LMFDB - Embedded newform 720.2.bg.a.557.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(53,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 3]))

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

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

chi := DirichletCharacter("720.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bg (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.11
Character	$\chi$	$=$	720.557
Dual form			720.2.bg.a.53.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01816 + 0.981505i) q^{2} +(0.0732970 - 1.99866i) q^{4} +(1.34765 - 1.78433i) q^{5} +(3.52140 - 3.52140i) q^{7} +(1.88706 + 2.10689i) q^{8} +O(q^{10})$	\(q+(-1.01816 + 0.981505i) q^{2} +(0.0732970 - 1.99866i) q^{4} +(1.34765 - 1.78433i) q^{5} +(3.52140 - 3.52140i) q^{7} +(1.88706 + 2.10689i) q^{8} +(0.379207 + 3.13946i) q^{10} +(0.794589 + 0.794589i) q^{11} -1.81495 q^{13} +(-0.129076 + 7.04162i) q^{14} +(-3.98926 - 0.292991i) q^{16} +(0.579924 - 0.579924i) q^{17} +(4.07807 - 4.07807i) q^{19} +(-3.46749 - 2.82428i) q^{20} +(-1.58891 - 0.0291254i) q^{22} +(-4.47496 + 4.47496i) q^{23} +(-1.36768 - 4.80931i) q^{25} +(1.84791 - 1.78138i) q^{26} +(-6.77997 - 7.29618i) q^{28} +(-2.53613 - 2.53613i) q^{29} -8.04252 q^{31} +(4.34927 - 3.61716i) q^{32} +(-0.0212569 + 1.15965i) q^{34} +(-1.53773 - 11.0290i) q^{35} +5.45883 q^{37} +(-0.149480 + 8.15476i) q^{38} +(6.30249 - 0.527791i) q^{40} +3.39090 q^{41} +4.86388i q^{43} +(1.64635 - 1.52987i) q^{44} +(0.164028 - 8.94842i) q^{46} +(-5.83824 + 5.83824i) q^{47} -17.8006i q^{49} +(6.11287 + 3.55426i) q^{50} +(-0.133030 + 3.62746i) q^{52} +7.71651 q^{53} +(2.48864 - 0.346982i) q^{55} +(14.0643 + 0.774108i) q^{56} +(5.07142 + 0.0929611i) q^{58} +(3.16642 - 3.16642i) q^{59} +(2.48943 + 2.48943i) q^{61} +(8.18857 - 7.89377i) q^{62} +(-0.877989 + 7.95167i) q^{64} +(-2.44591 + 3.23847i) q^{65} +2.85214i q^{67} +(-1.11656 - 1.20158i) q^{68} +(12.3906 + 9.71996i) q^{70} -7.31072 q^{71} +(10.1613 + 10.1613i) q^{73} +(-5.55796 + 5.35787i) q^{74} +(-7.85174 - 8.44956i) q^{76} +5.59614 q^{77} +9.50285i q^{79} +(-5.89891 + 6.72330i) q^{80} +(-3.45247 + 3.32818i) q^{82} -10.8245i q^{83} +(-0.253242 - 1.81631i) q^{85} +(-4.77392 - 4.95221i) q^{86} +(-0.174674 + 3.17355i) q^{88} -8.83938i q^{89} +(-6.39116 + 6.39116i) q^{91} +(8.61591 + 9.27191i) q^{92} +(0.213999 - 11.6745i) q^{94} +(-1.78081 - 12.7724i) q^{95} +(2.78908 + 2.78908i) q^{97} +(17.4713 + 18.1238i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{4}+O(q^{10}) $ 96 * q - 8 * q^4	$ 96 q - 8 q^{4} + 8 q^{16} - 16 q^{19} + 16 q^{22} - 32 q^{28} + 8 q^{34} + 40 q^{40} + 8 q^{46} + 56 q^{52} + 16 q^{58} + 32 q^{61} - 8 q^{64} + 56 q^{70} + 8 q^{76} - 80 q^{82} - 64 q^{88} - 40 q^{94}+O(q^{100}) $ 96 * q - 8 * q^4 + 8 * q^16 - 16 * q^19 + 16 * q^22 - 32 * q^28 + 8 * q^34 + 40 * q^40 + 8 * q^46 + 56 * q^52 + 16 * q^58 + 32 * q^61 - 8 * q^64 + 56 * q^70 + 8 * q^76 - 80 * q^82 - 64 * q^88 - 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.01816	+	0.981505i	−0.719947	+	0.694029i
$2$	−1.01816	+	0.981505i	−0.719947	+	0.694029i
$3$		0			0
$3$		0			0
$4$	0.0732970	−	1.99866i	0.0366485	−	0.999328i
$5$	1.34765	−	1.78433i	0.602688	−	0.797977i
$5$	1.34765	−	1.78433i	0.602688	−	0.797977i
$6$		0			0
$7$	3.52140	−	3.52140i	1.33097	−	1.33097i	0.426458	−	0.904507i	$-0.359761\pi$
$7$	3.52140	−	3.52140i	1.33097	−	1.33097i	0.904507	−	0.426458i	$-0.140239\pi$
$8$	1.88706	+	2.10689i	0.667177	+	0.744899i
$9$		0			0
$10$	0.379207	+	3.13946i	0.119916	+	0.992784i
$11$	0.794589	+	0.794589i	0.239578	+	0.239578i	0.816675	−	0.577098i	$-0.195815\pi$
$11$	0.794589	+	0.794589i	0.239578	+	0.239578i	−0.577098	+	0.816675i	$0.695815\pi$
$12$		0			0
$13$	−1.81495			−0.503376			−0.251688	−	0.967808i	$-0.580986\pi$
$13$	−1.81495			−0.503376			−0.251688	+	0.967808i	$0.580986\pi$
$14$	−0.129076	+	7.04162i	−0.0344970	+	1.88195i
$15$		0			0
$16$	−3.98926	−	0.292991i	−0.997314	−	0.0732478i
$17$	0.579924	−	0.579924i	0.140652	−	0.140652i	−0.633275	−	0.773927i	$-0.718290\pi$
$17$	0.579924	−	0.579924i	0.140652	−	0.140652i	0.773927	+	0.633275i	$0.218290\pi$
$18$		0			0
$19$	4.07807	−	4.07807i	0.935573	−	0.935573i	−0.0624739	−	0.998047i	$-0.519899\pi$
$19$	4.07807	−	4.07807i	0.935573	−	0.935573i	0.998047	+	0.0624739i	$0.0198990\pi$
$20$	−3.46749	−	2.82428i	−0.775354	−	0.631527i
$21$		0			0
$22$	−1.58891	−	0.0291254i	−0.338757	−	0.00620956i
$23$	−4.47496	+	4.47496i	−0.933094	+	0.933094i	−0.997898	−	0.0648038i	$-0.979358\pi$
$23$	−4.47496	+	4.47496i	−0.933094	+	0.933094i	0.0648038	+	0.997898i	$0.479358\pi$
$24$		0			0
$25$	−1.36768	−	4.80931i	−0.273535	−	0.961862i
$26$	1.84791	−	1.78138i	0.362404	−	0.349357i
$27$		0			0
$28$	−6.77997	−	7.29618i	−1.28129	−	1.37885i
$29$	−2.53613	−	2.53613i	−0.470948	−	0.470948i	0.431273	−	0.902221i	$-0.358065\pi$
$29$	−2.53613	−	2.53613i	−0.470948	−	0.470948i	−0.902221	+	0.431273i	$0.858065\pi$
$30$		0			0
$31$	−8.04252			−1.44448			−0.722239	−	0.691643i	$-0.756887\pi$
$31$	−8.04252			−1.44448			−0.722239	+	0.691643i	$0.756887\pi$
$32$	4.34927	−	3.61716i	0.768850	−	0.639430i
$33$		0			0
$34$	−0.0212569	+	1.15965i	−0.00364553	+	0.198879i
$35$	−1.53773	−	11.0290i	−0.259924	−	1.86424i
$36$		0			0
$37$	5.45883			0.897426			0.448713	−	0.893676i	$-0.351883\pi$
$37$	5.45883			0.897426			0.448713	+	0.893676i	$0.351883\pi$
$38$	−0.149480	+	8.15476i	−0.0242489	+	1.32288i
$39$		0			0
$40$	6.30249	−	0.527791i	0.996512	−	0.0834511i
$41$	3.39090			0.529569			0.264785	−	0.964308i	$-0.414699\pi$
$41$	3.39090			0.529569			0.264785	+	0.964308i	$0.414699\pi$
$42$		0			0
$43$			4.86388i			0.741735i	0.928686	+	0.370868i	$0.120940\pi$
$43$			4.86388i			0.741735i	−0.928686	+	0.370868i	$0.879060\pi$
$44$	1.64635	−	1.52987i	0.248197	−	0.230637i
$45$		0			0
$46$	0.164028	−	8.94842i	0.0241846	−	1.31937i
$47$	−5.83824	+	5.83824i	−0.851595	+	0.851595i	−0.990330	−	0.138735i	$-0.955696\pi$
$47$	−5.83824	+	5.83824i	−0.851595	+	0.851595i	0.138735	+	0.990330i	$0.455696\pi$
$48$		0			0
$49$		−	17.8006i		−	2.54294i
$50$	6.11287	+	3.55426i	0.864491	+	0.502649i
$51$		0			0
$52$	−0.133030	+	3.62746i	−0.0184480	+	0.503038i
$53$	7.71651			1.05994			0.529972	−	0.848015i	$-0.322202\pi$
$53$	7.71651			1.05994			0.529972	+	0.848015i	$0.322202\pi$
$54$		0			0
$55$	2.48864	−	0.346982i	0.335568	−	0.0467871i
$56$	14.0643	+	0.774108i	1.87942	+	0.103445i
$57$		0			0
$58$	5.07142	+	0.0929611i	0.665909	+	0.0122064i
$59$	3.16642	−	3.16642i	0.412232	−	0.412232i	−0.470283	−	0.882516i	$-0.655848\pi$
$59$	3.16642	−	3.16642i	0.412232	−	0.412232i	0.882516	+	0.470283i	$0.155848\pi$
$60$		0			0
$61$	2.48943	+	2.48943i	0.318739	+	0.318739i	0.848283	−	0.529544i	$-0.177637\pi$
$61$	2.48943	+	2.48943i	0.318739	+	0.318739i	−0.529544	+	0.848283i	$0.677637\pi$
$62$	8.18857	−	7.89377i	1.03995	−	1.00251i
$63$		0			0
$64$	−0.877989	+	7.95167i	−0.109749	+	0.993959i
$65$	−2.44591	+	3.23847i	−0.303378	+	0.401682i
$66$		0			0
$67$			2.85214i			0.348444i	0.984706	+	0.174222i	$0.0557411\pi$
$67$			2.85214i			0.348444i	−0.984706	+	0.174222i	$0.944259\pi$
$68$	−1.11656	−	1.20158i	−0.135403	−	0.145712i
$69$		0			0
$70$	12.3906	+	9.71996i	1.48097	+	1.16176i
$71$	−7.31072			−0.867623			−0.433812	−	0.901004i	$-0.642832\pi$
$71$	−7.31072			−0.867623			−0.433812	+	0.901004i	$0.642832\pi$
$72$		0			0
$73$	10.1613	+	10.1613i	1.18929	+	1.18929i	0.977263	+	0.212032i	$0.0680082\pi$
$73$	10.1613	+	10.1613i	1.18929	+	1.18929i	0.212032	+	0.977263i	$0.431992\pi$
$74$	−5.55796	+	5.35787i	−0.646099	+	0.622839i
$75$		0			0
$76$	−7.85174	−	8.44956i	−0.900657	−	0.969232i
$77$	5.59614			0.637739
$78$		0			0
$79$			9.50285i			1.06915i	0.845120	+	0.534577i	$0.179529\pi$
$79$			9.50285i			1.06915i	−0.845120	+	0.534577i	$0.820471\pi$
$80$	−5.89891	+	6.72330i	−0.659519	+	0.751688i
$81$		0			0
$82$	−3.45247	+	3.32818i	−0.381262	+	0.367536i
$83$		−	10.8245i		−	1.18814i	−0.804412	−	0.594072i	$-0.797519\pi$
$83$		−	10.8245i		−	1.18814i	0.804412	−	0.594072i	$-0.202481\pi$
$84$		0			0
$85$	−0.253242	−	1.81631i	−0.0274679	−	0.197007i
$86$	−4.77392	−	4.95221i	−0.514786	−	0.534010i
$87$		0			0
$88$	−0.174674	+	3.17355i	−0.0186203	+	0.338302i
$89$		−	8.83938i		−	0.936972i	−0.883471	−	0.468486i	$-0.844800\pi$
$89$		−	8.83938i		−	0.936972i	0.883471	−	0.468486i	$-0.155200\pi$
$90$		0			0
$91$	−6.39116	+	6.39116i	−0.669976	+	0.669976i
$92$	8.61591	+	9.27191i	0.898271	+	0.966664i
$93$		0			0
$94$	0.213999	−	11.6745i	0.0220723	−	1.20413i
$95$	−1.78081	−	12.7724i	−0.182708	−	1.31042i
$96$		0			0
$97$	2.78908	+	2.78908i	0.283188	+	0.283188i	0.834379	−	0.551191i	$-0.185826\pi$
$97$	2.78908	+	2.78908i	0.283188	+	0.283188i	−0.551191	+	0.834379i	$0.685826\pi$
$98$	17.4713	+	18.1238i	1.76487	+	1.83078i
$99$		0			0
$100$	−9.71240	+	2.38101i	−0.971240	+	0.238101i
$101$	−10.5540	−	10.5540i	−1.05016	−	1.05016i	−0.998674	−	0.0514876i	$-0.983604\pi$
$101$	−10.5540	−	10.5540i	−1.05016	−	1.05016i	−0.0514876	−	0.998674i	$-0.516396\pi$
$102$		0			0
$103$	2.12084	+	2.12084i	0.208973	+	0.208973i	0.803831	−	0.594858i	$-0.202792\pi$
$103$	2.12084	+	2.12084i	0.208973	+	0.208973i	−0.594858	+	0.803831i	$0.702792\pi$
$104$	−3.42492	−	3.82390i	−0.335841	−	0.374964i
$105$		0			0
$106$	−7.85664	+	7.57379i	−0.763104	+	0.735632i
$107$		−	3.88547i		−	0.375622i	−0.982205	−	0.187811i	$-0.939861\pi$
$107$		−	3.88547i		−	0.375622i	0.982205	−	0.187811i	$-0.0601393\pi$
$108$		0			0
$109$	12.4641	−	12.4641i	1.19385	−	1.19385i	0.217871	−	0.975978i	$-0.430089\pi$
$109$	12.4641	−	12.4641i	1.19385	−	1.19385i	0.975978	−	0.217871i	$-0.0699112\pi$
$110$	−2.19327	+	2.79589i	−0.209120	+	0.266578i
$111$		0			0
$112$	−15.0795	+	13.0160i	−1.42488	+	1.22990i
$113$	12.7492	+	12.7492i	1.19934	+	1.19934i	0.974364	+	0.224978i	$0.0722311\pi$
$113$	12.7492	+	12.7492i	1.19934	+	1.19934i	0.224978	+	0.974364i	$0.427769\pi$
$114$		0			0
$115$	1.95413	+	14.0155i	0.182224	+	1.30695i
$116$	−5.25475	+	4.88297i	−0.487891	+	0.453372i
$117$		0			0
$118$	−0.116064	+	6.33177i	−0.0106846	+	0.582887i
$119$		−	4.08429i		−	0.374406i
$120$		0			0
$121$		−	9.73726i		−	0.885205i
$122$	−4.97803	−	0.0912493i	−0.450689	−	0.00826132i
$123$		0			0
$124$	−0.589493	+	16.0742i	−0.0529380	+	1.44351i
$125$	−10.4246	−	4.04088i	−0.932400	−	0.361427i
$126$		0			0
$127$	9.37383	+	9.37383i	0.831793	+	0.831793i	0.987762	−	0.155969i	$-0.0498501\pi$
$127$	9.37383	+	9.37383i	0.831793	+	0.831793i	−0.155969	+	0.987762i	$0.549850\pi$
$128$	−6.91067	−	8.95782i	−0.610823	−	0.791767i
$129$		0			0
$130$	−0.688240	−	5.69795i	−0.0603627	−	0.499743i
$131$	0.885812	−	0.885812i	0.0773937	−	0.0773937i	−0.667350	−	0.744744i	$-0.732572\pi$
$131$	0.885812	−	0.885812i	0.0773937	−	0.0773937i	0.744744	+	0.667350i	$0.232572\pi$
$132$		0			0
$133$		−	28.7210i		−	2.49043i
$134$	−2.79939	−	2.90393i	−0.241830	−	0.250861i
$135$		0			0
$136$	2.31619	+	0.127484i	0.198612	+	0.0109317i
$137$	1.99530	+	1.99530i	0.170470	+	0.170470i	0.787186	−	0.616716i	$-0.211537\pi$
$137$	1.99530	+	1.99530i	0.170470	+	0.170470i	−0.616716	+	0.787186i	$0.711537\pi$
$138$		0			0
$139$	4.37150	+	4.37150i	0.370786	+	0.370786i	0.867763	−	0.496977i	$-0.165557\pi$
$139$	4.37150	+	4.37150i	0.370786	+	0.370786i	−0.496977	+	0.867763i	$0.665557\pi$
$140$	−22.1558	+	2.26500i	−1.87251	+	0.191428i
$141$		0			0
$142$	7.44348	−	7.17551i	0.624643	−	0.602155i
$143$	−1.44214	−	1.44214i	−0.120598	−	0.120598i
$144$		0			0
$145$	−7.94312	+	1.10748i	−0.659641	+	0.0919713i
$146$	−20.3193	−	0.372461i	−1.68163	−	0.0308251i
$147$		0			0
$148$	0.400116	−	10.9103i	0.0328893	−	0.896823i
$149$	−6.12416	+	6.12416i	−0.501711	+	0.501711i	−0.911969	−	0.410259i	$-0.865438\pi$
$149$	−6.12416	+	6.12416i	−0.501711	+	0.501711i	0.410259	+	0.911969i	$0.365438\pi$
$150$		0			0
$151$		−	5.97875i		−	0.486544i	−0.969958	−	0.243272i	$-0.921779\pi$
$151$		−	5.97875i		−	0.486544i	0.969958	−	0.243272i	$-0.0782207\pi$
$152$	16.2876	+	0.896479i	1.32110	+	0.0727141i
$153$		0			0
$154$	−5.69776	+	5.49264i	−0.459139	+	0.442609i
$155$	−10.8385	+	14.3505i	−0.870569	+	1.15266i
$156$		0			0
$157$			18.8879i			1.50742i	0.657209	+	0.753708i	$0.271737\pi$
$157$			18.8879i			1.50742i	−0.657209	+	0.753708i	$0.728263\pi$
$158$	−9.32710	−	9.67542i	−0.742024	−	0.769735i
$159$		0			0
$160$	−0.592920	−	12.6352i	−0.0468744	−	0.998901i
$161$			31.5163i			2.48383i
$162$		0			0
$163$	−14.5507			−1.13970			−0.569849	−	0.821749i	$-0.692998\pi$
$163$	−14.5507			−1.13970			−0.569849	+	0.821749i	$0.692998\pi$
$164$	0.248543	−	6.77724i	0.0194079	−	0.529213i
$165$		0			0
$166$	10.6243	+	11.0211i	0.824606	+	0.855402i
$167$	−15.6578	−	15.6578i	−1.21164	−	1.21164i	−0.970488	−	0.241151i	$-0.922475\pi$
$167$	−15.6578	−	15.6578i	−1.21164	−	1.21164i	−0.241151	−	0.970488i	$-0.577525\pi$
$168$		0			0
$169$	−9.70597			−0.746613
$170$	2.04056	+	1.60074i	0.156504	+	0.122771i
$171$		0			0
$172$	9.72123	+	0.356508i	0.741237	+	0.0271835i
$173$		−	7.10719i		−	0.540350i	−0.962811	−	0.270175i	$-0.912919\pi$
$173$		−	7.10719i		−	0.540350i	0.962811	−	0.270175i	$-0.0870815\pi$
$174$		0			0
$175$	−21.7517	−	12.1194i	−1.64427	−	0.916139i
$176$	−2.93701	−	3.40263i	−0.221386	−	0.256483i
$177$		0			0
$178$	8.67589	+	8.99989i	0.650285	+	0.674571i
$179$	15.6929	+	15.6929i	1.17294	+	1.17294i	0.981504	+	0.191440i	$0.0613157\pi$
$179$	15.6929	+	15.6929i	1.17294	+	1.17294i	0.191440	+	0.981504i	$0.438684\pi$
$180$		0			0
$181$	6.56063	−	6.56063i	0.487648	−	0.487648i	−0.419915	−	0.907563i	$-0.637940\pi$
$181$	6.56063	−	6.56063i	0.487648	−	0.487648i	0.907563	+	0.419915i	$0.137940\pi$
$182$	0.234266	−	12.7802i	0.0173649	−	0.947330i
$183$		0			0
$184$	−17.8728	−	0.983729i	−1.31760	−	0.0725214i
$185$	7.35659	−	9.74036i	0.540867	−	0.716125i
$186$		0			0
$187$	0.921603			0.0673943
$188$	11.2407	+	12.0966i	0.819813	+	0.882232i
$189$		0			0
$190$	14.3494	+	11.2565i	1.04101	+	0.816632i
$191$			20.4598i			1.48042i	0.672376	+	0.740210i	$0.265274\pi$
$191$			20.4598i			1.48042i	−0.672376	+	0.740210i	$0.734726\pi$
$192$		0			0
$193$	−15.7677	+	15.7677i	−1.13498	+	1.13498i	−0.145647	+	0.989337i	$0.546526\pi$
$193$	−15.7677	+	15.7677i	−1.13498	+	1.13498i	−0.989337	+	0.145647i	$0.953474\pi$
$194$	−5.57722	−	0.102233i	−0.400421	−	0.00733989i
$195$		0			0
$196$	−35.5772	−	1.30473i	−2.54123	−	0.0931949i
$197$		−	4.69499i		−	0.334504i	−0.985914	−	0.167252i	$-0.946511\pi$
$197$		−	4.69499i		−	0.334504i	0.985914	−	0.167252i	$-0.0534894\pi$
$198$		0			0
$199$	4.71983			0.334580			0.167290	−	0.985908i	$-0.446498\pi$
$199$	4.71983			0.334580			0.167290	+	0.985908i	$0.446498\pi$
$200$	7.55180	−	11.9570i	0.533993	−	0.845489i
$201$		0			0
$202$	21.1044	+	0.386853i	1.48490	+	0.0272189i
$203$	−17.8615			−1.25363
$204$		0			0
$205$	4.56974	−	6.05048i	0.319165	−	0.422584i
$206$	−4.24097	−	0.0777388i	−0.295483	−	0.00541632i
$207$		0			0
$208$	7.24029	+	0.531763i	0.502024	+	0.0368712i
$209$	6.48078			0.448285
$210$		0			0
$211$	8.98274	+	8.98274i	0.618397	+	0.618397i	0.945120	−	0.326723i	$-0.105944\pi$
$211$	8.98274	+	8.98274i	0.618397	+	0.618397i	−0.326723	+	0.945120i	$0.605944\pi$
$212$	0.565597	−	15.4227i	0.0388454	−	1.05923i
$213$		0			0
$214$	3.81360	+	3.95602i	0.260692	+	0.270428i
$215$	8.67878	+	6.55481i	0.591888	+	0.447035i
$216$		0			0
$217$	−28.3210	+	28.3210i	−1.92255	+	1.92255i
$218$	−0.456869	+	24.9241i	−0.0309431	+	1.68807i
$219$		0			0
$220$	−0.511088	−	4.99937i	−0.0344576	−	0.337057i
$221$	−1.05253	+	1.05253i	−0.0708009	+	0.0708009i
$222$		0			0
$223$	−3.38870	+	3.38870i	−0.226924	+	0.226924i	−0.811406	−	0.584482i	$-0.801298\pi$
$223$	−3.38870	+	3.38870i	−0.226924	+	0.226924i	0.584482	+	0.811406i	$0.301298\pi$
$224$	2.57805	−	28.0530i	0.172253	−	1.87437i
$225$		0			0
$226$	−25.4941	−	0.467317i	−1.69584	−	0.0310855i
$227$	12.7291			0.844857			0.422429	−	0.906396i	$-0.361178\pi$
$227$	12.7291			0.844857			0.422429	+	0.906396i	$0.361178\pi$
$228$		0			0
$229$	−18.3978	−	18.3978i	−1.21576	−	1.21576i	−0.969102	−	0.246662i	$-0.920666\pi$
$229$	−18.3978	−	18.3978i	−1.21576	−	1.21576i	−0.246662	−	0.969102i	$-0.579334\pi$
$230$	−15.7459	−	12.3520i	−1.03825	−	0.814468i
$231$		0			0
$232$	0.557517	−	10.1292i	0.0366028	−	0.665015i
$233$	4.78291	−	4.78291i	0.313339	−	0.313339i	−0.532863	−	0.846202i	$-0.678884\pi$
$233$	4.78291	−	4.78291i	0.313339	−	0.313339i	0.846202	+	0.532863i	$0.178884\pi$
$234$		0			0
$235$	2.54945	+	18.2853i	0.166308	+	1.19280i
$236$	−6.09649	−	6.56067i	−0.396848	−	0.427063i
$237$		0			0
$238$	4.00875	+	4.15846i	0.259849	+	0.269553i
$239$	−9.68868			−0.626709			−0.313354	−	0.949636i	$-0.601453\pi$
$239$	−9.68868			−0.626709			−0.313354	+	0.949636i	$0.601453\pi$
$240$		0			0
$241$	6.75923			0.435400			0.217700	−	0.976016i	$-0.430145\pi$
$241$	6.75923			0.435400			0.217700	+	0.976016i	$0.430145\pi$
$242$	9.55716	+	9.91408i	0.614358	+	0.637301i
$243$		0			0
$244$	5.15799	−	4.79305i	0.330206	−	0.306844i
$245$	−31.7621	−	23.9889i	−2.02921	−	1.53260i
$246$		0			0
$247$	−7.40148	+	7.40148i	−0.470945	+	0.470945i
$248$	−15.1767	−	16.9447i	−0.963724	−	1.07599i
$249$		0			0
$250$	14.5800	−	6.11749i	0.922120	−	0.386904i
$251$	11.0136	+	11.0136i	0.695172	+	0.695172i	0.963365	−	0.268193i	$-0.0864264\pi$
$251$	11.0136	+	11.0136i	0.695172	+	0.695172i	−0.268193	+	0.963365i	$0.586426\pi$
$252$		0			0
$253$	−7.11152			−0.447097
$254$	−18.7445	−	0.343594i	−1.17613	−	0.0215590i
$255$		0			0
$256$	15.8283	+	2.33763i	0.989270	+	0.146102i
$257$	−4.29957	+	4.29957i	−0.268200	+	0.268200i	−0.828374	−	0.560175i	$-0.810734\pi$
$257$	−4.29957	+	4.29957i	−0.268200	+	0.268200i	0.560175	+	0.828374i	$0.310734\pi$
$258$		0			0
$259$	19.2227	−	19.2227i	1.19444	−	1.19444i
$260$	6.29330	+	5.12591i	0.390294	+	0.317896i
$261$		0			0
$262$	−0.0324691	+	1.77133i	−0.00200595	+	0.109433i
$263$	−20.2348	+	20.2348i	−1.24773	+	1.24773i	−0.291012	+	0.956720i	$0.593992\pi$
$263$	−20.2348	+	20.2348i	−1.24773	+	1.24773i	−0.956720	+	0.291012i	$0.906008\pi$
$264$		0			0
$265$	10.3992	−	13.7688i	0.638815	−	0.845811i
$266$	28.1898	+	29.2426i	1.72843	+	1.79298i
$267$		0			0
$268$	5.70044	+	0.209053i	0.348210	+	0.0127700i
$269$	22.6091	+	22.6091i	1.37850	+	1.37850i	0.847152	+	0.531350i	$0.178315\pi$
$269$	22.6091	+	22.6091i	1.37850	+	1.37850i	0.531350	+	0.847152i	$0.321685\pi$
$270$		0			0
$271$	0.832633			0.0505788			0.0252894	−	0.999680i	$-0.491949\pi$
$271$	0.832633			0.0505788			0.0252894	+	0.999680i	$0.491949\pi$
$272$	−2.48338	+	2.14355i	−0.150577	+	0.129972i
$273$		0			0
$274$	−3.98993	−	0.0731371i	−0.241041	−	0.00441837i
$275$	2.73468	−	4.90817i	0.164908	−	0.295974i
$276$		0			0
$277$	24.8462			1.49286			0.746431	−	0.665463i	$-0.231766\pi$
$277$	24.8462			1.49286			0.746431	+	0.665463i	$0.231766\pi$
$278$	−8.74154	−	0.160236i	−0.524282	−	0.00961031i
$279$		0			0
$280$	20.3351	−	24.0522i	1.21525	−	1.43739i
$281$	11.4754			0.684563			0.342281	−	0.939597i	$-0.388800\pi$
$281$	11.4754			0.684563			0.342281	+	0.939597i	$0.388800\pi$
$282$		0			0
$283$			5.19216i			0.308642i	0.988021	+	0.154321i	$0.0493190\pi$
$283$			5.19216i			0.308642i	−0.988021	+	0.154321i	$0.950681\pi$
$284$	−0.535854	+	14.6116i	−0.0317971	+	0.867040i
$285$		0			0
$286$	2.88379	+	0.0528611i	0.170522	+	0.00312574i
$287$	11.9407	−	11.9407i	0.704838	−	0.704838i
$288$		0			0
$289$			16.3274i			0.960434i
$290$	7.00037	−	8.92381i	0.411076	−	0.524024i
$291$		0			0
$292$	21.0538	−	19.5642i	1.23208	−	1.14491i
$293$	17.0751			0.997538			0.498769	−	0.866735i	$-0.333786\pi$
$293$	17.0751			0.997538			0.498769	+	0.866735i	$0.333786\pi$
$294$		0			0
$295$	−1.38271	−	9.91716i	−0.0805048	−	0.577400i
$296$	10.3012	+	11.5012i	0.598742	+	0.668491i
$297$		0			0
$298$	0.224479	−	12.2463i	0.0130037	−	0.709407i
$299$	8.12182	−	8.12182i	0.469697	−	0.469697i
$300$		0			0
$301$	17.1277	+	17.1277i	0.987224	+	0.987224i
$302$	5.86817	+	6.08732i	0.337675	+	0.350286i
$303$		0			0
$304$	−17.4633	+	15.0736i	−1.00159	+	0.864531i
$305$	7.79685	−	1.08709i	0.446447	−	0.0622465i
$306$		0			0
$307$			14.8391i			0.846909i	0.905917	+	0.423455i	$0.139183\pi$
$307$			14.8391i			0.846909i	−0.905917	+	0.423455i	$0.860817\pi$
$308$	0.410180	−	11.1848i	0.0233722	−	0.637311i
$309$		0			0
$310$	−3.04978	−	25.2492i	−0.173216	−	1.43406i
$311$	−11.7454			−0.666020			−0.333010	−	0.942923i	$-0.608064\pi$
$311$	−11.7454			−0.666020			−0.333010	+	0.942923i	$0.608064\pi$
$312$		0			0
$313$	6.70099	+	6.70099i	0.378762	+	0.378762i	0.870655	−	0.491893i	$-0.163695\pi$
$313$	6.70099	+	6.70099i	0.378762	+	0.378762i	−0.491893	+	0.870655i	$0.663695\pi$
$314$	−18.5385	−	19.2309i	−1.04619	−	1.08526i
$315$		0			0
$316$	18.9929	+	0.696531i	1.06844	+	0.0391829i
$317$	18.6931			1.04991			0.524956	−	0.851130i	$-0.324082\pi$
$317$	18.6931			1.04991			0.524956	+	0.851130i	$0.324082\pi$
$318$		0			0
$319$		−	4.03037i		−	0.225657i
$320$	13.0052	+	12.2827i	0.727013	+	0.686624i
$321$		0			0
$322$	−30.9334	−	32.0886i	−1.72385	−	1.78823i
$323$		−	4.72994i		−	0.263181i
$324$		0			0
$325$	2.48226	+	8.72864i	0.137691	+	0.484178i
$326$	14.8149	−	14.2816i	0.820523	−	0.790983i
$327$		0			0
$328$	6.39884	+	7.14426i	0.353317	+	0.394475i
$329$			41.1176i			2.26689i
$330$		0			0
$331$	0.985138	−	0.985138i	0.0541481	−	0.0541481i	−0.679514	−	0.733662i	$-0.737809\pi$
$331$	0.985138	−	0.985138i	0.0541481	−	0.0541481i	0.733662	+	0.679514i	$0.237809\pi$
$332$	−21.6345	−	0.793404i	−1.18735	−	0.0435437i
$333$		0			0
$334$	31.3104	+	0.573932i	1.71323	+	0.0314042i
$335$	5.08916	+	3.84368i	0.278051	+	0.210003i
$336$		0			0
$337$	−12.2732	−	12.2732i	−0.668565	−	0.668565i	0.288819	−	0.957384i	$-0.406738\pi$
$337$	−12.2732	−	12.2732i	−0.668565	−	0.668565i	−0.957384	+	0.288819i	$0.906738\pi$
$338$	9.88222	−	9.52645i	0.537522	−	0.518171i
$339$		0			0
$340$	−3.64874	+	0.373013i	−0.197881	+	0.0202295i
$341$	−6.39050	−	6.39050i	−0.346065	−	0.346065i
$342$		0			0
$343$	−38.0332	−	38.0332i	−2.05360	−	2.05360i
$344$	−10.2477	+	9.17845i	−0.552518	+	0.494869i
$345$		0			0
$346$	6.97574	+	7.23625i	0.375018	+	0.389023i
$347$			9.51724i			0.510912i	0.966821	+	0.255456i	$0.0822257\pi$
$347$			9.51724i			0.510912i	−0.966821	+	0.255456i	$0.917774\pi$
$348$		0			0
$349$	−6.54235	+	6.54235i	−0.350204	+	0.350204i	−0.860185	−	0.509981i	$-0.829652\pi$
$349$	−6.54235	+	6.54235i	−0.350204	+	0.350204i	0.509981	+	0.860185i	$0.329652\pi$
$350$	34.0419	−	9.00990i	1.81962	−	0.481600i
$351$		0			0
$352$	6.33004	+	0.581726i	0.337392	+	0.0310061i
$353$	−9.78695	−	9.78695i	−0.520907	−	0.520907i	0.396938	−	0.917845i	$-0.370073\pi$
$353$	−9.78695	−	9.78695i	−0.520907	−	0.520907i	−0.917845	+	0.396938i	$0.870073\pi$
$354$		0			0
$355$	−9.85230	+	13.0448i	−0.522906	+	0.692344i
$356$	−17.6669	−	0.647900i	−0.936343	−	0.0343386i
$357$		0			0
$358$	−31.3806	−	0.575219i	−1.65852	−	0.0304013i
$359$		−	2.64535i		−	0.139616i	−0.997560	−	0.0698081i	$-0.977761\pi$
$359$		−	2.64535i		−	0.139616i	0.997560	−	0.0698081i	$-0.0222387\pi$
$360$		0			0
$361$		−	14.2613i		−	0.750593i
$362$	−0.240478	+	13.1191i	−0.0126392	+	0.689522i
$363$		0			0
$364$	12.3053	+	13.2422i	0.644972	+	0.694079i
$365$	31.8251	−	4.43727i	1.66580	−	0.232257i
$366$		0			0
$367$	6.03995	+	6.03995i	0.315283	+	0.315283i	0.846952	−	0.531669i	$-0.178435\pi$
$367$	6.03995	+	6.03995i	0.315283	+	0.315283i	−0.531669	+	0.846952i	$0.678435\pi$
$368$	19.1629	−	16.5406i	0.998935	−	0.862241i
$369$		0			0
$370$	2.07003	+	17.1378i	0.107615	+	0.890950i
$371$	27.1729	−	27.1729i	1.41075	−	1.41075i
$372$		0			0
$373$			14.7609i			0.764288i	0.924103	+	0.382144i	$0.124814\pi$
$373$			14.7609i			0.764288i	−0.924103	+	0.382144i	$0.875186\pi$
$374$	−0.938338	+	0.904557i	−0.0485203	+	0.0467736i
$375$		0			0
$376$	−23.3177	−	1.28342i	−1.20252	−	0.0661872i
$377$	4.60295	+	4.60295i	0.237064	+	0.237064i
$378$		0			0
$379$	−15.5335	−	15.5335i	−0.797902	−	0.797902i	0.184862	−	0.982764i	$-0.440816\pi$
$379$	−15.5335	−	15.5335i	−0.797902	−	0.797902i	−0.982764	+	0.184862i	$0.940816\pi$
$380$	−25.6582	+	2.62306i	−1.31624	+	0.134560i
$381$		0			0
$382$	−20.0814	−	20.8313i	−1.02745	−	1.06582i
$383$	9.61642	+	9.61642i	0.491376	+	0.491376i	0.908740	−	0.417363i	$-0.137046\pi$
$383$	9.61642	+	9.61642i	0.491376	+	0.491376i	−0.417363	+	0.908740i	$0.637046\pi$
$384$		0			0
$385$	7.54164	−	9.98537i	0.384358	−	0.508902i
$386$	0.577960	−	31.5301i	0.0294174	−	1.60484i
$387$		0			0
$388$	5.77885	−	5.36998i	0.293376	−	0.272620i
$389$	2.77405	−	2.77405i	0.140650	−	0.140650i	−0.633276	−	0.773926i	$-0.718290\pi$
$389$	2.77405	−	2.77405i	0.140650	−	0.140650i	0.773926	+	0.633276i	$0.218290\pi$
$390$		0			0
$391$			5.19028i			0.262483i
$392$	37.5039	−	33.5908i	1.89423	−	1.69659i
$393$		0			0
$394$	4.60816	+	4.78025i	0.232156	+	0.240826i
$395$	16.9562	+	12.8065i	0.853161	+	0.644366i
$396$		0			0
$397$		−	26.0603i		−	1.30793i	−0.756526	−	0.653963i	$-0.773105\pi$
$397$		−	26.0603i		−	1.30793i	0.756526	−	0.653963i	$-0.226895\pi$
$398$	−4.80554	+	4.63253i	−0.240880	+	0.232208i
$399$		0			0
$400$	4.04693	+	19.5863i	0.202346	+	0.979314i
$401$		−	2.43479i		−	0.121587i	−0.998150	−	0.0607937i	$-0.980637\pi$
$401$		−	2.43479i		−	0.121587i	0.998150	−	0.0607937i	$-0.0193632\pi$
$402$		0			0
$403$	14.5967			0.727116
$404$	−21.8674	+	20.3202i	−1.08794	+	1.01097i
$405$		0			0
$406$	18.1859	−	17.5311i	0.902549	−	0.870056i
$407$	4.33753	+	4.33753i	0.215003	+	0.215003i
$408$		0			0
$409$	11.9845			0.592596			0.296298	−	0.955096i	$-0.404248\pi$
$409$	11.9845			0.592596			0.296298	+	0.955096i	$0.404248\pi$
$410$	1.28585	+	10.6456i	0.0635037	+	0.525748i
$411$		0			0
$412$	4.39429	−	4.08339i	0.216491	−	0.201174i
$413$		−	22.3005i		−	1.09733i
$414$		0			0
$415$	−19.3145	−	14.5877i	−0.948112	−	0.716080i
$416$	−7.89369	+	6.56496i	−0.387020	+	0.321873i
$417$		0			0
$418$	−6.59846	+	6.36091i	−0.322741	+	0.311122i
$419$	−22.9083	−	22.9083i	−1.11914	−	1.11914i	−0.991867	−	0.127277i	$-0.959376\pi$
$419$	−22.9083	−	22.9083i	−1.11914	−	1.11914i	−0.127277	−	0.991867i	$-0.540624\pi$
$420$		0			0
$421$	−6.98144	+	6.98144i	−0.340255	+	0.340255i	−0.856463	−	0.516208i	$-0.827343\pi$
$421$	−6.98144	+	6.98144i	−0.340255	+	0.340255i	0.516208	+	0.856463i	$0.327343\pi$
$422$	−17.9625	−	0.329259i	−0.874399	−	0.0160281i
$423$		0			0
$424$	14.5615	+	16.2579i	0.707171	+	0.789551i
$425$	−3.58218	−	1.99588i	−0.173761	−	0.0968146i
$426$		0			0
$427$	17.5326			0.848461
$428$	−7.76571	−	0.284793i	−0.375370	−	0.0137660i
$429$		0			0
$430$	−15.2700	+	1.84442i	−0.736383	+	0.0889458i
$431$			18.2408i			0.878628i	0.898334	+	0.439314i	$0.144778\pi$
$431$			18.2408i			0.878628i	−0.898334	+	0.439314i	$0.855222\pi$
$432$		0			0
$433$	−11.5917	+	11.5917i	−0.557061	+	0.557061i	−0.928469	−	0.371409i	$-0.878875\pi$
$433$	−11.5917	+	11.5917i	−0.557061	+	0.557061i	0.371409	+	0.928469i	$0.378875\pi$
$434$	1.03810	−	56.6324i	0.0498302	−	2.71844i
$435$		0			0
$436$	−23.9980	−	25.8251i	−1.14929	−	1.23680i
$437$			36.4984i			1.74595i
$438$		0			0
$439$	1.15895			0.0553134			0.0276567	−	0.999617i	$-0.491195\pi$
$439$	1.15895			0.0553134			0.0276567	+	0.999617i	$0.491195\pi$
$440$	5.42727	+	4.58852i	0.258735	+	0.218749i
$441$		0			0
$442$	0.0385802	−	2.10471i	0.00183507	−	0.100111i
$443$	8.12743			0.386146			0.193073	−	0.981184i	$-0.438155\pi$
$443$	8.12743			0.386146			0.193073	+	0.981184i	$0.438155\pi$
$444$		0			0
$445$	−15.7724	−	11.9124i	−0.747682	−	0.564701i
$446$	0.124212	−	6.77625i	0.00588159	−	0.320865i
$447$		0			0
$448$	24.9093	+	31.0928i	1.17685	+	1.46900i
$449$	4.24882			0.200514			0.100257	−	0.994962i	$-0.468033\pi$
$449$	4.24882			0.200514			0.100257	+	0.994962i	$0.468033\pi$
$450$		0			0
$451$	2.69437	+	2.69437i	0.126873	+	0.126873i
$452$	26.4157	−	24.5468i	1.24249	−	1.15458i
$453$		0			0
$454$	−12.9602	+	12.4936i	−0.608253	+	0.586355i
$455$	2.79090	+	20.0170i	0.130839	+	0.938411i
$456$		0			0
$457$	8.58027	−	8.58027i	0.401368	−	0.401368i	−0.477347	−	0.878715i	$-0.658401\pi$
$457$	8.58027	−	8.58027i	0.401368	−	0.401368i	0.878715	+	0.477347i	$0.158401\pi$
$458$	36.7895	+	0.674367i	1.71906	+	0.0315111i
$459$		0			0
$460$	28.1554	−	2.87834i	1.31275	−	0.134203i
$461$	−27.2381	+	27.2381i	−1.26861	+	1.26861i	−0.321797	+	0.946809i	$0.604287\pi$
$461$	−27.2381	+	27.2381i	−1.26861	+	1.26861i	−0.946809	+	0.321797i	$0.895713\pi$
$462$		0			0
$463$	−20.5504	+	20.5504i	−0.955059	+	0.955059i	−0.999033	−	0.0439739i	$-0.985998\pi$
$463$	−20.5504	+	20.5504i	−0.955059	+	0.955059i	0.0439739	+	0.999033i	$0.485998\pi$
$464$	9.37422	+	10.8603i	0.435187	+	0.504179i
$465$		0			0
$466$	−0.175316	+	9.56421i	−0.00812135	+	0.443053i
$467$	7.62383			0.352789			0.176394	−	0.984320i	$-0.443557\pi$
$467$	7.62383			0.352789			0.176394	+	0.984320i	$0.443557\pi$
$468$		0			0
$469$	10.0435	+	10.0435i	0.463767	+	0.463767i
$470$	−20.5428	−	16.1150i	−0.947569	−	0.743330i
$471$		0			0
$472$	12.6465	+	0.696072i	0.582104	+	0.0320393i
$473$	−3.86479	+	3.86479i	−0.177703	+	0.177703i
$474$		0			0
$475$	−25.1902	−	14.0352i	−1.15580	−	0.643979i
$476$	−8.16310	−	0.299366i	−0.374155	−	0.0137214i
$477$		0			0
$478$	9.86462	−	9.50948i	0.451197	−	0.434954i
$479$	17.9717			0.821147			0.410574	−	0.911827i	$-0.365328\pi$
$479$	17.9717			0.821147			0.410574	+	0.911827i	$0.365328\pi$
$480$		0			0
$481$	−9.90748			−0.451742
$482$	−6.88197	+	6.63422i	−0.313465	+	0.302180i
$483$		0			0
$484$	−19.4614	−	0.713712i	−0.884610	−	0.0324414i
$485$	8.73535	−	1.21794i	0.396652	−	0.0553038i
$486$		0			0
$487$	19.4087	−	19.4087i	0.879492	−	0.879492i	−0.113990	−	0.993482i	$-0.536363\pi$
$487$	19.4087	−	19.4087i	0.879492	−	0.879492i	0.993482	+	0.113990i	$0.0363633\pi$
$488$	−0.547251	+	9.94268i	−0.0247729	+	0.450084i
$489$		0			0
$490$	55.8842	−	6.75010i	2.52459	−	0.304938i
$491$	−0.388463	−	0.388463i	−0.0175311	−	0.0175311i	0.698287	−	0.715818i	$-0.253946\pi$
$491$	−0.388463	−	0.388463i	−0.0175311	−	0.0175311i	−0.715818	+	0.698287i	$0.753946\pi$
$492$		0			0
$493$	−2.94153			−0.132480
$494$	0.271299	−	14.8005i	0.0122063	−	0.665904i
$495$		0			0
$496$	32.0837	+	2.35639i	1.44060	+	0.105805i
$497$	−25.7440	+	25.7440i	−1.15478	+	1.15478i
$498$		0			0
$499$	15.5827	−	15.5827i	0.697577	−	0.697577i	−0.266310	−	0.963887i	$-0.585805\pi$
$499$	15.5827	−	15.5827i	0.697577	−	0.697577i	0.963887	+	0.266310i	$0.0858045\pi$
$500$	−8.84042	+	20.5389i	−0.395355	+	0.918528i
$501$		0			0
$502$	−22.0235	−	0.403700i	−0.982957	−	0.0180180i
$503$	−10.5169	+	10.5169i	−0.468927	+	0.468927i	−0.901567	−	0.432640i	$-0.857582\pi$
$503$	−10.5169	+	10.5169i	−0.468927	+	0.468927i	0.432640	+	0.901567i	$0.357582\pi$
$504$		0			0
$505$	−33.0549	+	4.60873i	−1.47092	+	0.205086i
$506$	7.24066	−	6.97999i	0.321886	−	0.310298i
$507$		0			0
$508$	19.4221	−	18.0480i	0.861718	−	0.800750i
$509$	−5.82377	−	5.82377i	−0.258134	−	0.258134i	0.566161	−	0.824295i	$-0.308428\pi$
$509$	−5.82377	−	5.82377i	−0.258134	−	0.258134i	−0.824295	+	0.566161i	$0.808428\pi$
$510$		0			0
$511$	71.5644			3.16582
$512$	−18.4101	+	13.1555i	−0.813621	+	0.581396i
$513$		0			0
$514$	0.157599	−	8.59769i	0.00695140	−	0.379228i
$515$	6.64244	−	0.926132i	0.292701	−	0.0408103i
$516$		0			0
$517$	−9.27801			−0.408046
$518$	−0.704603	+	38.4390i	−0.0309585	+	1.68891i
$519$		0			0
$520$	−11.4387	+	0.957913i	−0.501620	+	0.0420073i
$521$	−8.44184			−0.369844			−0.184922	−	0.982753i	$-0.559203\pi$
$521$	−8.44184			−0.369844			−0.184922	+	0.982753i	$0.559203\pi$
$522$		0			0
$523$		−	21.7627i		−	0.951616i	−0.879549	−	0.475808i	$-0.842156\pi$
$523$		−	21.7627i		−	0.951616i	0.879549	−	0.475808i	$-0.157844\pi$
$524$	−1.70551	−	1.83536i	−0.0745054	−	0.0801781i
$525$		0			0
$526$	0.741700	−	40.4628i	0.0323396	−	1.76426i
$527$	−4.66405	+	4.66405i	−0.203169	+	0.203169i
$528$		0			0
$529$		−	17.0506i		−	0.741330i
$530$	2.92615	+	24.2257i	0.127104	+	1.05230i
$531$		0			0
$532$	−57.4035	−	2.10517i	−2.48876	−	0.0912705i
$533$	−6.15430			−0.266572
$534$		0			0
$535$	−6.93296	−	5.23625i	−0.299738	−	0.226383i
$536$	−6.00915	+	5.38216i	−0.259556	+	0.232474i
$537$		0			0
$538$	−45.2107	−	0.828730i	−1.94917	−	0.0357291i
$539$	14.1441	−	14.1441i	0.609231	−	0.609231i
$540$		0			0
$541$	−2.65146	−	2.65146i	−0.113995	−	0.113995i	0.647808	−	0.761803i	$-0.275686\pi$
$541$	−2.65146	−	2.65146i	−0.113995	−	0.113995i	−0.761803	+	0.647808i	$0.775686\pi$
$542$	−0.847753	+	0.817233i	−0.0364141	+	0.0351032i
$543$		0			0
$544$	0.424567	−	4.61992i	0.0182032	−	0.198078i
$545$	−5.44286	−	39.0375i	−0.233146	−	1.67218i
$546$		0			0
$547$			10.2297i			0.437388i	0.975793	+	0.218694i	$0.0701797\pi$
$547$			10.2297i			0.437388i	−0.975793	+	0.218694i	$0.929820\pi$
$548$	4.13417	−	3.84167i	0.176603	−	0.164108i
$549$		0			0
$550$	2.03305	+	7.68140i	0.0866894	+	0.327536i
$551$	−20.6850			−0.881212
$552$		0			0
$553$	33.4634	+	33.4634i	1.42301	+	1.42301i
$554$	−25.2974	+	24.3866i	−1.07478	+	1.03609i
$555$		0			0
$556$	9.05755	−	8.41671i	0.384126	−	0.356948i
$557$	−40.1061			−1.69935			−0.849676	−	0.527306i	$-0.823202\pi$
$557$	−40.1061			−1.69935			−0.849676	+	0.527306i	$0.823202\pi$
$558$		0			0
$559$		−	8.82769i		−	0.373372i
$560$	2.90301	+	44.4479i	0.122675	+	1.87827i
$561$		0			0
$562$	−11.6837	+	11.2631i	−0.492849	+	0.475106i
$563$			40.1102i			1.69044i	0.534417	+	0.845221i	$0.320531\pi$
$563$			40.1102i			1.69044i	−0.534417	+	0.845221i	$0.679469\pi$
$564$		0			0
$565$	39.9302	−	5.56733i	1.67988	−	0.234219i
$566$	−5.09613	−	5.28645i	−0.214206	−	0.222206i
$567$		0			0
$568$	−13.7958	−	15.4029i	−0.578859	−	0.646292i
$569$			4.26260i			0.178698i	0.996000	+	0.0893488i	$0.0284786\pi$
$569$			4.26260i			0.178698i	−0.996000	+	0.0893488i	$0.971521\pi$
$570$		0			0
$571$	−1.00161	+	1.00161i	−0.0419161	+	0.0419161i	−0.727754	−	0.685838i	$-0.759436\pi$
$571$	−1.00161	+	1.00161i	−0.0419161	+	0.0419161i	0.685838	+	0.727754i	$0.259436\pi$
$572$	−2.98804	+	2.77663i	−0.124936	+	0.116097i
$573$		0			0
$574$	−0.437683	+	23.8774i	−0.0182685	+	0.996625i
$575$	27.6418	+	15.4012i	1.15274	+	0.642273i
$576$		0			0
$577$	−3.57536	−	3.57536i	−0.148844	−	0.148844i	0.628757	−	0.777602i	$-0.283564\pi$
$577$	−3.57536	−	3.57536i	−0.148844	−	0.148844i	−0.777602	+	0.628757i	$0.783564\pi$
$578$	−16.0254	−	16.6239i	−0.666569	−	0.691462i
$579$		0			0
$580$	1.63127	+	15.9568i	0.0677347	+	0.662568i
$581$	−38.1175	−	38.1175i	−1.58138	−	1.58138i
$582$		0			0
$583$	6.13146	+	6.13146i	0.253939	+	0.253939i
$584$	−2.23376	+	40.5839i	−0.0924337	+	1.67938i
$585$		0			0
$586$	−17.3852	+	16.7593i	−0.718175	+	0.692320i
$587$		−	31.4094i		−	1.29640i	−0.761468	−	0.648202i	$-0.775521\pi$
$587$		−	31.4094i		−	1.29640i	0.761468	−	0.648202i	$-0.224479\pi$
$588$		0			0
$589$	−32.7979	+	32.7979i	−1.35142	+	1.35142i
$590$	11.1416	+	8.74011i	0.458691	+	0.359825i
$591$		0			0
$592$	−21.7767	−	1.59939i	−0.895015	−	0.0657344i
$593$	0.711706	+	0.711706i	0.0292263	+	0.0292263i	0.721569	−	0.692343i	$-0.243421\pi$
$593$	0.711706	+	0.711706i	0.0292263	+	0.0292263i	−0.692343	+	0.721569i	$0.743421\pi$
$594$		0			0
$595$	−7.28773	−	5.50420i	−0.298768	−	0.225650i
$596$	11.7912	+	12.6890i	0.482987	+	0.519761i
$597$		0			0
$598$	−0.297703	+	16.2409i	−0.0121740	+	0.664140i
$599$		−	22.7143i		−	0.928081i	−0.885814	−	0.464041i	$-0.846399\pi$
$599$		−	22.7143i		−	0.928081i	0.885814	−	0.464041i	$-0.153601\pi$
$600$		0			0
$601$		−	2.66757i		−	0.108812i	−0.998519	−	0.0544062i	$-0.982673\pi$
$601$		−	2.66757i		−	0.108812i	0.998519	−	0.0544062i	$-0.0173266\pi$
$602$	−34.2496	−	0.627810i	−1.39591	−	0.0255876i
$603$		0			0
$604$	−11.9495	−	0.438225i	−0.486217	−	0.0178311i
$605$	−17.3745	−	13.1224i	−0.706373	−	0.533502i
$606$		0			0
$607$	−19.7506	−	19.7506i	−0.801653	−	0.801653i	0.181701	−	0.983354i	$-0.441840\pi$
$607$	−19.7506	−	19.7506i	−0.801653	−	0.801653i	−0.983354	+	0.181701i	$0.941840\pi$
$608$	2.98559	−	32.4876i	0.121082	−	1.31755i
$609$		0			0
$610$	−6.87146	+	8.75948i	−0.278217	+	0.354661i
$611$	10.5961	−	10.5961i	0.428672	−	0.428672i
$612$		0			0
$613$			37.6286i			1.51981i	0.650037	+	0.759903i	$0.274753\pi$
$613$			37.6286i			1.51981i	−0.650037	+	0.759903i	$0.725247\pi$
$614$	−14.5646	−	15.1085i	−0.587779	−	0.609730i
$615$		0			0
$616$	10.5603	+	11.7905i	0.425485	+	0.475051i
$617$	−7.68313	−	7.68313i	−0.309311	−	0.309311i	0.535331	−	0.844642i	$-0.320187\pi$
$617$	−7.68313	−	7.68313i	−0.309311	−	0.309311i	−0.844642	+	0.535331i	$0.820187\pi$
$618$		0			0
$619$	−0.363070	−	0.363070i	−0.0145930	−	0.0145930i	0.699773	−	0.714366i	$-0.253285\pi$
$619$	−0.363070	−	0.363070i	−0.0145930	−	0.0145930i	−0.714366	+	0.699773i	$0.753285\pi$
$620$	27.8873	+	22.7143i	1.11998	+	0.912228i
$621$		0			0
$622$	11.9587	−	11.5282i	0.479499	−	0.462237i
$623$	−31.1270	−	31.1270i	−1.24708	−	1.24708i
$624$		0			0
$625$	−21.2589	+	13.1552i	−0.850357	+	0.526207i
$626$	−13.3997	−	0.245622i	−0.535561	−	0.00981705i
$627$		0			0
$628$	37.7504	+	1.38443i	1.50640	+	0.0552446i
$629$	3.16570	−	3.16570i	0.126225	−	0.126225i
$630$		0			0
$631$			38.2533i			1.52284i	0.648260	+	0.761419i	$0.275497\pi$
$631$			38.2533i			1.52284i	−0.648260	+	0.761419i	$0.724503\pi$
$632$	−20.0215	+	17.9325i	−0.796412	+	0.713316i
$633$		0			0
$634$	−19.0326	+	18.3474i	−0.755881	+	0.728669i
$635$	29.3587	−	4.09337i	1.16506	−	0.162441i
$636$		0			0
$637$			32.3071i			1.28005i
$638$	3.95583	+	4.10356i	0.156613	+	0.162461i
$639$		0			0
$640$	−25.2969	+	0.258919i	−0.999948	+	0.0102347i
$641$			8.83990i			0.349155i	0.984643	+	0.174577i	$0.0558560\pi$
$641$			8.83990i			0.349155i	−0.984643	+	0.174577i	$0.944144\pi$
$642$		0			0
$643$	17.2140			0.678853			0.339427	−	0.940633i	$-0.389767\pi$
$643$	17.2140			0.678853			0.339427	+	0.940633i	$0.389767\pi$
$644$	62.9903	+	2.31005i	2.48216	+	0.0910288i
$645$		0			0
$646$	4.64245	+	4.81583i	0.182655	+	0.189476i
$647$	−5.49908	−	5.49908i	−0.216191	−	0.216191i	0.590700	−	0.806891i	$-0.298852\pi$
$647$	−5.49908	−	5.49908i	−0.216191	−	0.216191i	−0.806891	+	0.590700i	$0.798852\pi$
$648$		0			0
$649$	5.03200			0.197523
$650$	−11.0945	−	6.45080i	−0.435164	−	0.253021i
$651$		0			0
$652$	−1.06652	+	29.0818i	−0.0417682	+	1.13893i
$653$		−	43.6753i		−	1.70914i	−0.519332	−	0.854572i	$-0.673819\pi$
$653$		−	43.6753i		−	1.70914i	0.519332	−	0.854572i	$-0.326181\pi$
$654$		0			0
$655$	−0.386817	−	2.77435i	−0.0151142	−	0.108403i
$656$	−13.5272	−	0.993503i	−0.528147	−	0.0387898i
$657$		0			0
$658$	−40.3571	−	41.8643i	−1.57328	−	1.63204i
$659$	12.1428	+	12.1428i	0.473018	+	0.473018i	0.902890	−	0.429872i	$-0.141441\pi$
$659$	12.1428	+	12.1428i	0.473018	+	0.473018i	−0.429872	+	0.902890i	$0.641441\pi$
$660$		0			0
$661$	−19.7181	+	19.7181i	−0.766947	+	0.766947i	−0.977568	−	0.210621i	$-0.932451\pi$
$661$	−19.7181	+	19.7181i	−0.766947	+	0.766947i	0.210621	+	0.977568i	$0.432451\pi$
$662$	−0.0361099	+	1.96994i	−0.00140345	+	0.0765641i
$663$		0			0
$664$	22.8061	−	20.4265i	0.885047	−	0.792703i
$665$	−51.2479	−	38.7059i	−1.98731	−	1.50095i
$666$		0			0
$667$	22.6982			0.878878
$668$	−32.4423	+	30.1469i	−1.25523	+	1.16642i
$669$		0			0
$670$	−8.95417	+	1.08155i	−0.345930	+	0.0417839i
$671$			3.95615i			0.152726i
$672$		0			0
$673$	−7.49777	+	7.49777i	−0.289018	+	0.289018i	−0.836692	−	0.547674i	$-0.815513\pi$
$673$	−7.49777	+	7.49777i	−0.289018	+	0.289018i	0.547674	+	0.836692i	$0.315513\pi$
$674$	24.5423	+	0.449871i	0.945335	+	0.0173284i
$675$		0			0
$676$	−0.711418	+	19.3989i	−0.0273622	+	0.746111i
$677$			9.66092i			0.371299i	0.982616	+	0.185650i	$0.0594389\pi$
$677$			9.66092i			0.371299i	−0.982616	+	0.185650i	$0.940561\pi$
$678$		0			0
$679$	19.6430			0.753828
$680$	3.34889	−	3.96105i	0.128424	−	0.151899i
$681$		0			0
$682$	12.7789	+	0.234242i	0.489328	+	0.00896958i
$683$	−13.1017			−0.501323			−0.250662	−	0.968075i	$-0.580648\pi$
$683$	−13.1017			−0.501323			−0.250662	+	0.968075i	$0.580648\pi$
$684$		0			0
$685$	6.24925	−	0.871310i	0.238771	−	0.0332911i
$686$	76.0536	+	1.39409i	2.90374	+	0.0532267i
$687$		0			0
$688$	1.42507	−	19.4033i	0.0543305	−	0.739743i
$689$	−14.0051			−0.533550
$690$		0			0
$691$	−4.80979	−	4.80979i	−0.182973	−	0.182973i	0.609677	−	0.792650i	$-0.291299\pi$
$691$	−4.80979	−	4.80979i	−0.182973	−	0.182973i	−0.792650	+	0.609677i	$0.791299\pi$
$692$	−14.2048	−	0.520936i	−0.539987	−	0.0198030i
$693$		0			0
$694$	−9.34122	−	9.69007i	−0.354588	−	0.367830i
$695$	13.6915	−	1.90895i	0.519347	−	0.0724107i
$696$		0			0
$697$	1.96646	−	1.96646i	0.0744851	−	0.0744851i
$698$	0.239808	−	13.0825i	0.00907686	−	0.495180i
$699$		0			0
$700$	−25.8168	+	42.5858i	−0.975783	+	1.60959i
$701$	6.13442	−	6.13442i	0.231694	−	0.231694i	−0.581706	−	0.813399i	$-0.697614\pi$
$701$	6.13442	−	6.13442i	0.231694	−	0.231694i	0.813399	+	0.581706i	$0.197614\pi$
$702$		0			0
$703$	22.2615	−	22.2615i	0.839607	−	0.839607i
$704$	−7.01596	+	5.62068i	−0.264424	+	0.211837i
$705$		0			0
$706$	19.5706	+	0.358738i	0.736550	+	0.0135013i
$707$	−74.3297			−2.79546
$708$		0			0
$709$	−27.7679	−	27.7679i	−1.04285	−	1.04285i	−0.999040	−	0.0438050i	$-0.986052\pi$
$709$	−27.7679	−	27.7679i	−1.04285	−	1.04285i	−0.0438050	−	0.999040i	$-0.513948\pi$
$710$	−2.77228	−	22.9517i	−0.104042	−	0.861363i
$711$		0			0
$712$	18.6236	−	16.6805i	0.697949	−	0.625127i
$713$	35.9900	−	35.9900i	1.34783	−	1.34783i
$714$		0			0
$715$	−4.51675	+	0.629754i	−0.168917	+	0.0235515i
$716$	32.5150	−	30.2145i	1.21514	−	1.12917i
$717$		0			0
$718$	2.59642	+	2.69339i	0.0968976	+	0.100516i
$719$	−1.11652			−0.0416391			−0.0208195	−	0.999783i	$-0.506628\pi$
$719$	−1.11652			−0.0416391			−0.0208195	+	0.999783i	$0.506628\pi$
$720$		0			0
$721$	14.9367			0.556271
$722$	13.9975	+	14.5202i	0.520933	+	0.540387i
$723$		0			0
$724$	−12.6316	−	13.5933i	−0.469449	−	0.505192i
$725$	−8.72844	+	15.6657i	−0.324166	+	0.581808i
$726$		0			0
$727$	22.7799	−	22.7799i	0.844859	−	0.844859i	−0.144627	−	0.989486i	$-0.546198\pi$
$727$	22.7799	−	22.7799i	0.844859	−	0.844859i	0.989486	+	0.144627i	$0.0461983\pi$
$728$	−25.5260	−	1.40497i	−0.946057	−	0.0520715i
$729$		0			0
$730$	−28.0479	+	35.7544i	−1.03810	+	1.32333i
$731$	2.82068	+	2.82068i	0.104327	+	0.104327i
$732$		0			0
$733$	14.3681			0.530699			0.265350	−	0.964152i	$-0.414513\pi$
$733$	14.3681			0.530699			0.265350	+	0.964152i	$0.414513\pi$
$734$	−12.0779	−	0.221393i	−0.445803	−	0.00817175i
$735$		0			0
$736$	−3.27616	+	35.6495i	−0.120761	+	1.31406i
$737$	−2.26628	+	2.26628i	−0.0834795	+	0.0834795i
$738$		0			0
$739$	−2.18646	+	2.18646i	−0.0804301	+	0.0804301i	−0.746177	−	0.665747i	$-0.768113\pi$
$739$	−2.18646	+	2.18646i	−0.0804301	+	0.0804301i	0.665747	+	0.746177i	$0.268113\pi$
$740$	−18.9284	−	15.4172i	−0.695822	−	0.566749i
$741$		0			0
$742$	−0.996015	+	54.3368i	−0.0365649	+	1.99477i
$743$	28.0875	−	28.0875i	1.03043	−	1.03043i	0.0309076	−	0.999522i	$-0.490160\pi$
$743$	28.0875	−	28.0875i	1.03043	−	1.03043i	0.999522	−	0.0309076i	$-0.00983975\pi$
$744$		0			0
$745$	2.67430	+	19.1808i	0.0979790	+	0.702729i
$746$	−14.4878	−	15.0289i	−0.530438	−	0.550247i
$747$		0			0
$748$	0.0675507	−	1.84197i	0.00246990	−	0.0673490i
$749$	−13.6823	−	13.6823i	−0.499940	−	0.499940i
$750$		0			0
$751$	15.9304			0.581307			0.290654	−	0.956828i	$-0.406127\pi$
$751$	15.9304			0.581307			0.290654	+	0.956828i	$0.406127\pi$
$752$	25.0008	−	21.5797i	0.911684	−	0.786930i
$753$		0			0
$754$	−9.20435	−	0.168720i	−0.335203	−	0.00614440i
$755$	−10.6681	−	8.05727i	−0.388251	−	0.293234i
$756$		0			0
$757$	−37.2691			−1.35457			−0.677285	−	0.735721i	$-0.736844\pi$
$757$	−37.2691			−1.35457			−0.677285	+	0.735721i	$0.736844\pi$
$758$	31.0618	+	0.569375i	1.12821	+	0.0206806i
$759$		0			0
$760$	23.5496	−	27.8544i	0.854235	−	1.01038i
$761$	17.3081			0.627419			0.313709	−	0.949519i	$-0.398428\pi$
$761$	17.3081			0.627419			0.313709	+	0.949519i	$0.398428\pi$
$762$		0			0
$763$		−	87.7826i		−	3.17794i
$764$	40.8921	+	1.49964i	1.47943	+	0.0542552i
$765$		0			0
$766$	−19.2296	−	0.352487i	−0.694794	−	0.0127359i
$767$	−5.74688	+	5.74688i	−0.207508	+	0.207508i
$768$		0			0
$769$			24.2688i			0.875155i	0.899181	+	0.437577i	$0.144163\pi$
$769$			24.2688i			0.875155i	−0.899181	+	0.437577i	$0.855837\pi$
$770$	2.12210	+	17.5689i	0.0764750	+	0.633138i
$771$		0			0
$772$	30.3585	+	32.6699i	1.09263	+	1.17582i
$773$	−13.0667			−0.469977			−0.234989	−	0.971998i	$-0.575505\pi$
$773$	−13.0667			−0.469977			−0.234989	+	0.971998i	$0.575505\pi$
$774$		0			0
$775$	10.9996	+	38.6790i	0.395116	+	1.38939i
$776$	−0.613122	+	11.1395i	−0.0220098	+	0.399883i
$777$		0			0
$778$	−0.101682	+	5.54717i	−0.00364547	+	0.198876i
$779$	13.8283	−	13.8283i	0.495450	−	0.495450i
$780$		0			0
$781$	−5.80902	−	5.80902i	−0.207863	−	0.207863i
$782$	−5.09428	−	5.28453i	−0.182171	−	0.188974i
$783$		0			0
$784$	−5.21541	+	71.0110i	−0.186265	+	2.53611i
$785$	33.7022	+	25.4543i	1.20288	+	0.908501i
$786$		0			0
$787$			19.0159i			0.677844i	0.940814	+	0.338922i	$0.110062\pi$
$787$			19.0159i			0.677844i	−0.940814	+	0.338922i	$0.889938\pi$
$788$	−9.38368	−	0.344129i	−0.334280	−	0.0122591i
$789$		0			0
$790$	−29.8338	+	3.60355i	−1.06144	+	0.128208i
$791$	89.7900			3.19257
$792$		0			0
$793$	−4.51819	−	4.51819i	−0.160446	−	0.160446i
$794$	25.5783	+	26.5335i	0.907739	+	0.941638i
$795$		0			0
$796$	0.345949	−	9.43331i	0.0122618	−	0.334355i
$797$	19.8027			0.701447			0.350723	−	0.936479i	$-0.385936\pi$
$797$	19.8027			0.701447			0.350723	+	0.936479i	$0.385936\pi$
$798$		0			0
$799$			6.77147i			0.239557i
$800$	−23.3444	−	15.9699i	−0.825351	−	0.564620i
$801$		0			0
$802$	2.38975	+	2.47900i	0.0843851	+	0.0875365i
$803$			16.1482i			0.569857i
$804$		0			0
$805$	56.2355	+	42.4730i	1.98204	+	1.49697i
$806$	−14.8618	+	14.3268i	−0.523485	+	0.504639i
$807$		0			0
$808$	2.32008	−	42.1522i	0.0816201	−	1.48291i
$809$			43.2999i			1.52234i	0.648550	+	0.761172i	$0.275376\pi$
$809$			43.2999i			1.52234i	−0.648550	+	0.761172i	$0.724624\pi$
$810$		0			0
$811$	−36.4064	+	36.4064i	−1.27840	+	1.27840i	−0.336837	+	0.941563i	$0.609357\pi$
$811$	−36.4064	+	36.4064i	−1.27840	+	1.27840i	−0.941563	+	0.336837i	$0.890643\pi$
$812$	−1.30919	+	35.6990i	−0.0459437	+	1.25279i
$813$		0			0
$814$	−8.67360	−	0.158991i	−0.304009	−	0.00557262i
$815$	−19.6092	+	25.9633i	−0.686882	+	0.909453i
$816$		0			0
$817$	19.8352	+	19.8352i	0.693947	+	0.693947i
$818$	−12.2021	+	11.7629i	−0.426638	+	0.411279i
$819$		0			0
$820$	−11.7579	−	9.57683i	−0.410603	−	0.334437i
$821$	2.11395	+	2.11395i	0.0737773	+	0.0737773i	0.743033	−	0.669255i	$-0.233387\pi$
$821$	2.11395	+	2.11395i	0.0737773	+	0.0737773i	−0.669255	+	0.743033i	$0.733387\pi$
$822$		0			0
$823$	0.790237	+	0.790237i	0.0275459	+	0.0275459i	0.720746	−	0.693200i	$-0.243800\pi$
$823$	0.790237	+	0.790237i	0.0275459	+	0.0275459i	−0.693200	+	0.720746i	$0.743800\pi$
$824$	−0.466224	+	8.47055i	−0.0162417	+	0.295086i
$825$		0			0
$826$	21.8880	+	22.7054i	0.761582	+	0.790023i
$827$			19.8813i			0.691342i	0.938356	+	0.345671i	$0.112349\pi$
$827$			19.8813i			0.691342i	−0.938356	+	0.345671i	$0.887651\pi$
$828$		0			0
$829$	29.8495	−	29.8495i	1.03671	−	1.03671i	0.0374151	−	0.999300i	$-0.488088\pi$
$829$	29.8495	−	29.8495i	1.03671	−	1.03671i	0.999300	−	0.0374151i	$-0.0119124\pi$
$830$	33.9831	−	4.10473i	1.17957	−	0.142477i
$831$		0			0
$832$	1.59350	−	14.4319i	0.0552448	−	0.500335i
$833$	−10.3230	−	10.3230i	−0.357670	−	0.357670i
$834$		0			0
$835$	−49.0400	+	6.83747i	−1.69710	+	0.236621i
$836$	0.475022	−	12.9528i	0.0164290	−	0.447984i
$837$		0			0
$838$	45.8089	+	0.839697i	1.58244	+	0.0290068i
$839$		−	38.6066i		−	1.33285i	−0.745573	−	0.666424i	$-0.767824\pi$
$839$		−	38.6066i		−	1.33285i	0.745573	−	0.666424i	$-0.232176\pi$
$840$		0			0
$841$		−	16.1361i		−	0.556416i
$842$	0.255903	−	13.9605i	0.00881898	−	0.481112i
$843$		0			0
$844$	18.6118	−	17.2950i	0.640645	−	0.595319i
$845$	−13.0802	+	17.3187i	−0.449974	+	0.595780i
$846$		0			0
$847$	−34.2888	−	34.2888i	−1.17818	−	1.17818i
$848$	−30.7831	−	2.26087i	−1.05710	−	0.0776386i
$849$		0			0
$850$	5.60620	−	1.48380i	0.192291	−	0.0508939i
$851$	−24.4281	+	24.4281i	−0.837383	+	0.837383i
$852$		0			0
$853$		−	6.72965i		−	0.230419i	−0.993341	−	0.115209i	$-0.963246\pi$
$853$		−	6.72965i		−	0.230419i	0.993341	−	0.115209i	$-0.0367539\pi$
$854$	−17.8510	+	17.2083i	−0.610848	+	0.588857i
$855$		0			0
$856$	8.18626	−	7.33212i	0.279800	−	0.250607i
$857$	14.8406	+	14.8406i	0.506945	+	0.506945i	0.913588	−	0.406642i	$-0.133300\pi$
$857$	14.8406	+	14.8406i	0.506945	+	0.506945i	−0.406642	+	0.913588i	$0.633300\pi$
$858$		0			0
$859$	−7.20839	−	7.20839i	−0.245947	−	0.245947i	0.573358	−	0.819305i	$-0.305640\pi$
$859$	−7.20839	−	7.20839i	−0.245947	−	0.245947i	−0.819305	+	0.573358i	$0.805640\pi$
$860$	13.7370	−	16.8655i	0.468426	−	0.575107i
$861$		0			0
$862$	−17.9034	−	18.5720i	−0.609793	−	0.632566i
$863$	−28.9476	−	28.9476i	−0.985388	−	0.985388i	0.0145070	−	0.999895i	$-0.495382\pi$
$863$	−28.9476	−	28.9476i	−0.985388	−	0.985388i	−0.999895	+	0.0145070i	$0.995382\pi$
$864$		0			0
$865$	−12.6816	−	9.57801i	−0.431187	−	0.325662i
$866$	0.424889	−	23.1795i	0.0144383	−	0.787671i
$867$		0			0
$868$	54.5280	+	58.6797i	1.85080	+	1.99172i
$869$	−7.55087	+	7.55087i	−0.256146	+	0.256146i
$870$		0			0
$871$		−	5.17648i		−	0.175398i
$872$	49.7812	+	2.73999i	1.68581	+	0.0927877i
$873$		0			0
$874$	−35.8233	−	37.1612i	−1.21174	−	1.25700i
$875$	−50.9386	+	22.4795i	−1.72204	+	0.759946i
$876$		0			0
$877$		−	26.1006i		−	0.881355i	−0.897666	−	0.440677i	$-0.854738\pi$
$877$		−	26.1006i		−	0.881355i	0.897666	−	0.440677i	$-0.145262\pi$
$878$	−1.17999	+	1.13751i	−0.0398228	+	0.0383891i
$879$		0			0
$880$	−10.0295	+	0.655051i	−0.338094	+	0.0220818i
$881$		−	52.3645i		−	1.76421i	−0.471057	−	0.882103i	$-0.656127\pi$
$881$		−	52.3645i		−	1.76421i	0.471057	−	0.882103i	$-0.343873\pi$
$882$		0			0
$883$	47.1364			1.58627			0.793134	−	0.609047i	$-0.208448\pi$
$883$	47.1364			1.58627			0.793134	+	0.609047i	$0.208448\pi$
$884$	2.02650	+	2.18080i	0.0681586	+	0.0733481i
$885$		0			0
$886$	−8.27502	+	7.97711i	−0.278005	+	0.267996i
$887$	−39.2668	−	39.2668i	−1.31845	−	1.31845i	−0.915004	−	0.403444i	$-0.867813\pi$
$887$	−39.2668	−	39.2668i	−1.31845	−	1.31845i	−0.403444	−	0.915004i	$-0.632187\pi$
$888$		0			0
$889$	66.0181			2.21417
$890$	27.7509	−	3.35195i	0.930211	−	0.112358i
$891$		0			0
$892$	6.52446	+	7.02122i	0.218455	+	0.235088i
$893$			47.6175i			1.59346i
$894$		0			0
$895$	49.1500	−	6.85280i	1.64290	−	0.229064i
$896$	−55.8794	−	7.20884i	−1.86680	−	0.240830i
$897$		0			0
$898$	−4.32597	+	4.17023i	−0.144360	+	0.139163i
$899$	20.3969	+	20.3969i	0.680275	+	0.680275i
$900$		0			0
$901$	4.47499	−	4.47499i	0.149083	−	0.149083i
$902$	−5.38784	−	0.0987613i	−0.179395	−	0.00328839i
$903$		0			0
$904$	−2.80265	+	50.9197i	−0.0932146	+	1.69356i
$905$	−2.86490	−	20.5478i	−0.0952326	−	0.683031i
$906$		0			0
$907$	0.853198			0.0283300			0.0141650	−	0.999900i	$-0.495491\pi$
$907$	0.853198			0.0283300			0.0141650	+	0.999900i	$0.495491\pi$
$908$	0.933002	−	25.4410i	0.0309628	−	0.844290i
$909$		0			0
$910$	−22.4884	−	17.6412i	−0.745482	−	0.584801i
$911$		−	0.383383i		−	0.0127020i	−0.999980	−	0.00635102i	$-0.997978\pi$
$911$		−	0.383383i		−	0.0127020i	0.999980	−	0.00635102i	$-0.00202161\pi$
$912$		0			0
$913$	8.60104	−	8.60104i	0.284653	−	0.284653i
$914$	−0.314507	+	17.1577i	−0.0104030	+	0.567525i
$915$		0			0
$916$	−38.1195	+	35.4224i	−1.25950	+	1.17039i
$917$		−	6.23860i		−	0.206017i
$918$		0			0
$919$	−20.4070			−0.673165			−0.336582	−	0.941654i	$-0.609271\pi$
$919$	−20.4070			−0.673165			−0.336582	+	0.941654i	$0.609271\pi$
$920$	−25.8416	+	30.5653i	−0.851972	+	1.00771i
$921$		0			0
$922$	0.998404	−	54.4671i	0.0328807	−	1.79378i
$923$	13.2686			0.436741
$924$		0			0
$925$	−7.46592	−	26.2532i	−0.245478	−	0.863200i
$926$	0.753269	−	41.0939i	0.0247539	−	1.35043i
$927$		0			0
$928$	−20.2039	−	1.85673i	−0.663227	−	0.0609500i
$929$	5.66448			0.185846			0.0929228	−	0.995673i	$-0.470379\pi$
$929$	5.66448			0.185846			0.0929228	+	0.995673i	$0.470379\pi$
$930$		0			0
$931$	−72.5919	−	72.5919i	−2.37910	−	2.37910i
$932$	−9.20882	−	9.90996i	−0.301645	−	0.324612i
$933$		0			0
$934$	−7.76227	+	7.48282i	−0.253989	+	0.244845i
$935$	1.24200	−	1.64444i	0.0406177	−	0.0537791i
$936$		0			0
$937$	−4.52855	+	4.52855i	−0.147941	+	0.147941i	−0.777198	−	0.629256i	$-0.783360\pi$
$937$	−4.52855	+	4.52855i	−0.147941	+	0.147941i	0.629256	+	0.777198i	$0.283360\pi$
$938$	−20.0837	−	0.368142i	−0.655756	−	0.0120203i
$939$		0			0
$940$	36.7328	−	3.75522i	1.19809	−	0.122482i
$941$	33.1033	−	33.1033i	1.07914	−	1.07914i	0.0825482	−	0.996587i	$-0.473694\pi$
$941$	33.1033	−	33.1033i	1.07914	−	1.07914i	0.996587	−	0.0825482i	$-0.0263058\pi$
$942$		0			0
$943$	−15.1741	+	15.1741i	−0.494138	+	0.494138i
$944$	−13.5594	+	11.7039i	−0.441320	+	0.380930i
$945$		0			0
$946$	0.141663	−	7.72828i	0.00460585	−	0.251268i
$947$	−42.2938			−1.37436			−0.687182	−	0.726486i	$-0.741152\pi$
$947$	−42.2938			−1.37436			−0.687182	+	0.726486i	$0.741152\pi$
$948$		0			0
$949$	−18.4423	−	18.4423i	−0.598662	−	0.598662i
$950$	39.4232	−	10.4342i	1.27906	−	0.338530i
$951$		0			0
$952$	8.60516	−	7.70731i	0.278895	−	0.249796i
$953$	−7.70327	+	7.70327i	−0.249533	+	0.249533i	−0.820779	−	0.571246i	$-0.806460\pi$
$953$	−7.70327	+	7.70327i	−0.249533	+	0.249533i	0.571246	+	0.820779i	$0.306460\pi$
$954$		0			0
$955$	36.5071	+	27.5727i	1.18134	+	0.892231i
$956$	−0.710151	+	19.3643i	−0.0229679	+	0.626287i
$957$		0			0
$958$	−18.2980	+	17.6393i	−0.591183	+	0.569900i
$959$	14.0525			0.453780
$960$		0			0
$961$	33.6821			1.08652
$962$	10.0874	−	9.72424i	0.325231	−	0.313522i
$963$		0			0
$964$	0.495431	−	13.5094i	0.0159568	−	0.435108i
$965$	6.88545	+	49.3841i	0.221651	+	1.58973i
$966$		0			0
$967$	−15.1520	+	15.1520i	−0.487255	+	0.487255i	−0.907439	−	0.420184i	$-0.861966\pi$
$967$	−15.1520	+	15.1520i	−0.487255	+	0.487255i	0.420184	+	0.907439i	$0.361966\pi$
$968$	20.5153	−	18.3748i	0.659388	−	0.590589i
$969$		0			0
$970$	−7.69857	+	9.81384i	−0.247186	+	0.315104i
$971$	−18.9617	−	18.9617i	−0.608508	−	0.608508i	0.334048	−	0.942556i	$-0.391585\pi$
$971$	−18.9617	−	18.9617i	−0.608508	−	0.608508i	−0.942556	+	0.334048i	$0.891585\pi$
$972$		0			0
$973$	30.7876			0.987007
$974$	−0.711419	+	38.8109i	−0.0227953	+	1.24358i
$975$		0			0
$976$	−9.20160	−	10.6604i	−0.294536	−	0.341230i
$977$	35.4983	−	35.4983i	1.13569	−	1.13569i	0.146477	−	0.989214i	$-0.453207\pi$
$977$	35.4983	−	35.4983i	1.13569	−	1.13569i	0.989214	−	0.146477i	$-0.0467934\pi$
$978$		0			0
$979$	7.02367	−	7.02367i	0.224478	−	0.224478i
$980$	−50.2737	+	61.7232i	−1.60594	+	1.97168i
$981$		0			0
$982$	0.776796	+	0.0142390i	0.0247886	+	0.000454384i
$983$	14.4359	−	14.4359i	0.460434	−	0.460434i	−0.438364	−	0.898798i	$-0.644442\pi$
$983$	14.4359	−	14.4359i	0.460434	−	0.460434i	0.898798	+	0.438364i	$0.144442\pi$
$984$		0			0
$985$	−8.37743	−	6.32721i	−0.266927	−	0.201602i
$986$	2.99494	−	2.88712i	0.0953785	−	0.0919448i
$987$		0			0
$988$	14.2505	+	15.3355i	0.453369	+	0.487888i
$989$	−21.7657	−	21.7657i	−0.692109	−	0.692109i
$990$		0			0
$991$	4.78714			0.152069			0.0760343	−	0.997105i	$-0.475774\pi$
$991$	4.78714			0.152069			0.0760343	+	0.997105i	$0.475774\pi$
$992$	−34.9791	+	29.0911i	−1.11059	+	0.923643i
$993$		0			0
$994$	0.943638	−	51.4794i	0.0299304	−	1.63283i
$995$	6.36068	−	8.42174i	0.201647	−	0.266987i
$996$		0			0
$997$	1.03678			0.0328350			0.0164175	−	0.999865i	$-0.494774\pi$
$997$	1.03678			0.0328350			0.0164175	+	0.999865i	$0.494774\pi$
$998$	−0.571178	+	31.1602i	−0.0180803	+	0.986357i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bg.a.557.11	yes	96
3.2	odd	2	inner	720.2.bg.a.557.38	yes	96
4.3	odd	2		2880.2.bg.a.17.34		96
5.3	odd	4		720.2.bc.a.413.35	yes	96
12.11	even	2		2880.2.bg.a.17.15		96
15.8	even	4		720.2.bc.a.413.14	yes	96
16.5	even	4		720.2.bc.a.197.14	✓	96
16.11	odd	4		2880.2.bc.a.1457.39		96
20.3	even	4		2880.2.bc.a.593.10		96
48.5	odd	4		720.2.bc.a.197.35	yes	96
48.11	even	4		2880.2.bc.a.1457.10		96
60.23	odd	4		2880.2.bc.a.593.39		96
80.43	even	4		2880.2.bg.a.2033.15		96
80.53	odd	4	inner	720.2.bg.a.53.38	yes	96
240.53	even	4	inner	720.2.bg.a.53.11	yes	96
240.203	odd	4		2880.2.bg.a.2033.34		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.14	✓	96	16.5	even	4
720.2.bc.a.197.35	yes	96	48.5	odd	4
720.2.bc.a.413.14	yes	96	15.8	even	4
720.2.bc.a.413.35	yes	96	5.3	odd	4
720.2.bg.a.53.11	yes	96	240.53	even	4	inner
720.2.bg.a.53.38	yes	96	80.53	odd	4	inner
720.2.bg.a.557.11	yes	96	1.1	even	1	trivial
720.2.bg.a.557.38	yes	96	3.2	odd	2	inner
2880.2.bc.a.593.10		96	20.3	even	4
2880.2.bc.a.593.39		96	60.23	odd	4
2880.2.bc.a.1457.10		96	48.11	even	4
2880.2.bc.a.1457.39		96	16.11	odd	4
2880.2.bg.a.17.15		96	12.11	even	2
2880.2.bg.a.17.34		96	4.3	odd	2
2880.2.bg.a.2033.15		96	80.43	even	4
2880.2.bg.a.2033.34		96	240.203	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bg (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01816 + 0.981505i) q^{2} +(0.0732970 - 1.99866i) q^{4} +(1.34765 - 1.78433i) q^{5} +(3.52140 - 3.52140i) q^{7} +(1.88706 + 2.10689i) q^{8} +O(q^{10})\)	\(q+(-1.01816 + 0.981505i) q^{2} +(0.0732970 - 1.99866i) q^{4} +(1.34765 - 1.78433i) q^{5} +(3.52140 - 3.52140i) q^{7} +(1.88706 + 2.10689i) q^{8} +(0.379207 + 3.13946i) q^{10} +(0.794589 + 0.794589i) q^{11} -1.81495 q^{13} +(-0.129076 + 7.04162i) q^{14} +(-3.98926 - 0.292991i) q^{16} +(0.579924 - 0.579924i) q^{17} +(4.07807 - 4.07807i) q^{19} +(-3.46749 - 2.82428i) q^{20} +(-1.58891 - 0.0291254i) q^{22} +(-4.47496 + 4.47496i) q^{23} +(-1.36768 - 4.80931i) q^{25} +(1.84791 - 1.78138i) q^{26} +(-6.77997 - 7.29618i) q^{28} +(-2.53613 - 2.53613i) q^{29} -8.04252 q^{31} +(4.34927 - 3.61716i) q^{32} +(-0.0212569 + 1.15965i) q^{34} +(-1.53773 - 11.0290i) q^{35} +5.45883 q^{37} +(-0.149480 + 8.15476i) q^{38} +(6.30249 - 0.527791i) q^{40} +3.39090 q^{41} +4.86388i q^{43} +(1.64635 - 1.52987i) q^{44} +(0.164028 - 8.94842i) q^{46} +(-5.83824 + 5.83824i) q^{47} -17.8006i q^{49} +(6.11287 + 3.55426i) q^{50} +(-0.133030 + 3.62746i) q^{52} +7.71651 q^{53} +(2.48864 - 0.346982i) q^{55} +(14.0643 + 0.774108i) q^{56} +(5.07142 + 0.0929611i) q^{58} +(3.16642 - 3.16642i) q^{59} +(2.48943 + 2.48943i) q^{61} +(8.18857 - 7.89377i) q^{62} +(-0.877989 + 7.95167i) q^{64} +(-2.44591 + 3.23847i) q^{65} +2.85214i q^{67} +(-1.11656 - 1.20158i) q^{68} +(12.3906 + 9.71996i) q^{70} -7.31072 q^{71} +(10.1613 + 10.1613i) q^{73} +(-5.55796 + 5.35787i) q^{74} +(-7.85174 - 8.44956i) q^{76} +5.59614 q^{77} +9.50285i q^{79} +(-5.89891 + 6.72330i) q^{80} +(-3.45247 + 3.32818i) q^{82} -10.8245i q^{83} +(-0.253242 - 1.81631i) q^{85} +(-4.77392 - 4.95221i) q^{86} +(-0.174674 + 3.17355i) q^{88} -8.83938i q^{89} +(-6.39116 + 6.39116i) q^{91} +(8.61591 + 9.27191i) q^{92} +(0.213999 - 11.6745i) q^{94} +(-1.78081 - 12.7724i) q^{95} +(2.78908 + 2.78908i) q^{97} +(17.4713 + 18.1238i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{4}+O(q^{10}) \) 96 * q - 8 * q^4	\( 96 q - 8 q^{4} + 8 q^{16} - 16 q^{19} + 16 q^{22} - 32 q^{28} + 8 q^{34} + 40 q^{40} + 8 q^{46} + 56 q^{52} + 16 q^{58} + 32 q^{61} - 8 q^{64} + 56 q^{70} + 8 q^{76} - 80 q^{82} - 64 q^{88} - 40 q^{94}+O(q^{100}) \) 96 * q - 8 * q^4 + 8 * q^16 - 16 * q^19 + 16 * q^22 - 32 * q^28 + 8 * q^34 + 40 * q^40 + 8 * q^46 + 56 * q^52 + 16 * q^58 + 32 * q^61 - 8 * q^64 + 56 * q^70 + 8 * q^76 - 80 * q^82 - 64 * q^88 - 40 * q^94

Introduction

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