LMFDB - Embedded newform 756.2.bq.a.25.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.16
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.898399 - 1.48084i) q^{3} +(-3.88836 - 1.41525i) q^{5} +(0.934219 - 2.47533i) q^{7} +(-1.38576 - 2.66077i) q^{9} +O(q^{10})$	\(q+(0.898399 - 1.48084i) q^{3} +(-3.88836 - 1.41525i) q^{5} +(0.934219 - 2.47533i) q^{7} +(-1.38576 - 2.66077i) q^{9} +(-3.38090 + 1.23055i) q^{11} +(0.578379 + 3.28015i) q^{13} +(-5.58906 + 4.48658i) q^{15} -2.24918 q^{17} +0.331536 q^{19} +(-2.82625 - 3.60726i) q^{21} +(1.55620 + 8.82567i) q^{23} +(9.28623 + 7.79207i) q^{25} +(-5.18512 - 0.338349i) q^{27} +(1.34335 - 7.61850i) q^{29} +(-1.30096 + 1.09163i) q^{31} +(-1.21516 + 6.11209i) q^{33} +(-7.13579 + 8.30281i) q^{35} +(0.451379 - 0.781811i) q^{37} +(5.37699 + 2.09040i) q^{39} +(-0.486327 - 2.75810i) q^{41} +(-9.27729 - 7.78457i) q^{43} +(1.62268 + 12.3072i) q^{45} +(-5.27406 - 4.42546i) q^{47} +(-5.25447 - 4.62499i) q^{49} +(-2.02066 + 3.33067i) q^{51} +(-4.64586 + 8.04687i) q^{53} +14.8877 q^{55} +(0.297852 - 0.490951i) q^{57} +(-1.82129 - 10.3290i) q^{59} +(-6.72097 - 5.63956i) q^{61} +(-7.88086 + 0.944461i) q^{63} +(2.39328 - 13.5730i) q^{65} +(6.79902 + 2.47464i) q^{67} +(14.4675 + 5.62449i) q^{69} +(4.97559 + 8.61798i) q^{71} +(-3.58835 - 6.21520i) q^{73} +(19.8815 - 6.75100i) q^{75} +(-0.112498 + 9.51844i) q^{77} +(-9.69355 + 3.52816i) q^{79} +(-5.15935 + 7.37435i) q^{81} +(2.06311 - 11.7005i) q^{83} +(8.74564 + 3.18315i) q^{85} +(-10.0749 - 8.83373i) q^{87} +7.33190 q^{89} +(8.65978 + 1.63270i) q^{91} +(0.447752 + 2.90723i) q^{93} +(-1.28913 - 0.469206i) q^{95} +(-2.26222 - 1.89822i) q^{97} +(7.95932 + 7.29055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.898399	−	1.48084i	0.518691	−	0.854962i
$3$	0.898399	−	1.48084i	0.518691	−	0.854962i
$4$		0			0
$5$	−3.88836	−	1.41525i	−1.73893	−	0.632919i	−0.739729	−	0.672904i	$-0.765047\pi$
$5$	−3.88836	−	1.41525i	−1.73893	−	0.632919i	−0.999200	+	0.0399858i	$0.987269\pi$
$6$		0			0
$7$	0.934219	−	2.47533i	0.353102	−	0.935585i
$7$	0.934219	−	2.47533i	0.353102	−	0.935585i
$8$		0			0
$9$	−1.38576	−	2.66077i	−0.461919	−	0.886922i
$10$		0			0
$11$	−3.38090	+	1.23055i	−1.01938	+	0.371024i	−0.797028	−	0.603942i	$-0.793596\pi$
$11$	−3.38090	+	1.23055i	−1.01938	+	0.371024i	−0.222353	+	0.974966i	$0.571374\pi$
$12$		0			0
$13$	0.578379	+	3.28015i	0.160414	+	0.909751i	0.953668	+	0.300861i	$0.0972739\pi$
$13$	0.578379	+	3.28015i	0.160414	+	0.909751i	−0.793255	+	0.608890i	$0.791615\pi$
$14$		0			0
$15$	−5.58906	+	4.48658i	−1.44309	+	1.15843i
$16$		0			0
$17$	−2.24918			−0.545507			−0.272754	−	0.962084i	$-0.587934\pi$
$17$	−2.24918			−0.545507			−0.272754	+	0.962084i	$0.587934\pi$
$18$		0			0
$19$	0.331536			0.0760596			0.0380298	−	0.999277i	$-0.487892\pi$
$19$	0.331536			0.0760596			0.0380298	+	0.999277i	$0.487892\pi$
$20$		0			0
$21$	−2.82625	−	3.60726i	−0.616739	−	0.787168i
$22$		0			0
$23$	1.55620	+	8.82567i	0.324491	+	1.84028i	0.513229	+	0.858252i	$0.328449\pi$
$23$	1.55620	+	8.82567i	0.324491	+	1.84028i	−0.188738	+	0.982027i	$0.560440\pi$
$24$		0			0
$25$	9.28623	+	7.79207i	1.85725	+	1.55841i
$26$		0			0
$27$	−5.18512	−	0.338349i	−0.997878	−	0.0651153i
$28$		0			0
$29$	1.34335	−	7.61850i	0.249453	−	1.41472i	−0.560466	−	0.828177i	$-0.689378\pi$
$29$	1.34335	−	7.61850i	0.249453	−	1.41472i	0.809919	−	0.586542i	$-0.199511\pi$
$30$		0			0
$31$	−1.30096	+	1.09163i	−0.233659	+	0.196063i	−0.752098	−	0.659051i	$-0.770958\pi$
$31$	−1.30096	+	1.09163i	−0.233659	+	0.196063i	0.518439	+	0.855115i	$0.326513\pi$
$32$		0			0
$33$	−1.21516	+	6.11209i	−0.211532	+	1.06398i
$34$		0			0
$35$	−7.13579	+	8.30281i	−1.20617	+	1.40343i
$36$		0			0
$37$	0.451379	−	0.781811i	0.0742062	−	0.128529i	−0.826535	−	0.562886i	$-0.809691\pi$
$37$	0.451379	−	0.781811i	0.0742062	−	0.128529i	0.900741	+	0.434357i	$0.143024\pi$
$38$		0			0
$39$	5.37699	+	2.09040i	0.861007	+	0.334732i
$40$		0			0
$41$	−0.486327	−	2.75810i	−0.0759515	−	0.430743i	−0.998945	−	0.0459265i	$-0.985376\pi$
$41$	−0.486327	−	2.75810i	−0.0759515	−	0.430743i	0.922993	−	0.384816i	$-0.125735\pi$
$42$		0			0
$43$	−9.27729	−	7.78457i	−1.41477	−	1.18714i	−0.954071	−	0.299582i	$-0.903153\pi$
$43$	−9.27729	−	7.78457i	−1.41477	−	1.18714i	−0.460703	−	0.887554i	$-0.652403\pi$
$44$		0			0
$45$	1.62268	+	12.3072i	0.241895	+	1.83465i
$46$		0			0
$47$	−5.27406	−	4.42546i	−0.769300	−	0.645520i	0.171229	−	0.985231i	$-0.445226\pi$
$47$	−5.27406	−	4.42546i	−0.769300	−	0.645520i	−0.940530	+	0.339712i	$0.889671\pi$
$48$		0			0
$49$	−5.25447	−	4.62499i	−0.750638	−	0.660713i
$50$		0			0
$51$	−2.02066	+	3.33067i	−0.282950	+	0.466388i
$52$		0			0
$53$	−4.64586	+	8.04687i	−0.638158	+	1.10532i	0.347678	+	0.937614i	$0.386970\pi$
$53$	−4.64586	+	8.04687i	−0.638158	+	1.10532i	−0.985837	+	0.167709i	$0.946363\pi$
$54$		0			0
$55$	14.8877			2.00746
$56$		0			0
$57$	0.297852	−	0.490951i	0.0394514	−	0.0650280i
$58$		0			0
$59$	−1.82129	−	10.3290i	−0.237111	−	1.34472i	−0.838122	−	0.545483i	$-0.816346\pi$
$59$	−1.82129	−	10.3290i	−0.237111	−	1.34472i	0.601011	−	0.799241i	$-0.294765\pi$
$60$		0			0
$61$	−6.72097	−	5.63956i	−0.860532	−	0.722072i	0.101550	−	0.994830i	$-0.467620\pi$
$61$	−6.72097	−	5.63956i	−0.860532	−	0.722072i	−0.962083	+	0.272758i	$0.912064\pi$
$62$		0			0
$63$	−7.88086	+	0.944461i	−0.992895	+	0.118991i
$64$		0			0
$65$	2.39328	−	13.5730i	0.296850	−	1.68352i
$66$		0			0
$67$	6.79902	+	2.47464i	0.830633	+	0.302326i	0.722119	−	0.691769i	$-0.243168\pi$
$67$	6.79902	+	2.47464i	0.830633	+	0.302326i	0.108514	+	0.994095i	$0.465391\pi$
$68$		0			0
$69$	14.4675	+	5.62449i	1.74168	+	0.677109i
$70$		0			0
$71$	4.97559	+	8.61798i	0.590494	+	1.02277i	0.994166	+	0.107862i	$0.0344005\pi$
$71$	4.97559	+	8.61798i	0.590494	+	1.02277i	−0.403671	+	0.914904i	$0.632266\pi$
$72$		0			0
$73$	−3.58835	−	6.21520i	−0.419984	−	0.727434i	0.575953	−	0.817483i	$-0.304631\pi$
$73$	−3.58835	−	6.21520i	−0.419984	−	0.727434i	−0.995937	+	0.0900488i	$0.971298\pi$
$74$		0			0
$75$	19.8815	−	6.75100i	2.29572	−	0.779539i
$76$		0			0
$77$	−0.112498	+	9.51844i	−0.0128204	+	1.08473i
$78$		0			0
$79$	−9.69355	+	3.52816i	−1.09061	+	0.396949i	−0.823847	−	0.566813i	$-0.808176\pi$
$79$	−9.69355	+	3.52816i	−1.09061	+	0.396949i	−0.266763	+	0.963762i	$0.585954\pi$
$80$		0			0
$81$	−5.15935	+	7.37435i	−0.573261	+	0.819373i
$82$		0			0
$83$	2.06311	−	11.7005i	0.226456	−	1.28430i	−0.633426	−	0.773804i	$-0.718352\pi$
$83$	2.06311	−	11.7005i	0.226456	−	1.28430i	0.859882	−	0.510493i	$-0.170537\pi$
$84$		0			0
$85$	8.74564	+	3.18315i	0.948598	+	0.345262i
$86$		0			0
$87$	−10.0749	−	8.83373i	−1.08014	−	0.947075i
$88$		0			0
$89$	7.33190			0.777180			0.388590	−	0.921411i	$-0.372962\pi$
$89$	7.33190			0.777180			0.388590	+	0.921411i	$0.372962\pi$
$90$		0			0
$91$	8.65978	+	1.63270i	0.907791	+	0.171154i
$92$		0			0
$93$	0.447752	+	2.90723i	0.0464297	+	0.301466i
$94$		0			0
$95$	−1.28913	−	0.469206i	−0.132262	−	0.0481395i
$96$		0			0
$97$	−2.26222	−	1.89822i	−0.229693	−	0.192735i	0.520676	−	0.853754i	$-0.325680\pi$
$97$	−2.26222	−	1.89822i	−0.229693	−	0.192735i	−0.750369	+	0.661019i	$0.770124\pi$
$98$		0			0
$99$	7.95932	+	7.29055i	0.799941	+	0.732728i
$100$		0			0
$101$	−0.520459	+	2.95167i	−0.0517876	+	0.293702i	−0.999691	−	0.0248556i	$-0.992087\pi$
$101$	−0.520459	+	2.95167i	−0.0517876	+	0.293702i	0.947903	+	0.318558i	$0.103199\pi$
$102$		0			0
$103$	−3.45456	−	1.25736i	−0.340388	−	0.123891i	0.166170	−	0.986097i	$-0.446860\pi$
$103$	−3.45456	−	1.25736i	−0.340388	−	0.123891i	−0.506558	+	0.862206i	$0.669082\pi$
$104$		0			0
$105$	5.88433	+	18.0262i	0.574252	+	1.75918i
$106$		0			0
$107$	−4.24725	−	7.35646i	−0.410597	−	0.711176i	0.584358	−	0.811496i	$-0.301346\pi$
$107$	−4.24725	−	7.35646i	−0.410597	−	0.711176i	−0.994955	+	0.100321i	$0.968013\pi$
$108$		0			0
$109$	−4.20280	+	7.27946i	−0.402555	+	0.697246i	−0.994034	−	0.109075i	$-0.965211\pi$
$109$	−4.20280	+	7.27946i	−0.402555	+	0.697246i	0.591478	+	0.806321i	$0.298544\pi$
$110$		0			0
$111$	−0.752216	−	1.37080i	−0.0713972	−	0.130110i
$112$		0			0
$113$	−3.18258	+	2.67050i	−0.299392	+	0.251219i	−0.780091	−	0.625666i	$-0.784827\pi$
$113$	−3.18258	+	2.67050i	−0.299392	+	0.251219i	0.480699	+	0.876885i	$0.340383\pi$
$114$		0			0
$115$	6.43943	−	36.5198i	0.600480	−	3.40549i
$116$		0			0
$117$	7.92623	−	6.08443i	0.732780	−	0.562506i
$118$		0			0
$119$	−2.10123	+	5.56746i	−0.192619	+	0.510368i
$120$		0			0
$121$	1.48978	−	1.25007i	0.135434	−	0.113643i
$122$		0			0
$123$	−4.52121	−	1.75770i	−0.407664	−	0.158487i
$124$		0			0
$125$	−14.7357	−	25.5231i	−1.31801	−	2.28285i
$126$		0			0
$127$	8.02019	−	13.8914i	0.711677	−	1.23266i	−0.252551	−	0.967584i	$-0.581269\pi$
$127$	8.02019	−	13.8914i	0.711677	−	1.23266i	0.964227	−	0.265077i	$-0.0853972\pi$
$128$		0			0
$129$	−19.8624	+	6.74450i	−1.74879	+	0.593820i
$130$		0			0
$131$	−2.55709	−	14.5020i	−0.223414	−	1.26704i	−0.865694	−	0.500574i	$-0.833122\pi$
$131$	−2.55709	−	14.5020i	−0.223414	−	1.26704i	0.642280	−	0.766470i	$-0.277989\pi$
$132$		0			0
$133$	0.309727	−	0.820659i	0.0268568	−	0.0711602i
$134$		0			0
$135$	19.6828	+	8.65387i	1.69403	+	0.744806i
$136$		0			0
$137$	3.63174	+	3.04739i	0.310280	+	0.260356i	0.784608	−	0.619992i	$-0.212864\pi$
$137$	3.63174	+	3.04739i	0.310280	+	0.260356i	−0.474328	+	0.880348i	$0.657309\pi$
$138$		0			0
$139$	0.112081	+	0.0407940i	0.00950654	+	0.00346010i	0.346769	−	0.937951i	$-0.387279\pi$
$139$	0.112081	+	0.0407940i	0.00950654	+	0.00346010i	−0.337262	+	0.941411i	$0.609501\pi$
$140$		0			0
$141$	−11.2916	+	3.83419i	−0.950924	+	0.322897i
$142$		0			0
$143$	−5.99183	−	10.3782i	−0.501062	−	0.867865i
$144$		0			0
$145$	−16.0055	+	27.7223i	−1.32918	+	2.30221i
$146$		0			0
$147$	−11.5695	+	3.62592i	−0.954234	+	0.299061i
$148$		0			0
$149$	−9.59024	+	8.04717i	−0.785663	+	0.659250i	−0.944668	−	0.328028i	$-0.893616\pi$
$149$	−9.59024	+	8.04717i	−0.785663	+	0.659250i	0.159005	+	0.987278i	$0.449171\pi$
$150$		0			0
$151$	0.557297	−	0.202839i	0.0453522	−	0.0165068i	−0.319244	−	0.947672i	$-0.603429\pi$
$151$	0.557297	−	0.202839i	0.0453522	−	0.0165068i	0.364597	+	0.931166i	$0.381207\pi$
$152$		0			0
$153$	3.11682	+	5.98455i	0.251980	+	0.483822i
$154$		0			0
$155$	6.60354	−	2.40349i	0.530409	−	0.193053i
$156$		0			0
$157$	3.86531	+	21.9213i	0.308485	+	1.74951i	0.606627	+	0.794986i	$0.292522\pi$
$157$	3.86531	+	21.9213i	0.308485	+	1.74951i	−0.298142	+	0.954522i	$0.596367\pi$
$158$		0			0
$159$	7.74227	+	14.1091i	0.614002	+	1.11892i
$160$		0			0
$161$	23.3002	+	4.39300i	1.83632	+	0.346217i
$162$		0			0
$163$	−0.128483	−	0.222539i	−0.0100636	−	0.0174306i	0.860950	−	0.508690i	$-0.169870\pi$
$163$	−0.128483	−	0.222539i	−0.0100636	−	0.0174306i	−0.871013	+	0.491259i	$0.836537\pi$
$164$		0			0
$165$	13.3751	−	22.0463i	1.04125	−	1.71630i
$166$		0			0
$167$	2.77806	−	2.33107i	0.214973	−	0.180384i	−0.528942	−	0.848658i	$-0.677411\pi$
$167$	2.77806	−	2.33107i	0.214973	−	0.180384i	0.743915	+	0.668274i	$0.232967\pi$
$168$		0			0
$169$	1.79113	−	0.651916i	0.137779	−	0.0501474i
$170$		0			0
$171$	−0.459428	−	0.882140i	−0.0351334	−	0.0674589i
$172$		0			0
$173$	1.46605	−	8.31440i	0.111462	−	0.632132i	−0.876979	−	0.480528i	$-0.840445\pi$
$173$	1.46605	−	8.31440i	0.111462	−	0.632132i	0.988441	−	0.151604i	$-0.0484439\pi$
$174$		0			0
$175$	27.9633	−	15.7069i	2.11383	−	1.18733i
$176$		0			0
$177$	−16.9318	−	6.58256i	−1.27268	−	0.494775i
$178$		0			0
$179$	−15.7139			−1.17451			−0.587257	−	0.809401i	$-0.699792\pi$
$179$	−15.7139			−1.17451			−0.587257	+	0.809401i	$0.699792\pi$
$180$		0			0
$181$	−4.50404	+	7.80122i	−0.334783	+	0.579860i	−0.983443	−	0.181217i	$-0.941996\pi$
$181$	−4.50404	+	7.80122i	−0.334783	+	0.579860i	0.648660	+	0.761078i	$0.275330\pi$
$182$		0			0
$183$	−14.3894	+	4.88608i	−1.06369	+	0.361190i
$184$		0			0
$185$	−2.86158	+	2.40115i	−0.210388	+	0.176536i
$186$		0			0
$187$	7.60427	−	2.76773i	0.556080	−	0.202396i
$188$		0			0
$189$	−5.68157	+	12.5188i	−0.413273	+	0.910607i
$190$		0			0
$191$	9.31494	−	3.39036i	0.674006	−	0.245318i	0.0177340	−	0.999843i	$-0.494355\pi$
$191$	9.31494	−	3.39036i	0.674006	−	0.245318i	0.656272	+	0.754525i	$0.272133\pi$
$192$		0			0
$193$	16.1850	−	13.5808i	1.16502	−	0.977566i	0.165056	−	0.986284i	$-0.447219\pi$
$193$	16.1850	−	13.5808i	1.16502	−	0.977566i	0.999962	+	0.00871768i	$0.00277496\pi$
$194$		0			0
$195$	−17.9493	−	15.7380i	−1.28537	−	1.12702i
$196$		0			0
$197$	6.05649	−	10.4902i	0.431507	−	0.747392i	−0.565496	−	0.824751i	$-0.691315\pi$
$197$	6.05649	−	10.4902i	0.431507	−	0.747392i	0.997003	+	0.0773585i	$0.0246486\pi$
$198$		0			0
$199$	3.30009			0.233937			0.116969	−	0.993136i	$-0.462682\pi$
$199$	3.30009			0.233937			0.116969	+	0.993136i	$0.462682\pi$
$200$		0			0
$201$	9.77278	−	7.84503i	0.689319	−	0.553346i
$202$		0			0
$203$	−17.6033	−	10.4426i	−1.23551	−	0.732924i
$204$		0			0
$205$	−2.01238	+	11.4128i	−0.140551	+	0.797102i
$206$		0			0
$207$	21.3265	−	16.3709i	1.48230	−	1.13786i
$208$		0			0
$209$	−1.12089	+	0.407971i	−0.0775337	+	0.0282200i
$210$		0			0
$211$	12.4243	−	10.4252i	0.855325	−	0.717703i	−0.105631	−	0.994405i	$-0.533686\pi$
$211$	12.4243	−	10.4252i	0.855325	−	0.717703i	0.960956	+	0.276703i	$0.0892417\pi$
$212$		0			0
$213$	17.2319	+	0.374344i	1.18071	+	0.0256496i
$214$		0			0
$215$	25.0564	+	43.3989i	1.70883	+	2.95978i
$216$		0			0
$217$	1.48677	+	4.24012i	0.100928	+	0.287838i
$218$		0			0
$219$	−12.4275	−	0.269973i	−0.839770	−	0.0182431i
$220$		0			0
$221$	−1.30088	−	7.37766i	−0.0875067	−	0.496275i
$222$		0			0
$223$	13.1656	−	4.79187i	0.881630	−	0.320887i	0.138763	−	0.990326i	$-0.455687\pi$
$223$	13.1656	−	4.79187i	0.881630	−	0.320887i	0.742868	+	0.669438i	$0.233465\pi$
$224$		0			0
$225$	7.86442	−	35.5064i	0.524295	−	2.36709i
$226$		0			0
$227$	8.81136	−	3.20707i	0.584830	−	0.212861i	−0.0326239	−	0.999468i	$-0.510386\pi$
$227$	8.81136	−	3.20707i	0.584830	−	0.212861i	0.617454	+	0.786607i	$0.288164\pi$
$228$		0			0
$229$	14.8740	−	12.4808i	0.982903	−	0.824753i	−0.00162222	−	0.999999i	$-0.500516\pi$
$229$	14.8740	−	12.4808i	0.982903	−	0.824753i	0.984525	+	0.175246i	$0.0560719\pi$
$230$		0			0
$231$	13.9942	+	8.71795i	0.920750	+	0.573599i
$232$		0			0
$233$	−3.86866	+	6.70071i	−0.253444	+	0.438978i	−0.964472	−	0.264186i	$-0.914897\pi$
$233$	−3.86866	+	6.70071i	−0.253444	+	0.438978i	0.711028	+	0.703164i	$0.248230\pi$
$234$		0			0
$235$	14.2443	+	24.6719i	0.929198	+	1.60942i
$236$		0			0
$237$	−3.48404	+	17.5243i	−0.226313	+	1.13832i
$238$		0			0
$239$	8.37562	+	3.04848i	0.541774	+	0.197190i	0.598388	−	0.801207i	$-0.295808\pi$
$239$	8.37562	+	3.04848i	0.541774	+	0.197190i	−0.0566140	+	0.998396i	$0.518030\pi$
$240$		0			0
$241$	−4.71187	−	3.95373i	−0.303518	−	0.254682i	0.478289	−	0.878203i	$-0.341257\pi$
$241$	−4.71187	−	3.95373i	−0.303518	−	0.254682i	−0.781807	+	0.623521i	$0.785702\pi$
$242$		0			0
$243$	6.28506	+	14.2653i	0.403187	+	0.915118i
$244$		0			0
$245$	13.8858	+	25.4200i	0.887130	+	1.62403i
$246$		0			0
$247$	0.191754	+	1.08749i	0.0122010	+	0.0691952i
$248$		0			0
$249$	−15.4730	−	13.5669i	−0.980564	−	0.859764i
$250$		0			0
$251$	−7.43672	+	12.8808i	−0.469402	+	0.813027i	−0.999388	−	0.0349788i	$-0.988864\pi$
$251$	−7.43672	+	12.8808i	−0.469402	+	0.813027i	0.529987	+	0.848006i	$0.322197\pi$
$252$		0			0
$253$	−16.1218	−	27.9238i	−1.01357	−	1.75555i
$254$		0			0
$255$	12.5708	−	10.0911i	0.787215	−	0.631931i
$256$		0			0
$257$	9.12433	−	7.65622i	0.569160	−	0.477582i	−0.312207	−	0.950014i	$-0.601068\pi$
$257$	9.12433	−	7.65622i	0.569160	−	0.477582i	0.881367	+	0.472432i	$0.156624\pi$
$258$		0			0
$259$	−1.51355	−	1.84769i	−0.0940474	−	0.114810i
$260$		0			0
$261$	−22.1326	+	6.98306i	−1.36997	+	0.432240i
$262$		0			0
$263$	−0.573845	+	3.25444i	−0.0353848	+	0.200677i	−0.997375	−	0.0724059i	$-0.976932\pi$
$263$	−0.573845	+	3.25444i	−0.0353848	+	0.200677i	0.961990	+	0.273083i	$0.0880434\pi$
$264$		0			0
$265$	29.4531	−	24.7141i	1.80929	−	1.51818i
$266$		0			0
$267$	6.58697	−	10.8574i	0.403116	−	0.664459i
$268$		0			0
$269$	−2.81866	+	4.88206i	−0.171857	+	0.297664i	−0.939069	−	0.343729i	$-0.888310\pi$
$269$	−2.81866	+	4.88206i	−0.171857	+	0.297664i	0.767212	+	0.641393i	$0.221643\pi$
$270$		0			0
$271$	−3.98963	−	6.91023i	−0.242352	−	0.419767i	0.719031	−	0.694978i	$-0.244586\pi$
$271$	−3.98963	−	6.91023i	−0.242352	−	0.419767i	−0.961384	+	0.275211i	$0.911252\pi$
$272$		0			0
$273$	10.1977	−	11.3569i	0.617193	−	0.687351i
$274$		0			0
$275$	−40.9844	−	14.9171i	−2.47145	−	0.899535i
$276$		0			0
$277$	−2.01699	+	11.4389i	−0.121189	+	0.687299i	0.862309	+	0.506382i	$0.169018\pi$
$277$	−2.01699	+	11.4389i	−0.121189	+	0.687299i	−0.983498	+	0.180917i	$0.942094\pi$
$278$		0			0
$279$	4.70740	+	1.94881i	0.281825	+	0.116672i
$280$		0			0
$281$	11.1898	+	9.38936i	0.667528	+	0.560123i	0.912333	−	0.409450i	$-0.134279\pi$
$281$	11.1898	+	9.38936i	0.667528	+	0.560123i	−0.244805	+	0.969572i	$0.578724\pi$
$282$		0			0
$283$	−23.1903	−	8.44058i	−1.37852	−	0.501741i	−0.456791	−	0.889574i	$-0.651001\pi$
$283$	−23.1903	−	8.44058i	−1.37852	−	0.501741i	−0.921730	+	0.387833i	$0.873224\pi$
$284$		0			0
$285$	−1.85297	+	1.48746i	−0.109761	+	0.0881096i
$286$		0			0
$287$	−7.28153	−	1.37285i	−0.429815	−	0.0810368i
$288$		0			0
$289$	−11.9412			−0.702422
$290$		0			0
$291$	−4.84333	+	1.64461i	−0.283921	+	0.0964087i
$292$		0			0
$293$	−19.2194	−	6.99530i	−1.12281	−	0.408670i	−0.287134	−	0.957890i	$-0.592703\pi$
$293$	−19.2194	−	6.99530i	−1.12281	−	0.408670i	−0.835678	+	0.549220i	$0.814925\pi$
$294$		0			0
$295$	−7.53632	+	42.7406i	−0.438781	+	2.48845i
$296$		0			0
$297$	17.9468	−	5.23662i	1.04138	−	0.303860i
$298$		0			0
$299$	−28.0495	+	10.2092i	−1.62214	+	0.590412i
$300$		0			0
$301$	−27.9364	+	15.6918i	−1.61023	+	0.904461i
$302$		0			0
$303$	3.90336	+	3.42249i	0.224242	+	0.196617i
$304$		0			0
$305$	18.1522	+	31.4405i	1.03939	+	1.80028i
$306$		0			0
$307$	2.35359	+	4.07653i	0.134326	+	0.232660i	0.925340	−	0.379139i	$-0.123780\pi$
$307$	2.35359	+	4.07653i	0.134326	+	0.232660i	−0.791014	+	0.611799i	$0.790446\pi$
$308$		0			0
$309$	−4.96552	+	3.98603i	−0.282478	+	0.226758i
$310$		0			0
$311$	−10.2889	−	3.74485i	−0.583430	−	0.212351i	0.0334076	−	0.999442i	$-0.489364\pi$
$311$	−10.2889	−	3.74485i	−0.583430	−	0.212351i	−0.616837	+	0.787091i	$0.711586\pi$
$312$		0			0
$313$	1.58876	−	9.01029i	0.0898019	−	0.509292i	−0.906415	−	0.422389i	$-0.861192\pi$
$313$	1.58876	−	9.01029i	0.0898019	−	0.509292i	0.996217	−	0.0869033i	$-0.0276971\pi$
$314$		0			0
$315$	31.9803	+	7.48097i	1.80189	+	0.421505i
$316$		0			0
$317$	−7.71338	−	6.47230i	−0.433227	−	0.363520i	0.399941	−	0.916541i	$-0.369031\pi$
$317$	−7.71338	−	6.47230i	−0.433227	−	0.363520i	−0.833168	+	0.553021i	$0.813475\pi$
$318$		0			0
$319$	4.83320	+	27.4105i	0.270607	+	1.53469i
$320$		0			0
$321$	−14.7094	−	0.319546i	−0.821001	−	0.0178353i
$322$		0			0
$323$	−0.745685			−0.0414910
$324$		0			0
$325$	−20.1882	+	34.9670i	−1.11984	+	1.93962i
$326$		0			0
$327$	7.00391	+	12.7635i	0.387317	+	0.705824i
$328$		0			0
$329$	−15.8816	+	8.92066i	−0.875580	+	0.491812i
$330$		0			0
$331$	−22.3368	−	18.7428i	−1.22774	−	1.03020i	−0.998382	−	0.0568571i	$-0.981892\pi$
$331$	−22.3368	−	18.7428i	−1.22774	−	1.03020i	−0.229361	−	0.973342i	$-0.573663\pi$
$332$		0			0
$333$	−2.70572	−	0.117613i	−0.148272	−	0.00644515i
$334$		0			0
$335$	−22.9348	−	19.2446i	−1.25306	−	1.05145i
$336$		0			0
$337$	5.17507	+	29.3493i	0.281904	+	1.59876i	0.716139	+	0.697958i	$0.245908\pi$
$337$	5.17507	+	29.3493i	0.281904	+	1.59876i	−0.434234	+	0.900800i	$0.642981\pi$
$338$		0			0
$339$	1.09535	+	7.11205i	0.0594912	+	0.386274i
$340$		0			0
$341$	3.05511	−	5.29161i	0.165444	−	0.286557i
$342$		0			0
$343$	−16.3572	+	8.68576i	−0.883205	+	0.468987i
$344$		0			0
$345$	−48.2948	−	42.3452i	−2.60010	−	2.27979i
$346$		0			0
$347$	22.0478	−	18.5003i	1.18359	−	0.993147i	0.183638	−	0.982994i	$-0.441213\pi$
$347$	22.0478	−	18.5003i	1.18359	−	0.993147i	0.999948	−	0.0101532i	$-0.00323193\pi$
$348$		0			0
$349$	−1.46803	+	8.32561i	−0.0785818	+	0.445660i	0.919976	+	0.391975i	$0.128208\pi$
$349$	−1.46803	+	8.32561i	−0.0785818	+	0.445660i	−0.998558	+	0.0536852i	$0.982903\pi$
$350$		0			0
$351$	−1.88913	−	17.2037i	−0.100834	−	0.918265i
$352$		0			0
$353$	17.2093	+	14.4403i	0.915959	+	0.768581i	0.973243	−	0.229777i	$-0.0737997\pi$
$353$	17.2093	+	14.4403i	0.915959	+	0.768581i	−0.0572843	+	0.998358i	$0.518244\pi$
$354$		0			0
$355$	−7.15033	−	40.5516i	−0.379500	−	2.15225i
$356$		0			0
$357$	6.35676	+	8.11338i	0.336435	+	0.429406i
$358$		0			0
$359$	9.88631			0.521779			0.260890	−	0.965369i	$-0.415984\pi$
$359$	9.88631			0.521779			0.260890	+	0.965369i	$0.415984\pi$
$360$		0			0
$361$	−18.8901			−0.994215
$362$		0			0
$363$	−0.512737	−	3.32918i	−0.0269117	−	0.174737i
$364$		0			0
$365$	5.15675	+	29.2454i	0.269916	+	1.53077i
$366$		0			0
$367$	−11.0734	+	4.03040i	−0.578029	+	0.210385i	−0.614456	−	0.788951i	$-0.710625\pi$
$367$	−11.0734	+	4.03040i	−0.578029	+	0.210385i	0.0364272	+	0.999336i	$0.488402\pi$
$368$		0			0
$369$	−6.66472	+	5.11606i	−0.346952	+	0.266331i
$370$		0			0
$371$	15.5784	+	19.0176i	0.808789	+	0.987343i
$372$		0			0
$373$	14.8367	+	5.40011i	0.768214	+	0.279607i	0.696249	−	0.717800i	$-0.254851\pi$
$373$	14.8367	+	5.40011i	0.768214	+	0.279607i	0.0719647	+	0.997407i	$0.477073\pi$
$374$		0			0
$375$	−51.0341	−	1.10866i	−2.63539	−	0.0572509i
$376$		0			0
$377$	25.7668			1.32706
$378$		0			0
$379$	−14.2382			−0.731369			−0.365684	−	0.930739i	$-0.619165\pi$
$379$	−14.2382			−0.731369			−0.365684	+	0.930739i	$0.619165\pi$
$380$		0			0
$381$	−13.3655	−	24.3566i	−0.684737	−	1.24783i
$382$		0			0
$383$	3.22405	+	1.17346i	0.164741	+	0.0599610i	0.423074	−	0.906095i	$-0.360951\pi$
$383$	3.22405	+	1.17346i	0.164741	+	0.0599610i	−0.258333	+	0.966056i	$0.583173\pi$
$384$		0			0
$385$	13.9084	−	36.8520i	0.708838	−	1.87815i
$386$		0			0
$387$	−7.85685	+	35.4722i	−0.399386	+	1.80315i
$388$		0			0
$389$	28.8863	−	10.5137i	1.46459	−	0.533068i	0.517965	−	0.855402i	$-0.326690\pi$
$389$	28.8863	−	10.5137i	1.46459	−	0.533068i	0.946626	+	0.322334i	$0.104467\pi$
$390$		0			0
$391$	−3.50019	−	19.8505i	−0.177012	−	1.00389i
$392$		0			0
$393$	−23.7724	−	9.24193i	−1.19916	−	0.466194i
$394$		0			0
$395$	42.6853			2.14773
$396$		0			0
$397$	−26.4261			−1.32629			−0.663145	−	0.748491i	$-0.730779\pi$
$397$	−26.4261			−1.32629			−0.663145	+	0.748491i	$0.730779\pi$
$398$		0			0
$399$	−0.937004	−	1.19594i	−0.0469089	−	0.0598717i
$400$		0			0
$401$	0.140059	+	0.794314i	0.00699421	+	0.0396662i	0.988105	−	0.153780i	$-0.0491447\pi$
$401$	0.140059	+	0.794314i	0.00699421	+	0.0396662i	−0.981111	+	0.193446i	$0.938034\pi$
$402$		0			0
$403$	−4.33318	−	3.63597i	−0.215851	−	0.181120i
$404$		0			0
$405$	30.4980	−	21.3724i	1.51546	−	1.06200i
$406$		0			0
$407$	−0.564012	+	3.19867i	−0.0279570	+	0.158552i
$408$		0			0
$409$	4.43708	−	3.72316i	0.219400	−	0.184098i	−0.526463	−	0.850198i	$-0.676482\pi$
$409$	4.43708	−	3.72316i	0.219400	−	0.184098i	0.745862	+	0.666100i	$0.232038\pi$
$410$		0			0
$411$	7.77543	−	2.64024i	0.383534	−	0.130233i
$412$		0			0
$413$	−27.2692	−	5.14130i	−1.34183	−	0.252987i
$414$		0			0
$415$	−24.5813	+	42.5760i	−1.20665	+	2.08997i
$416$		0			0
$417$	0.161102	−	0.129324i	0.00788921	−	0.00633301i
$418$		0			0
$419$	0.614055	+	3.48248i	0.0299985	+	0.170130i	0.996126	−	0.0879341i	$-0.0280265\pi$
$419$	0.614055	+	3.48248i	0.0299985	+	0.170130i	−0.966128	+	0.258064i	$0.916915\pi$
$420$		0			0
$421$	9.07166	+	7.61203i	0.442126	+	0.370988i	0.836504	−	0.547961i	$-0.184596\pi$
$421$	9.07166	+	7.61203i	0.442126	+	0.370988i	−0.394378	+	0.918948i	$0.629040\pi$
$422$		0			0
$423$	−4.46655	+	20.1656i	−0.217171	+	0.980487i
$424$		0			0
$425$	−20.8864	−	17.5258i	−1.01314	−	0.850126i
$426$		0			0
$427$	−20.2386	+	11.3680i	−0.979415	+	0.550136i
$428$		0			0
$429$	−20.7514	−	0.450802i	−1.00189	−	0.0217649i
$430$		0			0
$431$	4.94785	−	8.56993i	0.238329	−	0.412799i	−0.721906	−	0.691992i	$-0.756734\pi$
$431$	4.94785	−	8.56993i	0.238329	−	0.412799i	0.960235	+	0.279193i	$0.0900669\pi$
$432$		0			0
$433$	1.06390			0.0511277			0.0255639	−	0.999673i	$-0.491862\pi$
$433$	1.06390			0.0511277			0.0255639	+	0.999673i	$0.491862\pi$
$434$		0			0
$435$	26.6729	+	48.6072i	1.27887	+	2.33054i
$436$		0			0
$437$	0.515938	+	2.92603i	0.0246806	+	0.139971i
$438$		0			0
$439$	−1.54197	−	1.29387i	−0.0735944	−	0.0617530i	0.605248	−	0.796037i	$-0.293074\pi$
$439$	−1.54197	−	1.29387i	−0.0735944	−	0.0617530i	−0.678843	+	0.734284i	$0.737518\pi$
$440$		0			0
$441$	−5.02461	+	20.3900i	−0.239267	+	0.970954i
$442$		0			0
$443$	1.35941	−	7.70958i	0.0645874	−	0.366293i	−0.935334	−	0.353766i	$-0.884901\pi$
$443$	1.35941	−	7.70958i	0.0645874	−	0.366293i	0.999922	−	0.0125277i	$-0.00398781\pi$
$444$		0			0
$445$	−28.5091	−	10.3765i	−1.35146	−	0.491892i
$446$		0			0
$447$	3.30068	+	21.4312i	0.156117	+	1.01366i
$448$		0			0
$449$	−17.3030	−	29.9696i	−0.816577	−	1.41435i	−0.908190	−	0.418559i	$-0.862535\pi$
$449$	−17.3030	−	29.9696i	−0.816577	−	1.41435i	0.0916125	−	0.995795i	$-0.470798\pi$
$450$		0			0
$451$	5.03820	+	8.72642i	0.237240	+	0.410911i
$452$		0			0
$453$	0.200303	−	1.00750i	0.00941105	−	0.0473363i
$454$		0			0
$455$	−31.3617	−	18.6043i	−1.47026	−	0.872183i
$456$		0			0
$457$	5.04519	−	1.83630i	0.236004	−	0.0858985i	−0.221311	−	0.975203i	$-0.571033\pi$
$457$	5.04519	−	1.83630i	0.236004	−	0.0858985i	0.457315	+	0.889305i	$0.348811\pi$
$458$		0			0
$459$	11.6623	+	0.761009i	0.544349	+	0.0355209i
$460$		0			0
$461$	2.41637	−	13.7039i	0.112542	−	0.638255i	−0.875397	−	0.483405i	$-0.839400\pi$
$461$	2.41637	−	13.7039i	0.112542	−	0.638255i	0.987938	−	0.154849i	$-0.0494892\pi$
$462$		0			0
$463$	−33.1970	−	12.0827i	−1.54280	−	0.561532i	−0.576082	−	0.817392i	$-0.695419\pi$
$463$	−33.1970	−	12.0827i	−1.54280	−	0.561532i	−0.966714	+	0.255860i	$0.917641\pi$
$464$		0			0
$465$	2.37344	−	11.9381i	0.110065	−	0.553615i
$466$		0			0
$467$	17.7364			0.820741			0.410371	−	0.911919i	$-0.365399\pi$
$467$	17.7364			0.820741			0.410371	+	0.911919i	$0.365399\pi$
$468$		0			0
$469$	12.4773	−	14.5179i	0.576149	−	0.670376i
$470$		0			0
$471$	35.9344	+	13.9702i	1.65577	+	0.643711i
$472$		0			0
$473$	40.9449	+	14.9027i	1.88265	+	0.685228i
$474$		0			0
$475$	3.07872	+	2.58335i	0.141261	+	0.118532i
$476$		0			0
$477$	27.8489	+	1.21054i	1.27511	+	0.0554270i
$478$		0			0
$479$	3.90269	−	22.1332i	0.178318	−	1.01129i	−0.755925	−	0.654658i	$-0.772813\pi$
$479$	3.90269	−	22.1332i	0.178318	−	1.01129i	0.934244	−	0.356635i	$-0.116076\pi$
$480$		0			0
$481$	2.82553	+	1.02841i	0.128833	+	0.0468914i
$482$		0			0
$483$	27.4382	−	30.5572i	1.24848	−	1.39040i
$484$		0			0
$485$	6.10986	+	10.5826i	0.277434	+	0.480531i
$486$		0			0
$487$	3.02336	−	5.23662i	0.137002	−	0.237294i	−0.789359	−	0.613932i	$-0.789587\pi$
$487$	3.02336	−	5.23662i	0.137002	−	0.237294i	0.926360	+	0.376639i	$0.122920\pi$
$488$		0			0
$489$	−0.444974	−	0.00966656i	−0.0201224	−	0.000437137i
$490$		0			0
$491$	−4.83189	+	4.05444i	−0.218060	+	0.182974i	−0.745274	−	0.666759i	$-0.767681\pi$
$491$	−4.83189	+	4.05444i	−0.218060	+	0.182974i	0.527214	+	0.849733i	$0.323237\pi$
$492$		0			0
$493$	−3.02143	+	17.1354i	−0.136078	+	0.771739i
$494$		0			0
$495$	−20.6308	−	39.6128i	−0.927284	−	1.78046i
$496$		0			0
$497$	25.9806	−	4.26513i	1.16539	−	0.191317i
$498$		0			0
$499$	10.1391	−	8.50771i	0.453888	−	0.380858i	−0.386988	−	0.922085i	$-0.626485\pi$
$499$	10.1391	−	8.50771i	0.453888	−	0.380858i	0.840876	+	0.541227i	$0.182040\pi$
$500$		0			0
$501$	−0.956127	−	6.20809i	−0.0427166	−	0.277357i
$502$		0			0
$503$	−8.33842	−	14.4426i	−0.371792	−	0.643962i	0.618049	−	0.786139i	$-0.287923\pi$
$503$	−8.33842	−	14.4426i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$504$		0			0
$505$	6.20108	−	10.7406i	0.275945	−	0.477950i
$506$		0			0
$507$	0.643764	−	3.23805i	0.0285906	−	0.143807i
$508$		0			0
$509$	5.45655	+	30.9456i	0.241857	+	1.37164i	0.827680	+	0.561201i	$0.189661\pi$
$509$	5.45655	+	30.9456i	0.241857	+	1.37164i	−0.585822	+	0.810440i	$0.699228\pi$
$510$		0			0
$511$	−18.7369	+	3.07597i	−0.828873	+	0.136073i
$512$		0			0
$513$	−1.71906	−	0.112175i	−0.0758982	−	0.00495264i
$514$		0			0
$515$	11.6531	+	9.77813i	0.513498	+	0.430876i
$516$		0			0
$517$	23.2768	+	8.47207i	1.02371	+	0.372601i
$518$		0			0
$519$	−10.9952	−	9.64064i	−0.482635	−	0.423177i
$520$		0			0
$521$	7.59446	+	13.1540i	0.332719	+	0.576287i	0.983044	−	0.183370i	$-0.0587005\pi$
$521$	7.59446	+	13.1540i	0.332719	+	0.576287i	−0.650325	+	0.759656i	$0.725367\pi$
$522$		0			0
$523$	−12.8389	+	22.2376i	−0.561406	+	0.972383i	0.435968	+	0.899962i	$0.356406\pi$
$523$	−12.8389	+	22.2376i	−0.561406	+	0.972383i	−0.997374	+	0.0724212i	$0.976927\pi$
$524$		0			0
$525$	1.86278	−	55.5202i	0.0812986	−	2.42310i
$526$		0			0
$527$	2.92610	−	2.45529i	0.127463	−	0.106954i
$528$		0			0
$529$	−53.8577	+	19.6026i	−2.34164	+	0.852288i
$530$		0			0
$531$	−24.9592	+	19.1595i	−1.08314	+	0.831453i
$532$		0			0
$533$	8.76570	−	3.19045i	0.379685	−	0.138194i
$534$		0			0
$535$	6.10365	+	34.6155i	0.263884	+	1.49656i
$536$		0			0
$537$	−14.1174	+	23.2698i	−0.609210	+	1.00416i
$538$		0			0
$539$	23.4561	+	9.17078i	1.01033	+	0.395013i
$540$		0			0
$541$	9.29240	+	16.0949i	0.399512	+	0.691974i	0.993666	−	0.112377i	$-0.0358464\pi$
$541$	9.29240	+	16.0949i	0.399512	+	0.691974i	−0.594154	+	0.804351i	$0.702513\pi$
$542$		0			0
$543$	7.50592	+	13.6784i	0.322110	+	0.586995i
$544$		0			0
$545$	26.6443	−	22.3572i	1.14131	−	0.957677i
$546$		0			0
$547$	−40.1780	+	14.6236i	−1.71789	+	0.625260i	−0.997653	−	0.0684710i	$-0.978188\pi$
$547$	−40.1780	+	14.6236i	−1.71789	+	0.625260i	−0.720234	+	0.693731i	$0.755966\pi$
$548$		0			0
$549$	−5.69193	+	25.6980i	−0.242925	+	1.09676i
$550$		0			0
$551$	0.445368	−	2.52581i	0.0189733	−	0.107603i
$552$		0			0
$553$	−0.322549	+	27.2908i	−0.0137162	+	1.16052i
$554$		0			0
$555$	0.984873	+	6.39473i	0.0418055	+	0.271441i
$556$		0			0
$557$	14.6771			0.621891			0.310945	−	0.950428i	$-0.399354\pi$
$557$	14.6771			0.621891			0.310945	+	0.950428i	$0.399354\pi$
$558$		0			0
$559$	20.1688	−	34.9334i	0.853049	−	1.47752i
$560$		0			0
$561$	2.73312	−	13.7472i	0.115392	−	0.580408i
$562$		0			0
$563$	−16.8978	+	14.1789i	−0.712157	+	0.597570i	−0.925203	−	0.379472i	$-0.876106\pi$
$563$	−16.8978	+	14.1789i	−0.712157	+	0.597570i	0.213047	+	0.977042i	$0.431661\pi$
$564$		0			0
$565$	16.1544	−	5.87974i	0.679623	−	0.247362i
$566$		0			0
$567$	13.4340	+	19.6603i	0.564173	+	0.825657i
$568$		0			0
$569$	19.3149	−	7.03004i	0.809722	−	0.294715i	0.0962128	−	0.995361i	$-0.469327\pi$
$569$	19.3149	−	7.03004i	0.809722	−	0.294715i	0.713509	+	0.700646i	$0.247105\pi$
$570$		0			0
$571$	−5.21790	+	4.37833i	−0.218362	+	0.183228i	−0.745407	−	0.666610i	$-0.767745\pi$
$571$	−5.21790	+	4.37833i	−0.218362	+	0.183228i	0.527044	+	0.849838i	$0.323300\pi$
$572$		0			0
$573$	3.34796	−	16.8398i	0.139863	−	0.703493i
$574$		0			0
$575$	−54.3190	+	94.0833i	−2.26526	+	3.92354i
$576$		0			0
$577$	45.3175			1.88659			0.943296	−	0.331953i	$-0.107707\pi$
$577$	45.3175			1.88659			0.943296	+	0.331953i	$0.107707\pi$
$578$		0			0
$579$	−5.57039	−	36.1682i	−0.231497	−	1.50310i
$580$		0			0
$581$	−27.0351	−	16.0377i	−1.12161	−	0.665356i
$582$		0			0
$583$	5.80515	−	32.9227i	0.240425	−	1.36352i
$584$		0			0
$585$	−39.4310	+	12.4409i	−1.63027	+	0.514368i
$586$		0			0
$587$	8.09611	−	2.94674i	0.334162	−	0.121625i	−0.169489	−	0.985532i	$-0.554212\pi$
$587$	8.09611	−	2.94674i	0.334162	−	0.121625i	0.503651	+	0.863907i	$0.331990\pi$
$588$		0			0
$589$	−0.431315	+	0.361916i	−0.0177720	+	0.0149125i
$590$		0			0
$591$	−10.0931	−	18.3930i	−0.415173	−	0.756588i
$592$		0			0
$593$	8.23590	+	14.2650i	0.338208	+	0.585793i	0.984096	−	0.177639i	$-0.0568460\pi$
$593$	8.23590	+	14.2650i	0.338208	+	0.585793i	−0.645888	+	0.763432i	$0.723513\pi$
$594$		0			0
$595$	16.0497	−	18.6745i	0.657973	−	0.765582i
$596$		0			0
$597$	2.96480	−	4.88690i	0.121341	−	0.200007i
$598$		0			0
$599$	5.43720	+	30.8359i	0.222158	+	1.25992i	0.868045	+	0.496486i	$0.165377\pi$
$599$	5.43720	+	30.8359i	0.222158	+	1.25992i	−0.645887	+	0.763433i	$0.723512\pi$
$600$		0			0
$601$	−15.2901	+	5.56513i	−0.623694	+	0.227006i	−0.634485	−	0.772936i	$-0.718788\pi$
$601$	−15.2901	+	5.56513i	−0.623694	+	0.227006i	0.0107901	+	0.999942i	$0.496565\pi$
$602$		0			0
$603$	−2.83735	−	21.5199i	−0.115546	−	0.876357i
$604$		0			0
$605$	−7.56196	+	2.75233i	−0.307437	+	0.111898i
$606$		0			0
$607$	24.0428	−	20.1743i	0.975867	−	0.818850i	−0.00759331	−	0.999971i	$-0.502417\pi$
$607$	24.0428	−	20.1743i	0.975867	−	0.818850i	0.983461	+	0.181121i	$0.0579726\pi$
$608$		0			0
$609$	−31.2785	+	16.6860i	−1.26747	+	0.676150i
$610$		0			0
$611$	11.4658	−	19.8593i	0.463856	−	0.803422i
$612$		0			0
$613$	−6.45374	−	11.1782i	−0.260664	−	0.451484i	0.705754	−	0.708457i	$-0.250608\pi$
$613$	−6.45374	−	11.1782i	−0.260664	−	0.451484i	−0.966419	+	0.256973i	$0.917275\pi$
$614$		0			0
$615$	15.0925	+	13.2332i	0.608590	+	0.533615i
$616$		0			0
$617$	2.65011	+	0.964562i	0.106689	+	0.0388318i	0.394813	−	0.918761i	$-0.370809\pi$
$617$	2.65011	+	0.964562i	0.106689	+	0.0388318i	−0.288124	+	0.957593i	$0.593031\pi$
$618$		0			0
$619$	−11.3473	−	9.52148i	−0.456085	−	0.382701i	0.385603	−	0.922665i	$-0.373993\pi$
$619$	−11.3473	−	9.52148i	−0.456085	−	0.382701i	−0.841688	+	0.539964i	$0.818438\pi$
$620$		0			0
$621$	−5.08295	−	46.2887i	−0.203972	−	1.85750i
$622$		0			0
$623$	6.84960	−	18.1488i	0.274424	−	0.727118i
$624$		0			0
$625$	10.6514	+	60.4070i	0.426056	+	2.41628i
$626$		0			0
$627$	−0.402869	+	2.02638i	−0.0160890	+	0.0809258i
$628$		0			0
$629$	−1.01523	+	1.75844i	−0.0404800	+	0.0701134i
$630$		0			0
$631$	−7.31252	−	12.6657i	−0.291107	−	0.504212i	0.682965	−	0.730451i	$-0.260690\pi$
$631$	−7.31252	−	12.6657i	−0.291107	−	0.504212i	−0.974072	+	0.226239i	$0.927357\pi$
$632$		0			0
$633$	−4.27608	−	27.7644i	−0.169959	−	1.10354i
$634$		0			0
$635$	−50.8452	+	42.6642i	−2.01773	+	1.69308i
$636$		0			0
$637$	12.1316	−	19.9105i	0.480672	−	0.788881i
$638$		0			0
$639$	16.0355	−	25.1813i	0.634353	−	0.996158i
$640$		0			0
$641$	−2.67263	+	15.1572i	−0.105563	+	0.598675i	0.885432	+	0.464770i	$0.153863\pi$
$641$	−2.67263	+	15.1572i	−0.105563	+	0.598675i	−0.990994	+	0.133905i	$0.957248\pi$
$642$		0			0
$643$	5.21755	−	4.37804i	0.205760	−	0.172653i	−0.534084	−	0.845431i	$-0.679344\pi$
$643$	5.21755	−	4.37804i	0.205760	−	0.172653i	0.739844	+	0.672778i	$0.234899\pi$
$644$		0			0
$645$	86.7774	+	1.88514i	3.41686	+	0.0742274i
$646$		0			0
$647$	3.08596	−	5.34503i	0.121321	−	0.210135i	−0.798968	−	0.601374i	$-0.794620\pi$
$647$	3.08596	−	5.34503i	0.121321	−	0.210135i	0.920289	+	0.391239i	$0.127953\pi$
$648$		0			0
$649$	18.8680	+	32.6803i	0.740632	+	1.28281i
$650$		0			0
$651$	7.61465	+	1.60766i	0.298442	+	0.0630092i
$652$		0			0
$653$	25.4019	+	9.24555i	0.994055	+	0.361806i	0.787289	−	0.616584i	$-0.211484\pi$
$653$	25.4019	+	9.24555i	0.994055	+	0.361806i	0.206766	+	0.978390i	$0.433706\pi$
$654$		0			0
$655$	−10.5810	+	60.0079i	−0.413434	+	2.34470i
$656$		0			0
$657$	−11.5646	+	18.1605i	−0.451178	+	0.708509i
$658$		0			0
$659$	−8.06580	−	6.76801i	−0.314199	−	0.263644i	0.472026	−	0.881585i	$-0.343523\pi$
$659$	−8.06580	−	6.76801i	−0.314199	−	0.263644i	−0.786225	+	0.617940i	$0.787967\pi$
$660$		0			0
$661$	−2.85696	−	1.03985i	−0.111123	−	0.0404454i	0.285860	−	0.958271i	$-0.407721\pi$
$661$	−2.85696	−	1.03985i	−0.111123	−	0.0404454i	−0.396983	+	0.917826i	$0.629943\pi$
$662$		0			0
$663$	−12.0938	−	4.70169i	−0.469685	−	0.182599i
$664$		0			0
$665$	−2.36577	+	2.75268i	−0.0917406	+	0.106744i
$666$		0			0
$667$	69.3288			2.68442
$668$		0			0
$669$	4.73194	−	23.8010i	0.182948	−	0.920202i
$670$		0			0
$671$	29.6627	+	10.7963i	1.14512	+	0.416788i
$672$		0			0
$673$	7.12068	−	40.3834i	0.274482	−	1.55667i	−0.466120	−	0.884722i	$-0.654348\pi$
$673$	7.12068	−	40.3834i	0.274482	−	1.55667i	0.740602	−	0.671944i	$-0.234540\pi$
$674$		0			0
$675$	−45.5138	−	43.5449i	−1.75183	−	1.67604i
$676$		0			0
$677$	−28.6517	+	10.4284i	−1.10117	+	0.400795i	−0.827749	−	0.561098i	$-0.810379\pi$
$677$	−28.6517	+	10.4284i	−1.10117	+	0.400795i	−0.273425	+	0.961893i	$0.588157\pi$
$678$		0			0
$679$	−6.81213	+	3.82636i	−0.261425	+	0.146842i
$680$		0			0
$681$	3.16697	−	15.9294i	0.121358	−	0.610416i
$682$		0			0
$683$	−23.2074	−	40.1963i	−0.888005	−	1.53807i	−0.842231	−	0.539118i	$-0.818758\pi$
$683$	−23.2074	−	40.1963i	−0.888005	−	1.53807i	−0.0457742	−	0.998952i	$-0.514575\pi$
$684$		0			0
$685$	−9.80870	−	16.9892i	−0.374771	−	0.649123i
$686$		0			0
$687$	−5.11920	−	33.2387i	−0.195310	−	1.26814i
$688$		0			0
$689$	−29.0820	−	10.5850i	−1.10794	−	0.403256i
$690$		0			0
$691$	5.12410	−	29.0602i	0.194930	−	1.10550i	−0.717588	−	0.696467i	$-0.754754\pi$
$691$	5.12410	−	29.0602i	0.194930	−	1.10550i	0.912518	−	0.409036i	$-0.134135\pi$
$692$		0			0
$693$	25.4822	−	12.8909i	0.967990	−	0.489685i
$694$		0			0
$695$	−0.378076	−	0.317244i	−0.0143413	−	0.0120337i
$696$		0			0
$697$	1.09384	+	6.20347i	0.0414321	+	0.234973i
$698$		0			0
$699$	6.44707	+	11.7488i	0.243850	+	0.444379i
$700$		0			0
$701$	8.55325			0.323052			0.161526	−	0.986868i	$-0.448358\pi$
$701$	8.55325			0.323052			0.161526	+	0.986868i	$0.448358\pi$
$702$		0			0
$703$	0.149648	−	0.259198i	0.00564409	−	0.00977585i
$704$		0			0
$705$	49.3322	+	1.07169i	1.85796	+	0.0403621i
$706$		0			0
$707$	6.82012	+	4.04581i	0.256497	+	0.152158i
$708$		0			0
$709$	7.65984	+	6.42737i	0.287671	+	0.241385i	0.775191	−	0.631727i	$-0.217654\pi$
$709$	7.65984	+	6.42737i	0.287671	+	0.241385i	−0.487519	+	0.873112i	$0.662098\pi$
$710$		0			0
$711$	22.8205	+	20.9031i	0.855837	+	0.783927i
$712$		0			0
$713$	−11.6590	−	9.78303i	−0.436632	−	0.366378i
$714$		0			0
$715$	8.61075	+	48.8340i	0.322024	+	1.82629i
$716$		0			0
$717$	12.0389	−	9.66418i	0.449603	−	0.360915i
$718$		0			0
$719$	−18.3987	+	31.8675i	−0.686157	+	1.18846i	0.286915	+	0.957956i	$0.407370\pi$
$719$	−18.3987	+	31.8675i	−0.686157	+	1.18846i	−0.973072	+	0.230502i	$0.925963\pi$
$720$		0			0
$721$	−6.33969	+	7.37651i	−0.236102	+	0.274716i
$722$		0			0
$723$	−10.0880	+	3.42549i	−0.375176	+	0.127395i
$724$		0			0
$725$	71.8385	−	60.2797i	2.66801	−	2.23873i
$726$		0			0
$727$	7.32027	−	41.5153i	0.271494	−	1.53972i	−0.478390	−	0.878147i	$-0.658780\pi$
$727$	7.32027	−	41.5153i	0.271494	−	1.53972i	0.749884	−	0.661570i	$-0.230109\pi$
$728$		0			0
$729$	26.7710	+	3.50876i	0.991520	+	0.129954i
$730$		0			0
$731$	20.8663	+	17.5089i	0.771769	+	0.647591i
$732$		0			0
$733$	−3.07332	−	17.4297i	−0.113516	−	0.643780i	−0.987474	−	0.157780i	$-0.949566\pi$
$733$	−3.07332	−	17.4297i	−0.113516	−	0.643780i	0.873958	−	0.486001i	$-0.161545\pi$
$734$		0			0
$735$	50.1179	+	2.27478i	1.84863	+	0.0839064i
$736$		0			0
$737$	−26.0320			−0.958902
$738$		0			0
$739$	−13.8884			−0.510892			−0.255446	−	0.966823i	$-0.582222\pi$
$739$	−13.8884			−0.510892			−0.255446	+	0.966823i	$0.582222\pi$
$740$		0			0
$741$	1.78266	+	0.693043i	0.0654878	+	0.0254596i
$742$		0			0
$743$	−1.74969	−	9.92300i	−0.0641900	−	0.364039i	−0.999935	−	0.0113634i	$-0.996383\pi$
$743$	−1.74969	−	9.92300i	−0.0641900	−	0.364039i	0.935745	−	0.352676i	$-0.114728\pi$
$744$		0			0
$745$	48.6791	−	17.7177i	1.78346	−	0.649128i
$746$		0			0
$747$	−33.9913	+	10.7246i	−1.24368	+	0.392392i
$748$		0			0
$749$	−22.1775	+	3.64079i	−0.810348	+	0.133031i
$750$		0			0
$751$	−23.4898	−	8.54958i	−0.857154	−	0.311978i	−0.124200	−	0.992257i	$-0.539637\pi$
$751$	−23.4898	−	8.54958i	−0.857154	−	0.311978i	−0.732954	+	0.680279i	$0.761859\pi$
$752$		0			0
$753$	12.3932	+	22.5846i	0.451633	+	0.823030i
$754$		0			0
$755$	−2.45404			−0.0893117
$756$		0			0
$757$	−10.3795			−0.377248			−0.188624	−	0.982049i	$-0.560403\pi$
$757$	−10.3795			−0.377248			−0.188624	+	0.982049i	$0.560403\pi$
$758$		0			0
$759$	−55.8344	−	1.21294i	−2.02666	−	0.0440269i
$760$		0			0
$761$	25.0905	+	9.13219i	0.909529	+	0.331042i	0.754065	−	0.656800i	$-0.228090\pi$
$761$	25.0905	+	9.13219i	0.909529	+	0.331042i	0.155464	+	0.987842i	$0.450313\pi$
$762$		0			0
$763$	14.0927	+	17.2039i	0.510190	+	0.622823i
$764$		0			0
$765$	−3.64971	−	27.6812i	−0.131956	−	1.00082i
$766$		0			0
$767$	32.8274	−	11.9482i	1.18533	−	0.431424i
$768$		0			0
$769$	0.809802	+	4.59261i	0.0292022	+	0.165614i	0.995921	−	0.0902263i	$-0.0287590\pi$
$769$	0.809802	+	4.59261i	0.0292022	+	0.165614i	−0.966719	+	0.255840i	$0.917648\pi$
$770$		0			0
$771$	−3.14033	−	20.3900i	−0.113096	−	0.734328i
$772$		0			0
$773$	−15.2906			−0.549964			−0.274982	−	0.961449i	$-0.588672\pi$
$773$	−15.2906			−0.549964			−0.274982	+	0.961449i	$0.588672\pi$
$774$		0			0
$775$	−20.5871			−0.739511
$776$		0			0
$777$	−4.09590	+	0.581355i	−0.146940	+	0.0208560i
$778$		0			0
$779$	−0.161235	−	0.914409i	−0.00577684	−	0.0327621i
$780$		0			0
$781$	−27.4269	−	23.0139i	−0.981410	−	0.823501i
$782$		0			0
$783$	−9.54313	+	39.0483i	−0.341044	+	1.39547i
$784$		0			0
$785$	15.9943	−	90.7083i	0.570862	−	3.23752i
$786$		0			0
$787$	6.89394	−	5.78470i	0.245742	−	0.206202i	−0.511594	−	0.859227i	$-0.670945\pi$
$787$	6.89394	−	5.78470i	0.245742	−	0.206202i	0.757336	+	0.653025i	$0.226500\pi$
$788$		0			0
$789$	4.30375	+	3.77356i	0.153218	+	0.134342i
$790$		0			0
$791$	3.63713	+	10.3727i	0.129321	+	0.368812i
$792$		0			0
$793$	14.6114	−	25.3076i	0.518865	−	0.898700i
$794$		0			0
$795$	−10.1369	−	65.8184i	−0.359519	−	2.33434i
$796$		0			0
$797$	7.79157	+	44.1882i	0.275992	+	1.56523i	0.735794	+	0.677205i	$0.236809\pi$
$797$	7.79157	+	44.1882i	0.275992	+	1.56523i	−0.459803	+	0.888021i	$0.652080\pi$
$798$		0			0
$799$	11.8623	+	9.95367i	0.419659	+	0.352135i
$800$		0			0
$801$	−10.1602	−	19.5085i	−0.358994	−	0.689298i
$802$		0			0
$803$	19.7800	+	16.5974i	0.698020	+	0.585708i
$804$		0			0
$805$	−84.3826	−	50.0572i	−2.97410	−	1.76429i
$806$		0			0
$807$	4.69726	+	8.56001i	0.165351	+	0.301327i
$808$		0			0
$809$	11.0524	−	19.1433i	0.388581	−	0.673042i	−0.603678	−	0.797228i	$-0.706299\pi$
$809$	11.0524	−	19.1433i	0.388581	−	0.673042i	0.992259	+	0.124186i	$0.0396321\pi$
$810$		0			0
$811$	49.6048			1.74186			0.870930	−	0.491408i	$-0.163517\pi$
$811$	49.6048			1.74186			0.870930	+	0.491408i	$0.163517\pi$
$812$		0			0
$813$	−13.8172	−	0.300163i	−0.484591	−	0.0105272i
$814$		0			0
$815$	0.184641	+	1.04715i	0.00646768	+	0.0366801i
$816$		0			0
$817$	−3.07576	−	2.58087i	−0.107607	−	0.0902931i
$818$		0			0
$819$	−7.65611	−	25.3042i	−0.267526	−	0.884199i
$820$		0			0
$821$	−6.50063	+	36.8669i	−0.226874	+	1.28666i	0.632197	+	0.774807i	$0.282153\pi$
$821$	−6.50063	+	36.8669i	−0.226874	+	1.28666i	−0.859071	+	0.511857i	$0.828958\pi$
$822$		0			0
$823$	−22.8092	−	8.30187i	−0.795079	−	0.289385i	−0.0876330	−	0.996153i	$-0.527930\pi$
$823$	−22.8092	−	8.30187i	−0.795079	−	0.289385i	−0.707445	+	0.706768i	$0.750153\pi$
$824$		0			0
$825$	−58.9101	+	47.2897i	−2.05099	+	1.64642i
$826$		0			0
$827$	−8.70663	−	15.0803i	−0.302759	−	0.524394i	0.674001	−	0.738731i	$-0.264574\pi$
$827$	−8.70663	−	15.0803i	−0.302759	−	0.524394i	−0.976760	+	0.214336i	$0.931241\pi$
$828$		0			0
$829$	−14.3135	−	24.7917i	−0.497128	−	0.861051i	0.502866	−	0.864364i	$-0.332279\pi$
$829$	−14.3135	−	24.7917i	−0.497128	−	0.861051i	−0.999995	+	0.00331298i	$0.998945\pi$
$830$		0			0
$831$	15.1271	+	13.2636i	0.524755	+	0.460108i
$832$		0			0
$833$	11.8183	+	10.4025i	0.409479	+	0.360424i
$834$		0			0
$835$	−14.1012	+	5.13240i	−0.487991	+	0.177614i
$836$		0			0
$837$	7.11499	−	5.22008i	0.245930	−	0.180433i
$838$		0			0
$839$	−1.19374	+	6.77004i	−0.0412125	+	0.233728i	−0.998455	−	0.0555573i	$-0.982306\pi$
$839$	−1.19374	+	6.77004i	−0.0412125	+	0.233728i	0.957243	+	0.289285i	$0.0934175\pi$
$840$		0			0
$841$	−28.9858	−	10.5500i	−0.999511	−	0.363792i
$842$		0			0
$843$	23.9570	−	8.13489i	0.825124	−	0.280180i
$844$		0			0
$845$	−7.88717			−0.271327
$846$		0			0
$847$	−1.70255	−	4.85552i	−0.0585005	−	0.166838i
$848$		0			0
$849$	−33.3333	+	26.7581i	−1.14400	+	0.918334i
$850$		0			0
$851$	7.60244	+	2.76706i	0.260608	+	0.0948537i
$852$		0			0
$853$	16.1988	+	13.5924i	0.554638	+	0.465396i	0.876508	−	0.481388i	$-0.159867\pi$
$853$	16.1988	+	13.5924i	0.554638	+	0.465396i	−0.321870	+	0.946784i	$0.604311\pi$
$854$		0			0
$855$	0.537978	+	4.08029i	0.0183985	+	0.139543i
$856$		0			0
$857$	−1.49026	+	8.45167i	−0.0509063	+	0.288704i	−0.999624	−	0.0274208i	$-0.991271\pi$
$857$	−1.49026	+	8.45167i	−0.0509063	+	0.288704i	0.948718	+	0.316124i	$0.102382\pi$
$858$		0			0
$859$	36.3975	+	13.2476i	1.24187	+	0.452002i	0.877645	−	0.479311i	$-0.159113\pi$
$859$	36.3975	+	13.2476i	1.24187	+	0.452002i	0.364220	+	0.931313i	$0.381336\pi$
$860$		0			0
$861$	−8.57469	+	9.54939i	−0.292225	+	0.325442i
$862$		0			0
$863$	15.1192	+	26.1872i	0.514663	+	0.891423i	0.999855	+	0.0170153i	$0.00541638\pi$
$863$	15.1192	+	26.1872i	0.514663	+	0.891423i	−0.485192	+	0.874408i	$0.661250\pi$
$864$		0			0
$865$	−17.4675	+	30.2546i	−0.593913	+	1.02869i
$866$		0			0
$867$	−10.7279	+	17.6829i	−0.364340	+	0.600544i
$868$		0			0
$869$	28.4314	−	23.8568i	0.964469	−	0.809286i
$870$		0			0
$871$	−4.18479	+	23.7331i	−0.141796	+	0.804166i
$872$		0			0
$873$	−1.91585	+	8.64970i	−0.0648416	+	0.292748i
$874$		0			0
$875$	−76.9443	+	12.6316i	−2.60119	+	0.427027i
$876$		0			0
$877$	37.3765	−	31.3626i	1.26211	−	1.05904i	0.266660	−	0.963791i	$-0.414080\pi$
$877$	37.3765	−	31.3626i	1.26211	−	1.05904i	0.995454	−	0.0952485i	$-0.0303646\pi$
$878$		0			0
$879$	−27.6256	+	22.1763i	−0.931790	+	0.747987i
$880$		0			0
$881$	−27.8481	−	48.2343i	−0.938225	−	1.62505i	−0.768780	−	0.639514i	$-0.779136\pi$
$881$	−27.8481	−	48.2343i	−0.938225	−	1.62505i	−0.169446	−	0.985540i	$-0.554198\pi$
$882$		0			0
$883$	−6.82972	+	11.8294i	−0.229839	+	0.398092i	−0.957760	−	0.287568i	$-0.907153\pi$
$883$	−6.82972	+	11.8294i	−0.229839	+	0.398092i	0.727922	+	0.685660i	$0.240486\pi$
$884$		0			0
$885$	56.5212	+	49.5582i	1.89994	+	1.66588i
$886$		0			0
$887$	−6.53484	−	37.0609i	−0.219418	−	1.24438i	−0.873073	−	0.487590i	$-0.837876\pi$
$887$	−6.53484	−	37.0609i	−0.219418	−	1.24438i	0.653654	−	0.756793i	$-0.273235\pi$
$888$		0			0
$889$	−26.8931	−	32.8302i	−0.901964	−	1.10109i
$890$		0			0
$891$	8.36878	−	31.2808i	0.280365	−	1.04795i
$892$		0			0
$893$	−1.74854	−	1.46720i	−0.0585126	−	0.0490979i
$894$		0			0
$895$	61.1015	+	22.2391i	2.04240	+	0.743372i
$896$		0			0
$897$	−10.0815	+	50.7086i	−0.336612	+	1.69311i
$898$		0			0
$899$	6.56898	+	11.3778i	0.219088	+	0.379471i
$900$		0			0
$901$	10.4494	−	18.0989i	0.348120	−	0.602961i
$902$		0			0
$903$	−1.86099	+	55.4667i	−0.0619299	+	1.84582i
$904$		0			0
$905$	28.5540	−	23.9597i	0.949168	−	0.796446i
$906$		0			0
$907$	44.3985	−	16.1597i	1.47423	−	0.536575i	0.524983	−	0.851113i	$-0.324072\pi$
$907$	44.3985	−	16.1597i	1.47423	−	0.536575i	0.949245	+	0.314537i	$0.101849\pi$
$908$		0			0
$909$	8.57493	−	2.70548i	0.284413	−	0.0897351i
$910$		0			0
$911$	32.9308	−	11.9858i	1.09105	−	0.397108i	0.267037	−	0.963686i	$-0.413955\pi$
$911$	32.9308	−	11.9858i	1.09105	−	0.397108i	0.824008	+	0.566578i	$0.191733\pi$
$912$		0			0
$913$	7.42284	+	42.0970i	0.245660	+	1.39321i
$914$		0			0
$915$	62.8662	+	1.36570i	2.07829	+	0.0451486i
$916$		0			0
$917$	−38.2860	−	7.21840i	−1.26431	−	0.238373i
$918$		0			0
$919$	−18.6052	−	32.2252i	−0.613730	−	1.06301i	−0.990606	−	0.136748i	$-0.956335\pi$
$919$	−18.6052	−	32.2252i	−0.613730	−	1.06301i	0.376875	−	0.926264i	$-0.376998\pi$
$920$		0			0
$921$	8.15115	+	0.177075i	0.268589	+	0.00583481i
$922$		0			0
$923$	−25.3905	+	21.3052i	−0.835739	+	0.701268i
$924$		0			0
$925$	10.2835	−	3.74290i	0.338121	−	0.123066i
$926$		0			0
$927$	1.44165	+	10.9342i	0.0473500	+	0.359125i
$928$		0			0
$929$	−0.706786	+	4.00838i	−0.0231889	+	0.131511i	−0.994205	−	0.107505i	$-0.965714\pi$
$929$	−0.706786	+	4.00838i	−0.0231889	+	0.131511i	0.971016	+	0.239016i	$0.0768249\pi$
$930$		0			0
$931$	−1.74205	−	1.53335i	−0.0570932	−	0.0502536i
$932$		0			0
$933$	−14.7890	+	11.8718i	−0.484172	+	0.388665i
$934$		0			0
$935$	−33.4852			−1.09508
$936$		0			0
$937$	−28.5824	+	49.5062i	−0.933748	+	1.61730i	−0.156896	+	0.987615i	$0.550149\pi$
$937$	−28.5824	+	49.5062i	−0.933748	+	1.61730i	−0.776852	+	0.629684i	$0.783185\pi$
$938$		0			0
$939$	−11.9154	−	10.4475i	−0.388846	−	0.340942i
$940$		0			0
$941$	−14.3568	+	12.0468i	−0.468018	+	0.392714i	−0.846071	−	0.533070i	$-0.821038\pi$
$941$	−14.3568	+	12.0468i	−0.468018	+	0.392714i	0.378053	+	0.925784i	$0.376594\pi$
$942$		0			0
$943$	23.5852	−	8.58432i	0.768041	−	0.279544i
$944$		0			0
$945$	39.8092	−	40.6367i	1.29499	−	1.32191i
$946$		0			0
$947$	31.4112	−	11.4327i	1.02073	−	0.371514i	0.223183	−	0.974776i	$-0.428355\pi$
$947$	31.4112	−	11.4327i	1.02073	−	0.371514i	0.797543	+	0.603263i	$0.206133\pi$
$948$		0			0
$949$	18.3114	−	15.3651i	0.594412	−	0.498771i
$950$		0			0
$951$	−16.5141	+	5.60756i	−0.535507	+	0.181837i
$952$		0			0
$953$	−15.1471	+	26.2356i	−0.490663	+	0.849854i	−0.999942	−	0.0107478i	$-0.996579\pi$
$953$	−15.1471	+	26.2356i	−0.490663	+	0.849854i	0.509279	+	0.860602i	$0.329912\pi$
$954$		0			0
$955$	−41.0181			−1.32731
$956$		0			0
$957$	44.9326	+	17.4683i	1.45246	+	0.564672i
$958$		0			0
$959$	10.9361	−	6.14280i	0.353146	−	0.198361i
$960$		0			0
$961$	−4.88226	+	27.6887i	−0.157492	+	0.893184i
$962$		0			0
$963$	−13.6882	+	21.4952i	−0.441094	+	0.692674i
$964$		0			0
$965$	−82.1532	+	29.9013i	−2.64461	+	0.962558i
$966$		0			0
$967$	37.0551	−	31.0929i	1.19161	−	0.999880i	0.191781	−	0.981438i	$-0.438574\pi$
$967$	37.0551	−	31.0929i	1.19161	−	0.999880i	0.999830	−	0.0184425i	$-0.00587077\pi$
$968$		0			0
$969$	−0.669923	+	1.10424i	−0.0215210	+	0.0354732i
$970$		0			0
$971$	5.34005	+	9.24924i	0.171370	+	0.296822i	0.938899	−	0.344192i	$-0.111847\pi$
$971$	5.34005	+	9.24924i	0.171370	+	0.296822i	−0.767529	+	0.641014i	$0.778514\pi$
$972$		0			0
$973$	0.205686	−	0.239325i	0.00659399	−	0.00767241i
$974$		0			0
$975$	33.6434	+	61.3098i	1.07745	+	1.96349i
$976$		0			0
$977$	−8.01606	−	45.4614i	−0.256457	−	1.45444i	−0.792306	−	0.610124i	$-0.791120\pi$
$977$	−8.01606	−	45.4614i	−0.256457	−	1.45444i	0.535849	−	0.844314i	$-0.319991\pi$
$978$		0			0
$979$	−24.7885	+	9.02226i	−0.792243	+	0.288353i
$980$		0			0
$981$	25.1930	+	1.09510i	0.804351	+	0.0349637i
$982$		0			0
$983$	28.5271	−	10.3830i	0.909874	−	0.331167i	0.155671	−	0.987809i	$-0.450246\pi$
$983$	28.5271	−	10.3830i	0.909874	−	0.331167i	0.754203	+	0.656642i	$0.228024\pi$
$984$		0			0
$985$	−38.3960	+	32.2181i	−1.22340	+	1.02655i
$986$		0			0
$987$	−1.05796	+	31.5323i	−0.0336752	+	1.00369i
$988$		0			0
$989$	54.2667	−	93.9927i	1.72558	−	2.98879i
$990$		0			0
$991$	0.0957378	+	0.165823i	0.00304121	+	0.00526753i	0.867542	−	0.497364i	$-0.165699\pi$
$991$	0.0957378	+	0.165823i	0.00304121	+	0.00526753i	−0.864501	+	0.502631i	$0.832365\pi$
$992$		0			0
$993$	−47.8225	+	16.2387i	−1.51760	+	0.515318i
$994$		0			0
$995$	−12.8320	−	4.67045i	−0.406801	−	0.148063i
$996$		0			0
$997$	−29.7014	−	24.9224i	−0.940652	−	0.789301i	0.0370465	−	0.999314i	$-0.488205\pi$
$997$	−29.7014	−	24.9224i	−0.940652	−	0.789301i	−0.977699	+	0.210013i	$0.932649\pi$
$998$		0			0
$999$	−2.60498	+	3.90106i	−0.0824179	+	0.123424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.16	yes	144
7.2	even	3		756.2.bp.a.457.16	yes	144
27.13	even	9		756.2.bp.a.445.16	✓	144
189.121	even	9	inner	756.2.bq.a.121.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.16	✓	144	27.13	even	9
756.2.bp.a.457.16	yes	144	7.2	even	3
756.2.bq.a.25.16	yes	144	1.1	even	1	trivial
756.2.bq.a.121.16	yes	144	189.121	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.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.898399 - 1.48084i) q^{3} +(-3.88836 - 1.41525i) q^{5} +(0.934219 - 2.47533i) q^{7} +(-1.38576 - 2.66077i) q^{9} +O(q^{10})\)	\(q+(0.898399 - 1.48084i) q^{3} +(-3.88836 - 1.41525i) q^{5} +(0.934219 - 2.47533i) q^{7} +(-1.38576 - 2.66077i) q^{9} +(-3.38090 + 1.23055i) q^{11} +(0.578379 + 3.28015i) q^{13} +(-5.58906 + 4.48658i) q^{15} -2.24918 q^{17} +0.331536 q^{19} +(-2.82625 - 3.60726i) q^{21} +(1.55620 + 8.82567i) q^{23} +(9.28623 + 7.79207i) q^{25} +(-5.18512 - 0.338349i) q^{27} +(1.34335 - 7.61850i) q^{29} +(-1.30096 + 1.09163i) q^{31} +(-1.21516 + 6.11209i) q^{33} +(-7.13579 + 8.30281i) q^{35} +(0.451379 - 0.781811i) q^{37} +(5.37699 + 2.09040i) q^{39} +(-0.486327 - 2.75810i) q^{41} +(-9.27729 - 7.78457i) q^{43} +(1.62268 + 12.3072i) q^{45} +(-5.27406 - 4.42546i) q^{47} +(-5.25447 - 4.62499i) q^{49} +(-2.02066 + 3.33067i) q^{51} +(-4.64586 + 8.04687i) q^{53} +14.8877 q^{55} +(0.297852 - 0.490951i) q^{57} +(-1.82129 - 10.3290i) q^{59} +(-6.72097 - 5.63956i) q^{61} +(-7.88086 + 0.944461i) q^{63} +(2.39328 - 13.5730i) q^{65} +(6.79902 + 2.47464i) q^{67} +(14.4675 + 5.62449i) q^{69} +(4.97559 + 8.61798i) q^{71} +(-3.58835 - 6.21520i) q^{73} +(19.8815 - 6.75100i) q^{75} +(-0.112498 + 9.51844i) q^{77} +(-9.69355 + 3.52816i) q^{79} +(-5.15935 + 7.37435i) q^{81} +(2.06311 - 11.7005i) q^{83} +(8.74564 + 3.18315i) q^{85} +(-10.0749 - 8.83373i) q^{87} +7.33190 q^{89} +(8.65978 + 1.63270i) q^{91} +(0.447752 + 2.90723i) q^{93} +(-1.28913 - 0.469206i) q^{95} +(-2.26222 - 1.89822i) q^{97} +(7.95932 + 7.29055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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