LMFDB - Embedded newform 756.2.bo.b.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.2
Character	$\chi$	$=$	756.337
Dual form			756.2.bo.b.673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09514 + 1.34189i) q^{3} +(0.684464 + 0.574334i) q^{5} +(0.939693 + 0.342020i) q^{7} +(-0.601340 - 2.93911i) q^{9} +O(q^{10})$	\(q+(-1.09514 + 1.34189i) q^{3} +(0.684464 + 0.574334i) q^{5} +(0.939693 + 0.342020i) q^{7} +(-0.601340 - 2.93911i) q^{9} +(3.74353 - 3.14120i) q^{11} +(0.797816 - 4.52464i) q^{13} +(-1.52028 + 0.289501i) q^{15} +(-0.183107 + 0.317150i) q^{17} +(1.61024 + 2.78901i) q^{19} +(-1.48805 + 0.886405i) q^{21} +(2.34120 - 0.852125i) q^{23} +(-0.729609 - 4.13782i) q^{25} +(4.60252 + 2.41181i) q^{27} +(0.646594 + 3.66701i) q^{29} +(0.605945 - 0.220546i) q^{31} +(0.115453 + 8.46346i) q^{33} +(0.446752 + 0.773797i) q^{35} +(0.115378 - 0.199840i) q^{37} +(5.19785 + 6.02569i) q^{39} +(-1.29956 + 7.37018i) q^{41} +(-0.0797498 + 0.0669180i) q^{43} +(1.27644 - 2.35709i) q^{45} +(10.0754 + 3.66714i) q^{47} +(0.766044 + 0.642788i) q^{49} +(-0.225054 - 0.593033i) q^{51} +1.90672 q^{53} +4.36641 q^{55} +(-5.50599 - 0.893596i) q^{57} +(0.258925 + 0.217263i) q^{59} +(-3.76707 - 1.37110i) q^{61} +(0.440161 - 2.96753i) q^{63} +(3.14473 - 2.63874i) q^{65} +(2.21990 - 12.5897i) q^{67} +(-1.42048 + 4.07482i) q^{69} +(2.53427 - 4.38948i) q^{71} +(-3.80034 - 6.58238i) q^{73} +(6.35152 + 3.55243i) q^{75} +(4.59212 - 1.67140i) q^{77} +(1.59696 + 9.05683i) q^{79} +(-8.27678 + 3.53482i) q^{81} +(2.64348 + 14.9919i) q^{83} +(-0.307480 + 0.111914i) q^{85} +(-5.62884 - 3.14823i) q^{87} +(0.494525 + 0.856542i) q^{89} +(2.29722 - 3.97890i) q^{91} +(-0.367645 + 1.05464i) q^{93} +(-0.499674 + 2.83379i) q^{95} +(2.75088 - 2.30827i) q^{97} +(-11.4835 - 9.11374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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
$3$	−1.09514	+	1.34189i	−0.632279	+	0.774741i
$3$	−1.09514	+	1.34189i	−0.632279	+	0.774741i
$4$		0			0
$5$	0.684464	+	0.574334i	0.306102	+	0.256850i	0.782879	−	0.622175i	$-0.213751\pi$
$5$	0.684464	+	0.574334i	0.306102	+	0.256850i	−0.476777	+	0.879024i	$0.658195\pi$
$6$		0			0
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$8$		0			0
$9$	−0.601340	−	2.93911i	−0.200447	−	0.979705i
$10$		0			0
$11$	3.74353	−	3.14120i	1.12872	−	0.947107i	0.129706	−	0.991552i	$-0.458597\pi$
$11$	3.74353	−	3.14120i	1.12872	−	0.947107i	0.999012	+	0.0444458i	$0.0141522\pi$
$12$		0			0
$13$	0.797816	−	4.52464i	0.221274	−	1.25491i	−0.648406	−	0.761294i	$-0.724564\pi$
$13$	0.797816	−	4.52464i	0.221274	−	1.25491i	0.869681	−	0.493615i	$-0.164325\pi$
$14$		0			0
$15$	−1.52028	+	0.289501i	−0.392534	+	0.0747487i
$16$		0			0
$17$	−0.183107	+	0.317150i	−0.0444099	+	0.0769203i	−0.887376	−	0.461047i	$-0.847474\pi$
$17$	−0.183107	+	0.317150i	−0.0444099	+	0.0769203i	0.842966	+	0.537967i	$0.180807\pi$
$18$		0			0
$19$	1.61024	+	2.78901i	0.369414	+	0.639844i	0.989474	−	0.144711i	$-0.0462251\pi$
$19$	1.61024	+	2.78901i	0.369414	+	0.639844i	−0.620060	+	0.784554i	$0.712892\pi$
$20$		0			0
$21$	−1.48805	+	0.886405i	−0.324719	+	0.193429i
$22$		0			0
$23$	2.34120	−	0.852125i	0.488173	−	0.177680i	−0.0861940	−	0.996278i	$-0.527470\pi$
$23$	2.34120	−	0.852125i	0.488173	−	0.177680i	0.574367	+	0.818598i	$0.305248\pi$
$24$		0			0
$25$	−0.729609	−	4.13782i	−0.145922	−	0.827564i
$26$		0			0
$27$	4.60252	+	2.41181i	0.885755	+	0.464152i
$28$		0			0
$29$	0.646594	+	3.66701i	0.120069	+	0.680947i	0.984115	+	0.177533i	$0.0568118\pi$
$29$	0.646594	+	3.66701i	0.120069	+	0.680947i	−0.864045	+	0.503414i	$0.832077\pi$
$30$		0			0
$31$	0.605945	−	0.220546i	0.108831	−	0.0396112i	−0.287031	−	0.957921i	$-0.592668\pi$
$31$	0.605945	−	0.220546i	0.108831	−	0.0396112i	0.395862	+	0.918310i	$0.370446\pi$
$32$		0			0
$33$	0.115453	+	8.46346i	0.0200978	+	1.47330i
$34$		0			0
$35$	0.446752	+	0.773797i	0.0755149	+	0.130796i
$36$		0			0
$37$	0.115378	−	0.199840i	0.0189680	−	0.0328535i	−0.856386	−	0.516337i	$-0.827295\pi$
$37$	0.115378	−	0.199840i	0.0189680	−	0.0328535i	0.875354	+	0.483483i	$0.160629\pi$
$38$		0			0
$39$	5.19785	+	6.02569i	0.832322	+	0.964883i
$40$		0			0
$41$	−1.29956	+	7.37018i	−0.202957	+	1.15103i	0.697664	+	0.716425i	$0.254223\pi$
$41$	−1.29956	+	7.37018i	−0.202957	+	1.15103i	−0.900622	+	0.434604i	$0.856888\pi$
$42$		0			0
$43$	−0.0797498	+	0.0669180i	−0.0121617	+	0.0102049i	−0.648848	−	0.760918i	$-0.724749\pi$
$43$	−0.0797498	+	0.0669180i	−0.0121617	+	0.0102049i	0.636686	+	0.771123i	$0.280305\pi$
$44$		0			0
$45$	1.27644	−	2.35709i	0.190280	−	0.351374i
$46$		0			0
$47$	10.0754	+	3.66714i	1.46964	+	0.534907i	0.948004	−	0.318259i	$-0.103098\pi$
$47$	10.0754	+	3.66714i	1.46964	+	0.534907i	0.521640	+	0.853165i	$0.325320\pi$
$48$		0			0
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$		0			0
$51$	−0.225054	−	0.593033i	−0.0315138	−	0.0830412i
$52$		0			0
$53$	1.90672			0.261908			0.130954	−	0.991388i	$-0.458196\pi$
$53$	1.90672			0.261908			0.130954	+	0.991388i	$0.458196\pi$
$54$		0			0
$55$	4.36641			0.588766
$56$		0			0
$57$	−5.50599	−	0.893596i	−0.729286	−	0.118360i
$58$		0			0
$59$	0.258925	+	0.217263i	0.0337091	+	0.0282853i	0.659487	−	0.751716i	$-0.270774\pi$
$59$	0.258925	+	0.217263i	0.0337091	+	0.0282853i	−0.625777	+	0.780002i	$0.715218\pi$
$60$		0			0
$61$	−3.76707	−	1.37110i	−0.482323	−	0.175551i	0.0894033	−	0.995996i	$-0.471504\pi$
$61$	−3.76707	−	1.37110i	−0.482323	−	0.175551i	−0.571727	+	0.820444i	$0.693726\pi$
$62$		0			0
$63$	0.440161	−	2.96753i	0.0554551	−	0.373874i
$64$		0			0
$65$	3.14473	−	2.63874i	0.390055	−	0.327295i
$66$		0			0
$67$	2.21990	−	12.5897i	0.271204	−	1.53807i	−0.479565	−	0.877507i	$-0.659205\pi$
$67$	2.21990	−	12.5897i	0.271204	−	1.53807i	0.750768	−	0.660566i	$-0.229684\pi$
$68$		0			0
$69$	−1.42048	+	4.07482i	−0.171005	+	0.490551i
$70$		0			0
$71$	2.53427	−	4.38948i	0.300762	−	0.520936i	−0.675546	−	0.737317i	$-0.736092\pi$
$71$	2.53427	−	4.38948i	0.300762	−	0.520936i	0.976309	+	0.216382i	$0.0694255\pi$
$72$		0			0
$73$	−3.80034	−	6.58238i	−0.444796	−	0.770409i	0.553242	−	0.833020i	$-0.313390\pi$
$73$	−3.80034	−	6.58238i	−0.444796	−	0.770409i	−0.998038	+	0.0626116i	$0.980057\pi$
$74$		0			0
$75$	6.35152	+	3.55243i	0.733411	+	0.410199i
$76$		0			0
$77$	4.59212	−	1.67140i	0.523321	−	0.190473i
$78$		0			0
$79$	1.59696	+	9.05683i	0.179672	+	1.01897i	0.932611	+	0.360883i	$0.117524\pi$
$79$	1.59696	+	9.05683i	0.179672	+	1.01897i	−0.752939	+	0.658091i	$0.771364\pi$
$80$		0			0
$81$	−8.27678	+	3.53482i	−0.919642	+	0.392757i
$82$		0			0
$83$	2.64348	+	14.9919i	0.290159	+	1.64557i	0.686252	+	0.727364i	$0.259255\pi$
$83$	2.64348	+	14.9919i	0.290159	+	1.64557i	−0.396093	+	0.918211i	$0.629634\pi$
$84$		0			0
$85$	−0.307480	+	0.111914i	−0.0333509	+	0.0121387i
$86$		0			0
$87$	−5.62884	−	3.14823i	−0.603475	−	0.337526i
$88$		0			0
$89$	0.494525	+	0.856542i	0.0524195	+	0.0907932i	0.891045	−	0.453916i	$-0.149973\pi$
$89$	0.494525	+	0.856542i	0.0524195	+	0.0907932i	−0.838625	+	0.544709i	$0.816640\pi$
$90$		0			0
$91$	2.29722	−	3.97890i	0.240814	−	0.417102i
$92$		0			0
$93$	−0.367645	+	1.05464i	−0.0381230	+	0.109361i
$94$		0			0
$95$	−0.499674	+	2.83379i	−0.0512655	+	0.290741i
$96$		0			0
$97$	2.75088	−	2.30827i	0.279310	−	0.234369i	−0.492361	−	0.870391i	$-0.663866\pi$
$97$	2.75088	−	2.30827i	0.279310	−	0.234369i	0.771671	+	0.636022i	$0.219421\pi$
$98$		0			0
$99$	−11.4835	−	9.11374i	−1.15413	−	0.915966i
$100$		0			0
$101$	−8.55236	−	3.11281i	−0.850992	−	0.309736i	−0.120547	−	0.992708i	$-0.538465\pi$
$101$	−8.55236	−	3.11281i	−0.850992	−	0.309736i	−0.730445	+	0.682972i	$0.760687\pi$
$102$		0			0
$103$	9.16078	+	7.68681i	0.902639	+	0.757404i	0.970704	−	0.240277i	$-0.0772383\pi$
$103$	9.16078	+	7.68681i	0.902639	+	0.757404i	−0.0680656	+	0.997681i	$0.521683\pi$
$104$		0			0
$105$	−1.52761	−	0.247923i	−0.149079	−	0.0241948i
$106$		0			0
$107$	9.64254			0.932179			0.466090	−	0.884738i	$-0.345662\pi$
$107$	9.64254			0.932179			0.466090	+	0.884738i	$0.345662\pi$
$108$		0			0
$109$	−19.2881			−1.84746			−0.923731	−	0.383043i	$-0.874876\pi$
$109$	−19.2881			−1.84746			−0.923731	+	0.383043i	$0.874876\pi$
$110$		0			0
$111$	0.141809	+	0.373677i	0.0134599	+	0.0354678i
$112$		0			0
$113$	6.24442	+	5.23969i	0.587426	+	0.492909i	0.887376	−	0.461046i	$-0.152526\pi$
$113$	6.24442	+	5.23969i	0.587426	+	0.492909i	−0.299950	+	0.953955i	$0.596970\pi$
$114$		0			0
$115$	2.09187	+	0.761378i	0.195068	+	0.0709988i
$116$		0			0
$117$	−13.7782	+	0.375976i	−1.27379	+	0.0347590i
$118$		0			0
$119$	−0.280536	+	0.235398i	−0.0257167	+	0.0215789i
$120$		0			0
$121$	2.23679	−	12.6855i	0.203345	−	1.15322i
$122$		0			0
$123$	−8.46677	−	9.81524i	−0.763423	−	0.885010i
$124$		0			0
$125$	4.11086	−	7.12021i	0.367686	−	0.636851i
$126$		0			0
$127$	−9.46371	−	16.3916i	−0.839768	−	1.45452i	−0.890088	−	0.455788i	$-0.849358\pi$
$127$	−9.46371	−	16.3916i	−0.839768	−	1.45452i	0.0503203	−	0.998733i	$-0.483976\pi$
$128$		0			0
$129$	−0.00245954	−	0.180300i	−0.000216550	−	0.0158745i
$130$		0			0
$131$	−6.95629	+	2.53188i	−0.607774	+	0.221212i	−0.627529	−	0.778593i	$-0.715934\pi$
$131$	−6.95629	+	2.53188i	−0.607774	+	0.221212i	0.0197551	+	0.999805i	$0.493711\pi$
$132$		0			0
$133$	0.559230	+	3.17155i	0.0484914	+	0.275008i
$134$		0			0
$135$	1.76508	+	4.29418i	0.151914	+	0.369584i
$136$		0			0
$137$	−1.72887	−	9.80490i	−0.147707	−	0.837689i	−0.965154	−	0.261684i	$-0.915722\pi$
$137$	−1.72887	−	9.80490i	−0.147707	−	0.837689i	0.817446	−	0.576005i	$-0.195389\pi$
$138$		0			0
$139$	−2.90118	+	1.05594i	−0.246075	+	0.0895638i	−0.462113	−	0.886821i	$-0.652909\pi$
$139$	−2.90118	+	1.05594i	−0.246075	+	0.0895638i	0.216038	+	0.976385i	$0.430686\pi$
$140$		0			0
$141$	−15.9548	+	9.50402i	−1.34364	+	0.800383i
$142$		0			0
$143$	−11.2261	−	19.4442i	−0.938776	−	1.62601i
$144$		0			0
$145$	−1.66352	+	2.88130i	−0.138148	+	0.239279i
$146$		0			0
$147$	−1.70148	+	0.324006i	−0.140335	+	0.0267236i
$148$		0			0
$149$	−1.51053	+	8.56662i	−0.123747	+	0.701804i	0.858297	+	0.513153i	$0.171523\pi$
$149$	−1.51053	+	8.56662i	−0.123747	+	0.701804i	−0.982044	+	0.188651i	$0.939588\pi$
$150$		0			0
$151$	5.05506	−	4.24170i	0.411375	−	0.345184i	−0.413496	−	0.910506i	$-0.635692\pi$
$151$	5.05506	−	4.24170i	0.411375	−	0.345184i	0.824871	+	0.565322i	$0.191248\pi$
$152$		0			0
$153$	1.04225	+	0.347457i	0.0842610	+	0.0280902i
$154$		0			0
$155$	0.541414	+	0.197059i	0.0434874	+	0.0158281i
$156$		0			0
$157$	−5.26888	−	4.42112i	−0.420503	−	0.352844i	0.407852	−	0.913048i	$-0.366278\pi$
$157$	−5.26888	−	4.42112i	−0.420503	−	0.352844i	−0.828354	+	0.560205i	$0.810722\pi$
$158$		0			0
$159$	−2.08812	+	2.55861i	−0.165599	+	0.202911i
$160$		0			0
$161$	2.49145			0.196354
$162$		0			0
$163$	−23.0056			−1.80194			−0.900970	−	0.433880i	$-0.857144\pi$
$163$	−23.0056			−1.80194			−0.900970	+	0.433880i	$0.857144\pi$
$164$		0			0
$165$	−4.78183	+	5.85924i	−0.372265	+	0.456141i
$166$		0			0
$167$	7.57034	+	6.35227i	0.585810	+	0.491553i	0.886849	−	0.462059i	$-0.152889\pi$
$167$	7.57034	+	6.35227i	0.585810	+	0.491553i	−0.301039	+	0.953612i	$0.597333\pi$
$168$		0			0
$169$	−7.61984	−	2.77339i	−0.586141	−	0.213338i
$170$		0			0
$171$	7.22893	−	6.40982i	0.552810	−	0.490171i
$172$		0			0
$173$	9.24217	−	7.75510i	0.702669	−	0.589609i	−0.219863	−	0.975531i	$-0.570561\pi$
$173$	9.24217	−	7.75510i	0.702669	−	0.589609i	0.922532	+	0.385922i	$0.126116\pi$
$174$		0			0
$175$	0.729609	−	4.13782i	0.0551532	−	0.312790i
$176$		0			0
$177$	−0.575102	+	0.109515i	−0.0432273	+	0.00823162i
$178$		0			0
$179$	−10.3782	+	17.9755i	−0.775701	+	1.34355i	0.158699	+	0.987327i	$0.449270\pi$
$179$	−10.3782	+	17.9755i	−0.775701	+	1.34355i	−0.934400	+	0.356226i	$0.884063\pi$
$180$		0			0
$181$	−8.71372	−	15.0926i	−0.647686	−	1.12183i	−0.983674	−	0.179959i	$-0.942404\pi$
$181$	−8.71372	−	15.0926i	−0.647686	−	1.12183i	0.335988	−	0.941866i	$-0.390930\pi$
$182$		0			0
$183$	5.96533	−	3.55345i	0.440970	−	0.262678i
$184$		0			0
$185$	0.193747	−	0.0705180i	0.0142445	−	0.00518459i
$186$		0			0
$187$	0.310765	+	1.76244i	0.0227254	+	0.128882i
$188$		0			0
$189$	3.50007	+	3.84051i	0.254593	+	0.279356i
$190$		0			0
$191$	−0.367613	−	2.08484i	−0.0265995	−	0.150854i	0.968615	−	0.248565i	$-0.0799589\pi$
$191$	−0.367613	−	2.08484i	−0.0265995	−	0.150854i	−0.995215	+	0.0977113i	$0.968848\pi$
$192$		0			0
$193$	19.1792	−	6.98065i	1.38055	−	0.502478i	0.458203	−	0.888848i	$-0.348493\pi$
$193$	19.1792	−	6.98065i	1.38055	−	0.502478i	0.922344	+	0.386369i	$0.126271\pi$
$194$		0			0
$195$	0.0969855	+	7.10967i	0.00694528	+	0.509134i
$196$		0			0
$197$	−6.45038	−	11.1724i	−0.459571	−	0.796000i	0.539367	−	0.842070i	$-0.318663\pi$
$197$	−6.45038	−	11.1724i	−0.459571	−	0.796000i	−0.998938	+	0.0460707i	$0.985330\pi$
$198$		0			0
$199$	−2.04634	+	3.54437i	−0.145061	+	0.251254i	−0.929396	−	0.369085i	$-0.879671\pi$
$199$	−2.04634	+	3.54437i	−0.145061	+	0.251254i	0.784335	+	0.620338i	$0.213005\pi$
$200$		0			0
$201$	14.4629	+	16.7663i	1.02013	+	1.18260i
$202$		0			0
$203$	−0.646594	+	3.66701i	−0.0453820	+	0.257374i
$204$		0			0
$205$	−5.12244	+	4.29824i	−0.357767	+	0.300202i
$206$		0			0
$207$	−3.91235	−	6.36862i	−0.271927	−	0.442650i
$208$		0			0
$209$	14.7888	+	5.38269i	1.02296	+	0.372329i
$210$		0			0
$211$	−16.8246	−	14.1175i	−1.15825	−	0.971888i	−0.158371	−	0.987380i	$-0.550624\pi$
$211$	−16.8246	−	14.1175i	−1.15825	−	0.971888i	−0.999880	+	0.0154918i	$0.995069\pi$
$212$		0			0
$213$	3.11483	+	8.20781i	0.213425	+	0.562390i
$214$		0			0
$215$	−0.0930191			−0.00634385
$216$		0			0
$217$	0.644833			0.0437741
$218$		0			0
$219$	12.9947	+	2.10898i	0.878102	+	0.142512i
$220$		0			0
$221$	1.28891	+	1.08152i	0.0867011	+	0.0727509i
$222$		0			0
$223$	13.8829	+	5.05298i	0.929671	+	0.338373i	0.762079	−	0.647484i	$-0.224179\pi$
$223$	13.8829	+	5.05298i	0.929671	+	0.338373i	0.167592	+	0.985856i	$0.446401\pi$
$224$		0			0
$225$	−11.7228	+	4.63264i	−0.781518	+	0.308843i
$226$		0			0
$227$	3.19139	−	2.67790i	0.211820	−	0.177738i	−0.530705	−	0.847557i	$-0.678073\pi$
$227$	3.19139	−	2.67790i	0.211820	−	0.177738i	0.742525	+	0.669819i	$0.233628\pi$
$228$		0			0
$229$	−0.523436	+	2.96856i	−0.0345896	+	0.196168i	−0.997206	−	0.0747010i	$-0.976200\pi$
$229$	−0.523436	+	2.96856i	−0.0345896	+	0.196168i	0.962616	+	0.270869i	$0.0873109\pi$
$230$		0			0
$231$	−2.78618	+	7.99254i	−0.183317	+	0.525870i
$232$		0			0
$233$	−6.20626	+	10.7496i	−0.406586	+	0.704227i	−0.994505	−	0.104693i	$-0.966614\pi$
$233$	−6.20626	+	10.7496i	−0.406586	+	0.704227i	0.587919	+	0.808920i	$0.299947\pi$
$234$		0			0
$235$	4.79007	+	8.29665i	0.312470	+	0.541214i
$236$		0			0
$237$	−13.9022	−	7.77554i	−0.903043	−	0.505076i
$238$		0			0
$239$	−25.7195	+	9.36113i	−1.66366	+	0.605521i	−0.990931	−	0.134372i	$-0.957098\pi$
$239$	−25.7195	+	9.36113i	−1.66366	+	0.605521i	−0.672724	+	0.739893i	$0.734876\pi$
$240$		0			0
$241$	3.60781	+	20.4609i	0.232400	+	1.31800i	0.848021	+	0.529962i	$0.177794\pi$
$241$	3.60781	+	20.4609i	0.232400	+	1.31800i	−0.615622	+	0.788042i	$0.711095\pi$
$242$		0			0
$243$	4.32089	−	14.9776i	0.277185	−	0.960816i
$244$		0			0
$245$	0.155155	+	0.879930i	0.00991251	+	0.0562167i
$246$		0			0
$247$	13.9040	−	5.06063i	0.884688	−	0.322000i
$248$		0			0
$249$	−23.0125	−	12.8710i	−1.45836	−	0.815664i
$250$		0			0
$251$	−10.7425	−	18.6066i	−0.678063	−	1.17444i	−0.975563	−	0.219718i	$-0.929486\pi$
$251$	−10.7425	−	18.6066i	−0.678063	−	1.17444i	0.297500	−	0.954722i	$-0.403847\pi$
$252$		0			0
$253$	6.08765	−	10.5441i	0.382727	−	0.662903i
$254$		0			0
$255$	0.186558	−	0.535166i	0.0116827	−	0.0335134i
$256$		0			0
$257$	−4.62621	+	26.2366i	−0.288575	+	1.63659i	0.403652	+	0.914913i	$0.367741\pi$
$257$	−4.62621	+	26.2366i	−0.288575	+	1.63659i	−0.692227	+	0.721680i	$0.743370\pi$
$258$		0			0
$259$	0.176769	−	0.148327i	0.0109839	−	0.00921657i
$260$		0			0
$261$	10.3889	−	4.10554i	0.643060	−	0.254126i
$262$		0			0
$263$	21.3070	+	7.75513i	1.31385	+	0.478202i	0.901482	−	0.432816i	$-0.142480\pi$
$263$	21.3070	+	7.75513i	1.31385	+	0.478202i	0.412367	+	0.911018i	$0.364702\pi$
$264$		0			0
$265$	1.30508	+	1.09509i	0.0801704	+	0.0672710i
$266$		0			0
$267$	−1.69096	−	0.274435i	−0.103485	−	0.0167951i
$268$		0			0
$269$	−15.8273			−0.965008			−0.482504	−	0.875894i	$-0.660273\pi$
$269$	−15.8273			−0.965008			−0.482504	+	0.875894i	$0.660273\pi$
$270$		0			0
$271$	28.9400			1.75798			0.878991	−	0.476838i	$-0.158217\pi$
$271$	28.9400			1.75798			0.878991	+	0.476838i	$0.158217\pi$
$272$		0			0
$273$	2.82347	+	7.44007i	0.170884	+	0.450293i
$274$		0			0
$275$	−15.7290	−	13.1982i	−0.948495	−	0.795882i
$276$		0			0
$277$	−9.12579	−	3.32151i	−0.548315	−	0.199570i	0.0529825	−	0.998595i	$-0.483127\pi$
$277$	−9.12579	−	3.32151i	−0.548315	−	0.199570i	−0.601298	+	0.799025i	$0.705349\pi$
$278$		0			0
$279$	−1.01259	−	1.64832i	−0.0606221	−	0.0986822i
$280$		0			0
$281$	4.99350	−	4.19004i	0.297887	−	0.249957i	−0.481577	−	0.876404i	$-0.659936\pi$
$281$	4.99350	−	4.19004i	0.297887	−	0.249957i	0.779464	+	0.626447i	$0.215491\pi$
$282$		0			0
$283$	−3.93380	+	22.3097i	−0.233840	+	1.32617i	0.611203	+	0.791474i	$0.290686\pi$
$283$	−3.93380	+	22.3097i	−0.233840	+	1.32617i	−0.845043	+	0.534699i	$0.820425\pi$
$284$		0			0
$285$	−3.25543	−	3.77391i	−0.192835	−	0.223547i
$286$		0			0
$287$	−3.74194	+	6.48123i	−0.220880	+	0.382575i
$288$		0			0
$289$	8.43294	+	14.6063i	0.496056	+	0.859193i
$290$		0			0
$291$	0.0848391	+	6.21926i	0.00497335	+	0.364579i
$292$		0			0
$293$	18.7881	−	6.83831i	1.09761	−	0.399498i	0.271177	−	0.962530i	$-0.412587\pi$
$293$	18.7881	−	6.83831i	1.09761	−	0.399498i	0.826435	+	0.563032i	$0.190365\pi$
$294$		0			0
$295$	0.0524428	+	0.297418i	0.00305334	+	0.0173164i
$296$		0			0
$297$	24.8056	−	5.42875i	1.43937	−	0.315008i
$298$		0			0
$299$	−1.98772	−	11.2729i	−0.114953	−	0.651929i
$300$		0			0
$301$	−0.0978276	+	0.0356063i	−0.00563869	+	0.00205231i
$302$		0			0
$303$	13.5431	−	8.06738i	0.778029	−	0.463459i
$304$		0			0
$305$	−1.79095	−	3.10202i	−0.102550	−	0.177621i
$306$		0			0
$307$	−9.63126	+	16.6818i	−0.549685	+	0.952082i	0.448611	+	0.893727i	$0.351919\pi$
$307$	−9.63126	+	16.6818i	−0.549685	+	0.952082i	−0.998296	+	0.0583551i	$0.981414\pi$
$308$		0			0
$309$	−20.3472	+	3.87464i	−1.15751	+	0.220421i
$310$		0			0
$311$	2.48922	−	14.1171i	0.141151	−	0.800506i	−0.829227	−	0.558912i	$-0.811219\pi$
$311$	2.48922	−	14.1171i	0.141151	−	0.800506i	0.970378	−	0.241593i	$-0.0776700\pi$
$312$		0			0
$313$	−2.61141	+	2.19124i	−0.147606	+	0.123856i	−0.713600	−	0.700553i	$-0.752937\pi$
$313$	−2.61141	+	2.19124i	−0.147606	+	0.123856i	0.565995	+	0.824409i	$0.308492\pi$
$314$		0			0
$315$	2.00563	−	1.77837i	0.113004	−	0.100200i
$316$		0			0
$317$	23.4017	+	8.51753i	1.31437	+	0.478392i	0.901651	−	0.432465i	$-0.142356\pi$
$317$	23.4017	+	8.51753i	1.31437	+	0.478392i	0.412721	+	0.910857i	$0.364578\pi$
$318$		0			0
$319$	13.9394	+	11.6965i	0.780454	+	0.654879i
$320$		0			0
$321$	−10.5599	+	12.9392i	−0.589397	+	0.722197i
$322$		0			0
$323$	−1.17938			−0.0656226
$324$		0			0
$325$	−19.3042			−1.07081
$326$		0			0
$327$	21.1231	−	25.8825i	1.16811	−	1.43130i
$328$		0			0
$329$	8.21352	+	6.89196i	0.452826	+	0.379966i
$330$		0			0
$331$	23.5699	+	8.57873i	1.29552	+	0.471530i	0.895534	−	0.444993i	$-0.146794\pi$
$331$	23.5699	+	8.57873i	1.29552	+	0.471530i	0.399983	+	0.916523i	$0.369016\pi$
$332$		0			0
$333$	−0.656734	−	0.218936i	−0.0359888	−	0.0119976i
$334$		0			0
$335$	8.75011	−	7.34221i	0.478069	−	0.401148i
$336$		0			0
$337$	4.24634	−	24.0822i	0.231313	−	1.31184i	−0.618928	−	0.785448i	$-0.712433\pi$
$337$	4.24634	−	24.0822i	0.231313	−	1.31184i	0.850241	−	0.526394i	$-0.176456\pi$
$338$		0			0
$339$	−13.8696	+	2.64114i	−0.753294	+	0.143447i
$340$		0			0
$341$	1.57560	−	2.72901i	0.0853233	−	0.147784i
$342$		0			0
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$		0			0
$345$	−3.31257	+	1.97324i	−0.178343	+	0.106236i
$346$		0			0
$347$	−10.4157	+	3.79102i	−0.559146	+	0.203513i	−0.606106	−	0.795384i	$-0.707269\pi$
$347$	−10.4157	+	3.79102i	−0.559146	+	0.203513i	0.0469593	+	0.998897i	$0.485047\pi$
$348$		0			0
$349$	4.03178	+	22.8653i	0.215816	+	1.22395i	0.879485	+	0.475927i	$0.157887\pi$
$349$	4.03178	+	22.8653i	0.215816	+	1.22395i	−0.663669	+	0.748027i	$0.731001\pi$
$350$		0			0
$351$	14.5845	−	18.9006i	0.778464	−	1.00884i
$352$		0			0
$353$	−4.22962	−	23.9873i	−0.225120	−	1.27672i	−0.862456	−	0.506132i	$-0.831075\pi$
$353$	−4.22962	−	23.9873i	−0.225120	−	1.27672i	0.637336	−	0.770586i	$-0.280036\pi$
$354$		0			0
$355$	4.25564	−	1.54893i	0.225866	−	0.0822085i
$356$		0			0
$357$	−0.00865192	−	0.634242i	−0.000457908	−	0.0335676i
$358$		0			0
$359$	−10.3164	−	17.8686i	−0.544481	−	0.943068i	−0.998639	−	0.0521473i	$-0.983393\pi$
$359$	−10.3164	−	17.8686i	−0.544481	−	0.943068i	0.454159	−	0.890921i	$-0.349940\pi$
$360$		0			0
$361$	4.31427	−	7.47253i	0.227067	−	0.393291i
$362$		0			0
$363$	14.5729	+	16.8939i	0.764880	+	0.886699i
$364$		0			0
$365$	1.17929	−	6.68806i	0.0617266	−	0.350069i
$366$		0			0
$367$	−22.4003	+	18.7961i	−1.16929	+	0.981147i	−0.999990	−	0.00441800i	$-0.998594\pi$
$367$	−22.4003	+	18.7961i	−1.16929	+	0.981147i	−0.169296	+	0.985565i	$0.554149\pi$
$368$		0			0
$369$	22.4433	−	0.612427i	1.16835	−	0.0318817i
$370$		0			0
$371$	1.79173	+	0.652136i	0.0930219	+	0.0338572i
$372$		0			0
$373$	−1.40076	−	1.17538i	−0.0725286	−	0.0608587i	0.605803	−	0.795615i	$-0.292852\pi$
$373$	−1.40076	−	1.17538i	−0.0725286	−	0.0608587i	−0.678331	+	0.734756i	$0.737297\pi$
$374$		0			0
$375$	5.05259	+	13.3139i	0.260914	+	0.687529i
$376$		0			0
$377$	17.1078			0.881095
$378$		0			0
$379$	−12.2289			−0.628154			−0.314077	−	0.949397i	$-0.601695\pi$
$379$	−12.2289			−0.628154			−0.314077	+	0.949397i	$0.601695\pi$
$380$		0			0
$381$	32.3598	+	5.25185i	1.65784	+	0.269060i
$382$		0			0
$383$	−19.4030	−	16.2810i	−0.991446	−	0.831922i	−0.00566936	−	0.999984i	$-0.501805\pi$
$383$	−19.4030	−	16.2810i	−0.991446	−	0.831922i	−0.985776	+	0.168062i	$0.946249\pi$
$384$		0			0
$385$	4.10308	+	1.49340i	0.209112	+	0.0761107i
$386$		0			0
$387$	0.244636	+	0.194153i	0.0124356	+	0.00986936i
$388$		0			0
$389$	−0.0175934	+	0.0147626i	−0.000892020	+	0.000748494i	−0.643234	−	0.765670i	$-0.722408\pi$
$389$	−0.0175934	+	0.0147626i	−0.000892020	+	0.000748494i	0.642341	+	0.766419i	$0.277963\pi$
$390$		0			0
$391$	−0.158437	+	0.898541i	−0.00801250	+	0.0454412i
$392$		0			0
$393$	4.22060	−	12.1073i	0.212901	−	0.610735i
$394$		0			0
$395$	−4.10858	+	7.11626i	−0.206725	+	0.358058i
$396$		0			0
$397$	−15.5858	−	26.9954i	−0.782229	−	1.35486i	−0.930640	−	0.365935i	$-0.880749\pi$
$397$	−15.5858	−	26.9954i	−0.782229	−	1.35486i	0.148411	−	0.988926i	$-0.452584\pi$
$398$		0			0
$399$	−4.86831	−	2.72286i	−0.243720	−	0.136314i
$400$		0			0
$401$	−28.6759	+	10.4372i	−1.43201	+	0.521207i	−0.937506	−	0.347970i	$-0.886871\pi$
$401$	−28.6759	+	10.4372i	−1.43201	+	0.521207i	−0.494500	+	0.869178i	$0.664649\pi$
$402$		0			0
$403$	−0.514458	−	2.91764i	−0.0256270	−	0.145338i
$404$		0			0
$405$	−7.69532	−	2.33418i	−0.382384	−	0.115986i
$406$		0			0
$407$	−0.195817	−	1.11053i	−0.00970628	−	0.0550470i
$408$		0			0
$409$	1.33268	−	0.485054i	0.0658966	−	0.0239844i	−0.308862	−	0.951107i	$-0.599948\pi$
$409$	1.33268	−	0.485054i	0.0658966	−	0.0239844i	0.374758	+	0.927123i	$0.377726\pi$
$410$		0			0
$411$	15.0505	+	8.41778i	0.742384	+	0.415218i
$412$		0			0
$413$	0.169001	+	0.292718i	0.00831600	+	0.0144037i
$414$		0			0
$415$	−6.80098	+	11.7797i	−0.333847	+	0.578240i
$416$		0			0
$417$	1.76023	−	5.04946i	0.0861990	−	0.247273i
$418$		0			0
$419$	−3.10293	+	17.5976i	−0.151588	+	0.859698i	0.810251	+	0.586083i	$0.199331\pi$
$419$	−3.10293	+	17.5976i	−0.151588	+	0.859698i	−0.961839	+	0.273616i	$0.911780\pi$
$420$		0			0
$421$	5.03487	−	4.22476i	0.245384	−	0.205902i	−0.511797	−	0.859106i	$-0.671020\pi$
$421$	5.03487	−	4.22476i	0.245384	−	0.205902i	0.757182	+	0.653204i	$0.226576\pi$
$422$		0			0
$423$	4.71940	−	31.8179i	0.229465	−	1.54704i
$424$		0			0
$425$	1.44591	+	0.526267i	0.0701368	+	0.0255277i
$426$		0			0
$427$	−3.07094	−	2.57683i	−0.148613	−	0.124701i
$428$		0			0
$429$	38.3862	+	6.22990i	1.85330	+	0.300782i
$430$		0			0
$431$	19.1386			0.921874			0.460937	−	0.887433i	$-0.347513\pi$
$431$	19.1386			0.921874			0.460937	+	0.887433i	$0.347513\pi$
$432$		0			0
$433$	−9.28393			−0.446157			−0.223079	−	0.974800i	$-0.571611\pi$
$433$	−9.28393			−0.446157			−0.223079	+	0.974800i	$0.571611\pi$
$434$		0			0
$435$	−2.04460	−	5.38768i	−0.0980312	−	0.258320i
$436$		0			0
$437$	6.14647	+	5.15750i	0.294026	+	0.246717i
$438$		0			0
$439$	4.65772	+	1.69527i	0.222301	+	0.0809110i	0.450770	−	0.892640i	$-0.351150\pi$
$439$	4.65772	+	1.69527i	0.222301	+	0.0809110i	−0.228469	+	0.973551i	$0.573372\pi$
$440$		0			0
$441$	1.42857	−	2.63803i	0.0680273	−	0.125620i
$442$		0			0
$443$	−18.2983	+	15.3541i	−0.869378	+	0.729495i	−0.963967	−	0.266021i	$-0.914291\pi$
$443$	−18.2983	+	15.3541i	−0.869378	+	0.729495i	0.0945887	+	0.995516i	$0.469846\pi$
$444$		0			0
$445$	−0.153456	+	0.870294i	−0.00727453	+	0.0412559i
$446$		0			0
$447$	−9.84122	−	11.4086i	−0.465474	−	0.539608i
$448$		0			0
$449$	−7.08811	+	12.2770i	−0.334509	+	0.579386i	−0.983390	−	0.181503i	$-0.941904\pi$
$449$	−7.08811	+	12.2770i	−0.334509	+	0.579386i	0.648882	+	0.760889i	$0.275237\pi$
$450$		0			0
$451$	18.2862	+	31.6727i	0.861065	+	1.49141i
$452$		0			0
$453$	0.155901	+	11.4286i	0.00732488	+	0.536961i
$454$		0			0
$455$	3.85758	−	1.40404i	0.180846	−	0.0658226i
$456$		0			0
$457$	6.76033	+	38.3398i	0.316235	+	1.79346i	0.565209	+	0.824948i	$0.308796\pi$
$457$	6.76033	+	38.3398i	0.316235	+	1.79346i	−0.248974	+	0.968510i	$0.580093\pi$
$458$		0			0
$459$	−1.60766	+	1.01807i	−0.0750390	+	0.0475196i
$460$		0			0
$461$	4.06095	+	23.0308i	0.189137	+	1.07265i	0.920523	+	0.390687i	$0.127763\pi$
$461$	4.06095	+	23.0308i	0.189137	+	1.07265i	−0.731386	+	0.681964i	$0.761126\pi$
$462$		0			0
$463$	11.4486	−	4.16697i	0.532064	−	0.193655i	−0.0619958	−	0.998076i	$-0.519747\pi$
$463$	11.4486	−	4.16697i	0.532064	−	0.193655i	0.594060	+	0.804421i	$0.297524\pi$
$464$		0			0
$465$	−0.857355	+	0.510712i	−0.0397589	+	0.0236837i
$466$		0			0
$467$	−9.28256	−	16.0779i	−0.429546	−	0.743995i	0.567287	−	0.823520i	$-0.307993\pi$
$467$	−9.28256	−	16.0779i	−0.429546	−	0.743995i	−0.996833	+	0.0795252i	$0.974660\pi$
$468$		0			0
$469$	6.39194	−	11.0712i	0.295152	−	0.511219i
$470$		0			0
$471$	11.7028	−	2.22852i	0.539237	−	0.102685i
$472$		0			0
$473$	−0.0883433	+	0.501019i	−0.00406203	+	0.0230369i
$474$		0			0
$475$	10.3656	−	8.69776i	0.475606	−	0.399081i
$476$		0			0
$477$	−1.14659	−	5.60406i	−0.0524986	−	0.256592i
$478$		0			0
$479$	−29.2799	−	10.6570i	−1.33783	−	0.486932i	−0.428704	−	0.903445i	$-0.641030\pi$
$479$	−29.2799	−	10.6570i	−1.33783	−	0.486932i	−0.909130	+	0.416513i	$0.863252\pi$
$480$		0			0
$481$	−0.812154	−	0.681478i	−0.0370310	−	0.0310727i
$482$		0			0
$483$	−2.72848	+	3.34325i	−0.124150	+	0.152123i
$484$		0			0
$485$	3.20859			0.145695
$486$		0			0
$487$	9.73155			0.440979			0.220489	−	0.975389i	$-0.429235\pi$
$487$	9.73155			0.440979			0.220489	+	0.975389i	$0.429235\pi$
$488$		0			0
$489$	25.1944	−	30.8711i	1.13933	−	1.39604i
$490$		0			0
$491$	5.56165	+	4.66678i	0.250994	+	0.210609i	0.759600	−	0.650390i	$-0.225395\pi$
$491$	5.56165	+	4.66678i	0.250994	+	0.210609i	−0.508606	+	0.860999i	$0.669839\pi$
$492$		0			0
$493$	−1.28139	−	0.466388i	−0.0577109	−	0.0210051i
$494$		0			0
$495$	−2.62570	−	12.8334i	−0.118016	−	0.576817i
$496$		0			0
$497$	3.88273	−	3.25799i	0.174164	−	0.146141i
$498$		0			0
$499$	−2.60440	+	14.7703i	−0.116589	+	0.661209i	0.869362	+	0.494175i	$0.164530\pi$
$499$	−2.60440	+	14.7703i	−0.116589	+	0.661209i	−0.985951	+	0.167033i	$0.946581\pi$
$500$		0			0
$501$	−16.8146	+	3.20195i	−0.751222	+	0.143052i
$502$		0			0
$503$	−4.47554	+	7.75187i	−0.199555	+	0.345639i	−0.948384	−	0.317124i	$-0.897283\pi$
$503$	−4.47554	+	7.75187i	−0.199555	+	0.345639i	0.748830	+	0.662763i	$0.230616\pi$
$504$		0			0
$505$	−4.06600	−	7.04251i	−0.180934	−	0.313388i
$506$		0			0
$507$	12.0664	−	7.18774i	0.535886	−	0.319219i
$508$		0			0
$509$	30.3798	−	11.0574i	1.34656	−	0.490109i	0.434689	−	0.900581i	$-0.356858\pi$
$509$	30.3798	−	11.0574i	1.34656	−	0.490109i	0.911873	+	0.410472i	$0.134636\pi$
$510$		0			0
$511$	−1.31984	−	7.48520i	−0.0583864	−	0.331126i
$512$		0			0
$513$	0.684593	+	16.7201i	0.0302255	+	0.738209i
$514$		0			0
$515$	1.85543	+	10.5227i	0.0817602	+	0.463685i
$516$		0			0
$517$	49.2367	−	17.9207i	2.16543	−	0.788151i
$518$		0			0
$519$	0.285035	+	20.8949i	0.0125116	+	0.917184i
$520$		0			0
$521$	−18.9455	−	32.8147i	−0.830020	−	1.43764i	−0.898022	−	0.439951i	$-0.854996\pi$
$521$	−18.9455	−	32.8147i	−0.830020	−	1.43764i	0.0680022	−	0.997685i	$-0.478338\pi$
$522$		0			0
$523$	−19.9422	+	34.5410i	−0.872013	+	1.51037i	−0.0121022	+	0.999927i	$0.503852\pi$
$523$	−19.9422	+	34.5410i	−0.872013	+	1.51037i	−0.859911	+	0.510444i	$0.829481\pi$
$524$		0			0
$525$	4.75347	+	5.51054i	0.207459	+	0.240500i
$526$		0			0
$527$	−0.0410064	+	0.232559i	−0.00178627	+	0.0101304i
$528$		0			0
$529$	−12.8639	+	10.7941i	−0.559302	+	0.469310i
$530$		0			0
$531$	0.482860	−	0.891658i	0.0209544	−	0.0386947i
$532$		0			0
$533$	32.3106	+	11.7601i	1.39953	+	0.509386i
$534$		0			0
$535$	6.59997	+	5.53803i	0.285342	+	0.239430i
$536$		0			0
$537$	−12.7556	−	33.6121i	−0.550446	−	1.45047i
$538$		0			0
$539$	4.88684			0.210491
$540$		0			0
$541$	−23.3943			−1.00580			−0.502900	−	0.864345i	$-0.667733\pi$
$541$	−23.3943			−1.00580			−0.502900	+	0.864345i	$0.667733\pi$
$542$		0			0
$543$	29.7954	+	4.83565i	1.27864	+	0.207518i
$544$		0			0
$545$	−13.2020	−	11.0778i	−0.565511	−	0.474520i
$546$		0			0
$547$	26.2630	+	9.55894i	1.12292	+	0.408711i	0.835718	−	0.549159i	$-0.185052\pi$
$547$	26.2630	+	9.55894i	1.12292	+	0.408711i	0.287205	+	0.957869i	$0.407274\pi$
$548$		0			0
$549$	−1.76453	+	11.8963i	−0.0753083	+	0.507723i
$550$		0			0
$551$	−9.18619	+	7.70813i	−0.391345	+	0.328377i
$552$		0			0
$553$	−1.59696	+	9.05683i	−0.0679098	+	0.385136i
$554$		0			0
$555$	−0.117552	+	0.337214i	−0.00498981	+	0.0143139i
$556$		0			0
$557$	−0.909289	+	1.57494i	−0.0385278	+	0.0667321i	−0.884646	−	0.466263i	$-0.845600\pi$
$557$	−0.909289	+	1.57494i	−0.0385278	+	0.0667321i	0.846118	+	0.532995i	$0.178933\pi$
$558$		0			0
$559$	0.239154	+	0.414227i	0.0101151	+	0.0175199i
$560$		0			0
$561$	−2.70533	−	1.51310i	−0.114219	−	0.0638832i
$562$		0			0
$563$	−37.1978	+	13.5389i	−1.56770	+	0.570597i	−0.972484	−	0.232968i	$-0.925156\pi$
$563$	−37.1978	+	13.5389i	−1.56770	+	0.570597i	−0.595218	+	0.803565i	$0.702934\pi$
$564$		0			0
$565$	1.26475	+	7.17276i	0.0532085	+	0.301760i
$566$		0			0
$567$	−8.98661	+	0.490815i	−0.377402	+	0.0206123i
$568$		0			0
$569$	−0.442120	−	2.50739i	−0.0185346	−	0.105115i	0.974137	−	0.225958i	$-0.0725513\pi$
$569$	−0.442120	−	2.50739i	−0.0185346	−	0.105115i	−0.992672	+	0.120843i	$0.961440\pi$
$570$		0			0
$571$	−26.8650	+	9.77804i	−1.12426	+	0.409198i	−0.836206	−	0.548415i	$-0.815231\pi$
$571$	−26.8650	+	9.77804i	−1.12426	+	0.409198i	−0.288057	+	0.957613i	$0.593009\pi$
$572$		0			0
$573$	3.20021	+	1.78989i	0.133691	+	0.0747737i
$574$		0			0
$575$	−5.23410	−	9.06572i	−0.218277	−	0.378067i
$576$		0			0
$577$	1.49478	−	2.58903i	0.0622283	−	0.107783i	−0.833233	−	0.552922i	$-0.813513\pi$
$577$	1.49478	−	2.58903i	0.0622283	−	0.107783i	0.895461	+	0.445140i	$0.146846\pi$
$578$		0			0
$579$	−11.6366	+	33.3811i	−0.483601	+	1.38727i
$580$		0			0
$581$	−2.64348	+	14.9919i	−0.109670	+	0.621969i
$582$		0			0
$583$	7.13786	−	5.98938i	0.295620	−	0.248055i
$584$		0			0
$585$	−9.64661	−	7.65593i	−0.398838	−	0.316534i
$586$		0			0
$587$	−36.7883	−	13.3898i	−1.51842	−	0.552658i	−0.557664	−	0.830067i	$-0.688302\pi$
$587$	−36.7883	−	13.3898i	−1.51842	−	0.552658i	−0.960752	+	0.277409i	$0.910524\pi$
$588$		0			0
$589$	1.59082	+	1.33486i	0.0655486	+	0.0550018i
$590$		0			0
$591$	22.0562	+	3.57961i	0.907270	+	0.147246i
$592$		0			0
$593$	−14.8845			−0.611231			−0.305616	−	0.952155i	$-0.598862\pi$
$593$	−14.8845			−0.611231			−0.305616	+	0.952155i	$0.598862\pi$
$594$		0			0
$595$	−0.327214			−0.0134144
$596$		0			0
$597$	−2.51512	−	6.62754i	−0.102937	−	0.271247i
$598$		0			0
$599$	32.3935	+	27.1814i	1.32356	+	1.11060i	0.985536	+	0.169467i	$0.0542045\pi$
$599$	32.3935	+	27.1814i	1.32356	+	1.11060i	0.338029	+	0.941136i	$0.390240\pi$
$600$		0			0
$601$	−3.10740	−	1.13100i	−0.126753	−	0.0461344i	0.277865	−	0.960620i	$-0.410373\pi$
$601$	−3.10740	−	1.13100i	−0.126753	−	0.0461344i	−0.404618	+	0.914486i	$0.632596\pi$
$602$		0			0
$603$	−38.3374	+	1.04614i	−1.56122	+	0.0426022i
$604$		0			0
$605$	8.81669	−	7.39809i	0.358450	−	0.300775i
$606$		0			0
$607$	−2.95958	+	16.7846i	−0.120126	+	0.681267i	0.863958	+	0.503563i	$0.167978\pi$
$607$	−2.95958	+	16.7846i	−0.120126	+	0.681267i	−0.984084	+	0.177704i	$0.943133\pi$
$608$		0			0
$609$	−4.21262	−	4.88355i	−0.170704	−	0.197891i
$610$		0			0
$611$	24.6308	−	42.6617i	0.996454	−	1.72591i
$612$		0			0
$613$	−12.7310	−	22.0507i	−0.514200	−	0.890620i	−0.999864	−	0.0164750i	$-0.994756\pi$
$613$	−12.7310	−	22.0507i	−0.514200	−	0.890620i	0.485664	−	0.874145i	$-0.338578\pi$
$614$		0			0
$615$	−0.157980	−	11.5809i	−0.00637035	−	0.466988i
$616$		0			0
$617$	−6.67657	+	2.43007i	−0.268789	+	0.0978311i	−0.472899	−	0.881117i	$-0.656792\pi$
$617$	−6.67657	+	2.43007i	−0.268789	+	0.0978311i	0.204110	+	0.978948i	$0.434570\pi$
$618$		0			0
$619$	0.151804	+	0.860921i	0.00610151	+	0.0346034i	0.987707	−	0.156320i	$-0.0499630\pi$
$619$	0.151804	+	0.860921i	0.00610151	+	0.0346034i	−0.981605	+	0.190923i	$0.938852\pi$
$620$		0			0
$621$	12.8306	+	1.72458i	0.514873	+	0.0692052i
$622$		0			0
$623$	0.171747	+	0.974023i	0.00688088	+	0.0390234i
$624$		0			0
$625$	−12.8382	+	4.67272i	−0.513527	+	0.186909i
$626$		0			0
$627$	−23.4188	+	13.9502i	−0.935257	+	0.557117i
$628$		0			0
$629$	0.0422529	+	0.0731842i	0.00168473	+	0.00291804i
$630$		0			0
$631$	−14.1990	+	24.5933i	−0.565252	+	0.979045i	0.431774	+	0.901982i	$0.357888\pi$
$631$	−14.1990	+	24.5933i	−0.565252	+	0.979045i	−0.997026	+	0.0770637i	$0.975446\pi$
$632$		0			0
$633$	37.3694	−	7.11611i	1.48530	−	0.282840i
$634$		0			0
$635$	2.93669	−	16.6548i	0.116539	−	0.660925i
$636$		0			0
$637$	3.51954	−	2.95325i	0.139449	−	0.117012i
$638$		0			0
$639$	−14.4251	−	4.80893i	−0.570650	−	0.190238i
$640$		0			0
$641$	−28.3863	−	10.3318i	−1.12119	−	0.408080i	−0.286104	−	0.958199i	$-0.592360\pi$
$641$	−28.3863	−	10.3318i	−1.12119	−	0.408080i	−0.835086	+	0.550119i	$0.814582\pi$
$642$		0			0
$643$	−0.735073	−	0.616800i	−0.0289885	−	0.0243242i	0.628178	−	0.778069i	$-0.283801\pi$
$643$	−0.735073	−	0.616800i	−0.0289885	−	0.0243242i	−0.657167	+	0.753745i	$0.728245\pi$
$644$		0			0
$645$	0.101869	−	0.124821i	0.00401108	−	0.00491484i
$646$		0			0
$647$	−14.9346			−0.587139			−0.293570	−	0.955938i	$-0.594843\pi$
$647$	−14.9346			−0.587139			−0.293570	+	0.955938i	$0.594843\pi$
$648$		0			0
$649$	1.65176			0.0648373
$650$		0			0
$651$	−0.706182	+	0.865295i	−0.0276774	+	0.0339136i
$652$		0			0
$653$	−28.7934	−	24.1605i	−1.12677	−	0.945474i	−0.127845	−	0.991794i	$-0.540806\pi$
$653$	−28.7934	−	24.1605i	−1.12677	−	0.945474i	−0.998927	+	0.0463201i	$0.985251\pi$
$654$		0			0
$655$	−6.21547	−	2.26225i	−0.242859	−	0.0883933i
$656$		0			0
$657$	−17.0611	+	15.1279i	−0.665615	+	0.590194i
$658$		0			0
$659$	−10.0088	+	8.39836i	−0.389887	+	0.327154i	−0.816569	−	0.577248i	$-0.804127\pi$
$659$	−10.0088	+	8.39836i	−0.389887	+	0.327154i	0.426682	+	0.904401i	$0.359682\pi$
$660$		0			0
$661$	−7.64676	+	43.3669i	−0.297425	+	1.68678i	0.359757	+	0.933046i	$0.382860\pi$
$661$	−7.64676	+	43.3669i	−0.297425	+	1.68678i	−0.657182	+	0.753732i	$0.728252\pi$
$662$		0			0
$663$	−2.86281	+	0.545155i	−0.111182	+	0.0211721i
$664$		0			0
$665$	−1.43875	+	2.49200i	−0.0557925	+	0.0966355i
$666$		0			0
$667$	4.63856	+	8.03422i	0.179606	+	0.311086i
$668$		0			0
$669$	−21.9843	+	13.0957i	−0.849962	+	0.506308i
$670$		0			0
$671$	−18.4090	+	6.70034i	−0.710673	+	0.258664i
$672$		0			0
$673$	−0.336965	−	1.91102i	−0.0129891	−	0.0736646i	0.977624	−	0.210359i	$-0.0674633\pi$
$673$	−0.336965	−	1.91102i	−0.0129891	−	0.0736646i	−0.990613	+	0.136694i	$0.956352\pi$
$674$		0			0
$675$	6.62157	−	20.8041i	0.254864	−	0.800749i
$676$		0			0
$677$	−5.65333	−	32.0617i	−0.217275	−	1.23223i	−0.876914	−	0.480647i	$-0.840402\pi$
$677$	−5.65333	−	32.0617i	−0.217275	−	1.23223i	0.659639	−	0.751583i	$-0.270709\pi$
$678$		0			0
$679$	3.37446	−	1.22820i	0.129500	−	0.0471341i
$680$		0			0
$681$	0.0984246	+	7.21517i	0.00377164	+	0.276486i
$682$		0			0
$683$	−8.97980	−	15.5535i	−0.343602	−	0.595137i	0.641496	−	0.767126i	$-0.278314\pi$
$683$	−8.97980	−	15.5535i	−0.343602	−	0.595137i	−0.985099	+	0.171989i	$0.944981\pi$
$684$		0			0
$685$	4.44793	−	7.70405i	0.169947	−	0.294357i
$686$		0			0
$687$	−3.41024	−	3.95338i	−0.130109	−	0.150831i
$688$		0			0
$689$	1.52121	−	8.62721i	0.0579535	−	0.328670i
$690$		0			0
$691$	−22.9979	+	19.2976i	−0.874883	+	0.734114i	−0.965120	−	0.261807i	$-0.915682\pi$
$691$	−22.9979	+	19.2976i	−0.874883	+	0.734114i	0.0902377	+	0.995920i	$0.471237\pi$
$692$		0			0
$693$	−7.67385	−	12.4917i	−0.291506	−	0.474520i
$694$		0			0
$695$	−2.59221	−	0.943489i	−0.0983283	−	0.0357886i
$696$		0			0
$697$	−2.09950	−	1.76169i	−0.0795241	−	0.0667286i
$698$		0			0
$699$	−7.62802	−	20.1004i	−0.288518	−	0.760267i
$700$		0			0
$701$	38.7016			1.46174			0.730869	−	0.682518i	$-0.239115\pi$
$701$	38.7016			1.46174			0.730869	+	0.682518i	$0.239115\pi$
$702$		0			0
$703$	0.743142			0.0280281
$704$		0			0
$705$	−16.3790	−	2.65823i	−0.616868	−	0.100115i
$706$		0			0
$707$	−6.97195	−	5.85016i	−0.262207	−	0.220018i
$708$		0			0
$709$	14.9715	+	5.44919i	0.562267	+	0.204648i	0.607488	−	0.794329i	$-0.292177\pi$
$709$	14.9715	+	5.44919i	0.562267	+	0.204648i	−0.0452214	+	0.998977i	$0.514399\pi$
$710$		0			0
$711$	25.6587	−	10.1399i	0.962278	−	0.380276i
$712$		0			0
$713$	1.23070	−	1.03268i	0.0460901	−	0.0386742i
$714$		0			0
$715$	3.48359	−	19.7564i	0.130279	−	0.738848i
$716$		0			0
$717$	15.6048	−	44.7645i	0.582772	−	1.67176i
$718$		0			0
$719$	−23.9026	+	41.4005i	−0.891417	+	1.54398i	−0.0532387	+	0.998582i	$0.516954\pi$
$719$	−23.9026	+	41.4005i	−0.891417	+	1.54398i	−0.838178	+	0.545397i	$0.816379\pi$
$720$		0			0
$721$	5.97928	+	10.3564i	0.222680	+	0.385693i
$722$		0			0
$723$	−31.4074	−	17.5663i	−1.16805	−	0.653297i
$724$		0			0
$725$	14.7017	−	5.35097i	0.546007	−	0.198730i
$726$		0			0
$727$	−7.61418	−	43.1821i	−0.282394	−	1.60154i	−0.714448	−	0.699689i	$-0.753322\pi$
$727$	−7.61418	−	43.1821i	−0.282394	−	1.60154i	0.432053	−	0.901848i	$-0.357789\pi$
$728$		0			0
$729$	15.3664	+	22.2008i	0.569125	+	0.822251i
$730$		0			0
$731$	−0.00662034	−	0.0375458i	−0.000244862	−	0.00138868i
$732$		0			0
$733$	−9.80719	+	3.56953i	−0.362237	+	0.131843i	−0.516725	−	0.856151i	$-0.672849\pi$
$733$	−9.80719	+	3.56953i	−0.362237	+	0.131843i	0.154489	+	0.987995i	$0.450627\pi$
$734$		0			0
$735$	−1.35069	−	0.755444i	−0.0498208	−	0.0278650i
$736$		0			0
$737$	−31.2364	−	54.1030i	−1.15061	−	1.99291i
$738$		0			0
$739$	22.4731	−	38.9246i	0.826686	−	1.43186i	−0.0739372	−	0.997263i	$-0.523556\pi$
$739$	22.4731	−	38.9246i	0.826686	−	1.43186i	0.900624	−	0.434600i	$-0.143110\pi$
$740$		0			0
$741$	−8.43596	+	24.1997i	−0.309903	+	0.888997i
$742$		0			0
$743$	1.39131	−	7.89049i	0.0510421	−	0.289474i	−0.948593	−	0.316500i	$-0.897492\pi$
$743$	1.39131	−	7.89049i	0.0510421	−	0.289474i	0.999635	+	0.0270255i	$0.00860352\pi$
$744$		0			0
$745$	−5.95399	+	4.99599i	−0.218137	+	0.183039i
$746$		0			0
$747$	42.4733	−	16.7847i	1.55402	−	0.614120i
$748$		0			0
$749$	9.06102	+	3.29794i	0.331082	+	0.120504i
$750$		0			0
$751$	−22.2618	−	18.6798i	−0.812344	−	0.681637i	0.138822	−	0.990317i	$-0.455668\pi$
$751$	−22.2618	−	18.6798i	−0.812344	−	0.681637i	−0.951166	+	0.308680i	$0.900113\pi$
$752$		0			0
$753$	36.7326	+	5.96153i	1.33861	+	0.217250i
$754$		0			0
$755$	5.89615			0.214583
$756$		0			0
$757$	34.1940			1.24280			0.621401	−	0.783493i	$-0.286564\pi$
$757$	34.1940			1.24280			0.621401	+	0.783493i	$0.286564\pi$
$758$		0			0
$759$	7.48223	+	19.7162i	0.271588	+	0.715654i
$760$		0			0
$761$	30.8097	+	25.8524i	1.11685	+	0.937148i	0.998441	−	0.0558168i	$-0.0177763\pi$
$761$	30.8097	+	25.8524i	1.11685	+	0.937148i	0.118409	+	0.992965i	$0.462221\pi$
$762$		0			0
$763$	−18.1248	−	6.59691i	−0.656164	−	0.238824i
$764$		0			0
$765$	0.513827	+	0.836421i	0.0185775	+	0.0302409i
$766$		0			0
$767$	1.18961	−	0.998204i	0.0429544	−	0.0360430i
$768$		0			0
$769$	5.66421	−	32.1234i	0.204257	−	1.15840i	−0.694348	−	0.719639i	$-0.744307\pi$
$769$	5.66421	−	32.1234i	0.204257	−	1.15840i	0.898605	−	0.438759i	$-0.144582\pi$
$770$		0			0
$771$	−30.1403	−	34.9406i	−1.08547	−	1.25835i
$772$		0			0
$773$	−21.5551	+	37.3345i	−0.775282	+	1.34283i	0.159353	+	0.987222i	$0.449059\pi$
$773$	−21.5551	+	37.3345i	−0.775282	+	1.34283i	−0.934636	+	0.355607i	$0.884274\pi$
$774$		0			0
$775$	−1.35468	−	2.34638i	−0.0486616	−	0.0842843i
$776$		0			0
$777$	0.00545167	+	0.399643i	0.000195578	+	0.0143371i
$778$		0			0
$779$	−22.6481	+	8.24325i	−0.811454	+	0.295345i
$780$		0			0
$781$	−4.30111	−	24.3928i	−0.153906	−	0.872844i
$782$		0			0
$783$	−5.86817	+	18.4370i	−0.209711	+	0.658883i
$784$		0			0
$785$	−1.06716	−	6.05219i	−0.0380887	−	0.216012i
$786$		0			0
$787$	−26.6167	+	9.68767i	−0.948781	+	0.345328i	−0.769628	−	0.638493i	$-0.779558\pi$
$787$	−26.6167	+	9.68767i	−0.948781	+	0.345328i	−0.179154	+	0.983821i	$0.557336\pi$
$788$		0			0
$789$	−33.7407	+	20.0988i	−1.20120	+	0.715535i
$790$		0			0
$791$	4.07576	+	7.05942i	0.144917	+	0.251004i
$792$		0			0
$793$	−9.20916	+	15.9507i	−0.327027	+	0.566427i
$794$		0			0
$795$	−2.89874	+	0.551996i	−0.102808	+	0.0195773i
$796$		0			0
$797$	−0.0299368	+	0.169780i	−0.00106042	+	0.00601392i	−0.985333	−	0.170640i	$-0.945416\pi$
$797$	−0.0299368	+	0.169780i	−0.00106042	+	0.00601392i	0.984273	+	0.176654i	$0.0565275\pi$
$798$		0			0
$799$	−3.00790	+	2.52393i	−0.106412	+	0.0892903i
$800$		0			0
$801$	2.22010	−	1.96854i	0.0784432	−	0.0695548i
$802$		0			0
$803$	−34.9032	−	12.7037i	−1.23171	−	0.448305i
$804$		0			0
$805$	1.70531	+	1.43092i	0.0601042	+	0.0504334i
$806$		0			0
$807$	17.3331	−	21.2385i	0.610154	−	0.747631i
$808$		0			0
$809$	−15.4465			−0.543070			−0.271535	−	0.962429i	$-0.587531\pi$
$809$	−15.4465			−0.543070			−0.271535	+	0.962429i	$0.587531\pi$
$810$		0			0
$811$	−27.8000			−0.976189			−0.488095	−	0.872791i	$-0.662308\pi$
$811$	−27.8000			−0.976189			−0.488095	+	0.872791i	$0.662308\pi$
$812$		0			0
$813$	−31.6934	+	38.8344i	−1.11154	+	1.36198i
$814$		0			0
$815$	−15.7465	−	13.2129i	−0.551577	−	0.462828i
$816$		0			0
$817$	−0.315051	−	0.114669i	−0.0110223	−	0.00401177i
$818$		0			0
$819$	−13.0759	−	4.35911i	−0.456907	−	0.152320i
$820$		0			0
$821$	19.4435	−	16.3151i	0.678584	−	0.569400i	−0.237008	−	0.971508i	$-0.576167\pi$
$821$	19.4435	−	16.3151i	0.678584	−	0.569400i	0.915592	+	0.402108i	$0.131722\pi$
$822$		0			0
$823$	2.95460	−	16.7564i	0.102991	−	0.584090i	−0.889013	−	0.457882i	$-0.848608\pi$
$823$	2.95460	−	16.7564i	0.102991	−	0.584090i	0.992004	−	0.126208i	$-0.0402807\pi$
$824$		0			0
$825$	34.9360	−	6.65274i	1.21632	−	0.231619i
$826$		0			0
$827$	−9.25164	+	16.0243i	−0.321711	+	0.557220i	−0.980841	−	0.194809i	$-0.937591\pi$
$827$	−9.25164	+	16.0243i	−0.321711	+	0.557220i	0.659130	+	0.752029i	$0.270925\pi$
$828$		0			0
$829$	13.1951	+	22.8546i	0.458286	+	0.793775i	0.998871	−	0.0475152i	$-0.0151302\pi$
$829$	13.1951	+	22.8546i	0.458286	+	0.793775i	−0.540585	+	0.841290i	$0.681797\pi$
$830$		0			0
$831$	14.4511	−	8.60828i	0.501304	−	0.298618i
$832$		0			0
$833$	−0.344128	+	0.125252i	−0.0119233	+	0.00433974i
$834$		0			0
$835$	1.53330	+	8.69580i	0.0530622	+	0.300930i
$836$		0			0
$837$	3.32079	+	0.446354i	0.114783	+	0.0154283i
$838$		0			0
$839$	6.05748	+	34.3536i	0.209127	+	1.18602i	0.890811	+	0.454373i	$0.150137\pi$
$839$	6.05748	+	34.3536i	0.209127	+	1.18602i	−0.681684	+	0.731647i	$0.738752\pi$
$840$		0			0
$841$	14.2222	−	5.17645i	0.490420	−	0.178498i
$842$		0			0
$843$	0.154003	+	11.2894i	0.00530414	+	0.388828i
$844$		0			0
$845$	−3.62265	−	6.27462i	−0.124623	−	0.215853i
$846$		0			0
$847$	6.44058	−	11.1554i	0.221301	−	0.383305i
$848$		0			0
$849$	−25.6291	−	29.7109i	−0.879588	−	1.01968i
$850$		0			0
$851$	0.0998329	−	0.566181i	0.00342223	−	0.0194084i
$852$		0			0
$853$	−6.76882	+	5.67972i	−0.231760	+	0.194470i	−0.751271	−	0.659994i	$-0.770559\pi$
$853$	−6.76882	+	5.67972i	−0.231760	+	0.194470i	0.519511	+	0.854464i	$0.326114\pi$
$854$		0			0
$855$	8.62932	−	0.235475i	0.295116	−	0.00805307i
$856$		0			0
$857$	−15.2789	−	5.56108i	−0.521919	−	0.189963i	0.0676076	−	0.997712i	$-0.478463\pi$
$857$	−15.2789	−	5.56108i	−0.521919	−	0.189963i	−0.589526	+	0.807749i	$0.700686\pi$
$858$		0			0
$859$	−4.36299	−	3.66098i	−0.148863	−	0.124911i	0.565315	−	0.824875i	$-0.308755\pi$
$859$	−4.36299	−	3.66098i	−0.148863	−	0.124911i	−0.714178	+	0.699964i	$0.753199\pi$
$860$		0			0
$861$	−4.59915	−	12.1191i	−0.156739	−	0.413018i
$862$		0			0
$863$	48.4940			1.65076			0.825378	−	0.564581i	$-0.190962\pi$
$863$	48.4940			1.65076			0.825378	+	0.564581i	$0.190962\pi$
$864$		0			0
$865$	10.7799			0.366529
$866$		0			0
$867$	−28.8353	−	4.67983i	−0.979298	−	0.158935i
$868$		0			0
$869$	34.4276	+	28.8882i	1.16788	+	0.979964i
$870$		0			0
$871$	−55.1926	−	20.0885i	−1.87013	−	0.680672i
$872$		0			0
$873$	−8.43847	−	6.69711i	−0.285599	−	0.226663i
$874$		0			0
$875$	6.29820	−	5.28482i	0.212918	−	0.178659i
$876$		0			0
$877$	8.97467	−	50.8979i	0.303053	−	1.71870i	−0.329477	−	0.944164i	$-0.606872\pi$
$877$	8.97467	−	50.8979i	0.303053	−	1.71870i	0.632530	−	0.774536i	$-0.282017\pi$
$878$		0			0
$879$	−11.3993	+	32.7005i	−0.384489	+	1.10296i
$880$		0			0
$881$	−15.9983	+	27.7098i	−0.538995	+	0.933566i	0.459964	+	0.887938i	$0.347862\pi$
$881$	−15.9983	+	27.7098i	−0.538995	+	0.933566i	−0.998958	+	0.0456286i	$0.985471\pi$
$882$		0			0
$883$	−2.12219	−	3.67574i	−0.0714173	−	0.123698i	0.828105	−	0.560572i	$-0.189419\pi$
$883$	−2.12219	−	3.67574i	−0.0714173	−	0.123698i	−0.899523	+	0.436874i	$0.856086\pi$
$884$		0			0
$885$	−0.456535	−	0.255342i	−0.0153462	−	0.00858322i
$886$		0			0
$887$	18.2834	−	6.65462i	0.613897	−	0.223440i	−0.0163107	−	0.999867i	$-0.505192\pi$
$887$	18.2834	−	6.65462i	0.613897	−	0.223440i	0.630207	+	0.776427i	$0.282970\pi$
$888$		0			0
$889$	−3.28671	−	18.6399i	−0.110233	−	0.625161i
$890$		0			0
$891$	−19.8808	+	39.2317i	−0.666033	+	1.31431i
$892$		0			0
$893$	5.99606	+	34.0053i	0.200650	+	1.13794i
$894$		0			0
$895$	−17.4274	+	6.34306i	−0.582534	+	0.212025i
$896$		0			0
$897$	17.3038	+	9.67810i	0.577758	+	0.323142i
$898$		0			0
$899$	1.20054	+	2.07940i	0.0400404	+	0.0693520i
$900$		0			0
$901$	−0.349133	+	0.604716i	−0.0116313	+	0.0201460i
$902$		0			0
$903$	0.0593550	−	0.170268i	0.00197521	−	0.00566616i
$904$		0			0
$905$	2.70396	−	15.3349i	0.0898828	−	0.509751i
$906$		0			0
$907$	35.1526	−	29.4966i	1.16722	−	0.979417i	0.167245	−	0.985915i	$-0.446513\pi$
$907$	35.1526	−	29.4966i	1.16722	−	0.979417i	0.999979	+	0.00649789i	$0.00206836\pi$
$908$		0			0
$909$	−4.00601	+	27.0082i	−0.132871	+	0.895806i
$910$		0			0
$911$	12.7410	+	4.63734i	0.422128	+	0.153642i	0.544345	−	0.838861i	$-0.316778\pi$
$911$	12.7410	+	4.63734i	0.422128	+	0.153642i	−0.122217	+	0.992503i	$0.539000\pi$
$912$		0			0
$913$	56.9885	+	47.8190i	1.88604	+	1.58258i
$914$		0			0
$915$	6.12391	+	0.993882i	0.202450	+	0.0328567i
$916$		0			0
$917$	−7.40273			−0.244460
$918$		0			0
$919$	6.28122			0.207198			0.103599	−	0.994619i	$-0.466964\pi$
$919$	6.28122			0.207198			0.103599	+	0.994619i	$0.466964\pi$
$920$		0			0
$921$	−11.8376	−	31.1930i	−0.390063	−	1.02784i
$922$		0			0
$923$	−17.8389	−	14.9687i	−0.587176	−	0.492699i
$924$		0			0
$925$	−0.911082	−	0.331607i	−0.0299562	−	0.0109032i
$926$		0			0
$927$	17.0837	−	31.5470i	0.561101	−	1.03614i
$928$		0			0
$929$	−2.96548	+	2.48833i	−0.0972941	+	0.0816395i	−0.690137	−	0.723678i	$-0.742450\pi$
$929$	−2.96548	+	2.48833i	−0.0972941	+	0.0816395i	0.592843	+	0.805318i	$0.298005\pi$
$930$		0			0
$931$	−0.559230	+	3.17155i	−0.0183280	+	0.103943i
$932$		0			0
$933$	16.2175	+	18.8004i	0.530938	+	0.615498i
$934$		0			0
$935$	−0.799519	+	1.38481i	−0.0261471	+	0.0452881i
$936$		0			0
$937$	−0.905715	−	1.56874i	−0.0295884	−	0.0512487i	0.850852	−	0.525405i	$-0.176086\pi$
$937$	−0.905715	−	1.56874i	−0.0295884	−	0.0512487i	−0.880440	+	0.474157i	$0.842753\pi$
$938$		0			0
$939$	−0.0805377	−	5.90394i	−0.00262825	−	0.192668i
$940$		0			0
$941$	38.6899	−	14.0820i	1.26125	−	0.459059i	0.377065	−	0.926187i	$-0.376933\pi$
$941$	38.6899	−	14.0820i	1.26125	−	0.459059i	0.884190	+	0.467128i	$0.154711\pi$
$942$		0			0
$943$	3.23779	+	18.3624i	0.105437	+	0.597963i
$944$		0			0
$945$	0.189937	+	4.63890i	0.00617864	+	0.150903i
$946$		0			0
$947$	6.23602	+	35.3662i	0.202643	+	1.14925i	0.901105	+	0.433601i	$0.142757\pi$
$947$	6.23602	+	35.3662i	0.202643	+	1.14925i	−0.698462	+	0.715647i	$0.746132\pi$
$948$		0			0
$949$	−32.8148	+	11.9436i	−1.06521	+	0.387706i
$950$		0			0
$951$	−37.0577	+	22.0747i	−1.20168	+	0.715820i
$952$		0			0
$953$	30.3313	+	52.5353i	0.982526	+	1.70178i	0.652454	+	0.757828i	$0.273740\pi$
$953$	30.3313	+	52.5353i	0.982526	+	1.70178i	0.330071	+	0.943956i	$0.392927\pi$
$954$		0			0
$955$	0.945774	−	1.63813i	0.0306045	−	0.0530086i
$956$		0			0
$957$	−30.9610	+	5.89579i	−1.00083	+	0.190584i
$958$		0			0
$959$	1.72887	−	9.80490i	0.0558281	−	0.316617i
$960$		0			0
$961$	−23.4288	+	19.6591i	−0.755769	+	0.634166i
$962$		0			0
$963$	−5.79845	−	28.3405i	−0.186852	−	0.913260i
$964$		0			0
$965$	17.1367	+	6.23724i	0.551649	+	0.200784i
$966$		0			0
$967$	22.1183	+	18.5595i	0.711278	+	0.596833i	0.924957	−	0.380071i	$-0.124100\pi$
$967$	22.1183	+	18.5595i	0.711278	+	0.596833i	−0.213680	+	0.976904i	$0.568545\pi$
$968$		0			0
$969$	1.29159	−	1.58260i	0.0414918	−	0.0508405i
$970$		0			0
$971$	23.8246			0.764569			0.382284	−	0.924045i	$-0.375137\pi$
$971$	23.8246			0.764569			0.382284	+	0.924045i	$0.375137\pi$
$972$		0			0
$973$	−3.08737			−0.0989764
$974$		0			0
$975$	21.1408	−	25.9042i	0.677048	−	0.829597i
$976$		0			0
$977$	18.6211	+	15.6250i	0.595742	+	0.499887i	0.890074	−	0.455816i	$-0.150653\pi$
$977$	18.6211	+	15.6250i	0.595742	+	0.499887i	−0.294332	+	0.955703i	$0.595097\pi$
$978$		0			0
$979$	4.54184	+	1.65309i	0.145158	+	0.0528331i
$980$		0			0
$981$	11.5987	+	56.6898i	0.370318	+	1.80997i
$982$		0			0
$983$	21.2589	−	17.8384i	0.678055	−	0.568956i	−0.237382	−	0.971416i	$-0.576289\pi$
$983$	21.2589	−	17.8384i	0.678055	−	0.568956i	0.915437	+	0.402461i	$0.131845\pi$
$984$		0			0
$985$	2.00162	−	11.3518i	0.0637770	−	0.361697i
$986$		0			0
$987$	−18.2432	+	3.47399i	−0.580688	+	0.110578i
$988$		0			0
$989$	−0.129687	+	0.224625i	−0.00412381	+	0.00714265i
$990$		0			0
$991$	6.39172	+	11.0708i	0.203040	+	0.351675i	0.949506	−	0.313748i	$-0.101585\pi$
$991$	6.39172	+	11.0708i	0.203040	+	0.351675i	−0.746467	+	0.665423i	$0.768251\pi$
$992$		0			0
$993$	−37.3240	+	22.2333i	−1.18444	+	0.705552i
$994$		0			0
$995$	−3.43630	+	1.25071i	−0.108938	+	0.0396502i
$996$		0			0
$997$	−4.92145	−	27.9109i	−0.155864	−	0.883948i	−0.957992	−	0.286796i	$-0.907410\pi$
$997$	−4.92145	−	27.9109i	−0.155864	−	0.883948i	0.802128	−	0.597152i	$-0.203701\pi$
$998$		0			0
$999$	1.01300	−	0.641499i	0.0320500	−	0.0202961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.337.2	✓	54
27.25	even	9	inner	756.2.bo.b.673.2	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.337.2	✓	54	1.1	even	1	trivial
756.2.bo.b.673.2	yes	54	27.25	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09514 + 1.34189i) q^{3} +(0.684464 + 0.574334i) q^{5} +(0.939693 + 0.342020i) q^{7} +(-0.601340 - 2.93911i) q^{9} +O(q^{10})\)	\(q+(-1.09514 + 1.34189i) q^{3} +(0.684464 + 0.574334i) q^{5} +(0.939693 + 0.342020i) q^{7} +(-0.601340 - 2.93911i) q^{9} +(3.74353 - 3.14120i) q^{11} +(0.797816 - 4.52464i) q^{13} +(-1.52028 + 0.289501i) q^{15} +(-0.183107 + 0.317150i) q^{17} +(1.61024 + 2.78901i) q^{19} +(-1.48805 + 0.886405i) q^{21} +(2.34120 - 0.852125i) q^{23} +(-0.729609 - 4.13782i) q^{25} +(4.60252 + 2.41181i) q^{27} +(0.646594 + 3.66701i) q^{29} +(0.605945 - 0.220546i) q^{31} +(0.115453 + 8.46346i) q^{33} +(0.446752 + 0.773797i) q^{35} +(0.115378 - 0.199840i) q^{37} +(5.19785 + 6.02569i) q^{39} +(-1.29956 + 7.37018i) q^{41} +(-0.0797498 + 0.0669180i) q^{43} +(1.27644 - 2.35709i) q^{45} +(10.0754 + 3.66714i) q^{47} +(0.766044 + 0.642788i) q^{49} +(-0.225054 - 0.593033i) q^{51} +1.90672 q^{53} +4.36641 q^{55} +(-5.50599 - 0.893596i) q^{57} +(0.258925 + 0.217263i) q^{59} +(-3.76707 - 1.37110i) q^{61} +(0.440161 - 2.96753i) q^{63} +(3.14473 - 2.63874i) q^{65} +(2.21990 - 12.5897i) q^{67} +(-1.42048 + 4.07482i) q^{69} +(2.53427 - 4.38948i) q^{71} +(-3.80034 - 6.58238i) q^{73} +(6.35152 + 3.55243i) q^{75} +(4.59212 - 1.67140i) q^{77} +(1.59696 + 9.05683i) q^{79} +(-8.27678 + 3.53482i) q^{81} +(2.64348 + 14.9919i) q^{83} +(-0.307480 + 0.111914i) q^{85} +(-5.62884 - 3.14823i) q^{87} +(0.494525 + 0.856542i) q^{89} +(2.29722 - 3.97890i) q^{91} +(-0.367645 + 1.05464i) q^{93} +(-0.499674 + 2.83379i) q^{95} +(2.75088 - 2.30827i) q^{97} +(-11.4835 - 9.11374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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