LMFDB - Embedded newform 945.2.bj.l.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(26,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, 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("945.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bj (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 28 x^{18} + 322 x^{16} + 1978 x^{14} + 7075 x^{12} + 15064 x^{10} + 18679 x^{8} + 12544 x^{6} + \cdots + 9 $ x^20 + 28x^18 + 322x^16 + 1978x^14 + 7075x^12 + 15064x^10 + 18679x^8 + 12544x^6 + 3919x^4 + 438*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-2.76486i$ of defining polynomial
Character	$\chi$	$=$	945.26
Dual form			945.2.bj.l.836.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.39444 - 1.38243i) q^{2} +(2.82223 + 4.88825i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.44101 - 2.21890i) q^{7} -10.0764i q^{8} +O(q^{10})$	\(q+(-2.39444 - 1.38243i) q^{2} +(2.82223 + 4.88825i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.44101 - 2.21890i) q^{7} -10.0764i q^{8} +(-2.39444 + 1.38243i) q^{10} +(-3.35867 + 1.93913i) q^{11} +4.43338i q^{13} +(-6.51787 + 3.32093i) q^{14} +(-8.28550 + 14.3509i) q^{16} +(1.30883 + 2.26696i) q^{17} +(-5.60863 - 3.23815i) q^{19} +5.64446 q^{20} +10.7228 q^{22} +(-3.78512 - 2.18534i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(6.12884 - 10.6155i) q^{26} +(14.9134 + 0.781749i) q^{28} +3.31909i q^{29} +(-4.67916 + 2.70151i) q^{31} +(22.2254 - 12.8318i) q^{32} -7.23747i q^{34} +(-1.20112 - 2.35740i) q^{35} +(4.22328 - 7.31493i) q^{37} +(8.95303 + 15.5071i) q^{38} +(-8.72644 - 5.03821i) q^{40} -2.44513 q^{41} -10.1703 q^{43} +(-18.9579 - 10.9453i) q^{44} +(6.04217 + 10.4653i) q^{46} +(-0.364769 + 0.631799i) q^{47} +(-2.84701 - 6.39488i) q^{49} +2.76486i q^{50} +(-21.6715 + 12.5120i) q^{52} +(-6.92049 + 3.99554i) q^{53} +3.87826i q^{55} +(-22.3586 - 14.5202i) q^{56} +(4.58841 - 7.94736i) q^{58} +(-1.87534 - 3.24819i) q^{59} +(1.03271 + 0.596235i) q^{61} +14.9386 q^{62} -37.8145 q^{64} +(3.83942 + 2.21669i) q^{65} +(-0.259970 - 0.450281i) q^{67} +(-7.38764 + 12.7958i) q^{68} +(-0.382929 + 7.30511i) q^{70} -0.287787i q^{71} +(6.36235 - 3.67331i) q^{73} +(-20.2248 + 11.6768i) q^{74} -36.5552i q^{76} +(-0.537133 + 10.2468i) q^{77} +(-3.44143 + 5.96074i) q^{79} +(8.28550 + 14.3509i) q^{80} +(5.85472 + 3.38023i) q^{82} -3.35120 q^{83} +2.61766 q^{85} +(24.3522 + 14.0598i) q^{86} +(19.5395 + 33.8434i) q^{88} +(-6.50999 + 11.2756i) q^{89} +(9.83722 + 6.38853i) q^{91} -24.6701i q^{92} +(1.74684 - 1.00854i) q^{94} +(-5.60863 + 3.23815i) q^{95} -9.20175i q^{97} +(-2.02349 + 19.2480i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{4} + 10 q^{5} + 6 q^{7}+O(q^{10}) $ 20 * q + 8 * q^4 + 10 * q^5 + 6 * q^7	$ 20 q + 8 q^{4} + 10 q^{5} + 6 q^{7} - 6 q^{11} - 12 q^{14} - 12 q^{16} - 6 q^{19} + 16 q^{20} + 28 q^{22} - 24 q^{23} - 10 q^{25} + 12 q^{26} + 10 q^{28} + 18 q^{31} + 60 q^{32} + 24 q^{38} - 12 q^{41} - 36 q^{43} - 60 q^{44} + 4 q^{46} + 12 q^{47} - 22 q^{49} - 78 q^{52} - 24 q^{53} - 66 q^{56} + 16 q^{58} - 6 q^{61} + 72 q^{62} - 60 q^{64} + 24 q^{65} - 20 q^{67} - 12 q^{68} + 12 q^{70} + 42 q^{73} - 42 q^{74} + 36 q^{77} + 10 q^{79} + 12 q^{80} + 72 q^{82} - 48 q^{83} + 42 q^{86} + 44 q^{88} - 12 q^{89} - 24 q^{91} + 78 q^{94} - 6 q^{95} + 48 q^{98}+O(q^{100}) $ 20 * q + 8 * q^4 + 10 * q^5 + 6 * q^7 - 6 * q^11 - 12 * q^14 - 12 * q^16 - 6 * q^19 + 16 * q^20 + 28 * q^22 - 24 * q^23 - 10 * q^25 + 12 * q^26 + 10 * q^28 + 18 * q^31 + 60 * q^32 + 24 * q^38 - 12 * q^41 - 36 * q^43 - 60 * q^44 + 4 * q^46 + 12 * q^47 - 22 * q^49 - 78 * q^52 - 24 * q^53 - 66 * q^56 + 16 * q^58 - 6 * q^61 + 72 * q^62 - 60 * q^64 + 24 * q^65 - 20 * q^67 - 12 * q^68 + 12 * q^70 + 42 * q^73 - 42 * q^74 + 36 * q^77 + 10 * q^79 + 12 * q^80 + 72 * q^82 - 48 * q^83 + 42 * q^86 + 44 * q^88 - 12 * q^89 - 24 * q^91 + 78 * q^94 - 6 * q^95 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.39444	−	1.38243i	−1.69312	−	0.977526i	−0.951970	−	0.306193i	$-0.900945\pi$
$2$	−2.39444	−	1.38243i	−1.69312	−	0.977526i	−0.741155	−	0.671333i	$-0.765722\pi$
$3$		0			0
$3$		0			0
$4$	2.82223	+	4.88825i	1.41111	+	2.44412i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.44101	−	2.21890i	0.544649	−	0.838664i
$7$	1.44101	−	2.21890i	0.544649	−	0.838664i
$8$		−	10.0764i		−	3.56255i
$9$		0			0
$10$	−2.39444	+	1.38243i	−0.757189	+	0.437163i
$11$	−3.35867	+	1.93913i	−1.01268	+	0.584670i	−0.911974	−	0.410247i	$-0.865442\pi$
$11$	−3.35867	+	1.93913i	−1.01268	+	0.584670i	−0.100703	+	0.994917i	$0.532109\pi$
$12$		0			0
$13$			4.43338i			1.22960i	0.788683	+	0.614799i	$0.210763\pi$
$13$			4.43338i			1.22960i	−0.788683	+	0.614799i	$0.789237\pi$
$14$	−6.51787	+	3.32093i	−1.74197	+	0.887555i
$15$		0			0
$16$	−8.28550	+	14.3509i	−2.07138	+	3.58773i
$17$	1.30883	+	2.26696i	0.317438	+	0.549819i	0.979953	−	0.199230i	$-0.0638441\pi$
$17$	1.30883	+	2.26696i	0.317438	+	0.549819i	−0.662515	+	0.749049i	$0.730511\pi$
$18$		0			0
$19$	−5.60863	−	3.23815i	−1.28671	−	0.742882i	−0.308643	−	0.951178i	$-0.599875\pi$
$19$	−5.60863	−	3.23815i	−1.28671	−	0.742882i	−0.978066	+	0.208296i	$0.933208\pi$
$20$	5.64446			1.26214
$21$		0			0
$22$	10.7228			2.28612
$23$	−3.78512	−	2.18534i	−0.789252	−	0.455675i	0.0504469	−	0.998727i	$-0.483935\pi$
$23$	−3.78512	−	2.18534i	−0.789252	−	0.455675i	−0.839699	+	0.543052i	$0.817269\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	6.12884	−	10.6155i	1.20197	−	2.08186i
$27$		0			0
$28$	14.9134	+	0.781749i	2.81836	+	0.147737i
$29$			3.31909i			0.616339i	0.951331	+	0.308170i	$0.0997165\pi$
$29$			3.31909i			0.616339i	−0.951331	+	0.308170i	$0.900284\pi$
$30$		0			0
$31$	−4.67916	+	2.70151i	−0.840402	+	0.485206i	−0.857401	−	0.514649i	$-0.827922\pi$
$31$	−4.67916	+	2.70151i	−0.840402	+	0.485206i	0.0169989	+	0.999856i	$0.494589\pi$
$32$	22.2254	−	12.8318i	3.92893	−	2.26837i
$33$		0			0
$34$		−	7.23747i		−	1.24122i
$35$	−1.20112	−	2.35740i	−0.203026	−	0.398473i
$36$		0			0
$37$	4.22328	−	7.31493i	0.694303	−	1.20257i	−0.276112	−	0.961125i	$-0.589046\pi$
$37$	4.22328	−	7.31493i	0.694303	−	1.20257i	0.970415	−	0.241442i	$-0.0776205\pi$
$38$	8.95303	+	15.5071i	1.45237	+	2.51558i
$39$		0			0
$40$	−8.72644	−	5.03821i	−1.37977	−	0.796611i
$41$	−2.44513			−0.381866			−0.190933	−	0.981603i	$-0.561151\pi$
$41$	−2.44513			−0.381866			−0.190933	+	0.981603i	$0.561151\pi$
$42$		0			0
$43$	−10.1703			−1.55096			−0.775480	−	0.631372i	$-0.782492\pi$
$43$	−10.1703			−1.55096			−0.775480	+	0.631372i	$0.782492\pi$
$44$	−18.9579	−	10.9453i	−2.85801	−	1.65007i
$45$		0			0
$46$	6.04217	+	10.4653i	0.890869	+	1.54303i
$47$	−0.364769	+	0.631799i	−0.0532071	+	0.0921574i	−0.891402	−	0.453213i	$-0.850278\pi$
$47$	−0.364769	+	0.631799i	−0.0532071	+	0.0921574i	0.838195	+	0.545370i	$0.183611\pi$
$48$		0			0
$49$	−2.84701	−	6.39488i	−0.406716	−	0.913555i
$50$			2.76486i			0.391010i
$51$		0			0
$52$	−21.6715	+	12.5120i	−3.00529	+	1.73511i
$53$	−6.92049	+	3.99554i	−0.950602	+	0.548830i	−0.893268	−	0.449525i	$-0.851593\pi$
$53$	−6.92049	+	3.99554i	−0.950602	+	0.548830i	−0.0573340	+	0.998355i	$0.518260\pi$
$54$		0			0
$55$			3.87826i			0.522944i
$56$	−22.3586	−	14.5202i	−2.98779	−	1.94034i
$57$		0			0
$58$	4.58841	−	7.94736i	0.602488	−	1.04354i
$59$	−1.87534	−	3.24819i	−0.244149	−	0.422878i	0.717743	−	0.696308i	$-0.245175\pi$
$59$	−1.87534	−	3.24819i	−0.244149	−	0.422878i	−0.961892	+	0.273430i	$0.911842\pi$
$60$		0			0
$61$	1.03271	+	0.596235i	0.132225	+	0.0763401i	0.564653	−	0.825328i	$-0.309010\pi$
$61$	1.03271	+	0.596235i	0.132225	+	0.0763401i	−0.432428	+	0.901668i	$0.642343\pi$
$62$	14.9386			1.89721
$63$		0			0
$64$	−37.8145			−4.72681
$65$	3.83942	+	2.21669i	0.476222	+	0.274947i
$66$		0			0
$67$	−0.259970	−	0.450281i	−0.0317604	−	0.0550106i	0.849708	−	0.527253i	$-0.176778\pi$
$67$	−0.259970	−	0.450281i	−0.0317604	−	0.0550106i	−0.881469	+	0.472242i	$0.843445\pi$
$68$	−7.38764	+	12.7958i	−0.895884	+	1.55172i
$69$		0			0
$70$	−0.382929	+	7.30511i	−0.0457688	+	0.873127i
$71$		−	0.287787i		−	0.0341540i	−0.999854	−	0.0170770i	$-0.994564\pi$
$71$		−	0.287787i		−	0.0341540i	0.999854	−	0.0170770i	$-0.00543604\pi$
$72$		0			0
$73$	6.36235	−	3.67331i	0.744657	−	0.429928i	−0.0791032	−	0.996866i	$-0.525206\pi$
$73$	6.36235	−	3.67331i	0.744657	−	0.429928i	0.823760	+	0.566939i	$0.191872\pi$
$74$	−20.2248	+	11.6768i	−2.35108	+	1.35740i
$75$		0			0
$76$		−	36.5552i		−	4.19317i
$77$	−0.537133	+	10.2468i	−0.0612120	+	1.16774i
$78$		0			0
$79$	−3.44143	+	5.96074i	−0.387192	+	0.670636i	−0.992071	−	0.125682i	$-0.959888\pi$
$79$	−3.44143	+	5.96074i	−0.387192	+	0.670636i	0.604879	+	0.796317i	$0.293221\pi$
$80$	8.28550	+	14.3509i	0.926347	+	1.60448i
$81$		0			0
$82$	5.85472	+	3.38023i	0.646546	+	0.373284i
$83$	−3.35120			−0.367842			−0.183921	−	0.982941i	$-0.558879\pi$
$83$	−3.35120			−0.367842			−0.183921	+	0.982941i	$0.558879\pi$
$84$		0			0
$85$	2.61766			0.283925
$86$	24.3522	+	14.0598i	2.62597	+	1.51610i
$87$		0			0
$88$	19.5395	+	33.8434i	2.08292	+	3.60772i
$89$	−6.50999	+	11.2756i	−0.690057	+	1.19521i	0.281761	+	0.959485i	$0.409081\pi$
$89$	−6.50999	+	11.2756i	−0.690057	+	1.19521i	−0.971819	+	0.235730i	$0.924252\pi$
$90$		0			0
$91$	9.83722	+	6.38853i	1.03122	+	0.669699i
$92$		−	24.6701i		−	2.57204i
$93$		0			0
$94$	1.74684	−	1.00854i	0.180173	−	0.104023i
$95$	−5.60863	+	3.23815i	−0.575434	+	0.332227i
$96$		0			0
$97$		−	9.20175i		−	0.934296i	−0.884179	−	0.467148i	$-0.845281\pi$
$97$		−	9.20175i		−	0.934296i	0.884179	−	0.467148i	$-0.154719\pi$
$98$	−2.02349	+	19.2480i	−0.204403	+	1.94434i
$99$		0			0
$100$	2.82223	−	4.88825i	0.282223	−	0.488825i
$101$	0.514429	+	0.891017i	0.0511876	+	0.0886595i	0.890484	−	0.455015i	$-0.150366\pi$
$101$	0.514429	+	0.891017i	0.0511876	+	0.0886595i	−0.839296	+	0.543674i	$0.817033\pi$
$102$		0			0
$103$	−0.783706	−	0.452473i	−0.0772208	−	0.0445834i	0.460892	−	0.887456i	$-0.347529\pi$
$103$	−0.783706	−	0.452473i	−0.0772208	−	0.0445834i	−0.538113	+	0.842873i	$0.680863\pi$
$104$	44.6726			4.38051
$105$		0			0
$106$	22.0943			2.14598
$107$	4.05014	+	2.33835i	0.391542	+	0.226057i	0.682828	−	0.730579i	$-0.260750\pi$
$107$	4.05014	+	2.33835i	0.391542	+	0.226057i	−0.291286	+	0.956636i	$0.594083\pi$
$108$		0			0
$109$	5.32077	+	9.21584i	0.509637	+	0.882718i	0.999938	+	0.0111641i	$0.00355371\pi$
$109$	5.32077	+	9.21584i	0.509637	+	0.882718i	−0.490300	+	0.871553i	$0.663113\pi$
$110$	5.36142	−	9.28626i	0.511192	−	0.885410i
$111$		0			0
$112$	19.9037	+	39.0644i	1.88073	+	3.69124i
$113$		−	7.21562i		−	0.678789i	−0.940644	−	0.339394i	$-0.889778\pi$
$113$		−	7.21562i		−	0.678789i	0.940644	−	0.339394i	$-0.110222\pi$
$114$		0			0
$115$	−3.78512	+	2.18534i	−0.352964	+	0.203784i
$116$	−16.2245	+	9.36723i	−1.50641	+	0.869726i
$117$		0			0
$118$			10.3701i			0.954647i
$119$	6.91619	+	0.362542i	0.634006	+	0.0332342i
$120$		0			0
$121$	2.02045	−	3.49952i	0.183677	−	0.318138i
$122$	−1.64851	−	2.85530i	−0.149249	−	0.258507i
$123$		0			0
$124$	−26.4113	−	15.2486i	−2.37181	−	1.36936i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−9.27903			−0.823381			−0.411690	−	0.911324i	$-0.635061\pi$
$127$	−9.27903			−0.823381			−0.411690	+	0.911324i	$0.635061\pi$
$128$	46.0938	+	26.6123i	4.07415	+	2.35221i
$129$		0			0
$130$	−6.12884	−	10.6155i	−0.537535	−	0.931038i
$131$	−6.90870	+	11.9662i	−0.603616	+	1.04549i	0.388653	+	0.921384i	$0.372941\pi$
$131$	−6.90870	+	11.9662i	−0.603616	+	1.04549i	−0.992269	+	0.124109i	$0.960393\pi$
$132$		0			0
$133$	−15.2672	+	7.77880i	−1.32383	+	0.674507i
$134$			1.43756i			0.124186i
$135$		0			0
$136$	22.8429	−	13.1883i	1.95876	−	1.13089i
$137$	−5.71833	+	3.30148i	−0.488550	+	0.282065i	−0.723973	−	0.689829i	$-0.757686\pi$
$137$	−5.71833	+	3.30148i	−0.488550	+	0.282065i	0.235423	+	0.971893i	$0.424353\pi$
$138$		0			0
$139$			0.750160i			0.0636277i	0.999494	+	0.0318139i	$0.0101284\pi$
$139$			0.750160i			0.0636277i	−0.999494	+	0.0318139i	$0.989872\pi$
$140$	8.13369	−	12.5245i	0.687423	−	1.05851i
$141$		0			0
$142$	−0.397845	+	0.689088i	−0.0333864	+	0.0578270i
$143$	−8.59690	−	14.8903i	−0.718909	−	1.24519i
$144$		0			0
$145$	2.87442	+	1.65954i	0.238707	+	0.137818i
$146$	−20.3124			−1.68106
$147$		0			0
$148$	47.6763			3.91896
$149$	−12.8322	−	7.40868i	−1.05125	−	0.606942i	−0.128255	−	0.991741i	$-0.540937\pi$
$149$	−12.8322	−	7.40868i	−1.05125	−	0.606942i	−0.923000	+	0.384799i	$0.874271\pi$
$150$		0			0
$151$	4.63028	+	8.01989i	0.376807	+	0.652649i	0.990596	−	0.136821i	$-0.0436886\pi$
$151$	4.63028	+	8.01989i	0.376807	+	0.652649i	−0.613789	+	0.789470i	$0.710355\pi$
$152$	−32.6289	+	56.5150i	−2.64656	+	4.58397i
$153$		0			0
$154$	15.4517	−	23.7929i	1.24513	−	1.91729i
$155$			5.40303i			0.433982i
$156$		0			0
$157$	−17.0672	+	9.85374i	−1.36211	+	0.786414i	−0.989904	−	0.141737i	$-0.954731\pi$
$157$	−17.0672	+	9.85374i	−1.36211	+	0.786414i	−0.372204	+	0.928151i	$0.621398\pi$
$158$	16.4806	−	9.51509i	1.31113	−	0.756980i
$159$		0			0
$160$		−	25.6637i		−	2.02889i
$161$	−10.3034	+	5.24971i	−0.812024	+	0.413735i
$162$		0			0
$163$	−1.77376	+	3.07224i	−0.138931	+	0.240636i	−0.927092	−	0.374833i	$-0.877700\pi$
$163$	−1.77376	+	3.07224i	−0.138931	+	0.240636i	0.788161	+	0.615469i	$0.211033\pi$
$164$	−6.90073	−	11.9524i	−0.538856	−	0.933326i
$165$		0			0
$166$	8.02426	+	4.63281i	0.622803	+	0.359576i
$167$	−1.54371			−0.119456			−0.0597279	−	0.998215i	$-0.519023\pi$
$167$	−1.54371			−0.119456			−0.0597279	+	0.998215i	$0.519023\pi$
$168$		0			0
$169$	−6.65488			−0.511914
$170$	−6.26784	−	3.61874i	−0.480721	−	0.277544i
$171$		0			0
$172$	−28.7030	−	49.7150i	−2.18858	−	3.79074i
$173$	−1.38558	+	2.39990i	−0.105344	+	0.182461i	−0.913879	−	0.405987i	$-0.866928\pi$
$173$	−1.38558	+	2.39990i	−0.105344	+	0.182461i	0.808535	+	0.588448i	$0.200261\pi$
$174$		0			0
$175$	−2.64212	−	0.138498i	−0.199726	−	0.0104695i
$176$		−	64.2666i		−	4.84428i
$177$		0			0
$178$	31.1756	−	17.9992i	2.33671	−	1.34910i
$179$	18.2230	−	10.5210i	1.36205	−	0.786380i	0.372153	−	0.928171i	$-0.378620\pi$
$179$	18.2230	−	10.5210i	1.36205	−	0.786380i	0.989897	+	0.141792i	$0.0452863\pi$
$180$		0			0
$181$			15.7511i			1.17077i	0.810756	+	0.585384i	$0.199056\pi$
$181$			15.7511i			1.17077i	−0.810756	+	0.585384i	$0.800944\pi$
$182$	−14.7229	−	28.8962i	−1.09134	−	2.14193i
$183$		0			0
$184$	−22.0204	+	38.1405i	−1.62337	+	2.81175i
$185$	−4.22328	−	7.31493i	−0.310502	−	0.537805i
$186$		0			0
$187$	−8.79187	−	5.07599i	−0.642925	−	0.371193i
$188$	−4.11785			−0.300325
$189$		0			0
$190$	17.9061			1.29904
$191$	13.4813	+	7.78345i	0.975475	+	0.563191i	0.900901	−	0.434025i	$-0.142907\pi$
$191$	13.4813	+	7.78345i	0.975475	+	0.563191i	0.0745739	+	0.997215i	$0.476240\pi$
$192$		0			0
$193$	1.02819	+	1.78088i	0.0740109	+	0.128191i	0.900656	−	0.434533i	$-0.143087\pi$
$193$	1.02819	+	1.78088i	0.0740109	+	0.128191i	−0.826645	+	0.562724i	$0.809753\pi$
$194$	−12.7208	+	22.0330i	−0.913299	+	1.58188i
$195$		0			0
$196$	23.2248	−	31.9647i	1.65892	−	2.28319i
$197$			4.94878i			0.352586i	0.984338	+	0.176293i	$0.0564107\pi$
$197$			4.94878i			0.352586i	−0.984338	+	0.176293i	$0.943589\pi$
$198$		0			0
$199$	4.59706	−	2.65411i	0.325877	−	0.188145i	−0.328132	−	0.944632i	$-0.606419\pi$
$199$	4.59706	−	2.65411i	0.325877	−	0.188145i	0.654009	+	0.756487i	$0.273086\pi$
$200$	−8.72644	+	5.03821i	−0.617053	+	0.356255i
$201$		0			0
$202$		−	2.84465i		−	0.200149i
$203$	7.36472	+	4.78282i	0.516902	+	0.335688i
$204$		0			0
$205$	−1.22257	+	2.11755i	−0.0853877	+	0.147896i
$206$	1.25102	+	2.16684i	0.0871630	+	0.150971i
$207$		0			0
$208$	−63.6231	−	36.7328i	−4.41147	−	2.54696i
$209$	25.1167			1.73736
$210$		0			0
$211$	−27.6623			−1.90435			−0.952177	−	0.305548i	$-0.901160\pi$
$211$	−27.6623			−1.90435			−0.952177	+	0.305548i	$0.901160\pi$
$212$	−39.0624	−	22.5527i	−2.68282	−	1.54892i
$213$		0			0
$214$	−6.46521	−	11.1981i	−0.441953	−	0.765484i
$215$	−5.08516	+	8.80776i	−0.346805	+	0.600684i
$216$		0			0
$217$	−0.748311	+	14.2755i	−0.0507986	+	0.969082i
$218$		−	29.4224i		−	1.99273i
$219$		0			0
$220$	−18.9579	+	10.9453i	−1.27814	+	0.737935i
$221$	−10.0503	+	5.80255i	−0.676057	+	0.390322i
$222$		0			0
$223$		−	26.9856i		−	1.80709i	−0.428494	−	0.903545i	$-0.640956\pi$
$223$		−	26.9856i		−	1.80709i	0.428494	−	0.903545i	$-0.359044\pi$
$224$	3.55438	−	67.8066i	0.237487	−	4.53052i
$225$		0			0
$226$	−9.97510	+	17.2774i	−0.663534	+	1.14927i
$227$	−4.44783	−	7.70386i	−0.295213	−	0.511323i	0.679822	−	0.733377i	$-0.262057\pi$
$227$	−4.44783	−	7.70386i	−0.295213	−	0.511323i	−0.975034	+	0.222054i	$0.928724\pi$
$228$		0			0
$229$	−9.50457	−	5.48746i	−0.628079	−	0.362622i	0.151928	−	0.988391i	$-0.451452\pi$
$229$	−9.50457	−	5.48746i	−0.628079	−	0.362622i	−0.780008	+	0.625770i	$0.784785\pi$
$230$	12.0843			0.796817
$231$		0			0
$232$	33.4446			2.19574
$233$	24.0974	+	13.9126i	1.57867	+	0.911446i	0.995045	+	0.0994235i	$0.0316998\pi$
$233$	24.0974	+	13.9126i	1.57867	+	0.911446i	0.583626	+	0.812023i	$0.301633\pi$
$234$		0			0
$235$	0.364769	+	0.631799i	0.0237949	+	0.0412140i
$236$	10.5853	−	18.3343i	0.689044	−	1.19346i
$237$		0			0
$238$	−16.0592	−	10.4292i	−1.04096	−	0.676027i
$239$			6.54584i			0.423415i	0.977333	+	0.211708i	$0.0679025\pi$
$239$			6.54584i			0.423415i	−0.977333	+	0.211708i	$0.932098\pi$
$240$		0			0
$241$	−14.2647	+	8.23572i	−0.918869	+	0.530510i	−0.883274	−	0.468857i	$-0.844666\pi$
$241$	−14.2647	+	8.23572i	−0.918869	+	0.530510i	−0.0355952	+	0.999366i	$0.511333\pi$
$242$	−9.67568	+	5.58625i	−0.621976	+	0.359098i
$243$		0			0
$244$			6.73085i			0.430899i
$245$	−6.96164	−	0.731860i	−0.444763	−	0.0467568i
$246$		0			0
$247$	14.3559	−	24.8652i	0.913447	−	1.58214i
$248$	27.2216	+	47.1492i	1.72857	+	2.99398i
$249$		0			0
$250$	2.39444	+	1.38243i	0.151438	+	0.0874326i
$251$	21.7656			1.37383			0.686917	−	0.726736i	$-0.258964\pi$
$251$	21.7656			1.37383			0.686917	+	0.726736i	$0.258964\pi$
$252$		0			0
$253$	16.9506			1.06568
$254$	22.2181	+	12.8276i	1.39409	+	0.804876i
$255$		0			0
$256$	−35.7647	−	61.9463i	−2.23529	−	3.87164i
$257$	12.5540	−	21.7442i	0.783098	−	1.35636i	−0.147032	−	0.989132i	$-0.546972\pi$
$257$	12.5540	−	21.7442i	0.783098	−	1.35636i	0.930129	−	0.367233i	$-0.119695\pi$
$258$		0			0
$259$	−10.1453	−	19.9119i	−0.630400	−	1.23726i
$260$			25.0240i			1.55193i
$261$		0			0
$262$	33.0849	−	19.1016i	2.04399	−	1.18010i
$263$	−10.2439	+	5.91432i	−0.631666	+	0.364692i	−0.781397	−	0.624034i	$-0.785492\pi$
$263$	−10.2439	+	5.91432i	−0.631666	+	0.364692i	0.149731	+	0.988727i	$0.452159\pi$
$264$		0			0
$265$			7.99109i			0.490889i
$266$	47.3100	+	2.47996i	2.90076	+	0.152056i
$267$		0			0
$268$	1.46739	−	2.54159i	0.0896351	−	0.155252i
$269$	−14.3620	−	24.8758i	−0.875669	−	1.51670i	−0.856049	−	0.516895i	$-0.827088\pi$
$269$	−14.3620	−	24.8758i	−0.875669	−	1.51670i	−0.0196196	−	0.999808i	$-0.506246\pi$
$270$		0			0
$271$	19.2064	+	11.0888i	1.16670	+	0.673597i	0.952902	−	0.303279i	$-0.0980815\pi$
$271$	19.2064	+	11.0888i	1.16670	+	0.673597i	0.213803	+	0.976877i	$0.431415\pi$
$272$	−43.3773			−2.63013
$273$		0			0
$274$	18.2563			1.10290
$275$	3.35867	+	1.93913i	0.202535	+	0.116934i
$276$		0			0
$277$	−13.5448	−	23.4603i	−0.813828	−	1.40959i	−0.910166	−	0.414243i	$-0.864046\pi$
$277$	−13.5448	−	23.4603i	−0.813828	−	1.40959i	0.0963377	−	0.995349i	$-0.469287\pi$
$278$	1.03704	−	1.79621i	0.0621978	−	0.107730i
$279$		0			0
$280$	−23.7541	+	12.1030i	−1.41958	+	0.723292i
$281$		−	15.7619i		−	0.940277i	−0.882593	−	0.470139i	$-0.844204\pi$
$281$		−	15.7619i		−	0.940277i	0.882593	−	0.470139i	$-0.155796\pi$
$282$		0			0
$283$	0.494629	−	0.285574i	0.0294027	−	0.0169756i	−0.485227	−	0.874388i	$-0.661263\pi$
$283$	0.494629	−	0.285574i	0.0294027	−	0.0169756i	0.514629	+	0.857413i	$0.327930\pi$
$284$	1.40677	−	0.812200i	0.0834766	−	0.0481952i
$285$		0			0
$286$			47.5385i			2.81101i
$287$	−3.52345	+	5.42550i	−0.207983	+	0.320257i
$288$		0			0
$289$	5.07392	−	8.78829i	0.298466	−	0.516958i
$290$	−4.58841	−	7.94736i	−0.269441	−	0.466685i
$291$		0			0
$292$	35.9120	+	20.7338i	2.10159	+	1.21336i
$293$	12.5716			0.734444			0.367222	−	0.930133i	$-0.380309\pi$
$293$	12.5716			0.734444			0.367222	+	0.930133i	$0.380309\pi$
$294$		0			0
$295$	−3.75068			−0.218373
$296$	−73.7084	−	42.5556i	−4.28421	−	2.47349i
$297$		0			0
$298$	20.4840	+	35.4793i	1.18660	+	2.05526i
$299$	9.68845	−	16.7809i	0.560298	−	0.970464i
$300$		0			0
$301$	−14.6555	+	22.5669i	−0.844728	+	1.30073i
$302$		−	25.6042i		−	1.47336i
$303$		0			0
$304$	92.9407	−	53.6593i	5.33051	−	3.07757i
$305$	1.03271	−	0.596235i	0.0591328	−	0.0341403i
$306$		0			0
$307$		−	7.99249i		−	0.456156i	−0.973643	−	0.228078i	$-0.926756\pi$
$307$		−	7.99249i		−	0.456156i	0.973643	−	0.228078i	$-0.0732441\pi$
$308$	−51.6050	+	26.2933i	−2.94047	+	1.49820i
$309$		0			0
$310$	7.46931	−	12.9372i	0.424228	−	0.734785i
$311$	−11.2944	−	19.5624i	−0.640445	−	1.10928i	−0.985333	−	0.170640i	$-0.945417\pi$
$311$	−11.2944	−	19.5624i	−0.640445	−	1.10928i	0.344888	−	0.938644i	$-0.387917\pi$
$312$		0			0
$313$	28.4808	+	16.4434i	1.60983	+	0.929435i	0.989407	+	0.145166i	$0.0463715\pi$
$313$	28.4808	+	16.4434i	1.60983	+	0.929435i	0.620421	+	0.784269i	$0.286962\pi$
$314$	54.4884			3.07496
$315$		0			0
$316$	−38.8501			−2.18549
$317$	21.2165	+	12.2493i	1.19164	+	0.687992i	0.958678	−	0.284495i	$-0.0918259\pi$
$317$	21.2165	+	12.2493i	1.19164	+	0.687992i	0.232959	+	0.972487i	$0.425159\pi$
$318$		0			0
$319$	−6.43614	−	11.1477i	−0.360355	−	0.624153i
$320$	−18.9073	+	32.7483i	−1.05695	+	1.83069i
$321$		0			0
$322$	31.9283	+	1.67366i	1.77929	+	0.0932695i
$323$		−	16.9527i		−	0.943276i
$324$		0			0
$325$	3.83942	−	2.21669i	0.212973	−	0.122960i
$326$	8.49431	−	4.90419i	0.470456	−	0.271618i
$327$		0			0
$328$			24.6382i			1.36042i
$329$	0.876263	+	1.71981i	0.0483099	+	0.0948163i
$330$		0			0
$331$	−13.7529	+	23.8207i	−0.755927	+	1.30930i	0.188985	+	0.981980i	$0.439480\pi$
$331$	−13.7529	+	23.8207i	−0.755927	+	1.30930i	−0.944912	+	0.327324i	$0.893853\pi$
$332$	−9.45787	−	16.3815i	−0.519068	−	0.899052i
$333$		0			0
$334$	3.69632	+	2.13407i	0.202254	+	0.116771i
$335$	−0.519940			−0.0284073
$336$		0			0
$337$	−2.03162			−0.110669			−0.0553346	−	0.998468i	$-0.517623\pi$
$337$	−2.03162			−0.110669			−0.0553346	+	0.998468i	$0.517623\pi$
$338$	15.9347	+	9.19991i	0.866734	+	0.500409i
$339$		0			0
$340$	7.38764	+	12.7958i	0.400651	+	0.693948i
$341$	10.4772	−	18.1470i	0.567371	−	0.982715i
$342$		0			0
$343$	−18.2921	−	2.89784i	−0.987683	−	0.156469i
$344$			102.481i			5.52538i
$345$		0			0
$346$	6.63539	−	3.83095i	0.356721	−	0.205953i
$347$	−29.9570	+	17.2957i	−1.60818	+	0.928481i	−0.618397	+	0.785866i	$0.712218\pi$
$347$	−29.9570	+	17.2957i	−1.60818	+	0.928481i	−0.989778	+	0.142615i	$0.954449\pi$
$348$		0			0
$349$			10.4404i			0.558864i	0.960165	+	0.279432i	$0.0901462\pi$
$349$			10.4404i			0.558864i	−0.960165	+	0.279432i	$0.909854\pi$
$350$	6.13494	+	3.98418i	0.327927	+	0.212963i
$351$		0			0
$352$	−49.7652	+	86.1958i	−2.65249	+	4.59425i
$353$	−3.79372	−	6.57092i	−0.201919	−	0.349735i	0.747227	−	0.664568i	$-0.231385\pi$
$353$	−3.79372	−	6.57092i	−0.201919	−	0.349735i	−0.949147	+	0.314834i	$0.898051\pi$
$354$		0			0
$355$	−0.249231	−	0.143893i	−0.0132278	−	0.00763707i
$356$	−73.4907			−3.89500
$357$		0			0
$358$	−58.1785			−3.07483
$359$	−17.5862	−	10.1534i	−0.928162	−	0.535875i	−0.0419324	−	0.999120i	$-0.513351\pi$
$359$	−17.5862	−	10.1534i	−0.928162	−	0.535875i	−0.886230	+	0.463246i	$0.846685\pi$
$360$		0			0
$361$	11.4712	+	19.8687i	0.603747	+	1.04572i
$362$	21.7748	−	37.7150i	1.14446	−	1.98226i
$363$		0			0
$364$	−3.46579	+	66.1166i	−0.181657	+	3.46545i
$365$		−	7.34661i		−	0.384539i
$366$		0			0
$367$	5.07896	−	2.93234i	0.265120	−	0.153067i	−0.361548	−	0.932353i	$-0.617752\pi$
$367$	5.07896	−	2.93234i	0.265120	−	0.153067i	0.626668	+	0.779287i	$0.284418\pi$
$368$	62.7233	−	36.2133i	3.26968	−	1.88775i
$369$		0			0
$370$			23.3536i			1.21409i
$371$	−1.10675	+	21.1134i	−0.0574598	+	1.09616i
$372$		0			0
$373$	0.879513	−	1.52336i	0.0455395	−	0.0788767i	−0.842357	−	0.538920i	$-0.818833\pi$
$373$	0.879513	−	1.52336i	0.0455395	−	0.0788767i	0.887897	+	0.460043i	$0.152166\pi$
$374$	14.0344	+	24.3083i	0.725702	+	1.25695i
$375$		0			0
$376$	6.36628	+	3.67557i	0.328316	+	0.189553i
$377$	−14.7148			−0.757850
$378$		0			0
$379$	−7.62473			−0.391656			−0.195828	−	0.980638i	$-0.562739\pi$
$379$	−7.62473			−0.391656			−0.195828	+	0.980638i	$0.562739\pi$
$380$	−31.6577	−	18.2776i	−1.62401	−	0.937620i
$381$		0			0
$382$	−21.5202	−	37.2740i	−1.10107	−	1.90710i
$383$	15.2692	−	26.4470i	0.780219	−	1.35138i	−0.151596	−	0.988443i	$-0.548441\pi$
$383$	15.2692	−	26.4470i	0.780219	−	1.35138i	0.931814	−	0.362936i	$-0.118225\pi$
$384$		0			0
$385$	8.60546	+	5.58859i	0.438575	+	0.284821i
$386$		−	5.68562i		−	0.289390i
$387$		0			0
$388$	44.9804	−	25.9695i	2.28353	−	1.31840i
$389$	−20.8527	+	12.0393i	−1.05727	+	0.610417i	−0.924677	−	0.380753i	$-0.875665\pi$
$389$	−20.8527	+	12.0393i	−1.05727	+	0.610417i	−0.132597	+	0.991170i	$0.542332\pi$
$390$		0			0
$391$		−	11.4410i		−	0.578595i
$392$	−64.4376	+	28.6877i	−3.25459	+	1.44895i
$393$		0			0
$394$	6.84135	−	11.8496i	0.344662	−	0.596973i
$395$	3.44143	+	5.96074i	0.173157	+	0.299917i
$396$		0			0
$397$	9.89957	+	5.71552i	0.496845	+	0.286854i	0.727410	−	0.686203i	$-0.240724\pi$
$397$	9.89957	+	5.71552i	0.496845	+	0.286854i	−0.230565	+	0.973057i	$0.574057\pi$
$398$	−14.6765			−0.735667
$399$		0			0
$400$	16.5710			0.828550
$401$	−6.47597	−	3.73890i	−0.323395	−	0.186712i	0.329510	−	0.944152i	$-0.393116\pi$
$401$	−6.47597	−	3.73890i	−0.323395	−	0.186712i	−0.652905	+	0.757440i	$0.726450\pi$
$402$		0			0
$403$	−11.9768	−	20.7445i	−0.596609	−	1.03336i
$404$	−2.90367	+	5.02931i	−0.144463	+	0.250218i
$405$		0			0
$406$	−11.0225	−	21.6334i	−0.547035	−	1.07365i
$407$			32.7579i			1.62375i
$408$		0			0
$409$	14.1958	−	8.19595i	0.701937	−	0.405264i	−0.106131	−	0.994352i	$-0.533846\pi$
$409$	14.1958	−	8.19595i	0.701937	−	0.405264i	0.808069	+	0.589088i	$0.200513\pi$
$410$	5.85472	−	3.38023i	0.289144	−	0.166938i
$411$		0			0
$412$		−	5.10793i		−	0.251649i
$413$	−9.90977	−	0.519464i	−0.487628	−	0.0255611i
$414$		0			0
$415$	−1.67560	+	2.90223i	−0.0822521	+	0.142465i
$416$	56.8884	+	98.5337i	2.78919	+	4.83101i
$417$		0			0
$418$	−60.1405	−	34.7222i	−2.94157	−	1.69832i
$419$	15.5606			0.760187			0.380093	−	0.924948i	$-0.375892\pi$
$419$	15.5606			0.760187			0.380093	+	0.924948i	$0.375892\pi$
$420$		0			0
$421$	1.63765			0.0798140			0.0399070	−	0.999203i	$-0.487294\pi$
$421$	1.63765			0.0798140			0.0399070	+	0.999203i	$0.487294\pi$
$422$	66.2358	+	38.2413i	3.22431	+	1.86156i
$423$		0			0
$424$	40.2608	+	69.7338i	1.95524	+	3.38657i
$425$	1.30883	−	2.26696i	0.0634876	−	0.109964i
$426$		0			0
$427$	2.81112	−	1.43230i	0.136040	−	0.0693138i
$428$			26.3974i			1.27597i
$429$		0			0
$430$	24.3522	−	14.0598i	1.17437	−	0.678022i
$431$	28.8444	−	16.6533i	1.38939	−	0.802164i	0.396142	−	0.918189i	$-0.370349\pi$
$431$	28.8444	−	16.6533i	1.38939	−	0.802164i	0.993246	+	0.116026i	$0.0370155\pi$
$432$		0			0
$433$		−	14.2139i		−	0.683075i	−0.939868	−	0.341538i	$-0.889052\pi$
$433$		−	14.2139i		−	0.683075i	0.939868	−	0.341538i	$-0.110948\pi$
$434$	21.5266	−	33.1473i	1.03331	−	1.59112i
$435$		0			0
$436$	−30.0329	+	52.0184i	−1.43831	+	2.49123i
$437$	14.1529	+	24.5136i	0.677025	+	1.17264i
$438$		0			0
$439$	17.9098	+	10.3402i	0.854788	+	0.493512i	0.862264	−	0.506460i	$-0.169046\pi$
$439$	17.9098	+	10.3402i	0.854788	+	0.493512i	−0.00747528	+	0.999972i	$0.502379\pi$
$440$	39.0790			1.86302
$441$		0			0
$442$	32.0865			1.52620
$443$	−0.397227	−	0.229339i	−0.0188728	−	0.0108962i	0.490534	−	0.871422i	$-0.336802\pi$
$443$	−0.397227	−	0.229339i	−0.0188728	−	0.0108962i	−0.509407	+	0.860526i	$0.670135\pi$
$444$		0			0
$445$	6.50999	+	11.2756i	0.308603	+	0.534516i
$446$	−37.3057	+	64.6154i	−1.76648	+	3.05963i
$447$		0			0
$448$	−54.4909	+	83.9065i	−2.57445	+	3.96421i
$449$		−	29.1152i		−	1.37403i	−0.726642	−	0.687016i	$-0.758920\pi$
$449$		−	29.1152i		−	1.37403i	0.726642	−	0.687016i	$-0.241080\pi$
$450$		0			0
$451$	8.21240	−	4.74143i	0.386707	−	0.223265i
$452$	35.2717	−	20.3641i	1.65904	−	0.957849i
$453$		0			0
$454$			24.5952i			1.15431i
$455$	10.4512	−	5.32502i	0.489961	−	0.249641i
$456$		0			0
$457$	−2.57429	+	4.45880i	−0.120420	+	0.208574i	−0.919933	−	0.392074i	$-0.871758\pi$
$457$	−2.57429	+	4.45880i	−0.120420	+	0.208574i	0.799513	+	0.600649i	$0.205091\pi$
$458$	15.1721	+	26.2788i	0.708945	+	1.22793i
$459$		0			0
$460$	−21.3650	−	12.3351i	−0.996147	−	0.575126i
$461$	41.3985			1.92812			0.964060	−	0.265683i	$-0.0855975\pi$
$461$	41.3985			1.92812			0.964060	+	0.265683i	$0.0855975\pi$
$462$		0			0
$463$	−8.83715			−0.410697			−0.205349	−	0.978689i	$-0.565833\pi$
$463$	−8.83715			−0.410697			−0.205349	+	0.978689i	$0.565833\pi$
$464$	−47.6319	−	27.5003i	−2.21126	−	1.27667i
$465$		0			0
$466$	−38.4665	−	66.6259i	−1.78192	−	3.08638i
$467$	13.6591	−	23.6583i	0.632069	−	1.09478i	−0.355059	−	0.934844i	$-0.615539\pi$
$467$	13.6591	−	23.6583i	0.632069	−	1.09478i	0.987128	−	0.159932i	$-0.0511275\pi$
$468$		0			0
$469$	−1.37374	−	0.0720108i	−0.0634336	−	0.00332515i
$470$		−	2.01707i		−	0.0930407i
$471$		0			0
$472$	−32.7301	+	18.8967i	−1.50653	+	0.869793i
$473$	34.1588	−	19.7216i	1.57062	−	0.906799i
$474$		0			0
$475$			6.47629i			0.297153i
$476$	17.7469	+	34.8312i	0.813427	+	1.59649i
$477$		0			0
$478$	9.04917	−	15.6736i	0.413900	−	0.716895i
$479$	8.76723	+	15.1853i	0.400585	+	0.693834i	0.993797	−	0.111213i	$-0.0354735\pi$
$479$	8.76723	+	15.1853i	0.400585	+	0.693834i	−0.593211	+	0.805047i	$0.702140\pi$
$480$		0			0
$481$	32.4299	+	18.7234i	1.47868	+	0.853714i
$482$	45.5413			2.07435
$483$		0			0
$484$	22.8087			1.03676
$485$	−7.96895	−	4.60088i	−0.361851	−	0.208915i
$486$		0			0
$487$	−8.21612	−	14.2307i	−0.372308	−	0.644856i	0.617612	−	0.786483i	$-0.288100\pi$
$487$	−8.21612	−	14.2307i	−0.372308	−	0.644856i	−0.989920	+	0.141627i	$0.954767\pi$
$488$	6.00792	−	10.4060i	0.271966	−	0.471058i
$489$		0			0
$490$	15.6575	+	11.3764i	0.707333	+	0.513932i
$491$			1.83435i			0.0827829i	0.999143	+	0.0413914i	$0.0131791\pi$
$491$			1.83435i			0.0827829i	−0.999143	+	0.0413914i	$0.986821\pi$
$492$		0			0
$493$	−7.52425	+	4.34413i	−0.338875	+	0.195650i
$494$	−68.7489	+	39.6922i	−3.09316	+	1.78584i
$495$		0			0
$496$		−	89.5336i		−	4.02018i
$497$	−0.638569	−	0.414702i	−0.0286437	−	0.0186019i
$498$		0			0
$499$	−0.836542	+	1.44893i	−0.0374487	+	0.0648631i	−0.884142	−	0.467218i	$-0.845256\pi$
$499$	−0.836542	+	1.44893i	−0.0374487	+	0.0648631i	0.846694	+	0.532081i	$0.178590\pi$
$500$	−2.82223	−	4.88825i	−0.126214	−	0.218609i
$501$		0			0
$502$	−52.1165	−	30.0895i	−2.32607	−	1.34296i
$503$	−26.6476			−1.18816			−0.594080	−	0.804406i	$-0.702484\pi$
$503$	−26.6476			−1.18816			−0.594080	+	0.804406i	$0.702484\pi$
$504$		0			0
$505$	1.02886			0.0457836
$506$	−40.5873	−	23.4331i	−1.80433	−	1.04173i
$507$		0			0
$508$	−26.1876	−	45.3582i	−1.16188	−	2.01244i
$509$	12.9087	−	22.3586i	0.572170	−	0.991027i	−0.424173	−	0.905581i	$-0.639435\pi$
$509$	12.9087	−	22.3586i	0.572170	−	0.991027i	0.996343	−	0.0854460i	$-0.0272315\pi$
$510$		0			0
$511$	1.01749	−	19.4107i	0.0450113	−	0.858677i
$512$			91.3199i			4.03581i
$513$		0			0
$514$	−60.1196	+	34.7101i	−2.65176	+	1.53100i
$515$	−0.783706	+	0.452473i	−0.0345342	+	0.0199383i
$516$		0			0
$517$		−	2.82934i		−	0.124434i
$518$	−3.23443	+	61.7030i	−0.142113	+	2.71107i
$519$		0			0
$520$	22.3363	−	38.6876i	0.979513	−	1.69657i
$521$	6.84377	+	11.8538i	0.299831	+	0.519323i	0.976097	−	0.217335i	$-0.0697363\pi$
$521$	6.84377	+	11.8538i	0.299831	+	0.519323i	−0.676266	+	0.736658i	$0.736403\pi$
$522$		0			0
$523$	−6.49951	−	3.75249i	−0.284204	−	0.164085i	0.351121	−	0.936330i	$-0.385800\pi$
$523$	−6.49951	−	3.75249i	−0.284204	−	0.164085i	−0.635325	+	0.772245i	$0.719134\pi$
$524$	−77.9917			−3.40708
$525$		0			0
$526$	32.7045			1.42599
$527$	−12.2485	−	7.07165i	−0.533551	−	0.308046i
$528$		0			0
$529$	−1.94857	−	3.37502i	−0.0847204	−	0.146740i
$530$	11.0471	−	19.1342i	0.479857	−	0.831136i
$531$		0			0
$532$	−81.1122	−	52.6762i	−3.51666	−	2.28380i
$533$		−	10.8402i		−	0.469542i
$534$		0			0
$535$	4.05014	−	2.33835i	0.175103	−	0.101096i
$536$	−4.53722	+	2.61957i	−0.195978	+	0.113148i
$537$		0			0
$538$			79.4181i			3.42396i
$539$	21.9627	+	15.9576i	0.945999	+	0.687342i
$540$		0			0
$541$	−6.03869	+	10.4593i	−0.259623	+	0.449681i	−0.966141	−	0.258015i	$-0.916932\pi$
$541$	−6.03869	+	10.4593i	−0.259623	+	0.449681i	0.706518	+	0.707695i	$0.250265\pi$
$542$	−30.6590	−	53.1030i	−1.31692	−	2.28097i
$543$		0			0
$544$	58.1786	+	33.5894i	2.49439	+	1.44013i
$545$	10.6415			0.455833
$546$		0			0
$547$	−30.6935			−1.31236			−0.656180	−	0.754604i	$-0.727829\pi$
$547$	−30.6935			−1.31236			−0.656180	+	0.754604i	$0.727829\pi$
$548$	−32.2769	−	18.6351i	−1.37880	−	0.796051i
$549$		0			0
$550$	−5.36142	−	9.28626i	−0.228612	−	0.395967i
$551$	10.7477	−	18.6156i	0.457867	−	0.793049i
$552$		0			0
$553$	8.26714	+	16.2256i	0.351555	+	0.689985i
$554$			74.8990i			3.18215i
$555$		0			0
$556$	−3.66697	+	2.11712i	−0.155514	+	0.0897860i
$557$	−30.5512	+	17.6388i	−1.29450	+	0.747378i	−0.979448	−	0.201698i	$-0.935354\pi$
$557$	−30.5512	+	17.6388i	−1.29450	+	0.747378i	−0.315049	+	0.949076i	$0.602021\pi$
$558$		0			0
$559$		−	45.0889i		−	1.90706i
$560$	43.7826	+	2.29506i	1.85015	+	0.0969839i
$561$		0			0
$562$	−21.7898	+	37.7410i	−0.919146	+	1.59201i
$563$	−17.9772	−	31.1375i	−0.757650	−	1.31229i	−0.944046	−	0.329814i	$-0.893014\pi$
$563$	−17.9772	−	31.1375i	−0.757650	−	1.31229i	0.186396	−	0.982475i	$-0.440319\pi$
$564$		0			0
$565$	−6.24891	−	3.60781i	−0.262894	−	0.151782i
$566$	−1.57915			−0.0663765
$567$		0			0
$568$	−2.89986			−0.121675
$569$	−9.57327	−	5.52713i	−0.401332	−	0.231709i	0.285726	−	0.958311i	$-0.407765\pi$
$569$	−9.57327	−	5.52713i	−0.401332	−	0.231709i	−0.687059	+	0.726602i	$0.741098\pi$
$570$		0			0
$571$	4.14927	+	7.18674i	0.173641	+	0.300756i	0.939690	−	0.342027i	$-0.111113\pi$
$571$	4.14927	+	7.18674i	0.173641	+	0.300756i	−0.766049	+	0.642782i	$0.777780\pi$
$572$	48.5249	−	84.0475i	2.02893	−	3.51420i
$573$		0			0
$574$	15.9371	−	8.12011i	0.665200	−	0.338927i
$575$			4.37068i			0.182270i
$576$		0			0
$577$	23.8142	−	13.7491i	0.991397	−	0.572383i	0.0857053	−	0.996321i	$-0.472686\pi$
$577$	23.8142	−	13.7491i	0.991397	−	0.572383i	0.905692	+	0.423937i	$0.139352\pi$
$578$	−24.2984	+	14.0287i	−1.01068	+	0.583517i
$579$		0			0
$580$			18.7345i			0.777906i
$581$	−4.82910	+	7.43598i	−0.200345	+	0.308496i
$582$		0			0
$583$	15.4958	−	26.8394i	0.641769	−	1.11158i
$584$	−37.0138	−	64.1098i	−1.53164	−	2.65288i
$585$		0			0
$586$	−30.1021	−	17.3794i	−1.24350	−	0.717938i
$587$	30.6414			1.26471			0.632353	−	0.774680i	$-0.282089\pi$
$587$	30.6414			1.26471			0.632353	+	0.774680i	$0.282089\pi$
$588$		0			0
$589$	34.9916			1.44180
$590$	8.98079	+	5.18506i	0.369733	+	0.213466i
$591$		0			0
$592$	69.9840	+	121.216i	2.87632	+	4.98194i
$593$	−5.43874	+	9.42018i	−0.223342	+	0.386840i	−0.955821	−	0.293950i	$-0.905030\pi$
$593$	−5.43874	+	9.42018i	−0.223342	+	0.386840i	0.732478	+	0.680790i	$0.238363\pi$
$594$		0			0
$595$	3.77206	−	5.80832i	0.154640	−	0.238118i
$596$		−	83.6359i		−	3.42586i
$597$		0			0
$598$	−46.3968	+	26.7872i	−1.89731	+	1.09541i
$599$	−8.38404	+	4.84053i	−0.342563	+	0.197779i	−0.661405	−	0.750029i	$-0.730039\pi$
$599$	−8.38404	+	4.84053i	−0.342563	+	0.197779i	0.318842	+	0.947808i	$0.396706\pi$
$600$		0			0
$601$			11.7215i			0.478129i	0.971004	+	0.239064i	$0.0768407\pi$
$601$			11.7215i			0.478129i	−0.971004	+	0.239064i	$0.923159\pi$
$602$	66.2889	−	33.7749i	2.70173	−	1.37656i
$603$		0			0
$604$	−26.1355	+	45.2679i	−1.06344	+	1.84193i
$605$	−2.02045	−	3.49952i	−0.0821428	−	0.142276i
$606$		0			0
$607$	−34.6536	−	20.0073i	−1.40655	−	0.812070i	−0.411493	−	0.911413i	$-0.634992\pi$
$607$	−34.6536	−	20.0073i	−1.40655	−	0.812070i	−0.995053	+	0.0993435i	$0.968326\pi$
$608$	−166.205			−6.74052
$609$		0			0
$610$	−3.29702			−0.133492
$611$	−2.80101	−	1.61716i	−0.113317	−	0.0654234i
$612$		0			0
$613$	11.9556	+	20.7077i	0.482881	+	0.836375i	0.999807	−	0.0196555i	$-0.00625693\pi$
$613$	11.9556	+	20.7077i	0.482881	+	0.836375i	−0.516926	+	0.856030i	$0.672924\pi$
$614$	−11.0491	+	19.1375i	−0.445904	+	0.772329i
$615$		0			0
$616$	103.252	+	5.41238i	4.16012	+	0.218071i
$617$			12.3688i			0.497948i	0.968510	+	0.248974i	$0.0800933\pi$
$617$			12.3688i			0.497948i	−0.968510	+	0.248974i	$0.919907\pi$
$618$		0			0
$619$	−2.96489	+	1.71178i	−0.119169	+	0.0688023i	−0.558400	−	0.829572i	$-0.688584\pi$
$619$	−2.96489	+	1.71178i	−0.119169	+	0.0688023i	0.439231	+	0.898374i	$0.355251\pi$
$620$	−26.4113	+	15.2486i	−1.06070	+	0.612398i
$621$		0			0
$622$			62.4548i			2.50421i
$623$	15.6385	+	30.6932i	0.626545	+	1.22970i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−45.4637	−	78.7454i	−1.81709	−	3.14730i
$627$		0			0
$628$	−96.3350	−	55.6190i	−3.84418	−	2.21944i
$629$	22.1102			0.881593
$630$		0			0
$631$	37.1172			1.47761			0.738807	−	0.673917i	$-0.235390\pi$
$631$	37.1172			1.47761			0.738807	+	0.673917i	$0.235390\pi$
$632$	60.0629	+	34.6774i	2.38918	+	1.37939i
$633$		0			0
$634$	−33.8677	−	58.6606i	−1.34506	−	2.32971i
$635$	−4.63952	+	8.03588i	−0.184114	+	0.318894i
$636$		0			0
$637$	28.3510	−	12.6219i	1.12331	−	0.500097i
$638$			35.5901i			1.40903i
$639$		0			0
$640$	46.0938	−	26.6123i	1.82202	−	1.05194i
$641$	−6.40169	+	3.69602i	−0.252852	+	0.145984i	−0.621069	−	0.783756i	$-0.713301\pi$
$641$	−6.40169	+	3.69602i	−0.252852	+	0.145984i	0.368218	+	0.929740i	$0.379968\pi$
$642$		0			0
$643$			6.20095i			0.244541i	0.992497	+	0.122271i	$0.0390176\pi$
$643$			6.20095i			0.244541i	−0.992497	+	0.122271i	$0.960982\pi$
$644$	−54.7405	−	35.5498i	−2.15708	−	1.40086i
$645$		0			0
$646$	−23.4360	+	40.5923i	−0.922077	+	1.59708i
$647$	−0.337421	−	0.584430i	−0.0132654	−	0.0229763i	0.859317	−	0.511444i	$-0.170889\pi$
$647$	−0.337421	−	0.584430i	−0.0132654	−	0.0229763i	−0.872582	+	0.488468i	$0.837556\pi$
$648$		0			0
$649$	12.5973	+	7.27306i	0.494488	+	0.285493i
$650$	−12.2577			−0.480786
$651$		0			0
$652$	−20.0238			−0.784193
$653$	10.1096	+	5.83677i	0.395619	+	0.228411i	0.684592	−	0.728927i	$-0.259980\pi$
$653$	10.1096	+	5.83677i	0.395619	+	0.228411i	−0.288973	+	0.957337i	$0.593314\pi$
$654$		0			0
$655$	6.90870	+	11.9662i	0.269945	+	0.467559i
$656$	20.2592	−	35.0899i	0.790987	−	1.37003i
$657$		0			0
$658$	0.279362	−	5.32936i	0.0108906	−	0.207760i
$659$		−	2.91787i		−	0.113664i	−0.998384	−	0.0568320i	$-0.981900\pi$
$659$		−	2.91787i		−	0.113664i	0.998384	−	0.0568320i	$-0.0181000\pi$
$660$		0			0
$661$	12.2823	−	7.09117i	0.477725	−	0.275814i	−0.241743	−	0.970340i	$-0.577719\pi$
$661$	12.2823	−	7.09117i	0.477725	−	0.275814i	0.719468	+	0.694526i	$0.244386\pi$
$662$	65.8609	−	38.0248i	2.55976	−	1.47788i
$663$		0			0
$664$			33.7682i			1.31046i
$665$	−0.896956	+	17.1112i	−0.0347825	+	0.663543i
$666$		0			0
$667$	7.25334	−	12.5632i	0.280851	−	0.486447i
$668$	−4.35670	−	7.54603i	−0.168566	−	0.291965i
$669$		0			0
$670$	1.24496	+	0.718781i	0.0480972	+	0.0277689i
$671$	−4.62471			−0.178535
$672$		0			0
$673$	12.8921			0.496954			0.248477	−	0.968638i	$-0.420070\pi$
$673$	12.8921			0.496954			0.248477	+	0.968638i	$0.420070\pi$
$674$	4.86459	+	2.80857i	0.187377	+	0.108182i
$675$		0			0
$676$	−18.7816	−	32.5307i	−0.722369	−	1.25118i
$677$	−16.5010	+	28.5805i	−0.634183	+	1.09844i	0.352504	+	0.935810i	$0.385330\pi$
$677$	−16.5010	+	28.5805i	−0.634183	+	1.09844i	−0.986688	+	0.162627i	$0.948003\pi$
$678$		0			0
$679$	−20.4177	−	13.2598i	−0.783561	−	0.508863i
$680$		−	26.3767i		−	1.01150i
$681$		0			0
$682$	−50.1739	+	28.9679i	−1.92126	+	1.10924i
$683$	−38.7730	+	22.3856i	−1.48361	+	0.856561i	−0.999826	−	0.0186285i	$-0.994070\pi$
$683$	−38.7730	+	22.3856i	−1.48361	+	0.856561i	−0.483780	+	0.875189i	$0.660737\pi$
$684$		0			0
$685$			6.60296i			0.252286i
$686$	39.7934	+	32.2263i	1.51932	+	1.23041i
$687$		0			0
$688$	84.2663	−	145.953i	3.21262	−	5.56442i
$689$	−17.7138	−	30.6812i	−0.674841	−	1.16886i
$690$		0			0
$691$	10.2208	+	5.90100i	0.388819	+	0.224484i	0.681648	−	0.731680i	$-0.261264\pi$
$691$	10.2208	+	5.90100i	0.388819	+	0.224484i	−0.292830	+	0.956165i	$0.594597\pi$
$692$	−15.6417			−0.594610
$693$		0			0
$694$	95.6403			3.63046
$695$	0.649658	+	0.375080i	0.0246429	+	0.0142276i
$696$		0			0
$697$	−3.20027	−	5.54302i	−0.121219	−	0.209957i
$698$	14.4332	−	24.9990i	0.546304	−	0.946227i
$699$		0			0
$700$	−6.77967	−	13.3062i	−0.256247	−	0.502928i
$701$			0.838960i			0.0316871i	0.999874	+	0.0158435i	$0.00504337\pi$
$701$			0.838960i			0.0316871i	−0.999874	+	0.0158435i	$0.994957\pi$
$702$		0			0
$703$	−47.3737	+	27.3512i	−1.78673	+	1.03157i
$704$	127.006	−	73.3272i	4.78674	−	2.76362i
$705$		0			0
$706$			20.9782i			0.789526i
$707$	2.71837	+	0.142495i	0.102235	+	0.00535908i
$708$		0			0
$709$	−13.3559	+	23.1330i	−0.501590	+	0.868779i	0.498409	+	0.866942i	$0.333918\pi$
$709$	−13.3559	+	23.1330i	−0.501590	+	0.868779i	−0.999998	+	0.00183657i	$0.999415\pi$
$710$	0.397845	+	0.689088i	0.0149309	+	0.0258610i
$711$		0			0
$712$	113.618	+	65.5974i	4.25802	+	2.45837i
$713$	23.6149			0.884386
$714$		0			0
$715$	−17.1938			−0.643012
$716$	102.859	+	59.3856i	3.84402	+	2.21934i
$717$		0			0
$718$	28.0727	+	48.6233i	1.04766	+	1.81461i
$719$	−2.35129	+	4.07256i	−0.0876885	+	0.151881i	−0.906534	−	0.422134i	$-0.861281\pi$
$719$	−2.35129	+	4.07256i	−0.0876885	+	0.151881i	0.818845	+	0.574014i	$0.194615\pi$
$720$		0			0
$721$	−2.13331	+	1.08695i	−0.0794488	+	0.0404800i
$722$		−	63.4325i		−	2.36071i
$723$		0			0
$724$	−76.9951	+	44.4531i	−2.86150	+	1.65209i
$725$	2.87442	−	1.65954i	0.106753	−	0.0616339i
$726$		0			0
$727$		−	14.4547i		−	0.536096i	−0.963405	−	0.268048i	$-0.913621\pi$
$727$		−	14.4547i		−	0.536096i	0.963405	−	0.268048i	$-0.0863787\pi$
$728$	64.3735	−	99.1240i	2.38584	−	3.67378i
$729$		0			0
$730$	−10.1562	+	17.5910i	−0.375897	+	0.651073i
$731$	−13.3112	−	23.0557i	−0.492334	−	0.852748i
$732$		0			0
$733$	−16.4306	−	9.48622i	−0.606878	−	0.350381i	0.164864	−	0.986316i	$-0.447281\pi$
$733$	−16.4306	−	9.48622i	−0.606878	−	0.350381i	−0.771743	+	0.635935i	$0.780615\pi$
$734$	−16.2150			−0.598507
$735$		0			0
$736$	−112.168			−4.13456
$737$	1.74631	+	1.00823i	0.0643260	+	0.0371386i
$738$		0			0
$739$	14.4660	+	25.0559i	0.532142	+	0.921697i	0.999296	+	0.0375208i	$0.0119460\pi$
$739$	14.4660	+	25.0559i	0.532142	+	0.921697i	−0.467154	+	0.884176i	$0.654721\pi$
$740$	23.8381	−	41.2888i	0.876307	−	1.51781i
$741$		0			0
$742$	31.8379	−	49.0249i	1.16881	−	1.79976i
$743$		−	27.4925i		−	1.00860i	−0.863528	−	0.504301i	$-0.831750\pi$
$743$		−	27.4925i		−	1.00860i	0.863528	−	0.504301i	$-0.168250\pi$
$744$		0			0
$745$	−12.8322	+	7.40868i	−0.470136	+	0.271433i
$746$	−4.21188	+	2.43173i	−0.154208	+	0.0890320i
$747$		0			0
$748$		−	57.3024i		−	2.09518i
$749$	11.0248	−	5.61727i	0.402838	−	0.205250i
$750$		0			0
$751$	1.79320	−	3.10591i	0.0654347	−	0.113336i	−0.831452	−	0.555597i	$-0.812490\pi$
$751$	1.79320	−	3.10591i	0.0654347	−	0.113336i	0.896887	+	0.442260i	$0.145823\pi$
$752$	−6.04460	−	10.4695i	−0.220424	−	0.381785i
$753$		0			0
$754$	35.2337	+	20.3422i	1.28314	+	0.740818i
$755$	9.26057			0.337027
$756$		0			0
$757$	−50.0909			−1.82058			−0.910292	−	0.413967i	$-0.864143\pi$
$757$	−50.0909			−1.82058			−0.910292	+	0.413967i	$0.864143\pi$
$758$	18.2569	+	10.5407i	0.663122	+	0.382854i
$759$		0			0
$760$	32.6289	+	56.5150i	1.18358	+	2.05001i
$761$	−10.3151	+	17.8662i	−0.373921	+	0.647651i	−0.990165	−	0.139905i	$-0.955320\pi$
$761$	−10.3151	+	17.8662i	−0.373921	+	0.647651i	0.616244	+	0.787556i	$0.288654\pi$
$762$		0			0
$763$	28.1163	+	1.47384i	1.01788	+	0.0533564i
$764$			87.8667i			3.17891i
$765$		0			0
$766$	−73.1223	+	42.2172i	−2.64202	+	1.52537i
$767$	14.4005	−	8.31411i	0.519970	−	0.300205i
$768$		0			0
$769$		−	35.0869i		−	1.26527i	−0.774452	−	0.632633i	$-0.781974\pi$
$769$		−	35.0869i		−	1.26527i	0.774452	−	0.632633i	$-0.218026\pi$
$770$	−12.8794	−	25.2780i	−0.464142	−	0.910956i
$771$		0			0
$772$	−5.80359	+	10.0521i	−0.208876	+	0.361783i
$773$	0.918940	+	1.59165i	0.0330520	+	0.0572477i	0.882078	−	0.471103i	$-0.156144\pi$
$773$	0.918940	+	1.59165i	0.0330520	+	0.0572477i	−0.849026	+	0.528351i	$0.822811\pi$
$774$		0			0
$775$	4.67916	+	2.70151i	0.168080	+	0.0970412i
$776$	−92.7208			−3.32848
$777$		0			0
$778$	66.5740			2.38679
$779$	13.7139	+	7.91770i	0.491350	+	0.283681i
$780$		0			0
$781$	0.558056	+	0.966581i	0.0199688	+	0.0345870i
$782$	−15.8163	+	27.3947i	−0.565592	+	0.979633i
$783$		0			0
$784$	115.361	+	12.1277i	4.12005	+	0.433130i
$785$			19.7075i			0.703390i
$786$		0			0
$787$	39.6464	−	22.8898i	1.41324	−	0.815935i	0.417548	−	0.908655i	$-0.362890\pi$
$787$	39.6464	−	22.8898i	1.41324	−	0.815935i	0.995692	+	0.0927203i	$0.0295562\pi$
$788$	−24.1909	+	13.9666i	−0.861764	+	0.497540i
$789$		0			0
$790$		−	19.0302i		−	0.677063i
$791$	−16.0107	−	10.3978i	−0.569276	−	0.369701i
$792$		0			0
$793$	−2.64334	+	4.57840i	−0.0938677	+	0.162584i
$794$	−15.8026	−	27.3709i	−0.560814	−	0.971358i
$795$		0			0
$796$	25.9479	+	14.9810i	0.919700	+	0.530989i
$797$	−37.7770			−1.33813			−0.669065	−	0.743203i	$-0.733305\pi$
$797$	−37.7770			−1.33813			−0.669065	+	0.743203i	$0.733305\pi$
$798$		0			0
$799$	−1.90969			−0.0675599
$800$	−22.2254	−	12.8318i	−0.785786	−	0.453674i
$801$		0			0
$802$	10.3376	+	17.9052i	0.365032	+	0.632253i
$803$	−14.2460	+	24.6748i	−0.502731	+	0.870756i
$804$		0			0
$805$	−0.605333	+	11.5479i	−0.0213352	+	0.407009i
$806$			66.2286i			2.33280i
$807$		0			0
$808$	8.97827	−	5.18360i	0.315854	−	0.182359i
$809$	−20.7517	+	11.9810i	−0.729591	+	0.421230i	−0.818273	−	0.574830i	$-0.805068\pi$
$809$	−20.7517	+	11.9810i	−0.729591	+	0.421230i	0.0886813	+	0.996060i	$0.471735\pi$
$810$		0			0
$811$			11.4298i			0.401353i	0.979658	+	0.200677i	$0.0643141\pi$
$811$			11.4298i			0.401353i	−0.979658	+	0.200677i	$0.935686\pi$
$812$	−2.59469	+	49.4988i	−0.0910559	+	1.73707i
$813$		0			0
$814$	45.2856	−	78.4369i	1.58726	−	2.74921i
$815$	1.77376	+	3.07224i	0.0621320	+	0.107616i
$816$		0			0
$817$	57.0416	+	32.9330i	1.99563	+	1.15218i
$818$	−45.3213			−1.58462
$819$		0			0
$820$	−13.8015			−0.481968
$821$	−4.11195	−	2.37404i	−0.143508	−	0.0828545i	0.426527	−	0.904475i	$-0.359737\pi$
$821$	−4.11195	−	2.37404i	−0.143508	−	0.0828545i	−0.570035	+	0.821620i	$0.693070\pi$
$822$		0			0
$823$	13.6817	+	23.6974i	0.476914	+	0.826039i	0.999650	−	0.0264556i	$-0.00842207\pi$
$823$	13.6817	+	23.6974i	0.476914	+	0.826039i	−0.522736	+	0.852494i	$0.675089\pi$
$824$	−4.55931	+	7.89695i	−0.158831	+	0.275103i
$825$		0			0
$826$	23.0102	+	14.9434i	0.800628	+	0.519947i
$827$		−	21.8468i		−	0.759686i	−0.925051	−	0.379843i	$-0.875978\pi$
$827$		−	21.8468i		−	0.759686i	0.925051	−	0.379843i	$-0.124022\pi$
$828$		0			0
$829$	12.4824	−	7.20669i	0.433530	−	0.250299i	−0.267319	−	0.963608i	$-0.586138\pi$
$829$	12.4824	−	7.20669i	0.433530	−	0.250299i	0.700849	+	0.713309i	$0.252804\pi$
$830$	8.02426	−	4.63281i	0.278526	−	0.160807i
$831$		0			0
$832$		−	167.646i		−	5.81209i
$833$	10.7707	−	14.8239i	0.373183	−	0.513617i
$834$		0			0
$835$	−0.771855	+	1.33689i	−0.0267111	+	0.0462650i
$836$	70.8852	+	122.777i	2.45162	+	4.24632i
$837$		0			0
$838$	−37.2590	−	21.5115i	−1.28709	−	0.743103i
$839$	−39.4098			−1.36058			−0.680288	−	0.732945i	$-0.738145\pi$
$839$	−39.4098			−1.36058			−0.680288	+	0.732945i	$0.738145\pi$
$840$		0			0
$841$	17.9836			0.620126
$842$	−3.92125	−	2.26393i	−0.135135	−	0.0780203i
$843$		0			0
$844$	−78.0695	−	135.220i	−2.68726	−	4.65447i
$845$	−3.32744	+	5.76329i	−0.114467	+	0.198263i
$846$		0			0
$847$	−4.85359	−	9.52598i	−0.166771	−	0.327317i
$848$		−	132.420i		−	4.54733i
$849$		0			0
$850$	−6.26784	+	3.61874i	−0.214985	+	0.124122i
$851$	−31.9713	+	18.4586i	−1.09596	+	0.632753i
$852$		0			0
$853$		−	15.6546i		−	0.536002i	−0.963419	−	0.268001i	$-0.913637\pi$
$853$		−	15.6546i		−	0.536002i	0.963419	−	0.268001i	$-0.0863631\pi$
$854$	−8.71112	−	0.456631i	−0.298088	−	0.0156256i
$855$		0			0
$856$	23.5622	−	40.8109i	0.805339	−	1.39489i
$857$	−20.2216	−	35.0249i	−0.690758	−	1.19643i	−0.971590	−	0.236671i	$-0.923944\pi$
$857$	−20.2216	−	35.0249i	−0.690758	−	1.19643i	0.280832	−	0.959757i	$-0.409390\pi$
$858$		0			0
$859$	1.59156	+	0.918890i	0.0543034	+	0.0313521i	0.526906	−	0.849924i	$-0.323352\pi$
$859$	1.59156	+	0.918890i	0.0543034	+	0.0313521i	−0.472602	+	0.881276i	$0.656685\pi$
$860$	−57.4060			−1.95753
$861$		0			0
$862$	−92.0884			−3.13654
$863$	−0.253400	−	0.146300i	−0.00862582	−	0.00498012i	0.495681	−	0.868505i	$-0.334919\pi$
$863$	−0.253400	−	0.146300i	−0.00862582	−	0.00498012i	−0.504307	+	0.863525i	$0.668252\pi$
$864$		0			0
$865$	1.38558	+	2.39990i	0.0471113	+	0.0815991i
$866$	−19.6497	+	34.0343i	−0.667724	+	1.15653i
$867$		0			0
$868$	−71.8939	+	36.6307i	−2.44024	+	1.24333i
$869$		−	26.6935i		−	0.905517i
$870$		0			0
$871$	1.99627	−	1.15255i	0.0676409	−	0.0390525i
$872$	92.8627	−	53.6143i	3.14473	−	1.81561i
$873$		0			0
$874$		−	78.2617i		−	2.64724i
$875$	−1.44101	+	2.21890i	−0.0487149	+	0.0750124i
$876$		0			0
$877$	21.3058	−	36.9027i	0.719445	−	1.24611i	−0.241775	−	0.970332i	$-0.577730\pi$
$877$	21.3058	−	36.9027i	0.719445	−	1.24611i	0.961220	−	0.275783i	$-0.0889370\pi$
$878$	−28.5893	−	49.5181i	−0.964842	−	1.67116i
$879$		0			0
$880$	−55.6565	−	32.1333i	−1.87618	−	1.08321i
$881$	−43.1155			−1.45260			−0.726300	−	0.687378i	$-0.758762\pi$
$881$	−43.1155			−1.45260			−0.726300	+	0.687378i	$0.758762\pi$
$882$		0			0
$883$	0.656101			0.0220796			0.0110398	−	0.999939i	$-0.496486\pi$
$883$	0.656101			0.0220796			0.0110398	+	0.999939i	$0.496486\pi$
$884$	−56.7286	−	32.7523i	−1.90799	−	1.10158i
$885$		0			0
$886$	0.634091	+	1.09828i	0.0213027	+	0.0368973i
$887$	−22.6766	+	39.2771i	−0.761407	+	1.31880i	0.180719	+	0.983535i	$0.442158\pi$
$887$	−22.6766	+	39.2771i	−0.761407	+	1.31880i	−0.942126	+	0.335260i	$0.891176\pi$
$888$		0			0
$889$	−13.3711	+	20.5892i	−0.448453	+	0.690540i
$890$		−	35.9984i		−	1.20667i
$891$		0			0
$892$	131.912	−	76.1596i	4.41675	−	2.55001i
$893$	4.09172	−	2.36235i	0.136924	−	0.0790532i
$894$		0			0
$895$		−	21.0421i		−	0.703359i
$896$	125.471	−	63.9290i	4.19170	−	2.13572i
$897$		0			0
$898$	−40.2498	+	69.7147i	−1.34315	+	2.32641i
$899$	−8.96657	−	15.5305i	−0.299052	−	0.517973i
$900$		0			0
$901$	−18.1155	−	10.4590i	−0.603515	−	0.348439i
$902$	−26.2188			−0.872990
$903$		0			0
$904$	−72.7077			−2.41822
$905$	13.6408	+	7.87554i	0.453436	+	0.261792i
$906$		0			0
$907$	21.8645	+	37.8704i	0.725999	+	1.25747i	0.958562	+	0.284885i	$0.0919556\pi$
$907$	21.8645	+	37.8704i	0.725999	+	1.25747i	−0.232563	+	0.972581i	$0.574711\pi$
$908$	25.1056	−	43.4841i	0.833158	−	1.44307i
$909$		0			0
$910$	−32.3863	−	1.69767i	−1.07360	−	0.0562772i
$911$			43.3192i			1.43523i	0.696440	+	0.717615i	$0.254766\pi$
$911$			43.3192i			1.43523i	−0.696440	+	0.717615i	$0.745234\pi$
$912$		0			0
$913$	11.2556	−	6.49842i	0.372506	−	0.215066i
$914$	12.3280	−	7.11756i	0.407773	−	0.235428i
$915$		0			0
$916$		−	61.9475i		−	2.04680i
$917$	16.5963	+	32.5731i	0.548059	+	1.07566i
$918$		0			0
$919$	3.52078	−	6.09817i	0.116140	−	0.201160i	−0.802095	−	0.597196i	$-0.796281\pi$
$919$	3.52078	−	6.09817i	0.116140	−	0.201160i	0.918235	+	0.396036i	$0.129615\pi$
$920$	22.0204	+	38.1405i	0.725992	+	1.25745i
$921$		0			0
$922$	−99.1263	−	57.2306i	−3.26455	−	1.88479i
$923$	1.27587			0.0419957
$924$		0			0
$925$	−8.44656			−0.277721
$926$	21.1600	+	12.2168i	0.695362	+	0.401467i
$927$		0			0
$928$	42.5900	+	73.7681i	1.39809	+	2.42156i
$929$	1.77731	−	3.07839i	0.0583116	−	0.100999i	−0.835396	−	0.549649i	$-0.814762\pi$
$929$	1.77731	−	3.07839i	0.0583116	−	0.100999i	0.893708	+	0.448650i	$0.148095\pi$
$930$		0			0
$931$	−4.73974	+	45.0856i	−0.155339	+	1.47762i
$932$			157.058i			5.14462i
$933$		0			0
$934$	−65.4119	+	37.7656i	−2.14034	+	1.23573i
$935$	−8.79187	+	5.07599i	−0.287525	+	0.166003i
$936$		0			0
$937$			42.5415i			1.38977i	0.719121	+	0.694885i	$0.244545\pi$
$937$			42.5415i			1.38977i	−0.719121	+	0.694885i	$0.755455\pi$
$938$	3.18980	+	2.07153i	0.104151	+	0.0676379i
$939$		0			0
$940$	−2.05893	+	3.56617i	−0.0671548	+	0.116315i
$941$	−0.330429	−	0.572319i	−0.0107717	−	0.0186571i	0.860589	−	0.509300i	$-0.170095\pi$
$941$	−0.330429	−	0.572319i	−0.0107717	−	0.0186571i	−0.871361	+	0.490642i	$0.836762\pi$
$942$		0			0
$943$	9.25513	+	5.34345i	0.301388	+	0.174007i
$944$	62.1526			2.02289
$945$		0			0
$946$	−109.055			−3.54568
$947$	−14.7749	−	8.53031i	−0.480121	−	0.277198i	0.240346	−	0.970687i	$-0.422739\pi$
$947$	−14.7749	−	8.53031i	−0.480121	−	0.277198i	−0.720467	+	0.693489i	$0.756072\pi$
$948$		0			0
$949$	16.2852	+	28.2067i	0.528639	+	0.915629i
$950$	8.95303	−	15.5071i	0.290475	−	0.503117i
$951$		0			0
$952$	3.65313	−	69.6905i	0.118399	−	2.25868i
$953$			46.1260i			1.49417i	0.664730	+	0.747084i	$0.268547\pi$
$953$			46.1260i			1.49417i	−0.664730	+	0.747084i	$0.731453\pi$
$954$		0			0
$955$	13.4813	−	7.78345i	0.436246	−	0.251867i
$956$	−31.9977	+	18.4739i	−1.03488	+	0.597488i
$957$		0			0
$958$		−	48.4804i		−	1.56633i
$959$	−0.914500	+	17.4458i	−0.0295307	+	0.563356i
$960$		0			0
$961$	−0.903644	+	1.56516i	−0.0291498	+	0.0504890i
$962$	−51.7676	−	89.6642i	−1.66906	−	2.89089i
$963$		0			0
$964$	−80.5165	−	46.4862i	−2.59326	−	1.49722i
$965$	2.05638			0.0661973
$966$		0			0
$967$	−18.5998			−0.598130			−0.299065	−	0.954233i	$-0.596675\pi$
$967$	−18.5998			−0.598130			−0.299065	+	0.954233i	$0.596675\pi$
$968$	−35.2626	−	20.3589i	−1.13338	−	0.654359i
$969$		0			0
$970$	12.7208	+	22.0330i	0.408440	+	0.707438i
$971$	28.8326	−	49.9395i	0.925282	−	1.60264i	0.134174	−	0.990958i	$-0.457162\pi$
$971$	28.8326	−	49.9395i	0.925282	−	1.60264i	0.791107	−	0.611677i	$-0.209505\pi$
$972$		0			0
$973$	1.66453	+	1.08098i	0.0533623	+	0.0346548i
$974$			45.4328i			1.45576i
$975$		0			0
$976$	−17.1130	+	9.88021i	−0.547775	+	0.316258i
$977$	−46.2566	+	26.7063i	−1.47988	+	0.854410i	−0.999740	−	0.0227816i	$-0.992748\pi$
$977$	−46.2566	+	26.7063i	−1.47988	+	0.854410i	−0.480141	+	0.877191i	$0.659414\pi$
$978$		0			0
$979$		−	50.4948i		−	1.61382i
$980$	−16.0698	−	36.0957i	−0.513332	−	1.15303i
$981$		0			0
$982$	2.53586	−	4.39223i	0.0809224	−	0.140162i
$983$	7.72926	+	13.3875i	0.246525	+	0.426994i	0.962559	−	0.271071i	$-0.0873779\pi$
$983$	7.72926	+	13.3875i	0.246525	+	0.426994i	−0.716034	+	0.698065i	$0.754045\pi$
$984$		0			0
$985$	4.28577	+	2.47439i	0.136556	+	0.0788407i
$986$	24.0218			0.765011
$987$		0			0
$988$	162.063			5.15591
$989$	38.4959	+	22.2256i	1.22410	+	0.706734i
$990$		0			0
$991$	−27.5557	−	47.7279i	−0.875336	−	1.51613i	−0.856404	−	0.516306i	$-0.827307\pi$
$991$	−27.5557	−	47.7279i	−0.875336	−	1.51613i	−0.0189325	−	0.999821i	$-0.506027\pi$
$992$	−69.3308	+	120.084i	−2.20125	+	3.81268i
$993$		0			0
$994$	0.955719	+	1.87576i	0.0303136	+	0.0594954i
$995$		−	5.30823i		−	0.168282i
$996$		0			0
$997$	43.1385	−	24.9060i	1.36621	−	0.788782i	0.375768	−	0.926714i	$-0.377379\pi$
$997$	43.1385	−	24.9060i	1.36621	−	0.788782i	0.990442	+	0.137932i	$0.0440455\pi$
$998$	4.00610	−	2.31292i	0.126811	−	0.0732143i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bj.l.26.1	yes	20
3.2	odd	2		945.2.bj.k.26.10	✓	20
7.3	odd	6		945.2.bj.k.836.10	yes	20
21.17	even	6	inner	945.2.bj.l.836.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bj.k.26.10	✓	20	3.2	odd	2
945.2.bj.k.836.10	yes	20	7.3	odd	6
945.2.bj.l.26.1	yes	20	1.1	even	1	trivial
945.2.bj.l.836.1	yes	20	21.17	even	6	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39444 - 1.38243i) q^{2} +(2.82223 + 4.88825i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.44101 - 2.21890i) q^{7} -10.0764i q^{8} +O(q^{10})\)	\(q+(-2.39444 - 1.38243i) q^{2} +(2.82223 + 4.88825i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.44101 - 2.21890i) q^{7} -10.0764i q^{8} +(-2.39444 + 1.38243i) q^{10} +(-3.35867 + 1.93913i) q^{11} +4.43338i q^{13} +(-6.51787 + 3.32093i) q^{14} +(-8.28550 + 14.3509i) q^{16} +(1.30883 + 2.26696i) q^{17} +(-5.60863 - 3.23815i) q^{19} +5.64446 q^{20} +10.7228 q^{22} +(-3.78512 - 2.18534i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(6.12884 - 10.6155i) q^{26} +(14.9134 + 0.781749i) q^{28} +3.31909i q^{29} +(-4.67916 + 2.70151i) q^{31} +(22.2254 - 12.8318i) q^{32} -7.23747i q^{34} +(-1.20112 - 2.35740i) q^{35} +(4.22328 - 7.31493i) q^{37} +(8.95303 + 15.5071i) q^{38} +(-8.72644 - 5.03821i) q^{40} -2.44513 q^{41} -10.1703 q^{43} +(-18.9579 - 10.9453i) q^{44} +(6.04217 + 10.4653i) q^{46} +(-0.364769 + 0.631799i) q^{47} +(-2.84701 - 6.39488i) q^{49} +2.76486i q^{50} +(-21.6715 + 12.5120i) q^{52} +(-6.92049 + 3.99554i) q^{53} +3.87826i q^{55} +(-22.3586 - 14.5202i) q^{56} +(4.58841 - 7.94736i) q^{58} +(-1.87534 - 3.24819i) q^{59} +(1.03271 + 0.596235i) q^{61} +14.9386 q^{62} -37.8145 q^{64} +(3.83942 + 2.21669i) q^{65} +(-0.259970 - 0.450281i) q^{67} +(-7.38764 + 12.7958i) q^{68} +(-0.382929 + 7.30511i) q^{70} -0.287787i q^{71} +(6.36235 - 3.67331i) q^{73} +(-20.2248 + 11.6768i) q^{74} -36.5552i q^{76} +(-0.537133 + 10.2468i) q^{77} +(-3.44143 + 5.96074i) q^{79} +(8.28550 + 14.3509i) q^{80} +(5.85472 + 3.38023i) q^{82} -3.35120 q^{83} +2.61766 q^{85} +(24.3522 + 14.0598i) q^{86} +(19.5395 + 33.8434i) q^{88} +(-6.50999 + 11.2756i) q^{89} +(9.83722 + 6.38853i) q^{91} -24.6701i q^{92} +(1.74684 - 1.00854i) q^{94} +(-5.60863 + 3.23815i) q^{95} -9.20175i q^{97} +(-2.02349 + 19.2480i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{4} + 10 q^{5} + 6 q^{7}+O(q^{10}) \) 20 * q + 8 * q^4 + 10 * q^5 + 6 * q^7	\( 20 q + 8 q^{4} + 10 q^{5} + 6 q^{7} - 6 q^{11} - 12 q^{14} - 12 q^{16} - 6 q^{19} + 16 q^{20} + 28 q^{22} - 24 q^{23} - 10 q^{25} + 12 q^{26} + 10 q^{28} + 18 q^{31} + 60 q^{32} + 24 q^{38} - 12 q^{41} - 36 q^{43} - 60 q^{44} + 4 q^{46} + 12 q^{47} - 22 q^{49} - 78 q^{52} - 24 q^{53} - 66 q^{56} + 16 q^{58} - 6 q^{61} + 72 q^{62} - 60 q^{64} + 24 q^{65} - 20 q^{67} - 12 q^{68} + 12 q^{70} + 42 q^{73} - 42 q^{74} + 36 q^{77} + 10 q^{79} + 12 q^{80} + 72 q^{82} - 48 q^{83} + 42 q^{86} + 44 q^{88} - 12 q^{89} - 24 q^{91} + 78 q^{94} - 6 q^{95} + 48 q^{98}+O(q^{100}) \) 20 * q + 8 * q^4 + 10 * q^5 + 6 * q^7 - 6 * q^11 - 12 * q^14 - 12 * q^16 - 6 * q^19 + 16 * q^20 + 28 * q^22 - 24 * q^23 - 10 * q^25 + 12 * q^26 + 10 * q^28 + 18 * q^31 + 60 * q^32 + 24 * q^38 - 12 * q^41 - 36 * q^43 - 60 * q^44 + 4 * q^46 + 12 * q^47 - 22 * q^49 - 78 * q^52 - 24 * q^53 - 66 * q^56 + 16 * q^58 - 6 * q^61 + 72 * q^62 - 60 * q^64 + 24 * q^65 - 20 * q^67 - 12 * q^68 + 12 * q^70 + 42 * q^73 - 42 * q^74 + 36 * q^77 + 10 * q^79 + 12 * q^80 + 72 * q^82 - 48 * q^83 + 42 * q^86 + 44 * q^88 - 12 * q^89 - 24 * q^91 + 78 * q^94 - 6 * q^95 + 48 * q^98

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