LMFDB - Embedded newform 756.2.bo.b.337.1

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			337.1
Character	$\chi$	$=$	756.337
Dual form			756.2.bo.b.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70391 - 0.310978i) q^{3} +(-2.38170 - 1.99849i) q^{5} +(0.939693 + 0.342020i) q^{7} +(2.80659 + 1.05975i) q^{9} +O(q^{10})$	\(q+(-1.70391 - 0.310978i) q^{3} +(-2.38170 - 1.99849i) q^{5} +(0.939693 + 0.342020i) q^{7} +(2.80659 + 1.05975i) q^{9} +(4.15526 - 3.48667i) q^{11} +(-0.190166 + 1.07849i) q^{13} +(3.43671 + 4.14589i) q^{15} +(0.237967 - 0.412171i) q^{17} +(-1.56684 - 2.71385i) q^{19} +(-1.49479 - 0.874994i) q^{21} +(-7.29424 + 2.65489i) q^{23} +(0.810322 + 4.59556i) q^{25} +(-4.45259 - 2.67851i) q^{27} +(-1.60322 - 9.09232i) q^{29} +(-8.05103 + 2.93034i) q^{31} +(-8.16444 + 4.64877i) q^{33} +(-1.55455 - 2.69255i) q^{35} +(-3.30702 + 5.72792i) q^{37} +(0.659412 - 1.77850i) q^{39} +(0.120907 - 0.685699i) q^{41} +(-0.949211 + 0.796483i) q^{43} +(-4.56655 - 8.13294i) q^{45} +(-7.35323 - 2.67636i) q^{47} +(0.766044 + 0.642788i) q^{49} +(-0.533649 + 0.628298i) q^{51} +9.89793 q^{53} -16.8647 q^{55} +(1.82580 + 5.11140i) q^{57} +(0.605737 + 0.508274i) q^{59} +(-2.61812 - 0.952917i) q^{61} +(2.27487 + 1.95575i) q^{63} +(2.60826 - 2.18859i) q^{65} +(-0.320755 + 1.81909i) q^{67} +(13.2543 - 2.25533i) q^{69} +(-4.66476 + 8.07960i) q^{71} +(2.65253 + 4.59432i) q^{73} +(0.0484081 - 8.08240i) q^{75} +(5.09718 - 1.85522i) q^{77} +(-2.89655 - 16.4272i) q^{79} +(6.75384 + 5.94858i) q^{81} +(-0.727975 - 4.12855i) q^{83} +(-1.39048 + 0.506095i) q^{85} +(-0.0957754 + 15.9910i) q^{87} +(-6.24740 - 10.8208i) q^{89} +(-0.547563 + 0.948406i) q^{91} +(14.6295 - 2.48932i) q^{93} +(-1.69184 + 9.59491i) q^{95} +(2.89008 - 2.42506i) q^{97} +(15.3571 - 5.38210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.70391	−	0.310978i	−0.983750	−	0.179543i
$3$	−1.70391	−	0.310978i	−0.983750	−	0.179543i
$4$		0			0
$5$	−2.38170	−	1.99849i	−1.06513	−	0.893750i	−0.0705277	−	0.997510i	$-0.522468\pi$
$5$	−2.38170	−	1.99849i	−1.06513	−	0.893750i	−0.994602	+	0.103760i	$0.966913\pi$
$6$		0			0
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$8$		0			0
$9$	2.80659	+	1.05975i	0.935528	+	0.353251i
$10$		0			0
$11$	4.15526	−	3.48667i	1.25286	−	1.05127i	0.256452	−	0.966557i	$-0.417447\pi$
$11$	4.15526	−	3.48667i	1.25286	−	1.05127i	0.996405	−	0.0847146i	$-0.0269979\pi$
$12$		0			0
$13$	−0.190166	+	1.07849i	−0.0527427	+	0.299119i	−0.999756	−	0.0220747i	$-0.992973\pi$
$13$	−0.190166	+	1.07849i	−0.0527427	+	0.299119i	0.947014	+	0.321193i	$0.104084\pi$
$14$		0			0
$15$	3.43671	+	4.14589i	0.887355	+	1.07046i
$16$		0			0
$17$	0.237967	−	0.412171i	0.0577155	−	0.0999661i	−0.835724	−	0.549150i	$-0.814952\pi$
$17$	0.237967	−	0.412171i	0.0577155	−	0.0999661i	0.893440	+	0.449183i	$0.148285\pi$
$18$		0			0
$19$	−1.56684	−	2.71385i	−0.359459	−	0.622601i	0.628412	−	0.777881i	$-0.283705\pi$
$19$	−1.56684	−	2.71385i	−0.359459	−	0.622601i	−0.987870	+	0.155280i	$0.950372\pi$
$20$		0			0
$21$	−1.49479	−	0.874994i	−0.326189	−	0.190939i
$22$		0			0
$23$	−7.29424	+	2.65489i	−1.52095	+	0.553582i	−0.961386	−	0.275203i	$-0.911255\pi$
$23$	−7.29424	+	2.65489i	−1.52095	+	0.553582i	−0.559568	+	0.828785i	$0.689033\pi$
$24$		0			0
$25$	0.810322	+	4.59556i	0.162064	+	0.919113i
$26$		0			0
$27$	−4.45259	−	2.67851i	−0.856902	−	0.515479i
$28$		0			0
$29$	−1.60322	−	9.09232i	−0.297711	−	1.68840i	−0.655976	−	0.754782i	$-0.727743\pi$
$29$	−1.60322	−	9.09232i	−0.297711	−	1.68840i	0.358265	−	0.933620i	$-0.383368\pi$
$30$		0			0
$31$	−8.05103	+	2.93034i	−1.44601	+	0.526304i	−0.941473	−	0.337087i	$-0.890558\pi$
$31$	−8.05103	+	2.93034i	−1.44601	+	0.526304i	−0.504535	+	0.863391i	$0.668336\pi$
$32$		0			0
$33$	−8.16444	+	4.64877i	−1.42125	+	0.809247i
$34$		0			0
$35$	−1.55455	−	2.69255i	−0.262766	−	0.455125i
$36$		0			0
$37$	−3.30702	+	5.72792i	−0.543670	+	0.941664i	0.455019	+	0.890482i	$0.349632\pi$
$37$	−3.30702	+	5.72792i	−0.543670	+	0.941664i	−0.998689	+	0.0511824i	$0.983701\pi$
$38$		0			0
$39$	0.659412	−	1.77850i	0.105590	−	0.284788i
$40$		0			0
$41$	0.120907	−	0.685699i	0.0188825	−	0.107088i	−0.973910	−	0.226935i	$-0.927129\pi$
$41$	0.120907	−	0.685699i	0.0188825	−	0.107088i	0.992792	+	0.119847i	$0.0382405\pi$
$42$		0			0
$43$	−0.949211	+	0.796483i	−0.144753	+	0.121462i	−0.712289	−	0.701886i	$-0.752341\pi$
$43$	−0.949211	+	0.796483i	−0.144753	+	0.121462i	0.567536	+	0.823349i	$0.307897\pi$
$44$		0			0
$45$	−4.56655	−	8.13294i	−0.680741	−	1.21239i
$46$		0			0
$47$	−7.35323	−	2.67636i	−1.07258	−	0.390387i	−0.255438	−	0.966825i	$-0.582220\pi$
$47$	−7.35323	−	2.67636i	−1.07258	−	0.390387i	−0.817140	+	0.576439i	$0.804442\pi$
$48$		0			0
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$		0			0
$51$	−0.533649	+	0.628298i	−0.0747258	+	0.0879793i
$52$		0			0
$53$	9.89793			1.35959			0.679793	−	0.733404i	$-0.262070\pi$
$53$	9.89793			1.35959			0.679793	+	0.733404i	$0.262070\pi$
$54$		0			0
$55$	−16.8647			−2.27403
$56$		0			0
$57$	1.82580	+	5.11140i	0.241834	+	0.677022i
$58$		0			0
$59$	0.605737	+	0.508274i	0.0788603	+	0.0661716i	0.681366	−	0.731943i	$-0.261386\pi$
$59$	0.605737	+	0.508274i	0.0788603	+	0.0661716i	−0.602505	+	0.798115i	$0.705831\pi$
$60$		0			0
$61$	−2.61812	−	0.952917i	−0.335216	−	0.122009i	0.168928	−	0.985628i	$-0.445970\pi$
$61$	−2.61812	−	0.952917i	−0.335216	−	0.122009i	−0.504144	+	0.863620i	$0.668192\pi$
$62$		0			0
$63$	2.27487	+	1.95575i	0.286607	+	0.246402i
$64$		0			0
$65$	2.60826	−	2.18859i	0.323515	−	0.271462i
$66$		0			0
$67$	−0.320755	+	1.81909i	−0.0391865	+	0.222237i	−0.998112	−	0.0614205i	$-0.980437\pi$
$67$	−0.320755	+	1.81909i	−0.0391865	+	0.222237i	0.958926	+	0.283658i	$0.0915480\pi$
$68$		0			0
$69$	13.2543	−	2.25533i	1.59563	−	0.271509i
$70$		0			0
$71$	−4.66476	+	8.07960i	−0.553605	+	0.958872i	0.444405	+	0.895826i	$0.353415\pi$
$71$	−4.66476	+	8.07960i	−0.553605	+	0.958872i	−0.998011	+	0.0630466i	$0.979918\pi$
$72$		0			0
$73$	2.65253	+	4.59432i	0.310455	+	0.537724i	0.978461	−	0.206432i	$-0.0661852\pi$
$73$	2.65253	+	4.59432i	0.310455	+	0.537724i	−0.668006	+	0.744156i	$0.732852\pi$
$74$		0			0
$75$	0.0484081	−	8.08240i	0.00558969	−	0.933275i
$76$		0			0
$77$	5.09718	−	1.85522i	0.580877	−	0.211422i
$78$		0			0
$79$	−2.89655	−	16.4272i	−0.325888	−	1.84820i	−0.503362	−	0.864076i	$-0.667904\pi$
$79$	−2.89655	−	16.4272i	−0.325888	−	1.84820i	0.177474	−	0.984125i	$-0.443207\pi$
$80$		0			0
$81$	6.75384	+	5.94858i	0.750427	+	0.660954i
$82$		0			0
$83$	−0.727975	−	4.12855i	−0.0799056	−	0.453167i	−0.998340	−	0.0575942i	$-0.981657\pi$
$83$	−0.727975	−	4.12855i	−0.0799056	−	0.453167i	0.918434	−	0.395573i	$-0.129454\pi$
$84$		0			0
$85$	−1.39048	+	0.506095i	−0.150819	+	0.0548937i
$86$		0			0
$87$	−0.0957754	+	15.9910i	−0.0102682	+	1.71442i
$88$		0			0
$89$	−6.24740	−	10.8208i	−0.662223	−	1.14700i	−0.980030	−	0.198848i	$-0.936280\pi$
$89$	−6.24740	−	10.8208i	−0.662223	−	1.14700i	0.317808	−	0.948155i	$-0.397053\pi$
$90$		0			0
$91$	−0.547563	+	0.948406i	−0.0574002	+	0.0994200i
$92$		0			0
$93$	14.6295	−	2.48932i	1.51700	−	0.258130i
$94$		0			0
$95$	−1.69184	+	9.59491i	−0.173579	+	0.984417i
$96$		0			0
$97$	2.89008	−	2.42506i	0.293443	−	0.246228i	−0.484166	−	0.874976i	$-0.660877\pi$
$97$	2.89008	−	2.42506i	0.293443	−	0.246228i	0.777609	+	0.628748i	$0.216432\pi$
$98$		0			0
$99$	15.3571	−	5.38210i	1.54345	−	0.540921i
$100$		0			0
$101$	1.54274	+	0.561511i	0.153508	+	0.0558725i	0.417631	−	0.908617i	$-0.362860\pi$
$101$	1.54274	+	0.561511i	0.153508	+	0.0558725i	−0.264123	+	0.964489i	$0.585083\pi$
$102$		0			0
$103$	−1.72429	−	1.44685i	−0.169900	−	0.142563i	0.553873	−	0.832601i	$-0.313149\pi$
$103$	−1.72429	−	1.44685i	−0.169900	−	0.142563i	−0.723773	+	0.690038i	$0.757594\pi$
$104$		0			0
$105$	1.81147	+	5.07129i	0.176782	+	0.494907i
$106$		0			0
$107$	−13.4724			−1.30242			−0.651211	−	0.758897i	$-0.725739\pi$
$107$	−13.4724			−1.30242			−0.651211	+	0.758897i	$0.725739\pi$
$108$		0			0
$109$	−3.97476			−0.380713			−0.190356	−	0.981715i	$-0.560964\pi$
$109$	−3.97476			−0.380713			−0.190356	+	0.981715i	$0.560964\pi$
$110$		0			0
$111$	7.41610	−	8.73142i	0.703905	−	0.828750i
$112$		0			0
$113$	1.64004	+	1.37616i	0.154282	+	0.129458i	0.716661	−	0.697421i	$-0.245669\pi$
$113$	1.64004	+	1.37616i	0.154282	+	0.129458i	−0.562379	+	0.826879i	$0.690114\pi$
$114$		0			0
$115$	22.6785	+	8.25429i	2.11478	+	0.769716i
$116$		0			0
$117$	−1.67665	+	2.82534i	−0.155006	+	0.261203i
$118$		0			0
$119$	0.364587	−	0.305924i	0.0334216	−	0.0280440i
$120$		0			0
$121$	3.19913	−	18.1432i	0.290830	−	1.64938i
$122$		0			0
$123$	−0.419252	+	1.13077i	−0.0378027	+	0.101958i
$124$		0			0
$125$	−0.518505	+	0.898078i	−0.0463765	+	0.0803265i
$126$		0			0
$127$	0.636444	+	1.10235i	0.0564752	+	0.0978180i	0.892881	−	0.450293i	$-0.148680\pi$
$127$	0.636444	+	1.10235i	0.0564752	+	0.0978180i	−0.836406	+	0.548111i	$0.815347\pi$
$128$		0			0
$129$	1.86505	−	1.06195i	0.164209	−	0.0934992i
$130$		0			0
$131$	6.01387	−	2.18887i	0.525434	−	0.191242i	−0.0656643	−	0.997842i	$-0.520917\pi$
$131$	6.01387	−	2.18887i	0.525434	−	0.191242i	0.591099	+	0.806599i	$0.298694\pi$
$132$		0			0
$133$	−0.544159	−	3.08608i	−0.0471846	−	0.267597i
$134$		0			0
$135$	5.25180	+	15.2779i	0.452003	+	1.31491i
$136$		0			0
$137$	−3.74244	−	21.2244i	−0.319738	−	1.81333i	−0.544329	−	0.838872i	$-0.683216\pi$
$137$	−3.74244	−	21.2244i	−0.319738	−	1.81333i	0.224591	−	0.974453i	$-0.427895\pi$
$138$		0			0
$139$	−18.4439	+	6.71303i	−1.56439	+	0.569392i	−0.971737	−	0.236066i	$-0.924142\pi$
$139$	−18.4439	+	6.71303i	−1.56439	+	0.569392i	−0.592653	+	0.805458i	$0.701920\pi$
$140$		0			0
$141$	11.6969	+	6.84695i	0.985058	+	0.576617i
$142$		0			0
$143$	2.97014	+	5.14444i	0.248376	+	0.430200i
$144$		0			0
$145$	−14.3525	+	24.8592i	−1.19191	+	2.06445i
$146$		0			0
$147$	−1.10537	−	1.33347i	−0.0911697	−	0.109983i
$148$		0			0
$149$	−0.553594	+	3.13959i	−0.0453522	+	0.257205i	−0.999051	−	0.0435588i	$-0.986130\pi$
$149$	−0.553594	+	3.13959i	−0.0453522	+	0.257205i	0.953699	+	0.300764i	$0.0972415\pi$
$150$		0			0
$151$	−17.0117	+	14.2745i	−1.38439	+	1.16164i	−0.416833	+	0.908983i	$0.636860\pi$
$151$	−17.0117	+	14.2745i	−1.38439	+	1.16164i	−0.967556	+	0.252657i	$0.918696\pi$
$152$		0			0
$153$	1.10467	−	0.904606i	0.0893076	−	0.0731331i
$154$		0			0
$155$	25.0314	+	9.11069i	2.01057	+	0.731788i
$156$		0			0
$157$	17.7868	+	14.9249i	1.41954	+	1.19113i	0.951587	+	0.307379i	$0.0994518\pi$
$157$	17.7868	+	14.9249i	1.41954	+	1.19113i	0.467950	+	0.883755i	$0.344993\pi$
$158$		0			0
$159$	−16.8651	−	3.07804i	−1.33749	−	0.244104i
$160$		0			0
$161$	−7.76237			−0.611760
$162$		0			0
$163$	−3.69033			−0.289049			−0.144524	−	0.989501i	$-0.546165\pi$
$163$	−3.69033			−0.289049			−0.144524	+	0.989501i	$0.546165\pi$
$164$		0			0
$165$	28.7358	+	5.24454i	2.23708	+	0.408287i
$166$		0			0
$167$	5.30047	+	4.44763i	0.410163	+	0.344168i	0.824406	−	0.565999i	$-0.191509\pi$
$167$	5.30047	+	4.44763i	0.410163	+	0.344168i	−0.414243	+	0.910166i	$0.635954\pi$
$168$		0			0
$169$	11.0890	+	4.03608i	0.853002	+	0.310467i
$170$		0			0
$171$	−1.52146	−	9.27713i	−0.116349	−	0.709440i
$172$		0			0
$173$	8.55454	−	7.17812i	0.650390	−	0.545742i	−0.256799	−	0.966465i	$-0.582668\pi$
$173$	8.55454	−	7.17812i	0.650390	−	0.545742i	0.907189	+	0.420723i	$0.138223\pi$
$174$		0			0
$175$	−0.810322	+	4.59556i	−0.0612546	+	0.347392i
$176$		0			0
$177$	−0.874057	−	1.05442i	−0.0656981	−	0.0792552i
$178$		0			0
$179$	5.63994	−	9.76866i	0.421549	−	0.730144i	−0.574542	−	0.818475i	$-0.694820\pi$
$179$	5.63994	−	9.76866i	0.421549	−	0.730144i	0.996091	+	0.0883309i	$0.0281533\pi$
$180$		0			0
$181$	−6.05799	−	10.4927i	−0.450287	−	0.779920i	0.548117	−	0.836402i	$-0.315345\pi$
$181$	−6.05799	−	10.4927i	−0.450287	−	0.779920i	−0.998404	+	0.0564821i	$0.982012\pi$
$182$		0			0
$183$	4.16469	+	2.43786i	0.307863	+	0.180212i
$184$		0			0
$185$	19.3235	−	7.03318i	1.42069	−	0.517089i
$186$		0			0
$187$	−0.448292	−	2.54239i	−0.0327823	−	0.185918i
$188$		0			0
$189$	−3.26797	−	4.03985i	−0.237710	−	0.293856i
$190$		0			0
$191$	1.97473	+	11.1993i	0.142887	+	0.810351i	0.969040	+	0.246905i	$0.0794136\pi$
$191$	1.97473	+	11.1993i	0.142887	+	0.810351i	−0.826153	+	0.563446i	$0.809475\pi$
$192$		0			0
$193$	16.5036	−	6.00682i	1.18795	−	0.432380i	0.328950	−	0.944347i	$-0.393305\pi$
$193$	16.5036	−	6.00682i	1.18795	−	0.432380i	0.859005	+	0.511967i	$0.171083\pi$
$194$		0			0
$195$	−5.12484	+	2.91804i	−0.366997	+	0.208965i
$196$		0			0
$197$	−7.07875	−	12.2608i	−0.504340	−	0.873543i	−0.999987	−	0.00501873i	$-0.998402\pi$
$197$	−7.07875	−	12.2608i	−0.504340	−	0.873543i	0.495647	−	0.868524i	$-0.334931\pi$
$198$		0			0
$199$	9.67689	−	16.7609i	0.685977	−	1.18815i	−0.287152	−	0.957885i	$-0.592709\pi$
$199$	9.67689	−	16.7609i	0.685977	−	1.18815i	0.973129	−	0.230261i	$-0.0739581\pi$
$200$		0			0
$201$	1.11223	−	2.99981i	0.0784509	−	0.211590i
$202$		0			0
$203$	1.60322	−	9.09232i	0.112524	−	0.638156i
$204$		0			0
$205$	−1.65833	+	1.39150i	−0.115822	+	0.0971866i
$206$		0			0
$207$	−23.2854	−	0.278938i	−1.61845	−	0.0193875i
$208$		0			0
$209$	−15.9730	−	5.81368i	−1.10487	−	0.402141i
$210$		0			0
$211$	−7.16400	−	6.01131i	−0.493190	−	0.413836i	0.361978	−	0.932187i	$-0.382102\pi$
$211$	−7.16400	−	6.01131i	−0.493190	−	0.413836i	−0.855168	+	0.518351i	$0.826546\pi$
$212$		0			0
$213$	10.4609	−	12.3162i	0.716768	−	0.843895i
$214$		0			0
$215$	3.85250			0.262738
$216$		0			0
$217$	−8.56773			−0.581615
$218$		0			0
$219$	−3.09093	−	8.65316i	−0.208865	−	0.584726i
$220$		0			0
$221$	0.399268	+	0.335026i	0.0268577	+	0.0225363i
$222$		0			0
$223$	25.4839	+	9.27537i	1.70653	+	0.621125i	0.996542	−	0.0830933i	$-0.0264800\pi$
$223$	25.4839	+	9.27537i	1.70653	+	0.621125i	0.709984	+	0.704218i	$0.248702\pi$
$224$		0			0
$225$	−2.59593	+	13.7566i	−0.173062	+	0.917106i
$226$		0			0
$227$	3.38669	−	2.84177i	0.224783	−	0.188615i	−0.523440	−	0.852062i	$-0.675352\pi$
$227$	3.38669	−	2.84177i	0.224783	−	0.188615i	0.748223	+	0.663447i	$0.230907\pi$
$228$		0			0
$229$	2.57293	−	14.5918i	0.170024	−	0.964255i	−0.773708	−	0.633543i	$-0.781600\pi$
$229$	2.57293	−	14.5918i	0.170024	−	0.964255i	0.943732	−	0.330712i	$-0.107289\pi$
$230$		0			0
$231$	−9.26204	+	1.57601i	−0.609397	+	0.103694i
$232$		0			0
$233$	−10.5415	+	18.2584i	−0.690595	+	1.19615i	0.281048	+	0.959694i	$0.409318\pi$
$233$	−10.5415	+	18.2584i	−0.690595	+	1.19615i	−0.971643	+	0.236453i	$0.924015\pi$
$234$		0			0
$235$	12.1645	+	21.0696i	0.793528	+	1.37443i
$236$		0			0
$237$	−0.173038	+	28.8911i	−0.0112400	+	1.87668i
$238$		0			0
$239$	19.2687	−	7.01322i	1.24639	−	0.453648i	0.367207	−	0.930139i	$-0.380314\pi$
$239$	19.2687	−	7.01322i	1.24639	−	0.453648i	0.879179	+	0.476491i	$0.158092\pi$
$240$		0			0
$241$	2.24890	+	12.7541i	0.144864	+	0.821566i	0.967476	+	0.252963i	$0.0814050\pi$
$241$	2.24890	+	12.7541i	0.144864	+	0.821566i	−0.822612	+	0.568603i	$0.807484\pi$
$242$		0			0
$243$	−9.65803	−	12.2361i	−0.619563	−	0.784947i
$244$		0			0
$245$	−0.539888	−	3.06186i	−0.0344922	−	0.195615i
$246$		0			0
$247$	3.22482	−	1.17374i	0.205190	−	0.0746832i
$248$		0			0
$249$	−0.0434887	+	7.26104i	−0.00275599	+	0.460150i
$250$		0			0
$251$	−12.8639	−	22.2809i	−0.811962	−	1.40636i	−0.911489	−	0.411325i	$-0.865066\pi$
$251$	−12.8639	−	22.2809i	−0.811962	−	1.40636i	0.0995266	−	0.995035i	$-0.468267\pi$
$252$		0			0
$253$	−21.0527	+	36.4644i	−1.32357	+	2.29249i
$254$		0			0
$255$	2.52664	−	0.429928i	0.158224	−	0.0269231i
$256$		0			0
$257$	0.0478090	−	0.271138i	0.00298224	−	0.0169131i	−0.983280	−	0.182098i	$-0.941711\pi$
$257$	0.0478090	−	0.271138i	0.00298224	−	0.0169131i	0.986263	+	0.165185i	$0.0528222\pi$
$258$		0			0
$259$	−5.06664	+	4.25142i	−0.314826	+	0.264170i
$260$		0			0
$261$	5.13605	−	27.2174i	0.317913	−	1.68471i
$262$		0			0
$263$	−22.9536	−	8.35444i	−1.41538	−	0.515157i	−0.482677	−	0.875798i	$-0.660336\pi$
$263$	−22.9536	−	8.35444i	−1.41538	−	0.515157i	−0.932705	+	0.360641i	$0.882558\pi$
$264$		0			0
$265$	−23.5739	−	19.7809i	−1.44814	−	1.21513i
$266$		0			0
$267$	7.27993	+	20.3804i	0.445525	+	1.24726i
$268$		0			0
$269$	−6.89179			−0.420200			−0.210100	−	0.977680i	$-0.567379\pi$
$269$	−6.89179			−0.420200			−0.210100	+	0.977680i	$0.567379\pi$
$270$		0			0
$271$	28.4046			1.72546			0.862728	−	0.505668i	$-0.168754\pi$
$271$	28.4046			1.72546			0.862728	+	0.505668i	$0.168754\pi$
$272$		0			0
$273$	1.22793	−	1.44571i	0.0743176	−	0.0874986i
$274$		0			0
$275$	19.3903	+	16.2704i	1.16928	+	0.981143i
$276$		0			0
$277$	9.71176	+	3.53479i	0.583523	+	0.212385i	0.616878	−	0.787059i	$-0.288397\pi$
$277$	9.71176	+	3.53479i	0.583523	+	0.212385i	−0.0333554	+	0.999444i	$0.510619\pi$
$278$		0			0
$279$	−25.7013	−	0.307878i	−1.53870	−	0.0184322i
$280$		0			0
$281$	−1.69189	+	1.41967i	−0.100930	+	0.0846903i	−0.691856	−	0.722035i	$-0.743207\pi$
$281$	−1.69189	+	1.41967i	−0.100930	+	0.0846903i	0.590926	+	0.806726i	$0.298762\pi$
$282$		0			0
$283$	4.43555	−	25.1553i	0.263666	−	1.49533i	−0.509140	−	0.860684i	$-0.670036\pi$
$283$	4.43555	−	25.1553i	0.263666	−	1.49533i	0.772806	−	0.634642i	$-0.218853\pi$
$284$		0			0
$285$	5.86654	−	15.8227i	0.347504	−	0.937255i
$286$		0			0
$287$	0.348139	−	0.602994i	0.0205500	−	0.0355936i
$288$		0			0
$289$	8.38674	+	14.5263i	0.493338	+	0.854486i
$290$		0			0
$291$	−5.67856	+	3.23332i	−0.332883	+	0.189541i
$292$		0			0
$293$	−19.2314	+	6.99965i	−1.12351	+	0.408924i	−0.835932	−	0.548833i	$-0.815072\pi$
$293$	−19.2314	+	6.99965i	−1.12351	+	0.408924i	−0.287578	+	0.957757i	$0.592850\pi$
$294$		0			0
$295$	−0.426908	−	2.42112i	−0.0248555	−	0.140963i
$296$		0			0
$297$	−27.8408	+	4.39486i	−1.61548	+	0.255016i
$298$		0			0
$299$	−1.47614	−	8.37162i	−0.0853675	−	0.484143i
$300$		0			0
$301$	−1.16438	+	0.423799i	−0.0671137	+	0.0244274i
$302$		0			0
$303$	−2.45406	−	1.43652i	−0.140982	−	0.0825259i
$304$		0			0
$305$	4.33119	+	7.50184i	0.248003	+	0.429554i
$306$		0			0
$307$	14.5562	−	25.2121i	0.830765	−	1.43893i	−0.0666667	−	0.997775i	$-0.521236\pi$
$307$	14.5562	−	25.2121i	0.830765	−	1.43893i	0.897432	−	0.441153i	$-0.145430\pi$
$308$		0			0
$309$	2.48809	+	3.00152i	0.141543	+	0.170750i
$310$		0			0
$311$	−5.06767	+	28.7402i	−0.287361	+	1.62971i	0.409366	+	0.912370i	$0.365750\pi$
$311$	−5.06767	+	28.7402i	−0.287361	+	1.62971i	−0.696727	+	0.717336i	$0.745361\pi$
$312$		0			0
$313$	−10.8929	+	9.14026i	−0.615705	+	0.516638i	−0.896450	−	0.443144i	$-0.853863\pi$
$313$	−10.8929	+	9.14026i	−0.615705	+	0.516638i	0.280745	+	0.959782i	$0.409418\pi$
$314$		0			0
$315$	−1.50952	−	9.20432i	−0.0850519	−	0.518605i
$316$		0			0
$317$	14.0141	+	5.10073i	0.787112	+	0.286485i	0.704135	−	0.710066i	$-0.251335\pi$
$317$	14.0141	+	5.10073i	0.787112	+	0.286485i	0.0829772	+	0.996551i	$0.473557\pi$
$318$		0			0
$319$	−38.3637	−	32.1910i	−2.14796	−	1.80235i
$320$		0			0
$321$	22.9556	+	4.18961i	1.28126	+	0.233841i
$322$		0			0
$323$	−1.49143			−0.0829853
$324$		0			0
$325$	−5.11036			−0.283472
$326$		0			0
$327$	6.77261	+	1.23606i	0.374526	+	0.0683544i
$328$		0			0
$329$	−5.99441	−	5.02991i	−0.330482	−	0.277308i
$330$		0			0
$331$	6.15197	+	2.23913i	0.338143	+	0.123074i	0.505510	−	0.862821i	$-0.331304\pi$
$331$	6.15197	+	2.23913i	0.338143	+	0.123074i	−0.167367	+	0.985895i	$0.553527\pi$
$332$		0			0
$333$	−15.3516	+	12.5713i	−0.841263	+	0.688901i
$334$		0			0
$335$	4.39937	−	3.69151i	0.240363	−	0.201689i
$336$		0			0
$337$	−0.175569	+	0.995701i	−0.00956385	+	0.0542393i	−0.989216	−	0.146463i	$-0.953211\pi$
$337$	−0.175569	+	0.995701i	−0.00956385	+	0.0542393i	0.979652	+	0.200702i	$0.0643223\pi$
$338$		0			0
$339$	−2.36652	−	2.85486i	−0.128532	−	0.155055i
$340$		0			0
$341$	−23.2370	+	40.2476i	−1.25835	+	2.17953i
$342$		0			0
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$		0			0
$345$	−36.0751	−	21.1170i	−1.94222	−	1.13690i
$346$		0			0
$347$	−3.36786	+	1.22580i	−0.180796	+	0.0658044i	−0.430832	−	0.902432i	$-0.641780\pi$
$347$	−3.36786	+	1.22580i	−0.180796	+	0.0658044i	0.250036	+	0.968237i	$0.419558\pi$
$348$		0			0
$349$	1.44146	+	8.17493i	0.0771596	+	0.437594i	0.998775	+	0.0494887i	$0.0157592\pi$
$349$	1.44146	+	8.17493i	0.0771596	+	0.437594i	−0.921615	+	0.388105i	$0.873130\pi$
$350$		0			0
$351$	3.73547	−	4.29271i	0.199385	−	0.229128i
$352$		0			0
$353$	2.22711	+	12.6306i	0.118537	+	0.672258i	0.984938	+	0.172909i	$0.0553165\pi$
$353$	2.22711	+	12.6306i	0.118537	+	0.672258i	−0.866401	+	0.499349i	$0.833572\pi$
$354$		0			0
$355$	27.2571	−	9.92076i	1.44665	−	0.526539i
$356$		0			0
$357$	−0.716357	+	0.407888i	−0.0379136	+	0.0215877i
$358$		0			0
$359$	−18.5811	−	32.1835i	−0.980675	−	1.69858i	−0.659772	−	0.751466i	$-0.729347\pi$
$359$	−18.5811	−	32.1835i	−0.980675	−	1.69858i	−0.320903	−	0.947112i	$-0.603986\pi$
$360$		0			0
$361$	4.59000	−	7.95011i	0.241579	−	0.418427i
$362$		0			0
$363$	−11.0931	+	29.9194i	−0.582239	+	1.57036i
$364$		0			0
$365$	2.86414	−	16.2433i	0.149916	−	0.850215i
$366$		0			0
$367$	16.5071	−	13.8511i	0.861662	−	0.723020i	−0.100664	−	0.994921i	$-0.532097\pi$
$367$	16.5071	−	13.8511i	0.861662	−	0.723020i	0.962325	+	0.271900i	$0.0876521\pi$
$368$		0			0
$369$	1.06601	−	1.79634i	0.0554942	−	0.0935138i
$370$		0			0
$371$	9.30101	+	3.38529i	0.482885	+	0.175756i
$372$		0			0
$373$	−27.0753	−	22.7189i	−1.40190	−	1.17634i	−0.960246	−	0.279154i	$-0.909946\pi$
$373$	−27.0753	−	22.7189i	−1.40190	−	1.17634i	−0.441658	−	0.897183i	$-0.645610\pi$
$374$		0			0
$375$	1.16277	−	1.36900i	0.0600450	−	0.0706946i
$376$		0			0
$377$	10.1108			0.520734
$378$		0			0
$379$	8.53507			0.438417			0.219209	−	0.975678i	$-0.429652\pi$
$379$	8.53507			0.438417			0.219209	+	0.975678i	$0.429652\pi$
$380$		0			0
$381$	−0.741632	−	2.07622i	−0.0379950	−	0.106368i
$382$		0			0
$383$	4.62919	+	3.88435i	0.236540	+	0.198481i	0.753351	−	0.657619i	$-0.228436\pi$
$383$	4.62919	+	3.88435i	0.236540	+	0.198481i	−0.516810	+	0.856100i	$0.672881\pi$
$384$		0			0
$385$	−15.8476	−	5.76805i	−0.807668	−	0.293967i
$386$		0			0
$387$	−3.50812	+	1.22947i	−0.178328	+	0.0624973i
$388$		0			0
$389$	21.9926	−	18.4540i	1.11507	−	0.935655i	0.116725	−	0.993164i	$-0.462760\pi$
$389$	21.9926	−	18.4540i	1.11507	−	0.935655i	0.998345	+	0.0575093i	$0.0183159\pi$
$390$		0			0
$391$	−0.641521	+	3.63825i	−0.0324431	+	0.183994i
$392$		0			0
$393$	−10.9278	+	1.85944i	−0.551232	+	0.0937966i
$394$		0			0
$395$	−25.9307	+	44.9134i	−1.30472	+	2.25984i
$396$		0			0
$397$	−10.7664	−	18.6480i	−0.540352	−	0.935918i	−0.998884	−	0.0472393i	$-0.984958\pi$
$397$	−10.7664	−	18.6480i	−0.540352	−	0.935918i	0.458531	−	0.888678i	$-0.348376\pi$
$398$		0			0
$399$	−0.0325077	+	5.42761i	−0.00162742	+	0.271720i
$400$		0			0
$401$	−13.2050	+	4.80621i	−0.659424	+	0.240011i	−0.649988	−	0.759945i	$-0.725226\pi$
$401$	−13.2050	+	4.80621i	−0.659424	+	0.240011i	−0.00943631	+	0.999955i	$0.503004\pi$
$402$		0			0
$403$	−1.62929	−	9.24019i	−0.0811610	−	0.460287i
$404$		0			0
$405$	−4.19749	−	27.6652i	−0.208575	−	1.37470i
$406$		0			0
$407$	6.22989	+	35.3314i	0.308804	+	1.75131i
$408$		0			0
$409$	18.4901	−	6.72984i	0.914276	−	0.332769i	0.158317	−	0.987388i	$-0.449393\pi$
$409$	18.4901	−	6.72984i	0.914276	−	0.332769i	0.755959	+	0.654619i	$0.227171\pi$
$410$		0			0
$411$	−0.223571	+	37.3282i	−0.0110279	+	1.84127i
$412$		0			0
$413$	0.395367	+	0.684796i	0.0194547	+	0.0336966i
$414$		0			0
$415$	−6.51703	+	11.2878i	−0.319909	+	0.554098i
$416$		0			0
$417$	33.5142	−	5.70272i	1.64120	−	0.279263i
$418$		0			0
$419$	−3.94309	+	22.3624i	−0.192633	+	1.09247i	0.723117	+	0.690725i	$0.242709\pi$
$419$	−3.94309	+	22.3624i	−0.192633	+	1.09247i	−0.915750	+	0.401749i	$0.868403\pi$
$420$		0			0
$421$	1.71786	−	1.44146i	0.0837234	−	0.0702523i	−0.599965	−	0.800026i	$-0.704819\pi$
$421$	1.71786	−	1.44146i	0.0837234	−	0.0702523i	0.683689	+	0.729774i	$0.260375\pi$
$422$		0			0
$423$	−17.8012	−	15.3040i	−0.865523	−	0.744108i
$424$		0			0
$425$	2.08699	+	0.759601i	0.101234	+	0.0368461i
$426$		0			0
$427$	−2.13431	−	1.79090i	−0.103286	−	0.0866676i
$428$		0			0
$429$	−3.46104	−	9.68929i	−0.167100	−	0.467803i
$430$		0			0
$431$	2.31218			0.111374			0.0556870	−	0.998448i	$-0.482265\pi$
$431$	2.31218			0.111374			0.0556870	+	0.998448i	$0.482265\pi$
$432$		0			0
$433$	1.31983			0.0634269			0.0317135	−	0.999497i	$-0.489904\pi$
$433$	1.31983			0.0634269			0.0317135	+	0.999497i	$0.489904\pi$
$434$		0			0
$435$	32.1859	−	37.8945i	1.54320	−	1.81690i
$436$		0			0
$437$	18.6339	+	15.6357i	0.891381	+	0.747957i
$438$		0			0
$439$	−1.38006	−	0.502303i	−0.0658669	−	0.0239736i	0.308877	−	0.951102i	$-0.400047\pi$
$439$	−1.38006	−	0.502303i	−0.0658669	−	0.0239736i	−0.374743	+	0.927129i	$0.622269\pi$
$440$		0			0
$441$	1.46877	+	2.61586i	0.0699415	+	0.124565i
$442$		0			0
$443$	−0.0161125	+	0.0135200i	−0.000765529	+	0.000642355i	−0.643170	−	0.765723i	$-0.722381\pi$
$443$	−0.0161125	+	0.0135200i	−0.000765529	+	0.000642355i	0.642405	+	0.766366i	$0.277937\pi$
$444$		0			0
$445$	−6.74579	+	38.2573i	−0.319781	+	1.81357i
$446$		0			0
$447$	1.91961	−	5.17740i	0.0907946	−	0.244883i
$448$		0			0
$449$	3.64063	−	6.30576i	0.171812	−	0.297587i	−0.767241	−	0.641358i	$-0.778371\pi$
$449$	3.64063	−	6.30576i	0.171812	−	0.297587i	0.939053	+	0.343771i	$0.111705\pi$
$450$		0			0
$451$	−1.88841	−	3.27082i	−0.0889217	−	0.154017i
$452$		0			0
$453$	33.4253	−	19.0321i	1.57046	−	0.894206i
$454$		0			0
$455$	3.19951	−	1.16453i	0.149995	−	0.0545938i
$456$		0			0
$457$	2.85385	+	16.1850i	0.133497	+	0.757101i	0.975894	+	0.218244i	$0.0700328\pi$
$457$	2.85385	+	16.1850i	0.133497	+	0.757101i	−0.842397	+	0.538858i	$0.818856\pi$
$458$		0			0
$459$	−2.16357	+	1.19783i	−0.100987	+	0.0559101i
$460$		0			0
$461$	−6.36292	−	36.0859i	−0.296351	−	1.68069i	−0.661661	−	0.749803i	$-0.730148\pi$
$461$	−6.36292	−	36.0859i	−0.296351	−	1.68069i	0.365311	−	0.930886i	$-0.380963\pi$
$462$		0			0
$463$	21.4456	−	7.80556i	0.996662	−	0.362755i	0.208365	−	0.978051i	$-0.433186\pi$
$463$	21.4456	−	7.80556i	0.996662	−	0.362755i	0.788296	+	0.615296i	$0.210963\pi$
$464$		0			0
$465$	−39.8179	−	23.3080i	−1.84651	−	1.08088i
$466$		0			0
$467$	9.19739	+	15.9304i	0.425605	+	0.737169i	0.996477	−	0.0838703i	$-0.0267281\pi$
$467$	9.19739	+	15.9304i	0.425605	+	0.737169i	−0.570872	+	0.821039i	$0.693395\pi$
$468$		0			0
$469$	−0.923577	+	1.59968i	−0.0426468	+	0.0738665i
$470$		0			0
$471$	−25.6656	−	30.9618i	−1.18261	−	1.42665i
$472$		0			0
$473$	−1.16714	+	6.61918i	−0.0536651	+	0.304350i
$474$		0			0
$475$	11.2020	−	9.39963i	0.513985	−	0.431285i
$476$		0			0
$477$	27.7794	+	10.4894i	1.27193	+	0.480276i
$478$		0			0
$479$	−8.84990	−	3.22110i	−0.404362	−	0.147176i	0.131829	−	0.991273i	$-0.457915\pi$
$479$	−8.84990	−	3.22110i	−0.404362	−	0.147176i	−0.536191	+	0.844097i	$0.680137\pi$
$480$		0			0
$481$	−5.54861	−	4.65583i	−0.252995	−	0.212288i
$482$		0			0
$483$	13.2263	+	2.41393i	0.601819	+	0.109837i
$484$		0			0
$485$	−11.7298			−0.532621
$486$		0			0
$487$	−36.6303			−1.65988			−0.829939	−	0.557854i	$-0.811625\pi$
$487$	−36.6303			−1.65988			−0.829939	+	0.557854i	$0.811625\pi$
$488$		0			0
$489$	6.28797	+	1.14761i	0.284352	+	0.0518967i
$490$		0			0
$491$	17.4190	+	14.6163i	0.786108	+	0.659623i	0.944779	−	0.327709i	$-0.106276\pi$
$491$	17.4190	+	14.6163i	0.786108	+	0.659623i	−0.158671	+	0.987332i	$0.550721\pi$
$492$		0			0
$493$	−4.12910	−	1.50287i	−0.185965	−	0.0676859i
$494$		0			0
$495$	−47.3321	−	17.8724i	−2.12742	−	0.803304i
$496$		0			0
$497$	−7.14683	+	5.99690i	−0.320579	+	0.268998i
$498$		0			0
$499$	2.11791	−	12.0113i	0.0948108	−	0.537699i	−0.899994	−	0.435901i	$-0.856430\pi$
$499$	2.11791	−	12.0113i	0.0948108	−	0.537699i	0.994805	−	0.101797i	$-0.0324593\pi$
$500$		0			0
$501$	−7.64839	−	9.22666i	−0.341705	−	0.412217i
$502$		0			0
$503$	7.79133	−	13.4950i	0.347398	−	0.601712i	−0.638388	−	0.769715i	$-0.720398\pi$
$503$	7.79133	−	13.4950i	0.347398	−	0.601712i	0.985786	+	0.168003i	$0.0537318\pi$
$504$		0			0
$505$	−2.55218	−	4.42050i	−0.113570	−	0.196710i
$506$		0			0
$507$	−17.6395	−	10.3255i	−0.783399	−	0.458573i
$508$		0			0
$509$	5.06066	−	1.84193i	0.224310	−	0.0816420i	−0.227421	−	0.973797i	$-0.573029\pi$
$509$	5.06066	−	1.84193i	0.224310	−	0.0816420i	0.451730	+	0.892155i	$0.350807\pi$
$510$		0			0
$511$	0.921214	+	5.22446i	0.0407521	+	0.231117i
$512$		0			0
$513$	−0.292555	+	16.2805i	−0.0129166	+	0.718801i
$514$		0			0
$515$	1.21524	+	6.89195i	0.0535497	+	0.303695i
$516$		0			0
$517$	−39.8861	+	14.5174i	−1.75419	+	0.638473i
$518$		0			0
$519$	−16.8084	+	9.57055i	−0.737806	+	0.420101i
$520$		0			0
$521$	−1.42902	−	2.47514i	−0.0626066	−	0.108438i	0.833023	−	0.553238i	$-0.186608\pi$
$521$	−1.42902	−	2.47514i	−0.0626066	−	0.108438i	−0.895630	+	0.444800i	$0.853275\pi$
$522$		0			0
$523$	1.66093	−	2.87682i	0.0726276	−	0.125795i	−0.827425	−	0.561577i	$-0.810195\pi$
$523$	1.66093	−	2.87682i	0.0726276	−	0.125795i	0.900052	+	0.435782i	$0.143528\pi$
$524$		0			0
$525$	2.80983	−	7.57841i	0.122631	−	0.330749i
$526$		0			0
$527$	−0.708081	+	4.01572i	−0.0308445	+	0.174928i
$528$		0			0
$529$	28.5385	−	23.9466i	1.24080	−	1.04116i
$530$		0			0
$531$	1.16141	+	2.06845i	0.0504008	+	0.0897630i
$532$		0			0
$533$	0.716525	+	0.260794i	0.0310362	+	0.0112962i
$534$		0			0
$535$	32.0872	+	26.9243i	1.38725	+	1.16404i
$536$		0			0
$537$	−12.6478	+	14.8910i	−0.545791	+	0.642593i
$538$		0			0
$539$	5.42430			0.233641
$540$		0			0
$541$	−1.71560			−0.0737592			−0.0368796	−	0.999320i	$-0.511742\pi$
$541$	−1.71560			−0.0737592			−0.0368796	+	0.999320i	$0.511742\pi$
$542$		0			0
$543$	7.05923	+	19.7625i	0.302940	+	0.848092i
$544$		0			0
$545$	9.46669	+	7.94349i	0.405508	+	0.340262i
$546$		0			0
$547$	−20.0166	−	7.28546i	−0.855849	−	0.311504i	−0.123426	−	0.992354i	$-0.539388\pi$
$547$	−20.0166	−	7.28546i	−0.855849	−	0.311504i	−0.732423	+	0.680850i	$0.761611\pi$
$548$		0			0
$549$	−6.33811	−	5.44901i	−0.270504	−	0.232558i
$550$		0			0
$551$	−22.1632	+	18.5972i	−0.944185	+	0.792265i
$552$		0			0
$553$	2.89655	−	16.4272i	0.123174	−	0.698554i
$554$		0			0
$555$	−35.1126	+	5.97468i	−1.49045	+	0.253611i
$556$		0			0
$557$	−14.0259	+	24.2936i	−0.594297	+	1.02935i	0.399349	+	0.916799i	$0.369236\pi$
$557$	−14.0259	+	24.2936i	−0.594297	+	1.02935i	−0.993646	+	0.112553i	$0.964097\pi$
$558$		0			0
$559$	−0.678488	−	1.17518i	−0.0286970	−	0.0497047i
$560$		0			0
$561$	−0.0267807	+	4.47140i	−0.00113068	+	0.188783i
$562$		0			0
$563$	−36.9068	+	13.4330i	−1.55544	+	0.566132i	−0.969685	−	0.244359i	$-0.921422\pi$
$563$	−36.9068	+	13.4330i	−1.55544	+	0.566132i	−0.585751	+	0.810491i	$0.699200\pi$
$564$		0			0
$565$	−1.15586	−	6.55520i	−0.0486273	−	0.275779i
$566$		0			0
$567$	4.31200	+	7.89979i	0.181087	+	0.331760i
$568$		0			0
$569$	1.21522	+	6.89188i	0.0509449	+	0.288923i	0.999627	−	0.0273084i	$-0.00869362\pi$
$569$	1.21522	+	6.89188i	0.0509449	+	0.288923i	−0.948682	+	0.316231i	$0.897583\pi$
$570$		0			0
$571$	5.01806	−	1.82642i	0.209999	−	0.0764335i	−0.234879	−	0.972025i	$-0.575469\pi$
$571$	5.01806	−	1.82642i	0.209999	−	0.0764335i	0.444878	+	0.895591i	$0.353247\pi$
$572$		0			0
$573$	0.117969	−	19.6966i	0.00492824	−	0.822838i
$574$		0			0
$575$	−18.1114	−	31.3698i	−0.755297	−	1.30821i
$576$		0			0
$577$	14.2032	−	24.6006i	0.591286	−	1.02414i	−0.402774	−	0.915300i	$-0.631954\pi$
$577$	14.2032	−	24.6006i	0.591286	−	1.02414i	0.994060	−	0.108838i	$-0.0347129\pi$
$578$		0			0
$579$	−29.9885	+	5.10279i	−1.24628	+	0.212065i
$580$		0			0
$581$	0.727975	−	4.12855i	0.0302015	−	0.171281i
$582$		0			0
$583$	41.1284	−	34.5109i	1.70337	−	1.42929i
$584$		0			0
$585$	9.63968	−	3.37835i	0.398552	−	0.139678i
$586$		0			0
$587$	16.9950	+	6.18568i	0.701459	+	0.255310i	0.668034	−	0.744131i	$-0.267136\pi$
$587$	16.9950	+	6.18568i	0.701459	+	0.255310i	0.0334254	+	0.999441i	$0.489358\pi$
$588$		0			0
$589$	20.5672	+	17.2579i	0.847457	+	0.711101i
$590$		0			0
$591$	8.24869	+	23.0925i	0.339306	+	0.949898i
$592$		0			0
$593$	11.9743			0.491725			0.245862	−	0.969305i	$-0.420929\pi$
$593$	11.9743			0.491725			0.245862	+	0.969305i	$0.420929\pi$
$594$		0			0
$595$	−1.47972			−0.0606627
$596$		0			0
$597$	−21.7008	+	25.5496i	−0.888153	+	1.04568i
$598$		0			0
$599$	8.45872	+	7.09771i	0.345614	+	0.290005i	0.799026	−	0.601296i	$-0.205349\pi$
$599$	8.45872	+	7.09771i	0.345614	+	0.290005i	−0.453412	+	0.891301i	$0.649793\pi$
$600$		0			0
$601$	26.6258	+	9.69099i	1.08609	+	0.395304i	0.822171	−	0.569241i	$-0.192763\pi$
$601$	26.6258	+	9.69099i	1.08609	+	0.395304i	0.263918	+	0.964545i	$0.414985\pi$
$602$		0			0
$603$	−2.82802	+	4.76551i	−0.115166	+	0.194067i
$604$		0			0
$605$	−43.8782	+	36.8182i	−1.78390	+	1.49687i
$606$		0			0
$607$	−2.27216	+	12.8861i	−0.0922242	+	0.523030i	0.903338	+	0.428929i	$0.141109\pi$
$607$	−2.27216	+	12.8861i	−0.0922242	+	0.523030i	−0.995563	+	0.0941010i	$0.970002\pi$
$608$		0			0
$609$	−5.55925	+	14.9939i	−0.225272	+	0.607583i
$610$		0			0
$611$	4.28476	−	7.42141i	0.173343	−	0.300238i
$612$		0			0
$613$	−10.2419	−	17.7395i	−0.413666	−	0.716490i	0.581622	−	0.813460i	$-0.302418\pi$
$613$	−10.2419	−	17.7395i	−0.413666	−	0.716490i	−0.995287	+	0.0969693i	$0.969085\pi$
$614$		0			0
$615$	3.25836	−	1.85528i	0.131390	−	0.0748122i
$616$		0			0
$617$	18.2274	−	6.63424i	0.733809	−	0.267085i	0.0520327	−	0.998645i	$-0.483430\pi$
$617$	18.2274	−	6.63424i	0.733809	−	0.267085i	0.681776	+	0.731561i	$0.261208\pi$
$618$		0			0
$619$	−4.16898	−	23.6434i	−0.167565	−	0.950310i	−0.946380	−	0.323056i	$-0.895290\pi$
$619$	−4.16898	−	23.6434i	−0.167565	−	0.950310i	0.778815	−	0.627254i	$-0.215821\pi$
$620$		0			0
$621$	39.5894	+	7.71654i	1.58867	+	0.309654i
$622$		0			0
$623$	−2.16970	−	12.3050i	−0.0869271	−	0.492988i
$624$		0			0
$625$	24.9549	−	9.08284i	0.998196	−	0.363314i
$626$		0			0
$627$	25.4085	+	14.8732i	1.01472	+	0.593979i
$628$		0			0
$629$	1.57392	+	2.72611i	0.0627563	+	0.108697i
$630$		0			0
$631$	−11.3984	+	19.7426i	−0.453762	+	0.785939i	−0.998616	−	0.0525921i	$-0.983252\pi$
$631$	−11.3984	+	19.7426i	−0.453762	+	0.785939i	0.544854	+	0.838531i	$0.316585\pi$
$632$		0			0
$633$	10.3374	+	12.4706i	0.410875	+	0.495660i
$634$		0			0
$635$	0.687217	−	3.89740i	0.0272714	−	0.154664i
$636$		0			0
$637$	−0.838914	+	0.703933i	−0.0332390	+	0.0278908i
$638$		0			0
$639$	−21.6544	+	17.7326i	−0.856636	+	0.701491i
$640$		0			0
$641$	−21.0459	−	7.66007i	−0.831262	−	0.302555i	−0.108885	−	0.994054i	$-0.534728\pi$
$641$	−21.0459	−	7.66007i	−0.831262	−	0.302555i	−0.722377	+	0.691500i	$0.756950\pi$
$642$		0			0
$643$	17.6714	+	14.8280i	0.696890	+	0.584760i	0.920887	−	0.389829i	$-0.127466\pi$
$643$	17.6714	+	14.8280i	0.696890	+	0.584760i	−0.223997	+	0.974590i	$0.571910\pi$
$644$		0			0
$645$	−6.56429	−	1.19804i	−0.258469	−	0.0471729i
$646$		0			0
$647$	41.5044			1.63171			0.815854	−	0.578258i	$-0.196267\pi$
$647$	41.5044			1.63171			0.815854	+	0.578258i	$0.196267\pi$
$648$		0			0
$649$	4.28918			0.168365
$650$		0			0
$651$	14.5986	+	2.66438i	0.572164	+	0.104425i
$652$		0			0
$653$	−23.6796	−	19.8696i	−0.926655	−	0.777556i	0.0485590	−	0.998820i	$-0.484537\pi$
$653$	−23.6796	−	19.8696i	−0.926655	−	0.777556i	−0.975214	+	0.221265i	$0.928982\pi$
$654$		0			0
$655$	−18.6977	−	6.80540i	−0.730579	−	0.265909i
$656$		0			0
$657$	2.57570	+	15.7054i	0.100488	+	0.612725i
$658$		0			0
$659$	31.0941	−	26.0911i	1.21125	−	1.01636i	0.212019	−	0.977265i	$-0.431996\pi$
$659$	31.0941	−	26.0911i	1.21125	−	1.01636i	0.999235	−	0.0390980i	$-0.0124484\pi$
$660$		0			0
$661$	3.91124	−	22.1818i	0.152130	−	0.862770i	−0.809234	−	0.587487i	$-0.800117\pi$
$661$	3.91124	−	22.1818i	0.152130	−	0.862770i	0.961363	−	0.275283i	$-0.0887716\pi$
$662$		0			0
$663$	−0.576129	−	0.695015i	−0.0223750	−	0.0269922i
$664$		0			0
$665$	−4.87146	+	8.43762i	−0.188907	+	0.327197i
$666$		0			0
$667$	35.8334	+	62.0652i	1.38747	+	2.40317i
$668$		0			0
$669$	−40.5376	−	23.7293i	−1.56728	−	0.917427i
$670$		0			0
$671$	−14.2015	+	5.16891i	−0.548241	+	0.199544i
$672$		0			0
$673$	−1.04946	−	5.95180i	−0.0404538	−	0.229425i	0.957877	−	0.287179i	$-0.0927174\pi$
$673$	−1.04946	−	5.95180i	−0.0404538	−	0.229425i	−0.998331	+	0.0577535i	$0.981606\pi$
$674$		0			0
$675$	8.70122	−	22.6326i	0.334910	−	0.871131i
$676$		0			0
$677$	0.807918	+	4.58193i	0.0310508	+	0.176098i	0.996389	−	0.0849037i	$-0.0270583\pi$
$677$	0.807918	+	4.58193i	0.0310508	+	0.176098i	−0.965338	+	0.261002i	$0.915947\pi$
$678$		0			0
$679$	3.54520	−	1.29035i	0.136052	−	0.0495190i
$680$		0			0
$681$	−6.65433	+	3.78892i	−0.254994	+	0.145192i
$682$		0			0
$683$	−14.8390	−	25.7019i	−0.567799	−	0.983456i	−0.996783	−	0.0801445i	$-0.974462\pi$
$683$	−14.8390	−	25.7019i	−0.567799	−	0.983456i	0.428984	−	0.903312i	$-0.358872\pi$
$684$		0			0
$685$	−33.5033	+	58.0295i	−1.28010	+	2.21719i
$686$		0			0
$687$	−8.92177	+	24.0630i	−0.340387	+	0.918059i
$688$		0			0
$689$	−1.88226	+	10.6748i	−0.0717082	+	0.406677i
$690$		0			0
$691$	14.7955	−	12.4149i	0.562849	−	0.472286i	−0.316415	−	0.948621i	$-0.602479\pi$
$691$	14.7955	−	12.4149i	0.562849	−	0.472286i	0.879264	+	0.476334i	$0.158035\pi$
$692$		0			0
$693$	16.2717	+	0.194920i	0.618112	+	0.00740441i
$694$		0			0
$695$	57.3438	+	20.8714i	2.17517	+	0.791698i
$696$		0			0
$697$	−0.253853	−	0.213008i	−0.00961538	−	0.00806826i
$698$		0			0
$699$	23.6396	−	27.8324i	0.894133	−	1.05272i
$700$		0			0
$701$	6.90749			0.260892			0.130446	−	0.991455i	$-0.458359\pi$
$701$	6.90749			0.260892			0.130446	+	0.991455i	$0.458359\pi$
$702$		0			0
$703$	20.7263			0.781708
$704$		0			0
$705$	−14.1750	−	39.6835i	−0.533863	−	1.49457i
$706$		0			0
$707$	1.25765	+	1.05530i	0.0472989	+	0.0396885i
$708$		0			0
$709$	35.0290	+	12.7495i	1.31554	+	0.478818i	0.902027	−	0.431679i	$-0.142079\pi$
$709$	35.0290	+	12.7495i	1.31554	+	0.478818i	0.413515	+	0.910497i	$0.364301\pi$
$710$		0			0
$711$	9.27934	−	49.1739i	0.348003	−	1.84416i
$712$		0			0
$713$	50.9464	−	42.7491i	1.90796	−	1.60097i
$714$		0			0
$715$	3.20709	−	18.1883i	0.119938	−	0.680205i
$716$		0			0
$717$	−35.0129	+	5.95773i	−1.30758	+	0.222496i
$718$		0			0
$719$	−7.54295	+	13.0648i	−0.281304	+	0.487234i	−0.971706	−	0.236192i	$-0.924100\pi$
$719$	−7.54295	+	13.0648i	−0.281304	+	0.487234i	0.690402	+	0.723426i	$0.257434\pi$
$720$		0			0
$721$	−1.12545	−	1.94934i	−0.0419140	−	0.0725972i
$722$		0			0
$723$	0.134348	−	22.4312i	0.00499645	−	0.834225i
$724$		0			0
$725$	40.4852	−	14.7354i	1.50358	−	0.547260i
$726$		0			0
$727$	3.31046	+	18.7745i	0.122778	+	0.696309i	0.982603	+	0.185720i	$0.0594616\pi$
$727$	3.31046	+	18.7745i	0.122778	+	0.696309i	−0.859825	+	0.510589i	$0.829427\pi$
$728$		0			0
$729$	12.6512	+	23.8526i	0.468563	+	0.883430i
$730$		0			0
$731$	0.102406	+	0.580774i	0.00378762	+	0.0214807i
$732$		0			0
$733$	21.8156	−	7.94024i	0.805779	−	0.293280i	0.0939000	−	0.995582i	$-0.470067\pi$
$733$	21.8156	−	7.94024i	0.805779	−	0.293280i	0.711879	+	0.702302i	$0.247844\pi$
$734$		0			0
$735$	−0.0322526	+	5.38501i	−0.00118965	+	0.198629i
$736$		0			0
$737$	5.00976	+	8.67716i	0.184537	+	0.319627i
$738$		0			0
$739$	24.6678	−	42.7258i	0.907419	−	1.57170i	0.0897812	−	0.995962i	$-0.471383\pi$
$739$	24.6678	−	42.7258i	0.907419	−	1.57170i	0.817637	−	0.575734i	$-0.195283\pi$
$740$		0			0
$741$	−5.85979	+	0.997090i	−0.215265	+	0.0366290i
$742$		0			0
$743$	−0.985683	+	5.59009i	−0.0361612	+	0.205080i	−0.997535	−	0.0701641i	$-0.977648\pi$
$743$	−0.985683	+	5.59009i	−0.0361612	+	0.205080i	0.961374	+	0.275245i	$0.0887588\pi$
$744$		0			0
$745$	7.59292	−	6.37121i	0.278183	−	0.233423i
$746$		0			0
$747$	2.33213	−	12.3586i	0.0853280	−	0.452178i
$748$		0			0
$749$	−12.6599	−	4.60782i	−0.462582	−	0.168366i
$750$		0			0
$751$	31.9590	+	26.8168i	1.16620	+	0.978558i	0.999972	−	0.00752975i	$-0.00239682\pi$
$751$	31.9590	+	26.8168i	1.16620	+	0.978558i	0.166228	+	0.986087i	$0.446841\pi$
$752$		0			0
$753$	14.9900	+	41.9650i	0.546265	+	1.52929i
$754$		0			0
$755$	69.0441			2.51277
$756$		0			0
$757$	−18.3282			−0.666148			−0.333074	−	0.942901i	$-0.608086\pi$
$757$	−18.3282			−0.666148			−0.333074	+	0.942901i	$0.608086\pi$
$758$		0			0
$759$	47.2114	−	55.5849i	1.71367	−	2.01760i
$760$		0			0
$761$	14.6004	+	12.2512i	0.529264	+	0.444105i	0.867847	−	0.496831i	$-0.165503\pi$
$761$	14.6004	+	12.2512i	0.529264	+	0.444105i	−0.338583	+	0.940936i	$0.609948\pi$
$762$		0			0
$763$	−3.73505	−	1.35945i	−0.135218	−	0.0492153i
$764$		0			0
$765$	−4.43885	−	0.0531733i	−0.160487	−	0.00192249i
$766$		0			0
$767$	−0.663358	+	0.556624i	−0.0239525	+	0.0200985i
$768$		0			0
$769$	3.05363	−	17.3180i	0.110117	−	0.624503i	−0.878936	−	0.476940i	$-0.841746\pi$
$769$	3.05363	−	17.3180i	0.110117	−	0.624503i	0.989053	−	0.147563i	$-0.0471430\pi$
$770$		0			0
$771$	−0.165780	+	0.447126i	−0.00597042	+	0.0161029i
$772$		0			0
$773$	−17.3439	+	30.0406i	−0.623818	+	1.08048i	0.364951	+	0.931027i	$0.381086\pi$
$773$	−17.3439	+	30.0406i	−0.623818	+	1.08048i	−0.988768	+	0.149457i	$0.952247\pi$
$774$		0			0
$775$	−19.9905	−	34.6245i	−0.718079	−	1.24375i
$776$		0			0
$777$	9.95517	−	5.66840i	0.357140	−	0.203353i
$778$		0			0
$779$	−2.05033	+	0.746259i	−0.0734607	+	0.0267375i
$780$		0			0
$781$	8.78766	+	49.8373i	0.314447	+	1.78332i
$782$		0			0
$783$	−17.2154	+	44.7787i	−0.615226	+	1.60026i
$784$		0			0
$785$	−12.5356	−	71.0932i	−0.447416	−	2.53742i
$786$		0			0
$787$	−23.7925	+	8.65977i	−0.848112	+	0.308687i	−0.729270	−	0.684226i	$-0.760140\pi$
$787$	−23.7925	+	8.65977i	−0.848112	+	0.308687i	−0.118842	+	0.992913i	$0.537918\pi$
$788$		0			0
$789$	36.5128	+	21.3733i	1.29989	+	0.760908i
$790$		0			0
$791$	1.07046	+	1.85409i	0.0380612	+	0.0659239i
$792$		0			0
$793$	1.52559	−	2.64240i	0.0541752	−	0.0938342i
$794$		0			0
$795$	34.0163	+	41.0357i	1.20644	+	1.45539i
$796$		0			0
$797$	−5.93407	+	33.6538i	−0.210196	+	1.19208i	0.678856	+	0.734272i	$0.262476\pi$
$797$	−5.93407	+	33.6538i	−0.210196	+	1.19208i	−0.889051	+	0.457807i	$0.848635\pi$
$798$		0			0
$799$	−2.85294	+	2.39390i	−0.100930	+	0.0846902i
$800$		0			0
$801$	−6.06645	−	36.9902i	−0.214348	−	1.30699i
$802$		0			0
$803$	27.0408	+	9.84205i	0.954250	+	0.347318i
$804$		0			0
$805$	18.4877	+	15.5130i	0.651604	+	0.546761i
$806$		0			0
$807$	11.7430	+	2.14320i	0.413372	+	0.0754441i
$808$		0			0
$809$	32.5049			1.14281			0.571406	−	0.820667i	$-0.306398\pi$
$809$	32.5049			1.14281			0.571406	+	0.820667i	$0.306398\pi$
$810$		0			0
$811$	44.2170			1.55267			0.776335	−	0.630321i	$-0.217077\pi$
$811$	44.2170			1.55267			0.776335	+	0.630321i	$0.217077\pi$
$812$		0			0
$813$	−48.3987	−	8.83321i	−1.69742	−	0.309794i
$814$		0			0
$815$	8.78926	+	7.37507i	0.307874	+	0.258337i
$816$		0			0
$817$	3.64880	+	1.32806i	0.127655	+	0.0464628i
$818$		0			0
$819$	−2.54186	+	2.08150i	−0.0888197	+	0.0727335i
$820$		0			0
$821$	3.67295	−	3.08197i	0.128187	−	0.107562i	−0.576440	−	0.817139i	$-0.695559\pi$
$821$	3.67295	−	3.08197i	0.128187	−	0.107562i	0.704627	+	0.709578i	$0.251114\pi$
$822$		0			0
$823$	−8.73555	+	49.5417i	−0.304502	+	1.72692i	0.321338	+	0.946965i	$0.395868\pi$
$823$	−8.73555	+	49.5417i	−0.304502	+	1.72692i	−0.625839	+	0.779952i	$0.715244\pi$
$824$		0			0
$825$	−27.9795	−	33.7532i	−0.974123	−	1.17514i
$826$		0			0
$827$	−13.1450	+	22.7679i	−0.457098	+	0.791717i	−0.998806	−	0.0488496i	$-0.984444\pi$
$827$	−13.1450	+	22.7679i	−0.457098	+	0.791717i	0.541708	+	0.840567i	$0.317778\pi$
$828$		0			0
$829$	−4.83977	−	8.38273i	−0.168092	−	0.291144i	0.769657	−	0.638458i	$-0.220427\pi$
$829$	−4.83977	−	8.38273i	−0.168092	−	0.291144i	−0.937749	+	0.347313i	$0.887094\pi$
$830$		0			0
$831$	−15.4487	−	9.04309i	−0.535908	−	0.313701i
$832$		0			0
$833$	0.447232	−	0.162779i	0.0154957	−	0.00563996i
$834$		0			0
$835$	−3.73564	−	21.1858i	−0.129277	−	0.733166i
$836$		0			0
$837$	43.6969	+	8.51715i	1.51039	+	0.294396i
$838$		0			0
$839$	2.30840	+	13.0916i	0.0796948	+	0.451972i	0.998376	+	0.0569715i	$0.0181444\pi$
$839$	2.30840	+	13.0916i	0.0796948	+	0.451972i	−0.918681	+	0.395000i	$0.870744\pi$
$840$		0			0
$841$	−52.8489	+	19.2354i	−1.82238	+	0.663290i
$842$		0			0
$843$	3.32431	−	1.89284i	0.114495	−	0.0651928i
$844$		0			0
$845$	−18.3447	−	31.7740i	−0.631078	−	1.09306i
$846$		0			0
$847$	9.21152	−	15.9548i	0.316512	−	0.548214i
$848$		0			0
$849$	−15.3805	+	41.4828i	−0.527858	+	1.42369i
$850$		0			0
$851$	8.91519	−	50.5606i	0.305609	−	1.73319i
$852$		0			0
$853$	−12.8606	+	10.7913i	−0.440337	+	0.369487i	−0.835836	−	0.548980i	$-0.815016\pi$
$853$	−12.8606	+	10.7913i	−0.440337	+	0.369487i	0.395498	+	0.918467i	$0.370572\pi$
$854$		0			0
$855$	−14.9165	+	25.1360i	−0.510135	+	0.859633i
$856$		0			0
$857$	−36.2756	−	13.2032i	−1.23915	−	0.451014i	−0.362429	−	0.932011i	$-0.618052\pi$
$857$	−36.2756	−	13.2032i	−1.23915	−	0.451014i	−0.876722	+	0.480997i	$0.840275\pi$
$858$		0			0
$859$	7.20081	+	6.04220i	0.245689	+	0.206157i	0.757313	−	0.653052i	$-0.226512\pi$
$859$	7.20081	+	6.04220i	0.245689	+	0.206157i	−0.511625	+	0.859209i	$0.670956\pi$
$860$		0			0
$861$	−0.780713	+	0.919180i	−0.0266066	+	0.0313256i
$862$		0			0
$863$	31.3415			1.06688			0.533438	−	0.845839i	$-0.320900\pi$
$863$	31.3415			1.06688			0.533438	+	0.845839i	$0.320900\pi$
$864$		0			0
$865$	−34.7198			−1.18051
$866$		0			0
$867$	−9.77286	−	27.3595i	−0.331904	−	0.929176i
$868$		0			0
$869$	−69.3121	−	58.1598i	−2.35125	−	1.97293i
$870$		0			0
$871$	−1.90087	−	0.691861i	−0.0644086	−	0.0234428i
$872$		0			0
$873$	10.6812	−	3.74337i	0.361504	−	0.126694i
$874$		0			0
$875$	−0.794396	+	0.666578i	−0.0268555	+	0.0225344i
$876$		0			0
$877$	0.106438	−	0.603641i	0.00359416	−	0.0203835i	−0.982958	−	0.183831i	$-0.941150\pi$
$877$	0.106438	−	0.603641i	0.00359416	−	0.0203835i	0.986552	+	0.163447i	$0.0522613\pi$
$878$		0			0
$879$	34.9452	−	5.94620i	1.17867	−	0.200560i
$880$		0			0
$881$	−0.103927	+	0.180007i	−0.00350140	+	0.00606460i	−0.867771	−	0.496965i	$-0.834448\pi$
$881$	−0.103927	+	0.180007i	−0.00350140	+	0.00606460i	0.864269	+	0.503029i	$0.167781\pi$
$882$		0			0
$883$	1.94219	+	3.36397i	0.0653599	+	0.113207i	0.896854	−	0.442328i	$-0.145847\pi$
$883$	1.94219	+	3.36397i	0.0653599	+	0.113207i	−0.831494	+	0.555534i	$0.812514\pi$
$884$		0			0
$885$	−0.0255032	+	4.25811i	−0.000857281	+	0.143135i
$886$		0			0
$887$	−32.0615	+	11.6694i	−1.07652	+	0.391822i	−0.818612	−	0.574348i	$-0.805256\pi$
$887$	−32.0615	+	11.6694i	−1.07652	+	0.391822i	−0.257909	+	0.966169i	$0.583034\pi$
$888$		0			0
$889$	0.221035	+	1.25355i	0.00741326	+	0.0420427i
$890$		0			0
$891$	48.8047	+	1.16944i	1.63502	+	0.0391777i
$892$		0			0
$893$	4.25812	+	24.1490i	0.142493	+	0.808116i
$894$		0			0
$895$	−32.9552	+	11.9947i	−1.10157	+	0.400939i
$896$		0			0
$897$	−0.0881837	+	14.7235i	−0.00294437	+	0.491603i
$898$		0			0
$899$	39.5511	+	68.5046i	1.31910	+	2.28476i
$900$		0			0
$901$	2.35538	−	4.07964i	0.0784691	−	0.135913i
$902$		0			0
$903$	2.11578	−	0.360018i	0.0704089	−	0.0119806i
$904$		0			0
$905$	−6.54128	+	37.0974i	−0.217439	+	1.23316i
$906$		0			0
$907$	−27.8538	+	23.3721i	−0.924871	+	0.776059i	−0.974889	−	0.222690i	$-0.928516\pi$
$907$	−27.8538	+	23.3721i	−0.924871	+	0.776059i	0.0500188	+	0.998748i	$0.484072\pi$
$908$		0			0
$909$	3.73477	+	3.21085i	0.123874	+	0.106497i
$910$		0			0
$911$	−29.8400	−	10.8609i	−0.988642	−	0.359836i	−0.203448	−	0.979086i	$-0.565215\pi$
$911$	−29.8400	−	10.8609i	−0.988642	−	0.359836i	−0.785194	+	0.619249i	$0.787437\pi$
$912$		0			0
$913$	−17.4198	−	14.6170i	−0.576512	−	0.483751i
$914$		0			0
$915$	−5.04703	−	14.1293i	−0.166850	−	0.467101i
$916$		0			0
$917$	6.39983			0.211341
$918$		0			0
$919$	−32.6964			−1.07855			−0.539277	−	0.842129i	$-0.681302\pi$
$919$	−32.6964			−1.07855			−0.539277	+	0.842129i	$0.681302\pi$
$920$		0			0
$921$	−32.6428	+	38.4323i	−1.07562	+	1.26639i
$922$		0			0
$923$	−7.82667	−	6.56736i	−0.257618	−	0.216167i
$924$		0			0
$925$	−29.0028	−	10.5561i	−0.953605	−	0.347084i
$926$		0			0
$927$	−3.30606	−	5.88804i	−0.108585	−	0.193389i
$928$		0			0
$929$	−39.4667	+	33.1165i	−1.29486	+	1.08652i	−0.303850	+	0.952720i	$0.598272\pi$
$929$	−39.4667	+	33.1165i	−1.29486	+	1.08652i	−0.991009	+	0.133796i	$0.957283\pi$
$930$		0			0
$931$	0.544159	−	3.08608i	0.0178341	−	0.101142i
$932$		0			0
$933$	17.5724	−	47.3946i	0.575295	−	1.55163i
$934$		0			0
$935$	−4.01323	+	6.95112i	−0.131247	+	0.227326i
$936$		0			0
$937$	−12.7506	−	22.0846i	−0.416543	−	0.721474i	0.579046	−	0.815295i	$-0.303425\pi$
$937$	−12.7506	−	22.0846i	−0.416543	−	0.721474i	−0.995589	+	0.0938210i	$0.970092\pi$
$938$		0			0
$939$	21.4029	−	12.1867i	0.698459	−	0.397697i
$940$		0			0
$941$	4.84984	−	1.76520i	0.158100	−	0.0575438i	−0.261758	−	0.965134i	$-0.584302\pi$
$941$	4.84984	−	1.76520i	0.158100	−	0.0575438i	0.419858	+	0.907590i	$0.362080\pi$
$942$		0			0
$943$	0.938526	+	5.32265i	0.0305626	+	0.173329i
$944$		0			0
$945$	−0.290259	+	16.1527i	−0.00944213	+	0.525448i
$946$		0			0
$947$	−1.51468	−	8.59017i	−0.0492204	−	0.279143i	0.950257	−	0.311467i	$-0.100820\pi$
$947$	−1.51468	−	8.59017i	−0.0492204	−	0.279143i	−0.999477	+	0.0323239i	$0.989709\pi$
$948$		0			0
$949$	−5.45933	+	1.98704i	−0.177217	+	0.0645019i
$950$		0			0
$951$	−22.2925	−	13.0492i	−0.722885	−	0.423151i
$952$		0			0
$953$	−6.20537	−	10.7480i	−0.201012	−	0.348162i	0.747843	−	0.663876i	$-0.231090\pi$
$953$	−6.20537	−	10.7480i	−0.201012	−	0.348162i	−0.948855	+	0.315713i	$0.897756\pi$
$954$		0			0
$955$	17.6784	−	30.6198i	0.572059	−	0.990835i
$956$		0			0
$957$	55.3575	+	66.7807i	1.78945	+	2.15871i
$958$		0			0
$959$	3.74244	−	21.2244i	0.120850	−	0.685372i
$960$		0			0
$961$	32.4849	−	27.2580i	1.04790	−	0.879292i
$962$		0			0
$963$	−37.8113	−	14.2774i	−1.21845	−	0.460083i
$964$		0			0
$965$	−51.3112	−	18.6758i	−1.65177	−	0.601194i
$966$		0			0
$967$	−34.9261	−	29.3065i	−1.12315	−	0.942433i	−0.124389	−	0.992234i	$-0.539697\pi$
$967$	−34.9261	−	29.3065i	−1.12315	−	0.942433i	−0.998759	+	0.0498004i	$0.984141\pi$
$968$		0			0
$969$	2.54125	+	0.463802i	0.0816368	+	0.0148995i
$970$		0			0
$971$	−30.2448			−0.970602			−0.485301	−	0.874347i	$-0.661290\pi$
$971$	−30.2448			−0.970602			−0.485301	+	0.874347i	$0.661290\pi$
$972$		0			0
$973$	−19.6276			−0.629231
$974$		0			0
$975$	8.70756	+	1.58921i	0.278865	+	0.0508954i
$976$		0			0
$977$	5.74337	+	4.81926i	0.183747	+	0.154182i	0.730021	−	0.683424i	$-0.239510\pi$
$977$	5.74337	+	4.81926i	0.183747	+	0.154182i	−0.546275	+	0.837606i	$0.683955\pi$
$978$		0			0
$979$	−63.6881	−	23.1806i	−2.03548	−	0.740855i
$980$		0			0
$981$	−11.1555	−	4.21226i	−0.356167	−	0.134487i
$982$		0			0
$983$	10.3381	−	8.67469i	0.329734	−	0.276680i	−0.462857	−	0.886433i	$-0.653176\pi$
$983$	10.3381	−	8.67469i	0.329734	−	0.276680i	0.792592	+	0.609753i	$0.208731\pi$
$984$		0			0
$985$	−7.64347	+	43.3483i	−0.243541	+	1.38119i
$986$		0			0
$987$	8.64971	+	10.4346i	0.275323	+	0.332137i
$988$		0			0
$989$	4.80920	−	8.32978i	0.152924	−	0.264872i
$990$		0			0
$991$	−25.0817	−	43.4429i	−0.796748	−	1.38001i	−0.921723	−	0.387848i	$-0.873218\pi$
$991$	−25.0817	−	43.4429i	−0.796748	−	1.38001i	0.124975	−	0.992160i	$-0.460115\pi$
$992$		0			0
$993$	−9.78605	−	5.72840i	−0.310551	−	0.181785i
$994$		0			0
$995$	−56.5438	+	20.5803i	−1.79256	+	0.652439i
$996$		0			0
$997$	6.35038	+	36.0148i	0.201119	+	1.14060i	0.903432	+	0.428732i	$0.141040\pi$
$997$	6.35038	+	36.0148i	0.201119	+	1.14060i	−0.702313	+	0.711868i	$0.747849\pi$
$998$		0			0
$999$	30.0671	−	16.6462i	0.951280	−	0.526664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.337.1	✓	54
27.25	even	9	inner	756.2.bo.b.673.1	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.337.1	✓	54	1.1	even	1	trivial
756.2.bo.b.673.1	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)

\(f(q)\)	\(=\)	\(q+(-1.70391 - 0.310978i) q^{3} +(-2.38170 - 1.99849i) q^{5} +(0.939693 + 0.342020i) q^{7} +(2.80659 + 1.05975i) q^{9} +O(q^{10})\)	\(q+(-1.70391 - 0.310978i) q^{3} +(-2.38170 - 1.99849i) q^{5} +(0.939693 + 0.342020i) q^{7} +(2.80659 + 1.05975i) q^{9} +(4.15526 - 3.48667i) q^{11} +(-0.190166 + 1.07849i) q^{13} +(3.43671 + 4.14589i) q^{15} +(0.237967 - 0.412171i) q^{17} +(-1.56684 - 2.71385i) q^{19} +(-1.49479 - 0.874994i) q^{21} +(-7.29424 + 2.65489i) q^{23} +(0.810322 + 4.59556i) q^{25} +(-4.45259 - 2.67851i) q^{27} +(-1.60322 - 9.09232i) q^{29} +(-8.05103 + 2.93034i) q^{31} +(-8.16444 + 4.64877i) q^{33} +(-1.55455 - 2.69255i) q^{35} +(-3.30702 + 5.72792i) q^{37} +(0.659412 - 1.77850i) q^{39} +(0.120907 - 0.685699i) q^{41} +(-0.949211 + 0.796483i) q^{43} +(-4.56655 - 8.13294i) q^{45} +(-7.35323 - 2.67636i) q^{47} +(0.766044 + 0.642788i) q^{49} +(-0.533649 + 0.628298i) q^{51} +9.89793 q^{53} -16.8647 q^{55} +(1.82580 + 5.11140i) q^{57} +(0.605737 + 0.508274i) q^{59} +(-2.61812 - 0.952917i) q^{61} +(2.27487 + 1.95575i) q^{63} +(2.60826 - 2.18859i) q^{65} +(-0.320755 + 1.81909i) q^{67} +(13.2543 - 2.25533i) q^{69} +(-4.66476 + 8.07960i) q^{71} +(2.65253 + 4.59432i) q^{73} +(0.0484081 - 8.08240i) q^{75} +(5.09718 - 1.85522i) q^{77} +(-2.89655 - 16.4272i) q^{79} +(6.75384 + 5.94858i) q^{81} +(-0.727975 - 4.12855i) q^{83} +(-1.39048 + 0.506095i) q^{85} +(-0.0957754 + 15.9910i) q^{87} +(-6.24740 - 10.8208i) q^{89} +(-0.547563 + 0.948406i) q^{91} +(14.6295 - 2.48932i) q^{93} +(-1.69184 + 9.59491i) q^{95} +(2.89008 - 2.42506i) q^{97} +(15.3571 - 5.38210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more