LMFDB - Embedded newform 592.2.bq.b.321.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			321.1
Root			$-0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	592.321
Dual form			592.2.bq.b.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43969 - 1.20805i) q^{3} +(-1.45842 - 4.00698i) q^{5} +(3.39364 - 1.23518i) q^{7} +(0.0923963 + 0.524005i) q^{9} +O(q^{10})$	\(q+(-1.43969 - 1.20805i) q^{3} +(-1.45842 - 4.00698i) q^{5} +(3.39364 - 1.23518i) q^{7} +(0.0923963 + 0.524005i) q^{9} +(-1.05840 - 1.83321i) q^{11} +(2.84019 + 0.500802i) q^{13} +(-2.74094 + 7.53066i) q^{15} +(0.0263137 - 0.00463982i) q^{17} +(2.07522 - 2.47315i) q^{19} +(-6.37796 - 2.32139i) q^{21} +(-2.57421 - 1.48622i) q^{23} +(-10.0987 + 8.47380i) q^{25} +(-2.31908 + 4.01676i) q^{27} +(4.96493 - 2.86650i) q^{29} +6.76932i q^{31} +(-0.690823 + 3.91785i) q^{33} +(-9.89872 - 11.7968i) q^{35} +(-4.49375 + 4.09954i) q^{37} +(-3.48401 - 4.15208i) q^{39} +(0.259000 - 1.46886i) q^{41} -5.53737i q^{43} +(1.96493 - 1.13445i) q^{45} +(1.30654 - 2.26300i) q^{47} +(4.62880 - 3.88403i) q^{49} +(-0.0434888 - 0.0251083i) q^{51} +(-1.79389 - 0.652924i) q^{53} +(-5.80203 + 6.91459i) q^{55} +(-5.97536 + 1.05362i) q^{57} +(-1.92380 + 5.28560i) q^{59} +(-5.65366 - 0.996892i) q^{61} +(0.960802 + 1.66416i) q^{63} +(-2.13549 - 12.1110i) q^{65} +(6.50406 - 2.36728i) q^{67} +(1.91065 + 5.24947i) q^{69} +(7.10830 + 5.96457i) q^{71} +16.2707 q^{73} +24.7757 q^{75} +(-5.85619 - 4.91392i) q^{77} +(0.484006 + 1.32980i) q^{79} +(9.69119 - 3.52730i) q^{81} +(0.294580 + 1.67065i) q^{83} +(-0.0569682 - 0.0986718i) q^{85} +(-10.6108 - 1.87098i) q^{87} +(2.82882 - 7.77213i) q^{89} +(10.2572 - 1.80861i) q^{91} +(8.17765 - 9.74574i) q^{93} +(-12.9364 - 4.70847i) q^{95} +(5.65105 + 3.26264i) q^{97} +(0.862818 - 0.723990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.43969	−	1.20805i	−0.831207	−	0.697465i	0.124361	−	0.992237i	$-0.460312\pi$
$3$	−1.43969	−	1.20805i	−0.831207	−	0.697465i	−0.955568	+	0.294772i	$0.904756\pi$
$4$		0			0
$5$	−1.45842	−	4.00698i	−0.652226	−	1.79198i	−0.609358	−	0.792895i	$-0.708573\pi$
$5$	−1.45842	−	4.00698i	−0.652226	−	1.79198i	−0.0428683	−	0.999081i	$-0.513650\pi$
$6$		0			0
$7$	3.39364	−	1.23518i	1.28268	−	0.466856i	0.391359	−	0.920238i	$-0.372005\pi$
$7$	3.39364	−	1.23518i	1.28268	−	0.466856i	0.891316	+	0.453382i	$0.149783\pi$
$8$		0			0
$9$	0.0923963	+	0.524005i	0.0307988	+	0.174668i
$10$		0			0
$11$	−1.05840	−	1.83321i	−0.319120	−	0.552733i	0.661184	−	0.750223i	$-0.270054\pi$
$11$	−1.05840	−	1.83321i	−0.319120	−	0.552733i	−0.980305	+	0.197491i	$0.936721\pi$
$12$		0			0
$13$	2.84019	+	0.500802i	0.787726	+	0.138897i	0.553019	−	0.833169i	$-0.313476\pi$
$13$	2.84019	+	0.500802i	0.787726	+	0.138897i	0.234707	+	0.972066i	$0.424587\pi$
$14$		0			0
$15$	−2.74094	+	7.53066i	−0.707707	+	1.94441i
$16$		0			0
$17$	0.0263137	−	0.00463982i	0.00638202	−	0.00112532i	−0.170456	−	0.985365i	$-0.554524\pi$
$17$	0.0263137	−	0.00463982i	0.00638202	−	0.00112532i	0.176838	+	0.984240i	$0.443413\pi$
$18$		0			0
$19$	2.07522	−	2.47315i	0.476088	−	0.567380i	−0.473534	−	0.880775i	$-0.657022\pi$
$19$	2.07522	−	2.47315i	0.476088	−	0.567380i	0.949623	+	0.313395i	$0.101466\pi$
$20$		0			0
$21$	−6.37796	−	2.32139i	−1.39178	−	0.506568i
$22$		0			0
$23$	−2.57421	−	1.48622i	−0.536760	−	0.309899i	0.207005	−	0.978340i	$-0.433628\pi$
$23$	−2.57421	−	1.48622i	−0.536760	−	0.309899i	−0.743765	+	0.668441i	$0.766962\pi$
$24$		0			0
$25$	−10.0987	+	8.47380i	−2.01974	+	1.69476i
$26$		0			0
$27$	−2.31908	+	4.01676i	−0.446307	+	0.773026i
$28$		0			0
$29$	4.96493	−	2.86650i	0.921964	−	0.532296i	0.0377027	−	0.999289i	$-0.487996\pi$
$29$	4.96493	−	2.86650i	0.921964	−	0.532296i	0.884261	+	0.466993i	$0.154663\pi$
$30$		0			0
$31$			6.76932i			1.21581i	0.794011	+	0.607903i	$0.207989\pi$
$31$			6.76932i			1.21581i	−0.794011	+	0.607903i	$0.792011\pi$
$32$		0			0
$33$	−0.690823	+	3.91785i	−0.120257	+	0.682011i
$34$		0			0
$35$	−9.89872	−	11.7968i	−1.67319	−	1.99403i
$36$		0			0
$37$	−4.49375	+	4.09954i	−0.738767	+	0.673961i
$37$	−4.49375	+	4.09954i	−0.738767	+	0.673961i
$38$		0			0
$39$	−3.48401	−	4.15208i	−0.557887	−	0.664864i
$40$		0			0
$41$	0.259000	−	1.46886i	0.0404490	−	0.229398i	−0.957881	−	0.287165i	$-0.907287\pi$
$41$	0.259000	−	1.46886i	0.0404490	−	0.229398i	0.998330	+	0.0577674i	$0.0183982\pi$
$42$		0			0
$43$		−	5.53737i		−	0.844441i	−0.906493	−	0.422221i	$-0.861251\pi$
$43$		−	5.53737i		−	0.844441i	0.906493	−	0.422221i	$-0.138749\pi$
$44$		0			0
$45$	1.96493	−	1.13445i	0.292914	−	0.169114i
$46$		0			0
$47$	1.30654	−	2.26300i	0.190579	−	0.330092i	−0.754863	−	0.655882i	$-0.772297\pi$
$47$	1.30654	−	2.26300i	0.190579	−	0.330092i	0.945442	+	0.325790i	$0.105630\pi$
$48$		0			0
$49$	4.62880	−	3.88403i	0.661257	−	0.554861i
$50$		0			0
$51$	−0.0434888	−	0.0251083i	−0.00608965	−	0.00351586i
$52$		0			0
$53$	−1.79389	−	0.652924i	−0.246410	−	0.0896860i	0.215862	−	0.976424i	$-0.430744\pi$
$53$	−1.79389	−	0.652924i	−0.246410	−	0.0896860i	−0.462273	+	0.886738i	$0.652966\pi$
$54$		0			0
$55$	−5.80203	+	6.91459i	−0.782345	+	0.932363i
$56$		0			0
$57$	−5.97536	+	1.05362i	−0.791456	+	0.139555i
$58$		0			0
$59$	−1.92380	+	5.28560i	−0.250457	+	0.688126i	0.749210	+	0.662333i	$0.230433\pi$
$59$	−1.92380	+	5.28560i	−0.250457	+	0.688126i	−0.999667	+	0.0257935i	$0.991789\pi$
$60$		0			0
$61$	−5.65366	−	0.996892i	−0.723876	−	0.127639i	−0.200443	−	0.979705i	$-0.564238\pi$
$61$	−5.65366	−	0.996892i	−0.723876	−	0.127639i	−0.523434	+	0.852066i	$0.675349\pi$
$62$		0			0
$63$	0.960802	+	1.66416i	0.121050	+	0.209664i
$64$		0			0
$65$	−2.13549	−	12.1110i	−0.264875	−	1.50218i
$66$		0			0
$67$	6.50406	−	2.36728i	0.794597	−	0.289210i	0.0873516	−	0.996178i	$-0.472160\pi$
$67$	6.50406	−	2.36728i	0.794597	−	0.289210i	0.707246	+	0.706968i	$0.249937\pi$
$68$		0			0
$69$	1.91065	+	5.24947i	0.230015	+	0.631962i
$70$		0			0
$71$	7.10830	+	5.96457i	0.843600	+	0.707865i	0.958371	−	0.285527i	$-0.0921688\pi$
$71$	7.10830	+	5.96457i	0.843600	+	0.707865i	−0.114770	+	0.993392i	$0.536613\pi$
$72$		0			0
$73$	16.2707			1.90434			0.952169	−	0.305571i	$-0.0988473\pi$
$73$	16.2707			1.90434			0.952169	+	0.305571i	$0.0988473\pi$
$74$		0			0
$75$	24.7757			2.86085
$76$		0			0
$77$	−5.85619	−	4.91392i	−0.667374	−	0.559993i
$78$		0			0
$79$	0.484006	+	1.32980i	0.0544549	+	0.149614i	0.963938	−	0.266128i	$-0.0857443\pi$
$79$	0.484006	+	1.32980i	0.0544549	+	0.149614i	−0.909483	+	0.415742i	$0.863522\pi$
$80$		0			0
$81$	9.69119	−	3.52730i	1.07680	−	0.391923i
$82$		0			0
$83$	0.294580	+	1.67065i	0.0323343	+	0.183377i	0.996697	−	0.0812054i	$-0.0258770\pi$
$83$	0.294580	+	1.67065i	0.0323343	+	0.183377i	−0.964363	+	0.264583i	$0.914766\pi$
$84$		0			0
$85$	−0.0569682	−	0.0986718i	−0.00617907	−	0.0107025i
$86$		0			0
$87$	−10.6108	−	1.87098i	−1.13760	−	0.200590i
$88$		0			0
$89$	2.82882	−	7.77213i	0.299855	−	0.823844i	−0.694669	−	0.719330i	$-0.744449\pi$
$89$	2.82882	−	7.77213i	0.299855	−	0.823844i	0.994523	−	0.104514i	$-0.0333288\pi$
$90$		0			0
$91$	10.2572	−	1.80861i	1.07524	−	0.189594i
$92$		0			0
$93$	8.17765	−	9.74574i	0.847983	−	1.01059i
$94$		0			0
$95$	−12.9364	−	4.70847i	−1.32725	−	0.483079i
$96$		0			0
$97$	5.65105	+	3.26264i	0.573777	+	0.331270i	0.758657	−	0.651491i	$-0.225856\pi$
$97$	5.65105	+	3.26264i	0.573777	+	0.331270i	−0.184879	+	0.982761i	$0.559189\pi$
$98$		0			0
$99$	0.862818	−	0.723990i	0.0867164	−	0.0727637i
$100$		0			0
$101$	−8.29974	+	14.3756i	−0.825855	+	1.43042i	0.0754083	+	0.997153i	$0.475974\pi$
$101$	−8.29974	+	14.3756i	−0.825855	+	1.43042i	−0.901264	+	0.433271i	$0.857359\pi$
$102$		0			0
$103$	−1.64095	+	0.947403i	−0.161688	+	0.0933504i	−0.578660	−	0.815569i	$-0.696424\pi$
$103$	−1.64095	+	0.947403i	−0.161688	+	0.0933504i	0.416973	+	0.908919i	$0.363091\pi$
$104$		0			0
$105$			28.9419i			2.82444i
$106$		0			0
$107$	−0.0663781	+	0.376449i	−0.00641702	+	0.0363927i	−0.987848	−	0.155422i	$-0.950326\pi$
$107$	−0.0663781	+	0.376449i	−0.00641702	+	0.0363927i	0.981431	+	0.191815i	$0.0614373\pi$
$108$		0			0
$109$	−0.620666	−	0.739681i	−0.0594490	−	0.0708485i	0.735500	−	0.677524i	$-0.236947\pi$
$109$	−0.620666	−	0.739681i	−0.0594490	−	0.0708485i	−0.794949	+	0.606676i	$0.792503\pi$
$110$		0			0
$111$	11.4220	−	0.473431i	1.08413	−	0.0449361i
$112$		0			0
$113$	1.21535	+	1.44839i	0.114330	+	0.136254i	0.820174	−	0.572114i	$-0.193876\pi$
$113$	1.21535	+	1.44839i	0.114330	+	0.136254i	−0.705844	+	0.708367i	$0.749432\pi$
$114$		0			0
$115$	−2.20098	+	12.4824i	−0.205242	+	1.16399i
$116$		0			0
$117$			1.53455i			0.141869i
$118$		0			0
$119$	0.0835683	−	0.0482482i	0.00766070	−	0.00442291i
$120$		0			0
$121$	3.25957	−	5.64574i	0.296324	−	0.513249i
$122$		0			0
$123$	−2.14733	+	1.80183i	−0.193619	+	0.162465i
$124$		0			0
$125$	30.2182	+	17.4465i	2.70280	+	1.56046i
$126$		0			0
$127$	−15.1426	−	5.51145i	−1.34369	−	0.489062i	−0.432715	−	0.901531i	$-0.642444\pi$
$127$	−15.1426	−	5.51145i	−1.34369	−	0.489062i	−0.910972	+	0.412469i	$0.864666\pi$
$128$		0			0
$129$	−6.68940	+	7.97212i	−0.588969	+	0.701906i
$130$		0			0
$131$	0.810446	−	0.142903i	0.0708090	−	0.0124855i	−0.138131	−	0.990414i	$-0.544110\pi$
$131$	0.810446	−	0.142903i	0.0708090	−	0.0124855i	0.208940	+	0.977928i	$0.432999\pi$
$132$		0			0
$133$	3.98776	−	10.9563i	0.345782	−	0.950029i
$134$		0			0
$135$	19.4773	+	3.43437i	1.67634	+	0.295583i
$136$		0			0
$137$	−8.67847	−	15.0316i	−0.741452	−	1.28423i	−0.951834	−	0.306613i	$-0.900804\pi$
$137$	−8.67847	−	15.0316i	−0.741452	−	1.28423i	0.210382	−	0.977619i	$-0.432529\pi$
$138$		0			0
$139$	−1.60198	−	9.08528i	−0.135878	−	0.770604i	−0.974244	−	0.225496i	$-0.927600\pi$
$139$	−1.60198	−	9.08528i	−0.135878	−	0.770604i	0.838366	−	0.545108i	$-0.183511\pi$
$140$		0			0
$141$	−4.61482	+	1.67966i	−0.388638	+	0.141453i
$142$		0			0
$143$	−2.08799	−	5.73670i	−0.174606	−	0.479727i
$144$		0			0
$145$	−18.7270	−	15.7138i	−1.55519	−	1.30496i
$146$		0			0
$147$	−11.3561			−0.936638
$148$		0			0
$149$	−7.73776			−0.633902			−0.316951	−	0.948442i	$-0.602659\pi$
$149$	−7.73776			−0.633902			−0.316951	+	0.948442i	$0.602659\pi$
$150$		0			0
$151$	9.68000	+	8.12248i	0.787747	+	0.660998i	0.945187	−	0.326530i	$-0.105880\pi$
$151$	9.68000	+	8.12248i	0.787747	+	0.660998i	−0.157440	+	0.987529i	$0.550324\pi$
$152$		0			0
$153$	0.00486258	+	0.0133598i	0.000393117	+	0.00108008i
$154$		0			0
$155$	27.1245	−	9.87253i	2.17870	−	0.792980i
$156$		0			0
$157$	2.26554	+	12.8485i	0.180810	+	1.02542i	0.931222	+	0.364453i	$0.118744\pi$
$157$	2.26554	+	12.8485i	0.180810	+	1.02542i	−0.750412	+	0.660971i	$0.770145\pi$
$158$		0			0
$159$	1.79389	+	3.10712i	0.142265	+	0.246410i
$160$		0			0
$161$	−10.5717	−	1.86408i	−0.833167	−	0.146910i
$162$		0			0
$163$	8.63820	−	23.7332i	0.676596	−	1.85893i	0.200038	−	0.979788i	$-0.435893\pi$
$163$	8.63820	−	23.7332i	0.676596	−	1.85893i	0.476558	−	0.879143i	$-0.341884\pi$
$164$		0			0
$165$	16.7063	−	2.94577i	1.30058	−	0.229328i
$166$		0			0
$167$	6.60851	−	7.87572i	0.511382	−	0.609441i	−0.447139	−	0.894465i	$-0.647557\pi$
$167$	6.60851	−	7.87572i	0.511382	−	0.609441i	0.958521	+	0.285023i	$0.0920014\pi$
$168$		0			0
$169$	−4.40014	−	1.60152i	−0.338472	−	0.123194i
$170$		0			0
$171$	1.48769	+	0.858917i	0.113766	+	0.0656830i
$172$		0			0
$173$	18.1222	−	15.2064i	1.37781	−	1.15612i	0.407792	−	0.913075i	$-0.366299\pi$
$173$	18.1222	−	15.2064i	1.37781	−	1.15612i	0.970016	−	0.243043i	$-0.0781456\pi$
$174$		0			0
$175$	−23.8046	+	41.2307i	−1.79946	+	3.11675i
$176$		0			0
$177$	9.15492	−	5.28560i	0.688126	−	0.397290i
$178$		0			0
$179$			5.05746i			0.378013i	0.981976	+	0.189006i	$0.0605267\pi$
$179$			5.05746i			0.378013i	−0.981976	+	0.189006i	$0.939473\pi$
$180$		0			0
$181$	−0.181540	+	1.02956i	−0.0134938	+	0.0765269i	−0.990811	−	0.135254i	$-0.956815\pi$
$181$	−0.181540	+	1.02956i	−0.0134938	+	0.0765269i	0.977317	+	0.211781i	$0.0679262\pi$
$182$		0			0
$183$	6.93524	+	8.26509i	0.512667	+	0.610973i
$184$		0			0
$185$	22.9806	+	12.0275i	1.68956	+	0.884279i
$186$		0			0
$187$	−0.0363563	−	0.0433277i	−0.00265864	−	0.00316844i
$188$		0			0
$189$	−2.90868	+	16.4959i	−0.211575	+	1.19990i
$190$		0			0
$191$		−	13.4633i		−	0.974173i	−0.873354	−	0.487087i	$-0.838060\pi$
$191$		−	13.4633i		−	0.974173i	0.873354	−	0.487087i	$-0.161940\pi$
$192$		0			0
$193$	3.91641	−	2.26114i	0.281909	−	0.162760i	−0.352378	−	0.935858i	$-0.614627\pi$
$193$	3.91641	−	2.26114i	0.281909	−	0.162760i	0.634288	+	0.773097i	$0.281294\pi$
$194$		0			0
$195$	−11.5561	+	20.0158i	−0.827552	+	1.43336i
$196$		0			0
$197$	−9.47751	+	7.95257i	−0.675245	+	0.566597i	−0.914613	−	0.404331i	$-0.867504\pi$
$197$	−9.47751	+	7.95257i	−0.675245	+	0.566597i	0.239368	+	0.970929i	$0.423060\pi$
$198$		0			0
$199$	3.90547	+	2.25483i	0.276852	+	0.159840i	0.631997	−	0.774971i	$-0.282235\pi$
$199$	3.90547	+	2.25483i	0.276852	+	0.159840i	−0.355146	+	0.934811i	$0.615569\pi$
$200$		0			0
$201$	−12.2236	−	4.44904i	−0.862189	−	0.313811i
$202$		0			0
$203$	13.3085	−	15.8605i	0.934075	−	1.11319i
$204$		0			0
$205$	−6.26344	+	1.10441i	−0.437457	+	0.0771356i
$206$		0			0
$207$	0.540940	−	1.48622i	0.0375980	−	0.103300i
$208$		0			0
$209$	−6.73022	−	1.18672i	−0.465539	−	0.0820871i
$210$		0			0
$211$	−8.12299	−	14.0694i	−0.559209	−	0.968579i	−0.997563	−	0.0697764i	$-0.977771\pi$
$211$	−8.12299	−	14.0694i	−0.559209	−	0.968579i	0.438353	−	0.898803i	$-0.355562\pi$
$212$		0			0
$213$	−3.02829	−	17.1743i	−0.207495	−	1.17676i
$214$		0			0
$215$	−22.1881	+	8.07582i	−1.51322	+	0.550767i
$216$		0			0
$217$	8.36136	+	22.9726i	0.567606	+	1.55948i
$218$		0			0
$219$	−23.4248	−	19.6557i	−1.58290	−	1.32821i
$220$		0			0
$221$	0.0770596			0.00518359
$222$		0			0
$223$	0.847777			0.0567713			0.0283857	−	0.999597i	$-0.490963\pi$
$223$	0.847777			0.0567713			0.0283857	+	0.999597i	$0.490963\pi$
$224$		0			0
$225$	−5.37339	−	4.50881i	−0.358226	−	0.300588i
$226$		0			0
$227$	4.14827	+	11.3973i	0.275331	+	0.756464i	0.997876	+	0.0651411i	$0.0207497\pi$
$227$	4.14827	+	11.3973i	0.275331	+	0.756464i	−0.722546	+	0.691323i	$0.757028\pi$
$228$		0			0
$229$	−12.4674	+	4.53775i	−0.823867	+	0.299863i	−0.719339	−	0.694659i	$-0.755555\pi$
$229$	−12.4674	+	4.53775i	−0.823867	+	0.299863i	−0.104528	+	0.994522i	$0.533333\pi$
$230$		0			0
$231$	2.49486	+	14.1491i	0.164150	+	0.930941i
$232$		0			0
$233$	−2.15328	−	3.72960i	−0.141066	−	0.244334i	0.786832	−	0.617167i	$-0.211720\pi$
$233$	−2.15328	−	3.72960i	−0.141066	−	0.244334i	−0.927898	+	0.372833i	$0.878386\pi$
$234$		0			0
$235$	−10.9733	−	1.93489i	−0.715818	−	0.126218i
$236$		0			0
$237$	0.909634	−	2.49920i	0.0590871	−	0.162340i
$238$		0			0
$239$	14.0259	−	2.47315i	0.907262	−	0.159975i	0.299502	−	0.954096i	$-0.403179\pi$
$239$	14.0259	−	2.47315i	0.907262	−	0.159975i	0.607760	+	0.794121i	$0.292068\pi$
$240$		0			0
$241$	9.16681	−	10.9246i	0.590486	−	0.703714i	−0.385213	−	0.922828i	$-0.625872\pi$
$241$	9.16681	−	10.9246i	0.590486	−	0.703714i	0.975699	+	0.219114i	$0.0703166\pi$
$242$		0			0
$243$	−5.13816	−	1.87014i	−0.329613	−	0.119969i
$244$		0			0
$245$	−22.3140	−	12.8830i	−1.42559	−	0.823063i
$246$		0			0
$247$	7.13258	−	5.98494i	0.453835	−	0.380813i
$248$		0			0
$249$	1.59411	−	2.76108i	0.101023	−	0.174976i
$250$		0			0
$251$	−21.3974	+	12.3538i	−1.35059	+	0.779764i	−0.988332	−	0.152314i	$-0.951328\pi$
$251$	−21.3974	+	12.3538i	−1.35059	+	0.779764i	−0.362258	+	0.932078i	$0.617994\pi$
$252$		0			0
$253$			6.29208i			0.395580i
$254$		0			0
$255$	−0.0371834	+	0.210877i	−0.00232851	+	0.0132057i
$256$		0			0
$257$	−10.5496	−	12.5726i	−0.658068	−	0.784255i	0.329039	−	0.944316i	$-0.393275\pi$
$257$	−10.5496	−	12.5726i	−0.658068	−	0.784255i	−0.987107	+	0.160062i	$0.948831\pi$
$258$		0			0
$259$	−10.1865	+	19.4630i	−0.632956	+	1.20937i
$260$		0			0
$261$	1.96080	+	2.33679i	0.121371	+	0.144644i
$262$		0			0
$263$	4.88671	−	27.7139i	0.301327	−	1.70891i	−0.338980	−	0.940793i	$-0.610082\pi$
$263$	4.88671	−	27.7139i	0.301327	−	1.70891i	0.640308	−	0.768118i	$-0.278807\pi$
$264$		0			0
$265$			8.14034i			0.500057i
$266$		0			0
$267$	−13.4617	+	7.77213i	−0.823844	+	0.475647i
$268$		0			0
$269$	−11.5852	+	20.0661i	−0.706359	+	1.22345i	0.259840	+	0.965652i	$0.416330\pi$
$269$	−11.5852	+	20.0661i	−0.706359	+	1.22345i	−0.966199	+	0.257798i	$0.917003\pi$
$270$		0			0
$271$	−8.12679	+	6.81919i	−0.493667	+	0.414236i	−0.855338	−	0.518070i	$-0.826651\pi$
$271$	−8.12679	+	6.81919i	−0.493667	+	0.414236i	0.361671	+	0.932306i	$0.382206\pi$
$272$		0			0
$273$	−16.9520	−	9.78726i	−1.02598	−	0.592352i
$274$		0			0
$275$	26.2227	+	9.54428i	1.58129	+	0.575542i
$276$		0			0
$277$	15.4537	−	18.4170i	0.928521	−	1.10657i	−0.0655519	−	0.997849i	$-0.520881\pi$
$277$	15.4537	−	18.4170i	0.928521	−	1.10657i	0.994073	−	0.108719i	$-0.0346748\pi$
$278$		0			0
$279$	−3.54716	+	0.625460i	−0.212363	+	0.0374453i
$280$		0			0
$281$	4.35215	−	11.9574i	0.259628	−	0.713321i	−0.739563	−	0.673088i	$-0.764968\pi$
$281$	4.35215	−	11.9574i	0.259628	−	0.713321i	0.999190	−	0.0402335i	$-0.0128102\pi$
$282$		0			0
$283$	0.253793	+	0.0447506i	0.0150864	+	0.00266015i	0.181186	−	0.983449i	$-0.442006\pi$
$283$	0.253793	+	0.0447506i	0.0150864	+	0.00266015i	−0.166100	+	0.986109i	$0.553117\pi$
$284$		0			0
$285$	12.9364	+	22.4065i	0.766287	+	1.32725i
$286$		0			0
$287$	−0.935363	−	5.30471i	−0.0552127	−	0.313127i
$288$		0			0
$289$	−15.9741	+	5.81410i	−0.939653	+	0.342006i
$290$		0			0
$291$	−4.19436	−	11.5239i	−0.245878	−	0.675544i
$292$		0			0
$293$	−6.87967	−	5.77273i	−0.401914	−	0.337246i	0.419319	−	0.907839i	$-0.362269\pi$
$293$	−6.87967	−	5.77273i	−0.401914	−	0.337246i	−0.821233	+	0.570593i	$0.806713\pi$
$294$		0			0
$295$	23.9850			1.39646
$296$		0			0
$297$	9.81807			0.569702
$298$		0			0
$299$	−6.56694	−	5.51032i	−0.379776	−	0.318670i
$300$		0			0
$301$	−6.83967	−	18.7918i	−0.394232	−	1.08314i
$302$		0			0
$303$	29.3154	−	10.6699i	1.68413	−	0.612972i
$304$		0			0
$305$	4.25089	+	24.1080i	0.243405	+	1.38042i
$306$		0			0
$307$	−7.39912	−	12.8157i	−0.422290	−	0.731428i	0.573873	−	0.818944i	$-0.305440\pi$
$307$	−7.39912	−	12.8157i	−0.422290	−	0.731428i	−0.996163	+	0.0875163i	$0.972107\pi$
$308$		0			0
$309$	3.50697	+	0.618373i	0.199504	+	0.0351780i
$310$		0			0
$311$	−9.13738	+	25.1047i	−0.518133	+	1.42356i	0.354441	+	0.935078i	$0.384671\pi$
$311$	−9.13738	+	25.1047i	−0.518133	+	1.42356i	−0.872574	+	0.488481i	$0.837551\pi$
$312$		0			0
$313$	9.37905	−	1.65378i	0.530135	−	0.0934772i	0.0978278	−	0.995203i	$-0.468811\pi$
$313$	9.37905	−	1.65378i	0.530135	−	0.0934772i	0.432308	+	0.901726i	$0.357699\pi$
$314$		0			0
$315$	5.26700	−	6.27696i	0.296762	−	0.353667i
$316$		0			0
$317$	14.2417	+	5.18354i	0.799891	+	0.291137i	0.709441	−	0.704764i	$-0.248947\pi$
$317$	14.2417	+	5.18354i	0.799891	+	0.291137i	0.0904498	+	0.995901i	$0.471170\pi$
$318$		0			0
$319$	−10.5098	−	6.06783i	−0.588435	−	0.339733i
$320$		0			0
$321$	0.550332	−	0.461783i	0.0307165	−	0.0257742i
$322$		0			0
$323$	0.0431318	−	0.0747066i	0.00239992	−	0.00415678i
$324$		0			0
$325$	−32.9258	+	19.0097i	−1.82640	+	1.05447i
$326$		0			0
$327$			1.81470i			0.100353i
$328$		0			0
$329$	1.63872	−	9.29362i	0.0903453	−	0.512374i
$330$		0			0
$331$	−1.32812	−	1.58279i	−0.0729998	−	0.0869978i	0.728309	−	0.685249i	$-0.240307\pi$
$331$	−1.32812	−	1.58279i	−0.0729998	−	0.0869978i	−0.801308	+	0.598252i	$0.795862\pi$
$332$		0			0
$333$	−2.56339	−	1.97596i	−0.140473	−	0.108282i
$334$		0			0
$335$	−18.9713	−	22.6091i	−1.03651	−	1.23527i
$336$		0			0
$337$	−2.41835	+	13.7152i	−0.131736	+	0.747112i	0.845341	+	0.534227i	$0.179397\pi$
$337$	−2.41835	+	13.7152i	−0.131736	+	0.747112i	−0.977077	+	0.212885i	$0.931714\pi$
$338$		0			0
$339$		−	3.55344i		−	0.192996i
$340$		0			0
$341$	12.4096	−	7.16467i	0.672016	−	0.387989i
$342$		0			0
$343$	−1.72903	+	2.99477i	−0.0933588	+	0.161702i
$344$		0			0
$345$	18.2480	−	15.3119i	0.982438	−	0.824363i
$346$		0			0
$347$	17.5037	+	10.1058i	0.939647	+	0.542505i	0.889850	−	0.456254i	$-0.150809\pi$
$347$	17.5037	+	10.1058i	0.939647	+	0.542505i	0.0497972	+	0.998759i	$0.484143\pi$
$348$		0			0
$349$	−10.3271	−	3.75877i	−0.552799	−	0.201202i	0.0504906	−	0.998725i	$-0.483922\pi$
$349$	−10.3271	−	3.75877i	−0.552799	−	0.201202i	−0.603290	+	0.797522i	$0.706144\pi$
$350$		0			0
$351$	−8.59822	+	10.2470i	−0.458939	+	0.546942i
$352$		0			0
$353$	−4.29024	+	0.756485i	−0.228346	+	0.0402636i	−0.286650	−	0.958035i	$-0.592542\pi$
$353$	−4.29024	+	0.756485i	−0.228346	+	0.0402636i	0.0583041	+	0.998299i	$0.481431\pi$
$354$		0			0
$355$	13.5330	−	37.1817i	0.718259	−	1.97340i
$356$		0			0
$357$	−0.178599	−	0.0314918i	−0.00945245	−	0.00166672i
$358$		0			0
$359$	3.84332	+	6.65683i	0.202843	+	0.351334i	0.949443	−	0.313939i	$-0.101649\pi$
$359$	3.84332	+	6.65683i	0.202843	+	0.351334i	−0.746600	+	0.665273i	$0.768315\pi$
$360$		0			0
$361$	1.48938	+	8.44667i	0.0783882	+	0.444562i
$362$		0			0
$363$	−11.5131	+	4.19042i	−0.604280	+	0.219940i
$364$		0			0
$365$	−23.7295	−	65.1963i	−1.24206	−	3.41253i
$366$		0			0
$367$	−15.8706	−	13.3170i	−0.828440	−	0.695143i	0.126492	−	0.991968i	$-0.459628\pi$
$367$	−15.8706	−	13.3170i	−0.828440	−	0.695143i	−0.954932	+	0.296824i	$0.904072\pi$
$368$		0			0
$369$	0.793623			0.0413143
$370$		0			0
$371$	−6.89431			−0.357935
$372$		0			0
$373$	11.9553	+	10.0317i	0.619023	+	0.519422i	0.897496	−	0.441022i	$-0.145384\pi$
$373$	11.9553	+	10.0317i	0.619023	+	0.519422i	−0.278473	+	0.960444i	$0.589828\pi$
$374$		0			0
$375$	−22.4288	−	61.6225i	−1.15822	−	3.18217i
$376$		0			0
$377$	15.5369	−	5.65496i	0.800190	−	0.291245i
$378$		0			0
$379$	4.37193	+	24.7944i	0.224571	+	1.27360i	0.863504	+	0.504342i	$0.168265\pi$
$379$	4.37193	+	24.7944i	0.224571	+	1.27360i	−0.638933	+	0.769262i	$0.720624\pi$
$380$		0			0
$381$	15.1426	+	26.2277i	0.775778	+	1.34369i
$382$		0			0
$383$	29.7545	+	5.24652i	1.52038	+	0.268085i	0.870584	−	0.492020i	$-0.163741\pi$
$383$	29.7545	+	5.24652i	1.52038	+	0.268085i	0.649801	+	0.760105i	$0.274852\pi$
$384$		0			0
$385$	−11.1492	+	30.6322i	−0.568216	+	1.56116i
$386$		0			0
$387$	2.90161	−	0.511633i	0.147497	−	0.0260077i
$388$		0			0
$389$	16.0701	−	19.1516i	0.814786	−	0.971024i	−0.185146	−	0.982711i	$-0.559276\pi$
$389$	16.0701	−	19.1516i	0.814786	−	0.971024i	0.999932	+	0.0116872i	$0.00372024\pi$
$390$		0			0
$391$	−0.0746329	−	0.0271642i	−0.00377435	−	0.00137375i
$392$		0			0
$393$	−1.33943	−	0.773318i	−0.0675651	−	0.0390088i
$394$		0			0
$395$	4.62258	−	3.87881i	0.232587	−	0.195164i
$396$		0			0
$397$	−6.83681	+	11.8417i	−0.343130	+	0.594318i	−0.985012	−	0.172485i	$-0.944820\pi$
$397$	−6.83681	+	11.8417i	−0.343130	+	0.594318i	0.641882	+	0.766803i	$0.278154\pi$
$398$		0			0
$399$	−18.9768	+	10.9563i	−0.950029	+	0.548499i
$400$		0			0
$401$			1.62020i			0.0809089i	0.999181	+	0.0404544i	$0.0128806\pi$
$401$			1.62020i			0.0809089i	−0.999181	+	0.0404544i	$0.987119\pi$
$402$		0			0
$403$	−3.39009	+	19.2261i	−0.168872	+	0.957723i
$404$		0			0
$405$	−28.2677	−	33.6881i	−1.40463	−	1.67398i
$406$		0			0
$407$	12.2715	+	3.89900i	0.608276	+	0.193266i
$408$		0			0
$409$	−5.86780	−	6.99297i	−0.290144	−	0.345780i	0.601208	−	0.799093i	$-0.294686\pi$
$409$	−5.86780	−	6.99297i	−0.290144	−	0.345780i	−0.891351	+	0.453313i	$0.850242\pi$
$410$		0			0
$411$	−5.66447	+	32.1248i	−0.279408	+	1.58460i
$412$		0			0
$413$			20.3137i			0.999570i
$414$		0			0
$415$	6.26462	−	3.61688i	0.307518	−	0.177546i
$416$		0			0
$417$	−8.66908	+	15.0153i	−0.424526	+	0.735301i
$418$		0			0
$419$	−10.9146	+	9.15844i	−0.533213	+	0.447419i	−0.869209	−	0.494444i	$-0.835372\pi$
$419$	−10.9146	+	9.15844i	−0.533213	+	0.447419i	0.335996	+	0.941863i	$0.390927\pi$
$420$		0			0
$421$	29.2667	+	16.8971i	1.42637	+	0.823516i	0.996832	−	0.0795325i	$-0.0253427\pi$
$421$	29.2667	+	16.8971i	1.42637	+	0.823516i	0.429539	+	0.903048i	$0.358676\pi$
$422$		0			0
$423$	1.30654	+	0.475543i	0.0635263	+	0.0231217i
$424$		0			0
$425$	−0.226417	+	0.269833i	−0.0109828	+	0.0130888i
$426$		0			0
$427$	−20.4178	+	3.60021i	−0.988087	+	0.174226i
$428$		0			0
$429$	−3.92414	+	10.7815i	−0.189459	+	0.520534i
$430$		0			0
$431$	−38.2487	−	6.74428i	−1.84238	−	0.324861i	−0.859787	−	0.510652i	$-0.829404\pi$
$431$	−38.2487	−	6.74428i	−1.84238	−	0.324861i	−0.982589	+	0.185791i	$0.940515\pi$
$432$		0			0
$433$	−9.05610	−	15.6856i	−0.435208	−	0.753803i	0.562104	−	0.827066i	$-0.309992\pi$
$433$	−9.05610	−	15.6856i	−0.435208	−	0.753803i	−0.997313	+	0.0732633i	$0.976659\pi$
$434$		0			0
$435$	7.97810	+	45.2461i	0.382521	+	2.16938i
$436$		0			0
$437$	−9.01771	+	3.28218i	−0.431376	+	0.157008i
$438$		0			0
$439$	4.90855	+	13.4861i	0.234273	+	0.643659i	1.00000		0.000493184i	$0.000156985\pi$
$439$	4.90855	+	13.4861i	0.234273	+	0.643659i	−0.765727	+	0.643165i	$0.777621\pi$
$440$		0			0
$441$	2.46293	+	2.06665i	0.117283	+	0.0984117i
$442$		0			0
$443$	−5.43539			−0.258243			−0.129121	−	0.991629i	$-0.541216\pi$
$443$	−5.43539			−0.258243			−0.129121	+	0.991629i	$0.541216\pi$
$444$		0			0
$445$	−35.2684			−1.67188
$446$		0			0
$447$	11.1400	+	9.34757i	0.526904	+	0.442125i
$448$		0			0
$449$	−0.0445442	−	0.122384i	−0.00210217	−	0.00577566i	0.938637	−	0.344906i	$-0.112089\pi$
$449$	−0.0445442	−	0.122384i	−0.00210217	−	0.00577566i	−0.940739	+	0.339131i	$0.889867\pi$
$450$		0			0
$451$	−2.96686	+	1.07985i	−0.139704	+	0.0508480i
$452$		0			0
$453$	−4.12389	−	23.3878i	−0.193757	−	1.09885i
$454$		0			0
$455$	−22.2063	−	38.4625i	−1.04105	−	1.80315i
$456$		0			0
$457$	27.8381	+	4.90861i	1.30221	+	0.229615i	0.781386	−	0.624048i	$-0.214513\pi$
$457$	27.8381	+	4.90861i	1.30221	+	0.229615i	0.520825	+	0.853663i	$0.325624\pi$
$458$		0			0
$459$	−0.0423866	+	0.116456i	−0.00197844	+	0.00543571i
$460$		0			0
$461$	−7.89127	+	1.39144i	−0.367533	+	0.0648060i	−0.354365	−	0.935107i	$-0.615303\pi$
$461$	−7.89127	+	1.39144i	−0.367533	+	0.0648060i	−0.0131684	+	0.999913i	$0.504192\pi$
$462$		0			0
$463$	22.0020	−	26.2210i	1.02252	−	1.21859i	0.0469535	−	0.998897i	$-0.485049\pi$
$463$	22.0020	−	26.2210i	1.02252	−	1.21859i	0.975568	−	0.219697i	$-0.0705068\pi$
$464$		0			0
$465$	−50.9775	−	18.5543i	−2.36402	−	0.860434i
$466$		0			0
$467$	17.7860	+	10.2688i	0.823040	+	0.475182i	0.851464	−	0.524414i	$-0.175715\pi$
$467$	17.7860	+	10.2688i	0.823040	+	0.475182i	−0.0284236	+	0.999596i	$0.509049\pi$
$468$		0			0
$469$	19.1484	−	16.0674i	0.884191	−	0.741925i
$470$		0			0
$471$	12.2599	−	21.2348i	0.564907	−	0.978448i
$472$		0			0
$473$	−10.1512	+	5.86077i	−0.466750	+	0.269479i
$474$		0			0
$475$			42.5606i			1.95281i
$476$		0			0
$477$	0.176387	−	1.00034i	0.00807619	−	0.0458023i
$478$		0			0
$479$	4.04948	+	4.82598i	0.185025	+	0.220505i	0.850582	−	0.525843i	$-0.176250\pi$
$479$	4.04948	+	4.82598i	0.185025	+	0.220505i	−0.665556	+	0.746348i	$0.731806\pi$
$480$		0			0
$481$	−14.8161	+	9.39299i	−0.675558	+	0.428284i
$482$		0			0
$483$	12.9681	+	15.4548i	0.590070	+	0.703218i
$484$		0			0
$485$	4.83170	−	27.4019i	0.219396	−	1.24426i
$486$		0			0
$487$			27.5903i			1.25024i	0.780530	+	0.625118i	$0.214949\pi$
$487$			27.5903i			1.25024i	−0.780530	+	0.625118i	$0.785051\pi$
$488$		0			0
$489$	−41.1072	+	23.7332i	−1.85893	+	1.07325i
$490$		0			0
$491$	16.5100	−	28.5962i	0.745088	−	1.29053i	−0.205066	−	0.978748i	$-0.565741\pi$
$491$	16.5100	−	28.5962i	0.745088	−	1.29053i	0.950154	−	0.311781i	$-0.100926\pi$
$492$		0			0
$493$	0.117346	−	0.0984648i	0.00528499	−	0.00443463i
$494$		0			0
$495$	−4.15937	−	2.40141i	−0.186950	−	0.107935i
$496$		0			0
$497$	31.4904	+	11.4616i	1.41254	+	0.514121i
$498$		0			0
$499$	−13.5539	+	16.1529i	−0.606756	+	0.723103i	−0.978733	−	0.205139i	$-0.934235\pi$
$499$	−13.5539	+	16.1529i	−0.606756	+	0.723103i	0.371977	+	0.928242i	$0.378680\pi$
$500$		0			0
$501$	−19.0284	+	3.35523i	−0.850128	+	0.149901i
$502$		0			0
$503$	−6.03817	+	16.5897i	−0.269229	+	0.739700i	0.729234	+	0.684265i	$0.239877\pi$
$503$	−6.03817	+	16.5897i	−0.269229	+	0.739700i	−0.998462	+	0.0554349i	$0.982345\pi$
$504$		0			0
$505$	69.7072	+	12.2913i	3.10193	+	0.546954i
$506$		0			0
$507$	4.40014	+	7.62127i	0.195417	+	0.338472i
$508$		0			0
$509$	7.26094	+	41.1788i	0.321835	+	1.82522i	0.531039	+	0.847347i	$0.321802\pi$
$509$	7.26094	+	41.1788i	0.321835	+	1.82522i	−0.209203	+	0.977872i	$0.567087\pi$
$510$		0			0
$511$	55.2168	−	20.0973i	2.44265	−	0.889051i
$512$		0			0
$513$	5.12146	+	14.0711i	0.226118	+	0.621254i
$514$		0			0
$515$	6.18942	+	5.19354i	0.272738	+	0.228855i
$516$		0			0
$517$	−5.53139			−0.243270
$518$		0			0
$519$	−44.4604			−1.95160
$520$		0			0
$521$	27.5629	+	23.1280i	1.20755	+	1.01326i	0.999382	+	0.0351633i	$0.0111951\pi$
$521$	27.5629	+	23.1280i	1.20755	+	1.01326i	0.208170	+	0.978093i	$0.433249\pi$
$522$		0			0
$523$	11.2216	+	30.8312i	0.490688	+	1.34815i	0.900052	+	0.435783i	$0.143529\pi$
$523$	11.2216	+	30.8312i	0.490688	+	1.34815i	−0.409363	+	0.912371i	$0.634249\pi$
$524$		0			0
$525$	84.0799	−	30.6026i	3.66955	−	1.33561i
$526$		0			0
$527$	0.0314085	+	0.178126i	0.00136817	+	0.00775930i
$528$		0			0
$529$	−7.08229	−	12.2669i	−0.307926	−	0.533343i
$530$		0			0
$531$	−2.94743	−	0.519712i	−0.127908	−	0.0225536i
$532$		0			0
$533$	1.47122	−	4.04214i	0.0637255	−	0.175085i
$534$		0			0
$535$	1.60523	−	0.283046i	0.0694002	−	0.0122371i
$536$		0			0
$537$	6.10965	−	7.28119i	0.263651	−	0.314207i
$538$		0			0
$539$	−12.0194	−	4.37469i	−0.517710	−	0.188431i
$540$		0			0
$541$	32.4941	+	18.7605i	1.39703	+	0.806576i	0.994080	−	0.108646i	$-0.0346516\pi$
$541$	32.4941	+	18.7605i	1.39703	+	0.806576i	0.402950	+	0.915222i	$0.367985\pi$
$542$		0			0
$543$	1.50512	−	1.26295i	0.0645910	−	0.0541983i
$544$		0			0
$545$	−2.05869	+	3.56576i	−0.0881847	+	0.152740i
$546$		0			0
$547$	22.5841	−	13.0389i	0.965627	−	0.557505i	0.0677265	−	0.997704i	$-0.478425\pi$
$547$	22.5841	−	13.0389i	0.965627	−	0.557505i	0.897900	+	0.440199i	$0.145092\pi$
$548$		0			0
$549$		−	3.05465i		−	0.130369i
$550$		0			0
$551$	3.21403	−	18.2276i	0.136922	−	0.776524i
$552$		0			0
$553$	3.28508	+	3.91501i	0.139696	+	0.166483i
$554$		0			0
$555$	−18.5552	−	45.0775i	−0.787624	−	1.91343i
$556$		0			0
$557$	−4.18253	−	4.98455i	−0.177220	−	0.211202i	0.670121	−	0.742252i	$-0.266242\pi$
$557$	−4.18253	−	4.98455i	−0.177220	−	0.211202i	−0.847341	+	0.531050i	$0.821798\pi$
$558$		0			0
$559$	2.77313	−	15.7272i	0.117291	−	0.665189i
$560$		0			0
$561$			0.106299i			0.00448793i
$562$		0			0
$563$	33.5577	−	19.3746i	1.41429	−	0.816540i	0.418500	−	0.908217i	$-0.362556\pi$
$563$	33.5577	−	19.3746i	1.41429	−	0.816540i	0.995789	+	0.0916766i	$0.0292226\pi$
$564$		0			0
$565$	4.03120	−	6.98224i	0.169594	−	0.293745i
$566$		0			0
$567$	28.5315	−	23.9408i	1.19821	−	1.00542i
$568$		0			0
$569$	11.1846	+	6.45744i	0.468883	+	0.270710i	0.715772	−	0.698334i	$-0.246075\pi$
$569$	11.1846	+	6.45744i	0.468883	+	0.270710i	−0.246889	+	0.969044i	$0.579408\pi$
$570$		0			0
$571$	2.81875	+	1.02594i	0.117961	+	0.0429343i	0.400326	−	0.916373i	$-0.368897\pi$
$571$	2.81875	+	1.02594i	0.117961	+	0.0429343i	−0.282365	+	0.959307i	$0.591119\pi$
$572$		0			0
$573$	−16.2643	+	19.3831i	−0.679452	+	0.809739i
$574$		0			0
$575$	38.5901	−	6.80447i	1.60932	−	0.283766i
$576$		0			0
$577$	9.86791	−	27.1119i	0.410806	−	1.12868i	−0.545957	−	0.837813i	$-0.683834\pi$
$577$	9.86791	−	27.1119i	0.410806	−	1.12868i	0.956763	−	0.290868i	$-0.0939440\pi$
$578$		0			0
$579$	−8.36999	−	1.47586i	−0.347845	−	0.0613344i
$580$		0			0
$581$	3.06325	+	5.30571i	0.127085	+	0.220118i
$582$		0			0
$583$	0.701717	+	3.97964i	0.0290622	+	0.164820i
$584$		0			0
$585$	6.14889	−	2.23801i	0.254225	−	0.0925305i
$586$		0			0
$587$	−8.30296	−	22.8122i	−0.342700	−	0.941560i	−0.984608	−	0.174778i	$-0.944079\pi$
$587$	−8.30296	−	22.8122i	−0.342700	−	0.941560i	0.641908	−	0.766782i	$-0.278143\pi$
$588$		0			0
$589$	16.7416	+	14.0478i	0.689824	+	0.578831i
$590$		0			0
$591$	23.2518			0.956450
$592$		0			0
$593$	12.0052			0.492995			0.246497	−	0.969143i	$-0.420720\pi$
$593$	12.0052			0.492995			0.246497	+	0.969143i	$0.420720\pi$
$594$		0			0
$595$	−0.315207	−	0.264490i	−0.0129222	−	0.0108431i
$596$		0			0
$597$	−2.89875	−	7.96425i	−0.118638	−	0.325955i
$598$		0			0
$599$	−17.9026	+	6.51602i	−0.731481	+	0.266237i	−0.680792	−	0.732477i	$-0.738364\pi$
$599$	−17.9026	+	6.51602i	−0.731481	+	0.266237i	−0.0506895	+	0.998714i	$0.516142\pi$
$600$		0			0
$601$	−3.95300	−	22.4186i	−0.161246	−	0.914472i	−0.952851	−	0.303439i	$-0.901865\pi$
$601$	−3.95300	−	22.4186i	−0.161246	−	0.914472i	0.791605	−	0.611033i	$-0.209246\pi$
$602$		0			0
$603$	1.84142	+	3.18943i	0.0749884	+	0.129884i
$604$		0			0
$605$	−27.3762	−	4.82716i	−1.11300	−	0.196252i
$606$		0			0
$607$	6.70527	−	18.4226i	0.272159	−	0.747750i	−0.726034	−	0.687658i	$-0.758639\pi$
$607$	6.70527	−	18.4226i	0.272159	−	0.747750i	0.998193	−	0.0600911i	$-0.0191391\pi$
$608$		0			0
$609$	−38.3203	+	6.75691i	−1.55282	+	0.273804i
$610$		0			0
$611$	4.84414	−	5.77302i	0.195973	−	0.233551i
$612$		0			0
$613$	2.38568	+	0.868317i	0.0963568	+	0.0350710i	0.389749	−	0.920921i	$-0.372562\pi$
$613$	2.38568	+	0.868317i	0.0963568	+	0.0350710i	−0.293392	+	0.955992i	$0.594784\pi$
$614$		0			0
$615$	10.3516	+	5.97650i	0.417417	+	0.240996i
$616$		0			0
$617$	−14.5342	+	12.1956i	−0.585124	+	0.490977i	−0.886625	−	0.462489i	$-0.846957\pi$
$617$	−14.5342	+	12.1956i	−0.585124	+	0.490977i	0.301502	+	0.953466i	$0.402512\pi$
$618$		0			0
$619$	1.25679	−	2.17683i	0.0505147	−	0.0874940i	−0.839662	−	0.543109i	$-0.817247\pi$
$619$	1.25679	−	2.17683i	0.0505147	−	0.0874940i	0.890177	+	0.455615i	$0.150580\pi$
$620$		0			0
$621$	11.9396	−	6.89333i	0.479119	−	0.276620i
$622$		0			0
$623$		−	29.8699i		−	1.19671i
$624$		0			0
$625$	14.3909	−	81.6150i	0.575637	−	3.26460i
$626$		0			0
$627$	8.25584	+	9.83892i	0.329706	+	0.392929i
$628$		0			0
$629$	−0.0992261	+	0.128724i	−0.00395640	+	0.00513258i
$630$		0			0
$631$	4.27007	+	5.08887i	0.169989	+	0.202585i	0.844313	−	0.535851i	$-0.180009\pi$
$631$	4.27007	+	5.08887i	0.169989	+	0.202585i	−0.674324	+	0.738436i	$0.735565\pi$
$632$		0			0
$633$	−5.30190	+	30.0686i	−0.210732	+	1.19512i
$634$		0			0
$635$			68.7140i			2.72683i
$636$		0			0
$637$	15.0918	−	8.71325i	0.597958	−	0.345231i
$638$		0			0
$639$	−2.46869	+	4.27589i	−0.0976598	+	0.169152i
$640$		0			0
$641$	6.30793	−	5.29298i	0.249148	−	0.209060i	−0.509657	−	0.860378i	$-0.670228\pi$
$641$	6.30793	−	5.29298i	0.249148	−	0.209060i	0.758805	+	0.651317i	$0.225783\pi$
$642$		0			0
$643$	12.3142	+	7.10959i	0.485623	+	0.280375i	0.722757	−	0.691102i	$-0.242875\pi$
$643$	12.3142	+	7.10959i	0.485623	+	0.280375i	−0.237134	+	0.971477i	$0.576208\pi$
$644$		0			0
$645$	41.7001	+	15.1776i	1.64194	+	0.597617i
$646$		0			0
$647$	−25.6313	+	30.5462i	−1.00767	+	1.20089i	−0.0281389	+	0.999604i	$0.508958\pi$
$647$	−25.6313	+	30.5462i	−1.00767	+	1.20089i	−0.979532	+	0.201291i	$0.935486\pi$
$648$		0			0
$649$	11.7258	−	2.06757i	0.460276	−	0.0811591i
$650$		0			0
$651$	15.7142	−	43.1744i	0.615889	−	1.69214i
$652$		0			0
$653$	7.99174	+	1.40916i	0.312741	+	0.0551447i	0.327816	−	0.944742i	$-0.393687\pi$
$653$	7.99174	+	1.40916i	0.312741	+	0.0551447i	−0.0150747	+	0.999886i	$0.504799\pi$
$654$		0			0
$655$	−1.75458	−	3.03903i	−0.0685572	−	0.118745i
$656$		0			0
$657$	1.50335	+	8.52592i	0.0586513	+	0.332628i
$658$		0			0
$659$	−26.3535	+	9.59188i	−1.02659	+	0.373647i	−0.799780	−	0.600293i	$-0.795050\pi$
$659$	−26.3535	+	9.59188i	−1.02659	+	0.373647i	−0.226806	+	0.973940i	$0.572828\pi$
$660$		0			0
$661$	−1.54764	−	4.25209i	−0.0601961	−	0.165387i	0.905949	−	0.423387i	$-0.139159\pi$
$661$	−1.54764	−	4.25209i	−0.0601961	−	0.165387i	−0.966145	+	0.258000i	$0.916937\pi$
$662$		0			0
$663$	−0.110942	−	0.0930915i	−0.00430864	−	0.00361537i
$664$		0			0
$665$	−49.7174			−1.92796
$666$		0			0
$667$	−17.0410			−0.659831
$668$		0			0
$669$	−1.22054	−	1.02415i	−0.0471887	−	0.0395960i
$670$		0			0
$671$	4.15633	+	11.4194i	0.160454	+	0.440842i
$672$		0			0
$673$	−9.85346	+	3.58637i	−0.379823	+	0.138244i	−0.524874	−	0.851180i	$-0.675888\pi$
$673$	−9.85346	+	3.58637i	−0.379823	+	0.138244i	0.145051	+	0.989424i	$0.453665\pi$
$674$		0			0
$675$	−10.6176	−	60.2154i	−0.408671	−	2.31769i
$676$		0			0
$677$	−13.4277	−	23.2574i	−0.516067	−	0.893853i	−0.999826	−	0.0186525i	$-0.994062\pi$
$677$	−13.4277	−	23.2574i	−0.516067	−	0.893853i	0.483760	−	0.875201i	$-0.339271\pi$
$678$		0			0
$679$	23.2076	+	4.09212i	0.890625	+	0.157041i
$680$		0			0
$681$	7.79620	−	21.4199i	0.298751	−	0.820812i
$682$		0			0
$683$	−17.6006	+	3.10346i	−0.673469	+	0.118751i	−0.499916	−	0.866074i	$-0.666636\pi$
$683$	−17.6006	+	3.10346i	−0.673469	+	0.118751i	−0.173553	+	0.984825i	$0.555525\pi$
$684$		0			0
$685$	−47.5743	+	56.6968i	−1.81772	+	2.16627i
$686$		0			0
$687$	23.4310	+	8.52819i	0.893948	+	0.325371i
$688$		0			0
$689$	−4.76801	−	2.75281i	−0.181647	−	0.104874i
$690$		0			0
$691$	−16.1699	+	13.5682i	−0.615133	+	0.516158i	−0.896269	−	0.443510i	$-0.853733\pi$
$691$	−16.1699	+	13.5682i	−0.615133	+	0.516158i	0.281137	+	0.959668i	$0.409289\pi$
$692$		0			0
$693$	2.03383	−	3.52270i	0.0772589	−	0.133816i
$694$		0			0
$695$	−34.0682	+	19.6693i	−1.29228	+	0.746098i
$696$		0			0
$697$		−	0.0398530i		−	0.00150954i
$698$		0			0
$699$	−1.40546	+	7.97074i	−0.0531593	+	0.301481i
$700$		0			0
$701$	2.94056	+	3.50442i	0.111063	+	0.132360i	0.818712	−	0.574204i	$-0.194688\pi$
$701$	2.94056	+	3.50442i	0.111063	+	0.132360i	−0.707649	+	0.706564i	$0.750244\pi$
$702$		0			0
$703$	0.813275	+	19.6212i	0.0306733	+	0.740027i
$704$		0			0
$705$	13.4607	+	16.0419i	0.506960	+	0.604171i
$706$		0			0
$707$	−10.4099	+	59.0372i	−0.391503	+	2.22032i
$708$		0			0
$709$		−	4.67695i		−	0.175647i	−0.996136	−	0.0878233i	$-0.972009\pi$
$709$		−	4.67695i		−	0.175647i	0.996136	−	0.0878233i	$-0.0279911\pi$
$710$		0			0
$711$	−0.652100	+	0.376490i	−0.0244556	+	0.0141195i
$712$		0			0
$713$	10.0607	−	17.4257i	0.376777	−	0.652596i
$714$		0			0
$715$	−19.9417	+	16.7331i	−0.745777	+	0.625781i
$716$		0			0
$717$	−23.1807	−	13.3834i	−0.865699	−	0.499812i
$718$		0			0
$719$	43.2845	+	15.7543i	1.61424	+	0.587535i	0.982272	−	0.187460i	$-0.0600255\pi$
$719$	43.2845	+	15.7543i	1.61424	+	0.587535i	0.631967	+	0.774995i	$0.282248\pi$
$720$		0			0
$721$	−4.39857	+	5.24202i	−0.163811	+	0.195223i
$722$		0			0
$723$	−26.3948	+	4.65411i	−0.981632	+	0.173088i
$724$		0			0
$725$	−25.8490	+	71.0196i	−0.960009	+	2.63760i
$726$		0			0
$727$	42.9014	+	7.56467i	1.59112	+	0.280558i	0.897912	−	0.440175i	$-0.145084\pi$
$727$	42.9014	+	7.56467i	1.59112	+	0.280558i	0.693213	+	0.720733i	$0.256195\pi$
$728$		0			0
$729$	−10.3316	−	17.8948i	−0.382651	−	0.662770i
$730$		0			0
$731$	−0.0256924	−	0.145709i	−0.000950269	−	0.00538924i
$732$		0			0
$733$	26.1238	−	9.50828i	0.964904	−	0.351196i	0.188950	−	0.981987i	$-0.439491\pi$
$733$	26.1238	−	9.50828i	0.964904	−	0.351196i	0.775953	+	0.630790i	$0.217269\pi$
$734$		0			0
$735$	16.5620	+	45.5038i	0.610900	+	1.67843i
$736$		0			0
$737$	−11.2236	−	9.41775i	−0.413428	−	0.346907i
$738$		0			0
$739$	−26.4463			−0.972843			−0.486421	−	0.873724i	$-0.661698\pi$
$739$	−26.4463			−0.972843			−0.486421	+	0.873724i	$0.661698\pi$
$740$		0			0
$741$	−17.4988			−0.642835
$742$		0			0
$743$	−31.0557	−	26.0589i	−1.13932	−	0.956007i	−0.139908	−	0.990165i	$-0.544681\pi$
$743$	−31.0557	−	26.0589i	−1.13932	−	0.956007i	−0.999416	+	0.0341578i	$0.989125\pi$
$744$		0			0
$745$	11.2849	+	31.0051i	0.413447	+	1.13594i
$746$		0			0
$747$	−0.848209	+	0.308723i	−0.0310343	+	0.0112956i
$748$		0			0
$749$	0.239720	+	1.35952i	0.00875919	+	0.0496759i
$750$		0			0
$751$	5.14164	+	8.90559i	0.187621	+	0.324969i	0.944457	−	0.328636i	$-0.106589\pi$
$751$	5.14164	+	8.90559i	0.187621	+	0.324969i	−0.756835	+	0.653605i	$0.773256\pi$
$752$		0			0
$753$	45.7296	+	8.06336i	1.66648	+	0.293845i
$754$		0			0
$755$	18.4291	−	50.6336i	0.670704	−	1.84274i
$756$		0			0
$757$	−34.9139	+	6.15626i	−1.26897	+	0.223753i	−0.767289	−	0.641301i	$-0.778395\pi$
$757$	−34.9139	+	6.15626i	−1.26897	+	0.223753i	−0.501678	+	0.865054i	$0.667284\pi$
$758$		0			0
$759$	7.60112	−	9.05867i	0.275903	−	0.328809i
$760$		0			0
$761$	−4.68947	−	1.70683i	−0.169993	−	0.0618725i	0.255622	−	0.966777i	$-0.417720\pi$
$761$	−4.68947	−	1.70683i	−0.169993	−	0.0618725i	−0.425615	+	0.904904i	$0.639942\pi$
$762$		0			0
$763$	−3.01996	−	1.74357i	−0.109330	−	0.0631216i
$764$		0			0
$765$	0.0464409	−	0.0389686i	0.00167907	−	0.00140891i
$766$		0			0
$767$	−8.11099	+	14.0486i	−0.292871	+	0.507267i
$768$		0			0
$769$	−30.5000	+	17.6092i	−1.09986	+	0.635004i	−0.936184	−	0.351511i	$-0.885668\pi$
$769$	−30.5000	+	17.6092i	−1.09986	+	0.635004i	−0.163675	+	0.986514i	$0.552335\pi$
$770$		0			0
$771$			30.8451i			1.11086i
$772$		0			0
$773$	−1.86072	+	10.5527i	−0.0669255	+	0.379553i	0.932887	+	0.360170i	$0.117281\pi$
$773$	−1.86072	+	10.5527i	−0.0669255	+	0.379553i	−0.999812	+	0.0193832i	$0.993830\pi$
$774$		0			0
$775$	−57.3619	−	68.3612i	−2.06050	−	2.45561i
$776$		0			0
$777$	38.1775	−	15.7150i	1.36961	−	0.563772i
$778$		0			0
$779$	−3.09524	−	3.68876i	−0.110898	−	0.132164i
$780$		0			0
$781$	3.41085	−	19.3439i	0.122050	−	0.692180i
$782$		0			0
$783$			26.5906i			0.950269i
$784$		0			0
$785$	48.1797	−	27.8166i	1.71961	−	0.992815i
$786$		0			0
$787$	13.6101	−	23.5734i	0.485149	−	0.840302i	−0.514706	−	0.857367i	$-0.672099\pi$
$787$	13.6101	−	23.5734i	0.485149	−	0.840302i	0.999854	+	0.0170648i	$0.00543217\pi$
$788$		0			0
$789$	−40.5150	+	33.9961i	−1.44237	+	1.21029i
$790$		0			0
$791$	5.91349	+	3.41415i	0.210259	+	0.121393i
$792$		0			0
$793$	−15.5582	−	5.66272i	−0.552488	−	0.201089i
$794$		0			0
$795$	9.83390	−	11.7196i	0.348772	−	0.415651i
$796$		0			0
$797$	3.05954	−	0.539479i	0.108374	−	0.0191093i	−0.119198	−	0.992871i	$-0.538032\pi$
$797$	3.05954	−	0.539479i	0.108374	−	0.0191093i	0.227572	+	0.973761i	$0.426921\pi$
$798$		0			0
$799$	0.0238801	−	0.0656101i	0.000844818	−	0.00232112i
$800$		0			0
$801$	4.33401	+	0.764203i	0.153135	+	0.0270018i
$802$		0			0
$803$	−17.2209	−	29.8275i	−0.607713	−	1.05259i
$804$		0			0
$805$	7.94868	+	45.0792i	0.280154	+	1.58883i
$806$		0			0
$807$	40.9198	−	14.8936i	1.44044	−	0.524279i
$808$		0			0
$809$	−1.77678	−	4.88167i	−0.0624684	−	0.171630i	0.904532	−	0.426406i	$-0.140221\pi$
$809$	−1.77678	−	4.88167i	−0.0624684	−	0.171630i	−0.967000	+	0.254776i	$0.917998\pi$
$810$		0			0
$811$	−24.4994	−	20.5574i	−0.860289	−	0.721868i	0.101741	−	0.994811i	$-0.467559\pi$
$811$	−24.4994	−	20.5574i	−0.860289	−	0.721868i	−0.962030	+	0.272942i	$0.912003\pi$
$812$		0			0
$813$	19.9380			0.699255
$814$		0			0
$815$	−107.697			−3.77245
$816$		0			0
$817$	−13.6948	−	11.4913i	−0.479119	−	0.402029i
$818$		0			0
$819$	1.89545	+	5.20769i	0.0662322	+	0.181972i
$820$		0			0
$821$	−7.04269	+	2.56333i	−0.245792	+	0.0894608i	−0.461978	−	0.886891i	$-0.652860\pi$
$821$	−7.04269	+	2.56333i	−0.245792	+	0.0894608i	0.216187	+	0.976352i	$0.430638\pi$
$822$		0			0
$823$	7.11013	+	40.3235i	0.247843	+	1.40559i	0.813795	+	0.581152i	$0.197398\pi$
$823$	7.11013	+	40.3235i	0.247843	+	1.40559i	−0.565952	+	0.824438i	$0.691491\pi$
$824$		0			0
$825$	−26.2227	−	45.4190i	−0.912957	−	1.58129i
$826$		0			0
$827$	−43.1556	−	7.60950i	−1.50067	−	0.264608i	−0.637865	−	0.770148i	$-0.720182\pi$
$827$	−43.1556	−	7.60950i	−1.50067	−	0.264608i	−0.862803	+	0.505540i	$0.831293\pi$
$828$		0			0
$829$	12.4487	−	34.2026i	0.432362	−	1.18790i	−0.511997	−	0.858987i	$-0.671094\pi$
$829$	12.4487	−	34.2026i	0.432362	−	1.18790i	0.944359	−	0.328917i	$-0.106684\pi$
$830$		0			0
$831$	−44.4971	+	7.84603i	−1.54359	+	0.272176i
$832$		0			0
$833$	0.103780	−	0.123680i	0.00359576	−	0.00428526i
$834$		0			0
$835$	−41.1958	−	14.9941i	−1.42564	−	0.518891i
$836$		0			0
$837$	−27.1908	−	15.6986i	−0.939850	−	0.542623i
$838$		0			0
$839$	−16.9323	+	14.2079i	−0.584567	+	0.490510i	−0.886443	−	0.462837i	$-0.846832\pi$
$839$	−16.9323	+	14.2079i	−0.584567	+	0.490510i	0.301876	+	0.953347i	$0.402387\pi$
$840$		0			0
$841$	1.93366	−	3.34920i	0.0666780	−	0.115490i
$842$		0			0
$843$	−20.7109	+	11.9574i	−0.713321	+	0.411836i
$844$		0			0
$845$			19.9670i			0.686885i
$846$		0			0
$847$	4.08828	−	23.1858i	0.140475	−	0.796672i
$848$		0			0
$849$	−0.311324	−	0.371021i	−0.0106846	−	0.0127334i
$850$		0			0
$851$	17.6607	−	3.87439i	0.605400	−	0.132812i
$852$		0			0
$853$	26.8496	+	31.9982i	0.919314	+	1.09560i	0.995140	+	0.0984751i	$0.0313965\pi$
$853$	26.8496	+	31.9982i	0.919314	+	1.09560i	−0.0758251	+	0.997121i	$0.524159\pi$
$854$		0			0
$855$	1.27199	−	7.21380i	0.0435010	−	0.246707i
$856$		0			0
$857$			2.80039i			0.0956595i	0.998856	+	0.0478297i	$0.0152305\pi$
$857$			2.80039i			0.0956595i	−0.998856	+	0.0478297i	$0.984770\pi$
$858$		0			0
$859$	29.0965	−	16.7988i	0.992758	−	0.573169i	0.0866605	−	0.996238i	$-0.472380\pi$
$859$	29.0965	−	16.7988i	0.992758	−	0.573169i	0.906098	+	0.423069i	$0.139047\pi$
$860$		0			0
$861$	−5.06169	+	8.76711i	−0.172502	+	0.298782i
$862$		0			0
$863$	19.4640	−	16.3322i	0.662561	−	0.555955i	−0.248292	−	0.968685i	$-0.579869\pi$
$863$	19.4640	−	16.3322i	0.662561	−	0.555955i	0.910853	+	0.412730i	$0.135425\pi$
$864$		0			0
$865$	−87.3614	−	50.4381i	−2.97038	−	1.71495i
$866$		0			0
$867$	30.0215	+	10.9269i	1.01958	+	0.371098i
$868$		0			0
$869$	1.92552	−	2.29474i	0.0653187	−	0.0778438i
$870$		0			0
$871$	19.6583	−	3.46629i	0.666096	−	0.117451i
$872$		0			0
$873$	−1.18750	+	3.26264i	−0.0401909	+	0.110423i
$874$		0			0
$875$	124.099	+	21.8821i	4.19532	+	0.739749i
$876$		0			0
$877$	−10.5898	−	18.3420i	−0.357591	−	0.619367i	0.629966	−	0.776622i	$-0.283069\pi$
$877$	−10.5898	−	18.3420i	−0.357591	−	0.619367i	−0.987558	+	0.157256i	$0.949735\pi$
$878$		0			0
$879$	2.93089	+	16.6219i	0.0988564	+	0.560643i
$880$		0			0
$881$	13.6304	−	4.96105i	0.459219	−	0.167142i	−0.102044	−	0.994780i	$-0.532538\pi$
$881$	13.6304	−	4.96105i	0.459219	−	0.167142i	0.561262	+	0.827638i	$0.310316\pi$
$882$		0			0
$883$	−12.7053	−	34.9074i	−0.427566	−	1.17473i	−0.947285	−	0.320391i	$-0.896186\pi$
$883$	−12.7053	−	34.9074i	−0.427566	−	1.17473i	0.519719	−	0.854337i	$-0.326037\pi$
$884$		0			0
$885$	−34.5310	−	28.9750i	−1.16075	−	0.973983i
$886$		0			0
$887$	−2.08616			−0.0700464			−0.0350232	−	0.999386i	$-0.511151\pi$
$887$	−2.08616			−0.0700464			−0.0350232	+	0.999386i	$0.511151\pi$
$888$		0			0
$889$	−58.1961			−1.95183
$890$		0			0
$891$	−16.7235	−	14.0326i	−0.560257	−	0.470111i
$892$		0			0
$893$	−2.88537	−	7.92750i	−0.0965554	−	0.265284i
$894$		0			0
$895$	20.2652	−	7.37591i	0.677390	−	0.246550i
$896$		0			0
$897$	2.79766	+	15.8663i	0.0934112	+	0.529761i
$898$		0			0
$899$	19.4043	+	33.6092i	0.647169	+	1.12093i
$900$		0			0
$901$	−0.0502335	−	0.00885753i	−0.00167352	−	0.000295087i
$902$		0			0
$903$	−12.8544	+	35.3171i	−0.427767	+	1.17528i
$904$		0			0
$905$	4.39021	−	0.774112i	0.145935	−	0.0257323i
$906$		0			0
$907$	−6.67576	+	7.95586i	−0.221665	+	0.264170i	−0.865404	−	0.501075i	$-0.832938\pi$
$907$	−6.67576	+	7.95586i	−0.221665	+	0.264170i	0.643739	+	0.765245i	$0.277382\pi$
$908$		0			0
$909$	−8.29974	−	3.02086i	−0.275285	−	0.100196i
$910$		0			0
$911$	5.79035	+	3.34306i	0.191843	+	0.110761i	0.592845	−	0.805317i	$-0.298005\pi$
$911$	5.79035	+	3.34306i	0.191843	+	0.110761i	−0.401002	+	0.916077i	$0.631338\pi$
$912$		0			0
$913$	2.75086	−	2.30824i	0.0910400	−	0.0763916i
$914$		0			0
$915$	23.0036	−	39.8433i	0.760474	−	1.31718i
$916$		0			0
$917$	2.57385	−	1.48601i	0.0849960	−	0.0490725i
$918$		0			0
$919$		−	48.7881i		−	1.60937i	−0.593702	−	0.804685i	$-0.702334\pi$
$919$		−	48.7881i		−	1.60937i	0.593702	−	0.804685i	$-0.297666\pi$
$920$		0			0
$921$	−4.82943	+	27.3891i	−0.159135	+	0.902501i
$922$		0			0
$923$	17.2018	+	20.5004i	0.566206	+	0.674778i
$924$		0			0
$925$	10.6422	−	79.4790i	0.349914	−	2.61325i
$926$		0			0
$927$	−0.648062	−	0.772330i	−0.0212851	−	0.0253666i
$928$		0			0
$929$	−4.20149	+	23.8278i	−0.137846	+	0.781765i	0.834989	+	0.550267i	$0.185474\pi$
$929$	−4.20149	+	23.8278i	−0.137846	+	0.781765i	−0.972835	+	0.231499i	$0.925637\pi$
$930$		0			0
$931$		−	19.5079i		−	0.639347i
$932$		0			0
$933$	43.4827	−	25.1047i	1.42356	−	0.821892i
$934$		0			0
$935$	−0.120591	+	0.208869i	−0.00394373	+	0.00683075i
$936$		0			0
$937$	−44.8844	+	37.6625i	−1.46631	+	1.23038i	−0.546828	+	0.837245i	$0.684165\pi$
$937$	−44.8844	+	37.6625i	−1.46631	+	1.23038i	−0.919481	+	0.393134i	$0.871391\pi$
$938$		0			0
$939$	−15.5008	−	8.94939i	−0.505849	−	0.292052i
$940$		0			0
$941$	44.2420	+	16.1028i	1.44225	+	0.524936i	0.940415	−	0.340028i	$-0.110437\pi$
$941$	44.2420	+	16.1028i	1.44225	+	0.524936i	0.501834	+	0.864964i	$0.332659\pi$
$942$		0			0
$943$	−2.84978	+	3.39623i	−0.0928015	+	0.110597i
$944$		0			0
$945$	70.3409	−	12.4030i	2.28819	−	0.403470i
$946$		0			0
$947$	−6.54191	+	17.9738i	−0.212584	+	0.584068i	−0.999454	−	0.0330502i	$-0.989478\pi$
$947$	−6.54191	+	17.9738i	−0.212584	+	0.584068i	0.786870	+	0.617119i	$0.211700\pi$
$948$		0			0
$949$	46.2118	+	8.14838i	1.50010	+	0.264508i
$950$		0			0
$951$	−14.2417	−	24.6673i	−0.461817	−	0.799891i
$952$		0			0
$953$	0.149089	+	0.845526i	0.00482947	+	0.0273893i	0.987127	−	0.159937i	$-0.0511290\pi$
$953$	0.149089	+	0.845526i	0.00482947	+	0.0273893i	−0.982298	+	0.187326i	$0.940018\pi$
$954$		0			0
$955$	−53.9473	+	19.6352i	−1.74569	+	0.635381i
$956$		0			0
$957$	7.80065	+	21.4321i	0.252159	+	0.692801i
$958$		0			0
$959$	−48.0183	−	40.2922i	−1.55059	−	1.30110i
$960$		0			0
$961$	−14.8237			−0.478185
$962$		0			0
$963$	−0.203394			−0.00655429
$964$		0			0
$965$	−14.7721	−	12.3953i	−0.475532	−	0.399018i
$966$		0			0
$967$	−20.6459	−	56.7241i	−0.663927	−	1.82412i	−0.558160	−	0.829733i	$-0.688493\pi$
$967$	−20.6459	−	56.7241i	−0.663927	−	1.82412i	−0.105766	−	0.994391i	$-0.533730\pi$
$968$		0			0
$969$	−0.152346	+	0.0554492i	−0.00489404	+	0.00178129i
$970$		0			0
$971$	6.14330	+	34.8404i	0.197148	+	1.11808i	0.909327	+	0.416083i	$0.136597\pi$
$971$	6.14330	+	34.8404i	0.197148	+	1.11808i	−0.712179	+	0.701998i	$0.752291\pi$
$972$		0			0
$973$	−16.6585	−	28.8534i	−0.534048	−	0.924999i
$974$		0			0
$975$	70.3677	+	12.4077i	2.25357	+	0.397365i
$976$		0			0
$977$	−11.7238	+	32.2109i	−0.375078	+	1.03052i	0.598292	+	0.801278i	$0.295846\pi$
$977$	−11.7238	+	32.2109i	−0.375078	+	1.03052i	−0.973370	+	0.229240i	$0.926376\pi$
$978$		0			0
$979$	−17.2420	+	3.04022i	−0.551055	+	0.0971659i
$980$		0			0
$981$	0.330249	−	0.393576i	0.0105440	−	0.0125659i
$982$		0			0
$983$	15.2535	+	5.55182i	0.486511	+	0.177076i	0.573617	−	0.819123i	$-0.305540\pi$
$983$	15.2535	+	5.55182i	0.486511	+	0.177076i	−0.0871061	+	0.996199i	$0.527762\pi$
$984$		0			0
$985$	45.6880	+	26.3780i	1.45574	+	0.840473i
$986$		0			0
$987$	−13.5864	+	11.4003i	−0.432459	+	0.362876i
$988$		0			0
$989$	−8.22976	+	14.2544i	−0.261691	+	0.453263i
$990$		0			0
$991$	2.92903	−	1.69107i	0.0930436	−	0.0537187i	−0.452756	−	0.891634i	$-0.649559\pi$
$991$	2.92903	−	1.69107i	0.0930436	−	0.0537187i	0.545800	+	0.837916i	$0.316226\pi$
$992$		0			0
$993$			3.88315i			0.123228i
$994$		0			0
$995$	3.33922	−	18.9376i	0.105860	−	0.600364i
$996$		0			0
$997$	−25.7715	−	30.7132i	−0.816190	−	0.972698i	0.183757	−	0.982972i	$-0.441174\pi$
$997$	−25.7715	−	30.7132i	−0.816190	−	0.972698i	−0.999947	+	0.0102738i	$0.996730\pi$
$998$		0			0
$999$	−6.04553	−	27.5575i	−0.191272	−	0.871879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.b.321.1		12
4.3	odd	2		74.2.h.a.25.2	yes	12
12.11	even	2		666.2.bj.c.469.1		12
37.3	even	18	inner	592.2.bq.b.225.1		12
148.3	odd	18		74.2.h.a.3.2	✓	12
148.15	even	36		2738.2.a.r.1.2		6
148.59	even	36		2738.2.a.s.1.1		6
444.299	even	18		666.2.bj.c.595.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.3.2	✓	12	148.3	odd	18
74.2.h.a.25.2	yes	12	4.3	odd	2
592.2.bq.b.225.1		12	37.3	even	18	inner
592.2.bq.b.321.1		12	1.1	even	1	trivial
666.2.bj.c.469.1		12	12.11	even	2
666.2.bj.c.595.1		12	444.299	even	18
2738.2.a.r.1.2		6	148.15	even	36
2738.2.a.s.1.1		6	148.59	even	36

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.43969 - 1.20805i) q^{3} +(-1.45842 - 4.00698i) q^{5} +(3.39364 - 1.23518i) q^{7} +(0.0923963 + 0.524005i) q^{9} +O(q^{10})\)	\(q+(-1.43969 - 1.20805i) q^{3} +(-1.45842 - 4.00698i) q^{5} +(3.39364 - 1.23518i) q^{7} +(0.0923963 + 0.524005i) q^{9} +(-1.05840 - 1.83321i) q^{11} +(2.84019 + 0.500802i) q^{13} +(-2.74094 + 7.53066i) q^{15} +(0.0263137 - 0.00463982i) q^{17} +(2.07522 - 2.47315i) q^{19} +(-6.37796 - 2.32139i) q^{21} +(-2.57421 - 1.48622i) q^{23} +(-10.0987 + 8.47380i) q^{25} +(-2.31908 + 4.01676i) q^{27} +(4.96493 - 2.86650i) q^{29} +6.76932i q^{31} +(-0.690823 + 3.91785i) q^{33} +(-9.89872 - 11.7968i) q^{35} +(-4.49375 + 4.09954i) q^{37} +(-3.48401 - 4.15208i) q^{39} +(0.259000 - 1.46886i) q^{41} -5.53737i q^{43} +(1.96493 - 1.13445i) q^{45} +(1.30654 - 2.26300i) q^{47} +(4.62880 - 3.88403i) q^{49} +(-0.0434888 - 0.0251083i) q^{51} +(-1.79389 - 0.652924i) q^{53} +(-5.80203 + 6.91459i) q^{55} +(-5.97536 + 1.05362i) q^{57} +(-1.92380 + 5.28560i) q^{59} +(-5.65366 - 0.996892i) q^{61} +(0.960802 + 1.66416i) q^{63} +(-2.13549 - 12.1110i) q^{65} +(6.50406 - 2.36728i) q^{67} +(1.91065 + 5.24947i) q^{69} +(7.10830 + 5.96457i) q^{71} +16.2707 q^{73} +24.7757 q^{75} +(-5.85619 - 4.91392i) q^{77} +(0.484006 + 1.32980i) q^{79} +(9.69119 - 3.52730i) q^{81} +(0.294580 + 1.67065i) q^{83} +(-0.0569682 - 0.0986718i) q^{85} +(-10.6108 - 1.87098i) q^{87} +(2.82882 - 7.77213i) q^{89} +(10.2572 - 1.80861i) q^{91} +(8.17765 - 9.74574i) q^{93} +(-12.9364 - 4.70847i) q^{95} +(5.65105 + 3.26264i) q^{97} +(0.862818 - 0.723990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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