LMFDB - Embedded newform 476.2.bh.a.457.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(9,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

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

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

chi := DirichletCharacter("476.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bh (of order $24$, degree $8$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.8
Character	$\chi$	$=$	476.457
Dual form			476.2.bh.a.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.502054 - 0.654289i) q^{3} +(-0.0581723 + 0.441862i) q^{5} +(1.18794 + 2.36407i) q^{7} +(0.600421 + 2.24080i) q^{9} +O(q^{10})$	\(q+(0.502054 - 0.654289i) q^{3} +(-0.0581723 + 0.441862i) q^{5} +(1.18794 + 2.36407i) q^{7} +(0.600421 + 2.24080i) q^{9} +(1.69278 - 0.222859i) q^{11} -1.84519i q^{13} +(0.259900 + 0.259900i) q^{15} +(-0.961961 + 4.00932i) q^{17} +(-2.65307 + 0.710888i) q^{19} +(2.14319 + 0.409634i) q^{21} +(1.28741 + 1.67778i) q^{23} +(4.63777 + 1.24269i) q^{25} +(4.05338 + 1.67897i) q^{27} +(5.77458 - 2.39191i) q^{29} +(4.32258 - 5.63329i) q^{31} +(0.704053 - 1.21946i) q^{33} +(-1.11370 + 0.387382i) q^{35} +(-11.0584 - 1.45587i) q^{37} +(-1.20729 - 0.926383i) q^{39} +(-6.23698 - 2.58344i) q^{41} +(7.83604 - 7.83604i) q^{43} +(-1.02505 + 0.134951i) q^{45} +(10.6694 + 6.16000i) q^{47} +(-4.17761 + 5.61672i) q^{49} +(2.14030 + 2.64229i) q^{51} +(-1.01268 + 3.77938i) q^{53} +0.760940i q^{55} +(-0.866858 + 2.09278i) q^{57} +(-13.7582 - 3.68649i) q^{59} +(1.81054 - 1.38928i) q^{61} +(-4.58414 + 4.08136i) q^{63} +(0.815318 + 0.107339i) q^{65} +(-4.58265 - 7.93738i) q^{67} +1.74411 q^{69} +(2.21610 + 5.35013i) q^{71} +(-6.82152 - 5.23433i) q^{73} +(3.14149 - 2.41055i) q^{75} +(2.53777 + 3.73710i) q^{77} +(2.25004 + 2.93231i) q^{79} +(-2.89359 + 1.67062i) q^{81} +(-0.472537 - 0.472537i) q^{83} +(-1.71561 - 0.658285i) q^{85} +(1.33415 - 4.97912i) q^{87} +(-11.6089 - 6.70241i) q^{89} +(4.36214 - 2.19196i) q^{91} +(-1.51564 - 5.65643i) q^{93} +(-0.159779 - 1.21365i) q^{95} +(-7.98997 + 3.30955i) q^{97} +(1.51576 + 3.65937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{5}+O(q^{10}) $ 96 * q + 4 * q^5	$ 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) $ 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	0.502054	−	0.654289i	0.289861	−	0.377754i	−0.625611	−	0.780135i	$-0.715150\pi$
$3$	0.502054	−	0.654289i	0.289861	−	0.377754i	0.915472	+	0.402381i	$0.131817\pi$
$4$		0			0
$5$	−0.0581723	+	0.441862i	−0.0260154	+	0.197607i	−0.999517	−	0.0310730i	$-0.990108\pi$
$5$	−0.0581723	+	0.441862i	−0.0260154	+	0.197607i	0.973502	+	0.228680i	$0.0734409\pi$
$6$		0			0
$7$	1.18794	+	2.36407i	0.448998	+	0.893533i
$7$	1.18794	+	2.36407i	0.448998	+	0.893533i
$8$		0			0
$9$	0.600421	+	2.24080i	0.200140	+	0.746933i
$10$		0			0
$11$	1.69278	−	0.222859i	0.510392	−	0.0671944i	0.129068	−	0.991636i	$-0.458801\pi$
$11$	1.69278	−	0.222859i	0.510392	−	0.0671944i	0.381324	+	0.924441i	$0.375468\pi$
$12$		0			0
$13$		−	1.84519i		−	0.511762i	−0.966708	−	0.255881i	$-0.917634\pi$
$13$		−	1.84519i		−	0.511762i	0.966708	−	0.255881i	$-0.0823656\pi$
$14$		0			0
$15$	0.259900	+	0.259900i	0.0671060	+	0.0671060i
$16$		0			0
$17$	−0.961961	+	4.00932i	−0.233310	+	0.972402i
$17$	−0.961961	+	4.00932i	−0.233310	+	0.972402i
$18$		0			0
$19$	−2.65307	+	0.710888i	−0.608656	+	0.163089i	−0.549965	−	0.835187i	$-0.685359\pi$
$19$	−2.65307	+	0.710888i	−0.608656	+	0.163089i	−0.0586904	+	0.998276i	$0.518692\pi$
$20$		0			0
$21$	2.14319	+	0.409634i	0.467683	+	0.0893894i
$22$		0			0
$23$	1.28741	+	1.67778i	0.268443	+	0.349842i	0.908051	−	0.418859i	$-0.137570\pi$
$23$	1.28741	+	1.67778i	0.268443	+	0.349842i	−0.639608	+	0.768701i	$0.720903\pi$
$24$		0			0
$25$	4.63777	+	1.24269i	0.927554	+	0.248537i
$26$		0			0
$27$	4.05338	+	1.67897i	0.780074	+	0.323117i
$28$		0			0
$29$	5.77458	−	2.39191i	1.07231	−	0.444166i	0.224507	−	0.974473i	$-0.427923\pi$
$29$	5.77458	−	2.39191i	1.07231	−	0.444166i	0.847806	+	0.530306i	$0.177923\pi$
$30$		0			0
$31$	4.32258	−	5.63329i	0.776358	−	1.01177i	−0.222960	−	0.974828i	$-0.571572\pi$
$31$	4.32258	−	5.63329i	0.776358	−	1.01177i	0.999317	−	0.0369413i	$-0.0117615\pi$
$32$		0			0
$33$	0.704053	−	1.21946i	0.122560	−	0.212280i
$34$		0			0
$35$	−1.11370	+	0.387382i	−0.188249	+	0.0654794i
$36$		0			0
$37$	−11.0584	−	1.45587i	−1.81799	−	0.239343i	−0.856884	−	0.515509i	$-0.827603\pi$
$37$	−11.0584	−	1.45587i	−1.81799	−	0.239343i	−0.961110	+	0.276166i	$0.910936\pi$
$38$		0			0
$39$	−1.20729	−	0.926383i	−0.193320	−	0.148340i
$40$		0			0
$41$	−6.23698	−	2.58344i	−0.974053	−	0.403466i	−0.161834	−	0.986818i	$-0.551741\pi$
$41$	−6.23698	−	2.58344i	−0.974053	−	0.403466i	−0.812219	+	0.583352i	$0.801741\pi$
$42$		0			0
$43$	7.83604	−	7.83604i	1.19498	−	1.19498i	0.219335	−	0.975650i	$-0.429611\pi$
$43$	7.83604	−	7.83604i	1.19498	−	1.19498i	0.975650	−	0.219335i	$-0.0703889\pi$
$44$		0			0
$45$	−1.02505	+	0.134951i	−0.152806	+	0.0201173i
$46$		0			0
$47$	10.6694	+	6.16000i	1.55630	+	0.898529i	0.997606	+	0.0691531i	$0.0220297\pi$
$47$	10.6694	+	6.16000i	1.55630	+	0.898529i	0.558691	+	0.829376i	$0.311304\pi$
$48$		0			0
$49$	−4.17761	+	5.61672i	−0.596802	+	0.802389i
$50$		0			0
$51$	2.14030	+	2.64229i	0.299702	+	0.369995i
$52$		0			0
$53$	−1.01268	+	3.77938i	−0.139103	+	0.519138i	0.860845	+	0.508868i	$0.169936\pi$
$53$	−1.01268	+	3.77938i	−0.139103	+	0.519138i	−0.999947	+	0.0102703i	$0.996731\pi$
$54$		0			0
$55$			0.760940i			0.102605i
$56$		0			0
$57$	−0.866858	+	2.09278i	−0.114818	+	0.277195i
$58$		0			0
$59$	−13.7582	−	3.68649i	−1.79116	−	0.479940i	−0.798619	−	0.601837i	$-0.794436\pi$
$59$	−13.7582	−	3.68649i	−1.79116	−	0.479940i	−0.992543	+	0.121896i	$0.961102\pi$
$60$		0			0
$61$	1.81054	−	1.38928i	0.231816	−	0.177879i	−0.486322	−	0.873780i	$-0.661662\pi$
$61$	1.81054	−	1.38928i	0.231816	−	0.177879i	0.718137	+	0.695901i	$0.244995\pi$
$62$		0			0
$63$	−4.58414	+	4.08136i	−0.577547	+	0.514203i
$64$		0			0
$65$	0.815318	+	0.107339i	0.101128	+	0.0133137i
$66$		0			0
$67$	−4.58265	−	7.93738i	−0.559860	−	0.969705i	−0.997508	−	0.0705588i	$-0.977522\pi$
$67$	−4.58265	−	7.93738i	−0.559860	−	0.969705i	0.437648	−	0.899146i	$-0.355812\pi$
$68$		0			0
$69$	1.74411			0.209966
$70$		0			0
$71$	2.21610	+	5.35013i	0.263002	+	0.634944i	0.999121	−	0.0419080i	$-0.0133436\pi$
$71$	2.21610	+	5.35013i	0.263002	+	0.634944i	−0.736119	+	0.676852i	$0.763344\pi$
$72$		0			0
$73$	−6.82152	−	5.23433i	−0.798398	−	0.612632i	0.126882	−	0.991918i	$-0.459503\pi$
$73$	−6.82152	−	5.23433i	−0.798398	−	0.612632i	−0.925280	+	0.379285i	$0.876170\pi$
$74$		0			0
$75$	3.14149	−	2.41055i	0.362748	−	0.278346i
$76$		0			0
$77$	2.53777	+	3.73710i	0.289206	+	0.425882i
$78$		0			0
$79$	2.25004	+	2.93231i	0.253149	+	0.329911i	0.902590	−	0.430502i	$-0.141663\pi$
$79$	2.25004	+	2.93231i	0.253149	+	0.329911i	−0.649440	+	0.760413i	$0.724997\pi$
$80$		0			0
$81$	−2.89359	+	1.67062i	−0.321510	+	0.185624i
$82$		0			0
$83$	−0.472537	−	0.472537i	−0.0518677	−	0.0518677i	0.680697	−	0.732565i	$-0.261677\pi$
$83$	−0.472537	−	0.472537i	−0.0518677	−	0.0518677i	−0.732565	+	0.680697i	$0.761677\pi$
$84$		0			0
$85$	−1.71561	−	0.658285i	−0.186084	−	0.0714011i
$86$		0			0
$87$	1.33415	−	4.97912i	0.143036	−	0.533817i
$88$		0			0
$89$	−11.6089	−	6.70241i	−1.23054	−	0.710454i	−0.263400	−	0.964687i	$-0.584844\pi$
$89$	−11.6089	−	6.70241i	−1.23054	−	0.710454i	−0.967143	+	0.254232i	$0.918177\pi$
$90$		0			0
$91$	4.36214	−	2.19196i	0.457276	−	0.229780i
$92$		0			0
$93$	−1.51564	−	5.65643i	−0.157164	−	0.586545i
$94$		0			0
$95$	−0.159779	−	1.21365i	−0.0163930	−	0.124517i
$96$		0			0
$97$	−7.98997	+	3.30955i	−0.811259	+	0.336034i	−0.749456	−	0.662054i	$-0.769685\pi$
$97$	−7.98997	+	3.30955i	−0.811259	+	0.336034i	−0.0618025	+	0.998088i	$0.519685\pi$
$98$		0			0
$99$	1.51576	+	3.65937i	0.152340	+	0.367781i
$100$		0			0
$101$	−3.05193	−	5.28610i	−0.303678	−	0.525986i	0.673288	−	0.739380i	$-0.264881\pi$
$101$	−3.05193	−	5.28610i	−0.303678	−	0.525986i	−0.976966	+	0.213394i	$0.931548\pi$
$102$		0			0
$103$	7.36630	−	12.7588i	0.725823	−	1.25716i	−0.232811	−	0.972522i	$-0.574792\pi$
$103$	7.36630	−	12.7588i	0.725823	−	1.25716i	0.958634	−	0.284641i	$-0.0918744\pi$
$104$		0			0
$105$	−0.305676	+	0.923166i	−0.0298309	+	0.0900918i
$106$		0			0
$107$	−1.65175	+	12.5463i	−0.159681	+	1.21290i	0.704495	+	0.709709i	$0.251173\pi$
$107$	−1.65175	+	12.5463i	−0.159681	+	1.21290i	−0.864176	+	0.503189i	$0.832160\pi$
$108$		0			0
$109$	−0.0833548	−	0.633142i	−0.00798394	−	0.0606440i	0.986989	−	0.160787i	$-0.0514033\pi$
$109$	−0.0833548	−	0.633142i	−0.00798394	−	0.0606440i	−0.994973	+	0.100143i	$0.968070\pi$
$110$		0			0
$111$	−6.50449	+	6.50449i	−0.617379	+	0.617379i
$112$		0			0
$113$	−2.18272	+	5.26955i	−0.205333	+	0.495718i	−0.992677	−	0.120796i	$-0.961455\pi$
$113$	−2.18272	+	5.26955i	−0.205333	+	0.495718i	0.787344	+	0.616514i	$0.211455\pi$
$114$		0			0
$115$	−0.816241	+	0.471257i	−0.0761149	+	0.0439449i
$116$		0			0
$117$	4.13469	−	1.10789i	0.382252	−	0.102424i
$118$		0			0
$119$	−10.6210	+	2.48868i	−0.973629	+	0.228137i
$120$		0			0
$121$	−7.80935	+	2.09251i	−0.709940	+	0.190228i
$122$		0			0
$123$	−4.82162	+	2.78377i	−0.434751	+	0.251004i
$124$		0			0
$125$	−1.67165	+	4.03572i	−0.149517	+	0.360965i
$126$		0			0
$127$	11.1822	−	11.1822i	0.992262	−	0.992262i	−0.00770788	−	0.999970i	$-0.502454\pi$
$127$	11.1822	−	11.1822i	0.992262	−	0.992262i	0.999970	+	0.00770788i	$0.00245352\pi$
$128$		0			0
$129$	−1.19292	−	9.06115i	−0.105031	−	0.797790i
$130$		0			0
$131$	0.771092	−	5.85702i	0.0673706	−	0.511731i	−0.924175	−	0.381970i	$-0.875246\pi$
$131$	0.771092	−	5.85702i	0.0673706	−	0.511731i	0.991545	−	0.129761i	$-0.0414209\pi$
$132$		0			0
$133$	−4.83227	−	5.42754i	−0.419011	−	0.470627i
$134$		0			0
$135$	−0.977667	+	1.69337i	−0.0841441	+	0.145742i
$136$		0			0
$137$	−9.19682	−	15.9294i	−0.785737	−	1.36094i	−0.928558	−	0.371188i	$-0.878951\pi$
$137$	−9.19682	−	15.9294i	−0.785737	−	1.36094i	0.142821	−	0.989749i	$-0.454383\pi$
$138$		0			0
$139$	−0.829016	−	2.00142i	−0.0703163	−	0.169758i	0.884814	−	0.465944i	$-0.154285\pi$
$139$	−0.829016	−	2.00142i	−0.0703163	−	0.169758i	−0.955130	+	0.296186i	$0.904285\pi$
$140$		0			0
$141$	9.38706	−	3.88825i	0.790533	−	0.327449i
$142$		0			0
$143$	−0.411216	−	3.12349i	−0.0343876	−	0.261200i
$144$		0			0
$145$	0.720974	+	2.69071i	0.0598737	+	0.223452i
$146$		0			0
$147$	1.57758	+	5.55326i	0.130116	+	0.458026i
$148$		0			0
$149$	7.47176	+	4.31383i	0.612111	+	0.353402i	0.773791	−	0.633441i	$-0.218358\pi$
$149$	7.47176	+	4.31383i	0.612111	+	0.353402i	−0.161680	+	0.986843i	$0.551691\pi$
$150$		0			0
$151$	−0.182328	+	0.680459i	−0.0148377	+	0.0553750i	−0.972948	−	0.231025i	$-0.925792\pi$
$151$	−0.182328	+	0.680459i	−0.0148377	+	0.0553750i	0.958110	+	0.286400i	$0.0924587\pi$
$152$		0			0
$153$	−9.56166	+	0.251716i	−0.773015	+	0.0203500i
$154$		0			0
$155$	2.23768	+	2.23768i	0.179735	+	0.179735i
$156$		0			0
$157$	−7.48239	+	4.31996i	−0.597160	+	0.344770i	−0.767923	−	0.640542i	$-0.778710\pi$
$157$	−7.48239	+	4.31996i	−0.597160	+	0.344770i	0.170764	+	0.985312i	$0.445377\pi$
$158$		0			0
$159$	1.96439	+	2.56004i	0.155786	+	0.203025i
$160$		0			0
$161$	−2.43703	+	5.03662i	−0.192065	+	0.396941i
$162$		0			0
$163$	10.2566	−	7.87015i	0.803357	−	0.616438i	−0.123290	−	0.992371i	$-0.539344\pi$
$163$	10.2566	−	7.87015i	0.803357	−	0.616438i	0.926647	+	0.375933i	$0.122678\pi$
$164$		0			0
$165$	0.497875	+	0.382033i	0.0387595	+	0.0297412i
$166$		0			0
$167$	−0.892288	−	2.15417i	−0.0690473	−	0.166695i	0.885589	−	0.464470i	$-0.153755\pi$
$167$	−0.892288	−	2.15417i	−0.0690473	−	0.166695i	−0.954636	+	0.297775i	$0.903755\pi$
$168$		0			0
$169$	9.59529			0.738099
$170$		0			0
$171$	−3.18592	−	5.51817i	−0.243633	−	0.421985i
$172$		0			0
$173$	−11.2065	−	1.47536i	−0.852013	−	0.112170i	−0.308144	−	0.951340i	$-0.599708\pi$
$173$	−11.2065	−	1.47536i	−0.852013	−	0.112170i	−0.543869	+	0.839170i	$0.683041\pi$
$174$		0			0
$175$	2.57159	+	12.4402i	0.194394	+	0.940393i
$176$		0			0
$177$	−9.31938	+	7.15101i	−0.700487	+	0.537503i
$178$		0			0
$179$	1.92558	+	0.515957i	0.143924	+	0.0385645i	0.330062	−	0.943959i	$-0.392930\pi$
$179$	1.92558	+	0.515957i	0.143924	+	0.0385645i	−0.186138	+	0.982524i	$0.559597\pi$
$180$		0			0
$181$	7.58662	−	18.3157i	0.563909	−	1.36140i	−0.342708	−	0.939442i	$-0.611344\pi$
$181$	7.58662	−	18.3157i	0.563909	−	1.36140i	0.906617	−	0.421954i	$-0.138656\pi$
$182$		0			0
$183$		−	1.88211i		−	0.139129i
$184$		0			0
$185$	1.28659	−	4.80161i	0.0945918	−	0.353021i
$186$		0			0
$187$	−0.734876	+	7.00128i	−0.0537395	+	0.511984i
$188$		0			0
$189$	0.845979	+	11.5770i	0.0615359	+	0.842101i
$190$		0			0
$191$	−5.60809	−	3.23783i	−0.405787	−	0.234281i	0.283191	−	0.959064i	$-0.408607\pi$
$191$	−5.60809	−	3.23783i	−0.405787	−	0.234281i	−0.688978	+	0.724782i	$0.741940\pi$
$192$		0			0
$193$	17.0568	−	2.24557i	1.22777	−	0.161639i	0.511391	−	0.859348i	$-0.329130\pi$
$193$	17.0568	−	2.24557i	1.22777	−	0.161639i	0.716382	+	0.697709i	$0.245797\pi$
$194$		0			0
$195$	0.479564	−	0.479564i	0.0343423	−	0.0343423i
$196$		0			0
$197$	21.1741	+	8.77061i	1.50859	+	0.624880i	0.975267	−	0.221029i	$-0.0709416\pi$
$197$	21.1741	+	8.77061i	1.50859	+	0.624880i	0.533327	+	0.845909i	$0.320942\pi$
$198$		0			0
$199$	1.51579	+	1.16311i	0.107452	+	0.0824505i	0.661090	−	0.750307i	$-0.270094\pi$
$199$	1.51579	+	1.16311i	0.107452	+	0.0824505i	−0.553638	+	0.832757i	$0.686761\pi$
$200$		0			0
$201$	−7.49408	−	0.986614i	−0.528592	−	0.0695904i
$202$		0			0
$203$	12.5145	+	10.8100i	0.878344	+	0.758717i
$204$		0			0
$205$	1.50435	−	2.60560i	0.105068	−	0.181983i
$206$		0			0
$207$	−2.98659	+	3.89220i	−0.207582	+	0.270527i
$208$		0			0
$209$	−4.33264	+	1.79464i	−0.299695	+	0.124138i
$210$		0			0
$211$	−6.62836	−	2.74555i	−0.456315	−	0.189012i	0.142673	−	0.989770i	$-0.454430\pi$
$211$	−6.62836	−	2.74555i	−0.456315	−	0.189012i	−0.598988	+	0.800758i	$0.704430\pi$
$212$		0			0
$213$	4.61314	+	1.23609i	0.316087	+	0.0846953i
$214$		0			0
$215$	3.00661	+	3.91829i	0.205049	+	0.267225i
$216$		0			0
$217$	18.4524	+	3.52686i	1.25263	+	0.239419i
$218$		0			0
$219$	−6.84954	+	1.83533i	−0.462849	+	0.124020i
$220$		0			0
$221$	7.39794	+	1.77500i	0.497639	+	0.119399i
$222$		0			0
$223$	−1.73275	−	1.73275i	−0.116033	−	0.116033i	0.646706	−	0.762739i	$-0.276146\pi$
$223$	−1.73275	−	1.73275i	−0.116033	−	0.116033i	−0.762739	+	0.646706i	$0.776146\pi$
$224$		0			0
$225$			11.1385i			0.742564i
$226$		0			0
$227$	23.4903	−	3.09256i	1.55911	−	0.205260i	0.698906	−	0.715214i	$-0.253671\pi$
$227$	23.4903	−	3.09256i	1.55911	−	0.205260i	0.860202	+	0.509954i	$0.170337\pi$
$228$		0			0
$229$	−7.21937	−	26.9430i	−0.477069	−	1.78045i	−0.613389	−	0.789781i	$-0.710194\pi$
$229$	−7.21937	−	26.9430i	−0.477069	−	1.78045i	0.136319	−	0.990665i	$-0.456473\pi$
$230$		0			0
$231$	3.71924	+	0.215791i	0.244708	+	0.0141980i
$232$		0			0
$233$	−3.39353	+	25.7764i	−0.222318	+	1.68867i	0.408515	+	0.912752i	$0.366047\pi$
$233$	−3.39353	+	25.7764i	−0.222318	+	1.68867i	−0.630832	+	0.775919i	$0.717286\pi$
$234$		0			0
$235$	−3.34254	+	4.35608i	−0.218043	+	0.284159i
$236$		0			0
$237$	3.04822			0.198003
$238$		0			0
$239$	19.5068			1.26179			0.630895	−	0.775868i	$-0.282688\pi$
$239$	19.5068			1.26179			0.630895	+	0.775868i	$0.282688\pi$
$240$		0			0
$241$	−3.88726	+	5.06597i	−0.250400	+	0.326328i	−0.901594	−	0.432584i	$-0.857602\pi$
$241$	−3.88726	+	5.06597i	−0.250400	+	0.326328i	0.651193	+	0.758912i	$0.274269\pi$
$242$		0			0
$243$	−2.07767	+	15.7814i	−0.133282	+	1.01238i
$244$		0			0
$245$	−2.23880	−	2.17267i	−0.143031	−	0.138807i
$246$		0			0
$247$	1.31172	+	4.89541i	0.0834627	+	0.311487i
$248$		0			0
$249$	−0.546415	+	0.0719369i	−0.0346276	+	0.00455881i
$250$		0			0
$251$			12.8402i			0.810467i	0.914213	+	0.405234i	$0.132810\pi$
$251$			12.8402i			0.810467i	−0.914213	+	0.405234i	$0.867190\pi$
$252$		0			0
$253$	2.55321	+	2.55321i	0.160519	+	0.160519i
$254$		0			0
$255$	−1.29204	+	0.792009i	−0.0809105	+	0.0495975i
$256$		0			0
$257$	19.3675	−	5.18950i	1.20811	−	0.323712i	0.402089	−	0.915600i	$-0.368284\pi$
$257$	19.3675	−	5.18950i	1.20811	−	0.323712i	0.806020	+	0.591889i	$0.201617\pi$
$258$		0			0
$259$	−9.69494	−	27.8723i	−0.602415	−	1.73190i
$260$		0			0
$261$	8.82697	+	11.5035i	0.546376	+	0.712051i
$262$		0			0
$263$	−22.2441	−	5.96028i	−1.37163	−	0.367527i	−0.503555	−	0.863963i	$-0.667975\pi$
$263$	−22.2441	−	5.96028i	−1.37163	−	0.367527i	−0.868073	+	0.496437i	$0.834641\pi$
$264$		0			0
$265$	−1.61106	−	0.667322i	−0.0989664	−	0.0409932i
$266$		0			0
$267$	−10.2136	+	4.23062i	−0.625064	+	0.258910i
$268$		0			0
$269$	−5.27912	+	6.87988i	−0.321874	+	0.419474i	−0.926064	−	0.377366i	$-0.876830\pi$
$269$	−5.27912	+	6.87988i	−0.321874	+	0.419474i	0.604191	+	0.796840i	$0.293497\pi$
$270$		0			0
$271$	1.22512	−	2.12197i	0.0744208	−	0.128901i	−0.826413	−	0.563064i	$-0.809623\pi$
$271$	1.22512	−	2.12197i	0.0744208	−	0.128901i	0.900834	+	0.434163i	$0.142956\pi$
$272$		0			0
$273$	0.755850	−	3.95459i	0.0457461	−	0.239342i
$274$		0			0
$275$	8.12767	+	1.07003i	0.490117	+	0.0645251i
$276$		0			0
$277$	20.0240	+	15.3650i	1.20313	+	0.923192i	0.998451	−	0.0556378i	$-0.0177192\pi$
$277$	20.0240	+	15.3650i	1.20313	+	0.923192i	0.204676	+	0.978830i	$0.434386\pi$
$278$		0			0
$279$	15.2184	+	6.30369i	0.911104	+	0.377392i
$280$		0			0
$281$	−5.78512	+	5.78512i	−0.345112	+	0.345112i	−0.858285	−	0.513173i	$-0.828470\pi$
$281$	−5.78512	+	5.78512i	−0.345112	+	0.345112i	0.513173	+	0.858285i	$0.328470\pi$
$282$		0			0
$283$	−5.21827	+	0.686999i	−0.310194	+	0.0408378i	−0.284016	−	0.958819i	$-0.591667\pi$
$283$	−5.21827	+	0.686999i	−0.310194	+	0.0408378i	−0.0261779	+	0.999657i	$0.508334\pi$
$284$		0			0
$285$	−0.874293	−	0.504773i	−0.0517887	−	0.0299002i
$286$		0			0
$287$	−1.30172	−	17.8136i	−0.0768379	−	1.05150i
$288$		0			0
$289$	−15.1493	−	7.71361i	−0.891133	−	0.453742i
$290$		0			0
$291$	−1.84599	+	6.88933i	−0.108214	+	0.403860i
$292$		0			0
$293$		−	6.62901i		−	0.387271i	−0.981074	−	0.193635i	$-0.937972\pi$
$293$		−	6.62901i		−	0.387271i	0.981074	−	0.193635i	$-0.0620279\pi$
$294$		0			0
$295$	2.42927	−	5.86477i	0.141437	−	0.341460i
$296$		0			0
$297$	7.23566	+	1.93879i	0.419856	+	0.112500i
$298$		0			0
$299$	3.09582	−	2.37551i	0.179036	−	0.137379i
$300$		0			0
$301$	27.8336	+	9.21619i	1.60430	+	0.531212i
$302$		0			0
$303$	−4.99087	−	0.657061i	−0.286718	−	0.0377471i
$304$		0			0
$305$	0.508545	+	0.880826i	0.0291192	+	0.0504360i
$306$		0			0
$307$	−6.78015			−0.386964			−0.193482	−	0.981104i	$-0.561978\pi$
$307$	−6.78015			−0.386964			−0.193482	+	0.981104i	$0.561978\pi$
$308$		0			0
$309$	−4.64967	−	11.2253i	−0.264511	−	0.638585i
$310$		0			0
$311$	2.49811	+	1.91687i	0.141655	+	0.108695i	0.677158	−	0.735838i	$-0.263211\pi$
$311$	2.49811	+	1.91687i	0.141655	+	0.108695i	−0.535503	+	0.844533i	$0.679878\pi$
$312$		0			0
$313$	−9.22237	+	7.07657i	−0.521279	+	0.399991i	−0.835611	−	0.549322i	$-0.814886\pi$
$313$	−9.22237	+	7.07657i	−0.521279	+	0.399991i	0.314332	+	0.949313i	$0.398219\pi$
$314$		0			0
$315$	−1.53673	−	2.26298i	−0.0865850	−	0.127504i
$316$		0			0
$317$	8.06051	+	10.5047i	0.452723	+	0.590001i	0.962829	−	0.270111i	$-0.0870604\pi$
$317$	8.06051	+	10.5047i	0.452723	+	0.590001i	−0.510106	+	0.860112i	$0.670394\pi$
$318$		0			0
$319$	9.24204	−	5.33589i	0.517455	−	0.298753i
$320$		0			0
$321$	7.37965	+	7.37965i	0.411892	+	0.411892i
$322$		0			0
$323$	−0.298027	−	11.3208i	−0.0165827	−	0.629909i
$324$		0			0
$325$	2.29299	−	8.55755i	0.127192	−	0.474687i
$326$		0			0
$327$	−0.456107	−	0.263333i	−0.0252228	−	0.0145624i
$328$		0			0
$329$	−1.88803	+	32.5409i	−0.104090	+	1.79404i
$330$		0			0
$331$	−6.47089	−	24.1497i	−0.355672	−	1.32739i	−0.879636	−	0.475647i	$-0.842214\pi$
$331$	−6.47089	−	24.1497i	−0.355672	−	1.32739i	0.523964	−	0.851741i	$-0.324453\pi$
$332$		0			0
$333$	−3.37739	−	25.6539i	−0.185080	−	1.40582i
$334$		0			0
$335$	3.77381	−	1.56316i	0.206185	−	0.0854048i
$336$		0			0
$337$	3.27461	+	7.90561i	0.178379	+	0.430646i	0.987627	−	0.156822i	$-0.0501249\pi$
$337$	3.27461	+	7.90561i	0.178379	+	0.430646i	−0.809248	+	0.587468i	$0.800125\pi$
$338$		0			0
$339$	2.35197	+	4.07373i	0.127741	+	0.221255i
$340$		0			0
$341$	6.06174	−	10.4992i	0.328262	−	0.568566i
$342$		0			0
$343$	−18.2410	−	3.20383i	−0.984923	−	0.172991i
$344$		0			0
$345$	−0.101459	+	0.770654i	−0.00546235	+	0.0414906i
$346$		0			0
$347$	2.82796	+	21.4805i	0.151813	+	1.15313i	0.882464	+	0.470380i	$0.155883\pi$
$347$	2.82796	+	21.4805i	0.151813	+	1.15313i	−0.730651	+	0.682751i	$0.760783\pi$
$348$		0			0
$349$	6.24544	−	6.24544i	0.334311	−	0.334311i	−0.519910	−	0.854221i	$-0.674035\pi$
$349$	6.24544	−	6.24544i	0.334311	−	0.334311i	0.854221	+	0.519910i	$0.174035\pi$
$350$		0			0
$351$	3.09801	−	7.47925i	0.165359	−	0.399213i
$352$		0			0
$353$	2.33129	−	1.34597i	0.124082	−	0.0716389i	−0.436674	−	0.899620i	$-0.643844\pi$
$353$	2.33129	−	1.34597i	0.124082	−	0.0716389i	0.560756	+	0.827981i	$0.310510\pi$
$354$		0			0
$355$	−2.49294	+	0.667981i	−0.132311	+	0.0354527i
$356$		0			0
$357$	−3.70402	+	8.19869i	−0.196037	+	0.433920i
$358$		0			0
$359$	−32.9831	+	8.83780i	−1.74078	+	0.466441i	−0.982620	−	0.185626i	$-0.940569\pi$
$359$	−32.9831	+	8.83780i	−1.74078	+	0.466441i	−0.758161	+	0.652067i	$0.773902\pi$
$360$		0			0
$361$	−9.92107	+	5.72793i	−0.522161	+	0.301470i
$362$		0			0
$363$	−2.55161	+	6.16012i	−0.133925	+	0.323323i
$364$		0			0
$365$	2.70968	−	2.70968i	0.141831	−	0.141831i
$366$		0			0
$367$	−3.61517	−	27.4600i	−0.188710	−	1.43340i	−0.779414	−	0.626509i	$-0.784483\pi$
$367$	−3.61517	−	27.4600i	−0.188710	−	1.43340i	0.590703	−	0.806889i	$-0.298850\pi$
$368$		0			0
$369$	2.04417	−	15.5270i	0.106415	−	0.808303i
$370$		0			0
$371$	−10.1377	+	2.09562i	−0.526324	+	0.108799i
$372$		0			0
$373$	7.72875	−	13.3866i	0.400180	−	0.693131i	−0.593568	−	0.804784i	$-0.702281\pi$
$373$	7.72875	−	13.3866i	0.400180	−	0.693131i	0.993747	+	0.111653i	$0.0356144\pi$
$374$		0			0
$375$	1.80127	+	3.11989i	0.0930171	+	0.161110i
$376$		0			0
$377$	−4.41352	−	10.6552i	−0.227308	−	0.548769i
$378$		0			0
$379$	−16.0476	+	6.64714i	−0.824310	+	0.341440i	−0.754648	−	0.656130i	$-0.772192\pi$
$379$	−16.0476	+	6.64714i	−0.824310	+	0.341440i	−0.0696624	+	0.997571i	$0.522192\pi$
$380$		0			0
$381$	−1.70233	−	12.9305i	−0.0872131	−	0.662449i
$382$		0			0
$383$	−1.66180	−	6.20192i	−0.0849139	−	0.316903i	0.910384	−	0.413764i	$-0.135786\pi$
$383$	−1.66180	−	6.20192i	−0.0849139	−	0.316903i	−0.995298	+	0.0968614i	$0.969120\pi$
$384$		0			0
$385$	−1.79891	+	0.903949i	−0.0916810	+	0.0460695i
$386$		0			0
$387$	22.2639	+	12.8541i	1.13174	+	0.653410i
$388$		0			0
$389$	0.947244	−	3.53516i	0.0480272	−	0.179240i	−0.937746	−	0.347323i	$-0.887091\pi$
$389$	0.947244	−	3.53516i	0.0480272	−	0.179240i	0.985773	+	0.168083i	$0.0537576\pi$
$390$		0			0
$391$	−7.96521	+	3.54767i	−0.402818	+	0.179413i
$392$		0			0
$393$	−3.44506	−	3.44506i	−0.173780	−	0.173780i
$394$		0			0
$395$	−1.42657	+	0.823629i	−0.0717784	+	0.0414413i
$396$		0			0
$397$	12.4395	+	16.2115i	0.624321	+	0.813631i	0.993270	−	0.115819i	$-0.0369491\pi$
$397$	12.4395	+	16.2115i	0.624321	+	0.813631i	−0.368949	+	0.929449i	$0.620282\pi$
$398$		0			0
$399$	−5.97724	+	0.436782i	−0.299236	+	0.0218665i
$400$		0			0
$401$	18.2291	−	13.9877i	0.910316	−	0.698510i	−0.0434511	−	0.999056i	$-0.513835\pi$
$401$	18.2291	−	13.9877i	0.910316	−	0.698510i	0.953768	+	0.300545i	$0.0971686\pi$
$402$		0			0
$403$	−10.3945	−	7.97596i	−0.517785	−	0.397311i
$404$		0			0
$405$	−0.569855	−	1.37575i	−0.0283163	−	0.0683617i
$406$		0			0
$407$	−19.0439			−0.943973
$408$		0			0
$409$	−2.57979	−	4.46832i	−0.127562	−	0.220944i	0.795169	−	0.606387i	$-0.207382\pi$
$409$	−2.57979	−	4.46832i	−0.127562	−	0.220944i	−0.922732	+	0.385443i	$0.874049\pi$
$410$		0			0
$411$	−15.0397	−	1.98001i	−0.741854	−	0.0976669i
$412$		0			0
$413$	−7.62874	−	36.9045i	−0.375386	−	1.81595i
$414$		0			0
$415$	0.236285	−	0.181308i	0.0115988	−	0.00890004i
$416$		0			0
$417$	−1.72572	−	0.462405i	−0.0845089	−	0.0226441i
$418$		0			0
$419$	−6.86117	+	16.5643i	−0.335190	+	0.809220i	0.662974	+	0.748643i	$0.269294\pi$
$419$	−6.86117	+	16.5643i	−0.335190	+	0.809220i	−0.998164	+	0.0605772i	$0.980706\pi$
$420$		0			0
$421$			19.8214i			0.966036i	0.875610	+	0.483018i	$0.160459\pi$
$421$			19.8214i			0.966036i	−0.875610	+	0.483018i	$0.839541\pi$
$422$		0			0
$423$	−7.39719	+	27.6067i	−0.359663	+	1.34228i
$424$		0			0
$425$	−9.44368	+	17.3989i	−0.458086	+	0.843970i
$426$		0			0
$427$	5.43515	+	2.62986i	0.263025	+	0.127268i
$428$		0			0
$429$	−2.25012	−	1.29911i	−0.108637	−	0.0627215i
$430$		0			0
$431$	−18.4226	+	2.42538i	−0.887386	+	0.116827i	−0.560419	−	0.828209i	$-0.689360\pi$
$431$	−18.4226	+	2.42538i	−0.887386	+	0.116827i	−0.326967	+	0.945036i	$0.606027\pi$
$432$		0			0
$433$	−10.7134	+	10.7134i	−0.514853	+	0.514853i	−0.916010	−	0.401156i	$-0.868608\pi$
$433$	−10.7134	+	10.7134i	−0.514853	+	0.514853i	0.401156	+	0.916010i	$0.368608\pi$
$434$		0			0
$435$	2.12247	+	0.879157i	0.101765	+	0.0421524i
$436$		0			0
$437$	−4.60830	−	3.53607i	−0.220445	−	0.169153i
$438$		0			0
$439$	2.63096	+	0.346373i	0.125569	+	0.0165315i	0.193049	−	0.981189i	$-0.438162\pi$
$439$	2.63096	+	0.346373i	0.125569	+	0.0165315i	−0.0674797	+	0.997721i	$0.521496\pi$
$440$		0			0
$441$	−15.0943	−	5.98879i	−0.718775	−	0.285181i
$442$		0			0
$443$	12.1470	−	21.0392i	0.577120	−	0.999602i	−0.418687	−	0.908130i	$-0.637510\pi$
$443$	12.1470	−	21.0392i	0.577120	−	0.999602i	0.995808	−	0.0914712i	$-0.0291569\pi$
$444$		0			0
$445$	3.63686	−	4.73965i	0.172404	−	0.224681i
$446$		0			0
$447$	6.57372	−	2.72292i	0.310926	−	0.128790i
$448$		0			0
$449$	−11.6632	−	4.83106i	−0.550421	−	0.227992i	0.0900998	−	0.995933i	$-0.471281\pi$
$449$	−11.6632	−	4.83106i	−0.550421	−	0.227992i	−0.640521	+	0.767941i	$0.721281\pi$
$450$		0			0
$451$	−11.1336	−	2.98324i	−0.524260	−	0.140475i
$452$		0			0
$453$	0.353679	+	0.460923i	0.0166173	+	0.0216560i
$454$		0			0
$455$	0.714791	+	2.05498i	0.0335099	+	0.0963388i
$456$		0			0
$457$	20.7469	−	5.55911i	0.970498	−	0.260044i	0.261460	−	0.965214i	$-0.415796\pi$
$457$	20.7469	−	5.55911i	0.970498	−	0.260044i	0.709038	+	0.705170i	$0.249129\pi$
$458$		0			0
$459$	−10.6307	+	14.6362i	−0.496199	+	0.683160i
$460$		0			0
$461$	−4.64177	−	4.64177i	−0.216189	−	0.216189i	0.590702	−	0.806890i	$-0.298851\pi$
$461$	−4.64177	−	4.64177i	−0.216189	−	0.216189i	−0.806890	+	0.590702i	$0.798851\pi$
$462$		0			0
$463$		−	6.36889i		−	0.295988i	−0.988988	−	0.147994i	$-0.952718\pi$
$463$		−	6.36889i		−	0.295988i	0.988988	−	0.147994i	$-0.0472816\pi$
$464$		0			0
$465$	2.58753	−	0.340655i	0.119994	−	0.0157975i
$466$		0			0
$467$	1.78729	+	6.67026i	0.0827059	+	0.308663i	0.994870	−	0.101163i	$-0.0322563\pi$
$467$	1.78729	+	6.67026i	0.0827059	+	0.308663i	−0.912164	+	0.409825i	$0.865590\pi$
$468$		0			0
$469$	13.3206	−	20.2628i	0.615087	−	0.935649i
$470$		0			0
$471$	−0.930059	+	7.06450i	−0.0428549	+	0.325515i
$472$		0			0
$473$	11.5184	−	15.0110i	0.529615	−	0.690208i
$474$		0			0
$475$	−13.1877			−0.605095
$476$		0			0
$477$	−9.07688			−0.415602
$478$		0			0
$479$	−11.7212	+	15.2754i	−0.535555	+	0.697949i	−0.980257	−	0.197730i	$-0.936643\pi$
$479$	−11.7212	+	15.2754i	−0.535555	+	0.697949i	0.444701	+	0.895679i	$0.353310\pi$
$480$		0			0
$481$	−2.68635	+	20.4048i	−0.122487	+	0.930381i
$482$		0			0
$483$	2.07189	+	4.12318i	0.0942741	+	0.187611i
$484$		0			0
$485$	−0.997572	−	3.72299i	−0.0452974	−	0.169052i
$486$		0			0
$487$	−0.560889	+	0.0738424i	−0.0254163	+	0.00334612i	−0.143224	−	0.989690i	$-0.545747\pi$
$487$	−0.560889	+	0.0738424i	−0.0254163	+	0.00334612i	0.117807	+	0.993036i	$0.462413\pi$
$488$		0			0
$489$		−	10.6620i		−	0.482153i
$490$		0			0
$491$	−23.6440	−	23.6440i	−1.06704	−	1.06704i	−0.997585	−	0.0694514i	$-0.977875\pi$
$491$	−23.6440	−	23.6440i	−1.06704	−	1.06704i	−0.0694514	−	0.997585i	$-0.522125\pi$
$492$		0			0
$493$	4.03501	+	25.4531i	0.181728	+	1.14635i
$494$		0			0
$495$	−1.70511	+	0.456884i	−0.0766392	+	0.0205354i
$496$		0			0
$497$	−10.0155	+	11.5946i	−0.449256	+	0.520090i
$498$		0			0
$499$	−19.3291	−	25.1902i	−0.865292	−	1.12767i	−0.990767	−	0.135573i	$-0.956712\pi$
$499$	−19.3291	−	25.1902i	−0.865292	−	1.12767i	0.125476	−	0.992097i	$-0.459954\pi$
$500$		0			0
$501$	−1.85743	−	0.497697i	−0.0829839	−	0.0222355i
$502$		0			0
$503$	27.1444	+	11.2436i	1.21031	+	0.501326i	0.894316	−	0.447436i	$-0.147663\pi$
$503$	27.1444	+	11.2436i	1.21031	+	0.501326i	0.315992	+	0.948762i	$0.397663\pi$
$504$		0			0
$505$	2.51326	−	1.04103i	0.111839	−	0.0463251i
$506$		0			0
$507$	4.81735	−	6.27810i	0.213946	−	0.278820i
$508$		0			0
$509$	10.6517	−	18.4493i	0.472128	−	0.817750i	−0.527363	−	0.849640i	$-0.676819\pi$
$509$	10.6517	−	18.4493i	0.472128	−	0.817750i	0.999491	+	0.0318900i	$0.0101526\pi$
$510$		0			0
$511$	4.27077	−	22.3446i	0.188928	−	0.988466i
$512$		0			0
$513$	−11.9475	−	1.57291i	−0.527494	−	0.0694458i
$514$		0			0
$515$	5.20912	+	3.99710i	0.229541	+	0.176133i
$516$		0			0
$517$	19.4338	+	8.04975i	0.854699	+	0.354028i
$518$		0			0
$519$	−6.59157	+	6.59157i	−0.289338	+	0.289338i
$520$		0			0
$521$	−10.1733	+	1.33934i	−0.445699	+	0.0586774i	−0.350036	−	0.936736i	$-0.613831\pi$
$521$	−10.1733	+	1.33934i	−0.445699	+	0.0586774i	−0.0956636	+	0.995414i	$0.530497\pi$
$522$		0			0
$523$	13.7678	+	7.94887i	0.602026	+	0.347580i	0.769838	−	0.638239i	$-0.220337\pi$
$523$	13.7678	+	7.94887i	0.602026	+	0.347580i	−0.167812	+	0.985819i	$0.553670\pi$
$524$		0			0
$525$	9.43059	+	4.56310i	0.411585	+	0.199150i
$526$		0			0
$527$	18.4275	+	22.7496i	0.802715	+	0.990988i
$528$		0			0
$529$	4.79530	−	17.8963i	0.208491	−	0.778100i
$530$		0			0
$531$		−	33.0428i		−	1.43393i
$532$		0			0
$533$	−4.76693	+	11.5084i	−0.206479	+	0.498484i
$534$		0			0
$535$	−5.44766	−	1.45970i	−0.235523	−	0.0631081i
$536$		0			0
$537$	1.30433	−	1.00085i	0.0562860	−	0.0431898i
$538$		0			0
$539$	−5.82004	+	10.4389i	−0.250687	+	0.449635i
$540$		0			0
$541$	−19.3606	−	2.54887i	−0.832375	−	0.109584i	−0.297719	−	0.954654i	$-0.596226\pi$
$541$	−19.3606	−	2.54887i	−0.832375	−	0.109584i	−0.534657	+	0.845069i	$0.679559\pi$
$542$		0			0
$543$	−8.17489	−	14.1593i	−0.350818	−	0.607635i
$544$		0			0
$545$	0.284611			0.0121914
$546$		0			0
$547$	2.97778	+	7.18901i	0.127321	+	0.307380i	0.974667	−	0.223661i	$-0.0718010\pi$
$547$	2.97778	+	7.18901i	0.127321	+	0.307380i	−0.847346	+	0.531041i	$0.821801\pi$
$548$		0			0
$549$	4.20017	+	3.22291i	0.179259	+	0.137550i
$550$		0			0
$551$	−13.6200	+	10.4510i	−0.580231	+	0.445227i
$552$		0			0
$553$	−4.25927	+	8.80264i	−0.181122	+	0.374326i
$554$		0			0
$555$	−2.49571	−	3.25247i	−0.105937	−	0.138060i
$556$		0			0
$557$	23.2738	−	13.4371i	0.986142	−	0.569349i	0.0820229	−	0.996630i	$-0.473862\pi$
$557$	23.2738	−	13.4371i	0.986142	−	0.569349i	0.904119	+	0.427281i	$0.140529\pi$
$558$		0			0
$559$	−14.4589	−	14.4589i	−0.611548	−	0.611548i
$560$		0			0
$561$	4.21191	+	3.99584i	0.177827	+	0.168705i
$562$		0			0
$563$	2.54538	−	9.49947i	0.107275	−	0.400355i	−0.891319	−	0.453378i	$-0.850219\pi$
$563$	2.54538	−	9.49947i	0.107275	−	0.400355i	0.998593	+	0.0530227i	$0.0168856\pi$
$564$		0			0
$565$	−2.20144	−	1.27100i	−0.0926154	−	0.0534715i
$566$		0			0
$567$	−7.38685	−	4.85605i	−0.310219	−	0.203935i
$568$		0			0
$569$	−7.03783	−	26.2655i	−0.295041	−	1.10111i	−0.941185	−	0.337893i	$-0.890286\pi$
$569$	−7.03783	−	26.2655i	−0.295041	−	1.10111i	0.646144	−	0.763216i	$-0.276381\pi$
$570$		0			0
$571$	1.47113	+	11.1743i	0.0615649	+	0.467632i	0.994262	+	0.106971i	$0.0341153\pi$
$571$	1.47113	+	11.1743i	0.0615649	+	0.467632i	−0.932697	+	0.360660i	$0.882551\pi$
$572$		0			0
$573$	−4.93405	+	2.04375i	−0.206123	+	0.0853788i
$574$		0			0
$575$	3.88575	+	9.38102i	0.162047	+	0.391216i
$576$		0			0
$577$	16.6316	+	28.8067i	0.692381	+	1.19924i	0.971055	+	0.238854i	$0.0767718\pi$
$577$	16.6316	+	28.8067i	0.692381	+	1.19924i	−0.278674	+	0.960386i	$0.589895\pi$
$578$		0			0
$579$	7.09417	−	12.2875i	0.294824	−	0.510649i
$580$		0			0
$581$	0.555764	−	1.67845i	0.0230570	−	0.0696339i
$582$		0			0
$583$	−0.871981	+	6.62335i	−0.0361138	+	0.274311i
$584$		0			0
$585$	0.249009	+	1.89141i	0.0102953	+	0.0782003i
$586$		0			0
$587$	6.69341	−	6.69341i	0.276266	−	0.276266i	−0.555350	−	0.831617i	$-0.687416\pi$
$587$	6.69341	−	6.69341i	0.276266	−	0.276266i	0.831617	+	0.555350i	$0.187416\pi$
$588$		0			0
$589$	−7.46346	+	18.0184i	−0.307526	+	0.742434i
$590$		0			0
$591$	16.3691	−	9.45069i	0.673334	−	0.388749i
$592$		0			0
$593$	−12.4572	+	3.33791i	−0.511557	+	0.137071i	−0.505359	−	0.862909i	$-0.668640\pi$
$593$	−12.4572	+	3.33791i	−0.511557	+	0.137071i	−0.00619874	+	0.999981i	$0.501973\pi$
$594$		0			0
$595$	−0.481804	−	4.83781i	−0.0197520	−	0.198331i
$596$		0			0
$597$	1.52202	−	0.407824i	0.0622921	−	0.0166911i
$598$		0			0
$599$	−10.3095	+	5.95218i	−0.421234	+	0.243199i	−0.695605	−	0.718424i	$-0.744864\pi$
$599$	−10.3095	+	5.95218i	−0.421234	+	0.243199i	0.274371	+	0.961624i	$0.411530\pi$
$600$		0			0
$601$	−14.2980	+	34.5184i	−0.583226	+	1.40803i	0.306646	+	0.951824i	$0.400793\pi$
$601$	−14.2980	+	34.5184i	−0.583226	+	1.40803i	−0.889872	+	0.456210i	$0.849207\pi$
$602$		0			0
$603$	15.0346	−	15.0346i	0.612255	−	0.612255i
$604$		0			0
$605$	−0.470313	−	3.57238i	−0.0191209	−	0.145238i
$606$		0			0
$607$	−3.72780	+	28.3155i	−0.151307	+	1.14929i	0.732274	+	0.681010i	$0.238459\pi$
$607$	−3.72780	+	28.3155i	−0.151307	+	1.14929i	−0.883581	+	0.468279i	$0.844874\pi$
$608$		0			0
$609$	13.3558	−	2.76086i	0.541206	−	0.111876i
$610$		0			0
$611$	11.3663	−	19.6871i	0.459833	−	0.796454i
$612$		0			0
$613$	9.87607	+	17.1059i	0.398891	+	0.690899i	0.993589	−	0.113050i	$-0.0360619\pi$
$613$	9.87607	+	17.1059i	0.398891	+	0.690899i	−0.594698	+	0.803949i	$0.702729\pi$
$614$		0			0
$615$	−0.949556	−	2.29243i	−0.0382898	−	0.0924397i
$616$		0			0
$617$	−31.6097	+	13.0932i	−1.27256	+	0.527111i	−0.913741	−	0.406296i	$-0.866820\pi$
$617$	−31.6097	+	13.0932i	−1.27256	+	0.527111i	−0.358818	+	0.933408i	$0.616820\pi$
$618$		0			0
$619$	0.137004	+	1.04065i	0.00550665	+	0.0418271i	0.993978	−	0.109584i	$-0.0349517\pi$
$619$	0.137004	+	1.04065i	0.00550665	+	0.0418271i	−0.988471	+	0.151411i	$0.951618\pi$
$620$		0			0
$621$	2.40142	+	8.96222i	0.0963656	+	0.359641i
$622$		0			0
$623$	2.05428	−	35.4063i	0.0823028	−	1.41852i
$624$		0			0
$625$	19.1046	+	11.0300i	0.764183	+	0.441201i
$626$		0			0
$627$	−1.00101	+	3.73580i	−0.0399763	+	0.149194i
$628$		0			0
$629$	16.4748	−	42.9363i	0.656894	−	1.71198i
$630$		0			0
$631$	−3.30965	−	3.30965i	−0.131755	−	0.131755i	0.638154	−	0.769909i	$-0.279698\pi$
$631$	−3.30965	−	3.30965i	−0.131755	−	0.131755i	−0.769909	+	0.638154i	$0.779698\pi$
$632$		0			0
$633$	−5.12418	+	2.95845i	−0.203668	+	0.117588i
$634$		0			0
$635$	4.29051	+	5.59150i	0.170264	+	0.221892i
$636$		0			0
$637$	10.3639	+	7.70847i	0.410632	+	0.305421i
$638$		0			0
$639$	−10.6580	+	8.17816i	−0.421624	+	0.323523i
$640$		0			0
$641$	10.6873	+	8.20068i	0.422124	+	0.323907i	0.797885	−	0.602809i	$-0.205952\pi$
$641$	10.6873	+	8.20068i	0.422124	+	0.323907i	−0.375761	+	0.926717i	$0.622619\pi$
$642$		0			0
$643$	11.6824	+	28.2039i	0.460711	+	1.11225i	0.968106	+	0.250541i	$0.0806084\pi$
$643$	11.6824	+	28.2039i	0.460711	+	1.11225i	−0.507395	+	0.861713i	$0.669392\pi$
$644$		0			0
$645$	4.07318			0.160381
$646$		0			0
$647$	23.8706	+	41.3452i	0.938452	+	1.62545i	0.768360	+	0.640018i	$0.221073\pi$
$647$	23.8706	+	41.3452i	0.938452	+	1.62545i	0.170091	+	0.985428i	$0.445594\pi$
$648$		0			0
$649$	−24.1111	−	3.17429i	−0.946445	−	0.124602i
$650$		0			0
$651$	11.5717	−	10.3026i	0.453531	−	0.403789i
$652$		0			0
$653$	−0.505360	+	0.387776i	−0.0197763	+	0.0151749i	−0.618602	−	0.785704i	$-0.712301\pi$
$653$	−0.505360	+	0.387776i	−0.0197763	+	0.0151749i	0.598826	+	0.800879i	$0.295634\pi$
$654$		0			0
$655$	2.54314	+	0.681433i	0.0993688	+	0.0266258i
$656$		0			0
$657$	7.63332	−	18.4285i	0.297804	−	0.718963i
$658$		0			0
$659$		−	44.3619i		−	1.72810i	−0.503410	−	0.864048i	$-0.667922\pi$
$659$		−	44.3619i		−	1.72810i	0.503410	−	0.864048i	$-0.332078\pi$
$660$		0			0
$661$	−11.6910	+	43.6313i	−0.454727	+	1.69706i	0.234164	+	0.972197i	$0.424765\pi$
$661$	−11.6910	+	43.6313i	−0.454727	+	1.69706i	−0.688891	+	0.724865i	$0.741902\pi$
$662$		0			0
$663$	4.87552	−	3.94925i	0.189350	−	0.153376i
$664$		0			0
$665$	2.67933	−	1.81946i	0.103900	−	0.0705558i
$666$		0			0
$667$	11.4474	+	6.60913i	0.443243	+	0.255907i
$668$		0			0
$669$	−2.00365	+	0.263785i	−0.0774655	+	0.0101985i
$670$		0			0
$671$	2.75523	−	2.75523i	0.106365	−	0.106365i
$672$		0			0
$673$	−32.5452	−	13.4806i	−1.25452	−	0.519641i	−0.346299	−	0.938124i	$-0.612562\pi$
$673$	−32.5452	−	13.4806i	−1.25452	−	0.519641i	−0.908225	+	0.418483i	$0.862562\pi$
$674$		0			0
$675$	16.7122	+	12.8238i	0.643254	+	0.493586i
$676$		0			0
$677$	−15.1078	−	1.98898i	−0.580641	−	0.0764428i	−0.165516	−	0.986207i	$-0.552929\pi$
$677$	−15.1078	−	1.98898i	−0.580641	−	0.0764428i	−0.415125	+	0.909764i	$0.636262\pi$
$678$		0			0
$679$	−17.3156	−	14.9573i	−0.664511	−	0.574007i
$680$		0			0
$681$	9.76998	−	16.9221i	0.374386	−	0.648456i
$682$		0			0
$683$	−11.7157	+	15.2682i	−0.448290	+	0.584223i	−0.961763	−	0.273883i	$-0.911692\pi$
$683$	−11.7157	+	15.2682i	−0.448290	+	0.584223i	0.513473	+	0.858106i	$0.328359\pi$
$684$		0			0
$685$	7.57358	−	3.13708i	0.289372	−	0.119862i
$686$		0			0
$687$	−21.2531	−	8.80331i	−0.810855	−	0.335867i
$688$		0			0
$689$	6.97366	+	1.86859i	0.265675	+	0.0711875i
$690$		0			0
$691$	29.6349	+	38.6210i	1.12737	+	1.46921i	0.863289	+	0.504711i	$0.168401\pi$
$691$	29.6349	+	38.6210i	1.12737	+	1.46921i	0.264077	+	0.964502i	$0.414933\pi$
$692$		0			0
$693$	−6.85037	+	7.93047i	−0.260224	+	0.301254i
$694$		0			0
$695$	0.932579	−	0.249884i	0.0353747	−	0.00947863i
$696$		0			0
$697$	16.3576	−	22.5209i	0.619587	−	0.853039i
$698$		0			0
$699$	15.1615	+	15.1615i	0.573461	+	0.573461i
$700$		0			0
$701$			3.36011i			0.126910i	0.997985	+	0.0634548i	$0.0202119\pi$
$701$			3.36011i			0.126910i	−0.997985	+	0.0634548i	$0.979788\pi$
$702$		0			0
$703$	30.3737	−	3.99878i	1.14557	−	0.150817i
$704$		0			0
$705$	1.17200	+	4.37398i	0.0441402	+	0.164733i
$706$		0			0
$707$	8.87118	−	13.4945i	0.333635	−	0.507513i
$708$		0			0
$709$	5.95457	−	45.2294i	0.223629	−	1.69863i	−0.399683	−	0.916654i	$-0.630880\pi$
$709$	5.95457	−	45.2294i	0.223629	−	1.69863i	0.623311	−	0.781974i	$-0.285787\pi$
$710$		0			0
$711$	−5.21975	+	6.80251i	−0.195756	+	0.255114i
$712$		0			0
$713$	15.0164			0.562367
$714$		0			0
$715$	1.40408			0.0525094
$716$		0			0
$717$	9.79347	−	12.7631i	0.365744	−	0.476647i
$718$		0			0
$719$	0.208486	−	1.58361i	0.00777521	−	0.0590586i	−0.987117	−	0.159998i	$-0.948851\pi$
$719$	0.208486	−	1.58361i	0.00777521	−	0.0590586i	0.994893	+	0.100939i	$0.0321847\pi$
$720$		0			0
$721$	38.9134	+	2.25776i	1.44921	+	0.0840832i
$722$		0			0
$723$	1.36300	+	5.08678i	0.0506905	+	0.189180i
$724$		0			0
$725$	29.7536	−	3.91713i	1.10502	−	0.145479i
$726$		0			0
$727$			11.7168i			0.434553i	0.976110	+	0.217277i	$0.0697173\pi$
$727$			11.7168i			0.434553i	−0.976110	+	0.217277i	$0.930283\pi$
$728$		0			0
$729$	2.19471	+	2.19471i	0.0812854	+	0.0812854i
$730$		0			0
$731$	23.8792	+	38.9551i	0.883205	+	1.44081i
$732$		0			0
$733$	−27.9054	+	7.47723i	−1.03071	+	0.276178i	−0.734258	−	0.678870i	$-0.762470\pi$
$733$	−27.9054	+	7.47723i	−1.03071	+	0.276178i	−0.296451	+	0.955048i	$0.595803\pi$
$734$		0			0
$735$	−2.54555	+	0.374025i	−0.0938940	+	0.0137961i
$736$		0			0
$737$	−9.52633	−	12.4150i	−0.350907	−	0.457311i
$738$		0			0
$739$	27.8104	+	7.45178i	1.02302	+	0.274118i	0.731061	−	0.682312i	$-0.239025\pi$
$739$	27.8104	+	7.45178i	1.02302	+	0.274118i	0.291962	+	0.956430i	$0.405692\pi$
$740$		0			0
$741$	3.86157	+	1.59951i	0.141858	+	0.0587596i
$742$		0			0
$743$	18.6257	−	7.71501i	0.683310	−	0.283036i	−0.0138998	−	0.999903i	$-0.504425\pi$
$743$	18.6257	−	7.71501i	0.683310	−	0.283036i	0.697210	+	0.716867i	$0.254425\pi$
$744$		0			0
$745$	−2.34077	+	3.05055i	−0.0857590	+	0.111763i
$746$		0			0
$747$	0.775140	−	1.34258i	0.0283609	−	0.0491225i
$748$		0			0
$749$	−31.6225	+	10.9994i	−1.15546	+	0.401909i
$750$		0			0
$751$	−4.61441	−	0.607499i	−0.168382	−	0.0221679i	0.0458636	−	0.998948i	$-0.485396\pi$
$751$	−4.61441	−	0.607499i	−0.168382	−	0.0221679i	−0.214246	+	0.976780i	$0.568729\pi$
$752$		0			0
$753$	8.40122	+	6.44648i	0.306157	+	0.234923i
$754$		0			0
$755$	−0.290063	−	0.120148i	−0.0105565	−	0.00437263i
$756$		0			0
$757$	3.30984	−	3.30984i	0.120298	−	0.120298i	−0.644395	−	0.764693i	$-0.722891\pi$
$757$	3.30984	−	3.30984i	0.120298	−	0.120298i	0.764693	+	0.644395i	$0.222891\pi$
$758$		0			0
$759$	2.95239	−	0.388689i	0.107165	−	0.0141085i
$760$		0			0
$761$	20.0388	+	11.5694i	0.726404	+	0.419390i	0.817105	−	0.576488i	$-0.195577\pi$
$761$	20.0388	+	11.5694i	0.726404	+	0.419390i	−0.0907009	+	0.995878i	$0.528911\pi$
$762$		0			0
$763$	1.39777	−	0.949189i	0.0506027	−	0.0343630i
$764$		0			0
$765$	0.445000	−	4.23958i	0.0160890	−	0.153282i
$766$		0			0
$767$	−6.80226	+	25.3864i	−0.245615	+	0.916649i
$768$		0			0
$769$			9.81407i			0.353904i	0.984219	+	0.176952i	$0.0566238\pi$
$769$			9.81407i			0.353904i	−0.984219	+	0.176952i	$0.943376\pi$
$770$		0			0
$771$	6.32808	−	15.2773i	0.227900	−	0.550200i
$772$		0			0
$773$	12.2006	+	3.26914i	0.438824	+	0.117583i	0.471466	−	0.881884i	$-0.343725\pi$
$773$	12.2006	+	3.26914i	0.438824	+	0.117583i	−0.0326411	+	0.999467i	$0.510392\pi$
$774$		0			0
$775$	27.0475	−	20.7543i	0.971576	−	0.745517i
$776$		0			0
$777$	−23.1040	−	7.65011i	−0.828850	−	0.274446i
$778$		0			0
$779$	18.3837	+	2.42026i	0.658664	+	0.0867148i
$780$		0			0
$781$	4.94369	+	8.56273i	0.176899	+	0.306398i
$782$		0			0
$783$	27.4225			0.980001
$784$		0			0
$785$	−1.47356	−	3.55749i	−0.0525936	−	0.126972i
$786$		0			0
$787$	−26.0618	−	19.9979i	−0.929004	−	0.712850i	0.0290076	−	0.999579i	$-0.490765\pi$
$787$	−26.0618	−	19.9979i	−0.929004	−	0.712850i	−0.958012	+	0.286729i	$0.907432\pi$
$788$		0			0
$789$	−15.0675	+	11.5617i	−0.536416	+	0.411607i
$790$		0			0
$791$	−15.0505	+	1.09980i	−0.535134	+	0.0391045i
$792$		0			0
$793$	−2.56347	−	3.34078i	−0.0910315	−	0.118635i
$794$		0			0
$795$	−1.24546	+	0.719066i	−0.0441719	+	0.0255026i
$796$		0			0
$797$	5.25568	+	5.25568i	0.186166	+	0.186166i	0.794036	−	0.607871i	$-0.207976\pi$
$797$	5.25568	+	5.25568i	0.186166	+	0.186166i	−0.607871	+	0.794036i	$0.707976\pi$
$798$		0			0
$799$	−34.9610	+	36.8515i	−1.23683	+	1.30371i
$800$		0			0
$801$	8.04853	−	30.0375i	0.284381	−	1.06132i
$802$		0			0
$803$	−12.7138	−	7.34034i	−0.448662	−	0.259035i
$804$		0			0
$805$	−2.08373	−	1.36982i	−0.0734417	−	0.0482799i
$806$		0			0
$807$	1.85103	+	6.90815i	0.0651594	+	0.243178i
$808$		0			0
$809$	3.73646	+	28.3812i	0.131367	+	0.997831i	0.922449	+	0.386120i	$0.126185\pi$
$809$	3.73646	+	28.3812i	0.131367	+	0.997831i	−0.791082	+	0.611711i	$0.790482\pi$
$810$		0			0
$811$	−33.0903	+	13.7064i	−1.16196	+	0.481298i	−0.878526	−	0.477695i	$-0.841473\pi$
$811$	−33.0903	+	13.7064i	−1.16196	+	0.481298i	−0.283431	+	0.958993i	$0.591473\pi$
$812$		0			0
$813$	−0.773307	−	1.86693i	−0.0271211	−	0.0654761i
$814$		0			0
$815$	2.88087	+	4.98982i	0.100913	+	0.174786i
$816$		0			0
$817$	−15.2190	+	26.3601i	−0.532446	+	0.922223i
$818$		0			0
$819$	7.53087	+	8.45858i	0.263150	+	0.295567i
$820$		0			0
$821$	−3.78687	+	28.7641i	−0.132163	+	1.00388i	0.788917	+	0.614500i	$0.210642\pi$
$821$	−3.78687	+	28.7641i	−0.132163	+	1.00388i	−0.921079	+	0.389375i	$0.872691\pi$
$822$		0			0
$823$	2.35729	+	17.9054i	0.0821698	+	0.624142i	0.982135	+	0.188179i	$0.0602586\pi$
$823$	2.35729	+	17.9054i	0.0821698	+	0.624142i	−0.899965	+	0.435963i	$0.856408\pi$
$824$		0			0
$825$	4.78064	−	4.78064i	0.166440	−	0.166440i
$826$		0			0
$827$	−13.5987	+	32.8301i	−0.472872	+	1.14161i	0.490016	+	0.871714i	$0.336991\pi$
$827$	−13.5987	+	32.8301i	−0.472872	+	1.14161i	−0.962888	+	0.269901i	$0.913009\pi$
$828$		0			0
$829$	−41.8074	+	24.1375i	−1.45203	+	0.838331i	−0.998597	−	0.0529588i	$-0.983135\pi$
$829$	−41.8074	+	24.1375i	−1.45203	+	0.838331i	−0.453435	+	0.891289i	$0.649801\pi$
$830$		0			0
$831$	20.1063	−	5.38746i	0.697479	−	0.186889i
$832$		0			0
$833$	−18.5005	−	22.1524i	−0.641005	−	0.767536i
$834$		0			0
$835$	1.00375	−	0.268955i	0.0347364	−	0.00930758i
$836$		0			0
$837$	26.9792	−	15.5764i	0.932537	−	0.538400i
$838$		0			0
$839$	12.5352	−	30.2628i	0.432765	−	1.04479i	−0.545627	−	0.838028i	$-0.683708\pi$
$839$	12.5352	−	30.2628i	0.432765	−	1.04479i	0.978392	−	0.206759i	$-0.0662915\pi$
$840$		0			0
$841$	7.11846	−	7.11846i	0.245464	−	0.245464i
$842$		0			0
$843$	0.880701	+	6.68959i	0.0303330	+	0.230402i
$844$		0			0
$845$	−0.558180	+	4.23980i	−0.0192020	+	0.145853i
$846$		0			0
$847$	−14.2238	−	15.9760i	−0.488737	−	0.548943i
$848$		0			0
$849$	−2.17036	+	3.75917i	−0.0744865	+	0.129014i
$850$		0			0
$851$	−11.7941	−	20.4279i	−0.404296	−	0.700261i
$852$		0			0
$853$	9.61307	+	23.2080i	0.329145	+	0.794627i	0.998656	+	0.0518249i	$0.0165038\pi$
$853$	9.61307	+	23.2080i	0.329145	+	0.794627i	−0.669511	+	0.742802i	$0.733496\pi$
$854$		0			0
$855$	2.62360	−	1.08673i	0.0897253	−	0.0371654i
$856$		0			0
$857$	3.18244	+	24.1731i	0.108710	+	0.825736i	0.955745	+	0.294198i	$0.0950524\pi$
$857$	3.18244	+	24.1731i	0.108710	+	0.825736i	−0.847034	+	0.531538i	$0.821614\pi$
$858$		0			0
$859$	4.36103	+	16.2756i	0.148797	+	0.555316i	0.999557	+	0.0297625i	$0.00947511\pi$
$859$	4.36103	+	16.2756i	0.148797	+	0.555316i	−0.850760	+	0.525554i	$0.823858\pi$
$860$		0			0
$861$	−12.3088	−	8.09169i	−0.419482	−	0.275764i
$862$		0			0
$863$	6.12105	+	3.53399i	0.208363	+	0.120298i	0.600550	−	0.799587i	$-0.294948\pi$
$863$	6.12105	+	3.53399i	0.208363	+	0.120298i	−0.392187	+	0.919885i	$0.628282\pi$
$864$		0			0
$865$	1.30381	−	4.86590i	0.0443310	−	0.165446i
$866$		0			0
$867$	−12.6527	+	6.03935i	−0.429708	+	0.205107i
$868$		0			0
$869$	4.46232	+	4.46232i	0.151374	+	0.151374i
$870$		0			0
$871$	−14.6459	+	8.45584i	−0.496259	+	0.286515i
$872$		0			0
$873$	−12.2134	−	15.9168i	−0.413361	−	0.538702i
$874$		0			0
$875$	−11.5265	+	0.842291i	−0.389667	+	0.0284746i
$876$		0			0
$877$	3.04806	−	2.33886i	0.102926	−	0.0789778i	−0.556016	−	0.831171i	$-0.687671\pi$
$877$	3.04806	−	2.33886i	0.102926	−	0.0789778i	0.658942	+	0.752194i	$0.271004\pi$
$878$		0			0
$879$	−4.33729	−	3.32812i	−0.146293	−	0.112255i
$880$		0			0
$881$	−14.0509	−	33.9219i	−0.473387	−	1.14286i	−0.962657	−	0.270725i	$-0.912737\pi$
$881$	−14.0509	−	33.9219i	−0.473387	−	1.14286i	0.489269	−	0.872133i	$-0.337263\pi$
$882$		0			0
$883$	−23.2671			−0.783000			−0.391500	−	0.920178i	$-0.628044\pi$
$883$	−23.2671			−0.783000			−0.391500	+	0.920178i	$0.628044\pi$
$884$		0			0
$885$	−2.61763	−	4.53387i	−0.0879908	−	0.152404i
$886$		0			0
$887$	48.6676	+	6.40722i	1.63410	+	0.215133i	0.890985	−	0.454032i	$-0.150015\pi$
$887$	48.6676	+	6.40722i	1.63410	+	0.215133i	0.743114	+	0.669165i	$0.233348\pi$
$888$		0			0
$889$	39.7193	+	13.1517i	1.33214	+	0.441095i
$890$		0			0
$891$	−4.52590	+	3.47285i	−0.151623	+	0.116345i
$892$		0			0
$893$	−32.6858	−	8.75814i	−1.09379	−	0.293080i
$894$		0			0
$895$	−0.339997	+	0.820826i	−0.0113649	+	0.0274372i
$896$		0			0
$897$		−	3.21820i		−	0.107452i
$898$		0			0
$899$	11.4867	−	42.8691i	0.383104	−	1.42976i
$900$		0			0
$901$	−14.1786	−	7.69579i	−0.472357	−	0.256384i
$902$		0			0
$903$	20.0040	−	13.5842i	0.665693	−	0.452055i
$904$		0			0
$905$	7.65169	+	4.41771i	0.254351	+	0.146850i
$906$		0			0
$907$	−20.0916	+	2.64511i	−0.667132	+	0.0878296i	−0.456483	−	0.889732i	$-0.650891\pi$
$907$	−20.0916	+	2.64511i	−0.667132	+	0.0878296i	−0.210649	+	0.977562i	$0.567558\pi$
$908$		0			0
$909$	10.0126	−	10.0126i	0.332098	−	0.332098i
$910$		0			0
$911$	−33.1518	−	13.7319i	−1.09837	−	0.454959i	−0.241451	−	0.970413i	$-0.577623\pi$
$911$	−33.1518	−	13.7319i	−1.09837	−	0.454959i	−0.856918	+	0.515454i	$0.827623\pi$
$912$		0			0
$913$	−0.905210	−	0.694592i	−0.0299581	−	0.0229876i
$914$		0			0
$915$	0.831633	+	0.109487i	0.0274929	+	0.00361951i
$916$		0			0
$917$	14.7624	−	5.13487i	0.487497	−	0.169568i
$918$		0			0
$919$	14.8055	−	25.6439i	0.488389	−	0.845915i	−0.511521	−	0.859270i	$-0.670918\pi$
$919$	14.8055	−	25.6439i	0.488389	−	0.845915i	0.999911	+	0.0133554i	$0.00425127\pi$
$920$		0			0
$921$	−3.40400	+	4.43618i	−0.112166	+	0.146177i
$922$		0			0
$923$	9.87199	−	4.08911i	0.324941	−	0.134595i
$924$		0			0
$925$	−49.4773	−	20.4941i	−1.62680	−	0.673843i
$926$		0			0
$927$	33.0128	+	8.84576i	1.08428	+	0.290533i
$928$		0			0
$929$	−30.0692	−	39.1870i	−0.986539	−	1.28568i	−0.958205	−	0.286084i	$-0.907646\pi$
$929$	−30.0692	−	39.1870i	−0.986539	−	1.28568i	−0.0283343	−	0.999599i	$-0.509020\pi$
$930$		0			0
$931$	7.09063	−	17.8714i	0.232386	−	0.585710i
$932$		0			0
$933$	2.50837	−	0.672116i	0.0821204	−	0.0220041i
$934$		0			0
$935$	−3.05085	−	0.731994i	−0.0997735	−	0.0239388i
$936$		0			0
$937$	24.8277	+	24.8277i	0.811086	+	0.811086i	0.984797	−	0.173710i	$-0.0555756\pi$
$937$	24.8277	+	24.8277i	0.811086	+	0.811086i	−0.173710	+	0.984797i	$0.555576\pi$
$938$		0			0
$939$			9.58692i			0.312857i
$940$		0			0
$941$	53.3954	−	7.02963i	1.74064	−	0.229160i	0.807801	−	0.589455i	$-0.200657\pi$
$941$	53.3954	−	7.02963i	1.74064	−	0.229160i	0.932838	+	0.360295i	$0.117324\pi$
$942$		0			0
$943$	−3.69509	−	13.7903i	−0.120329	−	0.449073i
$944$		0			0
$945$	−5.16464	−	0.299653i	−0.168006	−	0.00974770i
$946$		0			0
$947$	0.378169	−	2.87248i	0.0122888	−	0.0933429i	−0.984201	−	0.177053i	$-0.943344\pi$
$947$	0.378169	−	2.87248i	0.0122888	−	0.0933429i	0.996490	+	0.0837100i	$0.0266769\pi$
$948$		0			0
$949$	−9.65832	+	12.5870i	−0.313522	+	0.408590i
$950$		0			0
$951$	10.9199			0.354102
$952$		0			0
$953$	−20.3294			−0.658534			−0.329267	−	0.944237i	$-0.606802\pi$
$953$	−20.3294			−0.658534			−0.329267	+	0.944237i	$0.606802\pi$
$954$		0			0
$955$	1.75691	−	2.28965i	0.0568524	−	0.0740914i
$956$		0			0
$957$	1.14878	−	8.72588i	0.0371349	−	0.282067i
$958$		0			0
$959$	26.7328	−	40.6649i	0.863247	−	1.31314i
$960$		0			0
$961$	−5.02591	−	18.7570i	−0.162126	−	0.605063i
$962$		0			0
$963$	−29.1055	+	3.83182i	−0.937913	+	0.123479i
$964$		0			0
$965$			7.66737i			0.246821i
$966$		0			0
$967$	15.7569	+	15.7569i	0.506708	+	0.506708i	0.913514	−	0.406806i	$-0.133358\pi$
$967$	15.7569	+	15.7569i	0.506708	+	0.506708i	−0.406806	+	0.913514i	$0.633358\pi$
$968$		0			0
$969$	−7.55674	−	5.48868i	−0.242757	−	0.176322i
$970$		0			0
$971$	−14.2462	+	3.81725i	−0.457182	+	0.122501i	−0.480058	−	0.877237i	$-0.659384\pi$
$971$	−14.2462	+	3.81725i	−0.457182	+	0.122501i	0.0228762	+	0.999738i	$0.492718\pi$
$972$		0			0
$973$	3.74667	−	4.33741i	0.120113	−	0.139051i
$974$		0			0
$975$	−4.44791	−	5.79663i	−0.142447	−	0.185641i
$976$		0			0
$977$	−50.3573	−	13.4932i	−1.61107	−	0.431685i	−0.662710	−	0.748876i	$-0.730594\pi$
$977$	−50.3573	−	13.4932i	−1.61107	−	0.431685i	−0.948362	+	0.317191i	$0.897260\pi$
$978$		0			0
$979$	−21.1450	−	8.75856i	−0.675798	−	0.279925i
$980$		0			0
$981$	1.36870	−	0.566933i	0.0436992	−	0.0181008i
$982$		0			0
$983$	−9.64582	+	12.5707i	−0.307654	+	0.400942i	−0.921434	−	0.388535i	$-0.872981\pi$
$983$	−9.64582	+	12.5707i	−0.307654	+	0.400942i	0.613780	+	0.789477i	$0.289648\pi$
$984$		0			0
$985$	−5.10715	+	8.84584i	−0.162727	+	0.281852i
$986$		0			0
$987$	20.3433	+	17.5726i	0.647535	+	0.559343i
$988$		0			0
$989$	23.2354	+	3.05899i	0.738842	+	0.0972704i
$990$		0			0
$991$	−6.67307	−	5.12043i	−0.211977	−	0.162656i	0.497316	−	0.867570i	$-0.334319\pi$
$991$	−6.67307	−	5.12043i	−0.211977	−	0.162656i	−0.709293	+	0.704914i	$0.750986\pi$
$992$		0			0
$993$	−19.0496	−	7.89062i	−0.604522	−	0.250401i
$994$		0			0
$995$	−0.602111	+	0.602111i	−0.0190882	+	0.0190882i
$996$		0			0
$997$	−14.9050	+	1.96228i	−0.472047	+	0.0621461i	−0.362797	−	0.931868i	$-0.618178\pi$
$997$	−14.9050	+	1.96228i	−0.472047	+	0.0621461i	−0.109250	+	0.994014i	$0.534845\pi$
$998$		0			0
$999$	−42.3797	−	24.4679i	−1.34083	−	0.774131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bh.a.457.8	yes	96
7.4	even	3	inner	476.2.bh.a.389.5	yes	96
17.8	even	8	inner	476.2.bh.a.93.5	yes	96
119.25	even	24	inner	476.2.bh.a.25.8	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bh.a.25.8	✓	96	119.25	even	24	inner
476.2.bh.a.93.5	yes	96	17.8	even	8	inner
476.2.bh.a.389.5	yes	96	7.4	even	3	inner
476.2.bh.a.457.8	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.502054 - 0.654289i) q^{3} +(-0.0581723 + 0.441862i) q^{5} +(1.18794 + 2.36407i) q^{7} +(0.600421 + 2.24080i) q^{9} +O(q^{10})\)	\(q+(0.502054 - 0.654289i) q^{3} +(-0.0581723 + 0.441862i) q^{5} +(1.18794 + 2.36407i) q^{7} +(0.600421 + 2.24080i) q^{9} +(1.69278 - 0.222859i) q^{11} -1.84519i q^{13} +(0.259900 + 0.259900i) q^{15} +(-0.961961 + 4.00932i) q^{17} +(-2.65307 + 0.710888i) q^{19} +(2.14319 + 0.409634i) q^{21} +(1.28741 + 1.67778i) q^{23} +(4.63777 + 1.24269i) q^{25} +(4.05338 + 1.67897i) q^{27} +(5.77458 - 2.39191i) q^{29} +(4.32258 - 5.63329i) q^{31} +(0.704053 - 1.21946i) q^{33} +(-1.11370 + 0.387382i) q^{35} +(-11.0584 - 1.45587i) q^{37} +(-1.20729 - 0.926383i) q^{39} +(-6.23698 - 2.58344i) q^{41} +(7.83604 - 7.83604i) q^{43} +(-1.02505 + 0.134951i) q^{45} +(10.6694 + 6.16000i) q^{47} +(-4.17761 + 5.61672i) q^{49} +(2.14030 + 2.64229i) q^{51} +(-1.01268 + 3.77938i) q^{53} +0.760940i q^{55} +(-0.866858 + 2.09278i) q^{57} +(-13.7582 - 3.68649i) q^{59} +(1.81054 - 1.38928i) q^{61} +(-4.58414 + 4.08136i) q^{63} +(0.815318 + 0.107339i) q^{65} +(-4.58265 - 7.93738i) q^{67} +1.74411 q^{69} +(2.21610 + 5.35013i) q^{71} +(-6.82152 - 5.23433i) q^{73} +(3.14149 - 2.41055i) q^{75} +(2.53777 + 3.73710i) q^{77} +(2.25004 + 2.93231i) q^{79} +(-2.89359 + 1.67062i) q^{81} +(-0.472537 - 0.472537i) q^{83} +(-1.71561 - 0.658285i) q^{85} +(1.33415 - 4.97912i) q^{87} +(-11.6089 - 6.70241i) q^{89} +(4.36214 - 2.19196i) q^{91} +(-1.51564 - 5.65643i) q^{93} +(-0.159779 - 1.21365i) q^{95} +(-7.98997 + 3.30955i) q^{97} +(1.51576 + 3.65937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{5}+O(q^{10}) \) 96 * q + 4 * q^5	\( 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) \) 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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