LMFDB - Embedded newform 825.2.d.f.824.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(824,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("825.824");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			824.8
Character	$\chi$	$=$	825.824
Dual form			825.2.d.f.824.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92586i q^{2} +(0.840091 + 1.51468i) q^{3} -1.70894 q^{4} +(2.91706 - 1.61790i) q^{6} -3.14352 q^{7} -0.560539i q^{8} +(-1.58849 + 2.54493i) q^{9} +O(q^{10})$	\(q-1.92586i q^{2} +(0.840091 + 1.51468i) q^{3} -1.70894 q^{4} +(2.91706 - 1.61790i) q^{6} -3.14352 q^{7} -0.560539i q^{8} +(-1.58849 + 2.54493i) q^{9} +(-0.166374 - 3.31245i) q^{11} +(-1.43567 - 2.58849i) q^{12} -1.94903 q^{13} +6.05398i q^{14} -4.49740 q^{16} -3.57551i q^{17} +(4.90119 + 3.05922i) q^{18} -6.65886i q^{19} +(-2.64084 - 4.76142i) q^{21} +(-6.37932 + 0.320413i) q^{22} -3.98060 q^{23} +(0.849035 - 0.470903i) q^{24} +3.75357i q^{26} +(-5.18923 - 0.268081i) q^{27} +5.37209 q^{28} +4.99736 q^{29} +6.03356 q^{31} +7.54030i q^{32} +(4.87752 - 3.03476i) q^{33} -6.88593 q^{34} +(2.71464 - 4.34914i) q^{36} -9.52676i q^{37} -12.8240 q^{38} +(-1.63736 - 2.95216i) q^{39} +0.227791 q^{41} +(-9.16983 + 5.08590i) q^{42} -7.57380 q^{43} +(0.284323 + 5.66078i) q^{44} +7.66608i q^{46} +4.32448 q^{47} +(-3.77823 - 6.81211i) q^{48} +2.88172 q^{49} +(5.41574 - 3.00375i) q^{51} +3.33078 q^{52} -1.53503 q^{53} +(-0.516287 + 9.99374i) q^{54} +1.76206i q^{56} +(10.0860 - 5.59404i) q^{57} -9.62423i q^{58} +5.56495i q^{59} +5.46437i q^{61} -11.6198i q^{62} +(4.99346 - 8.00005i) q^{63} +5.52676 q^{64} +(-5.84453 - 9.39343i) q^{66} +6.46805i q^{67} +6.11033i q^{68} +(-3.34407 - 6.02932i) q^{69} -9.07047i q^{71} +(1.42653 + 0.890413i) q^{72} -13.0382 q^{73} -18.3472 q^{74} +11.3796i q^{76} +(0.523000 + 10.4128i) q^{77} +(-5.68544 + 3.15334i) q^{78} +11.5641i q^{79} +(-3.95337 - 8.08522i) q^{81} -0.438693i q^{82} -5.54979i q^{83} +(4.51305 + 8.13699i) q^{84} +14.5861i q^{86} +(4.19824 + 7.56939i) q^{87} +(-1.85676 + 0.0932591i) q^{88} -3.01648i q^{89} +6.12682 q^{91} +6.80261 q^{92} +(5.06874 + 9.13890i) q^{93} -8.32835i q^{94} +(-11.4211 + 6.33453i) q^{96} +5.38853i q^{97} -5.54979i q^{98} +(8.69425 + 4.83840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 20 * q^9	$ 32 q - 32 q^{4} + 20 q^{9} + 64 q^{16} - 24 q^{31} - 56 q^{34} - 72 q^{36} + 56 q^{49} - 120 q^{64} - 60 q^{66} - 88 q^{69} - 52 q^{81} + 128 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 20 * q^9 + 64 * q^16 - 24 * q^31 - 56 * q^34 - 72 * q^36 + 56 * q^49 - 120 * q^64 - 60 * q^66 - 88 * q^69 - 52 * q^81 + 128 * q^91 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.92586i		−	1.36179i	−0.732381	−	0.680895i	$-0.761591\pi$
$2$		−	1.92586i		−	1.36179i	0.732381	−	0.680895i	$-0.238409\pi$
$3$	0.840091	+	1.51468i	0.485027	+	0.874499i
$3$	0.840091	+	1.51468i	0.485027	+	0.874499i
$4$	−1.70894			−0.854471
$5$		0			0
$5$		0			0
$6$	2.91706	−	1.61790i	1.19088	−	0.660504i
$7$	−3.14352			−1.18814			−0.594070	−	0.804414i	$-0.702480\pi$
$7$	−3.14352			−1.18814			−0.594070	+	0.804414i	$0.702480\pi$
$8$		−	0.560539i		−	0.198180i
$9$	−1.58849	+	2.54493i	−0.529498	+	0.848311i
$10$		0			0
$11$	−0.166374	−	3.31245i	−0.0501637	−	0.998741i
$11$	−0.166374	−	3.31245i	−0.0501637	−	0.998741i
$12$	−1.43567	−	2.58849i	−0.414441	−	0.747234i
$13$	−1.94903			−0.540564			−0.270282	−	0.962781i	$-0.587117\pi$
$13$	−1.94903			−0.540564			−0.270282	+	0.962781i	$0.587117\pi$
$14$			6.05398i			1.61800i
$15$		0			0
$16$	−4.49740			−1.12435
$17$		−	3.57551i		−	0.867188i	−0.901108	−	0.433594i	$-0.857245\pi$
$17$		−	3.57551i		−	0.867188i	0.901108	−	0.433594i	$-0.142755\pi$
$18$	4.90119	+	3.05922i	1.15522	+	0.721065i
$19$		−	6.65886i		−	1.52765i	−0.645426	−	0.763823i	$-0.723320\pi$
$19$		−	6.65886i		−	1.52765i	0.645426	−	0.763823i	$-0.276680\pi$
$20$		0			0
$21$	−2.64084	−	4.76142i	−0.576279	−	1.03903i
$22$	−6.37932	+	0.320413i	−1.36008	+	0.0683123i
$23$	−3.98060			−0.830012			−0.415006	−	0.909819i	$-0.636221\pi$
$23$	−3.98060			−0.830012			−0.415006	+	0.909819i	$0.636221\pi$
$24$	0.849035	−	0.470903i	0.173309	−	0.0961228i
$25$		0			0
$26$			3.75357i			0.736135i
$27$	−5.18923	−	0.268081i	−0.998668	−	0.0515923i
$28$	5.37209			1.01523
$29$	4.99736			0.927987			0.463993	−	0.885839i	$-0.346416\pi$
$29$	4.99736			0.927987			0.463993	+	0.885839i	$0.346416\pi$
$30$		0			0
$31$	6.03356			1.08366			0.541830	−	0.840488i	$-0.317732\pi$
$31$	6.03356			1.08366			0.541830	+	0.840488i	$0.317732\pi$
$32$			7.54030i			1.33295i
$33$	4.87752	−	3.03476i	0.849068	−	0.528284i
$34$	−6.88593			−1.18093
$35$		0			0
$36$	2.71464	−	4.34914i	0.452441	−	0.724857i
$37$		−	9.52676i		−	1.56619i	−0.621903	−	0.783095i	$-0.713640\pi$
$37$		−	9.52676i		−	1.56619i	0.621903	−	0.783095i	$-0.286360\pi$
$38$	−12.8240			−2.08033
$39$	−1.63736	−	2.95216i	−0.262188	−	0.472723i
$40$		0			0
$41$	0.227791			0.0355749			0.0177875	−	0.999842i	$-0.494338\pi$
$41$	0.227791			0.0355749			0.0177875	+	0.999842i	$0.494338\pi$
$42$	−9.16983	+	5.08590i	−1.41494	+	0.784771i
$43$	−7.57380			−1.15499			−0.577497	−	0.816393i	$-0.695971\pi$
$43$	−7.57380			−1.15499			−0.577497	+	0.816393i	$0.695971\pi$
$44$	0.284323	+	5.66078i	0.0428634	+	0.853395i
$45$		0			0
$46$			7.66608i			1.13030i
$47$	4.32448			0.630790			0.315395	−	0.948960i	$-0.397863\pi$
$47$	4.32448			0.630790			0.315395	+	0.948960i	$0.397863\pi$
$48$	−3.77823	−	6.81211i	−0.545340	−	0.983244i
$49$	2.88172			0.411674
$50$		0			0
$51$	5.41574	−	3.00375i	0.758355	−	0.420609i
$52$	3.33078			0.461896
$53$	−1.53503			−0.210853			−0.105426	−	0.994427i	$-0.533621\pi$
$53$	−1.53503			−0.210853			−0.105426	+	0.994427i	$0.533621\pi$
$54$	−0.516287	+	9.99374i	−0.0702578	+	1.35998i
$55$		0			0
$56$			1.76206i			0.235466i
$57$	10.0860	−	5.59404i	1.33593	−	0.740949i
$58$		−	9.62423i		−	1.26372i
$59$			5.56495i			0.724495i	0.932082	+	0.362248i	$0.117990\pi$
$59$			5.56495i			0.724495i	−0.932082	+	0.362248i	$0.882010\pi$
$60$		0			0
$61$			5.46437i			0.699641i	0.936817	+	0.349820i	$0.113757\pi$
$61$			5.46437i			0.699641i	−0.936817	+	0.349820i	$0.886243\pi$
$62$		−	11.6198i		−	1.47572i
$63$	4.99346	−	8.00005i	0.629117	−	1.00791i
$64$	5.52676			0.690845
$65$		0			0
$66$	−5.84453	−	9.39343i	−0.719412	−	1.15625i
$67$			6.46805i			0.790198i	0.918639	+	0.395099i	$0.129290\pi$
$67$			6.46805i			0.790198i	−0.918639	+	0.395099i	$0.870710\pi$
$68$			6.11033i			0.740987i
$69$	−3.34407	−	6.02932i	−0.402578	−	0.725845i
$70$		0			0
$71$		−	9.07047i		−	1.07647i	−0.842796	−	0.538233i	$-0.819092\pi$
$71$		−	9.07047i		−	1.07647i	0.842796	−	0.538233i	$-0.180908\pi$
$72$	1.42653	+	0.890413i	0.168119	+	0.104936i
$73$	−13.0382			−1.52600			−0.763001	−	0.646397i	$-0.776275\pi$
$73$	−13.0382			−1.52600			−0.763001	+	0.646397i	$0.776275\pi$
$74$	−18.3472			−2.13282
$75$		0			0
$76$			11.3796i			1.30533i
$77$	0.523000	+	10.4128i	0.0596014	+	1.18664i
$78$	−5.68544	+	3.15334i	−0.643749	+	0.357045i
$79$			11.5641i			1.30107i	0.759477	+	0.650534i	$0.225455\pi$
$79$			11.5641i			1.30107i	−0.759477	+	0.650534i	$0.774545\pi$
$80$		0			0
$81$	−3.95337	−	8.08522i	−0.439263	−	0.898358i
$82$		−	0.438693i		−	0.0484456i
$83$		−	5.54979i		−	0.609169i	−0.952485	−	0.304584i	$-0.901482\pi$
$83$		−	5.54979i		−	0.609169i	0.952485	−	0.304584i	$-0.0985176\pi$
$84$	4.51305	+	8.13699i	0.492414	+	0.887818i
$85$		0			0
$86$			14.5861i			1.57286i
$87$	4.19824	+	7.56939i	0.450098	+	0.811524i
$88$	−1.85676	+	0.0932591i	−0.197931	+	0.00994145i
$89$		−	3.01648i		−	0.319746i	−0.987138	−	0.159873i	$-0.948891\pi$
$89$		−	3.01648i		−	0.319746i	0.987138	−	0.159873i	$-0.0511085\pi$
$90$		0			0
$91$	6.12682			0.642266
$92$	6.80261			0.709221
$93$	5.06874	+	9.13890i	0.525604	+	0.947660i
$94$		−	8.32835i		−	0.859004i
$95$		0			0
$96$	−11.4211	+	6.33453i	−1.16566	+	0.646516i
$97$			5.38853i			0.547122i	0.961855	+	0.273561i	$0.0882016\pi$
$97$			5.38853i			0.547122i	−0.961855	+	0.273561i	$0.911798\pi$
$98$		−	5.54979i		−	0.560614i
$99$	8.69425	+	4.83840i	0.873805	+	0.486277i
$100$		0			0
$101$	13.8138			1.37452			0.687261	−	0.726411i	$-0.258813\pi$
$101$	13.8138			1.37452			0.687261	+	0.726411i	$0.258813\pi$
$102$	−5.78481	−	10.4300i	−0.572781	−	1.03272i
$103$		−	5.67018i		−	0.558700i	−0.960189	−	0.279350i	$-0.909881\pi$
$103$		−	5.67018i		−	0.558700i	0.960189	−	0.279350i	$-0.0901189\pi$
$104$			1.09251i			0.107129i
$105$		0			0
$106$			2.95626i			0.287137i
$107$			20.5657i			1.98817i	0.108626	+	0.994083i	$0.465355\pi$
$107$			20.5657i			1.98817i	−0.108626	+	0.994083i	$0.534645\pi$
$108$	8.86809	+	0.458135i	0.853333	+	0.0440841i
$109$			4.61755i			0.442281i	0.975242	+	0.221140i	$0.0709779\pi$
$109$			4.61755i			0.442281i	−0.975242	+	0.221140i	$0.929022\pi$
$110$		0			0
$111$	14.4300	−	8.00334i	1.36963	−	0.759644i
$112$	14.1377			1.33588
$113$	15.6135			1.46879			0.734396	−	0.678721i	$-0.237465\pi$
$113$	15.6135			1.46879			0.734396	+	0.678721i	$0.237465\pi$
$114$	−10.7734	−	19.4243i	−1.00902	−	1.81925i
$115$		0			0
$116$	−8.54020			−0.792938
$117$	3.09603	−	4.96016i	0.286228	−	0.458567i
$118$	10.7173			0.986610
$119$			11.2397i			1.03034i
$120$		0			0
$121$	−10.9446	+	1.10221i	−0.994967	+	0.100201i
$122$	10.5236			0.952763
$123$	0.191365	+	0.345029i	0.0172548	+	0.0311102i
$124$	−10.3110			−0.925956
$125$		0			0
$126$	−15.4070	−	9.61672i	−1.37256	−	0.856726i
$127$	5.09255			0.451891			0.225946	−	0.974140i	$-0.427453\pi$
$127$	5.09255			0.451891			0.225946	+	0.974140i	$0.427453\pi$
$128$			4.43682i			0.392164i
$129$	−6.36268	−	11.4719i	−0.560203	−	1.01004i
$130$		0			0
$131$	−19.9887			−1.74643			−0.873213	−	0.487340i	$-0.837967\pi$
$131$	−19.9887			−1.74643			−0.873213	+	0.487340i	$0.837967\pi$
$132$	−8.33540	+	5.18623i	−0.725503	+	0.451403i
$133$			20.9322i			1.81506i
$134$	12.4566			1.07608
$135$		0			0
$136$	−2.00421			−0.171860
$137$	21.6535			1.84998			0.924992	−	0.379985i	$-0.124071\pi$
$137$	21.6535			1.84998			0.924992	+	0.379985i	$0.124071\pi$
$138$	−11.6116	+	6.44021i	−0.988448	+	0.548227i
$139$		−	3.05124i		−	0.258803i	−0.991592	−	0.129402i	$-0.958694\pi$
$139$		−	3.05124i		−	0.258803i	0.991592	−	0.129402i	$-0.0413056\pi$
$140$		0			0
$141$	3.63296	+	6.55019i	0.305950	+	0.551626i
$142$	−17.4685			−1.46592
$143$	0.324268	+	6.45607i	0.0271167	+	0.539884i
$144$	7.14410	−	11.4456i	0.595342	−	0.953799i
$145$		0			0
$146$			25.1097i			2.07809i
$147$	2.42091	+	4.36488i	0.199673	+	0.360009i
$148$			16.2807i			1.33826i
$149$	7.40267			0.606450			0.303225	−	0.952919i	$-0.401937\pi$
$149$	7.40267			0.606450			0.303225	+	0.952919i	$0.401937\pi$
$150$		0			0
$151$		−	20.9947i		−	1.70853i	−0.519842	−	0.854263i	$-0.674009\pi$
$151$		−	20.9947i		−	1.70853i	0.519842	−	0.854263i	$-0.325991\pi$
$152$	−3.73255			−0.302750
$153$	9.09943	+	5.67967i	0.735645	+	0.459174i
$154$	20.0535	−	1.00723i	1.61596	−	0.0811646i
$155$		0			0
$156$	2.79816	+	5.04506i	0.224032	+	0.403928i
$157$			8.18120i			0.652931i	0.945209	+	0.326465i	$0.105858\pi$
$157$			8.18120i			0.652931i	−0.945209	+	0.326465i	$0.894142\pi$
$158$	22.2709			1.77178
$159$	−1.28957	−	2.32508i	−0.102269	−	0.184391i
$160$		0			0
$161$	12.5131			0.986170
$162$	−15.5710	+	7.61364i	−1.22337	+	0.598184i
$163$		−	1.00421i		−	0.0786558i	−0.999226	−	0.0393279i	$-0.987478\pi$
$163$		−	1.00421i		−	0.0786558i	0.999226	−	0.0393279i	$-0.0125217\pi$
$164$	−0.389281			−0.0303977
$165$		0			0
$166$	−10.6881			−0.829560
$167$		−	23.6454i		−	1.82973i	−0.403757	−	0.914866i	$-0.632296\pi$
$167$		−	23.6454i		−	1.82973i	0.403757	−	0.914866i	$-0.367704\pi$
$168$	−2.66896	+	1.48029i	−0.205915	+	0.114207i
$169$	−9.20127			−0.707790
$170$		0			0
$171$	16.9463	+	10.5776i	1.29592	+	0.808886i
$172$	12.9432			0.986909
$173$		−	11.5535i		−	0.878397i	−0.898390	−	0.439198i	$-0.855262\pi$
$173$		−	11.5535i		−	0.878397i	0.898390	−	0.439198i	$-0.144738\pi$
$174$	14.5776	−	8.08522i	1.10512	−	0.612939i
$175$		0			0
$176$	0.748251	+	14.8974i	0.0564015	+	1.12294i
$177$	−8.42911	+	4.67507i	−0.633570	+	0.351399i
$178$	−5.80933			−0.435427
$179$		−	18.2085i		−	1.36096i	−0.732765	−	0.680482i	$-0.761770\pi$
$179$		−	18.2085i		−	1.36096i	0.732765	−	0.680482i	$-0.238230\pi$
$180$		0			0
$181$	4.02935			0.299500			0.149750	−	0.988724i	$-0.452153\pi$
$181$	4.02935			0.299500			0.149750	+	0.988724i	$0.452153\pi$
$182$		−	11.7994i		−	0.874631i
$183$	−8.27675	+	4.59057i	−0.611835	+	0.339344i
$184$			2.23128i			0.164492i
$185$		0			0
$186$	17.6003	−	9.76170i	1.29051	−	0.715762i
$187$	−11.8437	+	0.594872i	−0.866096	+	0.0435013i
$188$	−7.39028			−0.538992
$189$	16.3125	+	0.842719i	1.18656	+	0.0612988i
$190$		0			0
$191$		−	0.475086i		−	0.0343760i	−0.999852	−	0.0171880i	$-0.994529\pi$
$191$		−	0.475086i		−	0.0343760i	0.999852	−	0.0171880i	$-0.00547138\pi$
$192$	4.64298	+	8.37125i	0.335078	+	0.604143i
$193$	7.01473			0.504931			0.252466	−	0.967606i	$-0.418759\pi$
$193$	7.01473			0.504931			0.252466	+	0.967606i	$0.418759\pi$
$194$	10.3776			0.745065
$195$		0			0
$196$	−4.92469			−0.351764
$197$		−	8.52444i		−	0.607342i	−0.952777	−	0.303671i	$-0.901788\pi$
$197$		−	8.52444i		−	0.607342i	0.952777	−	0.303671i	$-0.0982123\pi$
$198$	9.31808	−	16.7439i	0.662207	−	1.18994i
$199$	−18.9740			−1.34503			−0.672515	−	0.740083i	$-0.734786\pi$
$199$	−18.9740			−1.34503			−0.672515	+	0.740083i	$0.734786\pi$
$200$		0			0
$201$	−9.79700	+	5.43375i	−0.691027	+	0.383267i
$202$		−	26.6034i		−	1.87181i
$203$	−15.7093			−1.10258
$204$	−9.25518	+	5.13323i	−0.647992	+	0.359398i
$205$		0			0
$206$	−10.9200			−0.760831
$207$	6.32316	−	10.1304i	0.439490	−	0.704109i
$208$	8.76558			0.607784
$209$	−22.0571	+	1.10786i	−1.52572	+	0.0766323i
$210$		0			0
$211$		−	6.72698i		−	0.463105i	−0.972822	−	0.231552i	$-0.925620\pi$
$211$		−	6.72698i		−	0.463105i	0.972822	−	0.231552i	$-0.0743804\pi$
$212$	2.62328			0.180168
$213$	13.7388	−	7.62002i	0.941369	−	0.522115i
$214$	39.6068			2.70746
$215$		0			0
$216$	−0.150270	+	2.90877i	−0.0102246	+	0.197916i
$217$	−18.9666			−1.28754
$218$	8.89275			0.602293
$219$	−10.9533	−	19.7486i	−0.740152	−	1.33449i
$220$		0			0
$221$			6.96878i			0.468771i
$222$	−15.4133	−	27.7901i	−1.03447	−	1.86515i
$223$		−	22.6915i		−	1.51953i	−0.650196	−	0.759767i	$-0.725313\pi$
$223$		−	22.6915i		−	1.51953i	0.650196	−	0.759767i	$-0.274687\pi$
$224$		−	23.7031i		−	1.58373i
$225$		0			0
$226$		−	30.0694i		−	2.00019i
$227$		−	11.0750i		−	0.735075i	−0.930009	−	0.367538i	$-0.880201\pi$
$227$		−	11.0750i		−	0.735075i	0.930009	−	0.367538i	$-0.119799\pi$
$228$	−17.2364	+	9.55989i	−1.14151	+	0.633119i
$229$	11.0715			0.731623			0.365811	−	0.930689i	$-0.380792\pi$
$229$	11.0715			0.731623			0.365811	+	0.930689i	$0.380792\pi$
$230$		0			0
$231$	−15.3326	+	9.53983i	−1.00881	+	0.627675i
$232$		−	2.80122i		−	0.183909i
$233$			17.5686i			1.15096i	0.817816	+	0.575480i	$0.195185\pi$
$233$			17.5686i			1.15096i	−0.817816	+	0.575480i	$0.804815\pi$
$234$	−9.55258	−	5.96252i	−0.624471	−	0.389782i
$235$		0			0
$236$		−	9.51018i		−	0.619060i
$237$	−17.5160	+	9.71493i	−1.13778	+	0.631053i
$238$	21.6461			1.40311
$239$	9.94630			0.643373			0.321686	−	0.946846i	$-0.395750\pi$
$239$	9.94630			0.643373			0.321686	+	0.946846i	$0.395750\pi$
$240$		0			0
$241$		−	25.3569i		−	1.63338i	−0.577077	−	0.816690i	$-0.695807\pi$
$241$		−	25.3569i		−	1.63338i	0.577077	−	0.816690i	$-0.304193\pi$
$242$	2.12271	+	21.0779i	0.136453	+	1.35494i
$243$	8.92532	−	12.7804i	0.572559	−	0.819863i
$244$		−	9.33828i		−	0.597822i
$245$		0			0
$246$	0.664479	−	0.368542i	0.0423656	−	0.0234974i
$247$			12.9783i			0.825791i
$248$		−	3.38205i		−	0.214760i
$249$	8.40615	−	4.66233i	0.532718	−	0.295463i
$250$		0			0
$251$		−	16.9540i		−	1.07013i	−0.844811	−	0.535065i	$-0.820287\pi$
$251$		−	16.9540i		−	1.07013i	0.844811	−	0.535065i	$-0.179713\pi$
$252$	−8.53354	+	13.6716i	−0.537562	+	0.861231i
$253$	0.662268	+	13.1855i	0.0416365	+	0.828967i
$254$		−	9.80755i		−	0.615380i
$255$		0			0
$256$	19.5982			1.22489
$257$	24.4076			1.52250			0.761252	−	0.648456i	$-0.224585\pi$
$257$	24.4076			1.52250			0.761252	+	0.648456i	$0.224585\pi$
$258$	−22.0932	+	12.2536i	−1.37546	+	0.762879i
$259$			29.9476i			1.86085i
$260$		0			0
$261$	−7.93828	+	12.7180i	−0.491367	+	0.787222i
$262$			38.4956i			2.37826i
$263$		−	7.74352i		−	0.477486i	−0.971083	−	0.238743i	$-0.923265\pi$
$263$		−	7.74352i		−	0.477486i	0.971083	−	0.238743i	$-0.0767354\pi$
$264$	−1.70110	−	2.73404i	−0.104696	−	0.168269i
$265$		0			0
$266$	40.3126			2.47172
$267$	4.56900	−	2.53412i	0.279618	−	0.155086i
$268$		−	11.0535i		−	0.675201i
$269$			2.65825i			0.162076i	0.996711	+	0.0810380i	$0.0258235\pi$
$269$			2.65825i			0.162076i	−0.996711	+	0.0810380i	$0.974176\pi$
$270$		0			0
$271$			24.9768i			1.51724i	0.651536	+	0.758618i	$0.274125\pi$
$271$			24.9768i			1.51724i	−0.651536	+	0.758618i	$0.725875\pi$
$272$			16.0805i			0.975023i
$273$	5.14709	+	9.28016i	0.311516	+	0.561661i
$274$		−	41.7017i		−	2.51929i
$275$		0			0
$276$	5.71481	+	10.3038i	0.343991	+	0.620213i
$277$	2.13359			0.128195			0.0640974	−	0.997944i	$-0.479583\pi$
$277$	2.13359			0.128195			0.0640974	+	0.997944i	$0.479583\pi$
$278$	−5.87627			−0.352435
$279$	−9.58428	+	15.3550i	−0.573796	+	0.919281i
$280$		0			0
$281$	−15.6347			−0.932687			−0.466343	−	0.884604i	$-0.654429\pi$
$281$	−15.6347			−0.932687			−0.466343	+	0.884604i	$0.654429\pi$
$282$	12.6148	−	6.99657i	0.751198	−	0.416640i
$283$	10.4619			0.621898			0.310949	−	0.950427i	$-0.399353\pi$
$283$	10.4619			0.621898			0.310949	+	0.950427i	$0.399353\pi$
$284$			15.5009i			0.919809i
$285$		0			0
$286$	12.4335	−	0.624496i	0.735208	−	0.0369272i
$287$	−0.716065			−0.0422680
$288$	−19.1895	−	11.9777i	−1.13075	−	0.705794i
$289$	4.21575			0.247985
$290$		0			0
$291$	−8.16188	+	4.52685i	−0.478458	+	0.265369i
$292$	22.2815			1.30392
$293$			5.82601i			0.340359i	0.985413	+	0.170180i	$0.0544348\pi$
$293$			5.82601i			0.340359i	−0.985413	+	0.170180i	$0.945565\pi$
$294$	8.40615	−	4.66233i	0.490256	−	0.271913i
$295$		0			0
$296$	−5.34012			−0.310388
$297$	−0.0246519	+	17.2337i	−0.00143045	+	0.999999i
$298$		−	14.2565i		−	0.825857i
$299$	7.75832			0.448675
$300$		0			0
$301$	23.8084			1.37229
$302$	−40.4329			−2.32665
$303$	11.6048	+	20.9234i	0.666680	+	1.20202i
$304$			29.9476i			1.71761i
$305$		0			0
$306$	10.9383	−	17.5242i	0.625299	−	1.00179i
$307$	5.36118			0.305979			0.152989	−	0.988228i	$-0.451110\pi$
$307$	5.36118			0.305979			0.152989	+	0.988228i	$0.451110\pi$
$308$	−0.893777	−	17.7948i	−0.0509276	−	1.01395i
$309$	8.58849	−	4.76347i	0.488582	−	0.270984i
$310$		0			0
$311$		−	23.4789i		−	1.33136i	−0.746236	−	0.665682i	$-0.768141\pi$
$311$		−	23.4789i		−	1.33136i	0.746236	−	0.665682i	$-0.231859\pi$
$312$	−1.65480	+	0.917806i	−0.0936845	+	0.0519605i
$313$			7.19792i			0.406851i	0.979090	+	0.203425i	$0.0652074\pi$
$313$			7.19792i			0.406851i	−0.979090	+	0.203425i	$0.934793\pi$
$314$	15.7559			0.889154
$315$		0			0
$316$		−	19.7624i		−	1.11172i
$317$	10.9777			0.616568			0.308284	−	0.951294i	$-0.400245\pi$
$317$	10.9777			0.616568			0.308284	+	0.951294i	$0.400245\pi$
$318$	−4.47778	+	2.48353i	−0.251101	+	0.139269i
$319$	−0.831431	−	16.5535i	−0.0465512	−	0.926819i
$320$		0			0
$321$	−31.1505	+	17.2771i	−1.73865	+	0.964313i
$322$		−	24.0985i		−	1.34296i
$323$	−23.8088			−1.32476
$324$	6.75608	+	13.8172i	0.375338	+	0.767621i
$325$		0			0
$326$	−1.93397			−0.107113
$327$	−6.99409	+	3.87916i	−0.386774	+	0.214518i
$328$		−	0.127685i		−	0.00705025i
$329$	−13.5941			−0.749467
$330$		0			0
$331$	−11.8021			−0.648701			−0.324350	−	0.945937i	$-0.605146\pi$
$331$	−11.8021			−0.648701			−0.324350	+	0.945937i	$0.605146\pi$
$332$			9.48427i			0.520517i
$333$	24.2450	+	15.1332i	1.32862	+	0.829294i
$334$	−45.5377			−2.49171
$335$		0			0
$336$	11.8769	+	21.4140i	0.647940	+	1.16823i
$337$	24.2305			1.31992			0.659960	−	0.751301i	$-0.270573\pi$
$337$	24.2305			1.31992			0.659960	+	0.751301i	$0.270573\pi$
$338$			17.7204i			0.963861i
$339$	13.1167	+	23.6494i	0.712404	+	1.28446i
$340$		0			0
$341$	−1.00383	−	19.9859i	−0.0543604	−	1.08230i
$342$	20.3709	−	32.6363i	1.10153	−	1.76477i
$343$	12.9459			0.699013
$344$			4.24541i			0.228897i
$345$		0			0
$346$	−22.2505			−1.19619
$347$		−	1.60887i		−	0.0863685i	−0.999067	−	0.0431843i	$-0.986250\pi$
$347$		−	1.60887i		−	0.0863685i	0.999067	−	0.0431843i	$-0.0137503\pi$
$348$	−7.17454	−	12.9356i	−0.384596	−	0.693423i
$349$			35.5992i			1.90558i	0.303629	+	0.952790i	$0.401802\pi$
$349$			35.5992i			1.90558i	−0.303629	+	0.952790i	$0.598198\pi$
$350$		0			0
$351$	10.1140	+	0.522499i	0.539844	+	0.0278889i
$352$	24.9768	−	1.25451i	1.33127	−	0.0668656i
$353$	−12.0586			−0.641817			−0.320908	−	0.947110i	$-0.603988\pi$
$353$	−12.0586			−0.641817			−0.320908	+	0.947110i	$0.603988\pi$
$354$	9.00353	+	16.2333i	0.478532	+	0.862790i
$355$		0			0
$356$			5.15499i			0.273214i
$357$	−17.0245	+	9.44235i	−0.901031	+	0.499742i
$358$	−35.0670			−1.85335
$359$	−22.4611			−1.18545			−0.592725	−	0.805405i	$-0.701948\pi$
$359$	−22.4611			−1.18545			−0.592725	+	0.805405i	$0.701948\pi$
$360$		0			0
$361$	−25.3404			−1.33370
$362$		−	7.75998i		−	0.407855i
$363$	−10.8640	−	15.6516i	−0.570211	−	0.821498i
$364$	−10.4704			−0.548797
$365$		0			0
$366$	8.84079	+	15.9399i	0.462116	+	0.833191i
$367$		−	13.6953i		−	0.714890i	−0.933934	−	0.357445i	$-0.883648\pi$
$367$		−	13.6953i		−	0.714890i	0.933934	−	0.357445i	$-0.116352\pi$
$368$	17.9024			0.933225
$369$	−0.361844	+	0.579712i	−0.0188369	+	0.0301786i
$370$		0			0
$371$	4.82540			0.250522
$372$	−8.66218	−	15.6178i	−0.449113	−	0.809748i
$373$	11.1841			0.579092			0.289546	−	0.957164i	$-0.406496\pi$
$373$	11.1841			0.579092			0.289546	+	0.957164i	$0.406496\pi$
$374$	1.14564	+	22.8093i	0.0592396	+	1.17944i
$375$		0			0
$376$		−	2.42404i		−	0.125010i
$377$	−9.74002			−0.501637
$378$	1.62296	−	31.4155i	0.0834760	−	1.61584i
$379$	8.14256			0.418255			0.209128	−	0.977888i	$-0.432938\pi$
$379$	8.14256			0.418255			0.209128	+	0.977888i	$0.432938\pi$
$380$		0			0
$381$	4.27821	+	7.71357i	0.219179	+	0.395178i
$382$	−0.914949			−0.0468129
$383$	6.33460			0.323683			0.161841	−	0.986817i	$-0.448257\pi$
$383$	6.33460			0.323683			0.161841	+	0.986817i	$0.448257\pi$
$384$	−6.72036	+	3.72734i	−0.342947	+	0.190210i
$385$		0			0
$386$		−	13.5094i		−	0.687610i
$387$	12.0309	−	19.2748i	0.611567	−	0.979795i
$388$		−	9.20868i		−	0.467500i
$389$		−	27.5735i		−	1.39803i	−0.715106	−	0.699016i	$-0.753622\pi$
$389$		−	27.5735i		−	1.39803i	0.715106	−	0.699016i	$-0.246378\pi$
$390$		0			0
$391$			14.2327i			0.719777i
$392$		−	1.61532i		−	0.0815858i
$393$	−16.7924	−	30.2765i	−0.847063	−	1.52725i
$394$	−16.4169			−0.827071
$395$		0			0
$396$	−14.8580	−	8.26854i	−0.746640	−	0.415510i
$397$			3.66683i			0.184033i	0.995757	+	0.0920165i	$0.0293313\pi$
$397$			3.66683i			0.184033i	−0.995757	+	0.0920165i	$0.970669\pi$
$398$			36.5413i			1.83165i
$399$	−31.7056	+	17.5850i	−1.58727	+	0.880351i
$400$		0			0
$401$			24.7658i			1.23675i	0.785885	+	0.618373i	$0.212208\pi$
$401$			24.7658i			1.23675i	−0.785885	+	0.618373i	$0.787792\pi$
$402$	10.4646	+	18.8677i	0.521929	+	0.941034i
$403$	−11.7596			−0.585788
$404$	−23.6069			−1.17449
$405$		0			0
$406$			30.2540i			1.50148i
$407$	−31.5569	+	1.58500i	−1.56422	+	0.0785658i
$408$	−1.68372	−	3.03573i	−0.0833565	−	0.150291i
$409$			13.0140i			0.643502i	0.946824	+	0.321751i	$0.104271\pi$
$409$			13.0140i			0.643502i	−0.946824	+	0.321751i	$0.895729\pi$
$410$		0			0
$411$	18.1909	+	32.7981i	0.897292	+	1.61781i
$412$			9.69001i			0.477392i
$413$		−	17.4935i		−	0.860801i
$414$	−19.5097	−	12.1775i	−0.958848	−	0.598493i
$415$		0			0
$416$		−	14.6963i		−	0.720544i
$417$	4.62165	−	2.56332i	0.226323	−	0.125526i
$418$	2.13359	+	42.4790i	0.104357	+	2.07771i
$419$			19.0092i			0.928661i	0.885662	+	0.464331i	$0.153705\pi$
$419$			19.0092i			0.928661i	−0.885662	+	0.464331i	$0.846295\pi$
$420$		0			0
$421$	0.202133			0.00985138			0.00492569	−	0.999988i	$-0.498432\pi$
$421$	0.202133			0.00985138			0.00492569	+	0.999988i	$0.498432\pi$
$422$	−12.9552			−0.630651
$423$	−6.86941	+	11.0055i	−0.334002	+	0.535106i
$424$			0.860445i			0.0417869i
$425$		0			0
$426$	−14.6751	−	26.4591i	−0.711011	−	1.28195i
$427$		−	17.1774i		−	0.831270i
$428$		−	35.1456i		−	1.69883i
$429$	−9.50645	+	5.91485i	−0.458976	+	0.285572i
$430$		0			0
$431$	30.7310			1.48026			0.740131	−	0.672463i	$-0.234764\pi$
$431$	30.7310			1.48026			0.740131	+	0.672463i	$0.234764\pi$
$432$	23.3381	+	1.20567i	1.12285	+	0.0580078i
$433$			19.2649i			0.925813i	0.886407	+	0.462907i	$0.153194\pi$
$433$			19.2649i			0.925813i	−0.886407	+	0.462907i	$0.846806\pi$
$434$			36.5271i			1.75336i
$435$		0			0
$436$		−	7.89112i		−	0.377916i
$437$			26.5062i			1.26797i
$438$	−38.0331	+	21.0944i	−1.81729	+	1.00793i
$439$			19.7189i			0.941130i	0.882365	+	0.470565i	$0.155950\pi$
$439$			19.7189i			0.941130i	−0.882365	+	0.470565i	$0.844050\pi$
$440$		0			0
$441$	−4.57760	+	7.33379i	−0.217981	+	0.349228i
$442$	13.4209			0.638367
$443$	−25.6834			−1.22026			−0.610129	−	0.792302i	$-0.708882\pi$
$443$	−25.6834			−1.22026			−0.610129	+	0.792302i	$0.708882\pi$
$444$	−24.6600	+	13.6772i	−1.17031	+	0.649093i
$445$		0			0
$446$	−43.7006			−2.06929
$447$	6.21891	+	11.2127i	0.294145	+	0.530340i
$448$	−17.3735			−0.820819
$449$		−	16.9075i		−	0.797916i	−0.916969	−	0.398958i	$-0.869372\pi$
$449$		−	16.9075i		−	0.797916i	0.916969	−	0.398958i	$-0.130628\pi$
$450$		0			0
$451$	−0.0378984	−	0.754545i	−0.00178457	−	0.0355301i
$452$	−26.6825			−1.25504
$453$	31.8002	−	17.6375i	1.49410	−	0.828680i
$454$	−21.3290			−1.00102
$455$		0			0
$456$	−3.13568	−	5.65360i	−0.146842	−	0.264754i
$457$	−26.5623			−1.24253			−0.621265	−	0.783600i	$-0.713381\pi$
$457$	−26.5623			−1.24253			−0.621265	+	0.783600i	$0.713381\pi$
$458$		−	21.3221i		−	0.996316i
$459$	−0.958526	+	18.5541i	−0.0447402	+	0.866033i
$460$		0			0
$461$	−24.1584			−1.12517			−0.562585	−	0.826739i	$-0.690193\pi$
$461$	−24.1584			−1.12517			−0.562585	+	0.826739i	$0.690193\pi$
$462$	18.3724	+	29.5284i	0.854761	+	1.37379i
$463$		−	21.0922i		−	0.980235i	−0.871656	−	0.490118i	$-0.836954\pi$
$463$		−	21.0922i		−	0.980235i	0.871656	−	0.490118i	$-0.163046\pi$
$464$	−22.4751			−1.04338
$465$		0			0
$466$	33.8348			1.56737
$467$	−30.1009			−1.39291			−0.696453	−	0.717603i	$-0.745239\pi$
$467$	−30.1009			−1.39291			−0.696453	+	0.717603i	$0.745239\pi$
$468$	−5.29093	+	8.47662i	−0.244573	+	0.391832i
$469$		−	20.3324i		−	0.938865i
$470$		0			0
$471$	−12.3919	+	6.87295i	−0.570988	+	0.316689i
$472$	3.11937			0.143581
$473$	1.26008	+	25.0878i	0.0579387	+	1.15354i
$474$	18.7096	+	33.7333i	0.859361	+	1.54942i
$475$		0			0
$476$		−	19.2080i		−	0.880395i
$477$	2.43839	−	3.90655i	0.111646	−	0.178869i
$478$		−	19.1552i		−	0.876138i
$479$	12.9591			0.592119			0.296059	−	0.955170i	$-0.404327\pi$
$479$	12.9591			0.592119			0.296059	+	0.955170i	$0.404327\pi$
$480$		0			0
$481$			18.5680i			0.846626i
$482$	−48.8338			−2.22432
$483$	10.5121	+	18.9533i	0.478319	+	0.862405i
$484$	18.7037	−	1.88361i	0.850170	−	0.0856188i
$485$		0			0
$486$	−24.6133	−	17.1889i	−1.11648	−	0.779705i
$487$		−	18.2097i		−	0.825160i	−0.910921	−	0.412580i	$-0.864628\pi$
$487$		−	18.2097i		−	0.825160i	0.910921	−	0.412580i	$-0.135372\pi$
$488$	3.06299			0.138655
$489$	1.52105	−	0.843628i	0.0687845	−	0.0381502i
$490$		0			0
$491$	−7.17488			−0.323798			−0.161899	−	0.986807i	$-0.551762\pi$
$491$	−7.17488			−0.323798			−0.161899	+	0.986807i	$0.551762\pi$
$492$	−0.327031	−	0.589635i	−0.0147437	−	0.0265828i
$493$		−	17.8681i		−	0.804739i
$494$	24.9945			1.12455
$495$		0			0
$496$	−27.1354			−1.21841
$497$			28.5132i			1.27899i
$498$	−8.97900	−	16.1891i	−0.402359	−	0.725450i
$499$	−0.0852025			−0.00381419			−0.00190709	−	0.999998i	$-0.500607\pi$
$499$	−0.0852025			−0.00381419			−0.00190709	+	0.999998i	$0.500607\pi$
$500$		0			0
$501$	35.8151	−	19.8642i	1.60010	−	0.887469i
$502$	−32.6511			−1.45729
$503$		−	5.41861i		−	0.241604i	−0.992677	−	0.120802i	$-0.961453\pi$
$503$		−	5.41861i		−	0.241604i	0.992677	−	0.120802i	$-0.0385466\pi$
$504$	−4.48434	−	2.79903i	−0.199748	−	0.124679i
$505$		0			0
$506$	25.3935	−	1.27544i	1.12888	−	0.0567001i
$507$	−7.72990	−	13.9370i	−0.343297	−	0.618962i
$508$	−8.70287			−0.386128
$509$		−	16.1518i		−	0.715917i	−0.933737	−	0.357959i	$-0.883473\pi$
$509$		−	16.1518i		−	0.715917i	0.933737	−	0.357959i	$-0.116527\pi$
$510$		0			0
$511$	40.9858			1.81310
$512$		−	28.8698i		−	1.27588i
$513$	−1.78511	+	34.5544i	−0.0788147	+	1.52561i
$514$		−	47.0056i		−	2.07333i
$515$		0			0
$516$	10.8735	+	19.6048i	0.478677	+	0.863051i
$517$	−0.719481	−	14.3246i	−0.0316428	−	0.629996i
$518$	57.6748			2.53409
$519$	17.4998	−	9.70600i	0.768158	−	0.426046i
$520$		0			0
$521$			9.39333i			0.411529i	0.978602	+	0.205765i	$0.0659681\pi$
$521$			9.39333i			0.411529i	−0.978602	+	0.205765i	$0.934032\pi$
$522$	24.4930	+	15.2880i	1.07203	+	0.669139i
$523$	8.06475			0.352647			0.176324	−	0.984332i	$-0.443580\pi$
$523$	8.06475			0.352647			0.176324	+	0.984332i	$0.443580\pi$
$524$	34.1596			1.49227
$525$		0			0
$526$	−14.9130			−0.650236
$527$		−	21.5731i		−	0.939737i
$528$	−21.9362	+	13.6485i	−0.954650	+	0.593977i
$529$	−7.15483			−0.311080
$530$		0			0
$531$	−14.1624	−	8.83990i	−0.614597	−	0.383619i
$532$		−	35.7720i		−	1.55091i
$533$	−0.443971			−0.0192305
$534$	−4.88036	−	8.79925i	−0.211194	−	0.380781i
$535$		0			0
$536$	3.62559			0.156602
$537$	27.5799	−	15.2968i	1.19016	−	0.660104i
$538$	5.11941			0.220713
$539$	−0.479443	−	9.54555i	−0.0206511	−	0.411156i
$540$		0			0
$541$			10.6333i			0.457159i	0.973525	+	0.228580i	$0.0734081\pi$
$541$			10.6333i			0.457159i	−0.973525	+	0.228580i	$0.926592\pi$
$542$	48.1019			2.06615
$543$	3.38502	+	6.10317i	0.145265	+	0.261912i
$544$	26.9604			1.15592
$545$		0			0
$546$	17.8723	−	9.91258i	0.764864	−	0.424219i
$547$	7.05753			0.301758			0.150879	−	0.988552i	$-0.451790\pi$
$547$	7.05753			0.301758			0.150879	+	0.988552i	$0.451790\pi$
$548$	−37.0046			−1.58076
$549$	−13.9065	−	8.68012i	−0.593513	−	0.370458i
$550$		0			0
$551$		−	33.2767i		−	1.41764i
$552$	−3.37967	+	1.87448i	−0.143848	+	0.0797831i
$553$		−	36.3521i		−	1.54585i
$554$		−	4.10899i		−	0.174574i
$555$		0			0
$556$			5.21440i			0.221140i
$557$		−	17.5612i		−	0.744094i	−0.928214	−	0.372047i	$-0.878656\pi$
$557$		−	17.5612i		−	0.744094i	0.928214	−	0.372047i	$-0.121344\pi$
$558$	29.5716	+	18.4580i	1.25187	+	0.781389i
$559$	14.7616			0.624349
$560$		0			0
$561$	−10.8508	−	17.4396i	−0.458122	−	0.736301i
$562$			30.1102i			1.27012i
$563$		−	15.5944i		−	0.657224i	−0.944465	−	0.328612i	$-0.893419\pi$
$563$		−	15.5944i		−	0.657224i	0.944465	−	0.328612i	$-0.106581\pi$
$564$	−6.20851	−	11.1939i	−0.261425	−	0.471348i
$565$		0			0
$566$		−	20.1482i		−	0.846894i
$567$	12.4275	+	25.4161i	0.521906	+	1.06737i
$568$	−5.08435			−0.213334
$569$	26.0344			1.09142			0.545710	−	0.837974i	$-0.316260\pi$
$569$	26.0344			1.09142			0.545710	+	0.837974i	$0.316260\pi$
$570$		0			0
$571$		−	3.95528i		−	0.165523i	−0.996569	−	0.0827616i	$-0.973626\pi$
$571$		−	3.95528i		−	0.165523i	0.996569	−	0.0827616i	$-0.0263740\pi$
$572$	−0.554156	−	11.0330i	−0.0231704	−	0.461315i
$573$	0.719601	−	0.399115i	0.0300618	−	0.0166733i
$574$			1.37904i			0.0575601i
$575$		0			0
$576$	−8.77922	+	14.0652i	−0.365801	+	0.586051i
$577$			22.9607i			0.955868i	0.878396	+	0.477934i	$0.158614\pi$
$577$			22.9607i			0.955868i	−0.878396	+	0.477934i	$0.841386\pi$
$578$		−	8.11895i		−	0.337704i
$579$	5.89301	+	10.6250i	0.244905	+	0.441562i
$580$		0			0
$581$			17.4459i			0.723777i
$582$	8.71809	+	15.7186i	0.361377	+	0.651559i
$583$	0.255389	+	5.08472i	0.0105772	+	0.210587i
$584$			7.30840i			0.302424i
$585$		0			0
$586$	11.2201			0.463497
$587$	−23.6143			−0.974667			−0.487334	−	0.873216i	$-0.662030\pi$
$587$	−23.6143			−0.974667			−0.487334	+	0.873216i	$0.662030\pi$
$588$	−4.13719	−	7.45932i	−0.170615	−	0.307617i
$589$		−	40.1766i		−	1.65545i
$590$		0			0
$591$	12.9118	−	7.16131i	0.531120	−	0.294577i
$592$			42.8457i			1.76095i
$593$			23.7191i			0.974025i	0.873395	+	0.487013i	$0.161913\pi$
$593$			23.7191i			0.974025i	−0.873395	+	0.487013i	$0.838087\pi$
$594$	33.1897	+	0.0474761i	1.36179	+	0.00194797i
$595$		0			0
$596$	−12.6507			−0.518194
$597$	−15.9399	−	28.7395i	−0.652376	−	1.17623i
$598$		−	14.9414i		−	0.611001i
$599$			18.5481i			0.757854i	0.925427	+	0.378927i	$0.123707\pi$
$599$			18.5481i			0.757854i	−0.925427	+	0.378927i	$0.876293\pi$
$600$		0			0
$601$		−	26.1336i		−	1.06601i	−0.846112	−	0.533005i	$-0.821063\pi$
$601$		−	26.1336i		−	1.06601i	0.846112	−	0.533005i	$-0.178937\pi$
$602$		−	45.8517i		−	1.86878i
$603$	−16.4607	−	10.2745i	−0.670334	−	0.418408i
$604$			35.8787i			1.45988i
$605$		0			0
$606$	40.2956	−	22.3493i	1.63690	−	0.907878i
$607$	−29.4153			−1.19393			−0.596966	−	0.802267i	$-0.703627\pi$
$607$	−29.4153			−1.19393			−0.596966	+	0.802267i	$0.703627\pi$
$608$	50.2097			2.03627
$609$	−13.1972	−	23.7945i	−0.534780	−	0.964203i
$610$		0			0
$611$	−8.42855			−0.340983
$612$	−15.5504	−	9.70623i	−0.628587	−	0.392351i
$613$	12.5605			0.507312			0.253656	−	0.967294i	$-0.418367\pi$
$613$	12.5605			0.507312			0.253656	+	0.967294i	$0.418367\pi$
$614$		−	10.3249i		−	0.416678i
$615$		0			0
$616$	5.83675	−	0.293162i	0.235169	−	0.0118118i
$617$	11.1299			0.448073			0.224037	−	0.974581i	$-0.428077\pi$
$617$	11.1299			0.448073			0.224037	+	0.974581i	$0.428077\pi$
$618$	−9.17378	−	16.5402i	−0.369023	−	0.665346i
$619$	−25.4913			−1.02458			−0.512292	−	0.858811i	$-0.671203\pi$
$619$	−25.4913			−1.02458			−0.512292	+	0.858811i	$0.671203\pi$
$620$		0			0
$621$	20.6563	+	1.06712i	0.828907	+	0.0428222i
$622$	−45.2170			−1.81304
$623$			9.48237i			0.379903i
$624$	7.36389	+	13.2770i	0.294791	+	0.531507i
$625$		0			0
$626$	13.8622			0.554045
$627$	−20.2080	−	32.4787i	−0.807031	−	1.29708i
$628$		−	13.9812i		−	0.557910i
$629$	−34.0630			−1.35818
$630$		0			0
$631$	8.00941			0.318849			0.159425	−	0.987210i	$-0.449036\pi$
$631$	8.00941			0.318849			0.159425	+	0.987210i	$0.449036\pi$
$632$	6.48215			0.257846
$633$	10.1892	−	5.65128i	0.404985	−	0.224618i
$634$		−	21.1415i		−	0.839636i
$635$		0			0
$636$	2.20379	+	3.97342i	0.0873861	+	0.157556i
$637$	−5.61657			−0.222536
$638$	−31.8798	+	1.60122i	−1.26213	+	0.0633930i
$639$	23.0837	+	14.4084i	0.913178	+	0.569987i
$640$		0			0
$641$			5.53239i			0.218516i	0.994013	+	0.109258i	$0.0348475\pi$
$641$			5.53239i			0.218516i	−0.994013	+	0.109258i	$0.965152\pi$
$642$	33.2733	+	59.9915i	1.31319	+	2.36767i
$643$			39.0347i			1.53938i	0.638419	+	0.769689i	$0.279589\pi$
$643$			39.0347i			1.53938i	−0.638419	+	0.769689i	$0.720411\pi$
$644$	−21.3841			−0.842653
$645$		0			0
$646$			45.8524i			1.80404i
$647$	13.9123			0.546948			0.273474	−	0.961879i	$-0.411827\pi$
$647$	13.9123			0.546948			0.273474	+	0.961879i	$0.411827\pi$
$648$	−4.53208	+	2.21602i	−0.178037	+	0.0870534i
$649$	18.4336	−	0.925864i	0.723583	−	0.0363433i
$650$		0			0
$651$	−15.9337	−	28.7283i	−0.624491	−	1.12595i
$652$			1.71614i			0.0672091i
$653$	11.2114			0.438735			0.219368	−	0.975642i	$-0.429601\pi$
$653$	11.2114			0.438735			0.219368	+	0.975642i	$0.429601\pi$
$654$	7.47072	+	13.4697i	0.292128	+	0.526705i
$655$		0			0
$656$	−1.02447			−0.0399987
$657$	20.7111	−	33.1813i	0.808016	−	1.29453i
$658$			26.1803i			1.02062i
$659$	17.7213			0.690325			0.345163	−	0.938543i	$-0.387824\pi$
$659$	17.7213			0.690325			0.345163	+	0.938543i	$0.387824\pi$
$660$		0			0
$661$	−12.6323			−0.491339			−0.245669	−	0.969354i	$-0.579008\pi$
$661$	−12.6323			−0.491339			−0.245669	+	0.969354i	$0.579008\pi$
$662$			22.7292i			0.883394i
$663$	−10.5555	+	5.85441i	−0.409940	+	0.227366i
$664$	−3.11087			−0.120725
$665$		0			0
$666$	29.1444	−	46.6924i	1.12932	−	1.80929i
$667$	−19.8925			−0.770241
$668$			40.4085i			1.56345i
$669$	34.3703	−	19.0629i	1.32883	−	0.737015i
$670$		0			0
$671$	18.1004	−	0.909129i	0.698760	−	0.0350965i
$672$	35.9025	−	19.9127i	1.38497	−	0.768150i
$673$	−28.9430			−1.11567			−0.557836	−	0.829951i	$-0.688368\pi$
$673$	−28.9430			−1.11567			−0.557836	+	0.829951i	$0.688368\pi$
$674$		−	46.6646i		−	1.79745i
$675$		0			0
$676$	15.7244			0.604786
$677$		−	22.5741i		−	0.867594i	−0.901011	−	0.433797i	$-0.857174\pi$
$677$		−	22.5741i		−	0.867594i	0.901011	−	0.433797i	$-0.142826\pi$
$678$	45.5454	−	25.2610i	1.74916	−	0.970144i
$679$		−	16.9389i		−	0.650057i
$680$		0			0
$681$	16.7751	−	9.30403i	0.642823	−	0.356531i
$682$	−38.4900	+	1.93323i	−1.47386	+	0.0740274i
$683$	18.2535			0.698452			0.349226	−	0.937039i	$-0.386445\pi$
$683$	18.2535			0.698452			0.349226	+	0.937039i	$0.386445\pi$
$684$	−28.9603	−	18.0764i	−1.10732	−	0.691169i
$685$		0			0
$686$		−	24.9320i		−	0.951908i
$687$	9.30104	+	16.7697i	0.354857	+	0.639804i
$688$	34.0624			1.29862
$689$	2.99183			0.113980
$690$		0			0
$691$	−43.3199			−1.64797			−0.823984	−	0.566614i	$-0.808253\pi$
$691$	−43.3199			−1.64797			−0.823984	+	0.566614i	$0.808253\pi$
$692$			19.7443i			0.750564i
$693$	−27.3305	−	15.2096i	−1.03820	−	0.577765i
$694$	−3.09845			−0.117616
$695$		0			0
$696$	4.24294	−	2.35328i	0.160828	−	0.0892007i
$697$		−	0.814467i		−	0.0308501i
$698$	68.5591			2.59500
$699$	−26.6108	+	14.7593i	−1.00651	+	0.558247i
$700$		0			0
$701$	47.2425			1.78433			0.892163	−	0.451714i	$-0.149187\pi$
$701$	47.2425			1.78433			0.892163	+	0.451714i	$0.149187\pi$
$702$	1.00626	−	19.4781i	0.0379789	−	0.735155i
$703$	−63.4373			−2.39258
$704$	−0.919509	−	18.3071i	−0.0346553	−	0.689975i
$705$		0			0
$706$			23.2233i			0.874020i
$707$	−43.4239			−1.63312
$708$	14.4048	−	7.98941i	0.541367	−	0.300261i
$709$	33.8224			1.27023			0.635113	−	0.772419i	$-0.280953\pi$
$709$	33.8224			1.27023			0.635113	+	0.772419i	$0.280953\pi$
$710$		0			0
$711$	−29.4300	−	18.3696i	−1.10371	−	0.688913i
$712$	−1.69085			−0.0633675
$713$	−24.0172			−0.899451
$714$	18.1847	+	32.7868i	0.680544	+	1.22702i
$715$		0			0
$716$			31.1172i			1.16290i
$717$	8.35580	+	15.0654i	0.312053	+	0.562629i
$718$			43.2569i			1.61433i
$719$		−	7.16751i		−	0.267303i	−0.991028	−	0.133652i	$-0.957330\pi$
$719$		−	7.16751i		−	0.267303i	0.991028	−	0.133652i	$-0.0426703\pi$
$720$		0			0
$721$			17.8243i			0.663813i
$722$			48.8020i			1.81622i
$723$	38.4075	−	21.3021i	1.42839	−	0.792233i
$724$	−6.88593			−0.255914
$725$		0			0
$726$	−30.1429	+	20.9225i	−1.11871	+	0.776508i
$727$			6.99011i			0.259249i	0.991563	+	0.129624i	$0.0413771\pi$
$727$			6.99011i			0.259249i	−0.991563	+	0.129624i	$0.958623\pi$
$728$		−	3.43432i		−	0.127284i
$729$	26.8563	+	2.78227i	0.994676	+	0.103047i
$730$		0			0
$731$			27.0802i			1.00160i
$732$	14.1445	−	7.84501i	0.522795	−	0.289960i
$733$	9.54467			0.352540			0.176270	−	0.984342i	$-0.443597\pi$
$733$	9.54467			0.352540			0.176270	+	0.984342i	$0.443597\pi$
$734$	−26.3753			−0.973530
$735$		0			0
$736$		−	30.0149i		−	1.10636i
$737$	21.4251	−	1.07612i	0.789203	−	0.0396392i
$738$	1.11644	+	0.696862i	0.0410969	+	0.0256518i
$739$		−	33.8456i		−	1.24503i	−0.782607	−	0.622516i	$-0.786111\pi$
$739$		−	33.8456i		−	1.24503i	0.782607	−	0.622516i	$-0.213889\pi$
$740$		0			0
$741$	−19.6580	+	10.9030i	−0.722154	+	0.400531i
$742$		−	9.29306i		−	0.341159i
$743$		−	46.4146i		−	1.70279i	−0.524528	−	0.851393i	$-0.675758\pi$
$743$		−	46.4146i		−	1.70279i	0.524528	−	0.851393i	$-0.324242\pi$
$744$	5.12271	−	2.84123i	0.187808	−	0.104164i
$745$		0			0
$746$		−	21.5391i		−	0.788602i
$747$	14.1239	+	8.81582i	0.516765	+	0.322554i
$748$	20.2402	−	1.01660i	0.740054	−	0.0371706i
$749$		−	64.6488i		−	2.36222i
$750$		0			0
$751$	−21.7960			−0.795348			−0.397674	−	0.917527i	$-0.630183\pi$
$751$	−21.7960			−0.795348			−0.397674	+	0.917527i	$0.630183\pi$
$752$	−19.4489			−0.709230
$753$	25.6799	−	14.2429i	0.935828	−	0.519041i
$754$			18.7579i			0.683124i
$755$		0			0
$756$	−27.8770	−	1.44016i	−1.01388	−	0.0523780i
$757$		−	32.0990i		−	1.16666i	−0.812236	−	0.583328i	$-0.801750\pi$
$757$		−	32.0990i		−	1.16666i	0.812236	−	0.583328i	$-0.198250\pi$
$758$		−	15.6814i		−	0.569576i
$759$	−19.4155	+	12.0802i	−0.704737	+	0.438482i
$760$		0			0
$761$	−5.58080			−0.202304			−0.101152	−	0.994871i	$-0.532253\pi$
$761$	−5.58080			−0.202304			−0.101152	+	0.994871i	$0.532253\pi$
$762$	14.8553	−	8.23923i	0.538150	−	0.298476i
$763$		−	14.5154i		−	0.525491i
$764$			0.811894i			0.0293733i
$765$		0			0
$766$		−	12.1996i		−	0.440788i
$767$		−	10.8463i		−	0.391636i
$768$	16.4643	+	29.6850i	0.594104	+	1.07116i
$769$		−	4.91350i		−	0.177185i	−0.996068	−	0.0885926i	$-0.971763\pi$
$769$		−	4.91350i		−	0.177185i	0.996068	−	0.0885926i	$-0.0282369\pi$
$770$		0			0
$771$	20.5046	+	36.9696i	0.738455	+	1.33143i
$772$	−11.9878			−0.431449
$773$	−7.96546			−0.286498			−0.143249	−	0.989687i	$-0.545755\pi$
$773$	−7.96546			−0.286498			−0.143249	+	0.989687i	$0.545755\pi$
$774$	−37.1206	−	23.1699i	−1.33427	−	0.832826i
$775$		0			0
$776$	3.02048			0.108429
$777$	−45.3609	+	25.1587i	−1.62731	+	0.902562i
$778$	−53.1027			−1.90382
$779$		−	1.51683i		−	0.0543459i
$780$		0			0
$781$	−30.0455	+	1.50909i	−1.07511	+	0.0539995i
$782$	27.4101			0.980184
$783$	−25.9325	−	1.33970i	−0.926751	−	0.0478769i
$784$	−12.9603			−0.462866
$785$		0			0
$786$	−58.3083	+	32.3398i	−2.07979	+	1.15352i
$787$	41.9921			1.49686			0.748429	−	0.663215i	$-0.230809\pi$
$787$	41.9921			1.49686			0.748429	+	0.663215i	$0.230809\pi$
$788$			14.5678i			0.518956i
$789$	11.7289	−	6.50526i	0.417561	−	0.231594i
$790$		0			0
$791$	−49.0813			−1.74513
$792$	2.71211	−	4.87346i	0.0963706	−	0.173171i
$793$		−	10.6502i		−	0.378201i
$794$	7.06181			0.250614
$795$		0			0
$796$	32.4254			1.14929
$797$	−12.8380			−0.454745			−0.227372	−	0.973808i	$-0.573013\pi$
$797$	−12.8380			−0.454745			−0.227372	+	0.973808i	$0.573013\pi$
$798$	33.8663	+	61.0606i	1.19885	+	2.16152i
$799$		−	15.4622i		−	0.547014i
$800$		0			0
$801$	7.67675	+	4.79167i	0.271244	+	0.169305i
$802$	47.6956			1.68419
$803$	2.16921	+	43.1883i	0.0765499	+	1.52408i
$804$	16.7425	−	9.28596i	0.590463	−	0.327490i
$805$		0			0
$806$			22.6474i			0.797720i
$807$	−4.02638	+	2.23317i	−0.141735	+	0.0786112i
$808$		−	7.74316i		−	0.272403i
$809$	30.6914			1.07905			0.539526	−	0.841969i	$-0.318603\pi$
$809$	30.6914			1.07905			0.539526	+	0.841969i	$0.318603\pi$
$810$		0			0
$811$			43.6321i			1.53213i	0.642764	+	0.766064i	$0.277788\pi$
$811$			43.6321i			1.53213i	−0.642764	+	0.766064i	$0.722212\pi$
$812$	26.8463			0.942120
$813$	−37.8319	+	20.9828i	−1.32682	+	0.735900i
$814$	3.05250	+	60.7742i	0.106990	+	2.13013i
$815$		0			0
$816$	−24.3568	+	13.5091i	−0.852657	+	0.472912i
$817$			50.4329i			1.76442i
$818$	25.0632			0.876314
$819$	−9.73243	+	15.5924i	−0.340078	+	0.544841i
$820$		0			0
$821$	−29.5532			−1.03141			−0.515706	−	0.856765i	$-0.672470\pi$
$821$	−29.5532			−1.03141			−0.515706	+	0.856765i	$0.672470\pi$
$822$	63.1646	−	35.0332i	2.20312	−	1.22192i
$823$			31.0653i			1.08287i	0.840743	+	0.541434i	$0.182118\pi$
$823$			31.0653i			1.08287i	−0.840743	+	0.541434i	$0.817882\pi$
$824$	−3.17836			−0.110723
$825$		0			0
$826$	−33.6901			−1.17223
$827$			49.7363i			1.72950i	0.502201	+	0.864751i	$0.332524\pi$
$827$			49.7363i			1.72950i	−0.502201	+	0.864751i	$0.667476\pi$
$828$	−10.8059	+	17.3122i	−0.375531	+	0.601640i
$829$	21.6199			0.750890			0.375445	−	0.926845i	$-0.377490\pi$
$829$	21.6199			0.750890			0.375445	+	0.926845i	$0.377490\pi$
$830$		0			0
$831$	1.79241	+	3.23169i	0.0621779	+	0.112106i
$832$	−10.7718			−0.373446
$833$		−	10.3036i		−	0.356999i
$834$	−4.93660	−	8.90066i	−0.170941	−	0.308204i
$835$		0			0
$836$	37.6943	−	1.89327i	1.30369	−	0.0654801i
$837$	−31.3096	−	1.61749i	−1.08222	−	0.0559085i
$838$	36.6091			1.26464
$839$		−	2.37523i		−	0.0820019i	−0.999159	−	0.0410010i	$-0.986945\pi$
$839$		−	2.37523i		−	0.0820019i	0.999159	−	0.0410010i	$-0.0130547\pi$
$840$		0			0
$841$	−4.02637			−0.138840
$842$		−	0.389281i		−	0.0134155i
$843$	−13.1346	−	23.6815i	−0.452378	−	0.815634i
$844$			11.4960i			0.395709i
$845$		0			0
$846$	21.1951	+	13.2295i	0.728702	+	0.454841i
$847$	34.4047	−	3.46482i	1.18216	−	0.119053i
$848$	6.90366			0.237073
$849$	8.78898	+	15.8465i	0.301637	+	0.543849i
$850$		0			0
$851$			37.9222i			1.29996i
$852$	−23.4789	+	13.0222i	−0.804372	+	0.446132i
$853$	−1.30039			−0.0445244			−0.0222622	−	0.999752i	$-0.507087\pi$
$853$	−1.30039			−0.0445244			−0.0222622	+	0.999752i	$0.507087\pi$
$854$	−33.0812			−1.13202
$855$		0			0
$856$	11.5279			0.394015
$857$		−	13.6826i		−	0.467389i	−0.972310	−	0.233694i	$-0.924919\pi$
$857$		−	13.6826i		−	0.467389i	0.972310	−	0.233694i	$-0.0750815\pi$
$858$	11.3912	+	18.3081i	0.388888	+	0.625028i
$859$	−24.6408			−0.840734			−0.420367	−	0.907354i	$-0.638099\pi$
$859$	−24.6408			−0.840734			−0.420367	+	0.907354i	$0.638099\pi$
$860$		0			0
$861$	−0.601559	−	1.08461i	−0.0205011	−	0.0369633i
$862$		−	59.1837i		−	2.01580i
$863$	−56.6992			−1.93006			−0.965031	−	0.262135i	$-0.915573\pi$
$863$	−56.6992			−1.93006			−0.965031	+	0.262135i	$0.915573\pi$
$864$	2.02141	−	39.1283i	0.0687698	−	1.33117i
$865$		0			0
$866$	37.1016			1.26076
$867$	3.54161	+	6.38550i	0.120279	+	0.216863i
$868$	32.4129			1.10016
$869$	38.3056	−	1.92397i	1.29943	−	0.0652663i
$870$		0			0
$871$		−	12.6064i		−	0.427153i
$872$	2.58831			0.0876514
$873$	−13.7134	−	8.55965i	−0.464130	−	0.289700i
$874$	51.0473			1.72670
$875$		0			0
$876$	18.7185	+	33.7492i	0.632438	+	1.14028i
$877$	40.8654			1.37993			0.689963	−	0.723845i	$-0.257627\pi$
$877$	40.8654			1.37993			0.689963	+	0.723845i	$0.257627\pi$
$878$	37.9758			1.28162
$879$	−8.82452	+	4.89438i	−0.297644	+	0.165083i
$880$		0			0
$881$			46.8633i			1.57887i	0.613837	+	0.789433i	$0.289625\pi$
$881$			46.8633i			1.57887i	−0.613837	+	0.789433i	$0.710375\pi$
$882$	14.1239	+	8.81582i	0.475575	+	0.296844i
$883$		−	9.41752i		−	0.316925i	−0.987365	−	0.158462i	$-0.949346\pi$
$883$		−	9.41752i		−	0.316925i	0.987365	−	0.158462i	$-0.0506537\pi$
$884$		−	11.9092i		−	0.400551i
$885$		0			0
$886$			49.4627i			1.66173i
$887$			21.2410i			0.713203i	0.934257	+	0.356602i	$0.116065\pi$
$887$			21.2410i			0.713203i	−0.934257	+	0.356602i	$0.883935\pi$
$888$	−4.48618	−	8.08855i	−0.150546	−	0.271434i
$889$	−16.0085			−0.536909
$890$		0			0
$891$	−26.1242	+	14.4405i	−0.875192	+	0.483775i
$892$			38.7784i			1.29840i
$893$		−	28.7961i		−	0.963625i
$894$	21.5940	−	11.9768i	0.722212	−	0.400563i
$895$		0			0
$896$		−	13.9472i		−	0.465945i
$897$	6.51769	+	11.7513i	0.217619	+	0.392366i
$898$	−32.5616			−1.08659
$899$	30.1519			1.00562
$900$		0			0
$901$			5.48852i			0.182849i
$902$	−1.45315	+	0.0729872i	−0.0483846	+	0.00243021i
$903$	20.0012	+	36.0621i	0.665599	+	1.20007i
$904$		−	8.75196i		−	0.291086i
$905$		0			0
$906$	−33.9673	−	61.2428i	−1.12849	−	2.03466i
$907$		−	39.4518i		−	1.30998i	−0.755639	−	0.654988i	$-0.772674\pi$
$907$		−	39.4518i		−	1.30998i	0.755639	−	0.654988i	$-0.227326\pi$
$908$			18.9266i			0.628100i
$909$	−21.9431	+	35.1551i	−0.727807	+	1.16602i
$910$		0			0
$911$		−	43.9566i		−	1.45635i	−0.685393	−	0.728174i	$-0.740369\pi$
$911$		−	43.9566i		−	1.45635i	0.685393	−	0.728174i	$-0.259631\pi$
$912$	−45.3609	+	25.1587i	−1.50205	+	0.833087i
$913$	−18.3834	+	0.923341i	−0.608402	+	0.0305581i
$914$			51.1552i			1.69206i
$915$		0			0
$916$	−18.9205			−0.625150
$917$	62.8350			2.07500
$918$	35.7327	+	1.84599i	1.17935	+	0.0609267i
$919$		−	13.4719i		−	0.444397i	−0.975001	−	0.222199i	$-0.928677\pi$
$919$		−	13.4719i		−	0.444397i	0.975001	−	0.222199i	$-0.0713234\pi$
$920$		0			0
$921$	4.50388	+	8.12045i	0.148408	+	0.267578i
$922$			46.5258i			1.53224i
$923$			17.6786i			0.581899i
$924$	26.2025	−	16.3030i	0.861999	−	0.536330i
$925$		0			0
$926$	−40.6206			−1.33487
$927$	14.4302	+	9.00705i	0.473951	+	0.295830i
$928$			37.6816i			1.23696i
$929$		−	28.0769i		−	0.921172i	−0.887615	−	0.460586i	$-0.847639\pi$
$929$		−	28.0769i		−	0.921172i	0.887615	−	0.460586i	$-0.152361\pi$
$930$		0			0
$931$		−	19.1890i		−	0.628893i
$932$		−	30.0238i		−	0.983462i
$933$	35.5629	−	19.7244i	1.16428	−	0.645747i
$934$			57.9702i			1.89684i
$935$		0			0
$936$	−2.78036	−	1.73544i	−0.0908789	−	0.0567247i
$937$	12.1672			0.397485			0.198743	−	0.980052i	$-0.436314\pi$
$937$	12.1672			0.397485			0.198743	+	0.980052i	$0.436314\pi$
$938$	−39.1575			−1.27854
$939$	−10.9025	+	6.04691i	−0.355791	+	0.197333i
$940$		0			0
$941$	−13.6502			−0.444983			−0.222491	−	0.974935i	$-0.571419\pi$
$941$	−13.6502			−0.444983			−0.222491	+	0.974935i	$0.571419\pi$
$942$	13.2363	+	23.8650i	0.431264	+	0.777565i
$943$	−0.906743			−0.0295276
$944$		−	25.0278i		−	0.814586i
$945$		0			0
$946$	48.3157	−	2.42675i	1.57088	−	0.0789004i
$947$	−50.8540			−1.65253			−0.826267	−	0.563279i	$-0.809540\pi$
$947$	−50.8540			−1.65253			−0.826267	+	0.563279i	$0.809540\pi$
$948$	29.9337	−	16.6023i	0.972202	−	0.539216i
$949$	25.4118			0.824903
$950$		0			0
$951$	9.22225	+	16.6276i	0.299052	+	0.539188i
$952$	6.30028			0.204193
$953$		−	35.4121i		−	1.14711i	−0.819167	−	0.573555i	$-0.805564\pi$
$953$		−	35.4121i		−	1.14711i	0.819167	−	0.573555i	$-0.194436\pi$
$954$	−7.52348	−	4.69600i	−0.243582	−	0.152039i
$955$		0			0
$956$	−16.9976			−0.549743
$957$	24.3747	−	15.1658i	0.787924	−	0.490241i
$958$		−	24.9575i		−	0.806341i
$959$	−68.0683			−2.19804
$960$		0			0
$961$	5.40390			0.174319
$962$	35.7593			1.15293
$963$	−52.3384	−	32.6686i	−1.68658	−	1.05273i
$964$			43.3334i			1.39567i
$965$		0			0
$966$	36.5014	−	20.2449i	1.17441	−	0.651370i
$967$	11.2578			0.362025			0.181012	−	0.983481i	$-0.442063\pi$
$967$	11.2578			0.362025			0.181012	+	0.983481i	$0.442063\pi$
$968$	0.617832	+	6.13489i	0.0198579	+	0.197183i
$969$	−20.0015	−	36.0626i	−0.642542	−	1.15850i
$970$		0			0
$971$		−	20.8811i		−	0.670105i	−0.942199	−	0.335053i	$-0.891246\pi$
$971$		−	20.8811i		−	0.670105i	0.942199	−	0.335053i	$-0.108754\pi$
$972$	−15.2528	+	21.8410i	−0.489235	+	0.700549i
$973$			9.59165i			0.307494i
$974$	−35.0693			−1.12369
$975$		0			0
$976$		−	24.5755i		−	0.786641i
$977$	35.2258			1.12697			0.563486	−	0.826126i	$-0.309460\pi$
$977$	35.2258			1.12697			0.563486	+	0.826126i	$0.309460\pi$
$978$	−1.62471	−	2.92934i	−0.0519525	−	0.0936699i
$979$	−9.99194	+	0.501864i	−0.319344	+	0.0160397i
$980$		0			0
$981$	−11.7513	−	7.33495i	−0.375192	−	0.234187i
$982$			13.8178i			0.440944i
$983$	31.1665			0.994057			0.497029	−	0.867734i	$-0.334424\pi$
$983$	31.1665			0.994057			0.497029	+	0.867734i	$0.334424\pi$
$984$	0.193402	−	0.107267i	0.00616544	−	0.00341956i
$985$		0			0
$986$	−34.4115			−1.09589
$987$	−11.4203	−	20.5907i	−0.363511	−	0.655408i
$988$		−	22.1792i		−	0.705614i
$989$	30.1483			0.958660
$990$		0			0
$991$	50.0530			1.58999			0.794993	−	0.606618i	$-0.207474\pi$
$991$	50.0530			1.58999			0.794993	+	0.606618i	$0.207474\pi$
$992$			45.4949i			1.44446i
$993$	−9.91482	−	17.8763i	−0.314637	−	0.567288i
$994$	54.9125			1.74172
$995$		0			0
$996$	−14.3656	+	7.96765i	−0.455192	+	0.252465i
$997$	1.07806			0.0341426			0.0170713	−	0.999854i	$-0.494566\pi$
$997$	1.07806			0.0341426			0.0170713	+	0.999854i	$0.494566\pi$
$998$			0.164088i			0.00519412i
$999$	−2.55394	+	49.4366i	−0.0808032	+	1.56410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.d.f.824.8		32
3.2	odd	2	inner	825.2.d.f.824.26		32
5.2	odd	4		825.2.f.g.626.13	yes	16
5.3	odd	4		825.2.f.e.626.4	yes	16
5.4	even	2	inner	825.2.d.f.824.25		32
11.10	odd	2	inner	825.2.d.f.824.28		32
15.2	even	4		825.2.f.g.626.4	yes	16
15.8	even	4		825.2.f.e.626.13	yes	16
15.14	odd	2	inner	825.2.d.f.824.7		32
33.32	even	2	inner	825.2.d.f.824.6		32
55.32	even	4		825.2.f.g.626.3	yes	16
55.43	even	4		825.2.f.e.626.14	yes	16
55.54	odd	2	inner	825.2.d.f.824.5		32
165.32	odd	4		825.2.f.g.626.14	yes	16
165.98	odd	4		825.2.f.e.626.3	✓	16
165.164	even	2	inner	825.2.d.f.824.27		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.d.f.824.5		32	55.54	odd	2	inner
825.2.d.f.824.6		32	33.32	even	2	inner
825.2.d.f.824.7		32	15.14	odd	2	inner
825.2.d.f.824.8		32	1.1	even	1	trivial
825.2.d.f.824.25		32	5.4	even	2	inner
825.2.d.f.824.26		32	3.2	odd	2	inner
825.2.d.f.824.27		32	165.164	even	2	inner
825.2.d.f.824.28		32	11.10	odd	2	inner
825.2.f.e.626.3	✓	16	165.98	odd	4
825.2.f.e.626.4	yes	16	5.3	odd	4
825.2.f.e.626.13	yes	16	15.8	even	4
825.2.f.e.626.14	yes	16	55.43	even	4
825.2.f.g.626.3	yes	16	55.32	even	4
825.2.f.g.626.4	yes	16	15.2	even	4
825.2.f.g.626.13	yes	16	5.2	odd	4
825.2.f.g.626.14	yes	16	165.32	odd	4

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.92586i q^{2} +(0.840091 + 1.51468i) q^{3} -1.70894 q^{4} +(2.91706 - 1.61790i) q^{6} -3.14352 q^{7} -0.560539i q^{8} +(-1.58849 + 2.54493i) q^{9} +O(q^{10})\)	\(q-1.92586i q^{2} +(0.840091 + 1.51468i) q^{3} -1.70894 q^{4} +(2.91706 - 1.61790i) q^{6} -3.14352 q^{7} -0.560539i q^{8} +(-1.58849 + 2.54493i) q^{9} +(-0.166374 - 3.31245i) q^{11} +(-1.43567 - 2.58849i) q^{12} -1.94903 q^{13} +6.05398i q^{14} -4.49740 q^{16} -3.57551i q^{17} +(4.90119 + 3.05922i) q^{18} -6.65886i q^{19} +(-2.64084 - 4.76142i) q^{21} +(-6.37932 + 0.320413i) q^{22} -3.98060 q^{23} +(0.849035 - 0.470903i) q^{24} +3.75357i q^{26} +(-5.18923 - 0.268081i) q^{27} +5.37209 q^{28} +4.99736 q^{29} +6.03356 q^{31} +7.54030i q^{32} +(4.87752 - 3.03476i) q^{33} -6.88593 q^{34} +(2.71464 - 4.34914i) q^{36} -9.52676i q^{37} -12.8240 q^{38} +(-1.63736 - 2.95216i) q^{39} +0.227791 q^{41} +(-9.16983 + 5.08590i) q^{42} -7.57380 q^{43} +(0.284323 + 5.66078i) q^{44} +7.66608i q^{46} +4.32448 q^{47} +(-3.77823 - 6.81211i) q^{48} +2.88172 q^{49} +(5.41574 - 3.00375i) q^{51} +3.33078 q^{52} -1.53503 q^{53} +(-0.516287 + 9.99374i) q^{54} +1.76206i q^{56} +(10.0860 - 5.59404i) q^{57} -9.62423i q^{58} +5.56495i q^{59} +5.46437i q^{61} -11.6198i q^{62} +(4.99346 - 8.00005i) q^{63} +5.52676 q^{64} +(-5.84453 - 9.39343i) q^{66} +6.46805i q^{67} +6.11033i q^{68} +(-3.34407 - 6.02932i) q^{69} -9.07047i q^{71} +(1.42653 + 0.890413i) q^{72} -13.0382 q^{73} -18.3472 q^{74} +11.3796i q^{76} +(0.523000 + 10.4128i) q^{77} +(-5.68544 + 3.15334i) q^{78} +11.5641i q^{79} +(-3.95337 - 8.08522i) q^{81} -0.438693i q^{82} -5.54979i q^{83} +(4.51305 + 8.13699i) q^{84} +14.5861i q^{86} +(4.19824 + 7.56939i) q^{87} +(-1.85676 + 0.0932591i) q^{88} -3.01648i q^{89} +6.12682 q^{91} +6.80261 q^{92} +(5.06874 + 9.13890i) q^{93} -8.32835i q^{94} +(-11.4211 + 6.33453i) q^{96} +5.38853i q^{97} -5.54979i q^{98} +(8.69425 + 4.83840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 20 * q^9	\( 32 q - 32 q^{4} + 20 q^{9} + 64 q^{16} - 24 q^{31} - 56 q^{34} - 72 q^{36} + 56 q^{49} - 120 q^{64} - 60 q^{66} - 88 q^{69} - 52 q^{81} + 128 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 20 * q^9 + 64 * q^16 - 24 * q^31 - 56 * q^34 - 72 * q^36 + 56 * q^49 - 120 * q^64 - 60 * q^66 - 88 * q^69 - 52 * q^81 + 128 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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