i	0.802956	−	0.802956i	0.983557	+	0.180601i	$0.0578042\pi$
$138$		0			0
$139$			11.2621i			0.955236i	0.878568	+	0.477618i	$0.158500\pi$
$139$			11.2621i			0.955236i	−0.878568	+	0.477618i	$0.841500\pi$
$140$		0			0
$141$		0			0
$142$	−7.72741	−	7.72741i	−0.648470	−	0.648470i
$143$	−6.91359	−	6.91359i	−0.578144	−	0.578144i
$144$		0			0
$145$		0			0
$146$			3.55051i			0.293842i
$147$		0			0
$148$	6.87832	−	6.87832i	0.565394	−	0.565394i
$149$	3.18759			0.261138			0.130569	−	0.991439i	$-0.458320\pi$
$149$	3.18759			0.261138			0.130569	+	0.991439i	$0.458320\pi$
$150$		0			0
$151$	1.80725			0.147072			0.0735359	−	0.997293i	$-0.476572\pi$
$151$	1.80725			0.147072			0.0735359	+	0.997293i	$0.476572\pi$
$152$	3.44949	−	3.44949i	0.279791	−	0.279791i
$153$		0			0
$154$		−	3.41421i		−	0.275125i
$155$		0			0
$156$		0			0
$157$	12.8577	+	12.8577i	1.02615	+	1.02615i	0.999649	+	0.0265035i	$0.00843732\pi$
$157$	12.8577	+	12.8577i	1.02615	+	1.02615i	0.0265035	+	0.999649i	$0.491563\pi$
$158$	7.05986	+	7.05986i	0.561652	+	0.561652i
$159$		0			0
$160$		0			0
$161$			5.29253i			0.417110i
$162$		0			0
$163$	10.0884	−	10.0884i	0.790188	−	0.790188i	−0.191336	−	0.981525i	$-0.561282\pi$
$163$	10.0884	−	10.0884i	0.790188	−	0.790188i	0.981525	+	0.191336i	$0.0612821\pi$
$164$	−8.77729			−0.685392
$165$		0			0
$166$	−3.33245			−0.258648
$167$	3.31319	−	3.31319i	0.256383	−	0.256383i	−0.567199	−	0.823581i	$-0.691973\pi$
$167$	3.31319	−	3.31319i	0.256383	−	0.256383i	0.823581	+	0.567199i	$0.191973\pi$
$168$		0			0
$169$			4.79920i			0.369169i
$170$		0			0
$171$		0			0
$172$	−0.174857	−	0.174857i	−0.0133327	−	0.0133327i
$173$	8.88437	+	8.88437i	0.675466	+	0.675466i	0.958971	−	0.283505i	$-0.0914972\pi$
$173$	8.88437	+	8.88437i	0.675466	+	0.675466i	−0.283505	+	0.958971i	$0.591497\pi$
$174$		0			0
$175$		0			0
$176$		−	3.41421i		−	0.257356i
$177$		0			0
$178$	−2.87832	+	2.87832i	−0.215739	+	0.215739i
$179$	24.6556			1.84285			0.921423	−	0.388560i	$-0.127027\pi$
$179$	24.6556			1.84285			0.921423	+	0.388560i	$0.127027\pi$
$180$		0			0
$181$	−13.2432			−0.984356			−0.492178	−	0.870495i	$-0.663799\pi$
$181$	−13.2432			−0.984356			−0.492178	+	0.870495i	$0.663799\pi$
$182$	2.02494	−	2.02494i	0.150099	−	0.150099i
$183$		0			0
$184$			5.29253i			0.390170i
$185$		0			0
$186$		0			0
$187$	14.9236	+	14.9236i	1.09132	+	1.09132i
$188$	3.42883	+	3.42883i	0.250073	+	0.250073i
$189$		0			0
$190$		0			0
$191$			19.7228i			1.42709i	0.700610	+	0.713545i	$0.252911\pi$
$191$			19.7228i			1.42709i	−0.700610	+	0.713545i	$0.747089\pi$
$192$		0			0
$193$	−7.01461	+	7.01461i	−0.504923	+	0.504923i	−0.912964	−	0.408041i	$-0.866212\pi$
$193$	−7.01461	+	7.01461i	−0.504923	+	0.504923i	0.408041	+	0.912964i	$0.366212\pi$
$194$	−7.98414			−0.573228
$195$		0			0
$196$	1.00000			0.0714286
$197$	−17.5394	+	17.5394i	−1.24963	+	1.24963i	−0.293752	+	0.955882i	$0.594904\pi$
$197$	−17.5394	+	17.5394i	−1.24963	+	1.24963i	−0.955882	+	0.293752i	$0.905096\pi$
$198$		0			0
$199$		−	15.9683i		−	1.13196i	−0.824418	−	0.565981i	$-0.808498\pi$
$199$		−	15.9683i		−	1.13196i	0.824418	−	0.565981i	$-0.191502\pi$
$200$		0			0
$201$		0			0
$202$	−3.47531	−	3.47531i	−0.244522	−	0.244522i
$203$	3.68885	+	3.68885i	0.258906	+	0.258906i
$204$		0			0
$205$		0			0
$206$		−	11.4130i		−	0.795179i
$207$		0			0
$208$	2.02494	−	2.02494i	0.140405	−	0.140405i
$209$	16.6556			1.15209
$210$		0			0
$211$	−26.2686			−1.80841			−0.904203	−	0.427102i	$-0.859535\pi$
$211$	−26.2686			−1.80841			−0.904203	+	0.427102i	$0.859535\pi$
$212$	6.43916	−	6.43916i	0.442243	−	0.442243i
$213$		0			0
$214$			8.17033i			0.558512i
$215$		0			0
$216$		0			0
$217$	−3.49269	−	3.49269i	−0.237100	−	0.237100i
$218$	−4.29717	−	4.29717i	−0.291041	−	0.291041i
$219$		0			0
$220$		0			0
$221$			17.7021i			1.19077i
$222$		0			0
$223$	−12.6061	+	12.6061i	−0.844166	+	0.844166i	−0.989398	−	0.145232i	$-0.953607\pi$
$223$	−12.6061	+	12.6061i	−0.844166	+	0.844166i	0.145232	+	0.989398i	$0.453607\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−9.57045			−0.636617
$227$	3.02786	−	3.02786i	0.200966	−	0.200966i	−0.599448	−	0.800414i	$-0.704613\pi$
$227$	3.02786	−	3.02786i	0.200966	−	0.200966i	0.800414	+	0.599448i	$0.204613\pi$
$228$		0			0
$229$		−	3.50543i		−	0.231645i	−0.993270	−	0.115823i	$-0.963050\pi$
$229$		−	3.50543i		−	0.231645i	0.993270	−	0.115823i	$-0.0369504\pi$
$230$		0			0
$231$		0			0
$232$	3.68885	+	3.68885i	0.242185	+	0.242185i
$233$	−8.98074	−	8.98074i	−0.588348	−	0.588348i	0.348836	−	0.937184i	$-0.386577\pi$
$233$	−8.98074	−	8.98074i	−0.588348	−	0.588348i	−0.937184	+	0.348836i	$0.886577\pi$
$234$		0			0
$235$		0			0
$236$		−	2.22803i		−	0.145032i
$237$		0			0
$238$	−4.37101	+	4.37101i	−0.283330	+	0.283330i
$239$	−16.4853			−1.06634			−0.533172	−	0.846007i	$-0.679000\pi$
$239$	−16.4853			−1.06634			−0.533172	+	0.846007i	$0.679000\pi$
$240$		0			0
$241$	27.8179			1.79191			0.895954	−	0.444147i	$-0.146493\pi$
$241$	27.8179			1.79191			0.895954	+	0.444147i	$0.146493\pi$
$242$	0.464466	−	0.464466i	0.0298570	−	0.0298570i
$243$		0			0
$244$			15.2526i			0.976448i
$245$		0			0
$246$		0			0
$247$	9.87832	+	9.87832i	0.628542	+	0.628542i
$248$	−3.49269	−	3.49269i	−0.221786	−	0.221786i
$249$		0			0
$250$		0			0
$251$			8.43969i			0.532708i	0.963875	+	0.266354i	$0.0858191\pi$
$251$			8.43969i			0.532708i	−0.963875	+	0.266354i	$0.914181\pi$
$252$		0			0
$253$	−12.7773	+	12.7773i	−0.803302	+	0.803302i
$254$	−15.6052			−0.979158
$255$		0			0
$256$	1.00000			0.0625000
$257$	−14.7275	+	14.7275i	−0.918678	+	0.918678i	−0.996933	−	0.0782557i	$-0.975065\pi$
$257$	−14.7275	+	14.7275i	−0.918678	+	0.918678i	0.0782557	+	0.996933i	$0.475065\pi$
$258$		0			0
$259$			9.72741i			0.604432i
$260$		0			0
$261$		0			0
$262$	−1.70674	−	1.70674i	−0.105443	−	0.105443i
$263$	−3.42919	−	3.42919i	−0.211453	−	0.211453i	0.593432	−	0.804884i	$-0.297773\pi$
$263$	−3.42919	−	3.42919i	−0.211453	−	0.211453i	−0.804884	+	0.593432i	$0.797773\pi$
$264$		0			0
$265$		0			0
$266$			4.87832i			0.299109i
$267$		0			0
$268$	−3.81382	+	3.81382i	−0.232966	+	0.232966i
$269$	5.33510			0.325287			0.162643	−	0.986685i	$-0.447998\pi$
$269$	5.33510			0.325287			0.162643	+	0.986685i	$0.447998\pi$
$270$		0			0
$271$	17.0479			1.03559			0.517794	−	0.855506i	$-0.326754\pi$
$271$	17.0479			1.03559			0.517794	+	0.855506i	$0.326754\pi$
$272$	−4.37101	+	4.37101i	−0.265031	+	0.265031i
$273$		0			0
$274$			13.2913i			0.802956i
$275$		0			0
$276$		0			0
$277$	6.36360	+	6.36360i	0.382351	+	0.382351i	0.871949	−	0.489597i	$-0.162856\pi$
$277$	6.36360	+	6.36360i	0.382351	+	0.382351i	−0.489597	+	0.871949i	$0.662856\pi$
$278$	−7.96348	−	7.96348i	−0.477618	−	0.477618i
$279$		0			0
$280$		0			0
$281$		−	6.14214i		−	0.366409i	−0.983075	−	0.183205i	$-0.941353\pi$
$281$		−	6.14214i		−	0.366409i	0.983075	−	0.183205i	$-0.0586471\pi$
$282$		0			0
$283$	−14.4600	+	14.4600i	−0.859556	+	0.859556i	−0.991286	−	0.131730i	$-0.957947\pi$
$283$	−14.4600	+	14.4600i	−0.859556	+	0.859556i	0.131730	+	0.991286i	$0.457947\pi$
$284$	10.9282			0.648470
$285$		0			0
$286$	9.77729			0.578144
$287$	6.20648	−	6.20648i	0.366357	−	0.366357i
$288$		0			0
$289$		−	21.2114i		−	1.24773i
$290$		0			0
$291$		0			0
$292$	−2.51059	−	2.51059i	−0.146921	−	0.146921i
$293$	3.55708	+	3.55708i	0.207807	+	0.207807i	0.803335	−	0.595528i	$-0.203057\pi$
$293$	3.55708	+	3.55708i	0.207807	+	0.207807i	−0.595528	+	0.803335i	$0.703057\pi$
$294$		0			0
$295$		0			0
$296$			9.72741i			0.565394i
$297$		0			0
$298$	−2.25397	+	2.25397i	−0.130569	+	0.130569i
$299$	−15.1562			−0.876508
$300$		0			0
$301$	0.247285			0.0142533
$302$	−1.27792	+	1.27792i	−0.0735359	+	0.0735359i
$303$		0			0
$304$			4.87832i			0.279791i
$305$		0			0
$306$		0			0
$307$	−4.32729	−	4.32729i	−0.246971	−	0.246971i	0.572755	−	0.819727i	$-0.305875\pi$
$307$	−4.32729	−	4.32729i	−0.246971	−	0.246971i	−0.819727	+	0.572755i	$0.805875\pi$
$308$	2.41421	+	2.41421i	0.137563	+	0.137563i
$309$		0			0
$310$		0			0
$311$		−	3.69537i		−	0.209545i	−0.994496	−	0.104773i	$-0.966589\pi$
$311$		−	3.69537i		−	0.209545i	0.994496	−	0.104773i	$-0.0334114\pi$
$312$		0			0
$313$	13.3390	−	13.3390i	0.753966	−	0.753966i	−0.221251	−	0.975217i	$-0.571014\pi$
$313$	13.3390	−	13.3390i	0.753966	−	0.753966i	0.975217	+	0.221251i	$0.0710140\pi$
$314$	−18.1835			−1.02615
$315$		0			0
$316$	−9.98414			−0.561652
$317$	13.5601	−	13.5601i	0.761612	−	0.761612i	−0.215002	−	0.976614i	$-0.568976\pi$
$317$	13.5601	−	13.5601i	0.761612	−	0.761612i	0.976614	+	0.215002i	$0.0689757\pi$
$318$		0			0
$319$			17.8113i			0.997243i
$320$		0			0
$321$		0			0
$322$	−3.74238	−	3.74238i	−0.208555	−	0.208555i
$323$	−21.3232	−	21.3232i	−1.18645	−	1.18645i
$324$		0			0
$325$		0			0
$326$			14.2672i			0.790188i
$327$		0			0
$328$	6.20648	−	6.20648i	0.342696	−	0.342696i
$329$	−4.84909			−0.267339
$330$		0			0
$331$	12.1849			0.669745			0.334872	−	0.942263i	$-0.391307\pi$
$331$	12.1849			0.669745			0.334872	+	0.942263i	$0.391307\pi$
$332$	2.35640	−	2.35640i	0.129324	−	0.129324i
$333$		0			0
$334$			4.68556i			0.256383i
$335$		0			0
$336$		0			0
$337$	−14.8403	−	14.8403i	−0.808401	−	0.808401i	0.175991	−	0.984392i	$-0.443687\pi$
$337$	−14.8403	−	14.8403i	−0.808401	−	0.808401i	−0.984392	+	0.175991i	$0.943687\pi$
$338$	−3.39355	−	3.39355i	−0.184585	−	0.184585i
$339$		0			0
$340$		0			0
$341$		−	16.8642i		−	0.913249i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	0.247285			0.0133327
$345$		0			0
$346$	−12.5644			−0.675466
$347$	−13.5731	+	13.5731i	−0.728642	+	0.728642i	−0.970349	−	0.241707i	$-0.922293\pi$
$347$	−13.5731	+	13.5731i	−0.728642	+	0.728642i	0.241707	+	0.970349i	$0.422293\pi$
$348$		0			0
$349$		−	23.9467i		−	1.28184i	−0.767608	−	0.640920i	$-0.778553\pi$
$349$		−	23.9467i		−	1.28184i	0.767608	−	0.640920i	$-0.221447\pi$
$350$		0			0
$351$		0			0
$352$	2.41421	+	2.41421i	0.128678	+	0.128678i
$353$	17.0693	+	17.0693i	0.908508	+	0.908508i	0.996152	−	0.0876442i	$-0.0279339\pi$
$353$	17.0693	+	17.0693i	0.908508	+	0.908508i	−0.0876442	+	0.996152i	$0.527934\pi$
$354$		0			0
$355$		0			0
$356$		−	4.07055i		−	0.215739i
$357$		0			0
$358$	−17.4341	+	17.4341i	−0.921423	+	0.921423i
$359$	−11.9223			−0.629236			−0.314618	−	0.949218i	$-0.601876\pi$
$359$	−11.9223			−0.629236			−0.314618	+	0.949218i	$0.601876\pi$
$360$		0			0
$361$	−4.79796			−0.252524
$362$	9.36433	−	9.36433i	0.492178	−	0.492178i
$363$		0			0
$364$			2.86370i			0.150099i
$365$		0			0
$366$		0			0
$367$	17.6572	+	17.6572i	0.921699	+	0.921699i	0.997150	−	0.0754503i	$-0.0240394\pi$
$367$	17.6572	+	17.6572i	0.921699	+	0.921699i	−0.0754503	+	0.997150i	$0.524039\pi$
$368$	−3.74238	−	3.74238i	−0.195085	−	0.195085i
$369$		0			0
$370$		0			0
$371$			9.10634i			0.472778i
$372$		0			0
$373$	16.7980	−	16.7980i	0.869765	−	0.869765i	−0.122681	−	0.992446i	$-0.539149\pi$
$373$	16.7980	−	16.7980i	0.869765	−	0.869765i	0.992446	+	0.122681i	$0.0391491\pi$
$374$	−21.1051			−1.09132
$375$		0			0
$376$	−4.84909			−0.250073
$377$	−10.5638	+	10.5638i	−0.544061	+	0.544061i
$378$		0			0
$379$			14.7821i			0.759306i	0.925129	+	0.379653i	$0.123957\pi$
$379$			14.7821i			0.759306i	−0.925129	+	0.379653i	$0.876043\pi$
$380$		0			0
$381$		0			0
$382$	−13.9461	−	13.9461i	−0.713545	−	0.713545i
$383$	−19.2573	−	19.2573i	−0.984000	−	0.984000i	0.0158744	−	0.999874i	$-0.494947\pi$
$383$	−19.2573	−	19.2573i	−0.984000	−	0.984000i	−0.999874	+	0.0158744i	$0.994947\pi$
$384$		0			0
$385$		0			0
$386$		−	9.92016i		−	0.504923i
$387$		0			0
$388$	5.64564	−	5.64564i	0.286614	−	0.286614i
$389$	7.50397			0.380466			0.190233	−	0.981739i	$-0.439076\pi$
$389$	7.50397			0.380466			0.190233	+	0.981739i	$0.439076\pi$
$390$		0			0
$391$	32.7160			1.65452
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$		0			0
$394$		−	24.8045i		−	1.24963i
$395$		0			0
$396$		0			0
$397$	7.67324	+	7.67324i	0.385109	+	0.385109i	0.872939	−	0.487830i	$-0.162211\pi$
$397$	7.67324	+	7.67324i	0.385109	+	0.385109i	−0.487830	+	0.872939i	$0.662211\pi$
$398$	11.2913	+	11.2913i	0.565981	+	0.565981i
$399$		0			0
$400$		0			0
$401$			1.80828i			0.0903011i	0.998980	+	0.0451506i	$0.0143768\pi$
$401$			1.80828i			0.0903011i	−0.998980	+	0.0451506i	$0.985623\pi$
$402$		0			0
$403$	10.0020	−	10.0020i	0.498237	−	0.498237i
$404$	4.91484			0.244522
$405$		0			0
$406$	−5.21682			−0.258906
$407$	−23.4840	+	23.4840i	−1.16406	+	1.16406i
$408$		0			0
$409$		−	35.3440i		−	1.74765i	−0.486243	−	0.873824i	$-0.661633\pi$
$409$		−	35.3440i		−	1.74765i	0.486243	−	0.873824i	$-0.338367\pi$
$410$		0			0
$411$		0			0
$412$	8.07019	+	8.07019i	0.397590	+	0.397590i
$413$	1.57545	+	1.57545i	0.0775230	+	0.0775230i
$414$		0			0
$415$		0			0
$416$			2.86370i			0.140405i
$417$		0			0
$418$	−11.7773	+	11.7773i	−0.576046	+	0.576046i
$419$	27.4979			1.34336			0.671681	−	0.740841i	$-0.265573\pi$
$419$	27.4979			1.34336			0.671681	+	0.740841i	$0.265573\pi$
$420$		0			0
$421$	−5.86194			−0.285694			−0.142847	−	0.989745i	$-0.545626\pi$
$421$	−5.86194			−0.285694			−0.142847	+	0.989745i	$0.545626\pi$
$422$	18.5747	−	18.5747i	0.904203	−	0.904203i
$423$		0			0
$424$			9.10634i			0.442243i
$425$		0			0
$426$		0			0
$427$	−10.7852	−	10.7852i	−0.521934	−	0.521934i
$428$	−5.77729	−	5.77729i	−0.279256	−	0.279256i
$429$		0			0
$430$		0			0
$431$			21.4794i			1.03463i	0.855796	+	0.517313i	$0.173068\pi$
$431$			21.4794i			1.03463i	−0.855796	+	0.517313i	$0.826932\pi$
$432$		0			0
$433$	−16.0406	+	16.0406i	−0.770862	+	0.770862i	−0.978257	−	0.207395i	$-0.933501\pi$
$433$	−16.0406	+	16.0406i	−0.770862	+	0.770862i	0.207395	+	0.978257i	$0.433501\pi$
$434$	4.93942			0.237100
$435$		0			0
$436$	6.07712			0.291041
$437$	18.2565	−	18.2565i	0.873328	−	0.873328i
$438$		0			0
$439$		−	11.8583i		−	0.565967i	−0.959125	−	0.282984i	$-0.908676\pi$
$439$		−	11.8583i		−	0.565967i	0.959125	−	0.282984i	$-0.0913242\pi$
$440$		0			0
$441$		0			0
$442$	−12.5173	−	12.5173i	−0.595386	−	0.595386i
$443$	19.9223	+	19.9223i	0.946538	+	0.946538i	0.998642	−	0.0521039i	$-0.0165927\pi$
$443$	19.9223	+	19.9223i	0.946538	+	0.946538i	−0.0521039	+	0.998642i	$0.516593\pi$
$444$		0			0
$445$		0			0
$446$		−	17.8277i		−	0.844166i
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	23.6138			1.11440			0.557201	−	0.830377i	$-0.311875\pi$
$449$	23.6138			1.11440			0.557201	+	0.830377i	$0.311875\pi$
$450$		0			0
$451$	29.9676			1.41112
$452$	6.76733	−	6.76733i	0.318308	−	0.318308i
$453$		0			0
$454$			4.28205i			0.200966i
$455$		0			0
$456$		0			0
$457$	−19.4150	−	19.4150i	−0.908196	−	0.908196i	0.0879308	−	0.996127i	$-0.471975\pi$
$457$	−19.4150	−	19.4150i	−0.908196	−	0.908196i	−0.996127	+	0.0879308i	$0.971975\pi$
$458$	2.47871	+	2.47871i	0.115823	+	0.115823i
$459$		0			0
$460$		0			0
$461$			29.8406i			1.38981i	0.719100	+	0.694906i	$0.244554\pi$
$461$			29.8406i			1.38981i	−0.719100	+	0.694906i	$0.755446\pi$
$462$		0			0
$463$	9.13505	−	9.13505i	0.424542	−	0.424542i	−0.462222	−	0.886764i	$-0.652948\pi$
$463$	9.13505	−	9.13505i	0.424542	−	0.424542i	0.886764	+	0.462222i	$0.152948\pi$
$464$	−5.21682			−0.242185
$465$		0			0
$466$	12.7007			0.588348
$467$	−2.03591	+	2.03591i	−0.0942106	+	0.0942106i	−0.752641	−	0.658431i	$-0.771221\pi$
$467$	−2.03591	+	2.03591i	−0.0942106	+	0.0942106i	0.658431	+	0.752641i	$0.271221\pi$
$468$		0			0
$469$		−	5.39355i		−	0.249051i
$470$		0			0
$471$		0			0
$472$	1.57545	+	1.57545i	0.0725162	+	0.0725162i
$473$	0.596999	+	0.596999i	0.0274500	+	0.0274500i
$474$		0			0
$475$		0			0
$476$		−	6.18154i		−	0.283330i
$477$		0			0
$478$	11.6569	−	11.6569i	0.533172	−	0.533172i
$479$	−38.9202			−1.77831			−0.889154	−	0.457608i	$-0.848706\pi$
$479$	−38.9202			−1.77831			−0.889154	+	0.457608i	$0.848706\pi$
$480$		0			0
$481$	−27.8564			−1.27014
$482$	−19.6702	+	19.6702i	−0.895954	+	0.895954i
$483$		0			0
$484$			0.656854i			0.0298570i
$485$		0			0
$486$		0			0
$487$	−23.6040	−	23.6040i	−1.06960	−	1.06960i	−0.997390	−	0.0722080i	$-0.976995\pi$
$487$	−23.6040	−	23.6040i	−1.06960	−	1.06960i	−0.0722080	−	0.997390i	$-0.523005\pi$
$488$	−10.7852	−	10.7852i	−0.488224	−	0.488224i
$489$		0			0
$490$		0			0
$491$			26.4735i			1.19473i	0.801969	+	0.597366i	$0.203786\pi$
$491$			26.4735i			1.19473i	−0.801969	+	0.597366i	$0.796214\pi$
$492$		0			0
$493$	22.8028	−	22.8028i	1.02698	−	1.02698i
$494$	−13.9700			−0.628542
$495$		0			0
$496$	4.93942			0.221786
$497$	−7.72741	+	7.72741i	−0.346622	+	0.346622i
$498$		0			0
$499$			40.3855i			1.80790i	0.427634	+	0.903952i	$0.359347\pi$
$499$			40.3855i			1.80790i	−0.427634	+	0.903952i	$0.640653\pi$
$500$		0			0
$501$		0			0
$502$	−5.96776	−	5.96776i	−0.266354	−	0.266354i
$503$	−18.8113	−	18.8113i	−0.838756	−	0.838756i	0.149940	−	0.988695i	$-0.452092\pi$
$503$	−18.8113	−	18.8113i	−0.838756	−	0.838756i	−0.988695	+	0.149940i	$0.952092\pi$
$504$		0			0
$505$		0			0
$506$		−	18.0698i		−	0.803302i
$507$		0			0
$508$	11.0345	−	11.0345i	0.489579	−	0.489579i
$509$	−28.6793			−1.27119			−0.635594	−	0.772024i	$-0.719245\pi$
$509$	−28.6793			−1.27119			−0.635594	+	0.772024i	$0.719245\pi$
$510$		0			0
$511$	3.55051			0.157065
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	20.8279i		−	0.918678i
$515$		0			0
$516$		0			0
$517$	−11.7067	−	11.7067i	−0.514862	−	0.514862i
$518$	−6.87832	−	6.87832i	−0.302216	−	0.302216i
$519$		0			0
$520$		0			0
$521$		−	16.4916i		−	0.722509i	−0.932467	−	0.361254i	$-0.882349\pi$
$521$		−	16.4916i		−	0.722509i	0.932467	−	0.361254i	$-0.117651\pi$
$522$		0			0
$523$	−22.8596	+	22.8596i	−0.999579	+	0.999579i	−1.00000		0.000420508i	$-0.999866\pi$
$523$	−22.8596	+	22.8596i	−0.999579	+	0.999579i	0.000420508		1.00000i	$0.499866\pi$
$524$	2.41370			0.105443
$525$		0			0
$526$	4.84961			0.211453
$527$	−21.5902	+	21.5902i	−0.940485	+	0.940485i
$528$		0			0
$529$			5.01086i			0.217863i
$530$		0			0
$531$		0			0
$532$	−3.44949	−	3.44949i	−0.149554	−	0.149554i
$533$	17.7735	+	17.7735i	0.769857	+	0.769857i
$534$		0			0
$535$		0			0
$536$		−	5.39355i		−	0.232966i
$537$		0			0
$538$	−3.77249	+	3.77249i	−0.162643	+	0.162643i
$539$	−3.41421			−0.147061
$540$		0			0
$541$	30.4412			1.30877			0.654385	−	0.756161i	$-0.272927\pi$
$541$	30.4412			1.30877			0.654385	+	0.756161i	$0.272927\pi$
$542$	−12.0547	+	12.0547i	−0.517794	+	0.517794i
$543$		0			0
$544$		−	6.18154i		−	0.265031i
$545$		0			0
$546$		0			0
$547$	−22.9103	−	22.9103i	−0.979574	−	0.979574i	0.0202215	−	0.999796i	$-0.493563\pi$
$547$	−22.9103	−	22.9103i	−0.979574	−	0.979574i	−0.999796	+	0.0202215i	$0.993563\pi$
$548$	−9.39836	−	9.39836i	−0.401478	−	0.401478i
$549$		0			0
$550$		0			0
$551$		−	25.4493i		−	1.08418i
$552$		0			0
$553$	7.05986	−	7.05986i	0.300216	−	0.300216i
$554$	−8.99948			−0.382351
$555$		0			0
$556$	11.2621			0.477618
$557$	−4.43612	+	4.43612i	−0.187965	+	0.187965i	−0.794816	−	0.606851i	$-0.792432\pi$
$557$	−4.43612	+	4.43612i	−0.187965	+	0.187965i	0.606851	+	0.794816i	$0.292432\pi$
$558$		0			0
$559$			0.708151i			0.0299516i
$560$		0			0
$561$		0			0
$562$	4.34315	+	4.34315i	0.183205	+	0.183205i
$563$	−8.80589	−	8.80589i	−0.371124	−	0.371124i	0.496763	−	0.867886i	$-0.334522\pi$
$563$	−8.80589	−	8.80589i	−0.371124	−	0.371124i	−0.867886	+	0.496763i	$0.834522\pi$
$564$		0			0
$565$		0			0
$566$		−	20.4495i		−	0.859556i
$567$		0			0
$568$	−7.72741	+	7.72741i	−0.324235	+	0.324235i
$569$	−17.6654			−0.740573			−0.370286	−	0.928918i	$-0.620740\pi$
$569$	−17.6654			−0.740573			−0.370286	+	0.928918i	$0.620740\pi$
$570$		0			0
$571$	30.9852			1.29669			0.648345	−	0.761347i	$-0.275462\pi$
$571$	30.9852			1.29669			0.648345	+	0.761347i	$0.275462\pi$
$572$	−6.91359	+	6.91359i	−0.289072	+	0.289072i
$573$		0			0
$574$			8.77729i			0.366357i
$575$		0			0
$576$		0			0
$577$	16.4860	+	16.4860i	0.686322	+	0.686322i	0.961417	−	0.275095i	$-0.0887094\pi$
$577$	16.4860	+	16.4860i	0.686322	+	0.686322i	−0.275095	+	0.961417i	$0.588709\pi$
$578$	14.9988	+	14.9988i	0.623866	+	0.623866i
$579$		0			0
$580$		0			0
$581$			3.33245i			0.138253i
$582$		0			0
$583$	−21.9847	+	21.9847i	−0.910512	+	0.910512i
$584$	3.55051			0.146921
$585$		0			0
$586$	−5.03047			−0.207807
$587$	−29.4681	+	29.4681i	−1.21628	+	1.21628i	−0.247351	+	0.968926i	$0.579560\pi$
$587$	−29.4681	+	29.4681i	−1.21628	+	1.21628i	−0.968926	+	0.247351i	$0.920440\pi$
$588$		0			0
$589$			24.0960i			0.992859i
$590$		0			0
$591$		0			0
$592$	−6.87832	−	6.87832i	−0.282697	−	0.282697i
$593$	−22.7874	−	22.7874i	−0.935767	−	0.935767i	0.0622906	−	0.998058i	$-0.480159\pi$
$593$	−22.7874	−	22.7874i	−0.935767	−	0.935767i	−0.998058	+	0.0622906i	$0.980159\pi$
$594$		0			0
$595$		0			0
$596$		−	3.18759i		−	0.130569i
$597$		0			0
$598$	10.7171	−	10.7171i	0.438254	−	0.438254i
$599$	34.9314			1.42726			0.713629	−	0.700524i	$-0.247050\pi$
$599$	34.9314			1.42726			0.713629	+	0.700524i	$0.247050\pi$
$600$		0			0
$601$	−39.8254			−1.62451			−0.812256	−	0.583301i	$-0.801761\pi$
$601$	−39.8254			−1.62451			−0.812256	+	0.583301i	$0.801761\pi$
$602$	−0.174857	+	0.174857i	−0.00712663	+	0.00712663i
$603$		0			0
$604$		−	1.80725i		−	0.0735359i
$605$		0			0
$606$		0			0
$607$	22.7675	+	22.7675i	0.924104	+	0.924104i	0.997316	−	0.0732124i	$-0.0233251\pi$
$607$	22.7675	+	22.7675i	0.924104	+	0.924104i	−0.0732124	+	0.997316i	$0.523325\pi$
$608$	−3.44949	−	3.44949i	−0.139895	−	0.139895i
$609$		0			0
$610$		0			0
$611$		−	13.8864i		−	0.561782i
$612$		0			0
$613$	3.99446	−	3.99446i	0.161335	−	0.161335i	−0.621823	−	0.783158i	$-0.713608\pi$
$613$	3.99446	−	3.99446i	0.161335	−	0.161335i	0.783158	+	0.621823i	$0.213608\pi$
$614$	6.11971			0.246971
$615$		0			0
$616$	−3.41421			−0.137563
$617$	1.46002	−	1.46002i	0.0587783	−	0.0587783i	−0.677107	−	0.735885i	$-0.736766\pi$
$617$	1.46002	−	1.46002i	0.0587783	−	0.0587783i	0.735885	+	0.677107i	$0.236766\pi$
$618$		0			0
$619$		−	47.4138i		−	1.90572i	−0.303407	−	0.952861i	$-0.598124\pi$
$619$		−	47.4138i		−	1.90572i	0.303407	−	0.952861i	$-0.401876\pi$
$620$		0			0
$621$		0			0
$622$	2.61302	+	2.61302i	0.104773	+	0.104773i
$623$	2.87832	+	2.87832i	0.115317	+	0.115317i
$624$		0			0
$625$		0			0
$626$			18.8642i			0.753966i
$627$		0			0
$628$	12.8577	−	12.8577i	0.513076	−	0.513076i
$629$	60.1304			2.39755
$630$		0			0
$631$	4.98665			0.198515			0.0992577	−	0.995062i	$-0.468353\pi$
$631$	4.98665			0.198515			0.0992577	+	0.995062i	$0.468353\pi$
$632$	7.05986	−	7.05986i	0.280826	−	0.280826i
$633$		0			0
$634$			19.1769i			0.761612i
$635$		0			0
$636$		0			0
$637$	−2.02494	−	2.02494i	−0.0802312	−	0.0802312i
$638$	−12.5945	−	12.5945i	−0.498621	−	0.498621i
$639$		0			0
$640$		0			0
$641$		−	37.4961i		−	1.48101i	−0.672052	−	0.740504i	$-0.734587\pi$
$641$		−	37.4961i		−	1.48101i	0.672052	−	0.740504i	$-0.265413\pi$
$642$		0			0
$643$	4.58970	−	4.58970i	0.181000	−	0.181000i	−0.610791	−	0.791792i	$-0.709149\pi$
$643$	4.58970	−	4.58970i	0.181000	−	0.181000i	0.791792	+	0.610791i	$0.209149\pi$
$644$	5.29253			0.208555
$645$		0			0
$646$	30.1555			1.18645
$647$	27.4412	−	27.4412i	1.07883	−	1.07883i	0.0822112	−	0.996615i	$-0.473802\pi$
$647$	27.4412	−	27.4412i	1.07883	−	1.07883i	0.996615	−	0.0822112i	$-0.0261982\pi$
$648$		0			0
$649$			7.60697i			0.298600i
$650$		0			0
$651$		0			0
$652$	−10.0884	−	10.0884i	−0.395094	−	0.395094i
$653$	13.3212	+	13.3212i	0.521300	+	0.521300i	0.917964	−	0.396664i	$-0.129832\pi$
$653$	13.3212	+	13.3212i	0.521300	+	0.521300i	−0.396664	+	0.917964i	$0.629832\pi$
$654$		0			0
$655$		0			0
$656$			8.77729i			0.342696i
$657$		0			0
$658$	3.42883	−	3.42883i	0.133670	−	0.133670i
$659$	13.9355			0.542851			0.271425	−	0.962459i	$-0.412505\pi$
$659$	13.9355			0.542851			0.271425	+	0.962459i	$0.412505\pi$
$660$		0			0
$661$	38.5879			1.50089			0.750447	−	0.660930i	$-0.229838\pi$
$661$	38.5879			1.50089			0.750447	+	0.660930i	$0.229838\pi$
$662$	−8.61605	+	8.61605i	−0.334872	+	0.334872i
$663$		0			0
$664$			3.33245i			0.129324i
$665$		0			0
$666$		0			0
$667$	19.5233	+	19.5233i	0.755946	+	0.755946i
$668$	−3.31319	−	3.31319i	−0.128191	−	0.128191i
$669$		0			0
$670$		0			0
$671$		−	52.0757i		−	2.01036i
$672$		0			0
$673$	28.1223	−	28.1223i	1.08403	−	1.08403i	0.0879048	−	0.996129i	$-0.471983\pi$
$673$	28.1223	−	28.1223i	1.08403	−	1.08403i	0.996129	−	0.0879048i	$-0.0280171\pi$
$674$	20.9873			0.808401
$675$		0			0
$676$	4.79920			0.184585
$677$	−22.7408	+	22.7408i	−0.873999	+	0.873999i	−0.992905	−	0.118907i	$-0.962061\pi$
$677$	−22.7408	+	22.7408i	−0.873999	+	0.873999i	0.118907	+	0.992905i	$0.462061\pi$
$678$		0			0
$679$			7.98414i			0.306403i
$680$		0			0
$681$		0			0
$682$	11.9248	+	11.9248i	0.456624	+	0.456624i
$683$	−11.9549	−	11.9549i	−0.457442	−	0.457442i	0.440373	−	0.897815i	$-0.354846\pi$
$683$	−11.9549	−	11.9549i	−0.457442	−	0.457442i	−0.897815	+	0.440373i	$0.854846\pi$
$684$		0			0
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	−0.174857	+	0.174857i	−0.00666635	+	0.00666635i
$689$	−26.0779			−0.993488
$690$		0			0
$691$	6.79167			0.258367			0.129184	−	0.991621i	$-0.458764\pi$
$691$	6.79167			0.258367			0.129184	+	0.991621i	$0.458764\pi$
$692$	8.88437	−	8.88437i	0.337733	−	0.337733i
$693$		0			0
$694$		−	19.1953i		−	0.728642i
$695$		0			0
$696$		0			0
$697$	−38.3656	−	38.3656i	−1.45320	−	1.45320i
$698$	16.9329	+	16.9329i	0.640920	+	0.640920i
$699$		0			0
$700$		0			0
$701$		−	40.7354i		−	1.53855i	−0.638915	−	0.769277i	$-0.720617\pi$
$701$		−	40.7354i		−	1.53855i	0.638915	−	0.769277i	$-0.279383\pi$
$702$		0			0
$703$	33.5546	−	33.5546i	1.26554	−	1.26554i
$704$	−3.41421			−0.128678
$705$		0			0
$706$	−24.1396			−0.908508
$707$	−3.47531	+	3.47531i	−0.130703	+	0.130703i
$708$		0			0
$709$		−	30.8035i		−	1.15685i	−0.815735	−	0.578425i	$-0.803667\pi$
$709$		−	30.8035i		−	1.15685i	0.815735	−	0.578425i	$-0.196333\pi$
$710$		0			0
$711$		0			0
$712$	2.87832	+	2.87832i	0.107869	+	0.107869i
$713$	−18.4852	−	18.4852i	−0.692276	−	0.692276i
$714$		0			0
$715$		0			0
$716$		−	24.6556i		−	0.921423i
$717$		0			0
$718$	8.43035	−	8.43035i	0.314618	−	0.314618i
$719$	13.0945			0.488341			0.244170	−	0.969732i	$-0.421484\pi$
$719$	13.0945			0.488341			0.244170	+	0.969732i	$0.421484\pi$
$720$		0			0
$721$	−11.4130			−0.425041
$722$	3.39267	−	3.39267i	0.126262	−	0.126262i
$723$		0			0
$724$			13.2432i			0.492178i
$725$		0			0
$726$		0			0
$727$	−34.4418	−	34.4418i	−1.27738	−	1.27738i	−0.942131	−	0.335246i	$-0.891181\pi$
$727$	−34.4418	−	34.4418i	−1.27738	−	1.27738i	−0.335246	−	0.942131i	$-0.608819\pi$
$728$	−2.02494	−	2.02494i	−0.0750494	−	0.0750494i
$729$		0			0
$730$		0			0
$731$		−	1.52860i		−	0.0565374i
$732$		0			0
$733$	20.9524	−	20.9524i	0.773895	−	0.773895i	−0.204890	−	0.978785i	$-0.565684\pi$
$733$	20.9524	−	20.9524i	0.773895	−	0.773895i	0.978785	+	0.204890i	$0.0656836\pi$
$734$	−24.9711			−0.921699
$735$		0			0
$736$	5.29253			0.195085
$737$	13.0212	−	13.0212i	0.479641	−	0.479641i
$738$		0			0
$739$		−	51.0850i		−	1.87919i	−0.342288	−	0.939595i	$-0.611202\pi$
$739$		−	51.0850i		−	1.87919i	0.342288	−	0.939595i	$-0.388798\pi$
$740$		0			0
$741$		0			0
$742$	−6.43916	−	6.43916i	−0.236389	−	0.236389i
$743$	23.2763	+	23.2763i	0.853925	+	0.853925i	0.990614	−	0.136689i	$-0.0436461\pi$
$743$	23.2763	+	23.2763i	0.853925	+	0.853925i	−0.136689	+	0.990614i	$0.543646\pi$
$744$		0			0
$745$		0			0
$746$			23.7559i			0.869765i
$747$		0			0
$748$	14.9236	−	14.9236i	0.545659	−	0.545659i
$749$	8.17033			0.298537
$750$		0			0
$751$	16.7035			0.609520			0.304760	−	0.952429i	$-0.401424\pi$
$751$	16.7035			0.609520			0.304760	+	0.952429i	$0.401424\pi$
$752$	3.42883	−	3.42883i	0.125036	−	0.125036i
$753$		0			0
$754$		−	14.9394i		−	0.544061i
$755$		0			0
$756$		0			0
$757$	−6.56461	−	6.56461i	−0.238595	−	0.238595i	0.577673	−	0.816268i	$-0.303961\pi$
$757$	−6.56461	−	6.56461i	−0.238595	−	0.238595i	−0.816268	+	0.577673i	$0.803961\pi$
$758$	−10.4525	−	10.4525i	−0.379653	−	0.379653i
$759$		0			0
$760$		0			0
$761$		−	46.4642i		−	1.68433i	−0.539223	−	0.842163i	$-0.681282\pi$
$761$		−	46.4642i		−	1.68433i	0.539223	−	0.842163i	$-0.318718\pi$
$762$		0			0
$763$	−4.29717	+	4.29717i	−0.155568	+	0.155568i
$764$	19.7228			0.713545
$765$		0			0
$766$	27.2339			0.984000
$767$	−4.51163	+	4.51163i	−0.162906	+	0.162906i
$768$		0			0
$769$			39.1177i			1.41062i	0.708898	+	0.705311i	$0.249193\pi$
$769$			39.1177i			1.41062i	−0.708898	+	0.705311i	$0.750807\pi$
$770$		0			0
$771$		0			0
$772$	7.01461	+	7.01461i	0.252461	+	0.252461i
$773$	−4.88918	−	4.88918i	−0.175851	−	0.175851i	0.613693	−	0.789545i	$-0.289683\pi$
$773$	−4.88918	−	4.88918i	−0.175851	−	0.175851i	−0.789545	+	0.613693i	$0.789683\pi$
$774$		0			0
$775$		0			0
$776$			7.98414i			0.286614i
$777$		0			0
$778$	−5.30611	+	5.30611i	−0.190233	+	0.190233i
$779$	−42.8184			−1.53413
$780$		0			0
$781$	−37.3112			−1.33510
$782$	−23.1337	+	23.1337i	−0.827259	+	0.827259i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$		0			0
$786$		0			0
$787$	−10.6549	−	10.6549i	−0.379805	−	0.379805i	0.491226	−	0.871032i	$-0.336549\pi$
$787$	−10.6549	−	10.6549i	−0.379805	−	0.379805i	−0.871032	+	0.491226i	$0.836549\pi$
$788$	17.5394	+	17.5394i	0.624817	+	0.624817i
$789$		0			0
$790$		0			0
$791$			9.57045i			0.340286i
$792$		0			0
$793$	30.8857	−	30.8857i	1.09678	−	1.09678i
$794$	−10.8516			−0.385109
$795$		0			0
$796$	−15.9683			−0.565981
$797$	8.27135	−	8.27135i	0.292986	−	0.292986i	−0.545273	−	0.838259i	$-0.683574\pi$
$797$	8.27135	−	8.27135i	0.292986	−	0.292986i	0.838259	+	0.545273i	$0.183574\pi$
$798$		0			0
$799$			29.9749i			1.06043i
$800$		0			0
$801$		0			0
$802$	−1.27865	−	1.27865i	−0.0451506	−	0.0451506i
$803$	8.57169	+	8.57169i	0.302488	+	0.302488i
$804$		0			0
$805$		0			0
$806$			14.1450i			0.498237i
$807$		0			0
$808$	−3.47531	+	3.47531i	−0.122261	+	0.122261i
$809$	28.7785			1.01180			0.505900	−	0.862592i	$-0.331161\pi$
$809$	28.7785			1.01180			0.505900	+	0.862592i	$0.331161\pi$
$810$		0			0
$811$	19.8874			0.698341			0.349170	−	0.937059i	$-0.386463\pi$
$811$	19.8874			0.698341			0.349170	+	0.937059i	$0.386463\pi$
$812$	3.68885	−	3.68885i	0.129453	−	0.129453i
$813$		0			0
$814$		−	33.2114i		−	1.16406i
$815$		0			0
$816$		0			0
$817$	−0.853007	−	0.853007i	−0.0298429	−	0.0298429i
$818$	24.9920	+	24.9920i	0.873824	+	0.873824i
$819$		0			0
$820$		0			0
$821$		−	25.3394i		−	0.884352i	−0.896928	−	0.442176i	$-0.854207\pi$
$821$		−	25.3394i		−	0.884352i	0.896928	−	0.442176i	$-0.145793\pi$
$822$		0			0
$823$	−22.0270	+	22.0270i	−0.767814	+	0.767814i	−0.977721	−	0.209908i	$-0.932684\pi$
$823$	−22.0270	+	22.0270i	−0.767814	+	0.767814i	0.209908	+	0.977721i	$0.432684\pi$
$824$	−11.4130			−0.397590
$825$		0			0
$826$	−2.22803			−0.0775230
$827$	3.83272	−	3.83272i	0.133277	−	0.133277i	−0.637321	−	0.770598i	$-0.719958\pi$
$827$	3.83272	−	3.83272i	0.133277	−	0.133277i	0.770598	+	0.637321i	$0.219958\pi$
$828$		0			0
$829$		−	39.3021i		−	1.36502i	−0.730877	−	0.682509i	$-0.760889\pi$
$829$		−	39.3021i		−	1.36502i	0.730877	−	0.682509i	$-0.239111\pi$
$830$		0			0
$831$		0			0
$832$	−2.02494	−	2.02494i	−0.0702023	−	0.0702023i
$833$	4.37101	+	4.37101i	0.151446	+	0.151446i
$834$		0			0
$835$		0			0
$836$		−	16.6556i		−	0.576046i
$837$		0			0
$838$	−19.4440	+	19.4440i	−0.671681	+	0.671681i
$839$	−47.1174			−1.62667			−0.813337	−	0.581792i	$-0.802352\pi$
$839$	−47.1174			−1.62667			−0.813337	+	0.581792i	$0.802352\pi$
$840$		0			0
$841$	−1.78482			−0.0615456
$842$	4.14502	−	4.14502i	0.142847	−	0.142847i
$843$		0			0
$844$			26.2686i			0.904203i
$845$		0			0
$846$		0			0
$847$	−0.464466	−	0.464466i	−0.0159592	−	0.0159592i
$848$	−6.43916	−	6.43916i	−0.221122	−	0.221122i
$849$		0			0
$850$		0			0
$851$			51.4826i			1.76480i
$852$		0			0
$853$	10.5412	−	10.5412i	0.360924	−	0.360924i	−0.503229	−	0.864153i	$-0.667855\pi$
$853$	10.5412	−	10.5412i	0.360924	−	0.360924i	0.864153	+	0.503229i	$0.167855\pi$
$854$	15.2526			0.521934
$855$		0			0
$856$	8.17033			0.279256
$857$	30.2006	−	30.2006i	1.03163	−	1.03163i	0.0321492	−	0.999483i	$-0.489765\pi$
$857$	30.2006	−	30.2006i	1.03163	−	1.03163i	0.999483	−	0.0321492i	$-0.0102352\pi$
$858$		0			0
$859$			16.5437i			0.564465i	0.959346	+	0.282232i	$0.0910749\pi$
$859$			16.5437i			0.564465i	−0.959346	+	0.282232i	$0.908925\pi$
$860$		0			0
$861$		0			0
$862$	−15.1882	−	15.1882i	−0.517313	−	0.517313i
$863$	−8.61783	−	8.61783i	−0.293354	−	0.293354i	0.545050	−	0.838404i	$-0.316511\pi$
$863$	−8.61783	−	8.61783i	−0.293354	−	0.293354i	−0.838404	+	0.545050i	$0.816511\pi$
$864$		0			0
$865$		0			0
$866$		−	22.6848i		−	0.770862i
$867$		0			0
$868$	−3.49269	+	3.49269i	−0.118550	+	0.118550i
$869$	34.0880			1.15636
$870$		0			0
$871$	15.4455			0.523352
$872$	−4.29717	+	4.29717i	−0.145521	+	0.145521i
$873$		0			0
$874$			25.8186i			0.873328i
$875$		0			0
$876$		0			0
$877$	−4.75539	−	4.75539i	−0.160578	−	0.160578i	0.622245	−	0.782823i	$-0.286221\pi$
$877$	−4.75539	−	4.75539i	−0.160578	−	0.160578i	−0.782823	+	0.622245i	$0.786221\pi$
$878$	8.38511	+	8.38511i	0.282984	+	0.282984i
$879$		0			0
$880$		0			0
$881$		−	19.5569i		−	0.658888i	−0.944175	−	0.329444i	$-0.893139\pi$
$881$		−	19.5569i		−	0.658888i	0.944175	−	0.329444i	$-0.106861\pi$
$882$		0			0
$883$	−1.46863	+	1.46863i	−0.0494233	+	0.0494233i	−0.731387	−	0.681963i	$-0.761126\pi$
$883$	−1.46863	+	1.46863i	−0.0494233	+	0.0494233i	0.681963	+	0.731387i	$0.261126\pi$
$884$	17.7021			0.595386
$885$		0			0
$886$	−28.1744			−0.946538
$887$	−20.5833	+	20.5833i	−0.691119	+	0.691119i	−0.962478	−	0.271359i	$-0.912527\pi$
$887$	−20.5833	+	20.5833i	−0.691119	+	0.691119i	0.271359	+	0.962478i	$0.412527\pi$
$888$		0			0
$889$			15.6052i			0.523382i
$890$		0			0
$891$		0			0
$892$	12.6061	+	12.6061i	0.422083	+	0.422083i
$893$	16.7269	+	16.7269i	0.559744	+	0.559744i
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−16.6975	+	16.6975i	−0.557201	+	0.557201i
$899$	−25.7680			−0.859412
$900$		0			0
$901$	56.2912			1.87533
$902$	−21.1903	+	21.1903i	−0.705559	+	0.705559i
$903$		0			0
$904$			9.57045i			0.318308i
$905$		0			0
$906$		0			0
$907$	−18.5032	−	18.5032i	−0.614388	−	0.614388i	0.329698	−	0.944086i	$-0.393053\pi$
$907$	−18.5032	−	18.5032i	−0.614388	−	0.614388i	−0.944086	+	0.329698i	$0.893053\pi$
$908$	−3.02786	−	3.02786i	−0.100483	−	0.100483i
$909$		0			0
$910$		0			0
$911$			7.35968i			0.243837i	0.992540	+	0.121919i	$0.0389047\pi$
$911$			7.35968i			0.243837i	−0.992540	+	0.121919i	$0.961095\pi$
$912$		0			0
$913$	−8.04524	+	8.04524i	−0.266259	+	0.266259i
$914$	27.4570			0.908196
$915$		0			0
$916$	−3.50543			−0.115823
$917$	−1.70674	+	1.70674i	−0.0563616	+	0.0563616i
$918$		0			0
$919$		−	18.7527i		−	0.618593i	−0.950966	−	0.309297i	$-0.899906\pi$
$919$		−	18.7527i		−	0.618593i	0.950966	−	0.309297i	$-0.100094\pi$
$920$		0			0
$921$		0			0
$922$	−21.1005	−	21.1005i	−0.694906	−	0.694906i
$923$	−22.1290	−	22.1290i	−0.728385	−	0.728385i
$924$		0			0
$925$		0			0
$926$			12.9189i			0.424542i
$927$		0			0
$928$	3.68885	−	3.68885i	0.121092	−	0.121092i
$929$	−25.9196			−0.850396			−0.425198	−	0.905100i	$-0.639796\pi$
$929$	−25.9196			−0.850396			−0.425198	+	0.905100i	$0.639796\pi$
$930$		0			0
$931$	4.87832			0.159880
$932$	−8.98074	+	8.98074i	−0.294174	+	0.294174i
$933$		0			0
$934$		−	2.87921i		−	0.0942106i
$935$		0			0
$936$		0			0
$937$	−6.24994	−	6.24994i	−0.204177	−	0.204177i	0.597610	−	0.801787i	$-0.296117\pi$
$937$	−6.24994	−	6.24994i	−0.204177	−	0.204177i	−0.801787	+	0.597610i	$0.796117\pi$
$938$	3.81382	+	3.81382i	0.124525	+	0.124525i
$939$		0			0
$940$		0			0
$941$		−	47.7955i		−	1.55809i	−0.626969	−	0.779044i	$-0.715705\pi$
$941$		−	47.7955i		−	1.55809i	0.626969	−	0.779044i	$-0.284295\pi$
$942$		0			0
$943$	32.8480	−	32.8480i	1.06968	−	1.06968i
$944$	−2.22803			−0.0725162
$945$		0			0
$946$	−0.844283			−0.0274500
$947$	7.01173	−	7.01173i	0.227851	−	0.227851i	−0.583944	−	0.811794i	$-0.698491\pi$
$947$	7.01173	−	7.01173i	0.227851	−	0.227851i	0.811794	+	0.583944i	$0.198491\pi$
$948$		0			0
$949$			10.1676i			0.330055i
$950$		0			0
$951$		0			0
$952$	4.37101	+	4.37101i	0.141665	+	0.141665i
$953$	−4.50419	−	4.50419i	−0.145905	−	0.145905i	0.630381	−	0.776286i	$-0.282899\pi$
$953$	−4.50419	−	4.50419i	−0.145905	−	0.145905i	−0.776286	+	0.630381i	$0.782899\pi$
$954$		0			0
$955$		0			0
$956$			16.4853i			0.533172i
$957$		0			0
$958$	27.5207	−	27.5207i	0.889154	−	0.889154i
$959$	13.2913			0.429198
$960$		0			0
$961$	−6.60218			−0.212973
$962$	19.6975	−	19.6975i	0.635071	−	0.635071i
$963$		0			0
$964$		−	27.8179i		−	0.895954i
$965$		0			0
$966$		0			0
$967$	−10.4951	−	10.4951i	−0.337499	−	0.337499i	0.517926	−	0.855425i	$-0.326704\pi$
$967$	−10.4951	−	10.4951i	−0.337499	−	0.337499i	−0.855425	+	0.517926i	$0.826704\pi$
$968$	−0.464466	−	0.464466i	−0.0149285	−	0.0149285i
$969$		0			0
$970$		0			0
$971$			6.79671i			0.218117i	0.994035	+	0.109058i	$0.0347836\pi$
$971$			6.79671i			0.218117i	−0.994035	+	0.109058i	$0.965216\pi$
$972$		0			0
$973$	−7.96348	+	7.96348i	−0.255297	+	0.255297i
$974$	33.3810			1.06960
$975$		0			0
$976$	15.2526			0.488224
$977$	12.0348	−	12.0348i	0.385026	−	0.385026i	−0.487883	−	0.872909i	$-0.662231\pi$
$977$	12.0348	−	12.0348i	0.385026	−	0.385026i	0.872909	+	0.487883i	$0.162231\pi$
$978$		0			0
$979$			13.8977i			0.444174i
$980$		0			0
$981$		0			0
$982$	−18.7196	−	18.7196i	−0.597366	−	0.597366i
$983$	−39.3016	−	39.3016i	−1.25353	−	1.25353i	−0.954128	−	0.299398i	$-0.903214\pi$
$983$	−39.3016	−	39.3016i	−1.25353	−	1.25353i	−0.299398	−	0.954128i	$-0.596786\pi$
$984$		0			0
$985$		0			0
$986$			32.2480i			1.02698i
$987$		0			0
$988$	9.87832	−	9.87832i	0.314271	−	0.314271i
$989$	1.30876			0.0416162
$990$		0			0
$991$	−28.6002			−0.908516			−0.454258	−	0.890870i	$-0.650096\pi$
$991$	−28.6002			−0.908516			−0.454258	+	0.890870i	$0.650096\pi$
$992$	−3.49269	+	3.49269i	−0.110893	+	0.110893i
$993$		0			0
$994$		−	10.9282i		−	0.346622i
$995$		0			0
$996$		0			0
$997$	13.3736	+	13.3736i	0.423547	+	0.423547i	0.886423	−	0.462876i	$-0.153183\pi$
$997$	13.3736	+	13.3736i	0.423547	+	0.423547i	−0.462876	+	0.886423i	$0.653183\pi$
$998$	−28.5569	−	28.5569i	−0.903952	−	0.903952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.g.1457.1	✓	8
3.2	odd	2		3150.2.m.h.1457.3	yes	8
5.2	odd	4		3150.2.m.l.2843.2	yes	8
5.3	odd	4		3150.2.m.h.2843.3	yes	8
5.4	even	2		3150.2.m.k.1457.4	yes	8
15.2	even	4		3150.2.m.k.2843.4	yes	8
15.8	even	4	inner	3150.2.m.g.2843.1	yes	8
15.14	odd	2		3150.2.m.l.1457.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.m.g.1457.1	✓	8	1.1	even	1	trivial
3150.2.m.g.2843.1	yes	8	15.8	even	4	inner
3150.2.m.h.1457.3	yes	8	3.2	odd	2
3150.2.m.h.2843.3	yes	8	5.3	odd	4
3150.2.m.k.1457.4	yes	8	5.4	even	2
3150.2.m.k.2843.4	yes	8	15.2	even	4
3150.2.m.l.1457.2	yes	8	15.14	odd	2
3150.2.m.l.2843.2	yes	8	5.2	odd	4

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.41421i q^{11} +(-2.02494 + 2.02494i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(4.37101 - 4.37101i) q^{17} -4.87832i q^{19} +(-2.41421 - 2.41421i) q^{22} +(3.74238 + 3.74238i) q^{23} -2.86370i q^{26} +(0.707107 - 0.707107i) q^{28} +5.21682 q^{29} -4.93942 q^{31} +(0.707107 - 0.707107i) q^{32} +6.18154i q^{34} +(6.87832 + 6.87832i) q^{37} +(3.44949 + 3.44949i) q^{38} -8.77729i q^{41} +(0.174857 - 0.174857i) q^{43} +3.41421 q^{44} -5.29253 q^{46} +(-3.42883 + 3.42883i) q^{47} +1.00000i q^{49} +(2.02494 + 2.02494i) q^{52} +(6.43916 + 6.43916i) q^{53} +1.00000i q^{56} +(-3.68885 + 3.68885i) q^{58} +2.22803 q^{59} -15.2526 q^{61} +(3.49269 - 3.49269i) q^{62} +1.00000i q^{64} +(-3.81382 - 3.81382i) q^{67} +(-4.37101 - 4.37101i) q^{68} +10.9282i q^{71} +(2.51059 - 2.51059i) q^{73} -9.72741 q^{74} -4.87832 q^{76} +(-2.41421 + 2.41421i) q^{77} -9.98414i q^{79} +(6.20648 + 6.20648i) q^{82} +(2.35640 + 2.35640i) q^{83} +0.247285i q^{86} +(-2.41421 + 2.41421i) q^{88} +4.07055 q^{89} -2.86370 q^{91} +(3.74238 - 3.74238i) q^{92} -4.84909i q^{94} +(5.64564 + 5.64564i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 8 q^{13} - 8 q^{14} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 16 q^{37} + 8 q^{38} + 8 q^{43} + 16 q^{44} + 8 q^{46} - 8 q^{47} + 8 q^{52} + 32 q^{53} + 8 q^{58} - 8 q^{59} - 32 q^{61} + 32 q^{62} - 16 q^{67} - 16 q^{74} - 8 q^{77} + 8 q^{82} - 8 q^{83} - 8 q^{88} + 16 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^13 - 8 * q^14 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 16 * q^37 + 8 * q^38 + 8 * q^43 + 16 * q^44 + 8 * q^46 - 8 * q^47 + 8 * q^52 + 32 * q^53 + 8 * q^58 - 8 * q^59 - 32 * q^61 + 32 * q^62 - 16 * q^67 - 16 * q^74 - 8 * q^77 + 8 * q^82 - 8 * q^83 - 8 * q^88 + 16 * q^89 + 8 * q^91 + 16 * q^92 - 16 * q^97

Introduction

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