LMFDB - Embedded newform 756.2.bq.a.25.11

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			25.11
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247313 - 1.71430i) q^{3} +(-0.839073 - 0.305398i) q^{5} +(-1.83758 + 1.90350i) q^{7} +(-2.87767 + 0.847940i) q^{9} +O(q^{10})$	\(q+(-0.247313 - 1.71430i) q^{3} +(-0.839073 - 0.305398i) q^{5} +(-1.83758 + 1.90350i) q^{7} +(-2.87767 + 0.847940i) q^{9} +(-0.399258 + 0.145318i) q^{11} +(0.649267 + 3.68218i) q^{13} +(-0.316030 + 1.51395i) q^{15} +6.87529 q^{17} -4.61696 q^{19} +(3.71763 + 2.67940i) q^{21} +(1.53593 + 8.71070i) q^{23} +(-3.21945 - 2.70144i) q^{25} +(2.16531 + 4.72350i) q^{27} +(-1.20297 + 6.82236i) q^{29} +(-0.115067 + 0.0965526i) q^{31} +(0.347861 + 0.648511i) q^{33} +(2.12319 - 1.03598i) q^{35} +(3.73817 - 6.47469i) q^{37} +(6.15180 - 2.02369i) q^{39} +(-0.831623 - 4.71637i) q^{41} +(5.03724 + 4.22675i) q^{43} +(2.67354 + 0.167350i) q^{45} +(-0.932650 - 0.782586i) q^{47} +(-0.246617 - 6.99565i) q^{49} +(-1.70035 - 11.7863i) q^{51} +(-5.29593 + 9.17282i) q^{53} +0.379387 q^{55} +(1.14183 + 7.91486i) q^{57} +(2.09733 + 11.8946i) q^{59} +(10.4523 + 8.77049i) q^{61} +(3.67389 - 7.03580i) q^{63} +(0.579746 - 3.28790i) q^{65} +(-14.5638 - 5.30080i) q^{67} +(14.5529 - 4.78732i) q^{69} +(-3.20651 - 5.55384i) q^{71} +(0.847274 + 1.46752i) q^{73} +(-3.83487 + 6.18721i) q^{75} +(0.457055 - 1.02702i) q^{77} +(-10.7094 + 3.89790i) q^{79} +(7.56199 - 4.88019i) q^{81} +(-1.52025 + 8.62179i) q^{83} +(-5.76887 - 2.09970i) q^{85} +(11.9931 + 0.374988i) q^{87} +7.07127 q^{89} +(-8.20210 - 5.53041i) q^{91} +(0.193978 + 0.173381i) q^{93} +(3.87396 + 1.41001i) q^{95} +(2.78160 + 2.33404i) q^{97} +(1.02571 - 0.756725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.247313	−	1.71430i	−0.142786	−	0.989754i
$3$	−0.247313	−	1.71430i	−0.142786	−	0.989754i
$4$		0			0
$5$	−0.839073	−	0.305398i	−0.375245	−	0.136578i	0.147511	−	0.989060i	$-0.452874\pi$
$5$	−0.839073	−	0.305398i	−0.375245	−	0.136578i	−0.522756	+	0.852482i	$0.675096\pi$
$6$		0			0
$7$	−1.83758	+	1.90350i	−0.694539	+	0.719455i
$7$	−1.83758	+	1.90350i	−0.694539	+	0.719455i
$8$		0			0
$9$	−2.87767	+	0.847940i	−0.959224	+	0.282647i
$10$		0			0
$11$	−0.399258	+	0.145318i	−0.120381	+	0.0438151i	−0.401508	−	0.915855i	$-0.631514\pi$
$11$	−0.399258	+	0.145318i	−0.120381	+	0.0438151i	0.281127	+	0.959670i	$0.409292\pi$
$12$		0			0
$13$	0.649267	+	3.68218i	0.180074	+	1.02125i	0.932122	+	0.362144i	$0.117955\pi$
$13$	0.649267	+	3.68218i	0.180074	+	1.02125i	−0.752048	+	0.659109i	$0.770934\pi$
$14$		0			0
$15$	−0.316030	+	1.51395i	−0.0815987	+	0.390901i
$16$		0			0
$17$	6.87529			1.66750			0.833751	−	0.552140i	$-0.186189\pi$
$17$	6.87529			1.66750			0.833751	+	0.552140i	$0.186189\pi$
$18$		0			0
$19$	−4.61696			−1.05920			−0.529601	−	0.848247i	$-0.677658\pi$
$19$	−4.61696			−1.05920			−0.529601	+	0.848247i	$0.677658\pi$
$20$		0			0
$21$	3.71763	+	2.67940i	0.811254	+	0.584694i
$22$		0			0
$23$	1.53593	+	8.71070i	0.320264	+	1.81631i	0.541058	+	0.840985i	$0.318024\pi$
$23$	1.53593	+	8.71070i	0.320264	+	1.81631i	−0.220794	+	0.975320i	$0.570865\pi$
$24$		0			0
$25$	−3.21945	−	2.70144i	−0.643889	−	0.540287i
$26$		0			0
$27$	2.16531	+	4.72350i	0.416715	+	0.909037i
$28$		0			0
$29$	−1.20297	+	6.82236i	−0.223385	+	1.26688i	0.642363	+	0.766400i	$0.277954\pi$
$29$	−1.20297	+	6.82236i	−0.223385	+	1.26688i	−0.865748	+	0.500480i	$0.833157\pi$
$30$		0			0
$31$	−0.115067	+	0.0965526i	−0.0206666	+	0.0173414i	−0.653062	−	0.757304i	$-0.726516\pi$
$31$	−0.115067	+	0.0965526i	−0.0206666	+	0.0173414i	0.632396	+	0.774645i	$0.282072\pi$
$32$		0			0
$33$	0.347861	+	0.648511i	0.0605549	+	0.112891i
$34$		0			0
$35$	2.12319	−	1.03598i	0.358884	−	0.175113i
$36$		0			0
$37$	3.73817	−	6.47469i	0.614551	−	1.06443i	−0.375912	−	0.926655i	$-0.622671\pi$
$37$	3.73817	−	6.47469i	0.614551	−	1.06443i	0.990463	−	0.137778i	$-0.0439960\pi$
$38$		0			0
$39$	6.15180	−	2.02369i	0.985076	−	0.324050i
$40$		0			0
$41$	−0.831623	−	4.71637i	−0.129878	−	0.736573i	−0.978291	−	0.207238i	$-0.933553\pi$
$41$	−0.831623	−	4.71637i	−0.129878	−	0.736573i	0.848413	−	0.529335i	$-0.177559\pi$
$42$		0			0
$43$	5.03724	+	4.22675i	0.768172	+	0.644573i	0.940240	−	0.340512i	$-0.110600\pi$
$43$	5.03724	+	4.22675i	0.768172	+	0.644573i	−0.172068	+	0.985085i	$0.555045\pi$
$44$		0			0
$45$	2.67354	+	0.167350i	0.398547	+	0.0249471i
$46$		0			0
$47$	−0.932650	−	0.782586i	−0.136041	−	0.114152i	0.572228	−	0.820094i	$-0.306079\pi$
$47$	−0.932650	−	0.782586i	−0.136041	−	0.114152i	−0.708269	+	0.705943i	$0.750524\pi$
$48$		0			0
$49$	−0.246617	−	6.99565i	−0.0352310	−	0.999379i
$50$		0			0
$51$	−1.70035	−	11.7863i	−0.238097	−	1.65042i
$52$		0			0
$53$	−5.29593	+	9.17282i	−0.727452	+	1.25998i	0.230505	+	0.973071i	$0.425962\pi$
$53$	−5.29593	+	9.17282i	−0.727452	+	1.25998i	−0.957957	+	0.286912i	$0.907371\pi$
$54$		0			0
$55$	0.379387			0.0511565
$56$		0			0
$57$	1.14183	+	7.91486i	0.151240	+	1.04835i
$58$		0			0
$59$	2.09733	+	11.8946i	0.273050	+	1.54854i	0.745090	+	0.666964i	$0.232407\pi$
$59$	2.09733	+	11.8946i	0.273050	+	1.54854i	−0.472040	+	0.881577i	$0.656482\pi$
$60$		0			0
$61$	10.4523	+	8.77049i	1.33827	+	1.12295i	0.982066	+	0.188539i	$0.0603753\pi$
$61$	10.4523	+	8.77049i	1.33827	+	1.12295i	0.356209	+	0.934406i	$0.384069\pi$
$62$		0			0
$63$	3.67389	−	7.03580i	0.462867	−	0.886428i
$64$		0			0
$65$	0.579746	−	3.28790i	0.0719086	−	0.407814i
$66$		0			0
$67$	−14.5638	−	5.30080i	−1.77925	−	0.647596i	−0.999776	−	0.0211671i	$-0.993262\pi$
$67$	−14.5638	−	5.30080i	−1.77925	−	0.647596i	−0.779479	−	0.626429i	$-0.784516\pi$
$68$		0			0
$69$	14.5529	−	4.78732i	1.75197	−	0.576326i
$70$		0			0
$71$	−3.20651	−	5.55384i	−0.380543	−	0.659119i	0.610597	−	0.791941i	$-0.290929\pi$
$71$	−3.20651	−	5.55384i	−0.380543	−	0.659119i	−0.991140	+	0.132822i	$0.957596\pi$
$72$		0			0
$73$	0.847274	+	1.46752i	0.0991659	+	0.171760i	0.911340	−	0.411655i	$-0.135049\pi$
$73$	0.847274	+	1.46752i	0.0991659	+	0.171760i	−0.812174	+	0.583416i	$0.801716\pi$
$74$		0			0
$75$	−3.83487	+	6.18721i	−0.442813	+	0.714437i
$76$		0			0
$77$	0.457055	−	1.02702i	0.0520863	−	0.117040i
$78$		0			0
$79$	−10.7094	+	3.89790i	−1.20490	+	0.438548i	−0.864932	−	0.501889i	$-0.832639\pi$
$79$	−10.7094	+	3.89790i	−1.20490	+	0.438548i	−0.339969	+	0.940437i	$0.610417\pi$
$80$		0			0
$81$	7.56199	−	4.88019i	0.840222	−	0.542243i
$82$		0			0
$83$	−1.52025	+	8.62179i	−0.166870	+	0.946364i	0.780246	+	0.625472i	$0.215094\pi$
$83$	−1.52025	+	8.62179i	−0.166870	+	0.946364i	−0.947116	+	0.320892i	$0.896017\pi$
$84$		0			0
$85$	−5.76887	−	2.09970i	−0.625722	−	0.227744i
$86$		0			0
$87$	11.9931	+	0.374988i	1.28580	+	0.0402029i
$88$		0			0
$89$	7.07127			0.749553			0.374777	−	0.927115i	$-0.377719\pi$
$89$	7.07127			0.749553			0.374777	+	0.927115i	$0.377719\pi$
$90$		0			0
$91$	−8.20210	−	5.53041i	−0.859814	−	0.579744i
$92$		0			0
$93$	0.193978	+	0.173381i	0.0201146	+	0.0179788i
$94$		0			0
$95$	3.87396	+	1.41001i	0.397460	+	0.144664i
$96$		0			0
$97$	2.78160	+	2.33404i	0.282429	+	0.236986i	0.772986	−	0.634423i	$-0.218762\pi$
$97$	2.78160	+	2.33404i	0.282429	+	0.236986i	−0.490557	+	0.871409i	$0.663207\pi$
$98$		0			0
$99$	1.02571	−	0.756725i	0.103088	−	0.0760537i
$100$		0			0
$101$	−0.774371	+	4.39168i	−0.0770528	+	0.436988i	0.921737	+	0.387815i	$0.126770\pi$
$101$	−0.774371	+	4.39168i	−0.0770528	+	0.436988i	−0.998790	+	0.0491738i	$0.984341\pi$
$102$		0			0
$103$	−15.7486	−	5.73202i	−1.55176	−	0.564793i	−0.582927	−	0.812524i	$-0.698093\pi$
$103$	−15.7486	−	5.73202i	−1.55176	−	0.564793i	−0.968829	+	0.247731i	$0.920315\pi$
$104$		0			0
$105$	−2.30108	−	3.38357i	−0.224563	−	0.330203i
$106$		0			0
$107$	−2.43308	−	4.21421i	−0.235214	−	0.407403i	0.724121	−	0.689673i	$-0.242246\pi$
$107$	−2.43308	−	4.21421i	−0.235214	−	0.407403i	−0.959335	+	0.282270i	$0.908913\pi$
$108$		0			0
$109$	−2.66080	+	4.60864i	−0.254858	+	0.441427i	−0.964857	−	0.262775i	$-0.915362\pi$
$109$	−2.66080	+	4.60864i	−0.254858	+	0.441427i	0.709999	+	0.704203i	$0.248695\pi$
$110$		0			0
$111$	−12.0241	−	4.80707i	−1.14128	−	0.456267i
$112$		0			0
$113$	−3.45461	+	2.89876i	−0.324982	+	0.272692i	−0.790652	−	0.612266i	$-0.790258\pi$
$113$	−3.45461	+	2.89876i	−0.324982	+	0.272692i	0.465669	+	0.884959i	$0.345814\pi$
$114$		0			0
$115$	1.37147	−	7.77798i	0.127890	−	0.725300i
$116$		0			0
$117$	−4.99065	−	10.0456i	−0.461385	−	0.928713i
$118$		0			0
$119$	−12.6339	+	13.0871i	−1.15815	+	1.19969i
$120$		0			0
$121$	−8.28820	+	6.95462i	−0.753473	+	0.632239i
$122$		0			0
$123$	−7.87961	+	2.59207i	−0.710481	+	0.233719i
$124$		0			0
$125$	4.10865	+	7.11638i	0.367488	+	0.636509i
$126$		0			0
$127$	9.37701	−	16.2415i	0.832075	−	1.44120i	−0.0643151	−	0.997930i	$-0.520486\pi$
$127$	9.37701	−	16.2415i	0.832075	−	1.44120i	0.896390	−	0.443266i	$-0.146180\pi$
$128$		0			0
$129$	6.00015	−	9.68069i	0.528284	−	0.852337i
$130$		0			0
$131$	1.53441	+	8.70209i	0.134062	+	0.760305i	0.975508	+	0.219964i	$0.0705939\pi$
$131$	1.53441	+	8.70209i	0.134062	+	0.760305i	−0.841446	+	0.540342i	$0.818295\pi$
$132$		0			0
$133$	8.48401	−	8.78837i	0.735657	−	0.762048i
$134$		0			0
$135$	−0.374312	−	4.62464i	−0.0322157	−	0.398026i
$136$		0			0
$137$	−8.10481	−	6.80075i	−0.692441	−	0.581027i	0.227171	−	0.973855i	$-0.427052\pi$
$137$	−8.10481	−	6.80075i	−0.692441	−	0.581027i	−0.919612	+	0.392828i	$0.871497\pi$
$138$		0			0
$139$	5.05694	+	1.84058i	0.428924	+	0.156116i	0.547456	−	0.836835i	$-0.315596\pi$
$139$	5.05694	+	1.84058i	0.428924	+	0.156116i	−0.118532	+	0.992950i	$0.537819\pi$
$140$		0			0
$141$	−1.11093	+	1.79239i	−0.0935574	+	0.150946i
$142$		0			0
$143$	−0.794313	−	1.37579i	−0.0664238	−	0.115049i
$144$		0			0
$145$	3.09291	−	5.35707i	0.256852	−	0.444881i
$146$		0			0
$147$	−11.9317	+	2.15289i	−0.984109	+	0.177568i
$148$		0			0
$149$	12.6101	−	10.5811i	1.03306	−	0.866839i	0.0418467	−	0.999124i	$-0.486676\pi$
$149$	12.6101	−	10.5811i	1.03306	−	0.866839i	0.991212	+	0.132285i	$0.0422315\pi$
$150$		0			0
$151$	−22.0139	+	8.01240i	−1.79147	+	0.652040i	−0.792347	+	0.610071i	$0.791141\pi$
$151$	−22.0139	+	8.01240i	−1.79147	+	0.652040i	−0.999119	+	0.0419694i	$0.986637\pi$
$152$		0			0
$153$	−19.7848	+	5.82983i	−1.59951	+	0.471314i
$154$		0			0
$155$	0.126037	−	0.0458735i	0.0101235	−	0.00368465i
$156$		0			0
$157$	0.788738	+	4.47315i	0.0629481	+	0.356997i	0.999970	+	0.00772632i	$0.00245939\pi$
$157$	0.788738	+	4.47315i	0.0629481	+	0.356997i	−0.937022	+	0.349270i	$0.886430\pi$
$158$		0			0
$159$	17.0347	+	6.81027i	1.35094	+	0.540089i
$160$		0			0
$161$	−19.4032	−	13.0829i	−1.52919	−	1.03108i
$162$		0			0
$163$	−4.91016	−	8.50465i	−0.384594	−	0.666135i	0.607119	−	0.794611i	$-0.292325\pi$
$163$	−4.91016	−	8.50465i	−0.384594	−	0.666135i	−0.991713	+	0.128475i	$0.958992\pi$
$164$		0			0
$165$	−0.0938274	−	0.650384i	−0.00730445	−	0.0506323i
$166$		0			0
$167$	17.8494	−	14.9774i	1.38123	−	1.15899i	0.412476	−	0.910969i	$-0.364664\pi$
$167$	17.8494	−	14.9774i	1.38123	−	1.15899i	0.968755	−	0.248021i	$-0.0797803\pi$
$168$		0			0
$169$	−0.920888	+	0.335176i	−0.0708375	+	0.0257828i
$170$		0			0
$171$	13.2861	−	3.91490i	1.01601	−	0.299380i
$172$		0			0
$173$	−0.248036	+	1.40668i	−0.0188579	+	0.106948i	−0.992784	−	0.119918i	$-0.961737\pi$
$173$	−0.248036	+	1.40668i	−0.0188579	+	0.106948i	0.973926	+	0.226866i	$0.0728480\pi$
$174$		0			0
$175$	11.0582	−	1.16411i	0.835919	−	0.0879987i
$176$		0			0
$177$	19.8722	−	6.53715i	1.49369	−	0.491362i
$178$		0			0
$179$	−4.49720			−0.336136			−0.168068	−	0.985775i	$-0.553753\pi$
$179$	−4.49720			−0.336136			−0.168068	+	0.985775i	$0.553753\pi$
$180$		0			0
$181$	−1.36071	+	2.35682i	−0.101141	+	0.175181i	−0.912155	−	0.409845i	$-0.865583\pi$
$181$	−1.36071	+	2.35682i	−0.101141	+	0.175181i	0.811014	+	0.585027i	$0.198916\pi$
$182$		0			0
$183$	12.4503	−	20.0874i	0.920352	−	1.48490i
$184$		0			0
$185$	−5.11395	+	4.29111i	−0.375985	+	0.315489i
$186$		0			0
$187$	−2.74502	+	0.999104i	−0.200735	+	0.0730617i
$188$		0			0
$189$	−12.9701	−	4.55812i	−0.943436	−	0.331554i
$190$		0			0
$191$	7.44801	−	2.71085i	0.538919	−	0.196150i	−0.0581974	−	0.998305i	$-0.518535\pi$
$191$	7.44801	−	2.71085i	0.538919	−	0.196150i	0.597116	+	0.802155i	$0.296313\pi$
$192$		0			0
$193$	4.31452	−	3.62031i	0.310566	−	0.260596i	−0.474160	−	0.880439i	$-0.657248\pi$
$193$	4.31452	−	3.62031i	0.310566	−	0.260596i	0.784726	+	0.619843i	$0.212804\pi$
$194$		0			0
$195$	−5.77984	−	0.180718i	−0.413903	−	0.0129415i
$196$		0			0
$197$	−3.52042	+	6.09755i	−0.250820	+	0.434433i	−0.963752	−	0.266801i	$-0.914033\pi$
$197$	−3.52042	+	6.09755i	−0.250820	+	0.434433i	0.712932	+	0.701233i	$0.247367\pi$
$198$		0			0
$199$	−3.74484			−0.265464			−0.132732	−	0.991152i	$-0.542375\pi$
$199$	−3.74484			−0.265464			−0.132732	+	0.991152i	$0.542375\pi$
$200$		0			0
$201$	−5.48535	+	26.2778i	−0.386907	+	1.85349i
$202$		0			0
$203$	−10.7758	−	14.8265i	−0.756313	−	1.04061i
$204$		0			0
$205$	−0.742575	+	4.21135i	−0.0518637	+	0.294134i
$206$		0			0
$207$	−11.8061	−	23.7641i	−0.820578	−	1.65172i
$208$		0			0
$209$	1.84336	−	0.670927i	0.127508	−	0.0464090i
$210$		0			0
$211$	−11.6819	+	9.80231i	−0.804218	+	0.674819i	−0.949220	−	0.314612i	$-0.898126\pi$
$211$	−11.6819	+	9.80231i	−0.804218	+	0.674819i	0.145002	+	0.989431i	$0.453681\pi$
$212$		0			0
$213$	−8.72795	+	6.87047i	−0.598029	+	0.470757i
$214$		0			0
$215$	−2.93578	−	5.08491i	−0.200218	−	0.346788i
$216$		0			0
$217$	0.0276566	−	0.396453i	0.00187745	−	0.0269130i
$218$		0			0
$219$	2.30623	−	1.81542i	0.155841	−	0.122675i
$220$		0			0
$221$	4.46390	+	25.3160i	0.300275	+	1.70294i
$222$		0			0
$223$	0.765638	−	0.278669i	0.0512709	−	0.0186611i	−0.316257	−	0.948673i	$-0.602426\pi$
$223$	0.765638	−	0.278669i	0.0512709	−	0.0186611i	0.367528	+	0.930012i	$0.380204\pi$
$224$		0			0
$225$	11.5552	+	5.04395i	0.770344	+	0.336263i
$226$		0			0
$227$	1.33057	−	0.484288i	0.0883130	−	0.0321433i	−0.297486	−	0.954726i	$-0.596148\pi$
$227$	1.33057	−	0.484288i	0.0883130	−	0.0321433i	0.385799	+	0.922583i	$0.373926\pi$
$228$		0			0
$229$	7.35167	−	6.16879i	0.485812	−	0.407645i	−0.366710	−	0.930335i	$-0.619516\pi$
$229$	7.35167	−	6.16879i	0.485812	−	0.407645i	0.852523	+	0.522690i	$0.175072\pi$
$230$		0			0
$231$	−1.87366	−	0.529535i	−0.123278	−	0.0348409i
$232$		0			0
$233$	10.9381	−	18.9453i	0.716578	−	1.24115i	−0.245770	−	0.969328i	$-0.579041\pi$
$233$	10.9381	−	18.9453i	0.716578	−	1.24115i	0.962348	−	0.271821i	$-0.0876259\pi$
$234$		0			0
$235$	0.543561	+	0.941476i	0.0354580	+	0.0614151i
$236$		0			0
$237$	9.33076	+	17.3952i	0.606098	+	1.12994i
$238$		0			0
$239$	10.5555	+	3.84191i	0.682782	+	0.248512i	0.660041	−	0.751229i	$-0.270539\pi$
$239$	10.5555	+	3.84191i	0.682782	+	0.248512i	0.0227402	+	0.999741i	$0.492761\pi$
$240$		0			0
$241$	−6.54891	−	5.49519i	−0.421852	−	0.353976i	0.407015	−	0.913422i	$-0.366570\pi$
$241$	−6.54891	−	5.49519i	−0.421852	−	0.353976i	−0.828867	+	0.559445i	$0.811014\pi$
$242$		0			0
$243$	−10.2363	−	11.7566i	−0.656659	−	0.754187i
$244$		0			0
$245$	−1.92953	+	5.94518i	−0.123273	+	0.379824i
$246$		0			0
$247$	−2.99764	−	17.0005i	−0.190735	−	1.08171i
$248$		0			0
$249$	15.1563	+	0.473893i	0.960494	+	0.0300317i
$250$		0			0
$251$	13.3916	−	23.1950i	0.845272	−	1.46405i	−0.0401132	−	0.999195i	$-0.512772\pi$
$251$	13.3916	−	23.1950i	0.845272	−	1.46405i	0.885385	−	0.464859i	$-0.153895\pi$
$252$		0			0
$253$	−1.87906	−	3.25462i	−0.118135	−	0.204616i
$254$		0			0
$255$	−2.17280	+	10.4089i	−0.136066	+	0.651829i
$256$		0			0
$257$	−7.29937	+	6.12490i	−0.455322	+	0.382061i	−0.841406	−	0.540403i	$-0.818272\pi$
$257$	−7.29937	+	6.12490i	−0.455322	+	0.382061i	0.386084	+	0.922464i	$0.373827\pi$
$258$		0			0
$259$	5.45540	+	19.0133i	0.338982	+	1.18143i
$260$		0			0
$261$	−2.32321	−	20.6525i	−0.143803	−	1.27836i
$262$		0			0
$263$	−3.44094	+	19.5146i	−0.212178	+	1.20332i	0.673560	+	0.739133i	$0.264764\pi$
$263$	−3.44094	+	19.5146i	−0.212178	+	1.20332i	−0.885738	+	0.464186i	$0.846347\pi$
$264$		0			0
$265$	7.24503	−	6.07930i	0.445058	−	0.373448i
$266$		0			0
$267$	−1.74882	−	12.1223i	−0.107026	−	0.741873i
$268$		0			0
$269$	3.54410	−	6.13856i	0.216087	−	0.374274i	−0.737521	−	0.675324i	$-0.764004\pi$
$269$	3.54410	−	6.13856i	0.216087	−	0.374274i	0.953608	+	0.301050i	$0.0973370\pi$
$270$		0			0
$271$	−1.55220	−	2.68849i	−0.0942893	−	0.163314i	0.815022	−	0.579429i	$-0.196725\pi$
$271$	−1.55220	−	2.68849i	−0.0942893	−	0.163314i	−0.909312	+	0.416115i	$0.863391\pi$
$272$		0			0
$273$	−7.45231	+	15.4286i	−0.451034	+	0.933784i
$274$		0			0
$275$	1.67796	+	0.610727i	0.101185	+	0.0368282i
$276$		0			0
$277$	0.364400	−	2.06662i	0.0218947	−	0.124171i	−0.971901	−	0.235388i	$-0.924364\pi$
$277$	0.364400	−	2.06662i	0.0218947	−	0.124171i	0.993796	+	0.111217i	$0.0354749\pi$
$278$		0			0
$279$	0.249254	−	0.375417i	0.0149224	−	0.0224756i
$280$		0			0
$281$	12.0799	+	10.1362i	0.720626	+	0.604677i	0.927558	−	0.373678i	$-0.121904\pi$
$281$	12.0799	+	10.1362i	0.720626	+	0.604677i	−0.206933	+	0.978355i	$0.566348\pi$
$282$		0			0
$283$	−13.1686	−	4.79296i	−0.782789	−	0.284912i	−0.0804539	−	0.996758i	$-0.525637\pi$
$283$	−13.1686	−	4.79296i	−0.782789	−	0.284912i	−0.702335	+	0.711846i	$0.747859\pi$
$284$		0			0
$285$	1.45910	−	6.98986i	0.0864295	−	0.414044i
$286$		0			0
$287$	10.5058	+	7.08370i	0.620136	+	0.418137i
$288$		0			0
$289$	30.2696			1.78056
$290$		0			0
$291$	3.31332	−	5.34574i	0.194231	−	0.313373i
$292$		0			0
$293$	16.8572	+	6.13554i	0.984811	+	0.358442i	0.783709	−	0.621128i	$-0.213325\pi$
$293$	16.8572	+	6.13554i	0.984811	+	0.358442i	0.201102	+	0.979570i	$0.435548\pi$
$294$		0			0
$295$	1.87276	−	10.6209i	0.109036	−	0.618375i
$296$		0			0
$297$	−1.55093	−	1.57124i	−0.0899940	−	0.0911723i
$298$		0			0
$299$	−31.0771	+	11.3111i	−1.79724	+	0.654140i
$300$		0			0
$301$	−17.3019	+	1.82141i	−0.997267	+	0.104984i
$302$		0			0
$303$	7.72018	+	0.241387i	0.443513	+	0.0138673i
$304$		0			0
$305$	−6.09172	−	10.5512i	−0.348811	−	0.604158i
$306$		0			0
$307$	7.96422	+	13.7944i	0.454542	+	0.787290i	0.998662	−	0.0517177i	$-0.0164696\pi$
$307$	7.96422	+	13.7944i	0.454542	+	0.787290i	−0.544120	+	0.839008i	$0.683136\pi$
$308$		0			0
$309$	−5.93159	+	28.4155i	−0.337436	+	1.61650i
$310$		0			0
$311$	17.4120	+	6.33745i	0.987344	+	0.359364i	0.784691	−	0.619887i	$-0.212822\pi$
$311$	17.4120	+	6.33745i	0.987344	+	0.359364i	0.202653	+	0.979251i	$0.435044\pi$
$312$		0			0
$313$	2.57148	−	14.5836i	0.145349	−	0.824314i	−0.821738	−	0.569866i	$-0.806995\pi$
$313$	2.57148	−	14.5836i	0.145349	−	0.824314i	0.967086	−	0.254448i	$-0.0818938\pi$
$314$		0			0
$315$	−5.23138	+	4.78155i	−0.294755	+	0.269410i
$316$		0			0
$317$	−11.1021	−	9.31575i	−0.623555	−	0.523225i	0.275364	−	0.961340i	$-0.411202\pi$
$317$	−11.1021	−	9.31575i	−0.623555	−	0.523225i	−0.898919	+	0.438116i	$0.855646\pi$
$318$		0			0
$319$	−0.511118	−	2.89870i	−0.0286171	−	0.162296i
$320$		0			0
$321$	−6.62271	+	5.21326i	−0.369643	+	0.290976i
$322$		0			0
$323$	−31.7429			−1.76622
$324$		0			0
$325$	7.85689	−	13.6085i	0.435822	−	0.754865i
$326$		0			0
$327$	8.55865	+	3.42164i	0.473295	+	0.189217i
$328$		0			0
$329$	3.20347	−	0.337235i	0.176613	−	0.0185924i
$330$		0			0
$331$	18.5796	+	15.5901i	1.02123	+	0.856911i	0.989781	−	0.142594i	$-0.0455444\pi$
$331$	18.5796	+	15.5901i	1.02123	+	0.856911i	0.0314457	+	0.999505i	$0.489989\pi$
$332$		0			0
$333$	−5.26706	+	21.8018i	−0.288633	+	1.19473i
$334$		0			0
$335$	10.6013	+	8.89552i	0.579209	+	0.486014i
$336$		0			0
$337$	0.859100	+	4.87220i	0.0467982	+	0.265406i	0.999225	−	0.0393616i	$-0.0125324\pi$
$337$	0.859100	+	4.87220i	0.0467982	+	0.265406i	−0.952427	+	0.304767i	$0.901421\pi$
$338$		0			0
$339$	5.82373	+	5.20534i	0.316301	+	0.282715i
$340$		0			0
$341$	0.0319106	−	0.0552707i	0.00172805	−	0.00299308i
$342$		0			0
$343$	13.7694	+	12.3856i	0.743478	+	0.668761i
$344$		0			0
$345$	−13.6730	−	0.427513i	−0.736130	−	0.0230165i
$346$		0			0
$347$	−1.16834	+	0.980350i	−0.0627196	+	0.0526280i	−0.673609	−	0.739088i	$-0.735257\pi$
$347$	−1.16834	+	0.980350i	−0.0627196	+	0.0526280i	0.610889	+	0.791716i	$0.290812\pi$
$348$		0			0
$349$	−6.05985	+	34.3671i	−0.324376	+	1.83963i	0.189645	+	0.981853i	$0.439266\pi$
$349$	−6.05985	+	34.3671i	−0.324376	+	1.83963i	−0.514021	+	0.857777i	$0.671845\pi$
$350$		0			0
$351$	−15.9869	+	11.0399i	−0.853317	+	0.589265i
$352$		0			0
$353$	−14.9270	−	12.5253i	−0.794486	−	0.666653i	0.152366	−	0.988324i	$-0.451311\pi$
$353$	−14.9270	−	12.5253i	−0.794486	−	0.666653i	−0.946851	+	0.321671i	$0.895755\pi$
$354$		0			0
$355$	0.994367	+	5.63934i	0.0527755	+	0.299305i
$356$		0			0
$357$	25.5598	+	18.4217i	1.35277	+	0.974979i
$358$		0			0
$359$	23.3985			1.23492			0.617462	−	0.786601i	$-0.288161\pi$
$359$	23.3985			1.23492			0.617462	+	0.786601i	$0.288161\pi$
$360$		0			0
$361$	2.31627			0.121909
$362$		0			0
$363$	13.9721	+	12.4885i	0.733346	+	0.655477i
$364$		0			0
$365$	−0.262747	−	1.49011i	−0.0137528	−	0.0779961i
$366$		0			0
$367$	24.3266	−	8.85415i	1.26984	−	0.462183i	0.382779	−	0.923840i	$-0.374967\pi$
$367$	24.3266	−	8.85415i	1.26984	−	0.462183i	0.887058	+	0.461657i	$0.152745\pi$
$368$		0			0
$369$	6.39234	+	12.8670i	0.332772	+	0.669829i
$370$		0			0
$371$	−7.72877	−	26.9366i	−0.401258	−	1.39848i
$372$		0			0
$373$	−20.8553	−	7.59072i	−1.07985	−	0.393033i	−0.259997	−	0.965609i	$-0.583722\pi$
$373$	−20.8553	−	7.59072i	−1.07985	−	0.393033i	−0.819851	+	0.572577i	$0.805944\pi$
$374$		0			0
$375$	11.1835	−	8.80344i	0.577514	−	0.454608i
$376$		0			0
$377$	−25.9022			−1.33403
$378$		0			0
$379$	−12.8542			−0.660275			−0.330138	−	0.943933i	$-0.607095\pi$
$379$	−12.8542			−0.660275			−0.330138	+	0.943933i	$0.607095\pi$
$380$		0			0
$381$	−30.1618	−	12.0583i	−1.54524	−	0.617766i
$382$		0			0
$383$	9.79070	+	3.56352i	0.500282	+	0.182088i	0.579821	−	0.814744i	$-0.303123\pi$
$383$	9.79070	+	3.56352i	0.500282	+	0.182088i	−0.0795391	+	0.996832i	$0.525345\pi$
$384$		0			0
$385$	−0.697153	+	0.722162i	−0.0355302	+	0.0368048i
$386$		0			0
$387$	−18.0796	−	7.89191i	−0.919036	−	0.401169i
$388$		0			0
$389$	−2.82827	+	1.02940i	−0.143399	+	0.0521929i	−0.412722	−	0.910857i	$-0.635422\pi$
$389$	−2.82827	+	1.02940i	−0.143399	+	0.0521929i	0.269324	+	0.963050i	$0.413200\pi$
$390$		0			0
$391$	10.5600	+	59.8885i	0.534040	+	3.02869i
$392$		0			0
$393$	14.5385	−	4.78259i	0.733373	−	0.241250i
$394$		0			0
$395$	10.1764			0.512029
$396$		0			0
$397$	4.22735			0.212165			0.106082	−	0.994357i	$-0.466169\pi$
$397$	4.22735			0.212165			0.106082	+	0.994357i	$0.466169\pi$
$398$		0			0
$399$	−17.1641	−	12.3707i	−0.859282	−	0.619309i
$400$		0			0
$401$	0.470137	+	2.66628i	0.0234775	+	0.133148i	0.994294	−	0.106677i	$-0.0340211\pi$
$401$	0.470137	+	2.66628i	0.0234775	+	0.133148i	−0.970816	+	0.239825i	$0.922910\pi$
$402$		0			0
$403$	−0.430233	−	0.361009i	−0.0214314	−	0.0179831i
$404$		0			0
$405$	−7.83546	+	1.78542i	−0.389347	+	0.0887182i
$406$		0			0
$407$	−0.551603	+	3.12830i	−0.0273420	+	0.155064i
$408$		0			0
$409$	3.45241	−	2.89692i	0.170711	−	0.143243i	−0.553430	−	0.832896i	$-0.686681\pi$
$409$	3.45241	−	2.89692i	0.170711	−	0.143243i	0.724140	+	0.689653i	$0.242237\pi$
$410$		0			0
$411$	−9.65411	+	15.5760i	−0.476202	+	0.768309i
$412$		0			0
$413$	−26.4953	−	17.8649i	−1.30375	−	0.879075i
$414$		0			0
$415$	3.90868	−	6.77003i	0.191869	−	0.332328i
$416$		0			0
$417$	1.90466	−	9.12433i	0.0932715	−	0.446820i
$418$		0			0
$419$	4.93592	+	27.9930i	0.241135	+	1.36755i	0.829299	+	0.558805i	$0.188740\pi$
$419$	4.93592	+	27.9930i	0.241135	+	1.36755i	−0.588164	+	0.808742i	$0.700149\pi$
$420$		0			0
$421$	15.9055	+	13.3463i	0.775185	+	0.650458i	0.942031	−	0.335525i	$-0.108914\pi$
$421$	15.9055	+	13.3463i	0.775185	+	0.650458i	−0.166846	+	0.985983i	$0.553358\pi$
$422$		0			0
$423$	3.34745	+	1.46119i	0.162758	+	0.0710457i
$424$		0			0
$425$	−22.1346	−	18.5732i	−1.07369	−	0.900930i
$426$		0			0
$427$	−35.9014	+	3.77941i	−1.73739	+	0.182899i
$428$		0			0
$429$	−2.16208	+	1.70194i	−0.104386	+	0.0821707i
$430$		0			0
$431$	8.53711	−	14.7867i	0.411218	−	0.712251i	−0.583805	−	0.811894i	$-0.698437\pi$
$431$	8.53711	−	14.7867i	0.411218	−	0.712251i	0.995023	+	0.0996431i	$0.0317701\pi$
$432$		0			0
$433$	5.47236			0.262985			0.131493	−	0.991317i	$-0.458023\pi$
$433$	5.47236			0.262985			0.131493	+	0.991317i	$0.458023\pi$
$434$		0			0
$435$	−9.94857	−	3.97731i	−0.476997	−	0.190697i
$436$		0			0
$437$	−7.09132	−	40.2169i	−0.339224	−	1.92383i
$438$		0			0
$439$	16.0165	+	13.4395i	0.764427	+	0.641430i	0.939275	−	0.343165i	$-0.111499\pi$
$439$	16.0165	+	13.4395i	0.764427	+	0.641430i	−0.174848	+	0.984595i	$0.555943\pi$
$440$		0			0
$441$	6.64158	+	19.9221i	0.316266	+	0.948671i
$442$		0			0
$443$	−3.08453	+	17.4932i	−0.146550	+	0.831128i	0.819559	+	0.572995i	$0.194218\pi$
$443$	−3.08453	+	17.4932i	−0.146550	+	0.831128i	−0.966109	+	0.258133i	$0.916893\pi$
$444$		0			0
$445$	−5.93332	−	2.15955i	−0.281266	−	0.102373i
$446$		0			0
$447$	−21.2579	−	19.0007i	−1.00546	−	0.898700i
$448$		0			0
$449$	16.6232	+	28.7922i	0.784498	+	1.35879i	0.929299	+	0.369329i	$0.120413\pi$
$449$	16.6232	+	28.7922i	0.784498	+	1.35879i	−0.144801	+	0.989461i	$0.546254\pi$
$450$		0			0
$451$	1.01741	+	1.76220i	0.0479078	+	0.0829787i
$452$		0			0
$453$	19.1800	+	35.7569i	0.901156	+	1.68001i
$454$		0			0
$455$	5.19319	+	7.14532i	0.243461	+	0.334978i
$456$		0			0
$457$	25.9811	−	9.45635i	1.21535	−	0.442350i	0.346791	−	0.937943i	$-0.387271\pi$
$457$	25.9811	−	9.45635i	1.21535	−	0.442350i	0.868555	+	0.495593i	$0.165049\pi$
$458$		0			0
$459$	14.8872	+	32.4754i	0.694873	+	1.51582i
$460$		0			0
$461$	4.72950	−	26.8223i	0.220275	−	1.24924i	−0.651240	−	0.758872i	$-0.725751\pi$
$461$	4.72950	−	26.8223i	0.220275	−	1.24924i	0.871515	−	0.490369i	$-0.163138\pi$
$462$		0			0
$463$	3.27515	+	1.19206i	0.152209	+	0.0553997i	0.417001	−	0.908906i	$-0.363081\pi$
$463$	3.27515	+	1.19206i	0.152209	+	0.0553997i	−0.264792	+	0.964306i	$0.585303\pi$
$464$		0			0
$465$	−0.109812	−	0.204720i	−0.00509239	−	0.00949365i
$466$		0			0
$467$	−5.42274			−0.250935			−0.125467	−	0.992098i	$-0.540043\pi$
$467$	−5.42274			−0.250935			−0.125467	+	0.992098i	$0.540043\pi$
$468$		0			0
$469$	36.8522	−	17.9816i	1.70168	−	0.830313i
$470$		0			0
$471$	7.47328	−	2.45841i	0.344351	−	0.113277i
$472$		0			0
$473$	−2.62538	−	0.955562i	−0.120715	−	0.0439368i
$474$		0			0
$475$	14.8640	+	12.4724i	0.682009	+	0.572273i
$476$		0			0
$477$	7.46194	−	30.8870i	0.341659	−	1.41422i
$478$		0			0
$479$	0.361971	−	2.05284i	0.0165389	−	0.0937968i	−0.975421	−	0.220350i	$-0.929280\pi$
$479$	0.361971	−	2.05284i	0.0165389	−	0.0937968i	0.991960	+	0.126553i	$0.0403913\pi$
$480$		0			0
$481$	26.2680	+	9.56079i	1.19772	+	0.435934i
$482$		0			0
$483$	−17.6295	+	36.4985i	−0.802168	+	1.66074i
$484$		0			0
$485$	−1.62116	−	2.80792i	−0.0736129	−	0.127501i
$486$		0			0
$487$	−5.54424	+	9.60291i	−0.251234	+	0.435149i	−0.963866	−	0.266389i	$-0.914170\pi$
$487$	−5.54424	+	9.60291i	−0.251234	+	0.435149i	0.712632	+	0.701538i	$0.247503\pi$
$488$		0			0
$489$	−13.3652	+	10.5208i	−0.604395	+	0.475768i
$490$		0			0
$491$	17.6935	−	14.8466i	0.798494	−	0.670016i	−0.149338	−	0.988786i	$-0.547714\pi$
$491$	17.6935	−	14.8466i	0.798494	−	0.670016i	0.947832	+	0.318770i	$0.103270\pi$
$492$		0			0
$493$	−8.27074	+	46.9057i	−0.372495	+	2.11253i
$494$		0			0
$495$	−1.09175	+	0.321697i	−0.0490705	+	0.0144592i
$496$		0			0
$497$	16.4639	+	4.10202i	0.738508	+	0.184001i
$498$		0			0
$499$	0.340177	−	0.285442i	0.0152284	−	0.0127781i	−0.635142	−	0.772396i	$-0.719058\pi$
$499$	0.340177	−	0.285442i	0.0152284	−	0.0127781i	0.650370	+	0.759618i	$0.274614\pi$
$500$		0			0
$501$	−30.0903	−	26.8952i	−1.34434	−	1.20159i
$502$		0			0
$503$	0.973227	+	1.68568i	0.0433940	+	0.0751607i	0.886907	−	0.461949i	$-0.152850\pi$
$503$	0.973227	+	1.68568i	0.0433940	+	0.0751607i	−0.843513	+	0.537109i	$0.819516\pi$
$504$		0			0
$505$	1.99096	−	3.44845i	0.0885967	−	0.153454i
$506$		0			0
$507$	0.802341	+	1.49579i	0.0356332	+	0.0664303i
$508$		0			0
$509$	−2.06862	−	11.7317i	−0.0916901	−	0.520000i	−0.995711	−	0.0925130i	$-0.970510\pi$
$509$	−2.06862	−	11.7317i	−0.0916901	−	0.520000i	0.904021	−	0.427487i	$-0.140601\pi$
$510$		0			0
$511$	−4.35036	−	1.08390i	−0.192448	−	0.0479489i
$512$		0			0
$513$	−9.99716	−	21.8082i	−0.441385	−	0.962854i
$514$		0			0
$515$	11.4637	+	9.61917i	0.505150	+	0.423871i
$516$		0			0
$517$	0.486092	+	0.176923i	0.0213783	+	0.00778107i
$518$		0			0
$519$	2.47283	+	0.0773178i	0.108545	+	0.00339387i
$520$		0			0
$521$	4.49473	+	7.78509i	0.196917	+	0.341071i	0.947527	−	0.319674i	$-0.103574\pi$
$521$	4.49473	+	7.78509i	0.196917	+	0.341071i	−0.750610	+	0.660746i	$0.770240\pi$
$522$		0			0
$523$	20.6527	−	35.7714i	0.903077	−	1.56418i	0.0796002	−	0.996827i	$-0.474636\pi$
$523$	20.6527	−	35.7714i	0.903077	−	1.56418i	0.823477	−	0.567349i	$-0.192031\pi$
$524$		0			0
$525$	−4.73048	−	18.6691i	−0.206455	−	0.814788i
$526$		0			0
$527$	−0.791118	+	0.663827i	−0.0344617	+	0.0289168i
$528$		0			0
$529$	−51.9042	+	18.8916i	−2.25670	+	0.821373i
$530$		0			0
$531$	−16.1213	−	32.4503i	−0.699606	−	1.40822i
$532$		0			0
$533$	16.8266	−	6.12437i	0.728839	−	0.265276i
$534$		0			0
$535$	0.754519	+	4.27909i	0.0326207	+	0.185001i
$536$		0			0
$537$	1.11222	+	7.70956i	0.0479957	+	0.332692i
$538$		0			0
$539$	1.11506	+	2.75724i	0.0480290	+	0.118763i
$540$		0			0
$541$	0.985581	+	1.70708i	0.0423734	+	0.0733929i	0.886434	−	0.462854i	$-0.153175\pi$
$541$	0.985581	+	1.70708i	0.0423734	+	0.0733929i	−0.844061	+	0.536247i	$0.819841\pi$
$542$		0			0
$543$	4.37683	+	1.74980i	0.187828	+	0.0750911i
$544$		0			0
$545$	3.64007	−	3.05438i	0.155924	−	0.130835i
$546$		0			0
$547$	−4.16908	+	1.51742i	−0.178257	+	0.0648803i	−0.429607	−	0.903016i	$-0.641348\pi$
$547$	−4.16908	+	1.51742i	−0.178257	+	0.0648803i	0.251350	+	0.967896i	$0.419126\pi$
$548$		0			0
$549$	−37.5150	−	16.3757i	−1.60110	−	0.698897i
$550$		0			0
$551$	5.55404	−	31.4985i	0.236610	−	1.34188i
$552$		0			0
$553$	12.2597	−	27.5480i	0.521335	−	1.17146i
$554$		0			0
$555$	8.62102	+	7.70561i	0.365942	+	0.327085i
$556$		0			0
$557$	43.7325			1.85301			0.926503	−	0.376288i	$-0.122800\pi$
$557$	43.7325			1.85301			0.926503	+	0.376288i	$0.122800\pi$
$558$		0			0
$559$	−12.2931	+	21.2923i	−0.519944	+	0.900569i
$560$		0			0
$561$	2.39165	+	4.45870i	0.100975	+	0.188246i
$562$		0			0
$563$	−7.07399	+	5.93578i	−0.298133	+	0.250163i	−0.779567	−	0.626319i	$-0.784561\pi$
$563$	−7.07399	+	5.93578i	−0.298133	+	0.250163i	0.481434	+	0.876483i	$0.340116\pi$
$564$		0			0
$565$	3.78394	−	1.37724i	0.159192	−	0.0579410i
$566$		0			0
$567$	−4.60632	+	23.3620i	−0.193447	+	0.981111i
$568$		0			0
$569$	−11.9567	+	4.35187i	−0.501250	+	0.182440i	−0.580256	−	0.814434i	$-0.697047\pi$
$569$	−11.9567	+	4.35187i	−0.501250	+	0.182440i	0.0790064	+	0.996874i	$0.474825\pi$
$570$		0			0
$571$	23.1995	−	19.4667i	0.970870	−	0.814657i	−0.0118171	−	0.999930i	$-0.503762\pi$
$571$	23.1995	−	19.4667i	0.970870	−	0.814657i	0.982687	+	0.185274i	$0.0593171\pi$
$572$		0			0
$573$	−6.48922	−	12.0977i	−0.271091	−	0.505389i
$574$		0			0
$575$	18.5865	−	32.1928i	0.775112	−	1.34253i
$576$		0			0
$577$	11.7757			0.490230			0.245115	−	0.969494i	$-0.421174\pi$
$577$	11.7757			0.490230			0.245115	+	0.969494i	$0.421174\pi$
$578$		0			0
$579$	−7.27336	−	6.50105i	−0.302270	−	0.270174i
$580$		0			0
$581$	−13.6180	−	18.7370i	−0.564969	−	0.777342i
$582$		0			0
$583$	0.781467	−	4.43192i	0.0323650	−	0.183551i
$584$		0			0
$585$	1.11963	+	9.95309i	0.0462909	+	0.411510i
$586$		0			0
$587$	14.8813	−	5.41635i	0.614217	−	0.223557i	−0.0161305	−	0.999870i	$-0.505135\pi$
$587$	14.8813	−	5.41635i	0.614217	−	0.223557i	0.630347	+	0.776313i	$0.282913\pi$
$588$		0			0
$589$	0.531259	−	0.445779i	0.0218901	−	0.0183680i
$590$		0			0
$591$	11.3237	+	4.52707i	0.465795	+	0.186219i
$592$		0			0
$593$	−12.3254	−	21.3482i	−0.506143	−	0.876665i	−0.999975	−	0.00710788i	$-0.997737\pi$
$593$	−12.3254	−	21.3482i	−0.506143	−	0.876665i	0.493832	−	0.869557i	$-0.335596\pi$
$594$		0			0
$595$	14.5975	−	7.12268i	0.598440	−	0.292002i
$596$		0			0
$597$	0.926148	+	6.41978i	0.0379047	+	0.262744i
$598$		0			0
$599$	2.24029	+	12.7053i	0.0915356	+	0.519124i	0.995754	+	0.0920540i	$0.0293432\pi$
$599$	2.24029	+	12.7053i	0.0915356	+	0.519124i	−0.904218	+	0.427070i	$0.859546\pi$
$600$		0			0
$601$	30.0835	−	10.9495i	1.22713	−	0.446640i	0.354519	−	0.935049i	$-0.384645\pi$
$601$	30.0835	−	10.9495i	1.22713	−	0.446640i	0.872615	+	0.488409i	$0.162423\pi$
$602$		0			0
$603$	46.4047	+	2.90471i	1.88974	+	0.118289i
$604$		0			0
$605$	9.07833	−	3.30424i	0.369087	−	0.134337i
$606$		0			0
$607$	1.64404	−	1.37951i	0.0667294	−	0.0559926i	−0.608813	−	0.793314i	$-0.708354\pi$
$607$	1.64404	−	1.37951i	0.0667294	−	0.0559926i	0.675542	+	0.737321i	$0.263910\pi$
$608$		0			0
$609$	−22.7520	+	22.1398i	−0.921959	+	0.897149i
$610$		0			0
$611$	2.27608	−	3.94229i	0.0920804	−	0.159488i
$612$		0			0
$613$	3.02868	+	5.24583i	0.122327	+	0.211877i	0.920685	−	0.390306i	$-0.127631\pi$
$613$	3.02868	+	5.24583i	0.122327	+	0.211877i	−0.798358	+	0.602183i	$0.794298\pi$
$614$		0			0
$615$	7.40319	+	0.231475i	0.298525	+	0.00933398i
$616$		0			0
$617$	−43.9673	−	16.0028i	−1.77006	−	0.644248i	−0.999980	−	0.00629762i	$-0.997995\pi$
$617$	−43.9673	−	16.0028i	−1.77006	−	0.644248i	−0.770077	−	0.637951i	$-0.779782\pi$
$618$		0			0
$619$	12.9372	+	10.8556i	0.519991	+	0.436324i	0.864629	−	0.502412i	$-0.167554\pi$
$619$	12.9372	+	10.8556i	0.519991	+	0.436324i	−0.344638	+	0.938736i	$0.611998\pi$
$620$		0			0
$621$	−37.8192	+	26.1164i	−1.51763	+	1.04801i
$622$		0			0
$623$	−12.9940	+	13.4602i	−0.520594	+	0.539270i
$624$		0			0
$625$	2.37482	+	13.4683i	0.0949927	+	0.538731i
$626$		0			0
$627$	−1.60606	−	2.99415i	−0.0641399	−	0.119575i
$628$		0			0
$629$	25.7010	−	44.5154i	1.02476	−	1.77494i
$630$		0			0
$631$	−21.4674	−	37.1827i	−0.854605	−	1.48022i	−0.877011	−	0.480471i	$-0.840466\pi$
$631$	−21.4674	−	37.1827i	−0.854605	−	1.48022i	0.0224055	−	0.999749i	$-0.492868\pi$
$632$		0			0
$633$	19.6932	+	17.6022i	0.782736	+	0.699623i
$634$		0			0
$635$	−12.8281	+	10.7641i	−0.509068	+	0.427158i
$636$		0			0
$637$	25.5991	−	5.45014i	1.01427	−	0.215942i
$638$		0			0
$639$	13.9366	+	13.2632i	0.551324	+	0.524684i
$640$		0			0
$641$	−3.98244	+	22.5856i	−0.157297	+	0.892076i	0.799358	+	0.600854i	$0.205173\pi$
$641$	−3.98244	+	22.5856i	−0.157297	+	0.892076i	−0.956656	+	0.291222i	$0.905938\pi$
$642$		0			0
$643$	−16.3040	+	13.6807i	−0.642968	+	0.539514i	−0.904928	−	0.425564i	$-0.860076\pi$
$643$	−16.3040	+	13.6807i	−0.642968	+	0.539514i	0.261960	+	0.965079i	$0.415631\pi$
$644$		0			0
$645$	−7.99103	+	6.29038i	−0.314646	+	0.247683i
$646$		0			0
$647$	−14.3238	+	24.8096i	−0.563128	+	0.975367i	0.434093	+	0.900868i	$0.357069\pi$
$647$	−14.3238	+	24.8096i	−0.563128	+	0.975367i	−0.997221	+	0.0744987i	$0.976264\pi$
$648$		0			0
$649$	−2.56587	−	4.44422i	−0.100719	−	0.174451i
$650$		0			0
$651$	−0.686480	+	0.0506362i	−0.0269053	+	0.00198459i
$652$		0			0
$653$	11.6804	+	4.25132i	0.457090	+	0.166367i	0.560295	−	0.828293i	$-0.310688\pi$
$653$	11.6804	+	4.25132i	0.457090	+	0.166367i	−0.103205	+	0.994660i	$0.532910\pi$
$654$		0			0
$655$	1.37011	−	7.77030i	0.0535348	−	0.303611i
$656$		0			0
$657$	−3.68255	−	3.50461i	−0.143670	−	0.136728i
$658$		0			0
$659$	−17.5076	−	14.6906i	−0.682000	−	0.572266i	0.234590	−	0.972094i	$-0.424625\pi$
$659$	−17.5076	−	14.6906i	−0.682000	−	0.572266i	−0.916590	+	0.399828i	$0.869070\pi$
$660$		0			0
$661$	−11.5633	−	4.20868i	−0.449759	−	0.163699i	0.107203	−	0.994237i	$-0.465811\pi$
$661$	−11.5633	−	4.20868i	−0.449759	−	0.163699i	−0.556961	+	0.830538i	$0.688033\pi$
$662$		0			0
$663$	42.2954	−	13.9135i	1.64262	−	0.540355i
$664$		0			0
$665$	−9.80266	+	4.78309i	−0.380131	+	0.185480i
$666$		0			0
$667$	−61.2751			−2.37258
$668$		0			0
$669$	−0.667076	−	1.24362i	−0.0257907	−	0.0480810i
$670$		0			0
$671$	−5.44766	−	1.98279i	−0.210305	−	0.0765446i
$672$		0			0
$673$	−0.762843	+	4.32630i	−0.0294054	+	0.166767i	−0.995974	−	0.0896414i	$-0.971428\pi$
$673$	−0.762843	+	4.32630i	−0.0294054	+	0.166767i	0.966569	+	0.256408i	$0.0825390\pi$
$674$		0			0
$675$	5.78911	−	21.0565i	0.222823	−	0.810465i
$676$		0			0
$677$	−35.0958	+	12.7738i	−1.34884	+	0.490938i	−0.912586	−	0.408885i	$-0.865918\pi$
$677$	−35.0958	+	12.7738i	−1.34884	+	0.490938i	−0.436255	+	0.899823i	$0.643695\pi$
$678$		0			0
$679$	−9.55425	+	1.00579i	−0.366658	+	0.0385988i
$680$		0			0
$681$	−1.15928	−	2.16123i	−0.0444239	−	0.0828185i
$682$		0			0
$683$	−15.2898	−	26.4827i	−0.585048	−	1.01333i	−0.994869	−	0.101168i	$-0.967742\pi$
$683$	−15.2898	−	26.4827i	−0.585048	−	1.01333i	0.409821	−	0.912166i	$-0.365591\pi$
$684$		0			0
$685$	4.72360	+	8.18152i	0.180479	+	0.312600i
$686$		0			0
$687$	−12.3933	−	11.0774i	−0.472835	−	0.422628i
$688$		0			0
$689$	−37.2144	−	13.5449i	−1.41776	−	0.516021i
$690$		0			0
$691$	2.00225	−	11.3553i	0.0761690	−	0.431976i	−0.922746	−	0.385408i	$-0.874061\pi$
$691$	2.00225	−	11.3553i	0.0761690	−	0.431976i	0.998915	−	0.0465677i	$-0.0148283\pi$
$692$		0			0
$693$	−0.444402	+	3.34299i	−0.0168815	+	0.126990i
$694$		0			0
$695$	−3.68104	−	3.08876i	−0.139630	−	0.117163i
$696$		0			0
$697$	−5.71765	−	32.4264i	−0.216571	−	1.22824i
$698$		0			0
$699$	−35.1832	−	14.0658i	−1.33075	−	0.532016i
$700$		0			0
$701$	−43.4710			−1.64188			−0.820939	−	0.571017i	$-0.806549\pi$
$701$	−43.4710			−1.64188			−0.820939	+	0.571017i	$0.806549\pi$
$702$		0			0
$703$	−17.2589	+	29.8934i	−0.650933	+	1.12745i
$704$		0			0
$705$	1.47955	−	1.16467i	0.0557229	−	0.0438640i
$706$		0			0
$707$	−6.93659	−	9.54407i	−0.260877	−	0.358942i
$708$		0			0
$709$	−23.2586	−	19.5163i	−0.873495	−	0.732949i	0.0913362	−	0.995820i	$-0.470886\pi$
$709$	−23.2586	−	19.5163i	−0.873495	−	0.732949i	−0.964831	+	0.262871i	$0.915331\pi$
$710$		0			0
$711$	27.5129	−	20.2978i	1.03182	−	0.761227i
$712$		0			0
$713$	−1.01778	−	0.854015i	−0.0381160	−	0.0319831i
$714$		0			0
$715$	0.246323	+	1.39697i	0.00921198	+	0.0522437i
$716$		0			0
$717$	3.97566	−	19.0456i	0.148474	−	0.711270i
$718$		0			0
$719$	−3.04873	+	5.28055i	−0.113698	+	0.196931i	−0.917259	−	0.398292i	$-0.869603\pi$
$719$	−3.04873	+	5.28055i	−0.113698	+	0.196931i	0.803560	+	0.595223i	$0.202936\pi$
$720$		0			0
$721$	39.8502	−	19.4444i	1.48410	−	0.724148i
$722$		0			0
$723$	−7.80079	+	12.5859i	−0.290114	+	0.468073i
$724$		0			0
$725$	22.3030	−	18.7145i	0.828314	−	0.695038i
$726$		0			0
$727$	2.12025	−	12.0245i	0.0786357	−	0.445965i	−0.919914	−	0.392121i	$-0.871741\pi$
$727$	2.12025	−	12.0245i	0.0786357	−	0.445965i	0.998549	−	0.0538444i	$-0.0171475\pi$
$728$		0			0
$729$	−17.6228	+	20.4557i	−0.652697	+	0.757619i
$730$		0			0
$731$	34.6325	+	29.0601i	1.28093	+	1.07483i
$732$		0			0
$733$	−1.77777	−	10.0822i	−0.0656633	−	0.372395i	−0.999877	−	0.0156813i	$-0.995008\pi$
$733$	−1.77777	−	10.0822i	−0.0656633	−	0.372395i	0.934214	−	0.356714i	$-0.116103\pi$
$734$		0			0
$735$	10.6690	+	1.83747i	0.393534	+	0.0677762i
$736$		0			0
$737$	6.58503			0.242563
$738$		0			0
$739$	−14.1909			−0.522022			−0.261011	−	0.965336i	$-0.584056\pi$
$739$	−14.1909			−0.522022			−0.261011	+	0.965336i	$0.584056\pi$
$740$		0			0
$741$	−28.4026	+	9.34330i	−1.04339	+	0.343235i
$742$		0			0
$743$	2.52304	+	14.3089i	0.0925615	+	0.524942i	0.995467	+	0.0951039i	$0.0303183\pi$
$743$	2.52304	+	14.3089i	0.0925615	+	0.524942i	−0.902906	+	0.429838i	$0.858571\pi$
$744$		0			0
$745$	−13.8122	+	5.02724i	−0.506041	+	0.184184i
$746$		0			0
$747$	−2.93597	−	26.0998i	−0.107422	−	0.954940i
$748$		0			0
$749$	12.4927	+	3.11258i	0.456474	+	0.113731i
$750$		0			0
$751$	16.1627	+	5.88276i	0.589787	+	0.214665i	0.619636	−	0.784890i	$-0.287280\pi$
$751$	16.1627	+	5.88276i	0.589787	+	0.214665i	−0.0298488	+	0.999554i	$0.509503\pi$
$752$		0			0
$753$	−43.0751	−	17.2209i	−1.56975	−	0.627564i
$754$		0			0
$755$	20.9182			0.761293
$756$		0			0
$757$	24.2092			0.879897			0.439948	−	0.898023i	$-0.354997\pi$
$757$	24.2092			0.879897			0.439948	+	0.898023i	$0.354997\pi$
$758$		0			0
$759$	−5.11469	+	4.02618i	−0.185651	+	0.146141i
$760$		0			0
$761$	17.1764	+	6.25169i	0.622644	+	0.226624i	0.634026	−	0.773311i	$-0.281401\pi$
$761$	17.1764	+	6.25169i	0.622644	+	0.226624i	−0.0113827	+	0.999935i	$0.503623\pi$
$762$		0			0
$763$	−3.88311	−	13.5336i	−0.140578	−	0.489948i
$764$		0			0
$765$	18.3813	+	1.15058i	0.664579	+	0.0415994i
$766$		0			0
$767$	−42.4362	+	15.4455i	−1.53228	+	0.557705i
$768$		0			0
$769$	−8.20361	−	46.5250i	−0.295830	−	1.67773i	−0.663811	−	0.747901i	$-0.731062\pi$
$769$	−8.20361	−	46.5250i	−0.295830	−	1.67773i	0.367981	−	0.929833i	$-0.380049\pi$
$770$		0			0
$771$	12.3052	+	10.9986i	0.443160	+	0.396104i
$772$		0			0
$773$	4.16127			0.149670			0.0748352	−	0.997196i	$-0.476157\pi$
$773$	4.16127			0.149670			0.0748352	+	0.997196i	$0.476157\pi$
$774$		0			0
$775$	0.631283			0.0226763
$776$		0			0
$777$	31.2455	−	14.0545i	1.12092	−	0.504201i
$778$		0			0
$779$	3.83957	+	21.7753i	0.137567	+	0.780180i
$780$		0			0
$781$	2.08730	+	1.75145i	0.0746894	+	0.0626719i
$782$		0			0
$783$	−34.8302	+	9.09034i	−1.24473	+	0.324862i
$784$		0			0
$785$	0.704282	−	3.99418i	0.0251369	−	0.142558i
$786$		0			0
$787$	−3.88068	+	3.25628i	−0.138331	+	0.116074i	−0.709328	−	0.704879i	$-0.751001\pi$
$787$	−3.88068	+	3.25628i	−0.138331	+	0.116074i	0.570997	+	0.820952i	$0.306557\pi$
$788$		0			0
$789$	34.3049	+	1.07261i	1.22129	+	0.0381859i
$790$		0			0
$791$	0.830323	−	11.9025i	0.0295229	−	0.423206i
$792$		0			0
$793$	−25.5082	+	44.1815i	−0.905822	+	1.56893i
$794$		0			0
$795$	−12.2136	−	10.9167i	−0.433170	−	0.387175i
$796$		0			0
$797$	−0.125234	−	0.710240i	−0.00443603	−	0.0251580i	0.982509	−	0.186213i	$-0.0596215\pi$
$797$	−0.125234	−	0.710240i	−0.00443603	−	0.0251580i	−0.986945	+	0.161055i	$0.948510\pi$
$798$		0			0
$799$	−6.41224	−	5.38051i	−0.226849	−	0.190349i
$800$		0			0
$801$	−20.3488	+	5.99602i	−0.718990	+	0.211859i
$802$		0			0
$803$	−0.551539	−	0.462796i	−0.0194634	−	0.0163317i
$804$		0			0
$805$	12.2852	+	16.9032i	0.432996	+	0.595761i
$806$		0			0
$807$	−11.3999	−	4.55751i	−0.401294	−	0.160432i
$808$		0			0
$809$	−17.8420	+	30.9032i	−0.627291	+	1.08650i	0.360802	+	0.932643i	$0.382503\pi$
$809$	−17.8420	+	30.9032i	−0.627291	+	1.08650i	−0.988093	+	0.153858i	$0.950830\pi$
$810$		0			0
$811$	−11.7285			−0.411844			−0.205922	−	0.978568i	$-0.566019\pi$
$811$	−11.7285			−0.411844			−0.205922	+	0.978568i	$0.566019\pi$
$812$		0			0
$813$	−4.22500	+	3.32584i	−0.148177	+	0.116642i
$814$		0			0
$815$	1.52268	+	8.63557i	0.0533373	+	0.302491i
$816$		0			0
$817$	−23.2567	−	19.5147i	−0.813650	−	0.682733i
$818$		0			0
$819$	28.2924	+	8.95981i	0.988617	+	0.313081i
$820$		0			0
$821$	−2.62013	+	14.8595i	−0.0914433	+	0.518601i	0.904336	+	0.426821i	$0.140367\pi$
$821$	−2.62013	+	14.8595i	−0.0914433	+	0.518601i	−0.995779	+	0.0917797i	$0.970744\pi$
$822$		0			0
$823$	9.15171	+	3.33095i	0.319009	+	0.116110i	0.496561	−	0.868002i	$-0.334596\pi$
$823$	9.15171	+	3.33095i	0.319009	+	0.116110i	−0.177553	+	0.984111i	$0.556818\pi$
$824$		0			0
$825$	0.631990	−	3.02757i	0.0220031	−	0.105406i
$826$		0			0
$827$	16.1008	+	27.8873i	0.559878	+	0.969737i	0.997506	+	0.0705811i	$0.0224854\pi$
$827$	16.1008	+	27.8873i	0.559878	+	0.969737i	−0.437628	+	0.899156i	$0.644181\pi$
$828$		0			0
$829$	−6.55318	−	11.3504i	−0.227601	−	0.394217i	0.729495	−	0.683986i	$-0.239755\pi$
$829$	−6.55318	−	11.3504i	−0.227601	−	0.394217i	−0.957097	+	0.289769i	$0.906422\pi$
$830$		0			0
$831$	−3.63293	−	0.113591i	−0.126025	−	0.00394042i
$832$		0			0
$833$	−1.69556	−	48.0971i	−0.0587477	−	1.66647i
$834$		0			0
$835$	−19.5511	+	7.11600i	−0.676592	+	0.246259i
$836$		0			0
$837$	−0.705222	−	0.334451i	−0.0243760	−	0.0115603i
$838$		0			0
$839$	6.21641	−	35.2550i	0.214614	−	1.21714i	−0.666960	−	0.745094i	$-0.732405\pi$
$839$	6.21641	−	35.2550i	0.214614	−	1.21714i	0.881574	−	0.472045i	$-0.156484\pi$
$840$		0			0
$841$	−17.8463	−	6.49554i	−0.615391	−	0.223984i
$842$		0			0
$843$	14.3891	−	23.2154i	0.495585	−	0.799582i
$844$		0			0
$845$	0.875054			0.0301028
$846$		0			0
$847$	1.99209	−	28.5562i	0.0684490	−	0.981204i
$848$		0			0
$849$	−4.95983	+	23.7603i	−0.170221	+	0.815450i
$850$		0			0
$851$	62.1406	+	22.6173i	2.13015	+	0.775313i
$852$		0			0
$853$	−26.7670	−	22.4602i	−0.916485	−	0.769023i	0.0568563	−	0.998382i	$-0.481892\pi$
$853$	−26.7670	−	22.4602i	−0.916485	−	0.769023i	−0.973342	+	0.229360i	$0.926337\pi$
$854$		0			0
$855$	−12.3436	−	0.772649i	−0.422142	−	0.0264240i
$856$		0			0
$857$	5.45565	−	30.9405i	0.186361	−	1.05691i	−0.737832	−	0.674984i	$-0.764151\pi$
$857$	5.45565	−	30.9405i	0.186361	−	1.05691i	0.924194	−	0.381924i	$-0.124738\pi$
$858$		0			0
$859$	34.2715	+	12.4738i	1.16933	+	0.425601i	0.852421	−	0.522856i	$-0.175133\pi$
$859$	34.2715	+	12.4738i	1.16933	+	0.425601i	0.316907	+	0.948457i	$0.397356\pi$
$860$		0			0
$861$	9.54539	−	19.7620i	0.325306	−	0.673486i
$862$		0			0
$863$	−8.77333	−	15.1959i	−0.298648	−	0.517273i	0.677179	−	0.735818i	$-0.263202\pi$
$863$	−8.77333	−	15.1959i	−0.298648	−	0.517273i	−0.975827	+	0.218545i	$0.929869\pi$
$864$		0			0
$865$	0.637719	−	1.10456i	0.0216831	−	0.0375562i
$866$		0			0
$867$	−7.48608	−	51.8913i	−0.254241	−	1.76232i
$868$		0			0
$869$	3.70938	−	3.11254i	0.125832	−	0.105586i
$870$		0			0
$871$	10.0627	−	57.0683i	0.340961	−	1.93368i
$872$		0			0
$873$	−9.98366	−	4.35797i	−0.337896	−	0.147495i
$874$		0			0
$875$	−21.0960	−	5.25610i	−0.713174	−	0.177689i
$876$		0			0
$877$	4.07448	−	3.41889i	0.137585	−	0.115448i	−0.571398	−	0.820673i	$-0.693599\pi$
$877$	4.07448	−	3.41889i	0.137585	−	0.115448i	0.708983	+	0.705225i	$0.249154\pi$
$878$		0			0
$879$	6.34915	−	30.4158i	0.214151	−	1.02590i
$880$		0			0
$881$	6.16335	+	10.6752i	0.207648	+	0.359658i	0.950973	−	0.309273i	$-0.100086\pi$
$881$	6.16335	+	10.6752i	0.207648	+	0.359658i	−0.743325	+	0.668931i	$0.766752\pi$
$882$		0			0
$883$	12.4671	−	21.5937i	0.419551	−	0.726684i	−0.576343	−	0.817208i	$-0.695521\pi$
$883$	12.4671	−	21.5937i	0.419551	−	0.726684i	0.995894	+	0.0905237i	$0.0288541\pi$
$884$		0			0
$885$	−18.6707	−	0.583775i	−0.627607	−	0.0196234i
$886$		0			0
$887$	1.67062	+	9.47457i	0.0560940	+	0.318125i	0.999924	−	0.0123057i	$-0.00391713\pi$
$887$	1.67062	+	9.47457i	0.0560940	+	0.318125i	−0.943830	+	0.330431i	$0.892806\pi$
$888$		0			0
$889$	13.6846	+	47.6941i	0.458967	+	1.59961i
$890$		0			0
$891$	−2.31001	+	3.04735i	−0.0773882	+	0.102090i
$892$		0			0
$893$	4.30600	+	3.61316i	0.144095	+	0.120910i
$894$		0			0
$895$	3.77348	+	1.37343i	0.126133	+	0.0459088i
$896$		0			0
$897$	27.0765	+	50.4782i	0.904058	+	1.68542i
$898$		0			0
$899$	−0.520295	−	0.901177i	−0.0173528	−	0.0300559i
$900$		0			0
$901$	−36.4110	+	63.0658i	−1.21303	+	2.10102i
$902$		0			0
$903$	7.40144	+	29.2103i	0.246305	+	0.972058i
$904$		0			0
$905$	1.86151	−	1.56199i	0.0618785	−	0.0519223i
$906$		0			0
$907$	0.458557	−	0.166901i	0.0152261	−	0.00554186i	−0.334396	−	0.942433i	$-0.608532\pi$
$907$	0.458557	−	0.166901i	0.0152261	−	0.00554186i	0.349622	+	0.936891i	$0.386310\pi$
$908$		0			0
$909$	−1.49549	−	13.2944i	−0.0496024	−	0.440948i
$910$		0			0
$911$	−17.3397	+	6.31113i	−0.574490	+	0.209097i	−0.612894	−	0.790165i	$-0.709995\pi$
$911$	−17.3397	+	6.31113i	−0.574490	+	0.209097i	0.0384042	+	0.999262i	$0.487773\pi$
$912$		0			0
$913$	−0.645928	−	3.66324i	−0.0213771	−	0.121236i
$914$		0			0
$915$	−16.5813	+	13.0525i	−0.548162	+	0.431503i
$916$		0			0
$917$	−19.3840	−	13.0700i	−0.640117	−	0.431610i
$918$		0			0
$919$	13.8477	+	23.9849i	0.456793	+	0.791189i	0.998789	−	0.0491918i	$-0.0156646\pi$
$919$	13.8477	+	23.9849i	0.456793	+	0.791189i	−0.541996	+	0.840381i	$0.682331\pi$
$920$		0			0
$921$	21.6782	−	17.0646i	0.714321	−	0.562299i
$922$		0			0
$923$	18.3683	−	15.4129i	0.604601	−	0.507321i
$924$		0			0
$925$	−29.5258	+	10.7465i	−0.970802	+	0.353343i
$926$		0			0
$927$	50.1797	+	3.14101i	1.64812	+	0.103164i
$928$		0			0
$929$	8.13936	−	46.1606i	0.267044	−	1.51448i	−0.496108	−	0.868261i	$-0.665238\pi$
$929$	8.13936	−	46.1606i	0.267044	−	1.51448i	0.763152	−	0.646219i	$-0.223651\pi$
$930$		0			0
$931$	1.13862	+	32.2986i	0.0373167	+	1.05854i
$932$		0			0
$933$	6.55809	−	31.4168i	0.214702	−	1.02854i
$934$		0			0
$935$	2.60839			0.0853036
$936$		0			0
$937$	−10.9953	+	19.0445i	−0.359202	+	0.622155i	−0.987828	−	0.155552i	$-0.950284\pi$
$937$	−10.9953	+	19.0445i	−0.359202	+	0.622155i	0.628626	+	0.777708i	$0.283618\pi$
$938$		0			0
$939$	−25.6367	−	0.801581i	−0.836622	−	0.0261586i
$940$		0			0
$941$	−4.65068	+	3.90238i	−0.151608	+	0.127214i	−0.715437	−	0.698678i	$-0.753772\pi$
$941$	−4.65068	+	3.90238i	−0.151608	+	0.127214i	0.563829	+	0.825892i	$0.309328\pi$
$942$		0			0
$943$	39.8055	−	14.4880i	1.29625	−	0.471795i
$944$		0			0
$945$	9.49083	+	7.78563i	0.308737	+	0.253267i
$946$		0			0
$947$	31.3330	−	11.4043i	1.01819	−	0.370589i	0.221614	−	0.975134i	$-0.428867\pi$
$947$	31.3330	−	11.4043i	1.01819	−	0.370589i	0.796571	+	0.604545i	$0.206645\pi$
$948$		0			0
$949$	−4.85357	+	4.07263i	−0.157553	+	0.132203i
$950$		0			0
$951$	−13.2243	+	21.3362i	−0.428828	+	0.691875i
$952$		0			0
$953$	−13.1930	+	22.8510i	−0.427364	+	0.740217i	−0.996638	−	0.0819313i	$-0.973891\pi$
$953$	−13.1930	+	22.8510i	−0.427364	+	0.740217i	0.569274	+	0.822148i	$0.307225\pi$
$954$		0			0
$955$	−7.07731			−0.229016
$956$		0			0
$957$	−4.84284	+	1.59310i	−0.156547	+	0.0514975i
$958$		0			0
$959$	27.8384	−	2.93061i	0.898950	−	0.0946342i
$960$		0			0
$961$	−5.37918	+	30.5068i	−0.173522	+	0.984091i
$962$		0			0
$963$	10.5750	+	10.0640i	0.340775	+	0.324309i
$964$		0			0
$965$	−4.72584	+	1.72006i	−0.152130	+	0.0553708i
$966$		0			0
$967$	19.9556	−	16.7447i	0.641729	−	0.538475i	−0.262820	−	0.964845i	$-0.584652\pi$
$967$	19.9556	−	16.7447i	0.641729	−	0.538475i	0.904549	+	0.426370i	$0.140208\pi$
$968$		0			0
$969$	7.85044	+	54.4170i	0.252193	+	1.74812i
$970$		0			0
$971$	18.5419	+	32.1155i	0.595038	+	1.03064i	0.993541	+	0.113470i	$0.0361965\pi$
$971$	18.5419	+	32.1155i	0.595038	+	1.03064i	−0.398503	+	0.917167i	$0.630470\pi$
$972$		0			0
$973$	−12.7961	+	6.24368i	−0.410223	+	0.200163i
$974$		0			0
$975$	−25.2723	−	10.1035i	−0.809360	−	0.323572i
$976$		0			0
$977$	5.94102	+	33.6932i	0.190070	+	1.07794i	0.919266	+	0.393637i	$0.128783\pi$
$977$	5.94102	+	33.6932i	0.190070	+	1.07794i	−0.729196	+	0.684305i	$0.760106\pi$
$978$		0			0
$979$	−2.82326	+	1.02758i	−0.0902319	+	0.0328417i
$980$		0			0
$981$	3.74906	−	15.5183i	0.119698	−	0.495463i
$982$		0			0
$983$	−3.34768	+	1.21846i	−0.106774	+	0.0388627i	−0.394855	−	0.918743i	$-0.629205\pi$
$983$	−3.34768	+	1.21846i	−0.106774	+	0.0388627i	0.288081	+	0.957606i	$0.406983\pi$
$984$		0			0
$985$	4.81607	−	4.04116i	0.153453	−	0.128762i
$986$		0			0
$987$	−1.37038	−	5.40831i	−0.0436198	−	0.172149i
$988$		0			0
$989$	−29.0811	+	50.3699i	−0.924724	+	1.60167i
$990$		0			0
$991$	16.6504	+	28.8393i	0.528917	+	0.916110i	0.999431	+	0.0337183i	$0.0107349\pi$
$991$	16.6504	+	28.8393i	0.528917	+	0.916110i	−0.470515	+	0.882392i	$0.655932\pi$
$992$		0			0
$993$	22.1312	−	35.7067i	0.702313	−	1.13312i
$994$		0			0
$995$	3.14219	+	1.14366i	0.0996142	+	0.0362566i
$996$		0			0
$997$	−16.6862	−	14.0014i	−0.528457	−	0.443428i	0.339111	−	0.940746i	$-0.389874\pi$
$997$	−16.6862	−	14.0014i	−0.528457	−	0.443428i	−0.867568	+	0.497318i	$0.834318\pi$
$998$		0			0
$999$	38.6775	+	3.63747i	1.22370	+	0.115084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.11	yes	144
7.2	even	3		756.2.bp.a.457.21	yes	144
27.13	even	9		756.2.bp.a.445.21	✓	144
189.121	even	9	inner	756.2.bq.a.121.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.21	✓	144	27.13	even	9
756.2.bp.a.457.21	yes	144	7.2	even	3
756.2.bq.a.25.11	yes	144	1.1	even	1	trivial
756.2.bq.a.121.11	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)

\(f(q)\)	\(=\)	\(q+(-0.247313 - 1.71430i) q^{3} +(-0.839073 - 0.305398i) q^{5} +(-1.83758 + 1.90350i) q^{7} +(-2.87767 + 0.847940i) q^{9} +O(q^{10})\)	\(q+(-0.247313 - 1.71430i) q^{3} +(-0.839073 - 0.305398i) q^{5} +(-1.83758 + 1.90350i) q^{7} +(-2.87767 + 0.847940i) q^{9} +(-0.399258 + 0.145318i) q^{11} +(0.649267 + 3.68218i) q^{13} +(-0.316030 + 1.51395i) q^{15} +6.87529 q^{17} -4.61696 q^{19} +(3.71763 + 2.67940i) q^{21} +(1.53593 + 8.71070i) q^{23} +(-3.21945 - 2.70144i) q^{25} +(2.16531 + 4.72350i) q^{27} +(-1.20297 + 6.82236i) q^{29} +(-0.115067 + 0.0965526i) q^{31} +(0.347861 + 0.648511i) q^{33} +(2.12319 - 1.03598i) q^{35} +(3.73817 - 6.47469i) q^{37} +(6.15180 - 2.02369i) q^{39} +(-0.831623 - 4.71637i) q^{41} +(5.03724 + 4.22675i) q^{43} +(2.67354 + 0.167350i) q^{45} +(-0.932650 - 0.782586i) q^{47} +(-0.246617 - 6.99565i) q^{49} +(-1.70035 - 11.7863i) q^{51} +(-5.29593 + 9.17282i) q^{53} +0.379387 q^{55} +(1.14183 + 7.91486i) q^{57} +(2.09733 + 11.8946i) q^{59} +(10.4523 + 8.77049i) q^{61} +(3.67389 - 7.03580i) q^{63} +(0.579746 - 3.28790i) q^{65} +(-14.5638 - 5.30080i) q^{67} +(14.5529 - 4.78732i) q^{69} +(-3.20651 - 5.55384i) q^{71} +(0.847274 + 1.46752i) q^{73} +(-3.83487 + 6.18721i) q^{75} +(0.457055 - 1.02702i) q^{77} +(-10.7094 + 3.89790i) q^{79} +(7.56199 - 4.88019i) q^{81} +(-1.52025 + 8.62179i) q^{83} +(-5.76887 - 2.09970i) q^{85} +(11.9931 + 0.374988i) q^{87} +7.07127 q^{89} +(-8.20210 - 5.53041i) q^{91} +(0.193978 + 0.173381i) q^{93} +(3.87396 + 1.41001i) q^{95} +(2.78160 + 2.33404i) q^{97} +(1.02571 - 0.756725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 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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