LMFDB - Embedded newform 340.2.bd.a.57.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [340,2,Mod(57,340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(340, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 4, 15]))

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

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

chi := DirichletCharacter("340.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 340 = 2^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	340.bd (of order $16$, degree $8$, 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:	$2.71491366872$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.3
Character	$\chi$	$=$	340.57
Dual form			340.2.bd.a.173.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25555 + 1.87906i) q^{3} +(0.726829 + 2.11464i) q^{5} +(0.0284166 - 0.142860i) q^{7} +(-0.806426 - 1.94689i) q^{9} +(-1.00307 + 5.04279i) q^{11} -4.88905i q^{13} +(-4.88612 - 1.28928i) q^{15} +(-3.14609 + 2.66498i) q^{17} +(1.19092 - 2.87515i) q^{19} +(0.232765 + 0.232765i) q^{21} +(-5.31781 + 3.55325i) q^{23} +(-3.94344 + 3.07397i) q^{25} +(-1.97869 - 0.393586i) q^{27} +(4.15774 - 6.22249i) q^{29} +(1.27629 + 6.41632i) q^{31} +(-8.21632 - 8.21632i) q^{33} +(0.322752 - 0.0437437i) q^{35} +(-0.0626495 - 0.0418610i) q^{37} +(9.18685 + 6.13846i) q^{39} +(3.08944 + 4.62367i) q^{41} +(-1.83208 + 4.42304i) q^{43} +(3.53084 - 3.12036i) q^{45} +2.27438 q^{47} +(6.44756 + 2.67066i) q^{49} +(-1.05761 - 9.25772i) q^{51} +(7.30566 - 3.02611i) q^{53} +(-11.3928 + 1.54410i) q^{55} +(3.90732 + 5.84772i) q^{57} +(6.44471 - 2.66949i) q^{59} +(5.53142 - 3.69598i) q^{61} +(-0.301048 + 0.0598821i) q^{63} +(10.3386 - 3.55351i) q^{65} +(4.12977 - 4.12977i) q^{67} -14.4538i q^{69} +(-0.386174 + 0.0768148i) q^{71} +(1.88265 + 9.46472i) q^{73} +(-0.824998 - 11.2695i) q^{75} +(0.691909 + 0.286598i) q^{77} +(-8.07724 - 1.60666i) q^{79} +(7.69417 - 7.69417i) q^{81} +(4.48081 + 10.8176i) q^{83} +(-7.92216 - 4.71587i) q^{85} +(6.47222 + 15.6253i) q^{87} +(-9.42104 + 9.42104i) q^{89} +(-0.698450 - 0.138930i) q^{91} +(-13.6591 - 5.65780i) q^{93} +(6.94551 + 0.428642i) q^{95} +(-0.508199 - 2.55489i) q^{97} +(10.6266 - 2.11377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{15} + 8 q^{25} - 48 q^{27} - 32 q^{31} + 16 q^{33} + 32 q^{37} - 32 q^{39} - 40 q^{41} + 80 q^{47} - 40 q^{53} + 16 q^{55} + 8 q^{57} + 112 q^{59} - 48 q^{63} - 32 q^{67} - 16 q^{71} + 8 q^{73}+ \cdots + 96 q^{99}+O(q^{100}) $ 72 * q + 24 * q^15 + 8 * q^25 - 48 * q^27 - 32 * q^31 + 16 * q^33 + 32 * q^37 - 32 * q^39 - 40 * q^41 + 80 * q^47 - 40 * q^53 + 16 * q^55 + 8 * q^57 + 112 * q^59 - 48 * q^63 - 32 * q^67 - 16 * q^71 + 8 * q^73 - 88 * q^75 - 16 * q^77 - 64 * q^79 - 48 * q^81 - 40 * q^83 - 40 * q^85 - 8 * q^87 - 48 * q^91 - 120 * q^93 - 48 * q^95 - 80 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/340\mathbb{Z}\right)^\times$.

$n$	$137$	$171$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.25555	+	1.87906i	−0.724893	+	1.08488i	0.267713	+	0.963499i	$0.413732\pi$
$3$	−1.25555	+	1.87906i	−0.724893	+	1.08488i	−0.992606	+	0.121380i	$0.961268\pi$
$4$		0			0
$5$	0.726829	+	2.11464i	0.325048	+	0.945698i
$5$	0.726829	+	2.11464i	0.325048	+	0.945698i
$6$		0			0
$7$	0.0284166	−	0.142860i	0.0107405	−	0.0539960i	−0.975043	−	0.222014i	$-0.928737\pi$
$7$	0.0284166	−	0.142860i	0.0107405	−	0.0539960i	0.985784	+	0.168018i	$0.0537368\pi$
$8$		0			0
$9$	−0.806426	−	1.94689i	−0.268809	−	0.648962i
$10$		0			0
$11$	−1.00307	+	5.04279i	−0.302438	+	1.52046i	0.468451	+	0.883490i	$0.344812\pi$
$11$	−1.00307	+	5.04279i	−0.302438	+	1.52046i	−0.770889	+	0.636970i	$0.780188\pi$
$12$		0			0
$13$		−	4.88905i		−	1.35598i	−0.735071	−	0.677990i	$-0.762851\pi$
$13$		−	4.88905i		−	1.35598i	0.735071	−	0.677990i	$-0.237149\pi$
$14$		0			0
$15$	−4.88612	−	1.28928i	−1.26159	−	0.332892i
$16$		0			0
$17$	−3.14609	+	2.66498i	−0.763038	+	0.646354i
$17$	−3.14609	+	2.66498i	−0.763038	+	0.646354i
$18$		0			0
$19$	1.19092	−	2.87515i	0.273217	−	0.659604i	−0.726400	−	0.687272i	$-0.758808\pi$
$19$	1.19092	−	2.87515i	0.273217	−	0.659604i	0.999617	+	0.0276681i	$0.00880814\pi$
$20$		0			0
$21$	0.232765	+	0.232765i	0.0507934	+	0.0507934i
$22$		0			0
$23$	−5.31781	+	3.55325i	−1.10884	+	0.740904i	−0.968454	−	0.249193i	$-0.919835\pi$
$23$	−5.31781	+	3.55325i	−1.10884	+	0.740904i	−0.140387	+	0.990097i	$0.544835\pi$
$24$		0			0
$25$	−3.94344	+	3.07397i	−0.788688	+	0.614794i
$26$		0			0
$27$	−1.97869	−	0.393586i	−0.380799	−	0.0757457i
$28$		0			0
$29$	4.15774	−	6.22249i	0.772073	−	1.15549i	−0.211922	−	0.977287i	$-0.567972\pi$
$29$	4.15774	−	6.22249i	0.772073	−	1.15549i	0.983994	−	0.178201i	$-0.0570279\pi$
$30$		0			0
$31$	1.27629	+	6.41632i	0.229228	+	1.15241i	0.908295	+	0.418330i	$0.137384\pi$
$31$	1.27629	+	6.41632i	0.229228	+	1.15241i	−0.679068	+	0.734076i	$0.737616\pi$
$32$		0			0
$33$	−8.21632	−	8.21632i	−1.43028	−	1.43028i
$34$		0			0
$35$	0.322752	−	0.0437437i	0.0545550	−	0.00739404i
$36$		0			0
$37$	−0.0626495	−	0.0418610i	−0.0102995	−	0.00688191i	0.550410	−	0.834895i	$-0.314471\pi$
$37$	−0.0626495	−	0.0418610i	−0.0102995	−	0.00688191i	−0.560709	+	0.828013i	$0.689471\pi$
$38$		0			0
$39$	9.18685	+	6.13846i	1.47107	+	0.982940i
$40$		0			0
$41$	3.08944	+	4.62367i	0.482489	+	0.722096i	0.990235	−	0.139411i	$-0.0445210\pi$
$41$	3.08944	+	4.62367i	0.482489	+	0.722096i	−0.507746	+	0.861507i	$0.669521\pi$
$42$		0			0
$43$	−1.83208	+	4.42304i	−0.279390	+	0.674507i	−0.999819	−	0.0190215i	$-0.993945\pi$
$43$	−1.83208	+	4.42304i	−0.279390	+	0.674507i	0.720429	+	0.693529i	$0.243945\pi$
$44$		0			0
$45$	3.53084	−	3.12036i	0.526346	−	0.465155i
$46$		0			0
$47$	2.27438			0.331753			0.165876	−	0.986147i	$-0.446955\pi$
$47$	2.27438			0.331753			0.165876	+	0.986147i	$0.446955\pi$
$48$		0			0
$49$	6.44756	+	2.67066i	0.921079	+	0.381524i
$50$		0			0
$51$	−1.05761	−	9.25772i	−0.148095	−	1.29634i
$52$		0			0
$53$	7.30566	−	3.02611i	1.00351	−	0.415668i	0.180427	−	0.983588i	$-0.442252\pi$
$53$	7.30566	−	3.02611i	1.00351	−	0.415668i	0.823083	+	0.567921i	$0.192252\pi$
$54$		0			0
$55$	−11.3928	+	1.54410i	−1.53620	+	0.208207i
$56$		0			0
$57$	3.90732	+	5.84772i	0.517537	+	0.774549i
$58$		0			0
$59$	6.44471	−	2.66949i	0.839030	−	0.347537i	0.0785588	−	0.996909i	$-0.474968\pi$
$59$	6.44471	−	2.66949i	0.839030	−	0.347537i	0.760471	+	0.649372i	$0.224968\pi$
$60$		0			0
$61$	5.53142	−	3.69598i	0.708226	−	0.473221i	−0.148554	−	0.988904i	$-0.547462\pi$
$61$	5.53142	−	3.69598i	0.708226	−	0.473221i	0.856780	+	0.515683i	$0.172462\pi$
$62$		0			0
$63$	−0.301048	+	0.0598821i	−0.0379285	+	0.00754444i
$64$		0			0
$65$	10.3386	−	3.55351i	1.28235	−	0.440758i
$66$		0			0
$67$	4.12977	−	4.12977i	0.504532	−	0.504532i	−0.408311	−	0.912843i	$-0.633882\pi$
$67$	4.12977	−	4.12977i	0.504532	−	0.504532i	0.912843	+	0.408311i	$0.133882\pi$
$68$		0			0
$69$		−	14.4538i		−	1.74003i
$70$		0			0
$71$	−0.386174	+	0.0768148i	−0.0458304	+	0.00911624i	−0.217952	−	0.975959i	$-0.569938\pi$
$71$	−0.386174	+	0.0768148i	−0.0458304	+	0.00911624i	0.172122	+	0.985076i	$0.444938\pi$
$72$		0			0
$73$	1.88265	+	9.46472i	0.220347	+	1.10776i	0.919591	+	0.392878i	$0.128520\pi$
$73$	1.88265	+	9.46472i	0.220347	+	1.10776i	−0.699243	+	0.714884i	$0.746480\pi$
$74$		0			0
$75$	−0.824998	−	11.2695i	−0.0952626	−	1.30129i
$76$		0			0
$77$	0.691909	+	0.286598i	0.0788503	+	0.0326609i
$78$		0			0
$79$	−8.07724	−	1.60666i	−0.908761	−	0.180764i	−0.281489	−	0.959564i	$-0.590828\pi$
$79$	−8.07724	−	1.60666i	−0.908761	−	0.180764i	−0.627271	+	0.778801i	$0.715828\pi$
$80$		0			0
$81$	7.69417	−	7.69417i	0.854907	−	0.854907i
$82$		0			0
$83$	4.48081	+	10.8176i	0.491833	+	1.18739i	0.953787	+	0.300485i	$0.0971485\pi$
$83$	4.48081	+	10.8176i	0.491833	+	1.18739i	−0.461954	+	0.886904i	$0.652851\pi$
$84$		0			0
$85$	−7.92216	−	4.71587i	−0.859279	−	0.511507i
$86$		0			0
$87$	6.47222	+	15.6253i	0.693895	+	1.67521i
$88$		0			0
$89$	−9.42104	+	9.42104i	−0.998628	+	0.998628i	−0.999999	−	0.00137077i	$-0.999564\pi$
$89$	−9.42104	+	9.42104i	−0.998628	+	0.998628i	0.00137077	+	0.999999i	$0.499564\pi$
$90$		0			0
$91$	−0.698450	−	0.138930i	−0.0732174	−	0.0145639i
$92$		0			0
$93$	−13.6591	−	5.65780i	−1.41639	−	0.586686i
$94$		0			0
$95$	6.94551	+	0.428642i	0.712594	+	0.0439778i
$96$		0			0
$97$	−0.508199	−	2.55489i	−0.0515998	−	0.259410i	0.946371	−	0.323082i	$-0.104719\pi$
$97$	−0.508199	−	2.55489i	−0.0515998	−	0.259410i	−0.997971	+	0.0636720i	$0.979719\pi$
$98$		0			0
$99$	10.6266	−	2.11377i	1.06802	−	0.212442i
$100$		0			0
$101$			15.5098i			1.54328i	0.636059	+	0.771641i	$0.280564\pi$
$101$			15.5098i			1.54328i	−0.636059	+	0.771641i	$0.719436\pi$
$102$		0			0
$103$	12.2197	−	12.2197i	1.20405	−	1.20405i	0.231121	−	0.972925i	$-0.425761\pi$
$103$	12.2197	−	12.2197i	1.20405	−	1.20405i	0.972925	−	0.231121i	$-0.0742394\pi$
$104$		0			0
$105$	−0.323034	+	0.661394i	−0.0315249	+	0.0645455i
$106$		0			0
$107$	6.60117	−	1.31305i	0.638159	−	0.126938i	0.134602	−	0.990900i	$-0.457024\pi$
$107$	6.60117	−	1.31305i	0.638159	−	0.126938i	0.503557	+	0.863962i	$0.332024\pi$
$108$		0			0
$109$	1.43218	−	0.956950i	0.137178	−	0.0916592i	−0.485088	−	0.874465i	$-0.661212\pi$
$109$	1.43218	−	0.956950i	0.137178	−	0.0916592i	0.622266	+	0.782806i	$0.286212\pi$
$110$		0			0
$111$	0.157319	−	0.0651637i	0.0149321	−	0.00618507i
$112$		0			0
$113$	−3.46941	−	5.19234i	−0.326374	−	0.488454i	0.631605	−	0.775290i	$-0.282396\pi$
$113$	−3.46941	−	5.19234i	−0.326374	−	0.488454i	−0.957980	+	0.286836i	$0.907396\pi$
$114$		0			0
$115$	−11.3790	−	8.66268i	−1.06110	−	0.807799i
$116$		0			0
$117$	−9.51843	+	3.94266i	−0.879979	+	0.364499i
$118$		0			0
$119$	0.291318	+	0.525179i	0.0267051	+	0.0481431i
$120$		0			0
$121$	−14.2609	−	5.90707i	−1.29645	−	0.537006i
$122$		0			0
$123$	−12.5671			−1.13314
$124$		0			0
$125$	−9.36656	−	6.10472i	−0.837770	−	0.546023i
$126$		0			0
$127$	−4.65583	+	11.2402i	−0.413138	+	0.997404i	0.571152	+	0.820845i	$0.306497\pi$
$127$	−4.65583	+	11.2402i	−0.413138	+	0.997404i	−0.984290	+	0.176560i	$0.943503\pi$
$128$		0			0
$129$	−6.01090	−	8.99595i	−0.529231	−	0.792050i
$130$		0			0
$131$	10.8110	+	7.22365i	0.944557	+	0.631133i	0.929527	−	0.368754i	$-0.120216\pi$
$131$	10.8110	+	7.22365i	0.944557	+	0.631133i	0.0150303	+	0.999887i	$0.495216\pi$
$132$		0			0
$133$	−0.376901	−	0.251837i	−0.0326815	−	0.0218371i
$134$		0			0
$135$	−0.605875	−	4.47030i	−0.0521454	−	0.384742i
$136$		0			0
$137$	−12.1652	−	12.1652i	−1.03934	−	1.03934i	−0.999194	−	0.0401490i	$-0.987217\pi$
$137$	−12.1652	−	12.1652i	−1.03934	−	1.03934i	−0.0401490	−	0.999194i	$-0.512783\pi$
$138$		0			0
$139$	−0.931338	−	4.68215i	−0.0789951	−	0.397135i	−0.999972	−	0.00751740i	$-0.997607\pi$
$139$	−0.931338	−	4.68215i	−0.0789951	−	0.397135i	0.920977	−	0.389618i	$-0.127393\pi$
$140$		0			0
$141$	−2.85560	+	4.27371i	−0.240485	+	0.359911i
$142$		0			0
$143$	24.6545	+	4.90408i	2.06171	+	0.410100i
$144$		0			0
$145$	16.1803	+	4.26945i	1.34370	+	0.354558i
$146$		0			0
$147$	−13.1136	+	8.76222i	−1.08159	+	0.722696i
$148$		0			0
$149$	15.0177	+	15.0177i	1.23030	+	1.23030i	0.963849	+	0.266450i	$0.0858508\pi$
$149$	15.0177	+	15.0177i	1.23030	+	1.23030i	0.266450	+	0.963849i	$0.414149\pi$
$150$		0			0
$151$	0.662023	−	1.59826i	0.0538746	−	0.130065i	−0.894651	−	0.446767i	$-0.852575\pi$
$151$	0.662023	−	1.59826i	0.0538746	−	0.130065i	0.948525	+	0.316702i	$0.102575\pi$
$152$		0			0
$153$	7.72551	+	3.97596i	0.624570	+	0.321437i
$154$		0			0
$155$	−12.6406	+	7.36246i	−1.01532	+	0.591367i
$156$		0			0
$157$			18.3656i			1.46573i	0.680373	+	0.732866i	$0.261818\pi$
$157$			18.3656i			1.46573i	−0.680373	+	0.732866i	$0.738182\pi$
$158$		0			0
$159$	−3.48639	+	17.5272i	−0.276488	+	1.39000i
$160$		0			0
$161$	0.356503	+	0.860674i	0.0280964	+	0.0678306i
$162$		0			0
$163$	−0.517946	+	2.60389i	−0.0405686	+	0.203952i	−0.995754	−	0.0920568i	$-0.970656\pi$
$163$	−0.517946	+	2.60389i	−0.0405686	+	0.203952i	0.955185	+	0.296009i	$0.0956559\pi$
$164$		0			0
$165$	11.4027	−	23.3465i	0.887702	−	1.81752i
$166$		0			0
$167$	5.57418	−	8.34235i	0.431343	−	0.645550i	−0.550591	−	0.834775i	$-0.685598\pi$
$167$	5.57418	−	8.34235i	0.431343	−	0.645550i	0.981934	+	0.189225i	$0.0605975\pi$
$168$		0			0
$169$	−10.9029			−0.838681
$170$		0			0
$171$	−6.55797			−0.501501
$172$		0			0
$173$	2.51304	−	3.76103i	0.191063	−	0.285945i	−0.723554	−	0.690268i	$-0.757493\pi$
$173$	2.51304	−	3.76103i	0.191063	−	0.285945i	0.914617	+	0.404322i	$0.132493\pi$
$174$		0			0
$175$	0.327088	+	0.650711i	0.0247255	+	0.0491891i
$176$		0			0
$177$	−3.07552	+	15.4617i	−0.231171	+	1.16217i
$178$		0			0
$179$	−7.60849	−	18.3685i	−0.568685	−	1.37293i	−0.902664	−	0.430347i	$-0.858391\pi$
$179$	−7.60849	−	18.3685i	−0.568685	−	1.37293i	0.333979	−	0.942581i	$-0.391609\pi$
$180$		0			0
$181$	0.0944716	−	0.474941i	0.00702202	−	0.0353021i	−0.977115	−	0.212710i	$-0.931771\pi$
$181$	0.0944716	−	0.474941i	0.00702202	−	0.0353021i	0.984137	+	0.177408i	$0.0567711\pi$
$182$		0			0
$183$			15.0344i			1.11137i
$184$		0			0
$185$	0.0429857	−	0.162907i	0.00316037	−	0.0119772i
$186$		0			0
$187$	−10.2832	−	18.5382i	−0.751983	−	1.35565i
$188$		0			0
$189$	−0.112455	+	0.271491i	−0.00817992	+	0.0197481i
$190$		0			0
$191$	−4.30914	−	4.30914i	−0.311799	−	0.311799i	0.533807	−	0.845606i	$-0.320761\pi$
$191$	−4.30914	−	4.30914i	−0.311799	−	0.311799i	−0.845606	+	0.533807i	$0.820761\pi$
$192$		0			0
$193$	−5.32058	+	3.55510i	−0.382984	+	0.255902i	−0.732128	−	0.681167i	$-0.761473\pi$
$193$	−5.32058	+	3.55510i	−0.382984	+	0.255902i	0.349144	+	0.937069i	$0.386473\pi$
$194$		0			0
$195$	−6.30338	+	23.8885i	−0.451395	+	1.71069i
$196$		0			0
$197$	0.0854365	+	0.0169944i	0.00608710	+	0.00121080i	0.198133	−	0.980175i	$-0.436512\pi$
$197$	0.0854365	+	0.0169944i	0.00608710	+	0.00121080i	−0.192046	+	0.981386i	$0.561512\pi$
$198$		0			0
$199$	0.929300	−	1.39080i	0.0658763	−	0.0985909i	−0.797069	−	0.603888i	$-0.793617\pi$
$199$	0.929300	−	1.39080i	0.0658763	−	0.0985909i	0.862945	+	0.505298i	$0.168617\pi$
$200$		0			0
$201$	2.57497	+	12.9452i	0.181624	+	0.913087i
$202$		0			0
$203$	−0.770796	−	0.770796i	−0.0540993	−	0.0540993i
$204$		0			0
$205$	−7.53192	+	9.89367i	−0.526052	+	0.691004i
$206$		0			0
$207$	11.2062	+	7.48774i	0.778884	+	0.520434i
$208$		0			0
$209$	13.3042	+	8.88957i	0.920269	+	0.614904i
$210$		0			0
$211$	−15.3944	−	23.0393i	−1.05979	−	1.58609i	−0.779734	−	0.626110i	$-0.784646\pi$
$211$	−15.3944	−	23.0393i	−1.05979	−	1.58609i	−0.280059	−	0.959983i	$-0.590354\pi$
$212$		0			0
$213$	0.340521	−	0.822091i	0.0233321	−	0.0563287i
$214$		0			0
$215$	−10.6848	−	0.659410i	−0.728695	−	0.0449714i
$216$		0			0
$217$	0.952903			0.0646873
$218$		0			0
$219$	−20.1486	−	8.34581i	−1.36151	−	0.563958i
$220$		0			0
$221$	13.0293	+	15.3814i	0.876442	+	1.03466i
$222$		0			0
$223$	10.1557	−	4.20663i	0.680076	−	0.281697i	−0.0157824	−	0.999875i	$-0.505024\pi$
$223$	10.1557	−	4.20663i	0.680076	−	0.281697i	0.695859	+	0.718179i	$0.255024\pi$
$224$		0			0
$225$	9.16476	+	5.19849i	0.610984	+	0.346566i
$226$		0			0
$227$	3.51289	+	5.25741i	0.233159	+	0.348947i	0.929537	−	0.368728i	$-0.120207\pi$
$227$	3.51289	+	5.25741i	0.233159	+	0.348947i	−0.696379	+	0.717675i	$0.745207\pi$
$228$		0			0
$229$	−2.55004	+	1.05626i	−0.168512	+	0.0697998i	−0.465345	−	0.885130i	$-0.654070\pi$
$229$	−2.55004	+	1.05626i	−0.168512	+	0.0697998i	0.296833	+	0.954929i	$0.404070\pi$
$230$		0			0
$231$	−1.40726	+	0.940303i	−0.0925911	+	0.0618674i
$232$		0			0
$233$	−13.0566	+	2.59712i	−0.855367	+	0.170143i	−0.603249	−	0.797553i	$-0.706127\pi$
$233$	−13.0566	+	2.59712i	−0.855367	+	0.170143i	−0.252119	+	0.967696i	$0.581127\pi$
$234$		0			0
$235$	1.65309	+	4.80951i	0.107835	+	0.313738i
$236$		0			0
$237$	13.1604	−	13.1604i	0.854861	−	0.854861i
$238$		0			0
$239$		−	7.69856i		−	0.497979i	−0.968506	−	0.248989i	$-0.919902\pi$
$239$		−	7.69856i		−	0.497979i	0.968506	−	0.248989i	$-0.0800984\pi$
$240$		0			0
$241$	1.19133	−	0.236971i	0.0767405	−	0.0152646i	−0.156571	−	0.987667i	$-0.550044\pi$
$241$	1.19133	−	0.236971i	0.0767405	−	0.0152646i	0.233311	+	0.972402i	$0.425044\pi$
$242$		0			0
$243$	3.61666	+	18.1822i	0.232009	+	1.16639i
$244$		0			0
$245$	−0.961236	+	15.5754i	−0.0614111	+	0.995076i
$246$		0			0
$247$	−14.0567	−	5.82250i	−0.894409	−	0.370477i
$248$		0			0
$249$	−25.9529	−	5.16235i	−1.64470	−	0.327151i
$250$		0			0
$251$	12.9297	−	12.9297i	0.816115	−	0.816115i	−0.169428	−	0.985543i	$-0.554192\pi$
$251$	12.9297	−	12.9297i	0.816115	−	0.816115i	0.985543	+	0.169428i	$0.0541920\pi$
$252$		0			0
$253$	−12.5841	−	30.3808i	−0.791158	−	1.91003i
$254$		0			0
$255$	18.8081	−	8.96524i	1.17781	−	0.561425i
$256$		0			0
$257$	−6.24622	−	15.0797i	−0.389629	−	0.940647i	−0.990018	−	0.140939i	$-0.954988\pi$
$257$	−6.24622	−	15.0797i	−0.389629	−	0.940647i	0.600389	−	0.799708i	$-0.295012\pi$
$258$		0			0
$259$	−0.00776055	+	0.00776055i	−0.000482217	+	0.000482217i
$260$		0			0
$261$	−15.4674	−	3.07666i	−0.957408	−	0.190440i
$262$		0			0
$263$	−13.9762	−	5.78915i	−0.861812	−	0.356974i	−0.0923958	−	0.995722i	$-0.529453\pi$
$263$	−13.9762	−	5.78915i	−0.861812	−	0.356974i	−0.769416	+	0.638748i	$0.779453\pi$
$264$		0			0
$265$	11.7091	+	13.2494i	0.719285	+	0.813905i
$266$		0			0
$267$	−5.87415	−	29.5313i	−0.359492	−	1.80729i
$268$		0			0
$269$	−6.71226	+	1.33515i	−0.409254	+	0.0814057i	−0.395424	−	0.918499i	$-0.629402\pi$
$269$	−6.71226	+	1.33515i	−0.409254	+	0.0814057i	−0.0138299	+	0.999904i	$0.504402\pi$
$270$		0			0
$271$			19.1695i			1.16446i	0.813023	+	0.582231i	$0.197820\pi$
$271$			19.1695i			1.16446i	−0.813023	+	0.582231i	$0.802180\pi$
$272$		0			0
$273$	1.13800	−	1.13800i	0.0688748	−	0.0688748i
$274$		0			0
$275$	−11.5458	−	22.9694i	−0.696240	−	1.38510i
$276$		0			0
$277$	25.1984	−	5.01227i	1.51402	−	0.301158i	0.632971	−	0.774176i	$-0.281835\pi$
$277$	25.1984	−	5.01227i	1.51402	−	0.301158i	0.881053	+	0.473018i	$0.156835\pi$
$278$		0			0
$279$	11.4626	−	7.65907i	0.686249	−	0.458537i
$280$		0			0
$281$	11.2246	−	4.64936i	0.669601	−	0.277358i	−0.0218715	−	0.999761i	$-0.506962\pi$
$281$	11.2246	−	4.64936i	0.669601	−	0.277358i	0.691472	+	0.722403i	$0.256962\pi$
$282$		0			0
$283$	−9.33336	−	13.9684i	−0.554811	−	0.830333i	0.442996	−	0.896523i	$-0.353915\pi$
$283$	−9.33336	−	13.9684i	−0.554811	−	0.830333i	−0.997807	+	0.0661906i	$0.978915\pi$
$284$		0			0
$285$	−9.52589	+	12.5129i	−0.564265	+	0.741199i
$286$		0			0
$287$	0.748328	−	0.309968i	0.0441724	−	0.0182968i
$288$		0			0
$289$	2.79572	−	16.7685i	0.164454	−	0.986385i
$290$		0			0
$291$	5.43887	+	2.25286i	0.318832	+	0.132065i
$292$		0			0
$293$	10.5729			0.617678			0.308839	−	0.951114i	$-0.400060\pi$
$293$	10.5729			0.617678			0.308839	+	0.951114i	$0.400060\pi$
$294$		0			0
$295$	10.3292	+	11.6880i	0.601390	+	0.680502i
$296$		0			0
$297$	3.96955	−	9.58333i	0.230336	−	0.556081i
$298$		0			0
$299$	17.3720	+	25.9991i	1.00465	+	1.50357i
$300$		0			0
$301$	0.579813	+	0.387419i	0.0334199	+	0.0223305i
$302$		0			0
$303$	−29.1439	−	19.4733i	−1.67427	−	1.11871i
$304$		0			0
$305$	11.8361	+	9.01064i	0.677732	+	0.515948i
$306$		0			0
$307$	4.40877	+	4.40877i	0.251622	+	0.251622i	0.821635	−	0.570013i	$-0.193062\pi$
$307$	4.40877	+	4.40877i	0.251622	+	0.251622i	−0.570013	+	0.821635i	$0.693062\pi$
$308$		0			0
$309$	7.61917	+	38.3042i	0.433440	+	2.17905i
$310$		0			0
$311$	17.3818	−	26.0137i	0.985633	−	1.47510i	0.108943	−	0.994048i	$-0.465253\pi$
$311$	17.3818	−	26.0137i	0.985633	−	1.47510i	0.876690	−	0.481056i	$-0.159747\pi$
$312$		0			0
$313$	13.2147	+	2.62856i	0.746937	+	0.148575i	0.553861	−	0.832609i	$-0.313154\pi$
$313$	13.2147	+	2.62856i	0.746937	+	0.148575i	0.193076	+	0.981184i	$0.438154\pi$
$314$		0			0
$315$	−0.345440	−	0.593085i	−0.0194633	−	0.0334165i
$316$		0			0
$317$	25.7026	−	17.1739i	1.44360	−	0.964583i	0.446023	−	0.895021i	$-0.352840\pi$
$317$	25.7026	−	17.1739i	1.44360	−	0.964583i	0.997578	−	0.0695617i	$-0.0221601\pi$
$318$		0			0
$319$	27.2082	+	27.2082i	1.52337	+	1.52337i
$320$		0			0
$321$	−5.82079	+	14.0526i	−0.324885	+	0.784341i
$322$		0			0
$323$	3.91547	+	12.2193i	0.217862	+	0.679897i
$324$		0			0
$325$	15.0288	+	19.2797i	0.833648	+	1.06944i
$326$		0			0
$327$			3.89265i			0.215264i
$328$		0			0
$329$	0.0646302	−	0.324918i	0.00356318	−	0.0179133i
$330$		0			0
$331$	−12.3584	−	29.8359i	−0.679280	−	1.63993i	−0.765332	−	0.643636i	$-0.777425\pi$
$331$	−12.3584	−	29.8359i	−0.679280	−	1.63993i	0.0860516	−	0.996291i	$-0.472575\pi$
$332$		0			0
$333$	−0.0309765	+	0.155729i	−0.00169750	+	0.00853391i
$334$		0			0
$335$	11.7346	+	5.73136i	0.641131	+	0.313137i
$336$		0			0
$337$	11.5111	−	17.2276i	0.627049	−	0.938445i	−0.372895	−	0.927873i	$-0.621635\pi$
$337$	11.5111	−	17.2276i	0.627049	−	0.938445i	0.999944	−	0.0105716i	$-0.00336511\pi$
$338$		0			0
$339$	14.1128			0.766500
$340$		0			0
$341$	−33.6364			−1.82151
$342$		0			0
$343$	1.13121	−	1.69298i	0.0610798	−	0.0914124i
$344$		0			0
$345$	30.5647	−	10.5054i	1.64555	−	0.565594i
$346$		0			0
$347$	0.346328	−	1.74111i	0.0185918	−	0.0934675i	−0.970375	−	0.241602i	$-0.922327\pi$
$347$	0.346328	−	1.74111i	0.0185918	−	0.0934675i	0.988967	+	0.148135i	$0.0473270\pi$
$348$		0			0
$349$	6.03904	+	14.5795i	0.323263	+	0.780425i	0.999060	+	0.0433380i	$0.0137992\pi$
$349$	6.03904	+	14.5795i	0.323263	+	0.780425i	−0.675798	+	0.737087i	$0.736201\pi$
$350$		0			0
$351$	−1.92426	+	9.67393i	−0.102710	+	0.516356i
$352$		0			0
$353$			30.2215i			1.60853i	0.594274	+	0.804263i	$0.297440\pi$
$353$			30.2215i			1.60853i	−0.594274	+	0.804263i	$0.702560\pi$
$354$		0			0
$355$	−0.443118	−	0.760789i	−0.0235183	−	0.0403785i
$356$		0			0
$357$	−1.35261	−	0.111984i	−0.0715878	−	0.00592680i
$358$		0			0
$359$	−2.62734	+	6.34295i	−0.138665	+	0.334768i	−0.977923	−	0.208966i	$-0.932990\pi$
$359$	−2.62734	+	6.34295i	−0.138665	+	0.334768i	0.839257	+	0.543734i	$0.182990\pi$
$360$		0			0
$361$	6.58687	+	6.58687i	0.346677	+	0.346677i
$362$		0			0
$363$	29.0051	−	19.3806i	1.52237	−	1.01722i
$364$		0			0
$365$	−18.6461	+	10.8604i	−0.975984	+	0.568457i
$366$		0			0
$367$	5.64667	+	1.12319i	0.294754	+	0.0586302i	0.340252	−	0.940334i	$-0.389488\pi$
$367$	5.64667	+	1.12319i	0.294754	+	0.0586302i	−0.0454984	+	0.998964i	$0.514488\pi$
$368$		0			0
$369$	6.51035	−	9.74343i	0.338915	−	0.507223i
$370$		0			0
$371$	−0.224707	−	1.12968i	−0.0116662	−	0.0586500i
$372$		0			0
$373$	−0.104237	−	0.104237i	−0.00539718	−	0.00539718i	0.704403	−	0.709800i	$-0.251215\pi$
$373$	−0.104237	−	0.104237i	−0.00539718	−	0.00539718i	−0.709800	+	0.704403i	$0.751215\pi$
$374$		0			0
$375$	23.2314	−	9.93558i	1.19966	−	0.513071i
$376$		0			0
$377$	−30.4221	−	20.3274i	−1.56682	−	1.04691i
$378$		0			0
$379$	−27.6046	−	18.4448i	−1.41795	−	0.947445i	−0.999226	−	0.0393313i	$-0.987477\pi$
$379$	−27.6046	−	18.4448i	−1.41795	−	0.947445i	−0.418725	−	0.908113i	$-0.637523\pi$
$380$		0			0
$381$	−15.2754	−	22.8612i	−0.782581	−	1.17122i
$382$		0			0
$383$	−8.23126	+	19.8720i	−0.420597	+	1.01541i	0.561574	+	0.827426i	$0.310196\pi$
$383$	−8.23126	+	19.8720i	−0.420597	+	1.01541i	−0.982172	+	0.187986i	$0.939804\pi$
$384$		0			0
$385$	−0.103153	+	1.67145i	−0.00525719	+	0.0851849i
$386$		0			0
$387$	10.0886			0.512832
$388$		0			0
$389$	−29.5773	−	12.2513i	−1.49963	−	0.621166i	−0.526241	−	0.850335i	$-0.676399\pi$
$389$	−29.5773	−	12.2513i	−1.49963	−	0.621166i	−0.973387	+	0.229169i	$0.926399\pi$
$390$		0			0
$391$	7.26095	−	25.3507i	0.367202	−	1.28204i
$392$		0			0
$393$	−27.1474	+	11.2448i	−1.36941	+	0.567226i
$394$		0			0
$395$	−2.47325	−	18.2483i	−0.124443	−	0.918170i
$396$		0			0
$397$	−0.234611	−	0.351120i	−0.0117748	−	0.0176222i	0.825536	−	0.564350i	$-0.190873\pi$
$397$	−0.234611	−	0.351120i	−0.0117748	−	0.0176222i	−0.837310	+	0.546728i	$0.815873\pi$
$398$		0			0
$399$	0.946437	−	0.392027i	0.0473811	−	0.0196259i
$400$		0			0
$401$	−22.1326	+	14.7885i	−1.10525	+	0.738504i	−0.967729	−	0.251994i	$-0.918914\pi$
$401$	−22.1326	+	14.7885i	−1.10525	+	0.738504i	−0.137521	+	0.990499i	$0.543914\pi$
$402$		0			0
$403$	31.3697	−	6.23983i	1.56264	−	0.310828i
$404$		0			0
$405$	21.8628	+	10.6781i	1.08637	+	0.530598i
$406$		0			0
$407$	0.273939	−	0.273939i	0.0135786	−	0.0135786i
$408$		0			0
$409$		−	33.0879i		−	1.63609i	−0.575153	−	0.818046i	$-0.695058\pi$
$409$		−	33.0879i		−	1.63609i	0.575153	−	0.818046i	$-0.304942\pi$
$410$		0			0
$411$	38.1332	−	7.58517i	1.88097	−	0.374149i
$412$		0			0
$413$	−0.198226	−	0.996548i	−0.00975405	−	0.0490369i
$414$		0			0
$415$	−19.6187	+	17.3379i	−0.963042	+	0.851083i
$416$		0			0
$417$	9.96742	+	4.12864i	0.488106	+	0.202180i
$418$		0			0
$419$	−14.9919	−	2.98207i	−0.732401	−	0.145684i	−0.185219	−	0.982697i	$-0.559299\pi$
$419$	−14.9919	−	2.98207i	−0.732401	−	0.145684i	−0.547182	+	0.837014i	$0.684299\pi$
$420$		0			0
$421$	−9.05493	+	9.05493i	−0.441310	+	0.441310i	−0.892452	−	0.451142i	$-0.851017\pi$
$421$	−9.05493	+	9.05493i	−0.441310	+	0.441310i	0.451142	+	0.892452i	$0.351017\pi$
$422$		0			0
$423$	−1.83412	−	4.42796i	−0.0891780	−	0.215295i
$424$		0			0
$425$	4.21432	−	20.1802i	0.204425	−	0.978882i
$426$		0			0
$427$	−0.370823	−	0.895246i	−0.0179454	−	0.0433240i
$428$		0			0
$429$	−40.1701	+	40.1701i	−1.93943	+	1.93943i
$430$		0			0
$431$	35.6602	+	7.09326i	1.71769	+	0.341670i	0.953057	−	0.302791i	$-0.0979185\pi$
$431$	35.6602	+	7.09326i	1.71769	+	0.341670i	0.764637	+	0.644462i	$0.222918\pi$
$432$		0			0
$433$	23.3826	+	9.68540i	1.12370	+	0.465451i	0.865634	−	0.500677i	$-0.166916\pi$
$433$	23.3826	+	9.68540i	1.12370	+	0.465451i	0.258063	+	0.966128i	$0.416916\pi$
$434$		0			0
$435$	−28.3378	+	25.0434i	−1.35869	+	1.20074i
$436$		0			0
$437$	3.88300	+	19.5211i	0.185749	+	0.933823i
$438$		0			0
$439$	−22.5630	+	4.48807i	−1.07687	+	0.214204i	−0.701500	−	0.712669i	$-0.747486\pi$
$439$	−22.5630	+	4.48807i	−1.07687	+	0.214204i	−0.375375	+	0.926873i	$0.622486\pi$
$440$		0			0
$441$		−	14.7063i		−	0.700302i
$442$		0			0
$443$	14.6033	−	14.6033i	0.693824	−	0.693824i	−0.269247	−	0.963071i	$-0.586775\pi$
$443$	14.6033	−	14.6033i	0.693824	−	0.693824i	0.963071	+	0.269247i	$0.0867749\pi$
$444$		0			0
$445$	−26.7696	−	13.0747i	−1.26900	−	0.619798i
$446$		0			0
$447$	−47.0748	+	9.36375i	−2.22656	+	0.442890i
$448$		0			0
$449$	−16.5492	+	11.0578i	−0.781006	+	0.521852i	−0.880989	−	0.473138i	$-0.843121\pi$
$449$	−16.5492	+	11.0578i	−0.781006	+	0.521852i	0.0999825	+	0.994989i	$0.468121\pi$
$450$		0			0
$451$	−26.4151	+	10.9415i	−1.24384	+	0.515215i
$452$		0			0
$453$	2.17204	+	3.25069i	0.102051	+	0.152731i
$454$		0			0
$455$	−0.213865	−	1.57795i	−0.0100262	−	0.0739755i
$456$		0			0
$457$	16.7056	−	6.91968i	0.781455	−	0.323689i	0.0439524	−	0.999034i	$-0.486005\pi$
$457$	16.7056	−	6.91968i	0.781455	−	0.323689i	0.737502	+	0.675344i	$0.236005\pi$
$458$		0			0
$459$	7.27403	−	4.03492i	0.339523	−	0.188334i
$460$		0			0
$461$	−6.65135	−	2.75508i	−0.309784	−	0.128317i	0.222375	−	0.974961i	$-0.428619\pi$
$461$	−6.65135	−	2.75508i	−0.309784	−	0.128317i	−0.532159	+	0.846644i	$0.678619\pi$
$462$		0			0
$463$	25.8848			1.20297			0.601485	−	0.798884i	$-0.294576\pi$
$463$	25.8848			1.20297			0.601485	+	0.798884i	$0.294576\pi$
$464$		0			0
$465$	2.03638	−	32.9964i	0.0944346	−	1.53017i
$466$		0			0
$467$	−7.04646	+	17.0117i	−0.326071	+	0.787206i	0.672805	+	0.739820i	$0.265089\pi$
$467$	−7.04646	+	17.0117i	−0.326071	+	0.787206i	−0.998877	+	0.0473865i	$0.984911\pi$
$468$		0			0
$469$	−0.472624	−	0.707332i	−0.0218238	−	0.0326616i
$470$		0			0
$471$	−34.5101	−	23.0589i	−1.59014	−	1.06250i
$472$		0			0
$473$	−20.4668	−	13.6754i	−0.941062	−	0.628798i
$474$		0			0
$475$	4.14177	+	14.9988i	0.190038	+	0.688193i
$476$		0			0
$477$	−11.7830	−	11.7830i	−0.539505	−	0.539505i
$478$		0			0
$479$	3.42177	+	17.2024i	0.156345	+	0.785997i	0.976778	+	0.214255i	$0.0687323\pi$
$479$	3.42177	+	17.2024i	0.156345	+	0.785997i	−0.820433	+	0.571742i	$0.806268\pi$
$480$		0			0
$481$	−0.204661	+	0.306297i	−0.00933173	+	0.0139659i
$482$		0			0
$483$	−2.06487	−	0.410728i	−0.0939548	−	0.0186888i
$484$		0			0
$485$	5.03331	−	2.93163i	0.228551	−	0.133118i
$486$		0			0
$487$	−33.4007	+	22.3176i	−1.51353	+	1.01131i	−0.526607	+	0.850109i	$0.676536\pi$
$487$	−33.4007	+	22.3176i	−1.51353	+	1.01131i	−0.986922	+	0.161199i	$0.948464\pi$
$488$		0			0
$489$	−4.24257	−	4.24257i	−0.191856	−	0.191856i
$490$		0			0
$491$	1.76892	−	4.27055i	0.0798302	−	0.192727i	−0.878925	−	0.476960i	$-0.841739\pi$
$491$	1.76892	−	4.27055i	0.0798302	−	0.192727i	0.958755	+	0.284233i	$0.0917388\pi$
$492$		0			0
$493$	3.50225	+	30.6568i	0.157733	+	1.38071i
$494$		0			0
$495$	12.1936	+	20.9352i	0.548063	+	0.940968i
$496$		0			0
$497$			0.0573516i			0.00257257i
$498$		0			0
$499$	1.72698	−	8.68211i	0.0773102	−	0.388665i	−0.922685	−	0.385555i	$-0.874010\pi$
$499$	1.72698	−	8.68211i	0.0773102	−	0.388665i	0.999995	−	0.00310992i	$-0.000989920\pi$
$500$		0			0
$501$	8.67715	+	20.9485i	0.387666	+	0.935909i
$502$		0			0
$503$	5.44421	−	27.3699i	0.242745	−	1.22036i	−0.646493	−	0.762920i	$-0.723765\pi$
$503$	5.44421	−	27.3699i	0.242745	−	1.22036i	0.889239	−	0.457443i	$-0.151235\pi$
$504$		0			0
$505$	−32.7977	+	11.2730i	−1.45948	+	0.501640i
$506$		0			0
$507$	13.6891	−	20.4872i	0.607954	−	0.909868i
$508$		0			0
$509$	−20.1658			−0.893832			−0.446916	−	0.894576i	$-0.647478\pi$
$509$	−20.1658			−0.893832			−0.446916	+	0.894576i	$0.647478\pi$
$510$		0			0
$511$	1.40563			0.0621813
$512$		0			0
$513$	−3.48809	+	5.22029i	−0.154003	+	0.230482i
$514$		0			0
$515$	34.7220	+	16.9587i	1.53004	+	0.747291i
$516$		0			0
$517$	−2.28137	+	11.4692i	−0.100335	+	0.504416i
$518$		0			0
$519$	3.91197	+	9.44432i	0.171716	+	0.414560i
$520$		0			0
$521$	−2.25339	+	11.3286i	−0.0987229	+	0.496313i	0.899511	+	0.436899i	$0.143923\pi$
$521$	−2.25339	+	11.3286i	−0.0987229	+	0.496313i	−0.998233	+	0.0594144i	$0.981077\pi$
$522$		0			0
$523$			21.3896i			0.935304i	0.883913	+	0.467652i	$0.154900\pi$
$523$			21.3896i			0.935304i	−0.883913	+	0.467652i	$0.845100\pi$
$524$		0			0
$525$	−1.63340	−	0.202382i	−0.0712876	−	0.00883267i
$526$		0			0
$527$	−21.1147	−	16.7850i	−0.919771	−	0.731167i
$528$		0			0
$529$	6.85185	−	16.5418i	0.297906	−	0.719210i
$530$		0			0
$531$	−10.3944	−	10.3944i	−0.451077	−	0.451077i
$532$		0			0
$533$	22.6054	−	15.1044i	0.979147	−	0.654245i
$534$		0			0
$535$	7.57456	+	13.0048i	0.327477	+	0.562244i
$536$		0			0
$537$	44.0685	+	8.76577i	1.90170	+	0.378271i
$538$		0			0
$539$	−19.9350	+	29.8348i	−0.858661	+	1.28508i
$540$		0			0
$541$	8.30277	+	41.7409i	0.356964	+	1.79458i	0.574475	+	0.818522i	$0.305206\pi$
$541$	8.30277	+	41.7409i	0.356964	+	1.79458i	−0.217511	+	0.976058i	$0.569794\pi$
$542$		0			0
$543$	0.773831	+	0.773831i	0.0332083	+	0.0332083i
$544$		0			0
$545$	3.06456	+	2.33301i	0.131271	+	0.0999350i
$546$		0			0
$547$	17.0000	+	11.3590i	0.726868	+	0.485677i	0.863121	−	0.504997i	$-0.168506\pi$
$547$	17.0000	+	11.3590i	0.726868	+	0.485677i	−0.136254	+	0.990674i	$0.543506\pi$
$548$		0			0
$549$	−11.6563	−	7.78851i	−0.497480	−	0.332406i
$550$		0			0
$551$	−12.9390	−	19.3646i	−0.551221	−	0.824961i
$552$		0			0
$553$	−0.459056	+	1.10826i	−0.0195210	+	0.0471279i
$554$		0			0
$555$	0.252142	+	0.285311i	0.0107028	+	0.0121108i
$556$		0			0
$557$	−5.16909			−0.219021			−0.109511	−	0.993986i	$-0.534928\pi$
$557$	−5.16909			−0.219021			−0.109511	+	0.993986i	$0.534928\pi$
$558$		0			0
$559$	21.6245	+	8.95715i	0.914618	+	0.378847i
$560$		0			0
$561$	47.7456	+	3.95289i	2.01582	+	0.166891i
$562$		0			0
$563$	−22.5784	+	9.35229i	−0.951568	+	0.394152i	−0.803820	−	0.594873i	$-0.797202\pi$
$563$	−22.5784	+	9.35229i	−0.951568	+	0.394152i	−0.147748	+	0.989025i	$0.547202\pi$
$564$		0			0
$565$	8.45828	−	11.1105i	0.355842	−	0.467422i
$566$		0			0
$567$	−0.880546	−	1.31783i	−0.0369794	−	0.0553437i
$568$		0			0
$569$	−1.57885	+	0.653980i	−0.0661887	+	0.0274163i	−0.415532	−	0.909578i	$-0.636405\pi$
$569$	−1.57885	+	0.653980i	−0.0661887	+	0.0274163i	0.349343	+	0.936995i	$0.386405\pi$
$570$		0			0
$571$	−30.9104	+	20.6536i	−1.29356	+	0.864328i	−0.995910	−	0.0903473i	$-0.971202\pi$
$571$	−30.9104	+	20.6536i	−1.29356	+	0.864328i	−0.297648	+	0.954676i	$0.596202\pi$
$572$		0			0
$573$	13.5075	−	2.68681i	0.564284	−	0.112243i
$574$		0			0
$575$	10.0479	−	30.3588i	0.419026	−	1.26605i
$576$		0			0
$577$	−26.2464	+	26.2464i	−1.09265	+	1.09265i	−0.0974080	+	0.995245i	$0.531055\pi$
$577$	−26.2464	+	26.2464i	−1.09265	+	1.09265i	−0.995245	+	0.0974080i	$0.968945\pi$
$578$		0			0
$579$		−	14.4613i		−	0.600993i
$580$		0			0
$581$	1.67273	−	0.332728i	0.0693967	−	0.0138039i
$582$		0			0
$583$	7.93190	+	39.8764i	0.328506	+	1.65151i
$584$		0			0
$585$	−15.2556	−	17.2624i	−0.630741	−	0.713714i
$586$		0			0
$587$	1.80716	+	0.748550i	0.0745894	+	0.0308960i	0.419666	−	0.907678i	$-0.362147\pi$
$587$	1.80716	+	0.748550i	0.0745894	+	0.0308960i	−0.345077	+	0.938574i	$0.612147\pi$
$588$		0			0
$589$	19.9678	+	3.97185i	0.822760	+	0.163657i
$590$		0			0
$591$	−0.139203	+	0.139203i	−0.00572606	+	0.00572606i
$592$		0			0
$593$	−4.41519	−	10.6592i	−0.181310	−	0.437721i	0.806927	−	0.590651i	$-0.201129\pi$
$593$	−4.41519	−	10.6592i	−0.181310	−	0.437721i	−0.988237	+	0.152930i	$0.951129\pi$
$594$		0			0
$595$	−0.898829	+	0.997750i	−0.0368484	+	0.0409038i
$596$		0			0
$597$	1.44661	+	3.49243i	0.0592059	+	0.142936i
$598$		0			0
$599$	8.24683	−	8.24683i	0.336956	−	0.336956i	−0.518264	−	0.855221i	$-0.673422\pi$
$599$	8.24683	−	8.24683i	0.336956	−	0.336956i	0.855221	+	0.518264i	$0.173422\pi$
$600$		0			0
$601$	−37.3744	−	7.43422i	−1.52453	−	0.303248i	−0.639504	−	0.768787i	$-0.720860\pi$
$601$	−37.3744	−	7.43422i	−1.52453	−	0.303248i	−0.885027	+	0.465539i	$0.845860\pi$
$602$		0			0
$603$	−11.3705	−	4.70983i	−0.463044	−	0.191799i
$604$		0			0
$605$	2.12610	−	34.4502i	0.0864381	−	1.40060i
$606$		0			0
$607$	−3.55178	−	17.8560i	−0.144162	−	0.724753i	−0.983466	−	0.181091i	$-0.942037\pi$
$607$	−3.55178	−	17.8560i	−0.144162	−	0.724753i	0.839304	−	0.543662i	$-0.182963\pi$
$608$		0			0
$609$	2.41615	−	0.480602i	0.0979073	−	0.0194750i
$610$		0			0
$611$		−	11.1196i		−	0.449850i
$612$		0			0
$613$	17.3366	−	17.3366i	0.700217	−	0.700217i	−0.264240	−	0.964457i	$-0.585121\pi$
$613$	17.3366	−	17.3366i	0.700217	−	0.700217i	0.964457	+	0.264240i	$0.0851212\pi$
$614$		0			0
$615$	−9.13414	−	26.5750i	−0.368324	−	1.07161i
$616$		0			0
$617$	−25.0260	+	4.97798i	−1.00751	+	0.200406i	−0.671145	−	0.741327i	$-0.734197\pi$
$617$	−25.0260	+	4.97798i	−1.00751	+	0.200406i	−0.336363	+	0.941732i	$0.609197\pi$
$618$		0			0
$619$	−5.31105	+	3.54873i	−0.213469	+	0.142635i	−0.657708	−	0.753273i	$-0.728474\pi$
$619$	−5.31105	+	3.54873i	−0.213469	+	0.142635i	0.444239	+	0.895908i	$0.353474\pi$
$620$		0			0
$621$	11.9208	−	4.93777i	0.478366	−	0.198146i
$622$		0			0
$623$	1.07817	+	1.61360i	0.0431962	+	0.0646476i
$624$		0			0
$625$	6.10143	−	24.2440i	0.244057	−	0.969761i
$626$		0			0
$627$	−33.4082	+	13.8381i	−1.33419	+	0.552641i
$628$		0			0
$629$	0.308660	−	0.0352614i	0.0123071	−	0.00140596i
$630$		0			0
$631$	−9.60924	−	3.98028i	−0.382538	−	0.158452i	0.183124	−	0.983090i	$-0.441379\pi$
$631$	−9.60924	−	3.98028i	−0.382538	−	0.158452i	−0.565661	+	0.824638i	$0.691379\pi$
$632$		0			0
$633$	62.6208			2.48896
$634$		0			0
$635$	−27.1530	−	1.67574i	−1.07753	−	0.0664999i
$636$		0			0
$637$	13.0570	−	31.5225i	0.517338	−	1.24897i
$638$		0			0
$639$	0.460970	+	0.689891i	0.0182357	+	0.0272917i
$640$		0			0
$641$	29.4482	+	19.6767i	1.16313	+	0.777181i	0.978626	−	0.205650i	$-0.0659308\pi$
$641$	29.4482	+	19.6767i	1.16313	+	0.777181i	0.184508	+	0.982831i	$0.440931\pi$
$642$		0			0
$643$	5.46538	+	3.65185i	0.215534	+	0.144015i	0.658651	−	0.752449i	$-0.271127\pi$
$643$	5.46538	+	3.65185i	0.215534	+	0.144015i	−0.443117	+	0.896464i	$0.646127\pi$
$644$		0			0
$645$	14.6543	−	19.2494i	0.577014	−	0.757946i
$646$		0			0
$647$	26.2688	+	26.2688i	1.03273	+	1.03273i	0.999446	+	0.0332876i	$0.0105977\pi$
$647$	26.2688	+	26.2688i	1.03273	+	1.03273i	0.0332876	+	0.999446i	$0.489402\pi$
$648$		0			0
$649$	6.99715	+	35.1770i	0.274662	+	1.38082i
$650$		0			0
$651$	−1.19642	+	1.79057i	−0.0468913	+	0.0701778i
$652$		0			0
$653$	−28.0429	−	5.57808i	−1.09740	−	0.218287i	−0.386999	−	0.922080i	$-0.626488\pi$
$653$	−28.0429	−	5.57808i	−1.09740	−	0.218287i	−0.710405	+	0.703793i	$0.751488\pi$
$654$		0			0
$655$	−7.41773	+	28.1117i	−0.289835	+	1.09841i
$656$		0			0
$657$	16.9085	−	11.2979i	0.659663	−	0.440773i
$658$		0			0
$659$	−0.237874	−	0.237874i	−0.00926624	−	0.00926624i	0.702458	−	0.711725i	$-0.252086\pi$
$659$	−0.237874	−	0.237874i	−0.00926624	−	0.00926624i	−0.711725	+	0.702458i	$0.752086\pi$
$660$		0			0
$661$	14.8040	−	35.7401i	0.575810	−	1.39013i	−0.320731	−	0.947170i	$-0.603929\pi$
$661$	14.8040	−	35.7401i	0.575810	−	1.39013i	0.896542	−	0.442959i	$-0.146071\pi$
$662$		0			0
$663$	−45.2615	+	5.17070i	−1.75781	+	0.200813i
$664$		0			0
$665$	0.258604	−	0.980054i	0.0100282	−	0.0380049i
$666$		0			0
$667$			47.8636i			1.85328i
$668$		0			0
$669$	−4.84647	+	24.3649i	−0.187376	+	0.942000i
$670$		0			0
$671$	13.0896	+	31.6012i	0.505319	+	1.21995i
$672$		0			0
$673$	2.78502	−	14.0012i	0.107355	−	0.539708i	−0.889254	−	0.457414i	$-0.848776\pi$
$673$	2.78502	−	14.0012i	0.107355	−	0.539708i	0.996608	−	0.0822932i	$-0.0262244\pi$
$674$		0			0
$675$	9.01272	−	4.53035i	0.346900	−	0.174373i
$676$		0			0
$677$	6.74082	−	10.0884i	0.259071	−	0.387727i	−0.679018	−	0.734122i	$-0.737594\pi$
$677$	6.74082	−	10.0884i	0.259071	−	0.387727i	0.938089	+	0.346395i	$0.112594\pi$
$678$		0			0
$679$	−0.379433			−0.0145613
$680$		0			0
$681$	−14.2896			−0.547580
$682$		0			0
$683$	−5.28252	+	7.90585i	−0.202130	+	0.302509i	−0.918661	−	0.395046i	$-0.870729\pi$
$683$	−5.28252	+	7.90585i	−0.202130	+	0.302509i	0.716531	+	0.697555i	$0.245729\pi$
$684$		0			0
$685$	16.8830	−	34.5671i	0.645068	−	1.32074i
$686$		0			0
$687$	1.21692	−	6.11789i	0.0464286	−	0.233412i
$688$		0			0
$689$	−14.7948	−	35.7178i	−0.563637	−	1.36074i
$690$		0			0
$691$	4.11755	−	20.7003i	0.156639	−	0.787477i	−0.819962	−	0.572418i	$-0.806005\pi$
$691$	4.11755	−	20.7003i	0.156639	−	0.787477i	0.976601	−	0.215059i	$-0.0689945\pi$
$692$		0			0
$693$		−	1.57819i		−	0.0599504i
$694$		0			0
$695$	9.22417	−	5.37258i	0.349893	−	0.203793i
$696$		0			0
$697$	−22.0416	−	6.31316i	−0.834886	−	0.239128i
$698$		0			0
$699$	11.5131	−	27.7950i	0.435465	−	1.05130i
$700$		0			0
$701$	−6.92839	−	6.92839i	−0.261682	−	0.261682i	0.564055	−	0.825737i	$-0.309240\pi$
$701$	−6.92839	−	6.92839i	−0.261682	−	0.261682i	−0.825737	+	0.564055i	$0.809240\pi$
$702$		0			0
$703$	−0.194967	+	0.130273i	−0.00735333	+	0.00491334i
$704$		0			0
$705$	−11.1129	−	2.93233i	−0.418536	−	0.110438i
$706$		0			0
$707$	2.21573	+	0.440735i	0.0833310	+	0.0165756i
$708$		0			0
$709$	16.2911	−	24.3814i	0.611826	−	0.915663i	−0.388156	−	0.921594i	$-0.626888\pi$
$709$	16.2911	−	24.3814i	0.611826	−	0.915663i	0.999982	+	0.00593073i	$0.00188782\pi$
$710$		0			0
$711$	3.38571	+	17.0211i	0.126974	+	0.638342i
$712$		0			0
$713$	−29.5858	−	29.5858i	−1.10800	−	1.10800i
$714$		0			0
$715$	7.54921	+	55.6999i	0.282324	+	2.08306i
$716$		0			0
$717$	14.4661	+	9.66594i	0.540246	+	0.360981i
$718$		0			0
$719$	−23.1362	−	15.4591i	−0.862833	−	0.576527i	0.0435175	−	0.999053i	$-0.486144\pi$
$719$	−23.1362	−	15.4591i	−0.862833	−	0.576527i	−0.906351	+	0.422526i	$0.861144\pi$
$720$		0			0
$721$	−1.39847	−	2.09295i	−0.0520816	−	0.0779457i
$722$		0			0
$723$	−1.05050	+	2.53612i	−0.0390683	+	0.0943193i
$724$		0			0
$725$	2.73197	+	37.3188i	0.101463	+	1.38598i
$726$		0			0
$727$	3.29271			0.122120			0.0610598	−	0.998134i	$-0.480552\pi$
$727$	3.29271			0.122120			0.0610598	+	0.998134i	$0.480552\pi$
$728$		0			0
$729$	−8.54767	−	3.54056i	−0.316580	−	0.131132i
$730$		0			0
$731$	−6.02344	−	18.7977i	−0.222785	−	0.695259i
$732$		0			0
$733$	7.11097	−	2.94546i	0.262650	−	0.108793i	−0.247473	−	0.968895i	$-0.579600\pi$
$733$	7.11097	−	2.94546i	0.262650	−	0.108793i	0.510123	+	0.860102i	$0.329600\pi$
$734$		0			0
$735$	−28.0603	−	21.3619i	−1.03502	−	0.787947i
$736$		0			0
$737$	16.6831	+	24.9680i	0.614530	+	0.919709i
$738$		0			0
$739$	34.9301	−	14.4685i	1.28493	−	0.532234i	0.367457	−	0.930041i	$-0.380229\pi$
$739$	34.9301	−	14.4685i	1.28493	−	0.532234i	0.917469	+	0.397807i	$0.130229\pi$
$740$		0			0
$741$	28.5898	−	19.1031i	1.05027	−	0.701770i
$742$		0			0
$743$	−5.23703	+	1.04171i	−0.192128	+	0.0382166i	−0.290216	−	0.956961i	$-0.593727\pi$
$743$	−5.23703	+	1.04171i	−0.192128	+	0.0382166i	0.0980884	+	0.995178i	$0.468727\pi$
$744$		0			0
$745$	−20.8418	+	42.6724i	−0.763585	+	1.56340i
$746$		0			0
$747$	17.4472	−	17.4472i	0.638361	−	0.638361i
$748$		0			0
$749$		−	0.980354i		−	0.0358214i
$750$		0			0
$751$	−23.2719	+	4.62908i	−0.849205	+	0.168917i	−0.600463	−	0.799652i	$-0.705017\pi$
$751$	−23.2719	+	4.62908i	−0.849205	+	0.168917i	−0.248742	+	0.968570i	$0.580017\pi$
$752$		0			0
$753$	8.06184	+	40.5296i	0.293790	+	1.47698i
$754$		0			0
$755$	3.86094	+	0.238278i	0.140514	+	0.00867181i
$756$		0			0
$757$	−4.25401	−	1.76207i	−0.154615	−	0.0640434i	0.304034	−	0.952661i	$-0.401666\pi$
$757$	−4.25401	−	1.76207i	−0.154615	−	0.0640434i	−0.458649	+	0.888618i	$0.651666\pi$
$758$		0			0
$759$	72.8875	+	14.4982i	2.64565	+	0.526253i
$760$		0			0
$761$	33.0842	−	33.0842i	1.19930	−	1.19930i	0.224925	−	0.974376i	$-0.427786\pi$
$761$	33.0842	−	33.0842i	1.19930	−	1.19930i	0.974376	−	0.224925i	$-0.0722136\pi$
$762$		0			0
$763$	−0.0960122	−	0.231794i	−0.00347587	−	0.00839150i
$764$		0			0
$765$	−2.79261	+	19.2265i	−0.100967	+	0.695137i
$766$		0			0
$767$	−13.0513	−	31.5085i	−0.471254	−	1.13771i
$768$		0			0
$769$	36.7419	−	36.7419i	1.32495	−	1.32495i	0.415228	−	0.909717i	$-0.363702\pi$
$769$	36.7419	−	36.7419i	1.32495	−	1.32495i	0.909717	−	0.415228i	$-0.136298\pi$
$770$		0			0
$771$	36.1782	+	7.19630i	1.30293	+	0.259168i
$772$		0			0
$773$	−25.9297	−	10.7404i	−0.932627	−	0.386307i	−0.135952	−	0.990715i	$-0.543409\pi$
$773$	−25.9297	−	10.7404i	−0.932627	−	0.386307i	−0.796674	+	0.604409i	$0.793409\pi$
$774$		0			0
$775$	−24.7565	−	21.3791i	−0.889281	−	0.767960i
$776$		0			0
$777$	−0.00483881	−	0.0243263i	−0.000173591	−	0.000872702i
$778$		0			0
$779$	16.9730	−	3.37614i	0.608121	−	0.120963i
$780$		0			0
$781$		−	2.02445i		−	0.0724404i
$782$		0			0
$783$	−10.6760	+	10.6760i	−0.381528	+	0.381528i
$784$		0			0
$785$	−38.8366	+	13.3486i	−1.38614	+	0.476433i
$786$		0			0
$787$	52.5875	−	10.4603i	1.87454	−	0.372869i	0.879805	−	0.475335i	$-0.157673\pi$
$787$	52.5875	−	10.4603i	1.87454	−	0.372869i	0.994737	+	0.102466i	$0.0326732\pi$
$788$		0			0
$789$	28.4261	−	18.9937i	1.01199	−	0.676193i
$790$		0			0
$791$	−0.840365	+	0.348091i	−0.0298800	+	0.0123767i
$792$		0			0
$793$	−18.0698	−	27.0434i	−0.641679	−	0.960340i
$794$		0			0
$795$	−39.5979	+	5.36684i	−1.40439	+	0.190342i
$796$		0			0
$797$	14.2805	−	5.91516i	0.505840	−	0.209526i	−0.115144	−	0.993349i	$-0.536733\pi$
$797$	14.2805	−	5.91516i	0.505840	−	0.209526i	0.620984	+	0.783823i	$0.286733\pi$
$798$		0			0
$799$	−7.15540	+	6.06119i	−0.253140	+	0.214430i
$800$		0			0
$801$	25.9391	+	10.7443i	0.916512	+	0.379632i
$802$		0			0
$803$	−49.6170			−1.75095
$804$		0			0
$805$	−1.56090	+	1.37944i	−0.0550146	+	0.0486188i
$806$		0			0
$807$	5.91875	−	14.2891i	0.208350	−	0.503001i
$808$		0			0
$809$	18.0736	+	27.0490i	0.635433	+	0.950992i	0.999805	+	0.0197388i	$0.00628345\pi$
$809$	18.0736	+	27.0490i	0.635433	+	0.950992i	−0.364373	+	0.931253i	$0.618717\pi$
$810$		0			0
$811$	27.2786	+	18.2270i	0.957882	+	0.640036i	0.933085	−	0.359656i	$-0.117106\pi$
$811$	27.2786	+	18.2270i	0.957882	+	0.640036i	0.0247971	+	0.999693i	$0.492106\pi$
$812$		0			0
$813$	−36.0207	−	24.0683i	−1.26330	−	0.844110i
$814$		0			0
$815$	−5.88276	+	0.797311i	−0.206064	+	0.0279286i
$816$		0			0
$817$	10.5350	+	10.5350i	0.368573	+	0.368573i
$818$		0			0
$819$	0.292767	+	1.47184i	0.0102301	+	0.0514302i
$820$		0			0
$821$	−14.6490	+	21.9237i	−0.511253	+	0.765144i	−0.993854	−	0.110696i	$-0.964692\pi$
$821$	−14.6490	+	21.9237i	−0.511253	+	0.765144i	0.482602	+	0.875840i	$0.339692\pi$
$822$		0			0
$823$	43.0570	+	8.56458i	1.50087	+	0.298542i	0.876049	−	0.482223i	$-0.160170\pi$
$823$	43.0570	+	8.56458i	1.50087	+	0.298542i	0.624825	+	0.780765i	$0.285170\pi$
$824$		0			0
$825$	57.6573	+	7.14385i	2.00737	+	0.248717i
$826$		0			0
$827$	4.90120	−	3.27488i	0.170431	−	0.113879i	−0.467429	−	0.884031i	$-0.654820\pi$
$827$	4.90120	−	3.27488i	0.170431	−	0.113879i	0.637860	+	0.770152i	$0.279820\pi$
$828$		0			0
$829$	−9.07300	−	9.07300i	−0.315118	−	0.315118i	0.531770	−	0.846889i	$-0.321527\pi$
$829$	−9.07300	−	9.07300i	−0.315118	−	0.315118i	−0.846889	+	0.531770i	$0.821527\pi$
$830$		0			0
$831$	−22.2195	+	53.6425i	−0.770785	+	1.86084i
$832$		0			0
$833$	−27.4018	+	8.78049i	−0.949418	+	0.304226i
$834$		0			0
$835$	21.6926	+	5.72394i	0.750702	+	0.198085i
$836$		0			0
$837$		−	13.1982i		−	0.456198i
$838$		0			0
$839$	−2.22948	+	11.2084i	−0.0769703	+	0.386956i	0.923027	+	0.384735i	$0.125707\pi$
$839$	−2.22948	+	11.2084i	−0.0769703	+	0.386956i	−0.999998	+	0.00222120i	$0.999293\pi$
$840$		0			0
$841$	−10.3348	−	24.9505i	−0.356373	−	0.860362i
$842$		0			0
$843$	−5.35655	+	26.9292i	−0.184489	+	0.927490i
$844$		0			0
$845$	−7.92451	−	23.0557i	−0.272612	−	0.793139i
$846$		0			0
$847$	−1.24913	+	1.86946i	−0.0429206	+	0.0642353i
$848$		0			0
$849$	37.9660			1.30299
$850$		0			0
$851$	0.481901			0.0165194
$852$		0			0
$853$	26.6107	−	39.8257i	0.911132	−	1.36361i	−0.0203405	−	0.999793i	$-0.506475\pi$
$853$	26.6107	−	39.8257i	0.911132	−	1.36361i	0.931472	−	0.363812i	$-0.118525\pi$
$854$		0			0
$855$	−4.76652	−	13.8678i	−0.163012	−	0.474268i
$856$		0			0
$857$	−2.59513	+	13.0466i	−0.0886480	+	0.445664i	0.910812	+	0.412820i	$0.135456\pi$
$857$	−2.59513	+	13.0466i	−0.0886480	+	0.445664i	−0.999461	+	0.0328435i	$0.989544\pi$
$858$		0			0
$859$	−15.9762	−	38.5700i	−0.545102	−	1.31599i	−0.921084	−	0.389365i	$-0.872695\pi$
$859$	−15.9762	−	38.5700i	−0.545102	−	1.31599i	0.375982	−	0.926627i	$-0.377305\pi$
$860$		0			0
$861$	−0.357115	+	1.79534i	−0.0121704	+	0.0611849i
$862$		0			0
$863$		−	50.6771i		−	1.72507i	−0.505999	−	0.862534i	$-0.668876\pi$
$863$		−	50.6771i		−	1.72507i	0.505999	−	0.862534i	$-0.331124\pi$
$864$		0			0
$865$	9.77978	+	2.58056i	0.332522	+	0.0877416i
$866$		0			0
$867$	27.9990	+	26.3071i	0.950896	+	0.893436i
$868$		0			0
$869$	16.2041	−	39.1203i	0.549688	−	1.32706i
$870$		0			0
$871$	−20.1907	−	20.1907i	−0.684135	−	0.684135i
$872$		0			0
$873$	−4.56425	+	3.04974i	−0.154477	+	0.103218i
$874$		0			0
$875$	−1.13829	+	1.16463i	−0.0384811	+	0.0393717i
$876$		0			0
$877$	3.65086	+	0.726202i	0.123281	+	0.0245221i	0.256345	−	0.966585i	$-0.417482\pi$
$877$	3.65086	+	0.726202i	0.123281	+	0.0245221i	−0.133064	+	0.991107i	$0.542482\pi$
$878$		0			0
$879$	−13.2749	+	19.8672i	−0.447750	+	0.670105i
$880$		0			0
$881$	5.26746	+	26.4813i	0.177465	+	0.892178i	0.962199	+	0.272346i	$0.0877994\pi$
$881$	5.26746	+	26.4813i	0.177465	+	0.892178i	−0.784734	+	0.619832i	$0.787201\pi$
$882$		0			0
$883$	8.42922	+	8.42922i	0.283666	+	0.283666i	0.834569	−	0.550903i	$-0.185717\pi$
$883$	8.42922	+	8.42922i	0.283666	+	0.283666i	−0.550903	+	0.834569i	$0.685717\pi$
$884$		0			0
$885$	−34.9314	+	4.73437i	−1.17421	+	0.159144i
$886$		0			0
$887$	20.6756	+	13.8150i	0.694220	+	0.463863i	0.851953	−	0.523619i	$-0.175418\pi$
$887$	20.6756	+	13.8150i	0.694220	+	0.463863i	−0.157732	+	0.987482i	$0.550418\pi$
$888$		0			0
$889$	1.47347	+	0.984539i	0.0494185	+	0.0330204i
$890$		0			0
$891$	31.0823	+	46.5179i	1.04130	+	1.55841i
$892$		0			0
$893$	2.70862	−	6.53918i	0.0906404	−	0.218825i
$894$		0			0
$895$	33.3128	−	29.4400i	1.11352	−	0.984071i
$896$		0			0
$897$	−70.6654			−2.35945
$898$		0			0
$899$	45.2320	+	18.7357i	1.50857	+	0.624871i
$900$		0			0
$901$	−14.9197	+	28.9899i	−0.497048	+	0.965793i
$902$		0			0
$903$	−1.45597	+	0.603083i	−0.0484517	+	0.0200693i
$904$		0			0
$905$	1.07300	−	0.145427i	0.0356676	−	0.00483415i
$906$		0			0
$907$	−9.18892	−	13.7522i	−0.305113	−	0.456634i	0.646951	−	0.762531i	$-0.276044\pi$
$907$	−9.18892	−	13.7522i	−0.305113	−	0.456634i	−0.952065	+	0.305897i	$0.901044\pi$
$908$		0			0
$909$	30.1958	−	12.5075i	1.00153	−	0.414847i
$910$		0			0
$911$	4.01237	−	2.68098i	0.132936	−	0.0888248i	−0.487324	−	0.873221i	$-0.662027\pi$
$911$	4.01237	−	2.68098i	0.132936	−	0.0888248i	0.620260	+	0.784396i	$0.287027\pi$
$912$		0			0
$913$	−59.0456	+	11.7449i	−1.95413	+	0.388700i
$914$		0			0
$915$	−31.7924	+	10.9274i	−1.05102	+	0.361250i
$916$		0			0
$917$	1.33918	−	1.33918i	0.0442236	−	0.0442236i
$918$		0			0
$919$			28.3398i			0.934844i	0.884034	+	0.467422i	$0.154817\pi$
$919$			28.3398i			0.934844i	−0.884034	+	0.467422i	$0.845183\pi$
$920$		0			0
$921$	−13.8198	+	2.74893i	−0.455378	+	0.0905803i
$922$		0			0
$923$	0.375552	+	1.88803i	0.0123614	+	0.0621451i
$924$		0			0
$925$	0.375734	−	0.0275061i	0.0123541	−	0.000904394i
$926$		0			0
$927$	−33.6447	−	13.9361i	−1.10504	−	0.457722i
$928$		0			0
$929$	−35.3435	−	7.03026i	−1.15958	−	0.230655i	−0.422439	−	0.906391i	$-0.638826\pi$
$929$	−35.3435	−	7.03026i	−1.15958	−	0.230655i	−0.737144	+	0.675736i	$0.763826\pi$
$930$		0			0
$931$	15.3571	−	15.3571i	0.503309	−	0.503309i
$932$		0			0
$933$	27.0577	+	65.3232i	0.885831	+	2.13858i
$934$		0			0
$935$	31.7276	−	35.2194i	1.03760	−	1.15180i
$936$		0			0
$937$	15.4226	+	37.2335i	0.503835	+	1.21637i	0.947379	+	0.320113i	$0.103721\pi$
$937$	15.4226	+	37.2335i	0.503835	+	1.21637i	−0.443544	+	0.896252i	$0.646279\pi$
$938$		0			0
$939$	−21.5309	+	21.5309i	−0.702635	+	0.702635i
$940$		0			0
$941$	−12.7939	−	2.54486i	−0.417069	−	0.0829602i	−0.0179049	−	0.999840i	$-0.505700\pi$
$941$	−12.7939	−	2.54486i	−0.417069	−	0.0829602i	−0.399164	+	0.916880i	$0.630700\pi$
$942$		0			0
$943$	−32.8581	−	13.6103i	−1.07001	−	0.443211i
$944$		0			0
$945$	−0.655843	−	0.0404754i	−0.0213346	−	0.00131666i
$946$		0			0
$947$	7.64955	+	38.4569i	0.248577	+	1.24968i	0.880274	+	0.474466i	$0.157359\pi$
$947$	7.64955	+	38.4569i	0.248577	+	1.24968i	−0.631697	+	0.775215i	$0.717641\pi$
$948$		0			0
$949$	46.2735	−	9.20438i	1.50210	−	0.298787i
$950$		0			0
$951$			69.8595i			2.26535i
$952$		0			0
$953$	−35.9304	+	35.9304i	−1.16390	+	1.16390i	−0.180284	+	0.983615i	$0.557702\pi$
$953$	−35.9304	+	35.9304i	−1.16390	+	1.16390i	−0.983615	+	0.180284i	$0.942298\pi$
$954$		0			0
$955$	5.98029	−	12.2443i	0.193518	−	0.396217i
$956$		0			0
$957$	−85.2874	+	16.9647i	−2.75695	+	0.548391i
$958$		0			0
$959$	−2.08361	+	1.39222i	−0.0672833	+	0.0449573i
$960$		0			0
$961$	−10.9000	+	4.51493i	−0.351613	+	0.145643i
$962$		0			0
$963$	−7.87972	−	11.7928i	−0.253920	−	0.380019i
$964$		0			0
$965$	−11.3849	−	8.66719i	−0.366494	−	0.279007i
$966$		0			0
$967$	−6.01615	+	2.49197i	−0.193466	+	0.0801364i	−0.477313	−	0.878733i	$-0.658389\pi$
$967$	−6.01615	+	2.49197i	−0.193466	+	0.0801364i	0.283847	+	0.958870i	$0.408389\pi$
$968$		0			0
$969$	−27.8768	−	7.98448i	−0.895533	−	0.256498i
$970$		0			0
$971$	1.58783	+	0.657700i	0.0509558	+	0.0211066i	0.408016	−	0.912975i	$-0.366221\pi$
$971$	1.58783	+	0.657700i	0.0509558	+	0.0211066i	−0.357060	+	0.934081i	$0.616221\pi$
$972$		0			0
$973$	−0.695358			−0.0222921
$974$		0			0
$975$	−55.0972	+	4.03346i	−1.76452	+	0.129174i
$976$		0			0
$977$	10.8790	−	26.2642i	0.348050	−	0.840266i	−0.648801	−	0.760958i	$-0.724729\pi$
$977$	10.8790	−	26.2642i	0.348050	−	0.840266i	0.996850	−	0.0793075i	$-0.0252709\pi$
$978$		0			0
$979$	−38.0584	−	56.9584i	−1.21635	−	1.82040i
$980$		0			0
$981$	−3.01802	−	2.01657i	−0.0963579	−	0.0643843i
$982$		0			0
$983$	−17.9220	−	11.9751i	−0.571623	−	0.381946i	0.235904	−	0.971776i	$-0.424195\pi$
$983$	−17.9220	−	11.9751i	−0.571623	−	0.381946i	−0.807528	+	0.589830i	$0.799195\pi$
$984$		0			0
$985$	0.0261607	+	0.193020i	0.000833548	+	0.00615012i
$986$		0			0
$987$	0.529395	+	0.529395i	0.0168508	+	0.0168508i
$988$		0			0
$989$	−5.97349	−	30.0308i	−0.189946	−	0.954922i
$990$		0			0
$991$	30.4046	−	45.5038i	0.965835	−	1.44547i	0.0718306	−	0.997417i	$-0.477116\pi$
$991$	30.4046	−	45.5038i	0.965835	−	1.44547i	0.894005	−	0.448058i	$-0.147884\pi$
$992$		0			0
$993$	71.5801	+	14.2382i	2.27153	+	0.451835i
$994$		0			0
$995$	3.61648	+	0.954268i	0.114650	+	0.0302523i
$996$		0			0
$997$	−28.5735	+	19.0922i	−0.904933	+	0.604657i	−0.918573	−	0.395250i	$-0.870658\pi$
$997$	−28.5735	+	19.0922i	−0.904933	+	0.604657i	0.0136408	+	0.999907i	$0.495658\pi$
$998$		0			0
$999$	0.107488	+	0.107488i	0.00340077	+	0.00340077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	340.2.bd.a.57.3	✓	72
5.3	odd	4		340.2.bi.a.193.3	yes	72
17.3	odd	16		340.2.bi.a.37.3	yes	72
85.3	even	16	inner	340.2.bd.a.173.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
340.2.bd.a.57.3	✓	72	1.1	even	1	trivial
340.2.bd.a.173.3	yes	72	85.3	even	16	inner
340.2.bi.a.37.3	yes	72	17.3	odd	16
340.2.bi.a.193.3	yes	72	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25555 + 1.87906i) q^{3} +(0.726829 + 2.11464i) q^{5} +(0.0284166 - 0.142860i) q^{7} +(-0.806426 - 1.94689i) q^{9} +(-1.00307 + 5.04279i) q^{11} -4.88905i q^{13} +(-4.88612 - 1.28928i) q^{15} +(-3.14609 + 2.66498i) q^{17} +(1.19092 - 2.87515i) q^{19} +(0.232765 + 0.232765i) q^{21} +(-5.31781 + 3.55325i) q^{23} +(-3.94344 + 3.07397i) q^{25} +(-1.97869 - 0.393586i) q^{27} +(4.15774 - 6.22249i) q^{29} +(1.27629 + 6.41632i) q^{31} +(-8.21632 - 8.21632i) q^{33} +(0.322752 - 0.0437437i) q^{35} +(-0.0626495 - 0.0418610i) q^{37} +(9.18685 + 6.13846i) q^{39} +(3.08944 + 4.62367i) q^{41} +(-1.83208 + 4.42304i) q^{43} +(3.53084 - 3.12036i) q^{45} +2.27438 q^{47} +(6.44756 + 2.67066i) q^{49} +(-1.05761 - 9.25772i) q^{51} +(7.30566 - 3.02611i) q^{53} +(-11.3928 + 1.54410i) q^{55} +(3.90732 + 5.84772i) q^{57} +(6.44471 - 2.66949i) q^{59} +(5.53142 - 3.69598i) q^{61} +(-0.301048 + 0.0598821i) q^{63} +(10.3386 - 3.55351i) q^{65} +(4.12977 - 4.12977i) q^{67} -14.4538i q^{69} +(-0.386174 + 0.0768148i) q^{71} +(1.88265 + 9.46472i) q^{73} +(-0.824998 - 11.2695i) q^{75} +(0.691909 + 0.286598i) q^{77} +(-8.07724 - 1.60666i) q^{79} +(7.69417 - 7.69417i) q^{81} +(4.48081 + 10.8176i) q^{83} +(-7.92216 - 4.71587i) q^{85} +(6.47222 + 15.6253i) q^{87} +(-9.42104 + 9.42104i) q^{89} +(-0.698450 - 0.138930i) q^{91} +(-13.6591 - 5.65780i) q^{93} +(6.94551 + 0.428642i) q^{95} +(-0.508199 - 2.55489i) q^{97} +(10.6266 - 2.11377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{15} + 8 q^{25} - 48 q^{27} - 32 q^{31} + 16 q^{33} + 32 q^{37} - 32 q^{39} - 40 q^{41} + 80 q^{47} - 40 q^{53} + 16 q^{55} + 8 q^{57} + 112 q^{59} - 48 q^{63} - 32 q^{67} - 16 q^{71} + 8 q^{73}+ \cdots + 96 q^{99}+O(q^{100}) \) 72 * q + 24 * q^15 + 8 * q^25 - 48 * q^27 - 32 * q^31 + 16 * q^33 + 32 * q^37 - 32 * q^39 - 40 * q^41 + 80 * q^47 - 40 * q^53 + 16 * q^55 + 8 * q^57 + 112 * q^59 - 48 * q^63 - 32 * q^67 - 16 * q^71 + 8 * q^73 - 88 * q^75 - 16 * q^77 - 64 * q^79 - 48 * q^81 - 40 * q^83 - 40 * q^85 - 8 * q^87 - 48 * q^91 - 120 * q^93 - 48 * q^95 - 80 * q^97 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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