LMFDB - Embedded newform 630.2.be.a.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(341,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("630.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.be (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	630.521
Dual form			630.2.be.a.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.189469 - 2.63896i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.189469 - 2.63896i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(-3.44829 - 1.99087i) q^{11} +0.0681483i q^{13} +(1.48356 + 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.66390 + 6.34607i) q^{17} +(-1.76260 + 1.01764i) q^{19} -1.00000 q^{20} +3.98174 q^{22} +(-3.23205 + 1.86603i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.0340742 - 0.0590182i) q^{26} +(-2.38014 - 1.15539i) q^{28} -0.898979i q^{29} +(-4.18154 - 2.41421i) q^{31} +(0.866025 + 0.500000i) q^{32} -7.32780i q^{34} +(-2.19067 + 1.48356i) q^{35} +(2.03407 + 3.52312i) q^{37} +(1.01764 - 1.76260i) q^{38} +(0.866025 - 0.500000i) q^{40} -1.68921 q^{41} -0.964724 q^{43} +(-3.44829 + 1.99087i) q^{44} +(1.86603 - 3.23205i) q^{46} +(0.830749 + 1.43890i) q^{47} +(-6.92820 + 1.00000i) q^{49} -1.00000i q^{50} +(0.0590182 + 0.0340742i) q^{52} +(-11.4547 - 6.61339i) q^{53} +3.98174i q^{55} +(2.63896 - 0.189469i) q^{56} +(0.449490 + 0.778539i) q^{58} +(5.32112 - 9.21645i) q^{59} +(6.51299 - 3.76028i) q^{61} +4.82843 q^{62} -1.00000 q^{64} +(0.0590182 - 0.0340742i) q^{65} +(-5.33145 + 9.23435i) q^{67} +(3.66390 + 6.34607i) q^{68} +(1.15539 - 2.38014i) q^{70} -9.93426i q^{71} +(-10.0951 - 5.82843i) q^{73} +(-3.52312 - 2.03407i) q^{74} +2.03528i q^{76} +(-4.60048 + 9.47710i) q^{77} +(-8.77489 - 15.1986i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(1.46290 - 0.844605i) q^{82} +14.3490 q^{83} +7.32780 q^{85} +(0.835475 - 0.482362i) q^{86} +(1.99087 - 3.44829i) q^{88} +(0.913956 + 1.58302i) q^{89} +(0.179841 - 0.0129120i) q^{91} +3.73205i q^{92} +(-1.43890 - 0.830749i) q^{94} +(1.76260 + 1.01764i) q^{95} +17.1502i q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^5	$ 8 q + 4 q^{4} - 4 q^{5} - 24 q^{11} - 4 q^{16} - 8 q^{20} - 12 q^{23} - 4 q^{25} - 8 q^{26} + 24 q^{37} + 4 q^{38} - 32 q^{41} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{47} - 24 q^{53} - 16 q^{58} + 24 q^{59} + 16 q^{62} - 8 q^{64} - 24 q^{67} + 16 q^{77} - 24 q^{79} - 4 q^{80} + 16 q^{83} + 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 - 24 * q^11 - 4 * q^16 - 8 * q^20 - 12 * q^23 - 4 * q^25 - 8 * q^26 + 24 * q^37 + 4 * q^38 - 32 * q^41 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^47 - 24 * q^53 - 16 * q^58 + 24 * q^59 + 16 * q^62 - 8 * q^64 - 24 * q^67 + 16 * q^77 - 24 * q^79 - 4 * q^80 + 16 * q^83 + 16 * q^89 - 20 * q^91 - 12 * q^94 + 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$7$	−0.189469	−	2.63896i	−0.0716124	−	0.997433i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−3.44829	−	1.99087i	−1.03970	−	0.600270i	−0.119950	−	0.992780i	$-0.538273\pi$
$11$	−3.44829	−	1.99087i	−1.03970	−	0.600270i	−0.919748	+	0.392510i	$0.871607\pi$
$12$		0			0
$13$			0.0681483i			0.0189010i	0.999955	+	0.00945048i	$0.00300822\pi$
$13$			0.0681483i			0.0189010i	−0.999955	+	0.00945048i	$0.996992\pi$
$14$	1.48356	+	2.19067i	0.396499	+	0.585481i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.66390	+	6.34607i	−0.888627	+	1.53915i	−0.0471274	+	0.998889i	$0.515007\pi$
$17$	−3.66390	+	6.34607i	−0.888627	+	1.53915i	−0.841499	+	0.540258i	$0.818327\pi$
$18$		0			0
$19$	−1.76260	+	1.01764i	−0.404368	+	0.233462i	−0.688367	−	0.725362i	$-0.741672\pi$
$19$	−1.76260	+	1.01764i	−0.404368	+	0.233462i	0.283999	+	0.958825i	$0.408339\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	3.98174			0.848910
$23$	−3.23205	+	1.86603i	−0.673929	+	0.389093i	−0.797564	−	0.603235i	$-0.793878\pi$
$23$	−3.23205	+	1.86603i	−0.673929	+	0.389093i	0.123635	+	0.992328i	$0.460545\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.0340742	−	0.0590182i	−0.00668250	−	0.0115744i
$27$		0			0
$28$	−2.38014	−	1.15539i	−0.449804	−	0.218349i
$29$		−	0.898979i		−	0.166936i	−0.996510	−	0.0834681i	$-0.973400\pi$
$29$		−	0.898979i		−	0.166936i	0.996510	−	0.0834681i	$-0.0265997\pi$
$30$		0			0
$31$	−4.18154	−	2.41421i	−0.751027	−	0.433606i	0.0750380	−	0.997181i	$-0.476092\pi$
$31$	−4.18154	−	2.41421i	−0.751027	−	0.433606i	−0.826065	+	0.563575i	$0.809426\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	7.32780i		−	1.25671i
$35$	−2.19067	+	1.48356i	−0.370291	+	0.250768i
$36$		0			0
$37$	2.03407	+	3.52312i	0.334400	+	0.579197i	0.983369	−	0.181617i	$-0.0581331\pi$
$37$	2.03407	+	3.52312i	0.334400	+	0.579197i	−0.648970	+	0.760814i	$0.724800\pi$
$38$	1.01764	−	1.76260i	0.165083	−	0.285932i
$39$		0			0
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−1.68921			−0.263810			−0.131905	−	0.991262i	$-0.542109\pi$
$41$	−1.68921			−0.263810			−0.131905	+	0.991262i	$0.542109\pi$
$42$		0			0
$43$	−0.964724			−0.147119			−0.0735595	−	0.997291i	$-0.523436\pi$
$43$	−0.964724			−0.147119			−0.0735595	+	0.997291i	$0.523436\pi$
$44$	−3.44829	+	1.99087i	−0.519849	+	0.300135i
$45$		0			0
$46$	1.86603	−	3.23205i	0.275130	−	0.476540i
$47$	0.830749	+	1.43890i	0.121177	+	0.209885i	0.920232	−	0.391373i	$-0.128000\pi$
$47$	0.830749	+	1.43890i	0.121177	+	0.209885i	−0.799055	+	0.601258i	$0.794666\pi$
$48$		0			0
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		−	1.00000i		−	0.141421i
$51$		0			0
$52$	0.0590182	+	0.0340742i	0.00818435	+	0.00472524i
$53$	−11.4547	−	6.61339i	−1.57343	−	0.908419i	−0.995744	−	0.0921588i	$-0.970623\pi$
$53$	−11.4547	−	6.61339i	−1.57343	−	0.908419i	−0.577684	−	0.816260i	$-0.696043\pi$
$54$		0			0
$55$			3.98174i			0.536898i
$56$	2.63896	−	0.189469i	0.352646	−	0.0253188i
$57$		0			0
$58$	0.449490	+	0.778539i	0.0590209	+	0.102227i
$59$	5.32112	−	9.21645i	0.692751	−	1.19988i	−0.278182	−	0.960528i	$-0.589732\pi$
$59$	5.32112	−	9.21645i	0.692751	−	1.19988i	0.970933	−	0.239352i	$-0.0769348\pi$
$60$		0			0
$61$	6.51299	−	3.76028i	0.833903	−	0.481454i	−0.0212839	−	0.999773i	$-0.506775\pi$
$61$	6.51299	−	3.76028i	0.833903	−	0.481454i	0.855187	+	0.518319i	$0.173442\pi$
$62$	4.82843			0.613211
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.0590182	−	0.0340742i	0.00732031	−	0.00422638i
$66$		0			0
$67$	−5.33145	+	9.23435i	−0.651341	+	1.12816i	0.331457	+	0.943470i	$0.392460\pi$
$67$	−5.33145	+	9.23435i	−0.651341	+	1.12816i	−0.982798	+	0.184685i	$0.940874\pi$
$68$	3.66390	+	6.34607i	0.444313	+	0.769573i
$69$		0			0
$70$	1.15539	−	2.38014i	0.138096	−	0.284481i
$71$		−	9.93426i		−	1.17898i	−0.807776	−	0.589490i	$-0.799329\pi$
$71$		−	9.93426i		−	1.17898i	0.807776	−	0.589490i	$-0.200671\pi$
$72$		0			0
$73$	−10.0951	−	5.82843i	−1.18155	−	0.682166i	−0.225174	−	0.974319i	$-0.572295\pi$
$73$	−10.0951	−	5.82843i	−1.18155	−	0.682166i	−0.956372	+	0.292153i	$0.905628\pi$
$74$	−3.52312	−	2.03407i	−0.409554	−	0.236456i
$75$		0			0
$76$			2.03528i			0.233462i
$77$	−4.60048	+	9.47710i	−0.524273	+	1.08002i
$78$		0			0
$79$	−8.77489	−	15.1986i	−0.987252	−	1.70997i	−0.631465	−	0.775404i	$-0.717546\pi$
$79$	−8.77489	−	15.1986i	−0.987252	−	1.70997i	−0.355787	−	0.934567i	$-0.615787\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	1.46290	−	0.844605i	0.161550	−	0.0932711i
$83$	14.3490			1.57501			0.787503	−	0.616311i	$-0.211374\pi$
$83$	14.3490			1.57501			0.787503	+	0.616311i	$0.211374\pi$
$84$		0			0
$85$	7.32780			0.794812
$86$	0.835475	−	0.482362i	0.0900916	−	0.0520144i
$87$		0			0
$88$	1.99087	−	3.44829i	0.212227	−	0.367589i
$89$	0.913956	+	1.58302i	0.0968791	+	0.167800i	0.910391	−	0.413748i	$-0.135781\pi$
$89$	0.913956	+	1.58302i	0.0968791	+	0.167800i	−0.813512	+	0.581548i	$0.802447\pi$
$90$		0			0
$91$	0.179841	−	0.0129120i	0.0188524	−	0.00135354i
$92$			3.73205i			0.389093i
$93$		0			0
$94$	−1.43890	−	0.830749i	−0.148411	−	0.0856852i
$95$	1.76260	+	1.01764i	0.180839	+	0.104407i
$96$		0			0
$97$			17.1502i			1.74134i	0.491870	+	0.870668i	$0.336313\pi$
$97$			17.1502i			1.74134i	−0.491870	+	0.870668i	$0.663687\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	3.36773	−	5.83307i	0.335101	−	0.580412i	−0.648403	−	0.761297i	$-0.724563\pi$
$101$	3.36773	−	5.83307i	0.335101	−	0.580412i	0.983504	+	0.180885i	$0.0578962\pi$
$102$		0			0
$103$	0.450370	−	0.260021i	0.0443762	−	0.0256206i	−0.477648	−	0.878551i	$-0.658510\pi$
$103$	0.450370	−	0.260021i	0.0443762	−	0.0256206i	0.522024	+	0.852931i	$0.325177\pi$
$104$	−0.0681483			−0.00668250
$105$		0			0
$106$	13.2268			1.28470
$107$	−5.30614	+	3.06350i	−0.512964	+	0.296160i	−0.734051	−	0.679094i	$-0.762373\pi$
$107$	−5.30614	+	3.06350i	−0.512964	+	0.296160i	0.221087	+	0.975254i	$0.429040\pi$
$108$		0			0
$109$	−6.77729	+	11.7386i	−0.649147	+	1.12436i	0.334180	+	0.942509i	$0.391541\pi$
$109$	−6.77729	+	11.7386i	−0.649147	+	1.12436i	−0.983327	+	0.181846i	$0.941793\pi$
$110$	−1.99087	−	3.44829i	−0.189822	−	0.328781i
$111$		0			0
$112$	−2.19067	+	1.48356i	−0.206999	+	0.140184i
$113$		−	11.6982i		−	1.10047i	−0.835009	−	0.550236i	$-0.814538\pi$
$113$		−	11.6982i		−	1.10047i	0.835009	−	0.550236i	$-0.185462\pi$
$114$		0			0
$115$	3.23205	+	1.86603i	0.301390	+	0.174008i
$116$	−0.778539	−	0.449490i	−0.0722855	−	0.0417341i
$117$		0			0
$118$			10.6422i			0.979698i
$119$	17.4412	+	8.46651i	1.59883	+	0.776123i
$120$		0			0
$121$	2.42713	+	4.20390i	0.220648	+	0.382173i
$122$	−3.76028	+	6.51299i	−0.340440	+	0.589659i
$123$		0			0
$124$	−4.18154	+	2.41421i	−0.375513	+	0.216803i
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.7530			0.954173			0.477086	−	0.878856i	$-0.341693\pi$
$127$	10.7530			0.954173			0.477086	+	0.878856i	$0.341693\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.0340742	+	0.0590182i	−0.00298850	+	0.00517624i
$131$	−1.85457	−	3.21221i	−0.162035	−	0.280653i	0.773564	−	0.633719i	$-0.218472\pi$
$131$	−1.85457	−	3.21221i	−0.162035	−	0.280653i	−0.935598	+	0.353066i	$0.885139\pi$
$132$		0			0
$133$	3.01946	+	4.45862i	0.261821	+	0.386611i
$134$		−	10.6629i		−	0.921135i
$135$		0			0
$136$	−6.34607	−	3.66390i	−0.544171	−	0.314177i
$137$	−11.7091	−	6.76028i	−1.00038	−	0.577570i	−0.0920192	−	0.995757i	$-0.529332\pi$
$137$	−11.7091	−	6.76028i	−1.00038	−	0.577570i	−0.908361	+	0.418188i	$0.862665\pi$
$138$		0			0
$139$			9.06251i			0.768672i	0.923193	+	0.384336i	$0.125570\pi$
$139$			9.06251i			0.768672i	−0.923193	+	0.384336i	$0.874430\pi$
$140$	0.189469	+	2.63896i	0.0160130	+	0.223033i
$141$		0			0
$142$	4.96713	+	8.60332i	0.416832	+	0.721974i
$143$	0.135674	−	0.234995i	0.0113457	−	0.0196513i
$144$		0			0
$145$	−0.778539	+	0.449490i	−0.0646542	+	0.0373281i
$146$	11.6569			0.964728
$147$		0			0
$148$	4.06815			0.334400
$149$	13.2385	−	7.64324i	1.08454	−	0.626158i	0.152421	−	0.988316i	$-0.451293\pi$
$149$	13.2385	−	7.64324i	1.08454	−	0.626158i	0.932117	+	0.362157i	$0.117960\pi$
$150$		0			0
$151$	4.93942	−	8.55532i	0.401964	−	0.696222i	−0.591999	−	0.805939i	$-0.701661\pi$
$151$	4.93942	−	8.55532i	0.401964	−	0.696222i	0.993963	+	0.109717i	$0.0349944\pi$
$152$	−1.01764	−	1.76260i	−0.0825413	−	0.142966i
$153$		0			0
$154$	−0.754415	−	10.5076i	−0.0607925	−	0.846730i
$155$			4.82843i			0.387829i
$156$		0			0
$157$	12.3741	+	7.14418i	0.987560	+	0.570168i	0.904544	−	0.426380i	$-0.140212\pi$
$157$	12.3741	+	7.14418i	0.987560	+	0.570168i	0.0830157	+	0.996548i	$0.473545\pi$
$158$	15.1986	+	8.77489i	1.20913	+	0.698093i
$159$		0			0
$160$		−	1.00000i		−	0.0790569i
$161$	5.53674	+	8.17569i	0.436356	+	0.644335i
$162$		0			0
$163$	−4.98879	−	8.64083i	−0.390752	−	0.676802i	0.601797	−	0.798649i	$-0.294452\pi$
$163$	−4.98879	−	8.64083i	−0.390752	−	0.676802i	−0.992549	+	0.121847i	$0.961118\pi$
$164$	−0.844605	+	1.46290i	−0.0659526	+	0.114233i
$165$		0			0
$166$	−12.4266	+	7.17449i	−0.964490	+	0.556849i
$167$	13.7778			1.06616			0.533079	−	0.846065i	$-0.321035\pi$
$167$	13.7778			1.06616			0.533079	+	0.846065i	$0.321035\pi$
$168$		0			0
$169$	12.9954			0.999643
$170$	−6.34607	+	3.66390i	−0.486721	+	0.281008i
$171$		0			0
$172$	−0.482362	+	0.835475i	−0.0367798	+	0.0637044i
$173$	4.13638	+	7.16442i	0.314483	+	0.544701i	0.979327	−	0.202281i	$-0.0648355\pi$
$173$	4.13638	+	7.16442i	0.314483	+	0.544701i	−0.664844	+	0.746982i	$0.731502\pi$
$174$		0			0
$175$	2.38014	+	1.15539i	0.179922	+	0.0873396i
$176$			3.98174i			0.300135i
$177$		0			0
$178$	−1.58302	−	0.913956i	−0.118652	−	0.0685039i
$179$	9.97501	+	5.75908i	0.745568	+	0.430454i	0.824090	−	0.566459i	$-0.191687\pi$
$179$	9.97501	+	5.75908i	0.745568	+	0.430454i	−0.0785226	+	0.996912i	$0.525020\pi$
$180$		0			0
$181$			16.5924i			1.23330i	0.787237	+	0.616650i	$0.211511\pi$
$181$			16.5924i			1.23330i	−0.787237	+	0.616650i	$0.788489\pi$
$182$	−0.149291	+	0.101102i	−0.0110662	+	0.00749421i
$183$		0			0
$184$	−1.86603	−	3.23205i	−0.137565	−	0.238270i
$185$	2.03407	−	3.52312i	0.149548	−	0.259025i
$186$		0			0
$187$	25.2684	−	14.5887i	1.84781	−	1.06683i
$188$	1.66150			0.121177
$189$		0			0
$190$	−2.03528			−0.147654
$191$	−15.9640	+	9.21682i	−1.15511	+	0.666905i	−0.950128	−	0.311859i	$-0.899048\pi$
$191$	−15.9640	+	9.21682i	−1.15511	+	0.666905i	−0.204986	+	0.978765i	$0.565715\pi$
$192$		0			0
$193$	3.17914	−	5.50643i	0.228839	−	0.396361i	−0.728625	−	0.684913i	$-0.759840\pi$
$193$	3.17914	−	5.50643i	0.228839	−	0.396361i	0.957464	+	0.288552i	$0.0931736\pi$
$194$	−8.57509	−	14.8525i	−0.615656	−	1.06635i
$195$		0			0
$196$	−2.59808	+	6.50000i	−0.185577	+	0.464286i
$197$			12.8389i			0.914734i	0.889278	+	0.457367i	$0.151208\pi$
$197$			12.8389i			0.914734i	−0.889278	+	0.457367i	$0.848792\pi$
$198$		0			0
$199$	−8.33950	−	4.81481i	−0.591171	−	0.341313i	0.174389	−	0.984677i	$-0.444205\pi$
$199$	−8.33950	−	4.81481i	−0.591171	−	0.341313i	−0.765561	+	0.643364i	$0.777538\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$			6.73545i			0.473905i
$203$	−2.37237	+	0.170328i	−0.166508	+	0.0119547i
$204$		0			0
$205$	0.844605	+	1.46290i	0.0589898	+	0.102173i
$206$	−0.260021	+	0.450370i	−0.0181165	+	0.0313787i
$207$		0			0
$208$	0.0590182	−	0.0340742i	0.00409218	−	0.00236262i
$209$	8.10394			0.560561
$210$		0			0
$211$	−14.5619			−1.00248			−0.501241	−	0.865308i	$-0.667123\pi$
$211$	−14.5619			−1.00248			−0.501241	+	0.865308i	$0.667123\pi$
$212$	−11.4547	+	6.61339i	−0.786714	+	0.454210i
$213$		0			0
$214$	3.06350	−	5.30614i	0.209417	−	0.362721i
$215$	0.482362	+	0.835475i	0.0328968	+	0.0569789i
$216$		0			0
$217$	−5.57874	+	11.4923i	−0.378709	+	0.780150i
$218$		−	13.5546i		−	0.918033i
$219$		0			0
$220$	3.44829	+	1.99087i	0.232484	+	0.134224i
$221$	−0.432474	−	0.249689i	−0.0290913	−	0.0167959i
$222$		0			0
$223$		−	23.6609i		−	1.58445i	−0.610227	−	0.792227i	$-0.708922\pi$
$223$		−	23.6609i		−	1.58445i	0.610227	−	0.792227i	$-0.291078\pi$
$224$	1.15539	−	2.38014i	0.0771980	−	0.159030i
$225$		0			0
$226$	5.84909	+	10.1309i	0.389076	+	0.673899i
$227$	4.32024	−	7.48288i	0.286744	−	0.496656i	−0.686286	−	0.727332i	$-0.740760\pi$
$227$	4.32024	−	7.48288i	0.286744	−	0.496656i	0.973031	+	0.230676i	$0.0740936\pi$
$228$		0			0
$229$	−12.1896	+	7.03768i	−0.805513	+	0.465063i	−0.845395	−	0.534141i	$-0.820635\pi$
$229$	−12.1896	+	7.03768i	−0.805513	+	0.465063i	0.0398824	+	0.999204i	$0.487302\pi$
$230$	−3.73205			−0.246084
$231$		0			0
$232$	0.898979			0.0590209
$233$	−17.4916	+	10.0988i	−1.14591	+	0.661593i	−0.947888	−	0.318604i	$-0.896786\pi$
$233$	−17.4916	+	10.0988i	−1.14591	+	0.661593i	−0.198025	+	0.980197i	$0.563453\pi$
$234$		0			0
$235$	0.830749	−	1.43890i	0.0541921	−	0.0938635i
$236$	−5.32112	−	9.21645i	−0.346375	−	0.599940i
$237$		0			0
$238$	−19.3378	+	1.38839i	−1.25348	+	0.0899959i
$239$		−	23.5040i		−	1.52035i	−0.649721	−	0.760173i	$-0.725114\pi$
$239$		−	23.5040i		−	1.52035i	0.649721	−	0.760173i	$-0.274886\pi$
$240$		0			0
$241$	−12.8765	−	7.43426i	−0.829449	−	0.478883i	0.0242151	−	0.999707i	$-0.492291\pi$
$241$	−12.8765	−	7.43426i	−0.829449	−	0.478883i	−0.853664	+	0.520824i	$0.825625\pi$
$242$	−4.20390	−	2.42713i	−0.270237	−	0.156022i
$243$		0			0
$244$		−	7.52056i		−	0.481454i
$245$	4.33013	+	5.50000i	0.276642	+	0.351382i
$246$		0			0
$247$	−0.0693504	−	0.120118i	−0.00441266	−	0.00764295i
$248$	2.41421	−	4.18154i	0.153303	−	0.265528i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	4.31736			0.272509			0.136255	−	0.990674i	$-0.456493\pi$
$251$	4.31736			0.272509			0.136255	+	0.990674i	$0.456493\pi$
$252$		0			0
$253$	14.8601			0.934244
$254$	−9.31236	+	5.37649i	−0.584309	+	0.337351i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.41662	−	4.18570i	−0.150744	−	0.261097i	0.780757	−	0.624835i	$-0.214834\pi$
$257$	−2.41662	−	4.18570i	−0.150744	−	0.261097i	−0.931501	+	0.363738i	$0.881500\pi$
$258$		0			0
$259$	8.91197	−	6.03536i	0.553763	−	0.375019i
$260$		−	0.0681483i		−	0.00422638i
$261$		0			0
$262$	3.21221	+	1.85457i	0.198451	+	0.114576i
$263$	−5.77197	−	3.33245i	−0.355915	−	0.205488i	0.311372	−	0.950288i	$-0.399211\pi$
$263$	−5.77197	−	3.33245i	−0.355915	−	0.205488i	−0.667287	+	0.744800i	$0.732545\pi$
$264$		0			0
$265$			13.2268i			0.812515i
$266$	−4.84424	−	2.35155i	−0.297019	−	0.144183i
$267$		0			0
$268$	5.33145	+	9.23435i	0.325670	+	0.564078i
$269$	−15.8700	+	27.4877i	−0.967612	+	1.67595i	−0.265186	+	0.964197i	$0.585433\pi$
$269$	−15.8700	+	27.4877i	−0.967612	+	1.67595i	−0.702426	+	0.711757i	$0.747900\pi$
$270$		0			0
$271$	15.1244	−	8.73205i	0.918739	−	0.530434i	0.0355066	−	0.999369i	$-0.488696\pi$
$271$	15.1244	−	8.73205i	0.918739	−	0.530434i	0.883233	+	0.468935i	$0.155362\pi$
$272$	7.32780			0.444313
$273$		0			0
$274$	13.5206			0.816807
$275$	3.44829	−	1.99087i	0.207940	−	0.120054i
$276$		0			0
$277$	11.7524	−	20.3557i	0.706130	−	1.22305i	−0.260152	−	0.965568i	$-0.583773\pi$
$277$	11.7524	−	20.3557i	0.706130	−	1.22305i	0.966282	−	0.257486i	$-0.0828941\pi$
$278$	−4.53125	−	7.84836i	−0.271767	−	0.470714i
$279$		0			0
$280$	−1.48356	−	2.19067i	−0.0886599	−	0.130918i
$281$		−	15.4159i		−	0.919635i	−0.888013	−	0.459817i	$-0.847915\pi$
$281$		−	15.4159i		−	0.919635i	0.888013	−	0.459817i	$-0.152085\pi$
$282$		0			0
$283$	−23.9983	−	13.8554i	−1.42655	−	0.823619i	−0.429703	−	0.902970i	$-0.641382\pi$
$283$	−23.9983	−	13.8554i	−1.42655	−	0.823619i	−0.996847	+	0.0793517i	$0.974715\pi$
$284$	−8.60332	−	4.96713i	−0.510513	−	0.294745i
$285$		0			0
$286$			0.271349i			0.0160452i
$287$	0.320053	+	4.45776i	0.0188921	+	0.263133i
$288$		0			0
$289$	−18.3484	−	31.7803i	−1.07932	−	1.86943i
$290$	0.449490	−	0.778539i	0.0263949	−	0.0457174i
$291$		0			0
$292$	−10.0951	+	5.82843i	−0.590773	+	0.341083i
$293$	−2.84377			−0.166135			−0.0830673	−	0.996544i	$-0.526472\pi$
$293$	−2.84377			−0.166135			−0.0830673	+	0.996544i	$0.526472\pi$
$294$		0			0
$295$	−10.6422			−0.619615
$296$	−3.52312	+	2.03407i	−0.204777	+	0.118228i
$297$		0			0
$298$	−7.64324	+	13.2385i	−0.442761	+	0.766884i
$299$	−0.127167	−	0.220259i	−0.00735423	−	0.0127379i
$300$		0			0
$301$	0.182785	+	2.54587i	0.0105355	+	0.146741i
$302$			9.87883i			0.568463i
$303$		0			0
$304$	1.76260	+	1.01764i	0.101092	+	0.0583655i
$305$	−6.51299	−	3.76028i	−0.372933	−	0.215313i
$306$		0			0
$307$		−	2.52180i		−	0.143927i	−0.997407	−	0.0719634i	$-0.977074\pi$
$307$		−	2.52180i		−	0.143927i	0.997407	−	0.0719634i	$-0.0229265\pi$
$308$	5.90717	+	8.72268i	0.336592	+	0.497021i
$309$		0			0
$310$	−2.41421	−	4.18154i	−0.137118	−	0.237496i
$311$	−5.49697	+	9.52104i	−0.311705	+	0.539889i	−0.978732	−	0.205145i	$-0.934233\pi$
$311$	−5.49697	+	9.52104i	−0.311705	+	0.539889i	0.667027	+	0.745034i	$0.267567\pi$
$312$		0			0
$313$	21.6040	−	12.4731i	1.22113	−	0.705020i	0.255971	−	0.966684i	$-0.417605\pi$
$313$	21.6040	−	12.4731i	1.22113	−	0.705020i	0.965159	+	0.261665i	$0.0842714\pi$
$314$	−14.2884			−0.806339
$315$		0			0
$316$	−17.5498			−0.987252
$317$	−13.0504	+	7.53465i	−0.732984	+	0.423188i	−0.819513	−	0.573061i	$-0.805756\pi$
$317$	−13.0504	+	7.53465i	−0.732984	+	0.423188i	0.0865290	+	0.996249i	$0.472422\pi$
$318$		0			0
$319$	−1.78975	+	3.09994i	−0.100207	+	0.173563i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−8.88280	−	4.31199i	−0.495019	−	0.240298i
$323$		−	14.9141i		−	0.829843i
$324$		0			0
$325$	−0.0590182	−	0.0340742i	−0.00327374	−	0.00189010i
$326$	8.64083	+	4.98879i	0.478572	+	0.276303i
$327$		0			0
$328$		−	1.68921i		−	0.0932711i
$329$	3.63980	−	2.46494i	0.200668	−	0.135896i
$330$		0			0
$331$	−15.0904	−	26.1373i	−0.829444	−	1.43664i	−0.898475	−	0.439024i	$-0.855324\pi$
$331$	−15.0904	−	26.1373i	−0.829444	−	1.43664i	0.0690315	−	0.997614i	$-0.478009\pi$
$332$	7.17449	−	12.4266i	0.393751	−	0.681997i
$333$		0			0
$334$	−11.9319	+	6.88891i	−0.652886	+	0.376944i
$335$	10.6629			0.582577
$336$		0			0
$337$	−21.5911			−1.17614			−0.588071	−	0.808809i	$-0.700113\pi$
$337$	−21.5911			−1.17614			−0.588071	+	0.808809i	$0.700113\pi$
$338$	−11.2543	+	6.49768i	−0.612154	+	0.353427i
$339$		0			0
$340$	3.66390	−	6.34607i	0.198703	−	0.344164i
$341$	9.61277	+	16.6498i	0.520561	+	0.901638i
$342$		0			0
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$		−	0.964724i		−	0.0520144i
$345$		0			0
$346$	−7.16442	−	4.13638i	−0.385161	−	0.222373i
$347$	−20.0781	−	11.5921i	−1.07785	−	0.622297i	−0.147534	−	0.989057i	$-0.547134\pi$
$347$	−20.0781	−	11.5921i	−1.07785	−	0.622297i	−0.930316	+	0.366760i	$0.880467\pi$
$348$		0			0
$349$			10.7287i			0.574292i	0.957887	+	0.287146i	$0.0927064\pi$
$349$			10.7287i			0.574292i	−0.957887	+	0.287146i	$0.907294\pi$
$350$	−2.63896	+	0.189469i	−0.141058	+	0.0101275i
$351$		0			0
$352$	−1.99087	−	3.44829i	−0.106114	−	0.183794i
$353$	−4.37378	+	7.57561i	−0.232793	+	0.403209i	−0.958629	−	0.284659i	$-0.908120\pi$
$353$	−4.37378	+	7.57561i	−0.232793	+	0.403209i	0.725836	+	0.687868i	$0.241453\pi$
$354$		0			0
$355$	−8.60332	+	4.96713i	−0.456617	+	0.263628i
$356$	1.82791			0.0968791
$357$		0			0
$358$	−11.5182			−0.608753
$359$	22.3059	−	12.8783i	1.17726	−	0.679691i	0.221881	−	0.975074i	$-0.428780\pi$
$359$	22.3059	−	12.8783i	1.17726	−	0.679691i	0.955379	+	0.295382i	$0.0954470\pi$
$360$		0			0
$361$	−7.42883	+	12.8671i	−0.390991	+	0.677216i
$362$	−8.29618	−	14.3694i	−0.436037	−	0.755239i
$363$		0			0
$364$	0.0787382	−	0.162203i	0.00412700	−	0.00850172i
$365$			11.6569i			0.610148i
$366$		0			0
$367$	17.2665	+	9.96885i	0.901306	+	0.520369i	0.877624	−	0.479350i	$-0.159128\pi$
$367$	17.2665	+	9.96885i	0.901306	+	0.520369i	0.0236826	+	0.999720i	$0.492461\pi$
$368$	3.23205	+	1.86603i	0.168482	+	0.0972733i
$369$		0			0
$370$			4.06815i			0.211493i
$371$	−15.2822	+	31.4816i	−0.793410	+	1.63444i
$372$		0			0
$373$	−0.515762	−	0.893327i	−0.0267052	−	0.0462547i	0.852364	−	0.522949i	$-0.175168\pi$
$373$	−0.515762	−	0.893327i	−0.0267052	−	0.0462547i	−0.879069	+	0.476694i	$0.841835\pi$
$374$	−14.5887	+	25.2684i	−0.754364	+	1.30660i
$375$		0			0
$376$	−1.43890	+	0.830749i	−0.0742056	+	0.0428426i
$377$	0.0612640			0.00315525
$378$		0			0
$379$	5.09497			0.261711			0.130855	−	0.991401i	$-0.458228\pi$
$379$	5.09497			0.261711			0.130855	+	0.991401i	$0.458228\pi$
$380$	1.76260	−	1.01764i	0.0904195	−	0.0522037i
$381$		0			0
$382$	9.21682	−	15.9640i	0.471573	−	0.816789i
$383$	4.23375	+	7.33307i	0.216335	+	0.374702i	0.953685	−	0.300808i	$-0.0972565\pi$
$383$	4.23375	+	7.33307i	0.216335	+	0.374702i	−0.737350	+	0.675511i	$0.763923\pi$
$384$		0			0
$385$	10.5076	−	0.754415i	0.535519	−	0.0384485i
$386$			6.35827i			0.323628i
$387$		0			0
$388$	14.8525	+	8.57509i	0.754021	+	0.435334i
$389$	−4.97229	−	2.87075i	−0.252105	−	0.145553i	0.368623	−	0.929579i	$-0.379829\pi$
$389$	−4.97229	−	2.87075i	−0.252105	−	0.145553i	−0.620728	+	0.784026i	$0.713163\pi$
$390$		0			0
$391$		−	27.3477i		−	1.38303i
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$		0			0
$394$	−6.41946	−	11.1188i	−0.323407	−	0.560158i
$395$	−8.77489	+	15.1986i	−0.441513	+	0.764722i
$396$		0			0
$397$	14.6149	−	8.43791i	0.733501	−	0.423487i	−0.0862009	−	0.996278i	$-0.527473\pi$
$397$	14.6149	−	8.43791i	0.733501	−	0.423487i	0.819701	+	0.572791i	$0.194139\pi$
$398$	9.62962			0.482689
$399$		0			0
$400$	1.00000			0.0500000
$401$	1.63572	−	0.944382i	0.0816838	−	0.0471602i	−0.458602	−	0.888642i	$-0.651650\pi$
$401$	1.63572	−	0.944382i	0.0816838	−	0.0471602i	0.540286	+	0.841482i	$0.318316\pi$
$402$		0			0
$403$	0.164525	−	0.284965i	0.00819556	−	0.0141951i
$404$	−3.36773	−	5.83307i	−0.167551	−	0.290206i
$405$		0			0
$406$	1.96937	−	1.33369i	0.0977381	−	0.0661901i
$407$		−	16.1983i		−	0.802920i
$408$		0			0
$409$	28.5617	+	16.4901i	1.41228	+	0.815382i	0.995603	−	0.0936705i	$-0.0298600\pi$
$409$	28.5617	+	16.4901i	1.41228	+	0.815382i	0.416681	+	0.909053i	$0.363193\pi$
$410$	−1.46290	−	0.844605i	−0.0722475	−	0.0417121i
$411$		0			0
$412$		−	0.520042i		−	0.0256206i
$413$	−25.3300	−	12.2960i	−1.24641	−	0.605046i
$414$		0			0
$415$	−7.17449	−	12.4266i	−0.352182	−	0.609997i
$416$	−0.0340742	+	0.0590182i	−0.00167062	+	0.00289361i
$417$		0			0
$418$	−7.01822	+	4.05197i	−0.343272	+	0.198188i
$419$	−0.300470			−0.0146789			−0.00733945	−	0.999973i	$-0.502336\pi$
$419$	−0.300470			−0.0146789			−0.00733945	+	0.999973i	$0.502336\pi$
$420$		0			0
$421$	28.8625			1.40667			0.703335	−	0.710858i	$-0.251693\pi$
$421$	28.8625			1.40667			0.703335	+	0.710858i	$0.251693\pi$
$422$	12.6110	−	7.28094i	0.613892	−	0.354431i
$423$		0			0
$424$	6.61339	−	11.4547i	0.321175	−	0.556291i
$425$	−3.66390	−	6.34607i	−0.177725	−	0.307829i
$426$		0			0
$427$	−11.1572	−	16.4751i	−0.539936	−	0.797284i
$428$			6.12701i			0.296160i
$429$		0			0
$430$	−0.835475	−	0.482362i	−0.0402902	−	0.0232616i
$431$	29.0895	+	16.7948i	1.40119	+	0.808978i	0.994515	−	0.104594i	$-0.0333543\pi$
$431$	29.0895	+	16.7948i	1.40119	+	0.808978i	0.406677	+	0.913572i	$0.366688\pi$
$432$		0			0
$433$			11.2207i			0.539234i	0.962968	+	0.269617i	$0.0868971\pi$
$433$			11.2207i			0.539234i	−0.962968	+	0.269617i	$0.913103\pi$
$434$	−0.914836	−	12.7420i	−0.0439135	−	0.611636i
$435$		0			0
$436$	6.77729	+	11.7386i	0.324574	+	0.562178i
$437$	3.79788	−	6.57812i	0.181677	−	0.314674i
$438$		0			0
$439$	−14.6075	+	8.43363i	−0.697177	+	0.402515i	−0.806295	−	0.591513i	$-0.798531\pi$
$439$	−14.6075	+	8.43363i	−0.697177	+	0.402515i	0.109118	+	0.994029i	$0.465197\pi$
$440$	−3.98174			−0.189822
$441$		0			0
$442$	0.499378			0.0237530
$443$	1.78094	−	1.02823i	0.0846152	−	0.0488526i	−0.457095	−	0.889418i	$-0.651110\pi$
$443$	1.78094	−	1.02823i	0.0846152	−	0.0488526i	0.541711	+	0.840565i	$0.317777\pi$
$444$		0			0
$445$	0.913956	−	1.58302i	0.0433257	−	0.0750422i
$446$	11.8305	+	20.4910i	0.560189	+	0.970276i
$447$		0			0
$448$	0.189469	+	2.63896i	0.00895155	+	0.124679i
$449$		−	12.5892i		−	0.594122i	−0.954858	−	0.297061i	$-0.903994\pi$
$449$		−	12.5892i		−	0.594122i	0.954858	−	0.297061i	$-0.0960065\pi$
$450$		0			0
$451$	5.82489	+	3.36300i	0.274283	+	0.158357i
$452$	−10.1309	−	5.84909i	−0.476519	−	0.275118i
$453$		0			0
$454$			8.64048i			0.405518i
$455$	−0.101102	−	0.149291i	−0.00473975	−	0.00699885i
$456$		0			0
$457$	−17.4765	−	30.2701i	−0.817515	−	1.41598i	−0.907508	−	0.420035i	$-0.862018\pi$
$457$	−17.4765	−	30.2701i	−0.817515	−	1.41598i	0.0899930	−	0.995942i	$-0.471316\pi$
$458$	7.03768	−	12.1896i	0.328849	−	0.569584i
$459$		0			0
$460$	3.23205	−	1.86603i	0.150695	−	0.0870039i
$461$	−23.3750			−1.08868			−0.544341	−	0.838864i	$-0.683220\pi$
$461$	−23.3750			−1.08868			−0.544341	+	0.838864i	$0.683220\pi$
$462$		0			0
$463$	−6.35693			−0.295431			−0.147716	−	0.989030i	$-0.547192\pi$
$463$	−6.35693			−0.295431			−0.147716	+	0.989030i	$0.547192\pi$
$464$	−0.778539	+	0.449490i	−0.0361428	+	0.0208670i
$465$		0			0
$466$	10.0988	−	17.4916i	0.467817	−	0.810283i
$467$	−3.89658	−	6.74907i	−0.180312	−	0.312310i	0.761675	−	0.647960i	$-0.224377\pi$
$467$	−3.89658	−	6.74907i	−0.180312	−	0.312310i	−0.941987	+	0.335650i	$0.891044\pi$
$468$		0			0
$469$	25.3792	+	12.3199i	1.17190	+	0.568878i
$470$			1.66150i			0.0766392i
$471$		0			0
$472$	9.21645	+	5.32112i	0.424222	+	0.244924i
$473$	3.32665	+	1.92064i	0.152959	+	0.0883111i
$474$		0			0
$475$		−	2.03528i		−	0.0933849i
$476$	16.0528	−	10.8713i	0.735779	−	0.498284i
$477$		0			0
$478$	11.7520	+	20.3550i	0.537523	+	0.931018i
$479$	−13.7520	+	23.8191i	−0.628344	+	1.08832i	0.359540	+	0.933130i	$0.382934\pi$
$479$	−13.7520	+	23.8191i	−0.628344	+	1.08832i	−0.987884	+	0.155194i	$0.950400\pi$
$480$		0			0
$481$	−0.240095	+	0.138619i	−0.0109474	+	0.00632047i
$482$	14.8685			0.677242
$483$		0			0
$484$	4.85425			0.220648
$485$	14.8525	−	8.57509i	0.674417	−	0.389375i
$486$		0			0
$487$	−17.7234	+	30.6978i	−0.803124	+	1.39105i	0.114427	+	0.993432i	$0.463497\pi$
$487$	−17.7234	+	30.6978i	−0.803124	+	1.39105i	−0.917551	+	0.397619i	$0.869836\pi$
$488$	3.76028	+	6.51299i	0.170220	+	0.294829i
$489$		0			0
$490$	−6.50000	−	2.59808i	−0.293640	−	0.117369i
$491$		−	1.64349i		−	0.0741695i	−0.999312	−	0.0370848i	$-0.988193\pi$
$491$		−	1.64349i		−	0.0741695i	0.999312	−	0.0370848i	$-0.0118072\pi$
$492$		0			0
$493$	5.70498	+	3.29377i	0.256939	+	0.148344i
$494$	0.120118	+	0.0693504i	0.00540438	+	0.00312022i
$495$		0			0
$496$			4.82843i			0.216803i
$497$	−26.2161	+	1.88223i	−1.17595	+	0.0844296i
$498$		0			0
$499$	17.3665	+	30.0796i	0.777430	+	1.34655i	0.933418	+	0.358790i	$0.116811\pi$
$499$	17.3665	+	30.0796i	0.777430	+	1.34655i	−0.155988	+	0.987759i	$0.549856\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−3.73894	+	2.15868i	−0.166877	+	0.0963465i
$503$	−28.9613			−1.29132			−0.645660	−	0.763625i	$-0.723418\pi$
$503$	−28.9613			−1.29132			−0.645660	+	0.763625i	$0.723418\pi$
$504$		0			0
$505$	−6.73545			−0.299724
$506$	−12.8692	+	7.43003i	−0.572105	+	0.330305i
$507$		0			0
$508$	5.37649	−	9.31236i	0.238543	−	0.413169i
$509$	10.7311	+	18.5867i	0.475646	+	0.823842i	0.999611	−	0.0278973i	$-0.00888113\pi$
$509$	10.7311	+	18.5867i	0.475646	+	0.823842i	−0.523965	+	0.851740i	$0.675548\pi$
$510$		0			0
$511$	−13.4683	+	27.7449i	−0.595801	+	1.22736i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	4.18570	+	2.41662i	0.184624	+	0.106592i
$515$	−0.450370	−	0.260021i	−0.0198457	−	0.0114579i
$516$		0			0
$517$		−	6.61565i		−	0.290956i
$518$	−4.70032	+	9.68276i	−0.206520	+	0.425436i
$519$		0			0
$520$	0.0340742	+	0.0590182i	0.00149425	+	0.00258812i
$521$	20.1218	−	34.8520i	0.881552	−	1.52689i	0.0319362	−	0.999490i	$-0.489833\pi$
$521$	20.1218	−	34.8520i	0.881552	−	1.52689i	0.849616	−	0.527403i	$-0.176834\pi$
$522$		0			0
$523$	25.7113	−	14.8444i	1.12428	−	0.649102i	0.181789	−	0.983338i	$-0.441811\pi$
$523$	25.7113	−	14.8444i	1.12428	−	0.649102i	0.942490	+	0.334235i	$0.108478\pi$
$524$	−3.70915			−0.162035
$525$		0			0
$526$	6.66490			0.290603
$527$	30.6415	−	17.6909i	1.33477	−	0.770627i
$528$		0			0
$529$	−4.53590	+	7.85641i	−0.197213	+	0.341583i
$530$	−6.61339	−	11.4547i	−0.287267	−	0.497562i
$531$		0			0
$532$	5.37101	−	0.385621i	0.232863	−	0.0167188i
$533$		−	0.115117i		−	0.00498627i
$534$		0			0
$535$	5.30614	+	3.06350i	0.229405	+	0.132447i
$536$	−9.23435	−	5.33145i	−0.398863	−	0.230284i
$537$		0			0
$538$		−	31.7400i		−	1.36841i
$539$	25.8813	+	10.3449i	1.11479	+	0.445585i
$540$		0			0
$541$	8.62914	+	14.9461i	0.370996	+	0.642584i	0.989719	−	0.143026i	$-0.0456831\pi$
$541$	8.62914	+	14.9461i	0.370996	+	0.642584i	−0.618723	+	0.785609i	$0.712350\pi$
$542$	−8.73205	+	15.1244i	−0.375074	+	0.649647i
$543$		0			0
$544$	−6.34607	+	3.66390i	−0.272085	+	0.157089i
$545$	13.5546			0.580615
$546$		0			0
$547$	−17.9703			−0.768354			−0.384177	−	0.923260i	$-0.625515\pi$
$547$	−17.9703			−0.768354			−0.384177	+	0.923260i	$0.625515\pi$
$548$	−11.7091	+	6.76028i	−0.500190	+	0.288785i
$549$		0			0
$550$	−1.99087	+	3.44829i	−0.0848910	+	0.147035i
$551$	0.914836	+	1.58454i	0.0389733	+	0.0675038i
$552$		0			0
$553$	−38.4458	+	26.0362i	−1.63488	+	1.10717i
$554$			23.5047i			0.998619i
$555$		0			0
$556$	7.84836	+	4.53125i	0.332845	+	0.192168i
$557$	39.1916	+	22.6273i	1.66060	+	0.958748i	0.972428	+	0.233201i	$0.0749201\pi$
$557$	39.1916	+	22.6273i	1.66060	+	0.958748i	0.688172	+	0.725547i	$0.258413\pi$
$558$		0			0
$559$		−	0.0657443i		−	0.00278069i
$560$	2.38014	+	1.15539i	0.100579	+	0.0488243i
$561$		0			0
$562$	7.70794	+	13.3506i	0.325140	+	0.563159i
$563$	7.93336	−	13.7410i	0.334351	−	0.579114i	−0.649009	−	0.760781i	$-0.724816\pi$
$563$	7.93336	−	13.7410i	0.334351	−	0.579114i	0.983360	+	0.181667i	$0.0581494\pi$
$564$		0			0
$565$	−10.1309	+	5.84909i	−0.426211	+	0.246073i
$566$	27.7108			1.16477
$567$		0			0
$568$	9.93426			0.416832
$569$	0.0524375	−	0.0302748i	0.00219829	−	0.00126918i	−0.498900	−	0.866659i	$-0.666263\pi$
$569$	0.0524375	−	0.0302748i	0.00219829	−	0.00126918i	0.501099	+	0.865390i	$0.332929\pi$
$570$		0			0
$571$	6.78245	−	11.7476i	0.283837	−	0.491620i	−0.688490	−	0.725246i	$-0.741726\pi$
$571$	6.78245	−	11.7476i	0.283837	−	0.491620i	0.972326	+	0.233626i	$0.0750592\pi$
$572$	−0.135674	−	0.234995i	−0.00567284	−	0.00982564i
$573$		0			0
$574$	−2.50605	−	3.70050i	−0.104601	−	0.154456i
$575$		−	3.73205i		−	0.155637i
$576$		0			0
$577$	−37.8252	−	21.8384i	−1.57468	−	0.909144i	−0.995583	−	0.0938887i	$-0.970070\pi$
$577$	−37.8252	−	21.8384i	−1.57468	−	0.909144i	−0.579101	−	0.815256i	$-0.696596\pi$
$578$	31.7803	+	18.3484i	1.32189	+	0.763191i
$579$		0			0
$580$			0.898979i			0.0373281i
$581$	−2.71868	−	37.8664i	−0.112790	−	1.57096i
$582$		0			0
$583$	26.3328	+	45.6098i	1.09059	+	1.88896i
$584$	5.82843	−	10.0951i	0.241182	−	0.417740i
$585$		0			0
$586$	2.46278	−	1.42188i	0.101736	−	0.0587375i
$587$	45.4100			1.87427			0.937135	−	0.348967i	$-0.113468\pi$
$587$	45.4100			1.87427			0.937135	+	0.348967i	$0.113468\pi$
$588$		0			0
$589$	9.82718			0.404922
$590$	9.21645	−	5.32112i	0.379435	−	0.219067i
$591$		0			0
$592$	2.03407	−	3.52312i	0.0835999	−	0.144799i
$593$	12.8506	+	22.2579i	0.527711	+	0.914022i	0.999478	+	0.0322991i	$0.0102829\pi$
$593$	12.8506	+	22.2579i	0.527711	+	0.914022i	−0.471767	+	0.881723i	$0.656384\pi$
$594$		0			0
$595$	−1.38839	−	19.3378i	−0.0569184	−	0.792771i
$596$		−	15.2865i		−	0.626158i
$597$		0			0
$598$	0.220259	+	0.127167i	0.00900706	+	0.00520023i
$599$	−23.0347	−	13.2991i	−0.941173	−	0.543386i	−0.0508450	−	0.998707i	$-0.516191\pi$
$599$	−23.0347	−	13.2991i	−0.941173	−	0.543386i	−0.890328	+	0.455320i	$0.849525\pi$
$600$		0			0
$601$			12.9681i			0.528979i	0.964389	+	0.264489i	$0.0852034\pi$
$601$			12.9681i			0.528979i	−0.964389	+	0.264489i	$0.914797\pi$
$602$	−1.43123	−	2.11339i	−0.0583326	−	0.0861354i
$603$		0			0
$604$	−4.93942	−	8.55532i	−0.200982	−	0.348111i
$605$	2.42713	−	4.20390i	0.0986767	−	0.170913i
$606$		0			0
$607$	−14.1262	+	8.15576i	−0.573364	+	0.331032i	−0.758492	−	0.651682i	$-0.774063\pi$
$607$	−14.1262	+	8.15576i	−0.573364	+	0.331032i	0.185128	+	0.982714i	$0.440730\pi$
$608$	−2.03528			−0.0825413
$609$		0			0
$610$	7.52056			0.304498
$611$	−0.0980586	+	0.0566142i	−0.00396703	+	0.00229036i
$612$		0			0
$613$	7.19395	−	12.4603i	0.290561	−	0.503267i	−0.683381	−	0.730062i	$-0.739491\pi$
$613$	7.19395	−	12.4603i	0.290561	−	0.503267i	0.973943	+	0.226795i	$0.0728247\pi$
$614$	1.26090	+	2.18394i	0.0508858	+	0.0881368i
$615$		0			0
$616$	−9.47710	−	4.60048i	−0.381843	−	0.185359i
$617$			8.65760i			0.348542i	0.984698	+	0.174271i	$0.0557569\pi$
$617$			8.65760i			0.348542i	−0.984698	+	0.174271i	$0.944243\pi$
$618$		0			0
$619$	38.8459	+	22.4277i	1.56135	+	0.901444i	0.997121	+	0.0758230i	$0.0241584\pi$
$619$	38.8459	+	22.4277i	1.56135	+	0.901444i	0.564225	+	0.825621i	$0.309175\pi$
$620$	4.18154	+	2.41421i	0.167935	+	0.0969571i
$621$		0			0
$622$		−	10.9939i		−	0.440817i
$623$	4.00435	−	2.71182i	0.160431	−	0.108647i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.4731	+	21.6040i	−0.498524	+	0.863469i
$627$		0			0
$628$	12.3741	−	7.14418i	0.493780	−	0.285084i
$629$	−29.8106			−1.18863
$630$		0			0
$631$	−38.1878			−1.52023			−0.760116	−	0.649788i	$-0.774858\pi$
$631$	−38.1878			−1.52023			−0.760116	+	0.649788i	$0.774858\pi$
$632$	15.1986	−	8.77489i	0.604566	−	0.349046i
$633$		0			0
$634$	7.53465	−	13.0504i	0.299239	−	0.518298i
$635$	−5.37649	−	9.31236i	−0.213360	−	0.369550i
$636$		0			0
$637$	−0.0681483	−	0.472146i	−0.00270014	−	0.0187071i
$638$		−	3.57950i		−	0.141714i
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−7.40533	−	4.27547i	−0.292493	−	0.168871i	0.346573	−	0.938023i	$-0.387345\pi$
$641$	−7.40533	−	4.27547i	−0.292493	−	0.168871i	−0.639066	+	0.769152i	$0.720679\pi$
$642$		0			0
$643$			2.75058i			0.108472i	0.998528	+	0.0542361i	$0.0172724\pi$
$643$			2.75058i			0.108472i	−0.998528	+	0.0542361i	$0.982728\pi$
$644$	9.84873	−	0.707107i	0.388094	−	0.0278639i
$645$		0			0
$646$	7.45705	+	12.9160i	0.293394	+	0.508173i
$647$	13.8813	−	24.0431i	0.545731	−	0.945234i	−0.452830	−	0.891597i	$-0.649585\pi$
$647$	13.8813	−	24.0431i	0.545731	−	0.945234i	0.998561	−	0.0536365i	$-0.0170812\pi$
$648$		0			0
$649$	−36.6975	+	21.1873i	−1.44050	+	0.831675i
$650$	0.0681483			0.00267300
$651$		0			0
$652$	−9.97758			−0.390752
$653$	12.2282	−	7.05994i	0.478525	−	0.276277i	−0.241276	−	0.970456i	$-0.577566\pi$
$653$	12.2282	−	7.05994i	0.478525	−	0.276277i	0.719802	+	0.694180i	$0.244233\pi$
$654$		0			0
$655$	−1.85457	+	3.21221i	−0.0724642	+	0.125512i
$656$	0.844605	+	1.46290i	0.0329763	+	0.0571166i
$657$		0			0
$658$	−1.91969	+	3.95460i	−0.0748372	+	0.154166i
$659$			9.92570i			0.386650i	0.981135	+	0.193325i	$0.0619272\pi$
$659$			9.92570i			0.386650i	−0.981135	+	0.193325i	$0.938073\pi$
$660$		0			0
$661$	15.9029	+	9.18154i	0.618551	+	0.357121i	0.776305	−	0.630358i	$-0.217092\pi$
$661$	15.9029	+	9.18154i	0.618551	+	0.357121i	−0.157754	+	0.987478i	$0.550425\pi$
$662$	26.1373	+	15.0904i	1.01586	+	0.586505i
$663$		0			0
$664$			14.3490i			0.556849i
$665$	2.35155	−	4.84424i	0.0911891	−	0.187852i
$666$		0			0
$667$	1.67752	+	2.90555i	0.0649538	+	0.112503i
$668$	6.88891	−	11.9319i	0.266540	−	0.461660i
$669$		0			0
$670$	−9.23435	+	5.33145i	−0.356754	+	0.205972i
$671$	−29.9449			−1.15601
$672$		0			0
$673$	−32.6050			−1.25683			−0.628415	−	0.777878i	$-0.716296\pi$
$673$	−32.6050			−1.25683			−0.628415	+	0.777878i	$0.716296\pi$
$674$	18.6984	−	10.7956i	0.720237	−	0.415829i
$675$		0			0
$676$	6.49768	−	11.2543i	0.249911	−	0.432858i
$677$	−9.16923	−	15.8816i	−0.352402	−	0.610378i	0.634268	−	0.773113i	$-0.281302\pi$
$677$	−9.16923	−	15.8816i	−0.352402	−	0.610378i	−0.986670	+	0.162735i	$0.947968\pi$
$678$		0			0
$679$	45.2586	−	3.24942i	1.73687	−	0.124701i
$680$			7.32780i			0.281008i
$681$		0			0
$682$	−16.6498	−	9.61277i	−0.637554	−	0.368092i
$683$	−21.1977	−	12.2385i	−0.811108	−	0.468294i	0.0362323	−	0.999343i	$-0.488464\pi$
$683$	−21.1977	−	12.2385i	−0.811108	−	0.468294i	−0.847341	+	0.531050i	$0.821798\pi$
$684$		0			0
$685$			13.5206i			0.516594i
$686$	−12.4691	−	13.6938i	−0.476073	−	0.522834i
$687$		0			0
$688$	0.482362	+	0.835475i	0.0183899	+	0.0318522i
$689$	0.450692	−	0.780621i	0.0171700	−	0.0297393i
$690$		0			0
$691$	−15.9118	+	9.18670i	−0.605315	+	0.349479i	−0.771129	−	0.636678i	$-0.780308\pi$
$691$	−15.9118	+	9.18670i	−0.605315	+	0.349479i	0.165815	+	0.986157i	$0.446975\pi$
$692$	8.27276			0.314483
$693$		0			0
$694$	23.1842			0.880061
$695$	7.84836	−	4.53125i	0.297705	−	0.171880i
$696$		0			0
$697$	6.18910	−	10.7198i	0.234429	−	0.406043i
$698$	−5.36433	−	9.29128i	−0.203043	−	0.351680i
$699$		0			0
$700$	2.19067	−	1.48356i	0.0827996	−	0.0560734i
$701$			14.2399i			0.537834i	0.963163	+	0.268917i	$0.0866658\pi$
$701$			14.2399i			0.537834i	−0.963163	+	0.268917i	$0.913334\pi$
$702$		0			0
$703$	−7.17052	−	4.13990i	−0.270441	−	0.156139i
$704$	3.44829	+	1.99087i	0.129962	+	0.0750337i
$705$		0			0
$706$		−	8.74756i		−	0.329219i
$707$	−16.0313	−	7.78210i	−0.602920	−	0.292676i
$708$		0			0
$709$	−18.7586	−	32.4908i	−0.704492	−	1.22022i	−0.966874	−	0.255252i	$-0.917841\pi$
$709$	−18.7586	−	32.4908i	−0.704492	−	1.22022i	0.262382	−	0.964964i	$-0.415492\pi$
$710$	4.96713	−	8.60332i	0.186413	−	0.322877i
$711$		0			0
$712$	−1.58302	+	0.913956i	−0.0593261	+	0.0342519i
$713$	18.0199			0.674852
$714$		0			0
$715$	−0.271349			−0.0101479
$716$	9.97501	−	5.75908i	0.372784	−	0.215227i
$717$		0			0
$718$	−12.8783	+	22.3059i	−0.480614	+	0.832449i
$719$	−2.65733	−	4.60264i	−0.0991019	−	0.171649i	0.812211	−	0.583363i	$-0.198264\pi$
$719$	−2.65733	−	4.60264i	−0.0991019	−	0.171649i	−0.911313	+	0.411714i	$0.864930\pi$
$720$		0			0
$721$	−0.771516	−	1.13924i	−0.0287327	−	0.0424276i
$722$		−	14.8577i		−	0.552945i
$723$		0			0
$724$	14.3694	+	8.29618i	0.534035	+	0.308325i
$725$	0.778539	+	0.449490i	0.0289142	+	0.0166936i
$726$		0			0
$727$		−	2.93413i		−	0.108821i	−0.998519	−	0.0544104i	$-0.982672\pi$
$727$		−	2.93413i		−	0.108821i	0.998519	−	0.0544104i	$-0.0173279\pi$
$728$	0.0129120	+	0.179841i	0.000478550	+	0.00666534i
$729$		0			0
$730$	−5.82843	−	10.0951i	−0.215720	−	0.373638i
$731$	3.53465	−	6.12220i	0.130734	−	0.226438i
$732$		0			0
$733$	11.8197	−	6.82411i	0.436570	−	0.252054i	−0.265571	−	0.964091i	$-0.585561\pi$
$733$	11.8197	−	6.82411i	0.436570	−	0.252054i	0.702142	+	0.712037i	$0.252227\pi$
$734$	−19.9377			−0.735914
$735$		0			0
$736$	−3.73205			−0.137565
$737$	36.7688	−	21.2285i	1.35440	−	0.781960i
$738$		0			0
$739$	−15.6650	+	27.1325i	−0.576246	+	0.998087i	0.419659	+	0.907682i	$0.362149\pi$
$739$	−15.6650	+	27.1325i	−0.576246	+	0.998087i	−0.995905	+	0.0904051i	$0.971184\pi$
$740$	−2.03407	−	3.52312i	−0.0747741	−	0.129512i
$741$		0			0
$742$	−2.50606	−	34.9049i	−0.0920004	−	1.28140i
$743$			4.72061i			0.173182i	0.996244	+	0.0865911i	$0.0275974\pi$
$743$			4.72061i			0.173182i	−0.996244	+	0.0865911i	$0.972403\pi$
$744$		0			0
$745$	−13.2385	−	7.64324i	−0.485020	−	0.280027i
$746$	0.893327	+	0.515762i	0.0327070	+	0.0188834i
$747$		0			0
$748$		−	29.1774i		−	1.06683i
$749$	9.08981	+	13.4223i	0.332134	+	0.490439i
$750$		0			0
$751$	12.8394	+	22.2385i	0.468516	+	0.811494i	0.999352	−	0.0359807i	$-0.0114555\pi$
$751$	12.8394	+	22.2385i	0.468516	+	0.811494i	−0.530836	+	0.847474i	$0.678122\pi$
$752$	0.830749	−	1.43890i	0.0302943	−	0.0524713i
$753$		0			0
$754$	−0.0530562	+	0.0306320i	−0.00193219	+	0.00111555i
$755$	−9.87883			−0.359527
$756$		0			0
$757$	−37.8781			−1.37670			−0.688352	−	0.725377i	$-0.741665\pi$
$757$	−37.8781			−1.37670			−0.688352	+	0.725377i	$0.741665\pi$
$758$	−4.41237	+	2.54748i	−0.160265	+	0.0925288i
$759$		0			0
$760$	−1.01764	+	1.76260i	−0.0369136	+	0.0639363i
$761$	−10.3533	−	17.9325i	−0.375308	−	0.650052i	0.615065	−	0.788476i	$-0.289130\pi$
$761$	−10.3533	−	17.9325i	−0.375308	−	0.650052i	−0.990373	+	0.138424i	$0.955796\pi$
$762$		0			0
$763$	32.2618	+	15.6609i	1.16796	+	0.566963i
$764$			18.4336i			0.666905i
$765$		0			0
$766$	−7.33307	−	4.23375i	−0.264955	−	0.152972i
$767$	0.628086	+	0.362626i	0.0226789	+	0.0130937i
$768$		0			0
$769$		−	3.34563i		−	0.120647i	−0.998179	−	0.0603233i	$-0.980787\pi$
$769$		−	3.34563i		−	0.120647i	0.998179	−	0.0603233i	$-0.0192132\pi$
$770$	−8.72268	+	5.90717i	−0.314344	+	0.212879i
$771$		0			0
$772$	−3.17914	−	5.50643i	−0.114420	−	0.198181i
$773$	−14.3632	+	24.8778i	−0.516609	+	0.894793i	0.483205	+	0.875507i	$0.339473\pi$
$773$	−14.3632	+	24.8778i	−0.516609	+	0.894793i	−0.999814	+	0.0192861i	$0.993861\pi$
$774$		0			0
$775$	4.18154	−	2.41421i	0.150205	−	0.0867211i
$776$	−17.1502			−0.615656
$777$		0			0
$778$	5.74150			0.205843
$779$	2.97740	−	1.71901i	0.106677	−	0.0615898i
$780$		0			0
$781$	−19.7778	+	34.2562i	−0.707706	+	1.22578i
$782$	13.6739	+	23.6838i	0.488977	+	0.846932i
$783$		0			0
$784$	4.33013	+	5.50000i	0.154647	+	0.196429i
$785$		−	14.2884i		−	0.509974i
$786$		0			0
$787$	−4.75474	−	2.74515i	−0.169488	−	0.0978541i	0.412856	−	0.910796i	$-0.364531\pi$
$787$	−4.75474	−	2.74515i	−0.169488	−	0.0978541i	−0.582345	+	0.812942i	$0.697865\pi$
$788$	11.1188	+	6.41946i	0.396092	+	0.228684i
$789$		0			0
$790$		−	17.5498i		−	0.624393i
$791$	−30.8710	+	2.21644i	−1.09765	+	0.0788075i
$792$		0			0
$793$	0.256257	+	0.443850i	0.00909995	+	0.0157616i
$794$	−8.43791	+	14.6149i	−0.299450	+	0.518663i
$795$		0			0
$796$	−8.33950	+	4.81481i	−0.295586	+	0.170656i
$797$	−50.8854			−1.80245			−0.901227	−	0.433347i	$-0.857332\pi$
$797$	−50.8854			−1.80245			−0.901227	+	0.433347i	$0.857332\pi$
$798$		0			0
$799$	−12.1751			−0.430725
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−0.944382	+	1.63572i	−0.0333473	+	0.0577592i
$803$	23.2073	+	40.1962i	0.818967	+	1.41849i
$804$		0			0
$805$	4.31199	−	8.88280i	0.151978	−	0.313078i
$806$			0.329049i			0.0115903i
$807$		0			0
$808$	5.83307	+	3.36773i	0.205207	+	0.118476i
$809$	1.80508	+	1.04217i	0.0634634	+	0.0366406i	0.531396	−	0.847124i	$-0.321668\pi$
$809$	1.80508	+	1.04217i	0.0634634	+	0.0366406i	−0.467933	+	0.883764i	$0.655001\pi$
$810$		0			0
$811$		−	27.0199i		−	0.948797i	−0.880310	−	0.474398i	$-0.842666\pi$
$811$		−	27.0199i		−	0.948797i	0.880310	−	0.474398i	$-0.157334\pi$
$812$	−1.03868	+	2.13970i	−0.0364504	+	0.0750886i
$813$		0			0
$814$	8.09915	+	14.0281i	0.283875	+	0.491686i
$815$	−4.98879	+	8.64083i	−0.174750	+	0.302675i
$816$		0			0
$817$	1.70042	−	0.981740i	0.0594903	−	0.0343467i
$818$	−32.9802			−1.15312
$819$		0			0
$820$	1.68921			0.0589898
$821$	8.06085	−	4.65393i	0.281326	−	0.162423i	−0.352698	−	0.935737i	$-0.614736\pi$
$821$	8.06085	−	4.65393i	0.281326	−	0.162423i	0.634023	+	0.773314i	$0.281402\pi$
$822$		0			0
$823$	20.2593	−	35.0901i	0.706195	−	1.22316i	−0.260064	−	0.965591i	$-0.583744\pi$
$823$	20.2593	−	35.0901i	0.706195	−	1.22316i	0.966259	−	0.257573i	$-0.0829229\pi$
$824$	0.260021	+	0.450370i	0.00905826	+	0.0156894i
$825$		0			0
$826$	28.0844	−	2.01637i	0.977182	−	0.0701585i
$827$			14.0131i			0.487284i	0.969865	+	0.243642i	$0.0783423\pi$
$827$			14.0131i			0.487284i	−0.969865	+	0.243642i	$0.921658\pi$
$828$		0			0
$829$	18.8540	+	10.8854i	0.654827	+	0.378064i	0.790303	−	0.612716i	$-0.209923\pi$
$829$	18.8540	+	10.8854i	0.654827	+	0.378064i	−0.135476	+	0.990781i	$0.543256\pi$
$830$	12.4266	+	7.17449i	0.431333	+	0.249030i
$831$		0			0
$832$		−	0.0681483i		−	0.00236262i
$833$	19.0382	−	47.6307i	0.659634	−	1.65031i
$834$		0			0
$835$	−6.88891	−	11.9319i	−0.238400	−	0.412922i
$836$	4.05197	−	7.01822i	0.140140	−	0.242730i
$837$		0			0
$838$	0.260214	−	0.150235i	0.00898896	−	0.00518978i
$839$	−53.7026			−1.85402			−0.927009	−	0.375039i	$-0.877629\pi$
$839$	−53.7026			−1.85402			−0.927009	+	0.375039i	$0.877629\pi$
$840$		0			0
$841$	28.1918			0.972132
$842$	−24.9956	+	14.4312i	−0.861406	+	0.497333i
$843$		0			0
$844$	−7.28094	+	12.6110i	−0.250620	+	0.434087i
$845$	−6.49768	−	11.2543i	−0.223527	−	0.387160i
$846$		0			0
$847$	10.6341	−	7.20159i	0.365391	−	0.247450i
$848$			13.2268i			0.454210i
$849$		0			0
$850$	6.34607	+	3.66390i	0.217668	+	0.125671i
$851$	−13.1485	−	7.59127i	−0.450723	−	0.260225i
$852$		0			0
$853$			7.95355i			0.272324i	0.990687	+	0.136162i	$0.0434768\pi$
$853$			7.95355i			0.272324i	−0.990687	+	0.136162i	$0.956523\pi$
$854$	17.9000	+	8.68921i	0.612525	+	0.297339i
$855$		0			0
$856$	−3.06350	−	5.30614i	−0.104708	−	0.181360i
$857$	1.14651	−	1.98582i	0.0391641	−	0.0678343i	−0.845779	−	0.533534i	$-0.820864\pi$
$857$	1.14651	−	1.98582i	0.0391641	−	0.0678343i	0.884943	+	0.465699i	$0.154197\pi$
$858$		0			0
$859$	−38.1054	+	22.0002i	−1.30014	+	0.750636i	−0.980428	−	0.196879i	$-0.936919\pi$
$859$	−38.1054	+	22.0002i	−1.30014	+	0.750636i	−0.319712	+	0.947515i	$0.603586\pi$
$860$	0.964724			0.0328968
$861$		0			0
$862$	−33.5897			−1.14407
$863$	−28.6959	+	16.5676i	−0.976821	+	0.563968i	−0.901309	−	0.433177i	$-0.857393\pi$
$863$	−28.6959	+	16.5676i	−0.976821	+	0.563968i	−0.0755122	+	0.997145i	$0.524059\pi$
$864$		0			0
$865$	4.13638	−	7.16442i	0.140641	−	0.243598i
$866$	−5.61037	−	9.71744i	−0.190648	−	0.330212i
$867$		0			0
$868$	7.16328	+	10.5775i	0.243138	+	0.359024i
$869$			69.8787i			2.37047i
$870$		0			0
$871$	−0.629306	−	0.363330i	−0.0213232	−	0.0123110i
$872$	−11.7386	−	6.77729i	−0.397520	−	0.229508i
$873$		0			0
$874$			7.59575i			0.256930i
$875$	−0.189469	−	2.63896i	−0.00640521	−	0.0892131i
$876$		0			0
$877$	2.84436	+	4.92657i	0.0960471	+	0.166358i	0.910045	−	0.414509i	$-0.136047\pi$
$877$	2.84436	+	4.92657i	0.0960471	+	0.166358i	−0.813998	+	0.580868i	$0.802713\pi$
$878$	8.43363	−	14.6075i	0.284621	−	0.492979i
$879$		0			0
$880$	3.44829	−	1.99087i	0.116242	−	0.0671122i
$881$	22.4073			0.754923			0.377461	−	0.926025i	$-0.376797\pi$
$881$	22.4073			0.754923			0.377461	+	0.926025i	$0.376797\pi$
$882$		0			0
$883$	−18.7564			−0.631204			−0.315602	−	0.948892i	$-0.602206\pi$
$883$	−18.7564			−0.631204			−0.315602	+	0.948892i	$0.602206\pi$
$884$	−0.432474	+	0.249689i	−0.0145457	+	0.00839795i
$885$		0			0
$886$	−1.02823	+	1.78094i	−0.0345440	+	0.0598320i
$887$	0.735451	+	1.27384i	0.0246940	+	0.0427713i	0.878108	−	0.478462i	$-0.158806\pi$
$887$	0.735451	+	1.27384i	0.0246940	+	0.0427713i	−0.853414	+	0.521233i	$0.825472\pi$
$888$		0			0
$889$	−2.03735	−	28.3767i	−0.0683306	−	0.951723i
$890$			1.82791i			0.0612717i
$891$		0			0
$892$	−20.4910	−	11.8305i	−0.686088	−	0.396113i
$893$	−2.92856	−	1.69080i	−0.0980005	−	0.0565806i
$894$		0			0
$895$		−	11.5182i		−	0.385009i
$896$	−1.48356	−	2.19067i	−0.0495624	−	0.0731852i
$897$		0			0
$898$	6.29461	+	10.9026i	0.210054	+	0.363824i
$899$	−2.17033	+	3.75912i	−0.0723845	+	0.125374i
$900$		0			0
$901$	83.9380	−	48.4616i	2.79638	−	1.61449i
$902$	−6.72600			−0.223951
$903$		0			0
$904$	11.6982			0.389076
$905$	14.3694	−	8.29618i	0.477655	−	0.275774i
$906$		0			0
$907$	−9.42294	+	16.3210i	−0.312883	+	0.541930i	−0.978985	−	0.203931i	$-0.934628\pi$
$907$	−9.42294	+	16.3210i	−0.312883	+	0.541930i	0.666102	+	0.745861i	$0.267962\pi$
$908$	−4.32024	−	7.48288i	−0.143372	−	0.248328i
$909$		0			0
$910$	0.162203	+	0.0787382i	0.00537696	+	0.00261015i
$911$			5.45859i			0.180851i	0.995903	+	0.0904256i	$0.0288227\pi$
$911$			5.45859i			0.180851i	−0.995903	+	0.0904256i	$0.971177\pi$
$912$		0			0
$913$	−49.4794	−	28.5670i	−1.63753	−	0.945428i
$914$	30.2701	+	17.4765i	1.00125	+	0.578070i
$915$		0			0
$916$			14.0754i			0.465063i
$917$	−8.12552	+	5.50276i	−0.268328	+	0.181717i
$918$		0			0
$919$	−14.9805	−	25.9470i	−0.494162	−	0.855914i	0.505815	−	0.862642i	$-0.331192\pi$
$919$	−14.9805	−	25.9470i	−0.494162	−	0.855914i	−0.999977	+	0.00672796i	$0.997858\pi$
$920$	−1.86603	+	3.23205i	−0.0615210	+	0.106558i
$921$		0			0
$922$	20.2433	−	11.6875i	0.666678	−	0.384907i
$923$	0.677003			0.0222838
$924$		0			0
$925$	−4.06815			−0.133760
$926$	5.50526	−	3.17846i	0.180914	−	0.104451i
$927$		0			0
$928$	0.449490	−	0.778539i	0.0147552	−	0.0255568i
$929$	−23.3931	−	40.5181i	−0.767504	−	1.32936i	−0.938912	−	0.344156i	$-0.888165\pi$
$929$	−23.3931	−	40.5181i	−0.767504	−	1.32936i	0.171408	−	0.985200i	$-0.445168\pi$
$930$		0			0
$931$	11.1940	−	8.81300i	0.366869	−	0.288835i
$932$			20.1976i			0.661593i
$933$		0			0
$934$	6.74907	+	3.89658i	0.220836	+	0.127500i
$935$	−25.2684	−	14.5887i	−0.826364	−	0.477102i
$936$		0			0
$937$		−	19.1632i		−	0.626036i	−0.949747	−	0.313018i	$-0.898660\pi$
$937$		−	19.1632i		−	0.626036i	0.949747	−	0.313018i	$-0.101340\pi$
$938$	−28.1390	+	2.02029i	−0.918770	+	0.0659647i
$939$		0			0
$940$	−0.830749	−	1.43890i	−0.0270961	−	0.0469317i
$941$	25.2474	−	43.7299i	0.823043	−	1.42555i	−0.0803623	−	0.996766i	$-0.525608\pi$
$941$	25.2474	−	43.7299i	0.823043	−	1.42555i	0.903406	−	0.428787i	$-0.141059\pi$
$942$		0			0
$943$	5.45962	−	3.15211i	0.177790	−	0.102647i
$944$	−10.6422			−0.346375
$945$		0			0
$946$	−3.84128			−0.124891
$947$	−31.2304	+	18.0309i	−1.01485	+	0.585925i	−0.912609	−	0.408834i	$-0.865936\pi$
$947$	−31.2304	+	18.0309i	−1.01485	+	0.585925i	−0.102244	+	0.994759i	$0.532602\pi$
$948$		0			0
$949$	0.397198	−	0.687967i	0.0128936	−	0.0223323i
$950$	1.01764	+	1.76260i	0.0330165	+	0.0571863i
$951$		0			0
$952$	−8.46651	+	17.4412i	−0.274401	+	0.565272i
$953$			29.7944i			0.965137i	0.875858	+	0.482568i	$0.160296\pi$
$953$			29.7944i			0.965137i	−0.875858	+	0.482568i	$0.839704\pi$
$954$		0			0
$955$	15.9640	+	9.21682i	0.516583	+	0.298249i
$956$	−20.3550	−	11.7520i	−0.658329	−	0.380086i
$957$		0			0
$958$		−	27.5040i		−	0.888613i
$959$	−15.6216	+	32.1808i	−0.504447	+	1.03917i
$960$		0			0
$961$	−3.84315	−	6.65652i	−0.123972	−	0.214727i
$962$	0.138619	−	0.240095i	0.00446925	−	0.00774097i
$963$		0			0
$964$	−12.8765	+	7.43426i	−0.414724	+	0.239441i
$965$	−6.35827			−0.204680
$966$		0			0
$967$	−11.5198			−0.370453			−0.185226	−	0.982696i	$-0.559302\pi$
$967$	−11.5198			−0.370453			−0.185226	+	0.982696i	$0.559302\pi$
$968$	−4.20390	+	2.42713i	−0.135119	+	0.0780108i
$969$		0			0
$970$	−8.57509	+	14.8525i	−0.275330	+	0.476885i
$971$	21.2347	+	36.7795i	0.681453	+	1.18031i	0.974537	+	0.224225i	$0.0719849\pi$
$971$	21.2347	+	36.7795i	0.681453	+	1.18031i	−0.293084	+	0.956087i	$0.594682\pi$
$972$		0			0
$973$	23.9156	−	1.71706i	0.766698	−	0.0550465i
$974$		−	35.4468i		−	1.13579i
$975$		0			0
$976$	−6.51299	−	3.76028i	−0.208476	−	0.120364i
$977$	15.7279	+	9.08052i	0.503181	+	0.290512i	0.730026	−	0.683419i	$-0.239508\pi$
$977$	15.7279	+	9.08052i	0.503181	+	0.290512i	−0.226845	+	0.973931i	$0.572841\pi$
$978$		0			0
$979$		−	7.27827i		−	0.232614i
$980$	6.92820	−	1.00000i	0.221313	−	0.0319438i
$981$		0			0
$982$	0.821743	+	1.42330i	0.0262229	+	0.0454194i
$983$	−6.19988	+	10.7385i	−0.197746	+	0.342505i	−0.947797	−	0.318874i	$-0.896695\pi$
$983$	−6.19988	+	10.7385i	−0.197746	+	0.342505i	0.750052	+	0.661379i	$0.230029\pi$
$984$		0			0
$985$	11.1188	−	6.41946i	0.354275	−	0.204541i
$986$	−6.58755			−0.209790
$987$		0			0
$988$	−0.138701			−0.00441266
$989$	3.11804	−	1.80020i	0.0991478	−	0.0572430i
$990$		0			0
$991$	−10.8601	+	18.8102i	−0.344981	+	0.597525i	−0.985350	−	0.170543i	$-0.945448\pi$
$991$	−10.8601	+	18.8102i	−0.344981	+	0.597525i	0.640369	+	0.768067i	$0.278781\pi$
$992$	−2.41421	−	4.18154i	−0.0766514	−	0.132764i
$993$		0			0
$994$	21.7627	−	14.7381i	0.690270	−	0.467464i
$995$			9.62962i			0.305280i
$996$		0			0
$997$	−36.7856	−	21.2381i	−1.16501	−	0.672619i	−0.212510	−	0.977159i	$-0.568164\pi$
$997$	−36.7856	−	21.2381i	−1.16501	−	0.672619i	−0.952500	+	0.304540i	$0.901497\pi$
$998$	−30.0796	−	17.3665i	−0.952154	−	0.549726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.be.a.521.1	yes	8
3.2	odd	2		630.2.be.b.521.3	yes	8
5.2	odd	4		3150.2.bp.a.899.4		8
5.3	odd	4		3150.2.bp.d.899.1		8
5.4	even	2		3150.2.bf.b.1151.4		8
7.3	odd	6		4410.2.b.b.881.4		8
7.4	even	3		4410.2.b.e.881.4		8
7.5	odd	6		630.2.be.b.341.3	yes	8
15.2	even	4		3150.2.bp.f.899.4		8
15.8	even	4		3150.2.bp.c.899.1		8
15.14	odd	2		3150.2.bf.c.1151.2		8
21.5	even	6	inner	630.2.be.a.341.1	✓	8
21.11	odd	6		4410.2.b.b.881.5		8
21.17	even	6		4410.2.b.e.881.5		8
35.12	even	12		3150.2.bp.c.1349.1		8
35.19	odd	6		3150.2.bf.c.1601.2		8
35.33	even	12		3150.2.bp.f.1349.4		8
105.47	odd	12		3150.2.bp.d.1349.1		8
105.68	odd	12		3150.2.bp.a.1349.4		8
105.89	even	6		3150.2.bf.b.1601.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.1	✓	8	21.5	even	6	inner
630.2.be.a.521.1	yes	8	1.1	even	1	trivial
630.2.be.b.341.3	yes	8	7.5	odd	6
630.2.be.b.521.3	yes	8	3.2	odd	2
3150.2.bf.b.1151.4		8	5.4	even	2
3150.2.bf.b.1601.4		8	105.89	even	6
3150.2.bf.c.1151.2		8	15.14	odd	2
3150.2.bf.c.1601.2		8	35.19	odd	6
3150.2.bp.a.899.4		8	5.2	odd	4
3150.2.bp.a.1349.4		8	105.68	odd	12
3150.2.bp.c.899.1		8	15.8	even	4
3150.2.bp.c.1349.1		8	35.12	even	12
3150.2.bp.d.899.1		8	5.3	odd	4
3150.2.bp.d.1349.1		8	105.47	odd	12
3150.2.bp.f.899.4		8	15.2	even	4
3150.2.bp.f.1349.4		8	35.33	even	12
4410.2.b.b.881.4		8	7.3	odd	6
4410.2.b.b.881.5		8	21.11	odd	6
4410.2.b.e.881.4		8	7.4	even	3
4410.2.b.e.881.5		8	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.189469 - 2.63896i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.189469 - 2.63896i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(-3.44829 - 1.99087i) q^{11} +0.0681483i q^{13} +(1.48356 + 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.66390 + 6.34607i) q^{17} +(-1.76260 + 1.01764i) q^{19} -1.00000 q^{20} +3.98174 q^{22} +(-3.23205 + 1.86603i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.0340742 - 0.0590182i) q^{26} +(-2.38014 - 1.15539i) q^{28} -0.898979i q^{29} +(-4.18154 - 2.41421i) q^{31} +(0.866025 + 0.500000i) q^{32} -7.32780i q^{34} +(-2.19067 + 1.48356i) q^{35} +(2.03407 + 3.52312i) q^{37} +(1.01764 - 1.76260i) q^{38} +(0.866025 - 0.500000i) q^{40} -1.68921 q^{41} -0.964724 q^{43} +(-3.44829 + 1.99087i) q^{44} +(1.86603 - 3.23205i) q^{46} +(0.830749 + 1.43890i) q^{47} +(-6.92820 + 1.00000i) q^{49} -1.00000i q^{50} +(0.0590182 + 0.0340742i) q^{52} +(-11.4547 - 6.61339i) q^{53} +3.98174i q^{55} +(2.63896 - 0.189469i) q^{56} +(0.449490 + 0.778539i) q^{58} +(5.32112 - 9.21645i) q^{59} +(6.51299 - 3.76028i) q^{61} +4.82843 q^{62} -1.00000 q^{64} +(0.0590182 - 0.0340742i) q^{65} +(-5.33145 + 9.23435i) q^{67} +(3.66390 + 6.34607i) q^{68} +(1.15539 - 2.38014i) q^{70} -9.93426i q^{71} +(-10.0951 - 5.82843i) q^{73} +(-3.52312 - 2.03407i) q^{74} +2.03528i q^{76} +(-4.60048 + 9.47710i) q^{77} +(-8.77489 - 15.1986i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(1.46290 - 0.844605i) q^{82} +14.3490 q^{83} +7.32780 q^{85} +(0.835475 - 0.482362i) q^{86} +(1.99087 - 3.44829i) q^{88} +(0.913956 + 1.58302i) q^{89} +(0.179841 - 0.0129120i) q^{91} +3.73205i q^{92} +(-1.43890 - 0.830749i) q^{94} +(1.76260 + 1.01764i) q^{95} +17.1502i q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^5	\( 8 q + 4 q^{4} - 4 q^{5} - 24 q^{11} - 4 q^{16} - 8 q^{20} - 12 q^{23} - 4 q^{25} - 8 q^{26} + 24 q^{37} + 4 q^{38} - 32 q^{41} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{47} - 24 q^{53} - 16 q^{58} + 24 q^{59} + 16 q^{62} - 8 q^{64} - 24 q^{67} + 16 q^{77} - 24 q^{79} - 4 q^{80} + 16 q^{83} + 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 - 24 * q^11 - 4 * q^16 - 8 * q^20 - 12 * q^23 - 4 * q^25 - 8 * q^26 + 24 * q^37 + 4 * q^38 - 32 * q^41 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^47 - 24 * q^53 - 16 * q^58 + 24 * q^59 + 16 * q^62 - 8 * q^64 - 24 * q^67 + 16 * q^77 - 24 * q^79 - 4 * q^80 + 16 * q^83 + 16 * q^89 - 20 * q^91 - 12 * q^94 + 44 * q^98

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