LMFDB - Embedded newform 3150.2.bp.c.899.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

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.bp (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.1528766367$
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:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.c.1349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.63896 + 0.189469i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.63896 + 0.189469i) q^{7} +1.00000 q^{8} +(3.44829 + 1.99087i) q^{11} -0.0681483 q^{13} +(1.48356 + 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.34607 - 3.66390i) q^{17} +(1.76260 - 1.01764i) q^{19} -3.98174i q^{22} +(1.86603 + 3.23205i) q^{23} +(0.0340742 + 0.0590182i) q^{26} +(1.15539 - 2.38014i) q^{28} -0.898979i q^{29} +(-4.18154 - 2.41421i) q^{31} +(-0.500000 + 0.866025i) q^{32} +7.32780i q^{34} +(3.52312 - 2.03407i) q^{37} +(-1.76260 - 1.01764i) q^{38} +1.68921 q^{41} -0.964724i q^{43} +(-3.44829 + 1.99087i) q^{44} +(1.86603 - 3.23205i) q^{46} +(-1.43890 + 0.830749i) q^{47} +(6.92820 - 1.00000i) q^{49} +(0.0340742 - 0.0590182i) q^{52} +(-6.61339 + 11.4547i) q^{53} +(-2.63896 + 0.189469i) q^{56} +(-0.778539 + 0.449490i) q^{58} +(5.32112 - 9.21645i) q^{59} +(6.51299 - 3.76028i) q^{61} +4.82843i q^{62} +1.00000 q^{64} +(9.23435 + 5.33145i) q^{67} +(6.34607 - 3.66390i) q^{68} +9.93426i q^{71} +(5.82843 - 10.0951i) q^{73} +(-3.52312 - 2.03407i) q^{74} +2.03528i q^{76} +(-9.47710 - 4.60048i) q^{77} +(8.77489 + 15.1986i) q^{79} +(-0.844605 - 1.46290i) q^{82} -14.3490i q^{83} +(-0.835475 + 0.482362i) q^{86} +(3.44829 + 1.99087i) q^{88} +(0.913956 + 1.58302i) q^{89} +(0.179841 - 0.0129120i) q^{91} -3.73205 q^{92} +(1.43890 + 0.830749i) q^{94} +17.1502 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 24 q^{11} - 16 q^{13} - 4 q^{16} - 24 q^{17} + 8 q^{23} + 8 q^{26} - 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} - 12 q^{47} + 8 q^{52} - 4 q^{53} + 24 q^{59} + 8 q^{64} - 48 q^{67} + 24 q^{68} + 24 q^{73} + 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} + 16 q^{89} - 20 q^{91} - 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 24 * q^11 - 16 * q^13 - 4 * q^16 - 24 * q^17 + 8 * q^23 + 8 * q^26 - 4 * q^32 + 32 * q^41 - 24 * q^44 + 8 * q^46 - 12 * q^47 + 8 * q^52 - 4 * q^53 + 24 * q^59 + 8 * q^64 - 48 * q^67 + 24 * q^68 + 24 * q^73 + 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 + 16 * q^89 - 20 * q^91 - 16 * q^92 + 12 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.63896	+	0.189469i	−0.997433	+	0.0716124i
$7$	−2.63896	+	0.189469i	−0.997433	+	0.0716124i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	3.44829	+	1.99087i	1.03970	+	0.600270i	0.919748	−	0.392510i	$-0.128393\pi$
$11$	3.44829	+	1.99087i	1.03970	+	0.600270i	0.119950	+	0.992780i	$0.461727\pi$
$12$		0			0
$13$	−0.0681483			−0.0189010			−0.00945048	−	0.999955i	$-0.503008\pi$
$13$	−0.0681483			−0.0189010			−0.00945048	+	0.999955i	$0.503008\pi$
$14$	1.48356	+	2.19067i	0.396499	+	0.585481i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.34607	−	3.66390i	−1.53915	−	0.888627i	−0.998889	−	0.0471274i	$-0.984993\pi$
$17$	−6.34607	−	3.66390i	−1.53915	−	0.888627i	−0.540258	−	0.841499i	$-0.681673\pi$
$18$		0			0
$19$	1.76260	−	1.01764i	0.404368	−	0.233462i	−0.283999	−	0.958825i	$-0.591661\pi$
$19$	1.76260	−	1.01764i	0.404368	−	0.233462i	0.688367	+	0.725362i	$0.258328\pi$
$20$		0			0
$21$		0			0
$22$		−	3.98174i		−	0.848910i
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	0.992328	−	0.123635i	$-0.0394551\pi$
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	−0.603235	+	0.797564i	$0.706122\pi$
$24$		0			0
$25$		0			0
$26$	0.0340742	+	0.0590182i	0.00668250	+	0.0115744i
$27$		0			0
$28$	1.15539	−	2.38014i	0.218349	−	0.449804i
$29$		−	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	$0.809426\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			7.32780i			1.25671i
$35$		0			0
$36$		0			0
$37$	3.52312	−	2.03407i	0.579197	−	0.334400i	−0.181617	−	0.983369i	$-0.558133\pi$
$37$	3.52312	−	2.03407i	0.579197	−	0.334400i	0.760814	+	0.648970i	$0.224800\pi$
$38$	−1.76260	−	1.01764i	−0.285932	−	0.165083i
$39$		0			0
$40$		0			0
$41$	1.68921			0.263810			0.131905	−	0.991262i	$-0.457891\pi$
$41$	1.68921			0.263810			0.131905	+	0.991262i	$0.457891\pi$
$42$		0			0
$43$		−	0.964724i		−	0.147119i	−0.997291	−	0.0735595i	$-0.976564\pi$
$43$		−	0.964724i		−	0.147119i	0.997291	−	0.0735595i	$-0.0234359\pi$
$44$	−3.44829	+	1.99087i	−0.519849	+	0.300135i
$45$		0			0
$46$	1.86603	−	3.23205i	0.275130	−	0.476540i
$47$	−1.43890	+	0.830749i	−0.209885	+	0.121177i	−0.601258	−	0.799055i	$-0.705334\pi$
$47$	−1.43890	+	0.830749i	−0.209885	+	0.121177i	0.391373	+	0.920232i	$0.372000\pi$
$48$		0			0
$49$	6.92820	−	1.00000i	0.989743	−	0.142857i
$50$		0			0
$51$		0			0
$52$	0.0340742	−	0.0590182i	0.00472524	−	0.00818435i
$53$	−6.61339	+	11.4547i	−0.908419	+	1.57343i	−0.0921588	+	0.995744i	$0.529377\pi$
$53$	−6.61339	+	11.4547i	−0.908419	+	1.57343i	−0.816260	+	0.577684i	$0.803957\pi$
$54$		0			0
$55$		0			0
$56$	−2.63896	+	0.189469i	−0.352646	+	0.0253188i
$57$		0			0
$58$	−0.778539	+	0.449490i	−0.102227	+	0.0590209i
$59$	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	$0.173442\pi$
$62$			4.82843i			0.613211i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	9.23435	+	5.33145i	1.12816	+	0.651341i	0.943470	−	0.331457i	$-0.107540\pi$
$67$	9.23435	+	5.33145i	1.12816	+	0.651341i	0.184685	+	0.982798i	$0.440874\pi$
$68$	6.34607	−	3.66390i	0.769573	−	0.444313i
$69$		0			0
$70$		0			0
$71$			9.93426i			1.17898i	0.807776	+	0.589490i	$0.200671\pi$
$71$			9.93426i			1.17898i	−0.807776	+	0.589490i	$0.799329\pi$
$72$		0			0
$73$	5.82843	−	10.0951i	0.682166	−	1.18155i	−0.292153	−	0.956372i	$-0.594372\pi$
$73$	5.82843	−	10.0951i	0.682166	−	1.18155i	0.974319	−	0.225174i	$-0.0722951\pi$
$74$	−3.52312	−	2.03407i	−0.409554	−	0.236456i
$75$		0			0
$76$			2.03528i			0.233462i
$77$	−9.47710	−	4.60048i	−1.08002	−	0.524273i
$78$		0			0
$79$	8.77489	+	15.1986i	0.987252	+	1.70997i	0.631465	+	0.775404i	$0.282454\pi$
$79$	8.77489	+	15.1986i	0.987252	+	1.70997i	0.355787	+	0.934567i	$0.384213\pi$
$80$		0			0
$81$		0			0
$82$	−0.844605	−	1.46290i	−0.0932711	−	0.161550i
$83$		−	14.3490i		−	1.57501i	−0.616311	−	0.787503i	$-0.711374\pi$
$83$		−	14.3490i		−	1.57501i	0.616311	−	0.787503i	$-0.288626\pi$
$84$		0			0
$85$		0			0
$86$	−0.835475	+	0.482362i	−0.0900916	+	0.0520144i
$87$		0			0
$88$	3.44829	+	1.99087i	0.367589	+	0.212227i
$89$	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
$92$	−3.73205			−0.389093
$93$		0			0
$94$	1.43890	+	0.830749i	0.148411	+	0.0856852i
$95$		0			0
$96$		0			0
$97$	17.1502			1.74134			0.870668	−	0.491870i	$-0.163687\pi$
$97$	17.1502			1.74134			0.870668	+	0.491870i	$0.163687\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$		0			0
$100$		0			0
$101$	−3.36773	+	5.83307i	−0.335101	+	0.580412i	−0.983504	−	0.180885i	$-0.942104\pi$
$101$	−3.36773	+	5.83307i	−0.335101	+	0.580412i	0.648403	+	0.761297i	$0.275437\pi$
$102$		0			0
$103$	0.260021	+	0.450370i	0.0256206	+	0.0443762i	0.878551	−	0.477648i	$-0.158510\pi$
$103$	0.260021	+	0.450370i	0.0256206	+	0.0443762i	−0.852931	+	0.522024i	$0.825177\pi$
$104$	−0.0681483			−0.00668250
$105$		0			0
$106$	13.2268			1.28470
$107$	−3.06350	−	5.30614i	−0.296160	−	0.512964i	0.679094	−	0.734051i	$-0.262373\pi$
$107$	−3.06350	−	5.30614i	−0.296160	−	0.512964i	−0.975254	+	0.221087i	$0.929040\pi$
$108$		0			0
$109$	6.77729	−	11.7386i	0.649147	−	1.12436i	−0.334180	−	0.942509i	$-0.608459\pi$
$109$	6.77729	−	11.7386i	0.649147	−	1.12436i	0.983327	−	0.181846i	$-0.0582074\pi$
$110$		0			0
$111$		0			0
$112$	1.48356	+	2.19067i	0.140184	+	0.206999i
$113$	−11.6982			−1.10047			−0.550236	−	0.835009i	$-0.685462\pi$
$113$	−11.6982			−1.10047			−0.550236	+	0.835009i	$0.685462\pi$
$114$		0			0
$115$		0			0
$116$	0.778539	+	0.449490i	0.0722855	+	0.0417341i
$117$		0			0
$118$	−10.6422			−0.979698
$119$	17.4412	+	8.46651i	1.59883	+	0.776123i
$120$		0			0
$121$	2.42713	+	4.20390i	0.220648	+	0.382173i
$122$	−6.51299	−	3.76028i	−0.589659	−	0.340440i
$123$		0			0
$124$	4.18154	−	2.41421i	0.375513	−	0.216803i
$125$		0			0
$126$		0			0
$127$		−	10.7530i		−	0.954173i	−0.878856	−	0.477086i	$-0.841693\pi$
$127$		−	10.7530i		−	0.954173i	0.878856	−	0.477086i	$-0.158307\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	1.85457	+	3.21221i	0.162035	+	0.280653i	0.935598	−	0.353066i	$-0.114861\pi$
$131$	1.85457	+	3.21221i	0.162035	+	0.280653i	−0.773564	+	0.633719i	$0.781528\pi$
$132$		0			0
$133$	−4.45862	+	3.01946i	−0.386611	+	0.261821i
$134$		−	10.6629i		−	0.921135i
$135$		0			0
$136$	−6.34607	−	3.66390i	−0.544171	−	0.314177i
$137$	6.76028	−	11.7091i	0.577570	−	1.00038i	−0.418188	−	0.908361i	$-0.637335\pi$
$137$	6.76028	−	11.7091i	0.577570	−	1.00038i	0.995757	−	0.0920192i	$-0.0293321\pi$
$138$		0			0
$139$		−	9.06251i		−	0.768672i	−0.923193	−	0.384336i	$-0.874430\pi$
$139$		−	9.06251i		−	0.768672i	0.923193	−	0.384336i	$-0.125570\pi$
$140$		0			0
$141$		0			0
$142$	8.60332	−	4.96713i	0.721974	−	0.416832i
$143$	−0.234995	−	0.135674i	−0.0196513	−	0.0113457i
$144$		0			0
$145$		0			0
$146$	−11.6569			−0.964728
$147$		0			0
$148$			4.06815i			0.334400i
$149$	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	$0.0349944\pi$
$152$	1.76260	−	1.01764i	0.142966	−	0.0825413i
$153$		0			0
$154$	0.754415	+	10.5076i	0.0607925	+	0.846730i
$155$		0			0
$156$		0			0
$157$	7.14418	−	12.3741i	0.570168	−	0.987560i	−0.426380	−	0.904544i	$-0.640212\pi$
$157$	7.14418	−	12.3741i	0.570168	−	0.987560i	0.996548	−	0.0830157i	$-0.0264552\pi$
$158$	8.77489	−	15.1986i	0.698093	−	1.20913i
$159$		0			0
$160$		0			0
$161$	−5.53674	−	8.17569i	−0.436356	−	0.644335i
$162$		0			0
$163$	8.64083	−	4.98879i	0.676802	−	0.390752i	−0.121847	−	0.992549i	$-0.538882\pi$
$163$	8.64083	−	4.98879i	0.676802	−	0.390752i	0.798649	+	0.601797i	$0.205548\pi$
$164$	−0.844605	+	1.46290i	−0.0659526	+	0.114233i
$165$		0			0
$166$	−12.4266	+	7.17449i	−0.964490	+	0.556849i
$167$			13.7778i			1.06616i	0.846065	+	0.533079i	$0.178965\pi$
$167$			13.7778i			1.06616i	−0.846065	+	0.533079i	$0.821035\pi$
$168$		0			0
$169$	−12.9954			−0.999643
$170$		0			0
$171$		0			0
$172$	0.835475	+	0.482362i	0.0637044	+	0.0367798i
$173$	7.16442	−	4.13638i	0.544701	−	0.314483i	−0.202281	−	0.979327i	$-0.564836\pi$
$173$	7.16442	−	4.13638i	0.544701	−	0.314483i	0.746982	+	0.664844i	$0.231502\pi$
$174$		0			0
$175$		0			0
$176$		−	3.98174i		−	0.300135i
$177$		0			0
$178$	0.913956	−	1.58302i	0.0685039	−	0.118652i
$179$	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	$0.788489\pi$
$182$	−0.101102	−	0.149291i	−0.00749421	−	0.0110662i
$183$		0			0
$184$	1.86603	+	3.23205i	0.137565	+	0.238270i
$185$		0			0
$186$		0			0
$187$	−14.5887	−	25.2684i	−1.06683	−	1.84781i
$188$		−	1.66150i		−	0.121177i
$189$		0			0
$190$		0			0
$191$	15.9640	−	9.21682i	1.15511	−	0.666905i	0.204986	−	0.978765i	$-0.434285\pi$
$191$	15.9640	−	9.21682i	1.15511	−	0.666905i	0.950128	+	0.311859i	$0.100952\pi$
$192$		0			0
$193$	5.50643	+	3.17914i	0.396361	+	0.228839i	0.684913	−	0.728625i	$-0.259840\pi$
$193$	5.50643	+	3.17914i	0.396361	+	0.228839i	−0.288552	+	0.957464i	$0.593174\pi$
$194$	−8.57509	−	14.8525i	−0.615656	−	1.06635i
$195$		0			0
$196$	−2.59808	+	6.50000i	−0.185577	+	0.464286i
$197$	−12.8389			−0.914734			−0.457367	−	0.889278i	$-0.651208\pi$
$197$	−12.8389			−0.914734			−0.457367	+	0.889278i	$0.651208\pi$
$198$		0			0
$199$	8.33950	+	4.81481i	0.591171	+	0.341313i	0.765561	−	0.643364i	$-0.222462\pi$
$199$	8.33950	+	4.81481i	0.591171	+	0.341313i	−0.174389	+	0.984677i	$0.555795\pi$
$200$		0			0
$201$		0			0
$202$	6.73545			0.473905
$203$	0.170328	+	2.37237i	0.0119547	+	0.166508i
$204$		0			0
$205$		0			0
$206$	0.260021	−	0.450370i	0.0181165	−	0.0313787i
$207$		0			0
$208$	0.0340742	+	0.0590182i	0.00236262	+	0.00409218i
$209$	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	$0.667123\pi$
$212$	−6.61339	−	11.4547i	−0.454210	−	0.786714i
$213$		0			0
$214$	−3.06350	+	5.30614i	−0.209417	+	0.362721i
$215$		0			0
$216$		0			0
$217$	11.4923	+	5.57874i	0.780150	+	0.378709i
$218$	−13.5546			−0.918033
$219$		0			0
$220$		0			0
$221$	0.432474	+	0.249689i	0.0290913	+	0.0167959i
$222$		0			0
$223$	23.6609			1.58445			0.792227	−	0.610227i	$-0.208922\pi$
$223$	23.6609			1.58445			0.792227	+	0.610227i	$0.208922\pi$
$224$	1.15539	−	2.38014i	0.0771980	−	0.159030i
$225$		0			0
$226$	5.84909	+	10.1309i	0.389076	+	0.673899i
$227$	7.48288	+	4.32024i	0.496656	+	0.286744i	0.727332	−	0.686286i	$-0.240760\pi$
$227$	7.48288	+	4.32024i	0.496656	+	0.286744i	−0.230676	+	0.973031i	$0.574094\pi$
$228$		0			0
$229$	12.1896	−	7.03768i	0.805513	−	0.465063i	−0.0398824	−	0.999204i	$-0.512698\pi$
$229$	12.1896	−	7.03768i	0.805513	−	0.465063i	0.845395	+	0.534141i	$0.179365\pi$
$230$		0			0
$231$		0			0
$232$		−	0.898979i		−	0.0590209i
$233$	10.0988	+	17.4916i	0.661593	+	1.14591i	0.980197	+	0.198025i	$0.0634527\pi$
$233$	10.0988	+	17.4916i	0.661593	+	1.14591i	−0.318604	+	0.947888i	$0.603214\pi$
$234$		0			0
$235$		0			0
$236$	5.32112	+	9.21645i	0.346375	+	0.599940i
$237$		0			0
$238$	−1.38839	−	19.3378i	−0.0899959	−	1.25348i
$239$		−	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	$0.825625\pi$
$242$	2.42713	−	4.20390i	0.156022	−	0.270237i
$243$		0			0
$244$			7.52056i			0.481454i
$245$		0			0
$246$		0			0
$247$	−0.120118	+	0.0693504i	−0.00764295	+	0.00441266i
$248$	−4.18154	−	2.41421i	−0.265528	−	0.153303i
$249$		0			0
$250$		0			0
$251$	−4.31736			−0.272509			−0.136255	−	0.990674i	$-0.543507\pi$
$251$	−4.31736			−0.272509			−0.136255	+	0.990674i	$0.543507\pi$
$252$		0			0
$253$			14.8601i			0.934244i
$254$	−9.31236	+	5.37649i	−0.584309	+	0.337351i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.18570	−	2.41662i	0.261097	−	0.150744i	−0.363738	−	0.931501i	$-0.618500\pi$
$257$	4.18570	−	2.41662i	0.261097	−	0.150744i	0.624835	+	0.780757i	$0.285166\pi$
$258$		0			0
$259$	−8.91197	+	6.03536i	−0.553763	+	0.375019i
$260$		0			0
$261$		0			0
$262$	1.85457	−	3.21221i	0.114576	−	0.198451i
$263$	−3.33245	+	5.77197i	−0.205488	+	0.355915i	−0.950288	−	0.311372i	$-0.899211\pi$
$263$	−3.33245	+	5.77197i	−0.205488	+	0.355915i	0.744800	+	0.667287i	$0.232545\pi$
$264$		0			0
$265$		0			0
$266$	4.84424	+	2.35155i	0.297019	+	0.144183i
$267$		0			0
$268$	−9.23435	+	5.33145i	−0.564078	+	0.325670i
$269$	−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	$0.155362\pi$
$272$			7.32780i			0.444313i
$273$		0			0
$274$	−13.5206			−0.816807
$275$		0			0
$276$		0			0
$277$	−20.3557	−	11.7524i	−1.22305	−	0.706130i	−0.257486	−	0.966282i	$-0.582894\pi$
$277$	−20.3557	−	11.7524i	−1.22305	−	0.706130i	−0.965568	+	0.260152i	$0.916227\pi$
$278$	−7.84836	+	4.53125i	−0.470714	+	0.271767i
$279$		0			0
$280$		0			0
$281$			15.4159i			0.919635i	0.888013	+	0.459817i	$0.152085\pi$
$281$			15.4159i			0.919635i	−0.888013	+	0.459817i	$0.847915\pi$
$282$		0			0
$283$	13.8554	−	23.9983i	0.823619	−	1.42655i	−0.0793517	−	0.996847i	$-0.525285\pi$
$283$	13.8554	−	23.9983i	0.823619	−	1.42655i	0.902970	−	0.429703i	$-0.141382\pi$
$284$	−8.60332	−	4.96713i	−0.510513	−	0.294745i
$285$		0			0
$286$			0.271349i			0.0160452i
$287$	−4.45776	+	0.320053i	−0.263133	+	0.0188921i
$288$		0			0
$289$	18.3484	+	31.7803i	1.07932	+	1.86943i
$290$		0			0
$291$		0			0
$292$	5.82843	+	10.0951i	0.341083	+	0.590773i
$293$			2.84377i			0.166135i	0.996544	+	0.0830673i	$0.0264717\pi$
$293$			2.84377i			0.166135i	−0.996544	+	0.0830673i	$0.973528\pi$
$294$		0			0
$295$		0			0
$296$	3.52312	−	2.03407i	0.204777	−	0.118228i
$297$		0			0
$298$	−13.2385	−	7.64324i	−0.766884	−	0.442761i
$299$	−0.127167	−	0.220259i	−0.00735423	−	0.0127379i
$300$		0			0
$301$	0.182785	+	2.54587i	0.0105355	+	0.146741i
$302$	−9.87883			−0.568463
$303$		0			0
$304$	−1.76260	−	1.01764i	−0.101092	−	0.0583655i
$305$		0			0
$306$		0			0
$307$	−2.52180			−0.143927			−0.0719634	−	0.997407i	$-0.522926\pi$
$307$	−2.52180			−0.143927			−0.0719634	+	0.997407i	$0.522926\pi$
$308$	8.72268	−	5.90717i	0.497021	−	0.336592i
$309$		0			0
$310$		0			0
$311$	5.49697	−	9.52104i	0.311705	−	0.539889i	−0.667027	−	0.745034i	$-0.732433\pi$
$311$	5.49697	−	9.52104i	0.311705	−	0.539889i	0.978732	+	0.205145i	$0.0657667\pi$
$312$		0			0
$313$	12.4731	+	21.6040i	0.705020	+	1.22113i	0.966684	+	0.255971i	$0.0823952\pi$
$313$	12.4731	+	21.6040i	0.705020	+	1.22113i	−0.261665	+	0.965159i	$0.584271\pi$
$314$	−14.2884			−0.806339
$315$		0			0
$316$	−17.5498			−0.987252
$317$	−7.53465	−	13.0504i	−0.423188	−	0.732984i	0.573061	−	0.819513i	$-0.305756\pi$
$317$	−7.53465	−	13.0504i	−0.423188	−	0.732984i	−0.996249	+	0.0865290i	$0.972422\pi$
$318$		0			0
$319$	1.78975	−	3.09994i	0.100207	−	0.173563i
$320$		0			0
$321$		0			0
$322$	−4.31199	+	8.88280i	−0.240298	+	0.495019i
$323$	−14.9141			−0.829843
$324$		0			0
$325$		0			0
$326$	−8.64083	−	4.98879i	−0.478572	−	0.276303i
$327$		0			0
$328$	1.68921			0.0932711
$329$	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	$-0.478009\pi$
$332$	12.4266	+	7.17449i	0.681997	+	0.393751i
$333$		0			0
$334$	11.9319	−	6.88891i	0.652886	−	0.376944i
$335$		0			0
$336$		0			0
$337$			21.5911i			1.17614i	0.808809	+	0.588071i	$0.200113\pi$
$337$			21.5911i			1.17614i	−0.808809	+	0.588071i	$0.799887\pi$
$338$	6.49768	+	11.2543i	0.353427	+	0.612154i
$339$		0			0
$340$		0			0
$341$	−9.61277	−	16.6498i	−0.520561	−	0.901638i
$342$		0			0
$343$	−18.0938	+	3.95164i	−0.976972	+	0.213368i
$344$		−	0.964724i		−	0.0520144i
$345$		0			0
$346$	−7.16442	−	4.13638i	−0.385161	−	0.222373i
$347$	11.5921	−	20.0781i	0.622297	−	1.07785i	−0.366760	−	0.930316i	$-0.619533\pi$
$347$	11.5921	−	20.0781i	0.622297	−	1.07785i	0.989057	−	0.147534i	$-0.0471336\pi$
$348$		0			0
$349$		−	10.7287i		−	0.574292i	−0.957887	−	0.287146i	$-0.907294\pi$
$349$		−	10.7287i		−	0.574292i	0.957887	−	0.287146i	$-0.0927064\pi$
$350$		0			0
$351$		0			0
$352$	−3.44829	+	1.99087i	−0.183794	+	0.106114i
$353$	7.57561	+	4.37378i	0.403209	+	0.232793i	0.687868	−	0.725836i	$-0.258547\pi$
$353$	7.57561	+	4.37378i	0.403209	+	0.232793i	−0.284659	+	0.958629i	$0.591880\pi$
$354$		0			0
$355$		0			0
$356$	−1.82791			−0.0968791
$357$		0			0
$358$		−	11.5182i		−	0.608753i
$359$	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
$362$	14.3694	−	8.29618i	0.755239	−	0.436037i
$363$		0			0
$364$	−0.0787382	+	0.162203i	−0.00412700	+	0.00850172i
$365$		0			0
$366$		0			0
$367$	9.96885	−	17.2665i	0.520369	−	0.901306i	−0.479350	−	0.877624i	$-0.659128\pi$
$367$	9.96885	−	17.2665i	0.520369	−	0.901306i	0.999720	−	0.0236826i	$-0.00753911\pi$
$368$	1.86603	−	3.23205i	0.0972733	−	0.168482i
$369$		0			0
$370$		0			0
$371$	15.2822	−	31.4816i	0.793410	−	1.63444i
$372$		0			0
$373$	0.893327	−	0.515762i	0.0462547	−	0.0267052i	−0.476694	−	0.879069i	$-0.658165\pi$
$373$	0.893327	−	0.515762i	0.0462547	−	0.0267052i	0.522949	+	0.852364i	$0.324832\pi$
$374$	−14.5887	+	25.2684i	−0.754364	+	1.30660i
$375$		0			0
$376$	−1.43890	+	0.830749i	−0.0742056	+	0.0428426i
$377$			0.0612640i			0.00315525i
$378$		0			0
$379$	−5.09497			−0.261711			−0.130855	−	0.991401i	$-0.541772\pi$
$379$	−5.09497			−0.261711			−0.130855	+	0.991401i	$0.541772\pi$
$380$		0			0
$381$		0			0
$382$	−15.9640	−	9.21682i	−0.816789	−	0.471573i
$383$	7.33307	−	4.23375i	0.374702	−	0.216335i	−0.300808	−	0.953685i	$-0.597256\pi$
$383$	7.33307	−	4.23375i	0.374702	−	0.216335i	0.675511	+	0.737350i	$0.263923\pi$
$384$		0			0
$385$		0			0
$386$		−	6.35827i		−	0.323628i
$387$		0			0
$388$	−8.57509	+	14.8525i	−0.435334	+	0.754021i
$389$	−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
$392$	6.92820	−	1.00000i	0.349927	−	0.0505076i
$393$		0			0
$394$	6.41946	+	11.1188i	0.323407	+	0.560158i
$395$		0			0
$396$		0			0
$397$	−8.43791	−	14.6149i	−0.423487	−	0.733501i	0.572791	−	0.819701i	$-0.305861\pi$
$397$	−8.43791	−	14.6149i	−0.423487	−	0.733501i	−0.996278	+	0.0862009i	$0.972527\pi$
$398$		−	9.62962i		−	0.482689i
$399$		0			0
$400$		0			0
$401$	−1.63572	+	0.944382i	−0.0816838	+	0.0471602i	−0.540286	−	0.841482i	$-0.681684\pi$
$401$	−1.63572	+	0.944382i	−0.0816838	+	0.0471602i	0.458602	+	0.888642i	$0.348350\pi$
$402$		0			0
$403$	0.284965	+	0.164525i	0.0141951	+	0.00819556i
$404$	−3.36773	−	5.83307i	−0.167551	−	0.290206i
$405$		0			0
$406$	1.96937	−	1.33369i	0.0977381	−	0.0661901i
$407$	16.1983			0.802920
$408$		0			0
$409$	−28.5617	−	16.4901i	−1.41228	−	0.815382i	−0.416681	−	0.909053i	$-0.636807\pi$
$409$	−28.5617	−	16.4901i	−1.41228	−	0.815382i	−0.995603	+	0.0936705i	$0.970140\pi$
$410$		0			0
$411$		0			0
$412$	−0.520042			−0.0256206
$413$	−12.2960	+	25.3300i	−0.605046	+	1.24641i
$414$		0			0
$415$		0			0
$416$	0.0340742	−	0.0590182i	0.00167062	−	0.00289361i
$417$		0			0
$418$	−4.05197	−	7.01822i	−0.198188	−	0.343272i
$419$	−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	$0.251693\pi$
$422$	7.28094	+	12.6110i	0.354431	+	0.613892i
$423$		0			0
$424$	−6.61339	+	11.4547i	−0.321175	+	0.556291i
$425$		0			0
$426$		0			0
$427$	−16.4751	+	11.1572i	−0.797284	+	0.539936i
$428$	6.12701			0.296160
$429$		0			0
$430$		0			0
$431$	−29.0895	−	16.7948i	−1.40119	−	0.808978i	−0.406677	−	0.913572i	$-0.633312\pi$
$431$	−29.0895	−	16.7948i	−1.40119	−	0.808978i	−0.994515	+	0.104594i	$0.966646\pi$
$432$		0			0
$433$	−11.2207			−0.539234			−0.269617	−	0.962968i	$-0.586897\pi$
$433$	−11.2207			−0.539234			−0.269617	+	0.962968i	$0.586897\pi$
$434$	−0.914836	−	12.7420i	−0.0439135	−	0.611636i
$435$		0			0
$436$	6.77729	+	11.7386i	0.324574	+	0.562178i
$437$	6.57812	+	3.79788i	0.314674	+	0.181677i
$438$		0			0
$439$	14.6075	−	8.43363i	0.697177	−	0.402515i	−0.109118	−	0.994029i	$-0.534803\pi$
$439$	14.6075	−	8.43363i	0.697177	−	0.402515i	0.806295	+	0.591513i	$0.201469\pi$
$440$		0			0
$441$		0			0
$442$		−	0.499378i		−	0.0237530i
$443$	−1.02823	−	1.78094i	−0.0488526	−	0.0846152i	0.840565	−	0.541711i	$-0.182223\pi$
$443$	−1.02823	−	1.78094i	−0.0488526	−	0.0846152i	−0.889418	+	0.457095i	$0.848890\pi$
$444$		0			0
$445$		0			0
$446$	−11.8305	−	20.4910i	−0.560189	−	0.970276i
$447$		0			0
$448$	−2.63896	+	0.189469i	−0.124679	+	0.00895155i
$449$		−	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
$452$	5.84909	−	10.1309i	0.275118	−	0.476519i
$453$		0			0
$454$		−	8.64048i		−	0.405518i
$455$		0			0
$456$		0			0
$457$	−30.2701	+	17.4765i	−1.41598	+	0.817515i	−0.995942	−	0.0899930i	$-0.971316\pi$
$457$	−30.2701	+	17.4765i	−1.41598	+	0.817515i	−0.420035	+	0.907508i	$0.637982\pi$
$458$	−12.1896	−	7.03768i	−0.569584	−	0.328849i
$459$		0			0
$460$		0			0
$461$	23.3750			1.08868			0.544341	−	0.838864i	$-0.316780\pi$
$461$	23.3750			1.08868			0.544341	+	0.838864i	$0.316780\pi$
$462$		0			0
$463$		−	6.35693i		−	0.295431i	−0.989030	−	0.147716i	$-0.952808\pi$
$463$		−	6.35693i		−	0.295431i	0.989030	−	0.147716i	$-0.0471921\pi$
$464$	−0.778539	+	0.449490i	−0.0361428	+	0.0208670i
$465$		0			0
$466$	10.0988	−	17.4916i	0.467817	−	0.810283i
$467$	6.74907	−	3.89658i	0.312310	−	0.180312i	−0.335650	−	0.941987i	$-0.608956\pi$
$467$	6.74907	−	3.89658i	0.312310	−	0.180312i	0.647960	+	0.761675i	$0.275623\pi$
$468$		0			0
$469$	−25.3792	−	12.3199i	−1.17190	−	0.568878i
$470$		0			0
$471$		0			0
$472$	5.32112	−	9.21645i	0.244924	−	0.424222i
$473$	1.92064	−	3.32665i	0.0883111	−	0.152959i
$474$		0			0
$475$		0			0
$476$	−16.0528	+	10.8713i	−0.735779	+	0.498284i
$477$		0			0
$478$	−20.3550	+	11.7520i	−0.931018	+	0.537523i
$479$	−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
$482$			14.8685i			0.677242i
$483$		0			0
$484$	−4.85425			−0.220648
$485$		0			0
$486$		0			0
$487$	30.6978	+	17.7234i	1.39105	+	0.803124i	0.993432	−	0.114427i	$-0.0365032\pi$
$487$	30.6978	+	17.7234i	1.39105	+	0.803124i	0.397619	+	0.917551i	$0.369836\pi$
$488$	6.51299	−	3.76028i	0.294829	−	0.170220i
$489$		0			0
$490$		0			0
$491$			1.64349i			0.0741695i	0.999312	+	0.0370848i	$0.0118072\pi$
$491$			1.64349i			0.0741695i	−0.999312	+	0.0370848i	$0.988193\pi$
$492$		0			0
$493$	−3.29377	+	5.70498i	−0.148344	+	0.256939i
$494$	0.120118	+	0.0693504i	0.00540438	+	0.00312022i
$495$		0			0
$496$			4.82843i			0.216803i
$497$	−1.88223	−	26.2161i	−0.0844296	−	1.17595i
$498$		0			0
$499$	−17.3665	−	30.0796i	−0.777430	−	1.34655i	−0.933418	−	0.358790i	$-0.883189\pi$
$499$	−17.3665	−	30.0796i	−0.777430	−	1.34655i	0.155988	−	0.987759i	$-0.450144\pi$
$500$		0			0
$501$		0			0
$502$	2.15868	+	3.73894i	0.0963465	+	0.166877i
$503$			28.9613i			1.29132i	0.763625	+	0.645660i	$0.223418\pi$
$503$			28.9613i			1.29132i	−0.763625	+	0.645660i	$0.776582\pi$
$504$		0			0
$505$		0			0
$506$	12.8692	−	7.43003i	0.572105	−	0.330305i
$507$		0			0
$508$	9.31236	+	5.37649i	0.413169	+	0.238543i
$509$	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
$512$	1.00000			0.0441942
$513$		0			0
$514$	−4.18570	−	2.41662i	−0.184624	−	0.106592i
$515$		0			0
$516$		0			0
$517$	−6.61565			−0.290956
$518$	9.68276	+	4.70032i	0.425436	+	0.206520i
$519$		0			0
$520$		0			0
$521$	−20.1218	+	34.8520i	−0.881552	+	1.52689i	−0.0319362	+	0.999490i	$0.510167\pi$
$521$	−20.1218	+	34.8520i	−0.881552	+	1.52689i	−0.849616	+	0.527403i	$0.823166\pi$
$522$		0			0
$523$	14.8444	+	25.7113i	0.649102	+	1.12428i	0.983338	+	0.181789i	$0.0581887\pi$
$523$	14.8444	+	25.7113i	0.649102	+	1.12428i	−0.334235	+	0.942490i	$0.608478\pi$
$524$	−3.70915			−0.162035
$525$		0			0
$526$	6.66490			0.290603
$527$	17.6909	+	30.6415i	0.770627	+	1.33477i
$528$		0			0
$529$	4.53590	−	7.85641i	0.197213	−	0.341583i
$530$		0			0
$531$		0			0
$532$	−0.385621	−	5.37101i	−0.0167188	−	0.232863i
$533$	−0.115117			−0.00498627
$534$		0			0
$535$		0			0
$536$	9.23435	+	5.33145i	0.398863	+	0.230284i
$537$		0			0
$538$	31.7400			1.36841
$539$	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	$0.712350\pi$
$542$	−15.1244	−	8.73205i	−0.649647	−	0.375074i
$543$		0			0
$544$	6.34607	−	3.66390i	0.272085	−	0.157089i
$545$		0			0
$546$		0			0
$547$			17.9703i			0.768354i	0.923260	+	0.384177i	$0.125515\pi$
$547$			17.9703i			0.768354i	−0.923260	+	0.384177i	$0.874485\pi$
$548$	6.76028	+	11.7091i	0.288785	+	0.500190i
$549$		0			0
$550$		0			0
$551$	−0.914836	−	1.58454i	−0.0389733	−	0.0675038i
$552$		0			0
$553$	−26.0362	−	38.4458i	−1.10717	−	1.63488i
$554$			23.5047i			0.998619i
$555$		0			0
$556$	7.84836	+	4.53125i	0.332845	+	0.192168i
$557$	−22.6273	+	39.1916i	−0.958748	+	1.66060i	−0.233201	+	0.972428i	$0.574920\pi$
$557$	−22.6273	+	39.1916i	−0.958748	+	1.66060i	−0.725547	+	0.688172i	$0.758413\pi$
$558$		0			0
$559$			0.0657443i			0.00278069i
$560$		0			0
$561$		0			0
$562$	13.3506	−	7.70794i	0.563159	−	0.325140i
$563$	−13.7410	−	7.93336i	−0.579114	−	0.334351i	0.181667	−	0.983360i	$-0.441851\pi$
$563$	−13.7410	−	7.93336i	−0.579114	−	0.334351i	−0.760781	+	0.649009i	$0.775184\pi$
$564$		0			0
$565$		0			0
$566$	−27.7108			−1.16477
$567$		0			0
$568$			9.93426i			0.416832i
$569$	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	$0.0750592\pi$
$572$	0.234995	−	0.135674i	0.00982564	−	0.00567284i
$573$		0			0
$574$	2.50605	+	3.70050i	0.104601	+	0.154456i
$575$		0			0
$576$		0			0
$577$	−21.8384	+	37.8252i	−0.909144	+	1.57468i	−0.0938887	+	0.995583i	$0.529930\pi$
$577$	−21.8384	+	37.8252i	−0.909144	+	1.57468i	−0.815256	+	0.579101i	$0.803404\pi$
$578$	18.3484	−	31.7803i	0.763191	−	1.32189i
$579$		0			0
$580$		0			0
$581$	2.71868	+	37.8664i	0.112790	+	1.57096i
$582$		0			0
$583$	−45.6098	+	26.3328i	−1.88896	+	1.09059i
$584$	5.82843	−	10.0951i	0.241182	−	0.417740i
$585$		0			0
$586$	2.46278	−	1.42188i	0.101736	−	0.0587375i
$587$			45.4100i			1.87427i	0.348967	+	0.937135i	$0.386532\pi$
$587$			45.4100i			1.87427i	−0.348967	+	0.937135i	$0.613468\pi$
$588$		0			0
$589$	−9.82718			−0.404922
$590$		0			0
$591$		0			0
$592$	−3.52312	−	2.03407i	−0.144799	−	0.0835999i
$593$	22.2579	−	12.8506i	0.914022	−	0.527711i	0.0322991	−	0.999478i	$-0.489717\pi$
$593$	22.2579	−	12.8506i	0.914022	−	0.527711i	0.881723	+	0.471767i	$0.156384\pi$
$594$		0			0
$595$		0			0
$596$			15.2865i			0.626158i
$597$		0			0
$598$	−0.127167	+	0.220259i	−0.00520023	+	0.00900706i
$599$	−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	$0.914797\pi$
$602$	2.11339	−	1.43123i	0.0861354	−	0.0583326i
$603$		0			0
$604$	4.93942	+	8.55532i	0.200982	+	0.348111i
$605$		0			0
$606$		0			0
$607$	8.15576	+	14.1262i	0.331032	+	0.573364i	0.982714	−	0.185128i	$-0.0592698\pi$
$607$	8.15576	+	14.1262i	0.331032	+	0.573364i	−0.651682	+	0.758492i	$0.725937\pi$
$608$			2.03528i			0.0825413i
$609$		0			0
$610$		0			0
$611$	0.0980586	−	0.0566142i	0.00396703	−	0.00229036i
$612$		0			0
$613$	12.4603	+	7.19395i	0.503267	+	0.290561i	0.730062	−	0.683381i	$-0.239491\pi$
$613$	12.4603	+	7.19395i	0.503267	+	0.290561i	−0.226795	+	0.973943i	$0.572825\pi$
$614$	1.26090	+	2.18394i	0.0508858	+	0.0881368i
$615$		0			0
$616$	−9.47710	−	4.60048i	−0.381843	−	0.185359i
$617$	−8.65760			−0.348542			−0.174271	−	0.984698i	$-0.555757\pi$
$617$	−8.65760			−0.348542			−0.174271	+	0.984698i	$0.555757\pi$
$618$		0			0
$619$	−38.8459	−	22.4277i	−1.56135	−	0.901444i	−0.997121	−	0.0758230i	$-0.975842\pi$
$619$	−38.8459	−	22.4277i	−1.56135	−	0.901444i	−0.564225	−	0.825621i	$-0.690825\pi$
$620$		0			0
$621$		0			0
$622$	−10.9939			−0.440817
$623$	−2.71182	−	4.00435i	−0.108647	−	0.160431i
$624$		0			0
$625$		0			0
$626$	12.4731	−	21.6040i	0.498524	−	0.863469i
$627$		0			0
$628$	7.14418	+	12.3741i	0.285084	+	0.493780i
$629$	−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	$0.774858\pi$
$632$	8.77489	+	15.1986i	0.349046	+	0.604566i
$633$		0			0
$634$	−7.53465	+	13.0504i	−0.299239	+	0.518298i
$635$		0			0
$636$		0			0
$637$	−0.472146	+	0.0681483i	−0.0187071	+	0.00270014i
$638$	−3.57950			−0.141714
$639$		0			0
$640$		0			0
$641$	7.40533	+	4.27547i	0.292493	+	0.168871i	0.639066	−	0.769152i	$-0.279321\pi$
$641$	7.40533	+	4.27547i	0.292493	+	0.168871i	−0.346573	+	0.938023i	$0.612655\pi$
$642$		0			0
$643$	−2.75058			−0.108472			−0.0542361	−	0.998528i	$-0.517272\pi$
$643$	−2.75058			−0.108472			−0.0542361	+	0.998528i	$0.517272\pi$
$644$	9.84873	−	0.707107i	0.388094	−	0.0278639i
$645$		0			0
$646$	7.45705	+	12.9160i	0.293394	+	0.508173i
$647$	24.0431	+	13.8813i	0.945234	+	0.545731i	0.891597	−	0.452830i	$-0.149585\pi$
$647$	24.0431	+	13.8813i	0.945234	+	0.545731i	0.0536365	+	0.998561i	$0.482919\pi$
$648$		0			0
$649$	36.6975	−	21.1873i	1.44050	−	0.831675i
$650$		0			0
$651$		0			0
$652$			9.97758i			0.390752i
$653$	−7.05994	−	12.2282i	−0.276277	−	0.478525i	0.694180	−	0.719802i	$-0.255767\pi$
$653$	−7.05994	−	12.2282i	−0.276277	−	0.478525i	−0.970456	+	0.241276i	$0.922434\pi$
$654$		0			0
$655$		0			0
$656$	−0.844605	−	1.46290i	−0.0329763	−	0.0571166i
$657$		0			0
$658$	−3.95460	−	1.91969i	−0.154166	−	0.0748372i
$659$			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	$0.550425\pi$
$662$	−15.0904	+	26.1373i	−0.586505	+	1.01586i
$663$		0			0
$664$		−	14.3490i		−	0.556849i
$665$		0			0
$666$		0			0
$667$	2.90555	−	1.67752i	0.112503	−	0.0649538i
$668$	−11.9319	−	6.88891i	−0.461660	−	0.266540i
$669$		0			0
$670$		0			0
$671$	29.9449			1.15601
$672$		0			0
$673$		−	32.6050i		−	1.25683i	−0.777878	−	0.628415i	$-0.783704\pi$
$673$		−	32.6050i		−	1.25683i	0.777878	−	0.628415i	$-0.216296\pi$
$674$	18.6984	−	10.7956i	0.720237	−	0.415829i
$675$		0			0
$676$	6.49768	−	11.2543i	0.249911	−	0.432858i
$677$	15.8816	−	9.16923i	0.610378	−	0.352402i	−0.162735	−	0.986670i	$-0.552032\pi$
$677$	15.8816	−	9.16923i	0.610378	−	0.352402i	0.773113	+	0.634268i	$0.218698\pi$
$678$		0			0
$679$	−45.2586	+	3.24942i	−1.73687	+	0.124701i
$680$		0			0
$681$		0			0
$682$	−9.61277	+	16.6498i	−0.368092	+	0.637554i
$683$	−12.2385	+	21.1977i	−0.468294	+	0.811108i	−0.999343	−	0.0362323i	$-0.988464\pi$
$683$	−12.2385	+	21.1977i	−0.468294	+	0.811108i	0.531050	+	0.847341i	$0.321798\pi$
$684$		0			0
$685$		0			0
$686$	12.4691	+	13.6938i	0.476073	+	0.522834i
$687$		0			0
$688$	−0.835475	+	0.482362i	−0.0318522	+	0.0183899i
$689$	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	$0.446975\pi$
$692$			8.27276i			0.314483i
$693$		0			0
$694$	−23.1842			−0.880061
$695$		0			0
$696$		0			0
$697$	−10.7198	−	6.18910i	−0.406043	−	0.234429i
$698$	−9.29128	+	5.36433i	−0.351680	+	0.203043i
$699$		0			0
$700$		0			0
$701$		−	14.2399i		−	0.537834i	−0.963163	−	0.268917i	$-0.913334\pi$
$701$		−	14.2399i		−	0.537834i	0.963163	−	0.268917i	$-0.0866658\pi$
$702$		0			0
$703$	4.13990	−	7.17052i	0.156139	−	0.270441i
$704$	3.44829	+	1.99087i	0.129962	+	0.0750337i
$705$		0			0
$706$		−	8.74756i		−	0.329219i
$707$	7.78210	−	16.0313i	0.292676	−	0.602920i
$708$		0			0
$709$	18.7586	+	32.4908i	0.704492	+	1.22022i	0.966874	+	0.255252i	$0.0821586\pi$
$709$	18.7586	+	32.4908i	0.704492	+	1.22022i	−0.262382	+	0.964964i	$0.584508\pi$
$710$		0			0
$711$		0			0
$712$	0.913956	+	1.58302i	0.0342519	+	0.0593261i
$713$		−	18.0199i		−	0.674852i
$714$		0			0
$715$		0			0
$716$	−9.97501	+	5.75908i	−0.372784	+	0.215227i
$717$		0			0
$718$	−22.3059	−	12.8783i	−0.832449	−	0.480614i
$719$	−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
$722$	14.8577			0.552945
$723$		0			0
$724$	−14.3694	−	8.29618i	−0.534035	−	0.308325i
$725$		0			0
$726$		0			0
$727$	−2.93413			−0.108821			−0.0544104	−	0.998519i	$-0.517328\pi$
$727$	−2.93413			−0.108821			−0.0544104	+	0.998519i	$0.517328\pi$
$728$	0.179841	−	0.0129120i	0.00666534	−	0.000478550i
$729$		0			0
$730$		0			0
$731$	−3.53465	+	6.12220i	−0.130734	+	0.226438i
$732$		0			0
$733$	6.82411	+	11.8197i	0.252054	+	0.436570i	0.964091	−	0.265571i	$-0.0855606\pi$
$733$	6.82411	+	11.8197i	0.252054	+	0.436570i	−0.712037	+	0.702142i	$0.752227\pi$
$734$	−19.9377			−0.735914
$735$		0			0
$736$	−3.73205			−0.137565
$737$	21.2285	+	36.7688i	0.781960	+	1.35440i
$738$		0			0
$739$	15.6650	−	27.1325i	0.576246	−	0.998087i	−0.419659	−	0.907682i	$-0.637851\pi$
$739$	15.6650	−	27.1325i	0.576246	−	0.998087i	0.995905	−	0.0904051i	$-0.0288162\pi$
$740$		0			0
$741$		0			0
$742$	−34.9049	+	2.50606i	−1.28140	+	0.0920004i
$743$	4.72061			0.173182			0.0865911	−	0.996244i	$-0.472403\pi$
$743$	4.72061			0.173182			0.0865911	+	0.996244i	$0.472403\pi$
$744$		0			0
$745$		0			0
$746$	−0.893327	−	0.515762i	−0.0327070	−	0.0188834i
$747$		0			0
$748$	29.1774			1.06683
$749$	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	$0.678122\pi$
$752$	1.43890	+	0.830749i	0.0524713	+	0.0302943i
$753$		0			0
$754$	0.0530562	−	0.0306320i	0.00193219	−	0.00111555i
$755$		0			0
$756$		0			0
$757$			37.8781i			1.37670i	0.725377	+	0.688352i	$0.241665\pi$
$757$			37.8781i			1.37670i	−0.725377	+	0.688352i	$0.758335\pi$
$758$	2.54748	+	4.41237i	0.0925288	+	0.160265i
$759$		0			0
$760$		0			0
$761$	10.3533	+	17.9325i	0.375308	+	0.650052i	0.990373	−	0.138424i	$-0.0442038\pi$
$761$	10.3533	+	17.9325i	0.375308	+	0.650052i	−0.615065	+	0.788476i	$0.710870\pi$
$762$		0			0
$763$	−15.6609	+	32.2618i	−0.566963	+	1.16796i
$764$			18.4336i			0.666905i
$765$		0			0
$766$	−7.33307	−	4.23375i	−0.264955	−	0.152972i
$767$	−0.362626	+	0.628086i	−0.0130937	+	0.0226789i
$768$		0			0
$769$			3.34563i			0.120647i	0.998179	+	0.0603233i	$0.0192132\pi$
$769$			3.34563i			0.120647i	−0.998179	+	0.0603233i	$0.980787\pi$
$770$		0			0
$771$		0			0
$772$	−5.50643	+	3.17914i	−0.198181	+	0.114420i
$773$	24.8778	+	14.3632i	0.894793	+	0.516609i	0.875507	−	0.483205i	$-0.160527\pi$
$773$	24.8778	+	14.3632i	0.894793	+	0.516609i	0.0192861	+	0.999814i	$0.493861\pi$
$774$		0			0
$775$		0			0
$776$	17.1502			0.615656
$777$		0			0
$778$			5.74150i			0.205843i
$779$	2.97740	−	1.71901i	0.106677	−	0.0615898i
$780$		0			0
$781$	−19.7778	+	34.2562i	−0.707706	+	1.22578i
$782$	−23.6838	+	13.6739i	−0.846932	+	0.488977i
$783$		0			0
$784$	−4.33013	−	5.50000i	−0.154647	−	0.196429i
$785$		0			0
$786$		0			0
$787$	−2.74515	+	4.75474i	−0.0978541	+	0.169488i	−0.910796	−	0.412856i	$-0.864531\pi$
$787$	−2.74515	+	4.75474i	−0.0978541	+	0.169488i	0.812942	+	0.582345i	$0.197865\pi$
$788$	6.41946	−	11.1188i	0.228684	−	0.396092i
$789$		0			0
$790$		0			0
$791$	30.8710	−	2.21644i	1.09765	−	0.0788075i
$792$		0			0
$793$	−0.443850	+	0.256257i	−0.0157616	+	0.00909995i
$794$	−8.43791	+	14.6149i	−0.299450	+	0.518663i
$795$		0			0
$796$	−8.33950	+	4.81481i	−0.295586	+	0.170656i
$797$		−	50.8854i		−	1.80245i	−0.433347	−	0.901227i	$-0.642668\pi$
$797$		−	50.8854i		−	1.80245i	0.433347	−	0.901227i	$-0.357332\pi$
$798$		0			0
$799$	12.1751			0.430725
$800$		0			0
$801$		0			0
$802$	1.63572	+	0.944382i	0.0577592	+	0.0333473i
$803$	40.1962	−	23.2073i	1.41849	−	0.818967i
$804$		0			0
$805$		0			0
$806$		−	0.329049i		−	0.0115903i
$807$		0			0
$808$	−3.36773	+	5.83307i	−0.118476	+	0.205207i
$809$	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	$-0.157334\pi$
$812$	−2.13970	−	1.03868i	−0.0750886	−	0.0364504i
$813$		0			0
$814$	−8.09915	−	14.0281i	−0.283875	−	0.491686i
$815$		0			0
$816$		0			0
$817$	−0.981740	−	1.70042i	−0.0343467	−	0.0594903i
$818$			32.9802i			1.15312i
$819$		0			0
$820$		0			0
$821$	−8.06085	+	4.65393i	−0.281326	+	0.162423i	−0.634023	−	0.773314i	$-0.718598\pi$
$821$	−8.06085	+	4.65393i	−0.281326	+	0.162423i	0.352698	+	0.935737i	$0.385264\pi$
$822$		0			0
$823$	35.0901	+	20.2593i	1.22316	+	0.706195i	0.965591	−	0.260064i	$-0.0837437\pi$
$823$	35.0901	+	20.2593i	1.22316	+	0.706195i	0.257573	+	0.966259i	$0.417077\pi$
$824$	0.260021	+	0.450370i	0.00905826	+	0.0156894i
$825$		0			0
$826$	28.0844	−	2.01637i	0.977182	−	0.0701585i
$827$	−14.0131			−0.487284			−0.243642	−	0.969865i	$-0.578342\pi$
$827$	−14.0131			−0.487284			−0.243642	+	0.969865i	$0.578342\pi$
$828$		0			0
$829$	−18.8540	−	10.8854i	−0.654827	−	0.378064i	0.135476	−	0.990781i	$-0.456744\pi$
$829$	−18.8540	−	10.8854i	−0.654827	−	0.378064i	−0.790303	+	0.612716i	$0.790077\pi$
$830$		0			0
$831$		0			0
$832$	−0.0681483			−0.00236262
$833$	−47.6307	−	19.0382i	−1.65031	−	0.659634i
$834$		0			0
$835$		0			0
$836$	−4.05197	+	7.01822i	−0.140140	+	0.242730i
$837$		0			0
$838$	0.150235	+	0.260214i	0.00518978	+	0.00898896i
$839$	−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
$842$	−14.4312	−	24.9956i	−0.497333	−	0.861406i
$843$		0			0
$844$	7.28094	−	12.6110i	0.250620	−	0.434087i
$845$		0			0
$846$		0			0
$847$	−7.20159	−	10.6341i	−0.247450	−	0.365391i
$848$	13.2268			0.454210
$849$		0			0
$850$		0			0
$851$	13.1485	+	7.59127i	0.450723	+	0.260225i
$852$		0			0
$853$	−7.95355			−0.272324			−0.136162	−	0.990687i	$-0.543477\pi$
$853$	−7.95355			−0.272324			−0.136162	+	0.990687i	$0.543477\pi$
$854$	17.9000	+	8.68921i	0.612525	+	0.297339i
$855$		0			0
$856$	−3.06350	−	5.30614i	−0.104708	−	0.181360i
$857$	1.98582	+	1.14651i	0.0678343	+	0.0391641i	0.533534	−	0.845779i	$-0.320864\pi$
$857$	1.98582	+	1.14651i	0.0678343	+	0.0391641i	−0.465699	+	0.884943i	$0.654197\pi$
$858$		0			0
$859$	38.1054	−	22.0002i	1.30014	−	0.750636i	0.319712	−	0.947515i	$-0.396414\pi$
$859$	38.1054	−	22.0002i	1.30014	−	0.750636i	0.980428	+	0.196879i	$0.0630806\pi$
$860$		0			0
$861$		0			0
$862$			33.5897i			1.14407i
$863$	16.5676	+	28.6959i	0.563968	+	0.976821i	0.997145	+	0.0755122i	$0.0240592\pi$
$863$	16.5676	+	28.6959i	0.563968	+	0.976821i	−0.433177	+	0.901309i	$0.642607\pi$
$864$		0			0
$865$		0			0
$866$	5.61037	+	9.71744i	0.190648	+	0.330212i
$867$		0			0
$868$	−10.5775	+	7.16328i	−0.359024	+	0.243138i
$869$			69.8787i			2.37047i
$870$		0			0
$871$	−0.629306	−	0.363330i	−0.0213232	−	0.0123110i
$872$	6.77729	−	11.7386i	0.229508	−	0.397520i
$873$		0			0
$874$		−	7.59575i		−	0.256930i
$875$		0			0
$876$		0			0
$877$	4.92657	−	2.84436i	0.166358	−	0.0960471i	−0.414509	−	0.910045i	$-0.636047\pi$
$877$	4.92657	−	2.84436i	0.166358	−	0.0960471i	0.580868	+	0.813998i	$0.302713\pi$
$878$	−14.6075	−	8.43363i	−0.492979	−	0.284621i
$879$		0			0
$880$		0			0
$881$	−22.4073			−0.754923			−0.377461	−	0.926025i	$-0.623203\pi$
$881$	−22.4073			−0.754923			−0.377461	+	0.926025i	$0.623203\pi$
$882$		0			0
$883$		−	18.7564i		−	0.631204i	−0.948892	−	0.315602i	$-0.897794\pi$
$883$		−	18.7564i		−	0.631204i	0.948892	−	0.315602i	$-0.102206\pi$
$884$	−0.432474	+	0.249689i	−0.0145457	+	0.00839795i
$885$		0			0
$886$	−1.02823	+	1.78094i	−0.0345440	+	0.0598320i
$887$	−1.27384	+	0.735451i	−0.0427713	+	0.0246940i	−0.521233	−	0.853414i	$-0.674528\pi$
$887$	−1.27384	+	0.735451i	−0.0427713	+	0.0246940i	0.478462	+	0.878108i	$0.341194\pi$
$888$		0			0
$889$	2.03735	+	28.3767i	0.0683306	+	0.951723i
$890$		0			0
$891$		0			0
$892$	−11.8305	+	20.4910i	−0.396113	+	0.686088i
$893$	−1.69080	+	2.92856i	−0.0565806	+	0.0980005i
$894$		0			0
$895$		0			0
$896$	1.48356	+	2.19067i	0.0495624	+	0.0731852i
$897$		0			0
$898$	−10.9026	+	6.29461i	−0.363824	+	0.210054i
$899$	−2.17033	+	3.75912i	−0.0723845	+	0.125374i
$900$		0			0
$901$	83.9380	−	48.4616i	2.79638	−	1.61449i
$902$		−	6.72600i		−	0.223951i
$903$		0			0
$904$	−11.6982			−0.389076
$905$		0			0
$906$		0			0
$907$	16.3210	+	9.42294i	0.541930	+	0.312883i	0.745861	−	0.666102i	$-0.232038\pi$
$907$	16.3210	+	9.42294i	0.541930	+	0.312883i	−0.203931	+	0.978985i	$0.565372\pi$
$908$	−7.48288	+	4.32024i	−0.248328	+	0.143372i
$909$		0			0
$910$		0			0
$911$		−	5.45859i		−	0.180851i	−0.995903	−	0.0904256i	$-0.971177\pi$
$911$		−	5.45859i		−	0.180851i	0.995903	−	0.0904256i	$-0.0288227\pi$
$912$		0			0
$913$	28.5670	−	49.4794i	0.945428	−	1.63753i
$914$	30.2701	+	17.4765i	1.00125	+	0.578070i
$915$		0			0
$916$			14.0754i			0.465063i
$917$	−5.50276	−	8.12552i	−0.181717	−	0.268328i
$918$		0			0
$919$	14.9805	+	25.9470i	0.494162	+	0.855914i	0.999977	−	0.00672796i	$-0.00214159\pi$
$919$	14.9805	+	25.9470i	0.494162	+	0.855914i	−0.505815	+	0.862642i	$0.668808\pi$
$920$		0			0
$921$		0			0
$922$	−11.6875	−	20.2433i	−0.384907	−	0.666678i
$923$		−	0.677003i		−	0.0222838i
$924$		0			0
$925$		0			0
$926$	−5.50526	+	3.17846i	−0.180914	+	0.104451i
$927$		0			0
$928$	0.778539	+	0.449490i	0.0255568	+	0.0147552i
$929$	−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
$932$	−20.1976			−0.661593
$933$		0			0
$934$	−6.74907	−	3.89658i	−0.220836	−	0.127500i
$935$		0			0
$936$		0			0
$937$	−19.1632			−0.626036			−0.313018	−	0.949747i	$-0.601340\pi$
$937$	−19.1632			−0.626036			−0.313018	+	0.949747i	$0.601340\pi$
$938$	2.02029	+	28.1390i	0.0659647	+	0.918770i
$939$		0			0
$940$		0			0
$941$	−25.2474	+	43.7299i	−0.823043	+	1.42555i	0.0803623	+	0.996766i	$0.474392\pi$
$941$	−25.2474	+	43.7299i	−0.823043	+	1.42555i	−0.903406	+	0.428787i	$0.858941\pi$
$942$		0			0
$943$	3.15211	+	5.45962i	0.102647	+	0.177790i
$944$	−10.6422			−0.346375
$945$		0			0
$946$	−3.84128			−0.124891
$947$	−18.0309	−	31.2304i	−0.585925	−	1.01485i	−0.994759	−	0.102244i	$-0.967398\pi$
$947$	−18.0309	−	31.2304i	−0.585925	−	1.01485i	0.408834	−	0.912609i	$-0.365936\pi$
$948$		0			0
$949$	−0.397198	+	0.687967i	−0.0128936	+	0.0223323i
$950$		0			0
$951$		0			0
$952$	17.4412	+	8.46651i	0.565272	+	0.274401i
$953$	29.7944			0.965137			0.482568	−	0.875858i	$-0.339704\pi$
$953$	29.7944			0.965137			0.482568	+	0.875858i	$0.339704\pi$
$954$		0			0
$955$		0			0
$956$	20.3550	+	11.7520i	0.658329	+	0.380086i
$957$		0			0
$958$	27.5040			0.888613
$959$	−15.6216	+	32.1808i	−0.504447	+	1.03917i
$960$		0			0
$961$	−3.84315	−	6.65652i	−0.123972	−	0.214727i
$962$	0.240095	+	0.138619i	0.00774097	+	0.00446925i
$963$		0			0
$964$	12.8765	−	7.43426i	0.414724	−	0.239441i
$965$		0			0
$966$		0			0
$967$			11.5198i			0.370453i	0.982696	+	0.185226i	$0.0593018\pi$
$967$			11.5198i			0.370453i	−0.982696	+	0.185226i	$0.940698\pi$
$968$	2.42713	+	4.20390i	0.0780108	+	0.135119i
$969$		0			0
$970$		0			0
$971$	−21.2347	−	36.7795i	−0.681453	−	1.18031i	−0.974537	−	0.224225i	$-0.928015\pi$
$971$	−21.2347	−	36.7795i	−0.681453	−	1.18031i	0.293084	−	0.956087i	$-0.405318\pi$
$972$		0			0
$973$	1.71706	+	23.9156i	0.0550465	+	0.766698i
$974$		−	35.4468i		−	1.13579i
$975$		0			0
$976$	−6.51299	−	3.76028i	−0.208476	−	0.120364i
$977$	−9.08052	+	15.7279i	−0.290512	+	0.503181i	−0.973931	−	0.226845i	$-0.927159\pi$
$977$	−9.08052	+	15.7279i	−0.290512	+	0.503181i	0.683419	+	0.730026i	$0.260492\pi$
$978$		0			0
$979$			7.27827i			0.232614i
$980$		0			0
$981$		0			0
$982$	1.42330	−	0.821743i	0.0454194	−	0.0262229i
$983$	10.7385	+	6.19988i	0.342505	+	0.197746i	0.661379	−	0.750052i	$-0.269971\pi$
$983$	10.7385	+	6.19988i	0.342505	+	0.197746i	−0.318874	+	0.947797i	$0.603305\pi$
$984$		0			0
$985$		0			0
$986$	6.58755			0.209790
$987$		0			0
$988$		−	0.138701i		−	0.00441266i
$989$	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	$0.278781\pi$
$992$	4.18154	−	2.41421i	0.132764	−	0.0766514i
$993$		0			0
$994$	−21.7627	+	14.7381i	−0.690270	+	0.467464i
$995$		0			0
$996$		0			0
$997$	−21.2381	+	36.7856i	−0.672619	+	1.16501i	0.304540	+	0.952500i	$0.401497\pi$
$997$	−21.2381	+	36.7856i	−0.672619	+	1.16501i	−0.977159	+	0.212510i	$0.931836\pi$
$998$	−17.3665	+	30.0796i	−0.549726	+	0.952154i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.1	✓	8	35.12	even	12
630.2.be.a.521.1	yes	8	15.2	even	4
630.2.be.b.341.3	yes	8	105.47	odd	12
630.2.be.b.521.3	yes	8	5.2	odd	4
3150.2.bf.b.1151.4		8	15.8	even	4
3150.2.bf.b.1601.4		8	35.33	even	12
3150.2.bf.c.1151.2		8	5.3	odd	4
3150.2.bf.c.1601.2		8	105.68	odd	12
3150.2.bp.a.899.4		8	15.14	odd	2
3150.2.bp.a.1349.4		8	7.5	odd	6
3150.2.bp.c.899.1		8	1.1	even	1	trivial
3150.2.bp.c.1349.1		8	105.89	even	6	inner
3150.2.bp.d.899.1		8	3.2	odd	2
3150.2.bp.d.1349.1		8	35.19	odd	6
3150.2.bp.f.899.4		8	5.4	even	2
3150.2.bp.f.1349.4		8	21.5	even	6
4410.2.b.b.881.4		8	105.17	odd	12
4410.2.b.b.881.5		8	35.32	odd	12
4410.2.b.e.881.4		8	105.32	even	12
4410.2.b.e.881.5		8	35.17	even	12

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.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.63896 + 0.189469i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.63896 + 0.189469i) q^{7} +1.00000 q^{8} +(3.44829 + 1.99087i) q^{11} -0.0681483 q^{13} +(1.48356 + 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.34607 - 3.66390i) q^{17} +(1.76260 - 1.01764i) q^{19} -3.98174i q^{22} +(1.86603 + 3.23205i) q^{23} +(0.0340742 + 0.0590182i) q^{26} +(1.15539 - 2.38014i) q^{28} -0.898979i q^{29} +(-4.18154 - 2.41421i) q^{31} +(-0.500000 + 0.866025i) q^{32} +7.32780i q^{34} +(3.52312 - 2.03407i) q^{37} +(-1.76260 - 1.01764i) q^{38} +1.68921 q^{41} -0.964724i q^{43} +(-3.44829 + 1.99087i) q^{44} +(1.86603 - 3.23205i) q^{46} +(-1.43890 + 0.830749i) q^{47} +(6.92820 - 1.00000i) q^{49} +(0.0340742 - 0.0590182i) q^{52} +(-6.61339 + 11.4547i) q^{53} +(-2.63896 + 0.189469i) q^{56} +(-0.778539 + 0.449490i) q^{58} +(5.32112 - 9.21645i) q^{59} +(6.51299 - 3.76028i) q^{61} +4.82843i q^{62} +1.00000 q^{64} +(9.23435 + 5.33145i) q^{67} +(6.34607 - 3.66390i) q^{68} +9.93426i q^{71} +(5.82843 - 10.0951i) q^{73} +(-3.52312 - 2.03407i) q^{74} +2.03528i q^{76} +(-9.47710 - 4.60048i) q^{77} +(8.77489 + 15.1986i) q^{79} +(-0.844605 - 1.46290i) q^{82} -14.3490i q^{83} +(-0.835475 + 0.482362i) q^{86} +(3.44829 + 1.99087i) q^{88} +(0.913956 + 1.58302i) q^{89} +(0.179841 - 0.0129120i) q^{91} -3.73205 q^{92} +(1.43890 + 0.830749i) q^{94} +17.1502 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 24 q^{11} - 16 q^{13} - 4 q^{16} - 24 q^{17} + 8 q^{23} + 8 q^{26} - 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} - 12 q^{47} + 8 q^{52} - 4 q^{53} + 24 q^{59} + 8 q^{64} - 48 q^{67} + 24 q^{68} + 24 q^{73} + 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} + 16 q^{89} - 20 q^{91} - 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 24 * q^11 - 16 * q^13 - 4 * q^16 - 24 * q^17 + 8 * q^23 + 8 * q^26 - 4 * q^32 + 32 * q^41 - 24 * q^44 + 8 * q^46 - 12 * q^47 + 8 * q^52 - 4 * q^53 + 24 * q^59 + 8 * q^64 - 48 * q^67 + 24 * q^68 + 24 * q^73 + 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 + 16 * q^89 - 20 * q^91 - 16 * q^92 + 12 * q^94 + 48 * q^97

Introduction

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