LMFDB - Embedded newform 1890.2.t.c.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.1
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.c.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.104916 - 2.64367i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.104916 - 2.64367i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +6.11380i q^{11} +(3.86893 - 2.23373i) q^{13} +(1.23098 + 2.34194i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.11723 - 1.93509i) q^{17} +(-0.623812 - 0.360158i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.05690 - 5.29471i) q^{22} -6.71710i q^{23} +1.00000 q^{25} +(-2.23373 + 3.86893i) q^{26} +(-2.23703 - 1.41269i) q^{28} +(-0.633929 - 0.365999i) q^{29} +(5.28276 + 3.05000i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.93509 + 1.11723i) q^{34} +(-0.104916 + 2.64367i) q^{35} +(-4.53567 + 7.85602i) q^{37} +0.720316 q^{38} -1.00000i q^{40} +(-0.713952 - 1.23660i) q^{41} +(1.23875 - 2.14558i) q^{43} +(5.29471 + 3.05690i) q^{44} +(3.35855 + 5.81718i) q^{46} +(4.18805 + 7.25392i) q^{47} +(-6.97799 - 0.554724i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.46746i q^{52} +(-0.193943 + 0.111973i) q^{53} -6.11380i q^{55} +(2.64367 + 0.104916i) q^{56} +0.731999 q^{58} +(4.88106 - 8.45424i) q^{59} +(-1.59270 + 0.919547i) q^{61} -6.10001 q^{62} -1.00000 q^{64} +(-3.86893 + 2.23373i) q^{65} +(6.54114 - 11.3296i) q^{67} -2.23445 q^{68} +(-1.23098 - 2.34194i) q^{70} -7.83185i q^{71} +(10.7713 - 6.21880i) q^{73} -9.07135i q^{74} +(-0.623812 + 0.360158i) q^{76} +(16.1629 + 0.641432i) q^{77} +(-7.49899 - 12.9886i) q^{79} +(0.500000 + 0.866025i) q^{80} +(1.23660 + 0.713952i) q^{82} +(-1.95115 + 3.37949i) q^{83} +(1.11723 + 1.93509i) q^{85} +2.47750i q^{86} -6.11380 q^{88} +(5.83979 - 10.1148i) q^{89} +(-5.49933 - 10.4625i) q^{91} +(-5.81718 - 3.35855i) q^{92} +(-7.25392 - 4.18805i) q^{94} +(0.623812 + 0.360158i) q^{95} +(10.9748 + 6.33628i) q^{97} +(6.32047 - 3.00859i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.104916	−	2.64367i	0.0396543	−	0.999213i
$7$	0.104916	−	2.64367i	0.0396543	−	0.999213i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$			6.11380i			1.84338i	0.387927	+	0.921690i	$0.373191\pi$
$11$			6.11380i			1.84338i	−0.387927	+	0.921690i	$0.626809\pi$
$12$		0			0
$13$	3.86893	−	2.23373i	1.07305	−	0.619525i	0.144036	−	0.989572i	$-0.453992\pi$
$13$	3.86893	−	2.23373i	1.07305	−	0.619525i	0.929013	+	0.370048i	$0.120659\pi$
$14$	1.23098	+	2.34194i	0.328992	+	0.625911i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.11723	−	1.93509i	−0.270967	−	0.469329i	0.698142	−	0.715959i	$-0.254010\pi$
$17$	−1.11723	−	1.93509i	−0.270967	−	0.469329i	−0.969110	+	0.246630i	$0.920677\pi$
$18$		0			0
$19$	−0.623812	−	0.360158i	−0.143112	−	0.0826259i	0.426734	−	0.904377i	$-0.359664\pi$
$19$	−0.623812	−	0.360158i	−0.143112	−	0.0826259i	−0.569846	+	0.821751i	$0.692997\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−3.05690	−	5.29471i	−0.651733	−	1.12884i
$23$		−	6.71710i		−	1.40061i	−0.713842	−	0.700306i	$-0.753047\pi$
$23$		−	6.71710i		−	1.40061i	0.713842	−	0.700306i	$-0.246953\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.23373	+	3.86893i	−0.438070	+	0.758760i
$27$		0			0
$28$	−2.23703	−	1.41269i	−0.422759	−	0.266974i
$29$	−0.633929	−	0.365999i	−0.117718	−	0.0679644i	0.439985	−	0.898005i	$-0.354984\pi$
$29$	−0.633929	−	0.365999i	−0.117718	−	0.0679644i	−0.557703	+	0.830041i	$0.688317\pi$
$30$		0			0
$31$	5.28276	+	3.05000i	0.948812	+	0.547797i	0.892712	−	0.450628i	$-0.148800\pi$
$31$	5.28276	+	3.05000i	0.948812	+	0.547797i	0.0561004	+	0.998425i	$0.482133\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	1.93509	+	1.11723i	0.331866	+	0.191603i
$35$	−0.104916	+	2.64367i	−0.0177340	+	0.446862i
$36$		0			0
$37$	−4.53567	+	7.85602i	−0.745660	+	1.29152i	0.204226	+	0.978924i	$0.434532\pi$
$37$	−4.53567	+	7.85602i	−0.745660	+	1.29152i	−0.949886	+	0.312597i	$0.898801\pi$
$38$	0.720316			0.116851
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	−0.713952	−	1.23660i	−0.111501	−	0.193125i	0.804875	−	0.593444i	$-0.202232\pi$
$41$	−0.713952	−	1.23660i	−0.111501	−	0.193125i	−0.916375	+	0.400320i	$0.868899\pi$
$42$		0			0
$43$	1.23875	−	2.14558i	0.188907	−	0.327197i	−0.755979	−	0.654596i	$-0.772839\pi$
$43$	1.23875	−	2.14558i	0.188907	−	0.327197i	0.944886	+	0.327399i	$0.106172\pi$
$44$	5.29471	+	3.05690i	0.798207	+	0.460845i
$45$		0			0
$46$	3.35855	+	5.81718i	0.495191	+	0.857697i
$47$	4.18805	+	7.25392i	0.610890	+	1.05809i	0.991091	+	0.133189i	$0.0425217\pi$
$47$	4.18805	+	7.25392i	0.610890	+	1.05809i	−0.380200	+	0.924904i	$0.624145\pi$
$48$		0			0
$49$	−6.97799	−	0.554724i	−0.996855	−	0.0792463i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$		−	4.46746i		−	0.619525i
$53$	−0.193943	+	0.111973i	−0.0266401	+	0.0153807i	−0.513261	−	0.858233i	$-0.671563\pi$
$53$	−0.193943	+	0.111973i	−0.0266401	+	0.0153807i	0.486621	+	0.873613i	$0.338229\pi$
$54$		0			0
$55$		−	6.11380i		−	0.824385i
$56$	2.64367	+	0.104916i	0.353275	+	0.0140199i
$57$		0			0
$58$	0.731999			0.0961161
$59$	4.88106	−	8.45424i	0.635460	−	1.10065i	−0.350958	−	0.936391i	$-0.614144\pi$
$59$	4.88106	−	8.45424i	0.635460	−	1.10065i	0.986417	−	0.164258i	$-0.0525228\pi$
$60$		0			0
$61$	−1.59270	+	0.919547i	−0.203925	+	0.117736i	−0.598485	−	0.801134i	$-0.704230\pi$
$61$	−1.59270	+	0.919547i	−0.203925	+	0.117736i	0.394560	+	0.918870i	$0.370897\pi$
$62$	−6.10001			−0.774702
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.86893	+	2.23373i	−0.479882	+	0.277060i
$66$		0			0
$67$	6.54114	−	11.3296i	0.799127	−	1.38413i	−0.121058	−	0.992645i	$-0.538629\pi$
$67$	6.54114	−	11.3296i	0.799127	−	1.38413i	0.920185	−	0.391484i	$-0.128038\pi$
$68$	−2.23445			−0.270967
$69$		0			0
$70$	−1.23098	−	2.34194i	−0.147130	−	0.279916i
$71$		−	7.83185i		−	0.929470i	−0.885450	−	0.464735i	$-0.846150\pi$
$71$		−	7.83185i		−	0.929470i	0.885450	−	0.464735i	$-0.153850\pi$
$72$		0			0
$73$	10.7713	−	6.21880i	1.26068	−	0.727856i	0.287477	−	0.957788i	$-0.407184\pi$
$73$	10.7713	−	6.21880i	1.26068	−	0.727856i	0.973207	+	0.229932i	$0.0738502\pi$
$74$		−	9.07135i		−	1.05452i
$75$		0			0
$76$	−0.623812	+	0.360158i	−0.0715561	+	0.0413130i
$77$	16.1629	+	0.641432i	1.84193	+	0.0730980i
$78$		0			0
$79$	−7.49899	−	12.9886i	−0.843702	−	1.46133i	−0.886744	−	0.462262i	$-0.847038\pi$
$79$	−7.49899	−	12.9886i	−0.843702	−	1.46133i	0.0430414	−	0.999073i	$-0.486295\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	1.23660	+	0.713952i	0.136560	+	0.0788428i
$83$	−1.95115	+	3.37949i	−0.214167	+	0.370947i	−0.953014	−	0.302925i	$-0.902037\pi$
$83$	−1.95115	+	3.37949i	−0.214167	+	0.370947i	0.738848	+	0.673872i	$0.235370\pi$
$84$		0			0
$85$	1.11723	+	1.93509i	0.121180	+	0.209890i
$86$			2.47750i			0.267155i
$87$		0			0
$88$	−6.11380			−0.651733
$89$	5.83979	−	10.1148i	0.619016	−	1.07217i	−0.370649	−	0.928773i	$-0.620865\pi$
$89$	5.83979	−	10.1148i	0.619016	−	1.07217i	0.989666	−	0.143395i	$-0.0458019\pi$
$90$		0			0
$91$	−5.49933	−	10.4625i	−0.576487	−	1.09677i
$92$	−5.81718	−	3.35855i	−0.606483	−	0.350153i
$93$		0			0
$94$	−7.25392	−	4.18805i	−0.748185	−	0.431965i
$95$	0.623812	+	0.360158i	0.0640017	+	0.0369514i
$96$		0			0
$97$	10.9748	+	6.33628i	1.11432	+	0.643351i	0.939944	−	0.341328i	$-0.110877\pi$
$97$	10.9748	+	6.33628i	1.11432	+	0.643351i	0.174373	+	0.984680i	$0.444210\pi$
$98$	6.32047	−	3.00859i	0.638464	−	0.303913i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−0.196980			−0.0196002			−0.00980010	−	0.999952i	$-0.503120\pi$
$101$	−0.196980			−0.0196002			−0.00980010	+	0.999952i	$0.503120\pi$
$102$		0			0
$103$		−	6.81626i		−	0.671626i	−0.941929	−	0.335813i	$-0.890989\pi$
$103$		−	6.81626i		−	0.671626i	0.941929	−	0.335813i	$-0.109011\pi$
$104$	2.23373	+	3.86893i	0.219035	+	0.379380i
$105$		0			0
$106$	0.111973	−	0.193943i	0.0108758	−	0.0188374i
$107$	−4.67098	−	2.69679i	−0.451560	−	0.260709i	0.256929	−	0.966430i	$-0.417289\pi$
$107$	−4.67098	−	2.69679i	−0.451560	−	0.260709i	−0.708489	+	0.705722i	$0.750623\pi$
$108$		0			0
$109$	6.74410	+	11.6811i	0.645967	+	1.11885i	0.984077	+	0.177742i	$0.0568791\pi$
$109$	6.74410	+	11.6811i	0.645967	+	1.11885i	−0.338110	+	0.941107i	$0.609788\pi$
$110$	3.05690	+	5.29471i	0.291464	+	0.504830i
$111$		0			0
$112$	−2.34194	+	1.23098i	−0.221293	+	0.116316i
$113$	16.3111	−	9.41722i	1.53442	−	0.885897i	0.535269	−	0.844682i	$-0.320210\pi$
$113$	16.3111	−	9.41722i	1.53442	−	0.885897i	0.999150	−	0.0412153i	$-0.0131230\pi$
$114$		0			0
$115$			6.71710i			0.626373i
$116$	−0.633929	+	0.365999i	−0.0588589	+	0.0339822i
$117$		0			0
$118$			9.76212i			0.898676i
$119$	−5.23297	+	2.75056i	−0.479705	+	0.252143i
$120$		0			0
$121$	−26.3785			−2.39805
$122$	0.919547	−	1.59270i	0.0832519	−	0.144196i
$123$		0			0
$124$	5.28276	−	3.05000i	0.474406	−	0.273898i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	12.6907			1.12612			0.563060	−	0.826416i	$-0.309624\pi$
$127$	12.6907			1.12612			0.563060	+	0.826416i	$0.309624\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	2.23373	−	3.86893i	0.195911	−	0.339328i
$131$	8.69627			0.759796			0.379898	−	0.925028i	$-0.375959\pi$
$131$	8.69627			0.759796			0.379898	+	0.925028i	$0.375959\pi$
$132$		0			0
$133$	−1.01759	+	1.61137i	−0.0882359	+	0.139723i
$134$			13.0823i			1.13014i
$135$		0			0
$136$	1.93509	−	1.11723i	0.165933	−	0.0958014i
$137$		−	20.4737i		−	1.74919i	−0.484855	−	0.874594i	$-0.661128\pi$
$137$		−	20.4737i		−	1.74919i	0.484855	−	0.874594i	$-0.338872\pi$
$138$		0			0
$139$	1.45863	−	0.842140i	0.123719	−	0.0714294i	−0.436863	−	0.899528i	$-0.643911\pi$
$139$	1.45863	−	0.842140i	0.123719	−	0.0714294i	0.560583	+	0.828099i	$0.310577\pi$
$140$	2.23703	+	1.41269i	0.189063	+	0.119394i
$141$		0			0
$142$	3.91593	+	6.78258i	0.328617	+	0.569182i
$143$	13.6566	+	23.6539i	1.14202	+	1.97804i
$144$		0			0
$145$	0.633929	+	0.365999i	0.0526450	+	0.0303946i
$146$	−6.21880	+	10.7713i	−0.514672	+	0.891438i
$147$		0			0
$148$	4.53567	+	7.85602i	0.372830	+	0.645761i
$149$		−	5.72362i		−	0.468897i	−0.972129	−	0.234448i	$-0.924672\pi$
$149$		−	5.72362i		−	0.468897i	0.972129	−	0.234448i	$-0.0753284\pi$
$150$		0			0
$151$	−6.98531			−0.568456			−0.284228	−	0.958757i	$-0.591737\pi$
$151$	−6.98531			−0.568456			−0.284228	+	0.958757i	$0.591737\pi$
$152$	0.360158	−	0.623812i	0.0292127	−	0.0505978i
$153$		0			0
$154$	−14.3182	+	7.52594i	−1.15379	+	0.606457i
$155$	−5.28276	−	3.05000i	−0.424322	−	0.244982i
$156$		0			0
$157$	15.4710	+	8.93219i	1.23472	+	0.712867i	0.968010	−	0.250910i	$-0.0807299\pi$
$157$	15.4710	+	8.93219i	1.23472	+	0.712867i	0.266711	+	0.963777i	$0.414063\pi$
$158$	12.9886	+	7.49899i	1.03332	+	0.596588i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−17.7578	−	0.704728i	−1.39951	−	0.0555404i
$162$		0			0
$163$	−4.05646	+	7.02600i	−0.317727	+	0.550319i	−0.980013	−	0.198932i	$-0.936253\pi$
$163$	−4.05646	+	7.02600i	−0.317727	+	0.550319i	0.662287	+	0.749250i	$0.269586\pi$
$164$	−1.42790			−0.111501
$165$		0			0
$166$		−	3.90230i		−	0.302877i
$167$	−1.29948	−	2.25076i	−0.100557	−	0.174169i	0.811357	−	0.584550i	$-0.198729\pi$
$167$	−1.29948	−	2.25076i	−0.100557	−	0.174169i	−0.911914	+	0.410381i	$0.865396\pi$
$168$		0			0
$169$	3.47909	−	6.02595i	0.267622	−	0.463535i
$170$	−1.93509	−	1.11723i	−0.148415	−	0.0856874i
$171$		0			0
$172$	−1.23875	−	2.14558i	−0.0944537	−	0.163599i
$173$	−7.08170	−	12.2659i	−0.538412	−	0.932557i	−0.998990	−	0.0449373i	$-0.985691\pi$
$173$	−7.08170	−	12.2659i	−0.538412	−	0.932557i	0.460578	−	0.887619i	$-0.347642\pi$
$174$		0			0
$175$	0.104916	−	2.64367i	0.00793087	−	0.199843i
$176$	5.29471	−	3.05690i	0.399103	−	0.230422i
$177$		0			0
$178$			11.6796i			0.875421i
$179$	15.8658	−	9.16012i	1.18587	−	0.684660i	0.228501	−	0.973544i	$-0.426618\pi$
$179$	15.8658	−	9.16012i	1.18587	−	0.684660i	0.957364	+	0.288884i	$0.0932842\pi$
$180$		0			0
$181$		−	0.536166i		−	0.0398529i	−0.999801	−	0.0199265i	$-0.993657\pi$
$181$		−	0.536166i		−	0.0398529i	0.999801	−	0.0199265i	$-0.00634321\pi$
$182$	9.99383	+	6.31115i	0.740792	+	0.467814i
$183$		0			0
$184$	6.71710			0.495191
$185$	4.53567	−	7.85602i	0.333469	−	0.577586i
$186$		0			0
$187$	11.8308	−	6.83050i	0.865152	−	0.499496i
$188$	8.37611			0.610890
$189$		0			0
$190$	−0.720316			−0.0522572
$191$	4.04414	−	2.33488i	0.292623	−	0.168946i	−0.346501	−	0.938050i	$-0.612630\pi$
$191$	4.04414	−	2.33488i	0.292623	−	0.168946i	0.639124	+	0.769103i	$0.279297\pi$
$192$		0			0
$193$	9.89647	−	17.1412i	0.712363	−	1.23385i	−0.251604	−	0.967830i	$-0.580958\pi$
$193$	9.89647	−	17.1412i	0.712363	−	1.23385i	0.963968	−	0.266019i	$-0.0857085\pi$
$194$	−12.6726			−0.909836
$195$		0			0
$196$	−3.96940	+	5.76575i	−0.283528	+	0.411839i
$197$			16.1466i			1.15040i	0.818013	+	0.575199i	$0.195075\pi$
$197$			16.1466i			1.15040i	−0.818013	+	0.575199i	$0.804925\pi$
$198$		0			0
$199$	0.660045	−	0.381077i	0.0467894	−	0.0270139i	−0.476423	−	0.879216i	$-0.658067\pi$
$199$	0.660045	−	0.381077i	0.0467894	−	0.0270139i	0.523212	+	0.852202i	$0.324734\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	0.170589	−	0.0984898i	0.0120026	−	0.00692972i
$203$	−1.03409	+	1.63750i	−0.0725789	+	0.114930i
$204$		0			0
$205$	0.713952	+	1.23660i	0.0498646	+	0.0863679i
$206$	3.40813	+	5.90305i	0.237456	+	0.411285i
$207$		0			0
$208$	−3.86893	−	2.23373i	−0.268262	−	0.154881i
$209$	2.20193	−	3.81386i	0.152311	−	0.263810i
$210$		0			0
$211$	5.84214	+	10.1189i	0.402189	+	0.696613i	0.993990	−	0.109472i	$-0.0349160\pi$
$211$	5.84214	+	10.1189i	0.402189	+	0.696613i	−0.591800	+	0.806085i	$0.701583\pi$
$212$			0.223946i			0.0153807i
$213$		0			0
$214$	5.39358			0.368698
$215$	−1.23875	+	2.14558i	−0.0844819	+	0.146327i
$216$		0			0
$217$	8.61745	−	13.6459i	0.584991	−	0.926343i
$218$	−11.6811	−	6.74410i	−0.791145	−	0.456768i
$219$		0			0
$220$	−5.29471	−	3.05690i	−0.356969	−	0.206096i
$221$	−8.64495	−	4.99116i	−0.581522	−	0.335742i
$222$		0			0
$223$	−6.37774	−	3.68219i	−0.427085	−	0.246577i	0.271019	−	0.962574i	$-0.412639\pi$
$223$	−6.37774	−	3.68219i	−0.427085	−	0.246577i	−0.698104	+	0.715996i	$0.745973\pi$
$224$	1.41269	−	2.23703i	0.0943896	−	0.149468i
$225$		0			0
$226$	−9.41722	+	16.3111i	−0.626424	+	1.08500i
$227$	−13.8820			−0.921381			−0.460690	−	0.887561i	$-0.652398\pi$
$227$	−13.8820			−0.921381			−0.460690	+	0.887561i	$0.652398\pi$
$228$		0			0
$229$			16.4020i			1.08388i	0.840418	+	0.541939i	$0.182310\pi$
$229$			16.4020i			1.08388i	−0.840418	+	0.541939i	$0.817690\pi$
$230$	−3.35855	−	5.81718i	−0.221456	−	0.383574i
$231$		0			0
$232$	0.365999	−	0.633929i	0.0240290	−	0.0416195i
$233$	11.5552	+	6.67137i	0.757003	+	0.437056i	0.828219	−	0.560405i	$-0.189354\pi$
$233$	11.5552	+	6.67137i	0.757003	+	0.437056i	−0.0712156	+	0.997461i	$0.522688\pi$
$234$		0			0
$235$	−4.18805	−	7.25392i	−0.273198	−	0.473194i
$236$	−4.88106	−	8.45424i	−0.317730	−	0.550324i
$237$		0			0
$238$	3.15660	−	4.99854i	0.204612	−	0.324007i
$239$	5.40343	−	3.11967i	0.349519	−	0.201795i	−0.314954	−	0.949107i	$-0.601989\pi$
$239$	5.40343	−	3.11967i	0.349519	−	0.201795i	0.664473	+	0.747312i	$0.268656\pi$
$240$		0			0
$241$			2.52754i			0.162813i	0.996681	+	0.0814066i	$0.0259412\pi$
$241$			2.52754i			0.162813i	−0.996681	+	0.0814066i	$0.974059\pi$
$242$	22.8445	−	13.1893i	1.46850	−	0.847839i
$243$		0			0
$244$			1.83909i			0.117736i
$245$	6.97799	+	0.554724i	0.445807	+	0.0354400i
$246$		0			0
$247$	−3.21798			−0.204755
$248$	−3.05000	+	5.28276i	−0.193675	+	0.335456i
$249$		0			0
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−22.8300			−1.44102			−0.720508	−	0.693447i	$-0.756091\pi$
$251$	−22.8300			−1.44102			−0.720508	+	0.693447i	$0.756091\pi$
$252$		0			0
$253$	41.0670			2.58186
$254$	−10.9905	+	6.34536i	−0.689604	+	0.398143i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.7320			−1.10609			−0.553045	−	0.833151i	$-0.686534\pi$
$257$	−17.7320			−1.10609			−0.553045	+	0.833151i	$0.686534\pi$
$258$		0			0
$259$	20.2929	+	12.8150i	1.26094	+	0.796288i
$260$			4.46746i			0.277060i
$261$		0			0
$262$	−7.53119	+	4.34813i	−0.465278	+	0.268629i
$263$		−	7.48303i		−	0.461424i	−0.973022	−	0.230712i	$-0.925895\pi$
$263$		−	7.48303i		−	0.461424i	0.973022	−	0.230712i	$-0.0741054\pi$
$264$		0			0
$265$	0.193943	−	0.111973i	0.0119138	−	0.00687846i
$266$	0.0755723	−	1.90428i	0.00463364	−	0.116759i
$267$		0			0
$268$	−6.54114	−	11.3296i	−0.399564	−	0.692065i
$269$	3.58549	+	6.21025i	0.218611	+	0.378646i	0.954384	−	0.298583i	$-0.0965140\pi$
$269$	3.58549	+	6.21025i	0.218611	+	0.378646i	−0.735772	+	0.677229i	$0.763181\pi$
$270$		0			0
$271$	−16.4457	−	9.49493i	−0.999005	−	0.576776i	−0.0910514	−	0.995846i	$-0.529023\pi$
$271$	−16.4457	−	9.49493i	−0.999005	−	0.576776i	−0.907954	+	0.419070i	$0.862356\pi$
$272$	−1.11723	+	1.93509i	−0.0677419	+	0.117332i
$273$		0			0
$274$	10.2369	+	17.7308i	0.618432	+	1.07116i
$275$			6.11380i			0.368676i
$276$		0			0
$277$	−8.61527			−0.517641			−0.258821	−	0.965925i	$-0.583334\pi$
$277$	−8.61527			−0.517641			−0.258821	+	0.965925i	$0.583334\pi$
$278$	−0.842140	+	1.45863i	−0.0505082	+	0.0874828i
$279$		0			0
$280$	−2.64367	−	0.104916i	−0.157990	−	0.00626990i
$281$	19.0254	+	10.9843i	1.13496	+	0.655268i	0.945177	−	0.326558i	$-0.105889\pi$
$281$	19.0254	+	10.9843i	1.13496	+	0.655268i	0.189781	+	0.981827i	$0.439222\pi$
$282$		0			0
$283$	−13.9204	−	8.03697i	−0.827485	−	0.477749i	0.0255060	−	0.999675i	$-0.491880\pi$
$283$	−13.9204	−	8.03697i	−0.827485	−	0.477749i	−0.852991	+	0.521926i	$0.825214\pi$
$284$	−6.78258	−	3.91593i	−0.402472	−	0.232368i
$285$		0			0
$286$	−23.6539	−	13.6566i	−1.39868	−	0.807530i
$287$	−3.34407	+	1.75771i	−0.197394	+	0.103755i
$288$		0			0
$289$	6.00361	−	10.3986i	0.353153	−	0.611680i
$290$	−0.731999			−0.0429844
$291$		0			0
$292$		−	12.4376i		−	0.727856i
$293$	10.0760	+	17.4522i	0.588649	+	1.01957i	0.994410	+	0.105591i	$0.0336733\pi$
$293$	10.0760	+	17.4522i	0.588649	+	1.01957i	−0.405761	+	0.913979i	$0.632993\pi$
$294$		0			0
$295$	−4.88106	+	8.45424i	−0.284186	+	0.492225i
$296$	−7.85602	−	4.53567i	−0.456622	−	0.263631i
$297$		0			0
$298$	2.86181	+	4.95680i	0.165780	+	0.287140i
$299$	−15.0042	−	25.9880i	−0.867714	−	1.50293i
$300$		0			0
$301$	−5.54223	−	3.49995i	−0.319449	−	0.201734i
$302$	6.04945	−	3.49265i	0.348107	−	0.200980i
$303$		0			0
$304$			0.720316i			0.0413130i
$305$	1.59270	−	0.919547i	0.0911979	−	0.0526531i
$306$		0			0
$307$			9.18411i			0.524165i	0.965046	+	0.262082i	$0.0844092\pi$
$307$			9.18411i			0.524165i	−0.965046	+	0.262082i	$0.915591\pi$
$308$	8.63693	−	13.6767i	0.492135	−	0.779305i
$309$		0			0
$310$	6.10001			0.346457
$311$	−4.44185	+	7.69351i	−0.251874	+	0.436259i	−0.964042	−	0.265751i	$-0.914380\pi$
$311$	−4.44185	+	7.69351i	−0.251874	+	0.436259i	0.712168	+	0.702009i	$0.247714\pi$
$312$		0			0
$313$	−20.3812	+	11.7671i	−1.15202	+	0.665116i	−0.949377	−	0.314138i	$-0.898285\pi$
$313$	−20.3812	+	11.7671i	−1.15202	+	0.665116i	−0.202638	+	0.979254i	$0.564951\pi$
$314$	−17.8644			−1.00815
$315$		0			0
$316$	−14.9980			−0.843702
$317$	−9.40027	+	5.42725i	−0.527972	+	0.304825i	−0.740190	−	0.672398i	$-0.765265\pi$
$317$	−9.40027	+	5.42725i	−0.527972	+	0.304825i	0.212218	+	0.977222i	$0.431931\pi$
$318$		0			0
$319$	2.23765	−	3.87572i	0.125284	−	0.216999i
$320$	1.00000			0.0559017
$321$		0			0
$322$	15.7311	−	8.26859i	0.876659	−	0.460791i
$323$			1.60951i			0.0895557i
$324$		0			0
$325$	3.86893	−	2.23373i	0.214610	−	0.123905i
$326$		−	8.11292i		−	0.449333i
$327$		0			0
$328$	1.23660	−	0.713952i	0.0682798	−	0.0394214i
$329$	19.6164	−	10.3108i	1.08149	−	0.568452i
$330$		0			0
$331$	−2.43508	−	4.21769i	−0.133844	−	0.231825i	0.791311	−	0.611414i	$-0.209399\pi$
$331$	−2.43508	−	4.21769i	−0.133844	−	0.231825i	−0.925155	+	0.379589i	$0.876066\pi$
$332$	1.95115	+	3.37949i	0.107083	+	0.185474i
$333$		0			0
$334$	2.25076	+	1.29948i	0.123156	+	0.0711043i
$335$	−6.54114	+	11.3296i	−0.357381	+	0.619001i
$336$		0			0
$337$	−10.6309	−	18.4133i	−0.579103	−	1.00304i	−0.995583	−	0.0938903i	$-0.970070\pi$
$337$	−10.6309	−	18.4133i	−0.579103	−	1.00304i	0.416480	−	0.909145i	$-0.363264\pi$
$338$			6.95817i			0.378475i
$339$		0			0
$340$	2.23445			0.121180
$341$	−18.6471	+	32.2978i	−1.00980	+	1.74902i
$342$		0			0
$343$	−2.19861	+	18.3893i	−0.118714	+	0.992929i
$344$	2.14558	+	1.23875i	0.115682	+	0.0667888i
$345$		0			0
$346$	12.2659	+	7.08170i	0.659417	+	0.380715i
$347$	−0.561393	−	0.324120i	−0.0301371	−	0.0173997i	0.484856	−	0.874594i	$-0.338872\pi$
$347$	−0.561393	−	0.324120i	−0.0301371	−	0.0173997i	−0.514993	+	0.857194i	$0.672205\pi$
$348$		0			0
$349$	11.4424	+	6.60629i	0.612500	+	0.353627i	0.773943	−	0.633255i	$-0.218282\pi$
$349$	11.4424	+	6.60629i	0.612500	+	0.353627i	−0.161444	+	0.986882i	$0.551615\pi$
$350$	1.23098	+	2.34194i	0.0657984	+	0.125182i
$351$		0			0
$352$	−3.05690	+	5.29471i	−0.162933	+	0.282209i
$353$	15.9257			0.847639			0.423819	−	0.905747i	$-0.360689\pi$
$353$	15.9257			0.847639			0.423819	+	0.905747i	$0.360689\pi$
$354$		0			0
$355$			7.83185i			0.415672i
$356$	−5.83979	−	10.1148i	−0.309508	−	0.536084i
$357$		0			0
$358$	−9.16012	+	15.8658i	−0.484128	+	0.838533i
$359$	13.0760	+	7.54942i	0.690123	+	0.398443i	0.803658	−	0.595091i	$-0.202884\pi$
$359$	13.0760	+	7.54942i	0.690123	+	0.398443i	−0.113535	+	0.993534i	$0.536217\pi$
$360$		0			0
$361$	−9.24057	−	16.0051i	−0.486346	−	0.842376i
$362$	0.268083	+	0.464334i	0.0140901	+	0.0244048i
$363$		0			0
$364$	−11.8105	−	0.468706i	−0.619038	−	0.0245668i
$365$	−10.7713	+	6.21880i	−0.563795	+	0.325507i
$366$		0			0
$367$			12.7708i			0.666630i	0.942816	+	0.333315i	$0.108167\pi$
$367$			12.7708i			0.666630i	−0.942816	+	0.333315i	$0.891833\pi$
$368$	−5.81718	+	3.35855i	−0.303242	+	0.175077i
$369$		0			0
$370$			9.07135i			0.471597i
$371$	0.275672	+	0.524470i	0.0143122	+	0.0272291i
$372$		0			0
$373$	8.30398			0.429964			0.214982	−	0.976618i	$-0.431031\pi$
$373$	8.30398			0.429964			0.214982	+	0.976618i	$0.431031\pi$
$374$	−6.83050	+	11.8308i	−0.353197	+	0.611755i
$375$		0			0
$376$	−7.25392	+	4.18805i	−0.374092	+	0.215982i
$377$	−3.27017			−0.168422
$378$		0			0
$379$	−7.54965			−0.387800			−0.193900	−	0.981021i	$-0.562114\pi$
$379$	−7.54965			−0.387800			−0.193900	+	0.981021i	$0.562114\pi$
$380$	0.623812	−	0.360158i	0.0320009	−	0.0184757i
$381$		0			0
$382$	−2.33488	+	4.04414i	−0.119463	+	0.206916i
$383$	−10.8396			−0.553880			−0.276940	−	0.960887i	$-0.589320\pi$
$383$	−10.8396			−0.553880			−0.276940	+	0.960887i	$0.589320\pi$
$384$		0			0
$385$	−16.1629	−	0.641432i	−0.823736	−	0.0326904i
$386$			19.7929i			1.00743i
$387$		0			0
$388$	10.9748	−	6.33628i	0.557159	−	0.321676i
$389$			18.8709i			0.956790i	0.878145	+	0.478395i	$0.158781\pi$
$389$			18.8709i			0.956790i	−0.878145	+	0.478395i	$0.841219\pi$
$390$		0			0
$391$	−12.9982	+	7.50453i	−0.657349	+	0.379520i
$392$	0.554724	−	6.97799i	0.0280178	−	0.352441i
$393$		0			0
$394$	−8.07331	−	13.9834i	−0.406727	−	0.704472i
$395$	7.49899	+	12.9886i	0.377315	+	0.653529i
$396$		0			0
$397$	20.8331	+	12.0280i	1.04558	+	0.603667i	0.921409	−	0.388593i	$-0.127039\pi$
$397$	20.8331	+	12.0280i	1.04558	+	0.603667i	0.124173	+	0.992261i	$0.460372\pi$
$398$	−0.381077	+	0.660045i	−0.0191017	+	0.0330851i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	19.4786i		−	0.972715i	−0.873760	−	0.486357i	$-0.838325\pi$
$401$		−	19.4786i		−	0.972715i	0.873760	−	0.486357i	$-0.161675\pi$
$402$		0			0
$403$	27.2515			1.35750
$404$	−0.0984898	+	0.170589i	−0.00490005	+	0.00848714i
$405$		0			0
$406$	0.0767980	−	1.93516i	0.00381142	−	0.0960405i
$407$	−48.0301	−	27.7302i	−2.38076	−	1.37454i
$408$		0			0
$409$	24.8052	+	14.3213i	1.22654	+	0.708142i	0.966304	−	0.257404i	$-0.0828670\pi$
$409$	24.8052	+	14.3213i	1.22654	+	0.708142i	0.260234	+	0.965546i	$0.416200\pi$
$410$	−1.23660	−	0.713952i	−0.0610714	−	0.0352596i
$411$		0			0
$412$	−5.90305	−	3.40813i	−0.290823	−	0.167907i
$413$	−21.8381	−	13.7909i	−1.07458	−	0.678606i
$414$		0			0
$415$	1.95115	−	3.37949i	0.0957782	−	0.165893i
$416$	4.46746			0.219035
$417$		0			0
$418$			4.40387i			0.215400i
$419$	−13.3187	−	23.0686i	−0.650659	−	1.12697i	−0.982963	−	0.183802i	$-0.941159\pi$
$419$	−13.3187	−	23.0686i	−0.650659	−	1.12697i	0.332304	−	0.943172i	$-0.392174\pi$
$420$		0			0
$421$	−6.85328	+	11.8702i	−0.334008	+	0.578520i	−0.983294	−	0.182025i	$-0.941735\pi$
$421$	−6.85328	+	11.8702i	−0.334008	+	0.578520i	0.649285	+	0.760545i	$0.275068\pi$
$422$	−10.1189	−	5.84214i	−0.492579	−	0.284391i
$423$		0			0
$424$	−0.111973	−	0.193943i	−0.00543790	−	0.00941871i
$425$	−1.11723	−	1.93509i	−0.0541935	−	0.0938659i
$426$		0			0
$427$	2.26388	+	4.30705i	0.109557	+	0.208433i
$428$	−4.67098	+	2.69679i	−0.225780	+	0.130354i
$429$		0			0
$430$		−	2.47750i		−	0.119475i
$431$	−22.9075	+	13.2257i	−1.10342	+	0.637058i	−0.937116	−	0.349018i	$-0.886515\pi$
$431$	−22.9075	+	13.2257i	−1.10342	+	0.637058i	−0.166300	+	0.986075i	$0.553182\pi$
$432$		0			0
$433$		−	6.34697i		−	0.305016i	−0.988302	−	0.152508i	$-0.951265\pi$
$433$		−	6.34697i		−	0.305016i	0.988302	−	0.152508i	$-0.0487350\pi$
$434$	−0.639986	+	16.1264i	−0.0307203	+	0.774093i
$435$		0			0
$436$	13.4882			0.645967
$437$	−2.41922	+	4.19021i	−0.115727	+	0.200445i
$438$		0			0
$439$	13.6963	−	7.90756i	0.653689	−	0.377407i	−0.136179	−	0.990684i	$-0.543482\pi$
$439$	13.6963	−	7.90756i	0.653689	−	0.377407i	0.789868	+	0.613277i	$0.210149\pi$
$440$	6.11380			0.291464
$441$		0			0
$442$	9.98233			0.474811
$443$	1.98778	−	1.14765i	0.0944423	−	0.0545263i	−0.452035	−	0.892000i	$-0.649302\pi$
$443$	1.98778	−	1.14765i	0.0944423	−	0.0545263i	0.546477	+	0.837474i	$0.315968\pi$
$444$		0			0
$445$	−5.83979	+	10.1148i	−0.276833	+	0.479488i
$446$	7.36437			0.348713
$447$		0			0
$448$	−0.104916	+	2.64367i	−0.00495679	+	0.124902i
$449$		−	1.43524i		−	0.0677333i	−0.999426	−	0.0338666i	$-0.989218\pi$
$449$		−	1.43524i		−	0.0677333i	0.999426	−	0.0338666i	$-0.0107821\pi$
$450$		0			0
$451$	7.56033	−	4.36496i	0.356002	−	0.205538i
$452$		−	18.8344i		−	0.885897i
$453$		0			0
$454$	12.0222	−	6.94100i	0.564228	−	0.325757i
$455$	5.49933	+	10.4625i	0.257813	+	0.490491i
$456$		0			0
$457$	17.4266	+	30.1838i	0.815184	+	1.41194i	0.909196	+	0.416369i	$0.136697\pi$
$457$	17.4266	+	30.1838i	0.815184	+	1.41194i	−0.0940122	+	0.995571i	$0.529969\pi$
$458$	−8.20102	−	14.2046i	−0.383209	−	0.663737i
$459$		0			0
$460$	5.81718	+	3.35855i	0.271228	+	0.156593i
$461$	−8.41259	+	14.5710i	−0.391813	+	0.678641i	−0.992689	−	0.120702i	$-0.961485\pi$
$461$	−8.41259	+	14.5710i	−0.391813	+	0.678641i	0.600875	+	0.799343i	$0.294819\pi$
$462$		0			0
$463$	−3.64092	−	6.30627i	−0.169208	−	0.293077i	0.768934	−	0.639329i	$-0.220788\pi$
$463$	−3.64092	−	6.30627i	−0.169208	−	0.293077i	−0.938142	+	0.346252i	$0.887454\pi$
$464$			0.731999i			0.0339822i
$465$		0			0
$466$	−13.3427			−0.618091
$467$	15.5681	−	26.9647i	0.720404	−	1.24778i	−0.240434	−	0.970666i	$-0.577290\pi$
$467$	15.5681	−	26.9647i	0.720404	−	1.24778i	0.960838	−	0.277111i	$-0.0893769\pi$
$468$		0			0
$469$	−29.2654	−	18.4813i	−1.35135	−	0.853386i
$470$	7.25392	+	4.18805i	0.334598	+	0.193180i
$471$		0			0
$472$	8.45424	+	4.88106i	0.389138	+	0.224669i
$473$	13.1176	+	7.57346i	0.603149	+	0.348228i
$474$		0			0
$475$	−0.623812	−	0.360158i	−0.0286225	−	0.0165252i
$476$	−0.234429	+	5.90716i	−0.0107450	+	0.270754i
$477$		0			0
$478$	−3.11967	+	5.40343i	−0.142690	+	0.247147i
$479$	31.0310			1.41784			0.708922	−	0.705287i	$-0.249182\pi$
$479$	31.0310			1.41784			0.708922	+	0.705287i	$0.249182\pi$
$480$		0			0
$481$			40.5259i			1.84782i
$482$	−1.26377	−	2.18891i	−0.0575632	−	0.0997023i
$483$		0			0
$484$	−13.1893	+	22.8445i	−0.599512	+	1.03839i
$485$	−10.9748	−	6.33628i	−0.498338	−	0.287715i
$486$		0			0
$487$	−21.4771	−	37.1994i	−0.973221	−	1.68567i	−0.685686	−	0.727898i	$-0.740498\pi$
$487$	−21.4771	−	37.1994i	−0.973221	−	1.68567i	−0.287535	−	0.957770i	$-0.592836\pi$
$488$	−0.919547	−	1.59270i	−0.0416259	−	0.0720982i
$489$		0			0
$490$	−6.32047	+	3.00859i	−0.285530	+	0.135914i
$491$	−28.8133	+	16.6354i	−1.30033	+	0.750744i	−0.980460	−	0.196719i	$-0.936971\pi$
$491$	−28.8133	+	16.6354i	−1.30033	+	0.750744i	−0.319867	+	0.947463i	$0.603638\pi$
$492$		0			0
$493$			1.63562i			0.0736645i
$494$	2.78685	−	1.60899i	0.125386	−	0.0723919i
$495$		0			0
$496$		−	6.10001i		−	0.273898i
$497$	−20.7048	−	0.821683i	−0.928739	−	0.0368575i
$498$		0			0
$499$	−34.3513			−1.53778			−0.768888	−	0.639384i	$-0.779190\pi$
$499$	−34.3513			−1.53778			−0.768888	+	0.639384i	$0.779190\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	19.7713	−	11.4150i	0.882438	−	0.509476i
$503$	−29.6702			−1.32293			−0.661465	−	0.749976i	$-0.730065\pi$
$503$	−29.6702			−1.32293			−0.661465	+	0.749976i	$0.730065\pi$
$504$		0			0
$505$	0.196980			0.00876548
$506$	−35.5651	+	20.5335i	−1.58106	+	0.912826i
$507$		0			0
$508$	6.34536	−	10.9905i	0.281530	−	0.487624i
$509$	−33.5110			−1.48535			−0.742674	−	0.669653i	$-0.766443\pi$
$509$	−33.5110			−1.48535			−0.742674	+	0.669653i	$0.766443\pi$
$510$		0			0
$511$	−15.3104	−	29.1282i	−0.677292	−	1.28855i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	15.3563	−	8.86599i	0.677339	−	0.391062i
$515$			6.81626i			0.300360i
$516$		0			0
$517$	−44.3490	+	25.6049i	−1.95047	+	1.12610i
$518$	−23.9817	−	0.951725i	−1.05369	−	0.0418164i
$519$		0			0
$520$	−2.23373	−	3.86893i	−0.0979555	−	0.169664i
$521$	9.49346	+	16.4432i	0.415916	+	0.720388i	0.995524	−	0.0945075i	$-0.0301276\pi$
$521$	9.49346	+	16.4432i	0.415916	+	0.720388i	−0.579608	+	0.814895i	$0.696794\pi$
$522$		0			0
$523$	−24.1869	−	13.9643i	−1.05762	−	0.610617i	−0.132847	−	0.991137i	$-0.542412\pi$
$523$	−24.1869	−	13.9643i	−1.05762	−	0.610617i	−0.924773	+	0.380519i	$0.875745\pi$
$524$	4.34813	−	7.53119i	0.189949	−	0.329001i
$525$		0			0
$526$	3.74152	+	6.48050i	0.163138	+	0.282563i
$527$		−	13.6302i		−	0.593740i
$528$		0			0
$529$	−22.1195			−0.961716
$530$	−0.111973	+	0.193943i	−0.00486380	+	0.00842435i
$531$		0			0
$532$	0.886691	+	1.68694i	0.0384429	+	0.0731381i
$533$	−5.52446	−	3.18955i	−0.239291	−	0.138155i
$534$		0			0
$535$	4.67098	+	2.69679i	0.201944	+	0.116592i
$536$	11.3296	+	6.54114i	0.489364	+	0.282534i
$537$		0			0
$538$	−6.21025	−	3.58549i	−0.267743	−	0.154581i
$539$	3.39147	−	42.6620i	0.146081	−	1.83758i
$540$		0			0
$541$	−4.46304	+	7.73021i	−0.191881	+	0.332348i	−0.945874	−	0.324535i	$-0.894792\pi$
$541$	−4.46304	+	7.73021i	−0.191881	+	0.332348i	0.753993	+	0.656883i	$0.228125\pi$
$542$	18.9899			0.815684
$543$		0			0
$544$		−	2.23445i		−	0.0958014i
$545$	−6.74410	−	11.6811i	−0.288885	−	0.500364i
$546$		0			0
$547$	7.61080	−	13.1823i	0.325414	−	0.563634i	−0.656182	−	0.754603i	$-0.727830\pi$
$547$	7.61080	−	13.1823i	0.325414	−	0.563634i	0.981596	+	0.190969i	$0.0611629\pi$
$548$	−17.7308	−	10.2369i	−0.757421	−	0.437297i
$549$		0			0
$550$	−3.05690	−	5.29471i	−0.130347	−	0.225767i
$551$	0.263635	+	0.456629i	0.0112312	+	0.0194531i
$552$		0			0
$553$	−35.1244	+	18.4621i	−1.49364	+	0.785090i
$554$	7.46104	−	4.30763i	0.316989	−	0.183014i
$555$		0			0
$556$		−	1.68428i		−	0.0714294i
$557$	26.7294	−	15.4322i	1.13256	−	0.653884i	0.187983	−	0.982172i	$-0.439805\pi$
$557$	26.7294	−	15.4322i	1.13256	−	0.653884i	0.944578	+	0.328288i	$0.106472\pi$
$558$		0			0
$559$		−	11.0681i		−	0.468131i
$560$	2.34194	−	1.23098i	0.0989652	−	0.0520182i
$561$		0			0
$562$	−21.9686			−0.926689
$563$	−11.1561	+	19.3230i	−0.470174	+	0.814366i	−0.999418	−	0.0341041i	$-0.989142\pi$
$563$	−11.1561	+	19.3230i	−0.470174	+	0.814366i	0.529244	+	0.848470i	$0.322476\pi$
$564$		0			0
$565$	−16.3111	+	9.41722i	−0.686213	+	0.396185i
$566$	16.0739			0.675638
$567$		0			0
$568$	7.83185			0.328617
$569$	−33.2913	+	19.2208i	−1.39564	+	0.805776i	−0.993933	−	0.109990i	$-0.964918\pi$
$569$	−33.2913	+	19.2208i	−1.39564	+	0.805776i	−0.401712	+	0.915766i	$0.631585\pi$
$570$		0			0
$571$	−0.734675	+	1.27250i	−0.0307452	+	0.0532523i	−0.880989	−	0.473137i	$-0.843121\pi$
$571$	−0.734675	+	1.27250i	−0.0307452	+	0.0532523i	0.850243	+	0.526390i	$0.176455\pi$
$572$	27.3131			1.14202
$573$		0			0
$574$	2.01719	−	3.19426i	0.0841959	−	0.133326i
$575$		−	6.71710i		−	0.280123i
$576$		0			0
$577$	−19.6517	+	11.3459i	−0.818112	+	0.472337i	−0.849765	−	0.527162i	$-0.823256\pi$
$577$	−19.6517	+	11.3459i	−0.818112	+	0.472337i	0.0316532	+	0.999499i	$0.489923\pi$
$578$			12.0072i			0.499434i
$579$		0			0
$580$	0.633929	−	0.365999i	0.0263225	−	0.0151973i
$581$	8.72956	+	5.51276i	0.362163	+	0.228708i
$582$		0			0
$583$	−0.684581	−	1.18573i	−0.0283525	−	0.0491079i
$584$	6.21880	+	10.7713i	0.257336	+	0.445719i
$585$		0			0
$586$	−17.4522	−	10.0760i	−0.720945	−	0.416238i
$587$	21.7046	−	37.5934i	0.895843	−	1.55165i	0.0630853	−	0.998008i	$-0.479906\pi$
$587$	21.7046	−	37.5934i	0.895843	−	1.55165i	0.832758	−	0.553638i	$-0.186761\pi$
$588$		0			0
$589$	−2.19697	−	3.80526i	−0.0905244	−	0.156793i
$590$		−	9.76212i		−	0.401900i
$591$		0			0
$592$	9.07135			0.372830
$593$	−4.44261	+	7.69482i	−0.182436	+	0.315988i	−0.942710	−	0.333615i	$-0.891732\pi$
$593$	−4.44261	+	7.69482i	−0.182436	+	0.315988i	0.760274	+	0.649603i	$0.225065\pi$
$594$		0			0
$595$	5.23297	−	2.75056i	0.214531	−	0.112762i
$596$	−4.95680	−	2.86181i	−0.203038	−	0.117224i
$597$		0			0
$598$	25.9880	+	15.0042i	1.06273	+	0.613567i
$599$	31.1268	+	17.9711i	1.27181	+	0.734278i	0.975328	−	0.220761i	$-0.0708542\pi$
$599$	31.1268	+	17.9711i	1.27181	+	0.734278i	0.296479	+	0.955039i	$0.404187\pi$
$600$		0			0
$601$	18.2810	+	10.5545i	0.745696	+	0.430528i	0.824137	−	0.566391i	$-0.191661\pi$
$601$	18.2810	+	10.5545i	0.745696	+	0.430528i	−0.0784408	+	0.996919i	$0.524994\pi$
$602$	6.54968	+	0.259928i	0.266945	+	0.0105939i
$603$		0			0
$604$	−3.49265	+	6.04945i	−0.142114	+	0.246149i
$605$	26.3785			1.07244
$606$		0			0
$607$			32.5181i			1.31987i	0.751323	+	0.659935i	$0.229416\pi$
$607$			32.5181i			1.31987i	−0.751323	+	0.659935i	$0.770584\pi$
$608$	−0.360158	−	0.623812i	−0.0146063	−	0.0252989i
$609$		0			0
$610$	−0.919547	+	1.59270i	−0.0372314	+	0.0644866i
$611$	32.4066	+	18.7099i	1.31103	+	0.756923i
$612$		0			0
$613$	−15.2816	−	26.4686i	−0.617219	−	1.06905i	−0.989991	−	0.141132i	$-0.954926\pi$
$613$	−15.2816	−	26.4686i	−0.617219	−	1.06905i	0.372772	−	0.927923i	$-0.378407\pi$
$614$	−4.59205	−	7.95367i	−0.185320	−	0.320984i
$615$		0			0
$616$	−0.641432	+	16.1629i	−0.0258441	+	0.651221i
$617$	−12.0852	+	6.97739i	−0.486531	+	0.280899i	−0.723134	−	0.690707i	$-0.757299\pi$
$617$	−12.0852	+	6.97739i	−0.486531	+	0.280899i	0.236603	+	0.971606i	$0.423966\pi$
$618$		0			0
$619$			6.29052i			0.252837i	0.991977	+	0.126419i	$0.0403483\pi$
$619$			6.29052i			0.252837i	−0.991977	+	0.126419i	$0.959652\pi$
$620$	−5.28276	+	3.05000i	−0.212161	+	0.122491i
$621$		0			0
$622$		−	8.88370i		−	0.356204i
$623$	−26.1275	−	16.4997i	−1.04678	−	0.661046i
$624$		0			0
$625$	1.00000			0.0400000
$626$	11.7671	−	20.3812i	0.470308	−	0.814598i
$627$		0			0
$628$	15.4710	−	8.93219i	0.617361	−	0.356433i
$629$	20.2695			0.808198
$630$		0			0
$631$	−31.2195			−1.24283			−0.621415	−	0.783481i	$-0.713442\pi$
$631$	−31.2195			−1.24283			−0.621415	+	0.783481i	$0.713442\pi$
$632$	12.9886	−	7.49899i	0.516660	−	0.298294i
$633$		0			0
$634$	5.42725	−	9.40027i	0.215544	−	0.373332i
$635$	−12.6907			−0.503616
$636$		0			0
$637$	−28.2364	+	13.4407i	−1.11877	+	0.532541i
$638$			4.47529i			0.177179i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$			19.1446i			0.756167i	0.925771	+	0.378084i	$0.123417\pi$
$641$			19.1446i			0.756167i	−0.925771	+	0.378084i	$0.876583\pi$
$642$		0			0
$643$	18.7635	−	10.8331i	0.739961	−	0.427217i	−0.0820940	−	0.996625i	$-0.526161\pi$
$643$	18.7635	−	10.8331i	0.739961	−	0.427217i	0.822055	+	0.569408i	$0.192827\pi$
$644$	−9.48922	+	15.0263i	−0.373927	+	0.592121i
$645$		0			0
$646$	−0.804757	−	1.39388i	−0.0316627	−	0.0548414i
$647$	9.80085	+	16.9756i	0.385311	+	0.667379i	0.991812	−	0.127704i	$-0.0407608\pi$
$647$	9.80085	+	16.9756i	0.385311	+	0.667379i	−0.606501	+	0.795083i	$0.707427\pi$
$648$		0			0
$649$	51.6876	+	29.8418i	2.02891	+	1.17139i
$650$	−2.23373	+	3.86893i	−0.0876140	+	0.151752i
$651$		0			0
$652$	4.05646	+	7.02600i	0.158863	+	0.275159i
$653$		−	10.1644i		−	0.397763i	−0.980024	−	0.198881i	$-0.936269\pi$
$653$		−	10.1644i		−	0.397763i	0.980024	−	0.198881i	$-0.0637308\pi$
$654$		0			0
$655$	−8.69627			−0.339791
$656$	−0.713952	+	1.23660i	−0.0278751	+	0.0482811i
$657$		0			0
$658$	−11.8329	+	18.7376i	−0.461294	+	0.730467i
$659$	6.03415	+	3.48382i	0.235057	+	0.135710i	0.612903	−	0.790158i	$-0.290002\pi$
$659$	6.03415	+	3.48382i	0.235057	+	0.135710i	−0.377846	+	0.925869i	$0.623335\pi$
$660$		0			0
$661$	32.7721	+	18.9210i	1.27469	+	0.735941i	0.975866	−	0.218368i	$-0.0700733\pi$
$661$	32.7721	+	18.9210i	1.27469	+	0.735941i	0.298821	+	0.954309i	$0.403407\pi$
$662$	4.21769	+	2.43508i	0.163925	+	0.0946422i
$663$		0			0
$664$	−3.37949	−	1.95115i	−0.131150	−	0.0757193i
$665$	1.01759	−	1.61137i	0.0394603	−	0.0624861i
$666$		0			0
$667$	−2.45846	+	4.25817i	−0.0951918	+	0.164877i
$668$	−2.59896			−0.100557
$669$		0			0
$670$		−	13.0823i		−	0.505413i
$671$	−5.62193	−	9.73746i	−0.217032	−	0.375911i
$672$		0			0
$673$	−14.5047	+	25.1229i	−0.559115	+	0.968415i	0.438456	+	0.898753i	$0.355526\pi$
$673$	−14.5047	+	25.1229i	−0.559115	+	0.968415i	−0.997571	+	0.0696623i	$0.977808\pi$
$674$	18.4133	+	10.6309i	0.709253	+	0.409487i
$675$		0			0
$676$	−3.47909	−	6.02595i	−0.133811	−	0.231767i
$677$	20.8785	+	36.1626i	0.802426	+	1.38984i	0.918015	+	0.396545i	$0.129791\pi$
$677$	20.8785	+	36.1626i	0.802426	+	1.38984i	−0.115589	+	0.993297i	$0.536876\pi$
$678$		0			0
$679$	17.9024	−	28.3488i	0.687033	−	1.08793i
$680$	−1.93509	+	1.11723i	−0.0742075	+	0.0428437i
$681$		0			0
$682$		−	37.2942i		−	1.42807i
$683$	11.7954	−	6.81007i	0.451338	−	0.260580i	−0.257057	−	0.966396i	$-0.582753\pi$
$683$	11.7954	−	6.81007i	0.451338	−	0.260580i	0.708395	+	0.705816i	$0.249420\pi$
$684$		0			0
$685$			20.4737i			0.782261i
$686$	−7.29060	−	17.0249i	−0.278356	−	0.650014i
$687$		0			0
$688$	−2.47750			−0.0944537
$689$	−0.500235	+	0.866433i	−0.0190574	+	0.0330085i
$690$		0			0
$691$	−3.99544	+	2.30677i	−0.151994	+	0.0877537i	−0.574068	−	0.818808i	$-0.694636\pi$
$691$	−3.99544	+	2.30677i	−0.151994	+	0.0877537i	0.422074	+	0.906561i	$0.361302\pi$
$692$	−14.1634			−0.538412
$693$		0			0
$694$	0.648240			0.0246069
$695$	−1.45863	+	0.842140i	−0.0553290	+	0.0319442i
$696$		0			0
$697$	−1.59529	+	2.76313i	−0.0604260	+	0.104661i
$698$	−13.2126			−0.500104
$699$		0			0
$700$	−2.23703	−	1.41269i	−0.0845517	−	0.0533948i
$701$		−	13.6110i		−	0.514081i	−0.966401	−	0.257040i	$-0.917253\pi$
$701$		−	13.6110i		−	0.514081i	0.966401	−	0.257040i	$-0.0827474\pi$
$702$		0			0
$703$	5.65881	−	3.26712i	0.213426	−	0.123222i
$704$		−	6.11380i		−	0.230422i
$705$		0			0
$706$	−13.7921	+	7.96285i	−0.519071	+	0.299686i
$707$	−0.0206662	+	0.520749i	−0.000777233	+	0.0195848i
$708$		0			0
$709$	−5.71967	−	9.90676i	−0.214807	−	0.372056i	0.738406	−	0.674356i	$-0.235579\pi$
$709$	−5.71967	−	9.90676i	−0.214807	−	0.372056i	−0.953213	+	0.302300i	$0.902246\pi$
$710$	−3.91593	−	6.78258i	−0.146962	−	0.254546i
$711$		0			0
$712$	10.1148	+	5.83979i	0.379069	+	0.218855i
$713$	20.4872	−	35.4849i	0.767251	−	1.32892i
$714$		0			0
$715$	−13.6566	−	23.6539i	−0.510727	−	0.884605i
$716$		−	18.3202i		−	0.684660i
$717$		0			0
$718$	−15.0988			−0.563483
$719$	−15.0806	+	26.1204i	−0.562412	+	0.974126i	0.434873	+	0.900492i	$0.356793\pi$
$719$	−15.0806	+	26.1204i	−0.562412	+	0.974126i	−0.997285	+	0.0736344i	$0.976540\pi$
$720$		0			0
$721$	−18.0199	−	0.715131i	−0.671098	−	0.0266329i
$722$	16.0051	+	9.24057i	0.595650	+	0.343898i
$723$		0			0
$724$	−0.464334	−	0.268083i	−0.0172568	−	0.00996323i
$725$	−0.633929	−	0.365999i	−0.0235435	−	0.0135929i
$726$		0			0
$727$	33.9927	+	19.6257i	1.26072	+	0.727878i	0.973214	−	0.229901i	$-0.0738401\pi$
$727$	33.9927	+	19.6257i	1.26072	+	0.727878i	0.287507	+	0.957778i	$0.407173\pi$
$728$	10.4625	−	5.49933i	0.387767	−	0.203819i
$729$		0			0
$730$	6.21880	−	10.7713i	0.230168	−	0.398663i
$731$	−5.53585			−0.204751
$732$		0			0
$733$		−	45.6277i		−	1.68530i	−0.538463	−	0.842649i	$-0.680995\pi$
$733$		−	45.6277i		−	1.68530i	0.538463	−	0.842649i	$-0.319005\pi$
$734$	−6.38539	−	11.0598i	−0.235689	−	0.408226i
$735$		0			0
$736$	3.35855	−	5.81718i	0.123798	−	0.214424i
$737$	69.2668	+	39.9912i	2.55148	+	1.47310i
$738$		0			0
$739$	−0.454714	−	0.787588i	−0.0167269	−	0.0289719i	0.857541	−	0.514416i	$-0.171991\pi$
$739$	−0.454714	−	0.787588i	−0.0167269	−	0.0289719i	−0.874268	+	0.485444i	$0.838658\pi$
$740$	−4.53567	−	7.85602i	−0.166735	−	0.288793i
$741$		0			0
$742$	−0.500974	−	0.316368i	−0.0183913	−	0.0116142i
$743$	14.2357	−	8.21897i	0.522256	−	0.301525i	−0.215601	−	0.976482i	$-0.569171\pi$
$743$	14.2357	−	8.21897i	0.522256	−	0.301525i	0.737857	+	0.674957i	$0.235838\pi$
$744$		0			0
$745$			5.72362i			0.209697i
$746$	−7.19146	+	4.15199i	−0.263298	+	0.152015i
$747$		0			0
$748$		−	13.6610i		−	0.499496i
$749$	−7.61948	+	12.0656i	−0.278410	+	0.440867i
$750$		0			0
$751$	4.45127			0.162429			0.0812146	−	0.996697i	$-0.474120\pi$
$751$	4.45127			0.162429			0.0812146	+	0.996697i	$0.474120\pi$
$752$	4.18805	−	7.25392i	0.152723	−	0.264523i
$753$		0			0
$754$	2.83205	−	1.63509i	0.103137	−	0.0595463i
$755$	6.98531			0.254221
$756$		0			0
$757$	24.4655			0.889213			0.444606	−	0.895726i	$-0.353344\pi$
$757$	24.4655			0.889213			0.444606	+	0.895726i	$0.353344\pi$
$758$	6.53819	−	3.77483i	0.237478	−	0.137108i
$759$		0			0
$760$	−0.360158	+	0.623812i	−0.0130643	+	0.0226280i
$761$	20.0231			0.725836			0.362918	−	0.931821i	$-0.381780\pi$
$761$	20.0231			0.725836			0.362918	+	0.931821i	$0.381780\pi$
$762$		0			0
$763$	31.5886	−	16.6036i	1.14358	−	0.601092i
$764$		−	4.66977i		−	0.168946i
$765$		0			0
$766$	9.38741	−	5.41982i	0.339181	−	0.195826i
$767$		−	43.6119i		−	1.57473i
$768$		0			0
$769$	−26.6527	+	15.3880i	−0.961122	+	0.554904i	−0.896518	−	0.443007i	$-0.853912\pi$
$769$	−26.6527	+	15.3880i	−0.961122	+	0.554904i	−0.0646039	+	0.997911i	$0.520578\pi$
$770$	14.3182	−	7.52594i	0.515991	−	0.271216i
$771$		0			0
$772$	−9.89647	−	17.1412i	−0.356182	−	0.616925i
$773$	−7.03900	−	12.1919i	−0.253175	−	0.438512i	0.711223	−	0.702966i	$-0.248142\pi$
$773$	−7.03900	−	12.1919i	−0.253175	−	0.438512i	−0.964398	+	0.264454i	$0.914808\pi$
$774$		0			0
$775$	5.28276	+	3.05000i	0.189762	+	0.109559i
$776$	−6.33628	+	10.9748i	−0.227459	+	0.393971i
$777$		0			0
$778$	−9.43543	−	16.3426i	−0.338276	−	0.585912i
$779$			1.02854i			0.0368513i
$780$		0			0
$781$	47.8824			1.71337
$782$	7.50453	−	12.9982i	0.268361	−	0.464816i
$783$		0			0
$784$	3.00859	+	6.32047i	0.107450	+	0.225731i
$785$	−15.4710	−	8.93219i	−0.552184	−	0.318804i
$786$		0			0
$787$	38.2737	+	22.0973i	1.36431	+	0.787685i	0.990194	−	0.139697i	$-0.0446130\pi$
$787$	38.2737	+	22.0973i	1.36431	+	0.787685i	0.374116	+	0.927382i	$0.377946\pi$
$788$	13.9834	+	8.07331i	0.498137	+	0.287600i
$789$		0			0
$790$	−12.9886	−	7.49899i	−0.462115	−	0.266802i
$791$	−23.1847	−	44.1092i	−0.824354	−	1.56834i
$792$		0			0
$793$	−4.10804	+	7.11533i	−0.145881	+	0.252673i
$794$	−24.0560			−0.853715
$795$		0			0
$796$		−	0.762155i		−	0.0270139i
$797$	18.7299	+	32.4411i	0.663446	+	1.14912i	0.979704	+	0.200449i	$0.0642400\pi$
$797$	18.7299	+	32.4411i	0.663446	+	1.14912i	−0.316259	+	0.948673i	$0.602427\pi$
$798$		0			0
$799$	9.35801	−	16.2086i	0.331063	−	0.573417i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	9.73930	+	16.8690i	0.343907	+	0.595664i
$803$	38.0205	+	65.8535i	1.34172	+	2.32392i
$804$		0			0
$805$	17.7578	+	0.704728i	0.625880	+	0.0248384i
$806$	−23.6005	+	13.6258i	−0.831293	+	0.479947i
$807$		0			0
$808$		−	0.196980i		−	0.00692972i
$809$	−11.6506	+	6.72649i	−0.409614	+	0.236491i	−0.690624	−	0.723214i	$-0.742664\pi$
$809$	−11.6506	+	6.72649i	−0.409614	+	0.236491i	0.281010	+	0.959705i	$0.409331\pi$
$810$		0			0
$811$		−	7.87677i		−	0.276591i	−0.990391	−	0.138295i	$-0.955838\pi$
$811$		−	7.87677i		−	0.276591i	0.990391	−	0.138295i	$-0.0441623\pi$
$812$	0.901073	+	1.71430i	0.0316214	+	0.0601601i
$813$		0			0
$814$	55.4604			1.94389
$815$	4.05646	−	7.02600i	0.142092	−	0.246110i
$816$		0			0
$817$	−1.54549	+	0.892290i	−0.0540699	+	0.0312173i
$818$	−28.6426			−1.00146
$819$		0			0
$820$	1.42790			0.0498646
$821$	−20.0805	+	11.5935i	−0.700814	+	0.404615i	−0.807650	−	0.589662i	$-0.799261\pi$
$821$	−20.0805	+	11.5935i	−0.700814	+	0.404615i	0.106837	+	0.994277i	$0.465928\pi$
$822$		0			0
$823$	−7.46576	+	12.9311i	−0.260240	+	0.450749i	−0.966306	−	0.257398i	$-0.917135\pi$
$823$	−7.46576	+	12.9311i	−0.260240	+	0.450749i	0.706066	+	0.708146i	$0.250468\pi$
$824$	6.81626			0.237456
$825$		0			0
$826$	25.8078	+	1.02420i	0.897969	+	0.0356364i
$827$			20.3605i			0.708004i	0.935245	+	0.354002i	$0.115179\pi$
$827$			20.3605i			0.708004i	−0.935245	+	0.354002i	$0.884821\pi$
$828$		0			0
$829$	−26.4740	+	15.2848i	−0.919482	+	0.530863i	−0.883470	−	0.468488i	$-0.844799\pi$
$829$	−26.4740	+	15.2848i	−0.919482	+	0.530863i	−0.0360120	+	0.999351i	$0.511465\pi$
$830$			3.90230i			0.135451i
$831$		0			0
$832$	−3.86893	+	2.23373i	−0.134131	+	0.0774406i
$833$	6.72255	+	14.1228i	0.232923	+	0.489326i
$834$		0			0
$835$	1.29948	+	2.25076i	0.0449703	+	0.0778909i
$836$	−2.20193	−	3.81386i	−0.0761555	−	0.131905i
$837$		0			0
$838$	23.0686	+	13.3187i	0.796891	+	0.460085i
$839$	7.60897	−	13.1791i	0.262691	−	0.454994i	−0.704265	−	0.709937i	$-0.748723\pi$
$839$	7.60897	−	13.1791i	0.262691	−	0.454994i	0.966956	+	0.254943i	$0.0820568\pi$
$840$		0			0
$841$	−14.2321	−	24.6507i	−0.490762	−	0.850024i
$842$		−	13.7066i		−	0.472359i
$843$		0			0
$844$	11.6843			0.402189
$845$	−3.47909	+	6.02595i	−0.119684	+	0.207299i
$846$		0			0
$847$	−2.76752	+	69.7362i	−0.0950931	+	2.39616i
$848$	0.193943	+	0.111973i	0.00666004	+	0.00384517i
$849$		0			0
$850$	1.93509	+	1.11723i	0.0663732	+	0.0383206i
$851$	52.7697	+	30.4666i	1.80892	+	1.04438i
$852$		0			0
$853$	2.19189	+	1.26549i	0.0750488	+	0.0433294i	0.537055	−	0.843547i	$-0.319537\pi$
$853$	2.19189	+	1.26549i	0.0750488	+	0.0433294i	−0.462006	+	0.886877i	$0.652870\pi$
$854$	−4.11410	−	2.59808i	−0.140782	−	0.0889044i
$855$		0			0
$856$	2.69679	−	4.67098i	0.0921744	−	0.159651i
$857$	1.76354			0.0602412			0.0301206	−	0.999546i	$-0.490411\pi$
$857$	1.76354			0.0602412			0.0301206	+	0.999546i	$0.490411\pi$
$858$		0			0
$859$		−	30.7125i		−	1.04790i	−0.851749	−	0.523949i	$-0.824458\pi$
$859$		−	30.7125i		−	1.04790i	0.851749	−	0.523949i	$-0.175542\pi$
$860$	1.23875	+	2.14558i	0.0422410	+	0.0731635i
$861$		0			0
$862$	13.2257	−	22.9075i	0.450468	−	0.780233i
$863$	−36.6863	−	21.1809i	−1.24882	−	0.721005i	−0.277943	−	0.960598i	$-0.589653\pi$
$863$	−36.6863	−	21.1809i	−1.24882	−	0.721005i	−0.970873	+	0.239593i	$0.922986\pi$
$864$		0			0
$865$	7.08170	+	12.2659i	0.240785	+	0.417052i
$866$	3.17349	+	5.49664i	0.107839	+	0.186783i
$867$		0			0
$868$	−7.50896	−	14.2859i	−0.254871	−	0.484894i
$869$	79.4099	−	45.8473i	2.69380	−	1.55526i
$870$		0			0
$871$		−	58.4445i		−	1.98032i
$872$	−11.6811	+	6.74410i	−0.395573	+	0.228384i
$873$		0			0
$874$		−	4.83844i		−	0.163663i
$875$	−0.104916	+	2.64367i	−0.00354679	+	0.0893724i
$876$		0			0
$877$	28.7641			0.971296			0.485648	−	0.874154i	$-0.338584\pi$
$877$	28.7641			0.971296			0.485648	+	0.874154i	$0.338584\pi$
$878$	−7.90756	+	13.6963i	−0.266867	+	0.462228i
$879$		0			0
$880$	−5.29471	+	3.05690i	−0.178484	+	0.103048i
$881$	−0.505687			−0.0170370			−0.00851852	−	0.999964i	$-0.502712\pi$
$881$	−0.505687			−0.0170370			−0.00851852	+	0.999964i	$0.502712\pi$
$882$		0			0
$883$	30.2642			1.01847			0.509235	−	0.860627i	$-0.329928\pi$
$883$	30.2642			1.01847			0.509235	+	0.860627i	$0.329928\pi$
$884$	−8.64495	+	4.99116i	−0.290761	+	0.167871i
$885$		0			0
$886$	−1.14765	+	1.98778i	−0.0385559	+	0.0667808i
$887$	−41.9418			−1.40827			−0.704134	−	0.710068i	$-0.748664\pi$
$887$	−41.9418			−1.40827			−0.704134	+	0.710068i	$0.748664\pi$
$888$		0			0
$889$	1.33145	−	33.5501i	0.0446555	−	1.12523i
$890$		−	11.6796i		−	0.391500i
$891$		0			0
$892$	−6.37774	+	3.68219i	−0.213542	+	0.123289i
$893$		−	6.03344i		−	0.201901i
$894$		0			0
$895$	−15.8658	+	9.16012i	−0.530335	+	0.306189i
$896$	−1.23098	−	2.34194i	−0.0411240	−	0.0782388i
$897$		0			0
$898$	0.717621	+	1.24296i	0.0239473	+	0.0414780i
$899$	−2.23260	−	3.86698i	−0.0744613	−	0.128971i
$900$		0			0
$901$	0.433357	+	0.250199i	0.0144372	+	0.00833533i
$902$	−4.36496	+	7.56033i	−0.145337	+	0.251731i
$903$		0			0
$904$	9.41722	+	16.3111i	0.313212	+	0.542499i
$905$			0.536166i			0.0178228i
$906$		0			0
$907$	56.4502			1.87440			0.937199	−	0.348795i	$-0.113409\pi$
$907$	56.4502			1.87440			0.937199	+	0.348795i	$0.113409\pi$
$908$	−6.94100	+	12.0222i	−0.230345	+	0.398970i
$909$		0			0
$910$	−9.99383	−	6.31115i	−0.331292	−	0.209213i
$911$	7.58916	+	4.38160i	0.251440	+	0.145169i	0.620424	−	0.784267i	$-0.286961\pi$
$911$	7.58916	+	4.38160i	0.251440	+	0.145169i	−0.368983	+	0.929436i	$0.620294\pi$
$912$		0			0
$913$	−20.6615	−	11.9289i	−0.683797	−	0.394790i
$914$	−30.1838	−	17.4266i	−0.998392	−	0.576422i
$915$		0			0
$916$	14.2046	+	8.20102i	0.469333	+	0.270969i
$917$	0.912373	−	22.9901i	0.0301292	−	0.759199i
$918$		0			0
$919$	−1.64091	+	2.84214i	−0.0541287	+	0.0937536i	−0.891820	−	0.452390i	$-0.850571\pi$
$919$	−1.64091	+	2.84214i	−0.0541287	+	0.0937536i	0.837691	+	0.546144i	$0.183905\pi$
$920$	−6.71710			−0.221456
$921$		0			0
$922$		−	16.8252i		−	0.554108i
$923$	−17.4942	−	30.3009i	−0.575830	−	0.997366i
$924$		0			0
$925$	−4.53567	+	7.85602i	−0.149132	+	0.258304i
$926$	6.30627	+	3.64092i	0.207237	+	0.119648i
$927$		0			0
$928$	−0.365999	−	0.633929i	−0.0120145	−	0.0208098i
$929$	30.0905	+	52.1182i	0.987236	+	1.70994i	0.631546	+	0.775339i	$0.282421\pi$
$929$	30.0905	+	52.1182i	0.987236	+	1.70994i	0.355690	+	0.934604i	$0.384246\pi$
$930$		0			0
$931$	4.15316	+	2.85922i	0.136114	+	0.0937072i
$932$	11.5552	−	6.67137i	0.378502	−	0.218528i
$933$		0			0
$934$			31.1361i			1.01881i
$935$	−11.8308	+	6.83050i	−0.386908	+	0.223381i
$936$		0			0
$937$			6.30376i			0.205935i	0.994685	+	0.102967i	$0.0328337\pi$
$937$			6.30376i			0.205935i	−0.994685	+	0.102967i	$0.967166\pi$
$938$	34.5852	+	1.37253i	1.12925	+	0.0448148i
$939$		0			0
$940$	−8.37611			−0.273198
$941$	−12.9299	+	22.3953i	−0.421503	+	0.730065i	−0.996087	−	0.0883810i	$-0.971831\pi$
$941$	−12.9299	+	22.3953i	−0.421503	+	0.730065i	0.574584	+	0.818446i	$0.305164\pi$
$942$		0			0
$943$	−8.30637	+	4.79569i	−0.270493	+	0.156169i
$944$	−9.76212			−0.317730
$945$		0			0
$946$	−15.1469			−0.492469
$947$	32.6775	−	18.8663i	1.06187	−	0.613074i	0.135924	−	0.990719i	$-0.456600\pi$
$947$	32.6775	−	18.8663i	1.06187	−	0.613074i	0.925950	+	0.377646i	$0.123266\pi$
$948$		0			0
$949$	27.7822	−	48.1203i	0.901850	−	1.56205i
$950$	0.720316			0.0233701
$951$		0			0
$952$	−2.75056	−	5.23297i	−0.0891461	−	0.169601i
$953$			19.5292i			0.632613i	0.948657	+	0.316306i	$0.102443\pi$
$953$			19.5292i			0.632613i	−0.948657	+	0.316306i	$0.897557\pi$
$954$		0			0
$955$	−4.04414	+	2.33488i	−0.130865	+	0.0755550i
$956$		−	6.23934i		−	0.201795i
$957$		0			0
$958$	−26.8737	+	15.5155i	−0.868249	+	0.501284i
$959$	−54.1258	−	2.14801i	−1.74781	−	0.0693629i
$960$		0			0
$961$	3.10505	+	5.37811i	0.100163	+	0.173487i
$962$	−20.2629	−	35.0964i	−0.653303	−	1.13155i
$963$		0			0
$964$	2.18891	+	1.26377i	0.0705002	+	0.0407033i
$965$	−9.89647	+	17.1412i	−0.318579	+	0.551794i
$966$		0			0
$967$	−17.7544	−	30.7515i	−0.570943	−	0.988902i	−0.996469	−	0.0839557i	$-0.973245\pi$
$967$	−17.7544	−	30.7515i	−0.570943	−	0.988902i	0.425527	−	0.904946i	$-0.360089\pi$
$968$		−	26.3785i		−	0.847839i
$969$		0			0
$970$	12.6726			0.406891
$971$	16.8585	−	29.1998i	0.541016	−	0.937067i	−0.457830	−	0.889040i	$-0.651373\pi$
$971$	16.8585	−	29.1998i	0.541016	−	0.937067i	0.998846	−	0.0480271i	$-0.0152934\pi$
$972$		0			0
$973$	−2.07331	−	3.94449i	−0.0664672	−	0.126455i
$974$	37.1994	+	21.4771i	1.19195	+	0.688171i
$975$		0			0
$976$	1.59270	+	0.919547i	0.0509812	+	0.0294340i
$977$	7.04757	+	4.06891i	0.225472	+	0.130176i	0.608481	−	0.793568i	$-0.291779\pi$
$977$	7.04757	+	4.06891i	0.225472	+	0.130176i	−0.383010	+	0.923744i	$0.625112\pi$
$978$		0			0
$979$	61.8399	+	35.7033i	1.97641	+	1.14108i
$980$	3.96940	−	5.76575i	0.126798	−	0.184180i
$981$		0			0
$982$	16.6354	−	28.8133i	0.530856	−	0.919470i
$983$	−44.5437			−1.42072			−0.710362	−	0.703836i	$-0.751469\pi$
$983$	−44.5437			−1.42072			−0.710362	+	0.703836i	$0.751469\pi$
$984$		0			0
$985$		−	16.1466i		−	0.514474i
$986$	−0.817809	−	1.41649i	−0.0260443	−	0.0451101i
$987$		0			0
$988$	−1.60899	+	2.78685i	−0.0511888	+	0.0886616i
$989$	−14.4120	−	8.32080i	−0.458276	−	0.264586i
$990$		0			0
$991$	−30.3539	−	52.5745i	−0.964223	−	1.67008i	−0.711688	−	0.702496i	$-0.752069\pi$
$991$	−30.3539	−	52.5745i	−0.964223	−	1.67008i	−0.252535	−	0.967588i	$-0.581264\pi$
$992$	3.05000	+	5.28276i	0.0968377	+	0.167728i
$993$		0			0
$994$	18.3418	−	9.64082i	0.581765	−	0.305788i
$995$	−0.660045	+	0.381077i	−0.0209248	+	0.0120810i
$996$		0			0
$997$			17.7082i			0.560825i	0.959880	+	0.280412i	$0.0904712\pi$
$997$			17.7082i			0.560825i	−0.959880	+	0.280412i	$0.909529\pi$
$998$	29.7491	−	17.1757i	0.941692	−	0.543686i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.c.1601.1		32
3.2	odd	2		630.2.t.c.551.11	yes	32
7.3	odd	6		1890.2.bk.c.521.1		32
9.4	even	3		630.2.bk.c.131.1	yes	32
9.5	odd	6		1890.2.bk.c.341.1		32
21.17	even	6		630.2.bk.c.101.9	yes	32
63.31	odd	6		630.2.t.c.311.11	✓	32
63.59	even	6	inner	1890.2.t.c.1151.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.11	✓	32	63.31	odd	6
630.2.t.c.551.11	yes	32	3.2	odd	2
630.2.bk.c.101.9	yes	32	21.17	even	6
630.2.bk.c.131.1	yes	32	9.4	even	3
1890.2.t.c.1151.1		32	63.59	even	6	inner
1890.2.t.c.1601.1		32	1.1	even	1	trivial
1890.2.bk.c.341.1		32	9.5	odd	6
1890.2.bk.c.521.1		32	7.3	odd	6

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.104916 - 2.64367i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.104916 - 2.64367i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +6.11380i q^{11} +(3.86893 - 2.23373i) q^{13} +(1.23098 + 2.34194i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.11723 - 1.93509i) q^{17} +(-0.623812 - 0.360158i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.05690 - 5.29471i) q^{22} -6.71710i q^{23} +1.00000 q^{25} +(-2.23373 + 3.86893i) q^{26} +(-2.23703 - 1.41269i) q^{28} +(-0.633929 - 0.365999i) q^{29} +(5.28276 + 3.05000i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.93509 + 1.11723i) q^{34} +(-0.104916 + 2.64367i) q^{35} +(-4.53567 + 7.85602i) q^{37} +0.720316 q^{38} -1.00000i q^{40} +(-0.713952 - 1.23660i) q^{41} +(1.23875 - 2.14558i) q^{43} +(5.29471 + 3.05690i) q^{44} +(3.35855 + 5.81718i) q^{46} +(4.18805 + 7.25392i) q^{47} +(-6.97799 - 0.554724i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.46746i q^{52} +(-0.193943 + 0.111973i) q^{53} -6.11380i q^{55} +(2.64367 + 0.104916i) q^{56} +0.731999 q^{58} +(4.88106 - 8.45424i) q^{59} +(-1.59270 + 0.919547i) q^{61} -6.10001 q^{62} -1.00000 q^{64} +(-3.86893 + 2.23373i) q^{65} +(6.54114 - 11.3296i) q^{67} -2.23445 q^{68} +(-1.23098 - 2.34194i) q^{70} -7.83185i q^{71} +(10.7713 - 6.21880i) q^{73} -9.07135i q^{74} +(-0.623812 + 0.360158i) q^{76} +(16.1629 + 0.641432i) q^{77} +(-7.49899 - 12.9886i) q^{79} +(0.500000 + 0.866025i) q^{80} +(1.23660 + 0.713952i) q^{82} +(-1.95115 + 3.37949i) q^{83} +(1.11723 + 1.93509i) q^{85} +2.47750i q^{86} -6.11380 q^{88} +(5.83979 - 10.1148i) q^{89} +(-5.49933 - 10.4625i) q^{91} +(-5.81718 - 3.35855i) q^{92} +(-7.25392 - 4.18805i) q^{94} +(0.623812 + 0.360158i) q^{95} +(10.9748 + 6.33628i) q^{97} +(6.32047 - 3.00859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

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