LMFDB - Embedded newform 825.2.bi.h.326.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(101,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("825.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bi (of order $10$, degree $4$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			326.8
Character	$\chi$	$=$	825.326
Dual form			825.2.bi.h.701.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.568905 - 0.413334i) q^{2} +(0.247937 - 1.71421i) q^{3} +(-0.465226 - 1.43182i) q^{4} +(-0.849595 + 0.872744i) q^{6} +(1.89391 - 0.615368i) q^{7} +(-0.761754 + 2.34444i) q^{8} +(-2.87705 - 0.850033i) q^{9} +O(q^{10})$	\(q+(-0.568905 - 0.413334i) q^{2} +(0.247937 - 1.71421i) q^{3} +(-0.465226 - 1.43182i) q^{4} +(-0.849595 + 0.872744i) q^{6} +(1.89391 - 0.615368i) q^{7} +(-0.761754 + 2.34444i) q^{8} +(-2.87705 - 0.850033i) q^{9} +(-3.26241 + 0.597209i) q^{11} +(-2.56979 + 0.442496i) q^{12} +(-2.49497 + 3.43403i) q^{13} +(-1.33181 - 0.432730i) q^{14} +(-1.03355 + 0.750920i) q^{16} +(-3.45873 + 2.51291i) q^{17} +(1.28542 + 1.67277i) q^{18} +(-0.257486 - 0.0836623i) q^{19} +(-0.585303 - 3.39914i) q^{21} +(2.10285 + 1.00871i) q^{22} +4.30856i q^{23} +(3.83000 + 1.88708i) q^{24} +(2.83880 - 0.922383i) q^{26} +(-2.17047 + 4.72113i) q^{27} +(-1.76219 - 2.42545i) q^{28} +(-2.26468 - 6.96997i) q^{29} +(-5.24479 - 3.81056i) q^{31} +5.82855 q^{32} +(0.214872 + 5.74054i) q^{33} +3.00636 q^{34} +(0.121388 + 4.51488i) q^{36} +(-1.84185 - 5.66863i) q^{37} +(0.111905 + 0.154024i) q^{38} +(5.26807 + 5.12834i) q^{39} +(2.95108 - 9.08248i) q^{41} +(-1.07200 + 2.17571i) q^{42} -1.68949i q^{43} +(2.37285 + 4.39334i) q^{44} +(1.78087 - 2.45116i) q^{46} +(-0.222639 - 0.0723398i) q^{47} +(1.03098 + 1.95791i) q^{48} +(-2.45491 + 1.78359i) q^{49} +(3.45012 + 6.55204i) q^{51} +(6.07763 + 1.97474i) q^{52} +(-4.07659 + 5.61095i) q^{53} +(3.18619 - 1.78875i) q^{54} +4.90891i q^{56} +(-0.207255 + 0.420643i) q^{57} +(-1.59253 + 4.90132i) q^{58} +(-10.0360 + 3.26089i) q^{59} +(5.68030 + 7.81826i) q^{61} +(1.40875 + 4.33570i) q^{62} +(-5.97196 + 0.160564i) q^{63} +(-1.24878 - 0.907295i) q^{64} +(2.25052 - 3.35464i) q^{66} -0.901700 q^{67} +(5.20712 + 3.78319i) q^{68} +(7.38579 + 1.06825i) q^{69} +(-0.309146 - 0.425503i) q^{71} +(4.18446 - 6.09756i) q^{72} +(9.79830 - 3.18366i) q^{73} +(-1.29520 + 3.98621i) q^{74} +0.407595i q^{76} +(-5.81121 + 3.13864i) q^{77} +(-0.877318 - 5.09501i) q^{78} +(-0.132574 + 0.182473i) q^{79} +(7.55489 + 4.89118i) q^{81} +(-5.43298 + 3.94729i) q^{82} +(1.62687 - 1.18199i) q^{83} +(-4.59464 + 2.41941i) q^{84} +(-0.698323 + 0.961159i) q^{86} +(-12.5095 + 2.15403i) q^{87} +(1.08504 - 8.10345i) q^{88} -15.8563i q^{89} +(-2.61205 + 8.03907i) q^{91} +(6.16907 - 2.00445i) q^{92} +(-7.83249 + 8.04591i) q^{93} +(0.0967600 + 0.133179i) q^{94} +(1.44511 - 9.99138i) q^{96} +(2.67133 + 1.94083i) q^{97} +2.13383 q^{98} +(9.89379 + 1.05496i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	$ 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) $ 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.568905	−	0.413334i	−0.402277	−	0.292271i	0.368191	−	0.929750i	$-0.379977\pi$
$2$	−0.568905	−	0.413334i	−0.402277	−	0.292271i	−0.770468	+	0.637479i	$0.779977\pi$
$3$	0.247937	−	1.71421i	0.143146	−	0.989702i
$3$	0.247937	−	1.71421i	0.143146	−	0.989702i
$4$	−0.465226	−	1.43182i	−0.232613	−	0.715909i
$5$		0			0
$5$		0			0
$6$	−0.849595	+	0.872744i	−0.346846	+	0.356296i
$7$	1.89391	−	0.615368i	0.715830	−	0.232587i	0.0716158	−	0.997432i	$-0.477184\pi$
$7$	1.89391	−	0.615368i	0.715830	−	0.232587i	0.644214	+	0.764845i	$0.277184\pi$
$8$	−0.761754	+	2.34444i	−0.269321	+	0.828884i
$9$	−2.87705	−	0.850033i	−0.959018	−	0.283344i
$10$		0			0
$11$	−3.26241	+	0.597209i	−0.983655	+	0.180065i
$11$	−3.26241	+	0.597209i	−0.983655	+	0.180065i
$12$	−2.56979	+	0.442496i	−0.741834	+	0.127738i
$13$	−2.49497	+	3.43403i	−0.691980	+	0.952429i	0.308019	+	0.951380i	$0.400334\pi$
$13$	−2.49497	+	3.43403i	−0.691980	+	0.952429i	−0.999999	+	0.00104920i	$0.999666\pi$
$14$	−1.33181	−	0.432730i	−0.355940	−	0.115652i
$15$		0			0
$16$	−1.03355	+	0.750920i	−0.258388	+	0.187730i
$17$	−3.45873	+	2.51291i	−0.838864	+	0.609471i	−0.922053	−	0.387063i	$-0.873490\pi$
$17$	−3.45873	+	2.51291i	−0.838864	+	0.609471i	0.0831888	+	0.996534i	$0.473490\pi$
$18$	1.28542	+	1.67277i	0.302977	+	0.394276i
$19$	−0.257486	−	0.0836623i	−0.0590714	−	0.0191935i	0.279332	−	0.960195i	$-0.409887\pi$
$19$	−0.257486	−	0.0836623i	−0.0590714	−	0.0191935i	−0.338404	+	0.941001i	$0.609887\pi$
$20$		0			0
$21$	−0.585303	−	3.39914i	−0.127724	−	0.741752i
$22$	2.10285	+	1.00871i	0.448329	+	0.215058i
$23$			4.30856i			0.898397i	0.893432	+	0.449198i	$0.148290\pi$
$23$			4.30856i			0.898397i	−0.893432	+	0.449198i	$0.851710\pi$
$24$	3.83000	+	1.88708i	0.781795	+	0.385199i
$25$		0			0
$26$	2.83880	−	0.922383i	0.556735	−	0.180894i
$27$	−2.17047	+	4.72113i	−0.417706	+	0.908582i
$28$	−1.76219	−	2.42545i	−0.333023	−	0.458366i
$29$	−2.26468	−	6.96997i	−0.420540	−	1.29429i	−0.907200	−	0.420699i	$-0.861785\pi$
$29$	−2.26468	−	6.96997i	−0.420540	−	1.29429i	0.486660	−	0.873591i	$-0.338215\pi$
$30$		0			0
$31$	−5.24479	−	3.81056i	−0.941992	−	0.684397i	0.00690742	−	0.999976i	$-0.497801\pi$
$31$	−5.24479	−	3.81056i	−0.941992	−	0.684397i	−0.948899	+	0.315579i	$0.897801\pi$
$32$	5.82855			1.03035
$33$	0.214872	+	5.74054i	0.0374044	+	0.999300i
$34$	3.00636			0.515586
$35$		0			0
$36$	0.121388	+	4.51488i	0.0202313	+	0.752479i
$37$	−1.84185	−	5.66863i	−0.302798	−	0.931917i	−0.980490	−	0.196571i	$-0.937020\pi$
$37$	−1.84185	−	5.66863i	−0.302798	−	0.931917i	0.677692	−	0.735346i	$-0.262980\pi$
$38$	0.111905	+	0.154024i	0.0181533	+	0.0249859i
$39$	5.26807	+	5.12834i	0.843566	+	0.821191i
$40$		0			0
$41$	2.95108	−	9.08248i	0.460881	−	1.41844i	−0.403210	−	0.915108i	$-0.632105\pi$
$41$	2.95108	−	9.08248i	0.460881	−	1.41844i	0.864090	−	0.503337i	$-0.167895\pi$
$42$	−1.07200	+	2.17571i	−0.165413	+	0.335719i
$43$		−	1.68949i		−	0.257645i	−0.991668	−	0.128822i	$-0.958880\pi$
$43$		−	1.68949i		−	0.257645i	0.991668	−	0.128822i	$-0.0411197\pi$
$44$	2.37285	+	4.39334i	0.357721	+	0.662322i
$45$		0			0
$46$	1.78087	−	2.45116i	0.262575	−	0.361404i
$47$	−0.222639	−	0.0723398i	−0.0324752	−	0.0105518i	0.292734	−	0.956194i	$-0.405435\pi$
$47$	−0.222639	−	0.0723398i	−0.0324752	−	0.0105518i	−0.325210	+	0.945642i	$0.605435\pi$
$48$	1.03098	+	1.95791i	0.148809	+	0.282600i
$49$	−2.45491	+	1.78359i	−0.350701	+	0.254799i
$50$		0			0
$51$	3.45012	+	6.55204i	0.483114	+	0.917469i
$52$	6.07763	+	1.97474i	0.842816	+	0.273848i
$53$	−4.07659	+	5.61095i	−0.559963	+	0.770723i	−0.991322	−	0.131458i	$-0.958034\pi$
$53$	−4.07659	+	5.61095i	−0.559963	+	0.770723i	0.431359	+	0.902180i	$0.358034\pi$
$54$	3.18619	−	1.78875i	0.433586	−	0.243418i
$55$		0			0
$56$			4.90891i			0.655981i
$57$	−0.207255	+	0.420643i	−0.0274516	+	0.0557156i
$58$	−1.59253	+	4.90132i	−0.209110	+	0.643574i
$59$	−10.0360	+	3.26089i	−1.30657	+	0.424531i	−0.877864	−	0.478911i	$-0.841032\pi$
$59$	−10.0360	+	3.26089i	−1.30657	+	0.424531i	−0.428710	+	0.903442i	$0.641032\pi$
$60$		0			0
$61$	5.68030	+	7.81826i	0.727288	+	1.00103i	0.999250	+	0.0387180i	$0.0123274\pi$
$61$	5.68030	+	7.81826i	0.727288	+	1.00103i	−0.271962	+	0.962308i	$0.587673\pi$
$62$	1.40875	+	4.33570i	0.178912	+	0.550634i
$63$	−5.97196	+	0.160564i	−0.752396	+	0.0202291i
$64$	−1.24878	−	0.907295i	−0.156098	−	0.113412i
$65$		0			0
$66$	2.25052	−	3.35464i	0.277020	−	0.412927i
$67$	−0.901700			−0.110160			−0.0550801	−	0.998482i	$-0.517541\pi$
$67$	−0.901700			−0.110160			−0.0550801	+	0.998482i	$0.517541\pi$
$68$	5.20712	+	3.78319i	0.631456	+	0.458780i
$69$	7.38579	+	1.06825i	0.889145	+	0.128602i
$70$		0			0
$71$	−0.309146	−	0.425503i	−0.0366889	−	0.0504979i	0.790278	−	0.612748i	$-0.209936\pi$
$71$	−0.309146	−	0.425503i	−0.0366889	−	0.0504979i	−0.826967	+	0.562250i	$0.809936\pi$
$72$	4.18446	−	6.09756i	0.493143	−	0.718604i
$73$	9.79830	−	3.18366i	1.14680	−	0.372619i	0.326866	−	0.945071i	$-0.394008\pi$
$73$	9.79830	−	3.18366i	1.14680	−	0.372619i	0.819939	+	0.572451i	$0.194008\pi$
$74$	−1.29520	+	3.98621i	−0.150564	+	0.463387i
$75$		0			0
$76$			0.407595i			0.0467544i
$77$	−5.81121	+	3.13864i	−0.662249	+	0.357682i
$78$	−0.877318	−	5.09501i	−0.0993367	−	0.576896i
$79$	−0.132574	+	0.182473i	−0.0149158	+	0.0205298i	−0.816410	−	0.577473i	$-0.804039\pi$
$79$	−0.132574	+	0.182473i	−0.0149158	+	0.0205298i	0.801494	+	0.598003i	$0.204039\pi$
$80$		0			0
$81$	7.55489	+	4.89118i	0.839432	+	0.543465i
$82$	−5.43298	+	3.94729i	−0.599972	+	0.435905i
$83$	1.62687	−	1.18199i	0.178572	−	0.129740i	−0.494909	−	0.868945i	$-0.664799\pi$
$83$	1.62687	−	1.18199i	0.178572	−	0.129740i	0.673480	+	0.739205i	$0.264799\pi$
$84$	−4.59464	+	2.41941i	−0.501317	+	0.263980i
$85$		0			0
$86$	−0.698323	+	0.961159i	−0.0753021	+	0.103644i
$87$	−12.5095	+	2.15403i	−1.34116	+	0.230937i
$88$	1.08504	−	8.10345i	0.115665	−	0.863831i
$89$		−	15.8563i		−	1.68076i	−0.541995	−	0.840382i	$-0.682331\pi$
$89$		−	15.8563i		−	1.68076i	0.541995	−	0.840382i	$-0.317669\pi$
$90$		0			0
$91$	−2.61205	+	8.03907i	−0.273817	+	0.842724i
$92$	6.16907	−	2.00445i	0.643170	−	0.208979i
$93$	−7.83249	+	8.04591i	−0.812192	+	0.834322i
$94$	0.0967600	+	0.133179i	0.00998003	+	0.0137363i
$95$		0			0
$96$	1.44511	−	9.99138i	0.147491	−	1.01974i
$97$	2.67133	+	1.94083i	0.271232	+	0.197062i	0.715084	−	0.699038i	$-0.246388\pi$
$97$	2.67133	+	1.94083i	0.271232	+	0.197062i	−0.443852	+	0.896100i	$0.646388\pi$
$98$	2.13383			0.215549
$99$	9.89379	+	1.05496i	0.994363	+	0.106027i
$100$		0			0
$101$	−1.38290	−	1.00474i	−0.137604	−	0.0999752i	0.516854	−	0.856074i	$-0.327103\pi$
$101$	−1.38290	−	1.00474i	−0.137604	−	0.0999752i	−0.654458	+	0.756098i	$0.727103\pi$
$102$	0.745387	−	5.15354i	0.0738043	−	0.510276i
$103$	−1.83229	−	5.63920i	−0.180541	−	0.555647i	0.819303	−	0.573361i	$-0.194361\pi$
$103$	−1.83229	−	5.63920i	−0.180541	−	0.555647i	−0.999843	+	0.0177148i	$0.994361\pi$
$104$	−6.15032	−	8.46519i	−0.603089	−	0.830080i
$105$		0			0
$106$	4.63839	−	1.50710i	0.450520	−	0.146383i
$107$	−0.977849	+	3.00951i	−0.0945322	+	0.290940i	−0.987131	−	0.159911i	$-0.948879\pi$
$107$	−0.977849	+	3.00951i	−0.0945322	+	0.290940i	0.892599	+	0.450851i	$0.148879\pi$
$108$	7.76956	+	0.911318i	0.747626	+	0.0876917i
$109$			3.60358i			0.345160i	0.984996	+	0.172580i	$0.0552103\pi$
$109$			3.60358i			0.345160i	−0.984996	+	0.172580i	$0.944790\pi$
$110$		0			0
$111$	−10.1739	+	1.75186i	−0.965664	+	0.166279i
$112$	−1.49536	+	2.05819i	−0.141298	+	0.194481i
$113$	−7.31255	−	2.37599i	−0.687907	−	0.223515i	−0.0558532	−	0.998439i	$-0.517788\pi$
$113$	−7.31255	−	2.37599i	−0.687907	−	0.223515i	−0.632054	+	0.774924i	$0.717788\pi$
$114$	0.291775	−	0.153640i	0.0273272	−	0.0143897i
$115$		0			0
$116$	−8.92613	+	6.48522i	−0.828771	+	0.602137i
$117$	10.0972	−	7.75909i	0.933487	−	0.717328i
$118$	7.05735	+	2.29307i	0.649682	+	0.211095i
$119$	−5.00415	+	6.88762i	−0.458729	+	0.631387i
$120$		0			0
$121$	10.2867	−	3.89669i	0.935153	−	0.354244i
$122$		−	6.79571i		−	0.615254i
$123$	−14.8376	−	7.31065i	−1.33786	−	0.659179i
$124$	−3.01602	+	9.28235i	−0.270847	+	0.833580i
$125$		0			0
$126$	3.46385	+	2.37707i	0.308584	+	0.211766i
$127$	−5.91381	−	8.13967i	−0.524766	−	0.722279i	0.461555	−	0.887111i	$-0.347292\pi$
$127$	−5.91381	−	8.13967i	−0.524766	−	0.722279i	−0.986322	+	0.164833i	$0.947292\pi$
$128$	−3.26682	−	10.0542i	−0.288749	−	0.888677i
$129$	−2.89614	−	0.418886i	−0.254991	−	0.0368809i
$130$		0			0
$131$	−15.8485			−1.38469			−0.692345	−	0.721567i	$-0.743422\pi$
$131$	−15.8485			−1.38469			−0.692345	+	0.721567i	$0.743422\pi$
$132$	8.11945	−	2.97831i	0.706707	−	0.259228i
$133$	−0.539138			−0.0467492
$134$	0.512982	+	0.372703i	0.0443149	+	0.0321966i
$135$		0			0
$136$	−3.25667	−	10.0230i	−0.279257	−	0.859464i
$137$	−7.45199	−	10.2568i	−0.636667	−	0.876296i	0.361766	−	0.932269i	$-0.382174\pi$
$137$	−7.45199	−	10.2568i	−0.636667	−	0.876296i	−0.998432	+	0.0559727i	$0.982174\pi$
$138$	−3.76027	−	3.66053i	−0.320095	−	0.311605i
$139$	14.4997	−	4.71125i	1.22985	−	0.399603i	0.379192	−	0.925318i	$-0.376202\pi$
$139$	14.4997	−	4.71125i	1.22985	−	0.399603i	0.850661	+	0.525715i	$0.176202\pi$
$140$		0			0
$141$	−0.179206	+	0.363715i	−0.0150919	+	0.0306303i
$142$			0.369851i			0.0310372i
$143$	6.08879	−	12.6933i	0.509170	−	1.06146i
$144$	3.61190	−	1.28188i	0.300991	−	0.106824i
$145$		0			0
$146$	−6.89022	−	2.23877i	−0.570238	−	0.185282i
$147$	2.44880	+	4.65045i	0.201974	+	0.383563i
$148$	−7.25957	+	5.27438i	−0.596733	+	0.433552i
$149$	−7.06258	+	5.13126i	−0.578589	+	0.420370i	−0.838215	−	0.545340i	$-0.816401\pi$
$149$	−7.06258	+	5.13126i	−0.578589	+	0.420370i	0.259626	+	0.965709i	$0.416401\pi$
$150$		0			0
$151$	−17.9932	−	5.84634i	−1.46426	−	0.475768i	−0.534895	−	0.844919i	$-0.679649\pi$
$151$	−17.9932	−	5.84634i	−1.46426	−	0.475768i	−0.929370	+	0.369150i	$0.879649\pi$
$152$	0.392282	−	0.539930i	0.0318183	−	0.0437941i
$153$	12.0870	−	4.28975i	0.977176	−	0.346806i
$154$	4.60333	+	0.616378i	0.370947	+	0.0496691i
$155$		0			0
$156$	4.89200	−	9.92875i	0.391673	−	0.794936i
$157$	−4.41663	+	13.5930i	−0.352486	+	1.08484i	0.604968	+	0.796250i	$0.293186\pi$
$157$	−4.41663	+	13.5930i	−0.352486	+	1.08484i	−0.957453	+	0.288589i	$0.906814\pi$
$158$	0.150845	−	0.0490124i	0.0120005	−	0.00389921i
$159$	8.60762	+	8.37931i	0.682629	+	0.664522i
$160$		0			0
$161$	2.65135	+	8.16002i	0.208956	+	0.643100i
$162$	−2.27632	−	5.90531i	−0.178845	−	0.463965i
$163$	18.2456	+	13.2562i	1.42910	+	1.03831i	0.990183	+	0.139780i	$0.0446395\pi$
$163$	18.2456	+	13.2562i	1.42910	+	1.03831i	0.438922	+	0.898525i	$0.355360\pi$
$164$	−14.3774			−1.12268
$165$		0			0
$166$	−1.41409			−0.109754
$167$	−4.33906	−	3.15252i	−0.335767	−	0.243949i	0.407107	−	0.913381i	$-0.366538\pi$
$167$	−4.33906	−	3.15252i	−0.335767	−	0.243949i	−0.742874	+	0.669432i	$0.766538\pi$
$168$	8.41492	+	1.21710i	0.649225	+	0.0939012i
$169$	−1.55048	−	4.77189i	−0.119268	−	0.367069i
$170$		0			0
$171$	0.669686	+	0.459573i	0.0512122	+	0.0351444i
$172$	−2.41904	+	0.785994i	−0.184450	+	0.0599315i
$173$	5.03829	−	15.5063i	0.383054	−	1.17892i	−0.554828	−	0.831965i	$-0.687216\pi$
$173$	5.03829	−	15.5063i	0.383054	−	1.17892i	0.937882	−	0.346954i	$-0.112784\pi$
$174$	8.00706	+	3.94516i	0.607013	+	0.299082i
$175$		0			0
$176$	2.92342	−	3.06706i	0.220361	−	0.231188i
$177$	3.10157	+	18.0123i	0.233128	+	1.35389i
$178$	−6.55394	+	9.02072i	−0.491239	+	0.676132i
$179$	−0.255080	−	0.0828804i	−0.0190655	−	0.00619477i	0.299469	−	0.954106i	$-0.403191\pi$
$179$	−0.255080	−	0.0828804i	−0.0190655	−	0.00619477i	−0.318534	+	0.947911i	$0.603191\pi$
$180$		0			0
$181$	−0.172984	+	0.125680i	−0.0128578	+	0.00934174i	−0.594196	−	0.804321i	$-0.702529\pi$
$181$	−0.172984	+	0.125680i	−0.0128578	+	0.00934174i	0.581338	+	0.813662i	$0.302529\pi$
$182$	4.80883	−	3.49382i	0.356454	−	0.258979i
$183$	14.8105	−	7.79881i	1.09483	−	0.576505i
$184$	−10.1012	−	3.28206i	−0.744667	−	0.241957i
$185$		0			0
$186$	7.78159	−	1.33993i	0.570574	−	0.0982481i
$187$	9.78306	−	10.2637i	0.715408	−	0.750559i
$188$			0.352433i			0.0257038i
$189$	−1.20543	+	10.2770i	−0.0876820	+	0.747544i
$190$		0			0
$191$	3.78974	−	1.23136i	0.274216	−	0.0890981i	−0.168681	−	0.985671i	$-0.553951\pi$
$191$	3.78974	−	1.23136i	0.274216	−	0.0890981i	0.442897	+	0.896573i	$0.353951\pi$
$192$	−1.86492	+	1.91573i	−0.134589	+	0.138256i
$193$	−9.51974	−	13.1028i	−0.685246	−	0.943160i	0.314736	−	0.949179i	$-0.398084\pi$
$193$	−9.51974	−	13.1028i	−0.685246	−	0.943160i	−0.999982	+	0.00601903i	$0.998084\pi$
$194$	−0.717520	−	2.20830i	−0.0515149	−	0.158547i
$195$		0			0
$196$	3.69587	+	2.68521i	0.263991	+	0.191800i
$197$	5.69572			0.405803			0.202902	−	0.979199i	$-0.434963\pi$
$197$	5.69572			0.405803			0.202902	+	0.979199i	$0.434963\pi$
$198$	−5.19258	−	4.68961i	−0.369020	−	0.333276i
$199$	−12.2362			−0.867398			−0.433699	−	0.901058i	$-0.642792\pi$
$199$	−12.2362			−0.867398			−0.433699	+	0.901058i	$0.642792\pi$
$200$		0			0
$201$	−0.223565	+	1.54571i	−0.0157690	+	0.109026i
$202$	0.371449	+	1.14320i	0.0261350	+	0.0804354i
$203$	−8.57819	−	11.8069i	−0.602071	−	0.828680i
$204$	7.77624	−	7.98812i	0.544446	−	0.559280i
$205$		0			0
$206$	−1.28847	+	3.96551i	−0.0897722	+	0.276290i
$207$	3.66242	−	12.3960i	0.254556	−	0.861579i
$208$		−	5.42278i		−	0.376002i
$209$	0.889990	+	0.119168i	0.0615619	+	0.00824303i
$210$		0			0
$211$	−2.15988	+	2.97283i	−0.148693	+	0.204658i	−0.876866	−	0.480736i	$-0.840370\pi$
$211$	−2.15988	+	2.97283i	−0.148693	+	0.204658i	0.728173	+	0.685393i	$0.240370\pi$
$212$	9.93039	+	3.22658i	0.682022	+	0.221602i
$213$	−0.806051	+	0.424444i	−0.0552297	+	0.0290824i
$214$	1.80023	−	1.30795i	0.123061	−	0.0894094i
$215$		0			0
$216$	−9.41504	−	8.68486i	−0.640612	−	0.590930i
$217$	−12.2780	−	3.98938i	−0.833488	−	0.270817i
$218$	1.48948	−	2.05009i	0.100880	−	0.138850i
$219$	−3.02812	−	17.5857i	−0.204621	−	1.18833i
$220$		0			0
$221$		−	18.1470i		−	1.22070i
$222$	6.51209	+	3.20857i	0.437063	+	0.215345i
$223$	−4.88195	+	15.0251i	−0.326920	+	1.00616i	0.643647	+	0.765323i	$0.277421\pi$
$223$	−4.88195	+	15.0251i	−0.326920	+	1.00616i	−0.970567	+	0.240833i	$0.922579\pi$
$224$	11.0387	−	3.58670i	0.737557	−	0.239647i
$225$		0			0
$226$	3.17807	+	4.37424i	0.211402	+	0.290970i
$227$	0.431484	+	1.32797i	0.0286386	+	0.0881405i	0.964354	−	0.264615i	$-0.0852448\pi$
$227$	0.431484	+	1.32797i	0.0286386	+	0.0881405i	−0.935716	+	0.352755i	$0.885245\pi$
$228$	0.698705	+	0.101058i	0.0462729	+	0.00669272i
$229$	−8.52126	−	6.19106i	−0.563101	−	0.409117i	0.269492	−	0.963003i	$-0.413144\pi$
$229$	−8.52126	−	6.19106i	−0.563101	−	0.409117i	−0.832593	+	0.553886i	$0.813144\pi$
$230$		0			0
$231$	3.93949	+	10.7398i	0.259200	+	0.706629i
$232$	18.0658			1.18608
$233$	12.6635	+	9.20055i	0.829611	+	0.602748i	0.919449	−	0.393208i	$-0.128635\pi$
$233$	12.6635	+	9.20055i	0.829611	+	0.602748i	−0.0898380	+	0.995956i	$0.528635\pi$
$234$	−8.95145	+	0.240671i	−0.585174	+	0.0157331i
$235$		0			0
$236$	9.33799	+	12.8526i	0.607852	+	0.836636i
$237$	0.279928	+	0.272503i	0.0181833	+	0.0177009i
$238$	5.69377	−	1.85002i	0.369072	−	0.119919i
$239$	5.67665	−	17.4709i	0.367192	−	1.13010i	−0.581405	−	0.813614i	$-0.697497\pi$
$239$	5.67665	−	17.4709i	0.367192	−	1.13010i	0.948597	−	0.316487i	$-0.102503\pi$
$240$		0			0
$241$			1.75403i			0.112987i	0.998403	+	0.0564935i	$0.0179920\pi$
$241$			1.75403i			0.112987i	−0.998403	+	0.0564935i	$0.982008\pi$
$242$	−7.46278	−	2.03499i	−0.479725	−	0.130814i
$243$	10.2577	−	11.7380i	0.658029	−	0.752992i
$244$	8.55170	−	11.7704i	0.547467	−	0.753523i
$245$		0			0
$246$	5.41946	+	10.2920i	0.345532	+	0.656191i
$247$	0.929720	−	0.675481i	0.0591567	−	0.0429798i
$248$	12.9289	−	9.39337i	0.820984	−	0.596480i
$249$	−1.62282	−	3.08185i	−0.102842	−	0.195304i
$250$		0			0
$251$	6.58509	−	9.06359i	0.415647	−	0.572089i	−0.548937	−	0.835863i	$-0.684967\pi$
$251$	6.58509	−	9.06359i	0.415647	−	0.572089i	0.964584	+	0.263775i	$0.0849675\pi$
$252$	3.00821	+	8.47606i	0.189499	+	0.533942i
$253$	−2.57311	−	14.0563i	−0.161770	−	0.883712i
$254$			7.07508i			0.443930i
$255$		0			0
$256$	−3.25123	+	10.0063i	−0.203202	+	0.625391i
$257$	−5.91235	+	1.92104i	−0.368802	+	0.119831i	−0.487554	−	0.873093i	$-0.662111\pi$
$257$	−5.91235	+	1.92104i	−0.368802	+	0.119831i	0.118752	+	0.992924i	$0.462111\pi$
$258$	1.47449	+	1.43538i	0.0917978	+	0.0893629i
$259$	−6.97659	−	9.60245i	−0.433504	−	0.596667i
$260$		0			0
$261$	0.590906	+	21.9780i	0.0365762	+	1.36041i
$262$	9.01629	+	6.55072i	0.557028	+	0.404705i
$263$	−24.0702			−1.48423			−0.742116	−	0.670272i	$-0.766178\pi$
$263$	−24.0702			−1.48423			−0.742116	+	0.670272i	$0.766178\pi$
$264$	−13.6220	−	3.86913i	−0.838378	−	0.238128i
$265$		0			0
$266$	0.306719	+	0.222844i	0.0188061	+	0.0136634i
$267$	−27.1811	−	3.93136i	−1.66345	−	0.240595i
$268$	0.419494	+	1.29107i	0.0256247	+	0.0788647i
$269$	14.8417	+	20.4278i	0.904912	+	1.24550i	0.968875	+	0.247552i	$0.0796262\pi$
$269$	14.8417	+	20.4278i	0.904912	+	1.24550i	−0.0639625	+	0.997952i	$0.520374\pi$
$270$		0			0
$271$	21.3742	−	6.94489i	1.29839	−	0.421872i	0.423368	−	0.905958i	$-0.360848\pi$
$271$	21.3742	−	6.94489i	1.29839	−	0.421872i	0.875020	+	0.484086i	$0.160848\pi$
$272$	1.68778	−	5.19446i	0.102337	−	0.314960i
$273$	13.1331	+	6.47080i	0.794849	+	0.391630i
$274$			8.91530i			0.538593i
$275$		0			0
$276$	−1.90652	−	11.0721i	−0.114759	−	0.666461i
$277$	−5.74963	+	7.91369i	−0.345462	+	0.475488i	−0.946027	−	0.324088i	$-0.894942\pi$
$277$	−5.74963	+	7.91369i	−0.345462	+	0.475488i	0.600565	+	0.799576i	$0.294942\pi$
$278$	−10.1963	−	3.31298i	−0.611533	−	0.198699i
$279$	11.8504	+	15.4214i	0.709467	+	0.923257i
$280$		0			0
$281$	11.0817	−	8.05131i	0.661078	−	0.480301i	−0.205949	−	0.978563i	$-0.566028\pi$
$281$	11.0817	−	8.05131i	0.661078	−	0.480301i	0.867027	+	0.498262i	$0.166028\pi$
$282$	0.252287	−	0.132847i	0.0150235	−	0.00791095i
$283$	−28.3920	−	9.22512i	−1.68773	−	0.548376i	−0.701343	−	0.712824i	$-0.747416\pi$
$283$	−28.3920	−	9.22512i	−1.68773	−	0.548376i	−0.986386	+	0.164448i	$0.947416\pi$
$284$	−0.465420	+	0.640595i	−0.0276176	+	0.0380123i
$285$		0			0
$286$	−8.71049	+	4.70455i	−0.515062	+	0.278186i
$287$		−	19.0174i		−	1.12256i
$288$	−16.7691	−	4.95446i	−0.988126	−	0.291944i
$289$	0.394774	−	1.21499i	0.0232220	−	0.0714700i
$290$		0			0
$291$	3.98932	−	4.09802i	0.233858	−	0.240230i
$292$	−9.11684	−	12.5483i	−0.533523	−	0.734331i
$293$	7.53977	+	23.2050i	0.440478	+	1.35565i	0.887367	+	0.461063i	$0.152532\pi$
$293$	7.53977	+	23.2050i	0.440478	+	1.35565i	−0.446889	+	0.894589i	$0.647468\pi$
$294$	0.529055	−	3.65784i	0.0308551	−	0.213329i
$295$		0			0
$296$	14.6928			0.854001
$297$	4.26145	−	16.6985i	0.247275	−	0.968945i
$298$	6.13886			0.355615
$299$	−14.7957	−	10.7497i	−0.855660	−	0.621673i
$300$		0			0
$301$	−1.03966	−	3.19974i	−0.0599249	−	0.184430i
$302$	7.81992	+	10.7632i	0.449986	+	0.619353i
$303$	−2.06521	+	2.12148i	−0.118643	+	0.121876i
$304$	0.328949	−	0.106882i	0.0188665	−	0.00613011i
$305$		0			0
$306$	−8.64946	−	2.55550i	−0.494457	−	0.146088i
$307$		−	7.28242i		−	0.415630i	−0.978168	−	0.207815i	$-0.933365\pi$
$307$		−	7.28242i		−	0.415630i	0.978168	−	0.207815i	$-0.0666352\pi$
$308$	7.19749	+	6.86041i	0.410115	+	0.390908i
$309$	−10.1211	+	1.74277i	−0.575768	+	0.0991425i
$310$		0			0
$311$	−2.25383	−	0.732315i	−0.127803	−	0.0415258i	0.244417	−	0.969670i	$-0.421403\pi$
$311$	−2.25383	−	0.732315i	−0.127803	−	0.0415258i	−0.372220	+	0.928144i	$0.621403\pi$
$312$	−16.0360	+	8.44413i	−0.907862	+	0.478055i
$313$	−11.8212	+	8.58863i	−0.668175	+	0.485458i	−0.869414	−	0.494084i	$-0.835503\pi$
$313$	−11.8212	+	8.58863i	−0.668175	+	0.485458i	0.201239	+	0.979542i	$0.435503\pi$
$314$	8.13109	−	5.90758i	0.458864	−	0.333384i
$315$		0			0
$316$	0.322945	+	0.104931i	0.0181671	+	0.00590284i
$317$	−14.5698	+	20.0536i	−0.818319	+	1.12632i	0.171667	+	0.985155i	$0.445085\pi$
$317$	−14.5698	+	20.0536i	−0.818319	+	1.12632i	−0.989986	+	0.141165i	$0.954915\pi$
$318$	−1.43347	−	8.32485i	−0.0803850	−	0.466834i
$319$	11.5508	+	21.3864i	0.646723	+	1.19741i
$320$		0			0
$321$	4.91649	+	2.42241i	0.274412	+	0.135206i
$322$	1.86444	−	5.73817i	0.103901	−	0.319776i
$323$	1.10081	−	0.357675i	0.0612507	−	0.0199016i
$324$	3.48855	−	13.0927i	0.193808	−	0.727374i
$325$		0			0
$326$	−4.90077	−	15.0830i	−0.271429	−	0.835372i
$327$	6.17730	+	0.893459i	0.341605	+	0.0494084i
$328$	19.0453	+	13.8372i	1.05160	+	0.764033i
$329$	−0.466174			−0.0257010
$330$		0			0
$331$	10.2699			0.564483			0.282242	−	0.959343i	$-0.408922\pi$
$331$	10.2699			0.564483			0.282242	+	0.959343i	$0.408922\pi$
$332$	−2.44925	−	1.77948i	−0.134420	−	0.0976619i
$333$	0.480580	+	17.8746i	0.0263356	+	0.979521i
$334$	1.16548	+	3.58696i	0.0637720	+	0.196270i
$335$		0			0
$336$	3.15742	+	3.07367i	0.172251	+	0.167683i
$337$	8.33932	−	2.70961i	0.454272	−	0.147602i	−0.0729391	−	0.997336i	$-0.523238\pi$
$337$	8.33932	−	2.70961i	0.454272	−	0.147602i	0.527211	+	0.849735i	$0.323238\pi$
$338$	−1.09031	+	3.35562i	−0.0593049	+	0.182522i
$339$	−5.88601	+	11.9462i	−0.319684	+	0.648827i
$340$		0			0
$341$	19.3864	+	9.29939i	1.04983	+	0.503590i
$342$	−0.191031	−	0.538257i	−0.0103298	−	0.0291056i
$343$	−11.7453	+	16.1660i	−0.634187	+	0.872883i
$344$	3.96090	+	1.28697i	0.213558	+	0.0693890i
$345$		0			0
$346$	−9.27557	+	6.73910i	−0.498658	+	0.362296i
$347$	−12.6554	+	9.19468i	−0.679377	+	0.493596i	−0.873151	−	0.487450i	$-0.837927\pi$
$347$	−12.6554	+	9.19468i	−0.679377	+	0.493596i	0.193774	+	0.981046i	$0.437927\pi$
$348$	8.90393	+	16.9092i	0.477301	+	0.906429i
$349$	28.9739	+	9.41418i	1.55094	+	0.503929i	0.954368	−	0.298633i	$-0.0965308\pi$
$349$	28.9739	+	9.41418i	1.55094	+	0.503929i	0.596567	+	0.802563i	$0.296531\pi$
$350$		0			0
$351$	−10.7973	−	19.2325i	−0.576316	−	1.02656i
$352$	−19.0151	+	3.48086i	−1.01351	+	0.185531i
$353$			18.4443i			0.981692i	0.871246	+	0.490846i	$0.163312\pi$
$353$			18.4443i			0.981692i	−0.871246	+	0.490846i	$0.836688\pi$
$354$	5.68059	−	11.5293i	0.301920	−	0.612774i
$355$		0			0
$356$	−22.7033	+	7.37676i	−1.20327	+	0.390967i
$357$	10.5661	+	10.2859i	0.559219	+	0.544386i
$358$	0.110859	+	0.152584i	0.00585907	+	0.00806432i
$359$	5.34445	+	16.4485i	0.282069	+	0.868120i	0.987262	+	0.159104i	$0.0508606\pi$
$359$	5.34445	+	16.4485i	0.282069	+	0.868120i	−0.705192	+	0.709016i	$0.749139\pi$
$360$		0			0
$361$	−15.3120	−	11.1248i	−0.805896	−	0.585518i
$362$	0.150359			0.00790271
$363$	−4.12930	−	18.5997i	−0.216732	−	0.976231i
$364$	12.7257			0.667007
$365$		0			0
$366$	−11.6493	−	1.68491i	−0.608918	−	0.0880714i
$367$	−0.703945	−	2.16652i	−0.0367456	−	0.113091i	0.931001	−	0.365016i	$-0.118937\pi$
$367$	−0.703945	−	2.16652i	−0.0367456	−	0.113091i	−0.967747	+	0.251925i	$0.918937\pi$
$368$	−3.23539	−	4.45313i	−0.168656	−	0.232135i
$369$	−16.2108	+	23.6223i	−0.843901	+	1.22973i
$370$		0			0
$371$	−4.26789	+	13.1352i	−0.221578	+	0.681947i
$372$	15.1642	+	7.47154i	0.786225	+	0.387381i
$373$		−	29.7264i		−	1.53917i	−0.638542	−	0.769587i	$-0.720462\pi$
$373$		−	29.7264i		−	1.53917i	0.638542	−	0.769587i	$-0.279538\pi$
$374$	−9.80798	+	1.79542i	−0.507159	+	0.0928392i
$375$		0			0
$376$	0.339192	−	0.466858i	0.0174925	−	0.0240764i
$377$	29.5854	+	9.61288i	1.52373	+	0.495089i
$378$	4.93362	−	5.34841i	0.253758	−	0.275092i
$379$	−16.8851	+	12.2677i	−0.867328	+	0.630151i	−0.929869	−	0.367892i	$-0.880080\pi$
$379$	−16.8851	+	12.2677i	−0.867328	+	0.630151i	0.0625406	+	0.998042i	$0.480080\pi$
$380$		0			0
$381$	−15.4194	+	8.11942i	−0.789959	+	0.415970i
$382$	−2.66496	−	0.865899i	−0.136351	−	0.0443032i
$383$	−4.97522	+	6.84780i	−0.254222	+	0.349906i	−0.916984	−	0.398924i	$-0.869384\pi$
$383$	−4.97522	+	6.84780i	−0.254222	+	0.349906i	0.662763	+	0.748830i	$0.269384\pi$
$384$	−18.0451	+	3.10721i	−0.920858	+	0.158564i
$385$		0			0
$386$			11.3891i			0.579689i
$387$	−1.43612	+	4.86075i	−0.0730021	+	0.247086i
$388$	1.53615	−	4.72778i	0.0779861	−	0.240017i
$389$	25.0694	−	8.14555i	1.27107	−	0.412996i	0.405643	−	0.914031i	$-0.367048\pi$
$389$	25.0694	−	8.14555i	1.27107	−	0.412996i	0.865427	+	0.501036i	$0.167048\pi$
$390$		0			0
$391$	−10.8270	−	14.9021i	−0.547547	−	0.753633i
$392$	−2.31149	−	7.11404i	−0.116748	−	0.359313i
$393$	−3.92942	+	27.1677i	−0.198213	+	1.37043i
$394$	−3.24032	−	2.35423i	−0.163245	−	0.118605i
$395$		0			0
$396$	−3.09234	−	14.6569i	−0.155396	−	0.736537i
$397$	−19.7388			−0.990662			−0.495331	−	0.868704i	$-0.664953\pi$
$397$	−19.7388			−0.990662			−0.495331	+	0.868704i	$0.664953\pi$
$398$	6.96121	+	5.05761i	0.348934	+	0.253515i
$399$	−0.133672	+	0.924198i	−0.00669198	+	0.0462678i
$400$		0			0
$401$	−20.7738	−	28.5926i	−1.03739	−	1.42785i	−0.899249	−	0.437436i	$-0.855887\pi$
$401$	−20.7738	−	28.5926i	−1.03739	−	1.42785i	−0.138143	−	0.990412i	$-0.544113\pi$
$402$	0.766079	−	0.786953i	0.0382086	−	0.0392497i
$403$	26.1712	−	8.50354i	1.30368	−	0.423591i
$404$	−0.795240	+	2.44750i	−0.0395647	+	0.121768i
$405$		0			0
$406$			10.2626i			0.509326i
$407$	9.39423	+	17.3934i	0.465655	+	0.862161i
$408$	−17.9890	+	3.09755i	−0.890588	+	0.153352i
$409$	−3.86369	+	5.31791i	−0.191047	+	0.262954i	−0.893786	−	0.448495i	$-0.851960\pi$
$409$	−3.86369	+	5.31791i	−0.191047	+	0.262954i	0.702739	+	0.711448i	$0.251960\pi$
$410$		0			0
$411$	−19.4299	+	10.2313i	−0.958408	+	0.504671i
$412$	−7.22188	+	5.24700i	−0.355796	+	0.258501i
$413$	−17.0006	+	12.3516i	−0.836544	+	0.607785i
$414$	−7.20724	+	5.53833i	−0.354216	+	0.272194i
$415$		0			0
$416$	−14.5421	+	20.0154i	−0.712983	+	0.981337i
$417$	−4.48107	−	26.0238i	−0.219439	−	1.27439i
$418$	−0.457064	−	0.435658i	−0.0223557	−	0.0213087i
$419$		−	1.69814i		−	0.0829594i	−0.999139	−	0.0414797i	$-0.986793\pi$
$419$		−	1.69814i		−	0.0829594i	0.999139	−	0.0414797i	$-0.0132072\pi$
$420$		0			0
$421$	5.97401	−	18.3861i	0.291155	−	0.896084i	−0.693330	−	0.720620i	$-0.743857\pi$
$421$	5.97401	−	18.3861i	0.291155	−	0.896084i	0.984486	−	0.175464i	$-0.0561427\pi$
$422$	2.45754	−	0.798503i	0.119631	−	0.0388705i
$423$	0.579054	+	0.397376i	0.0281546	+	0.0193211i
$424$	−10.0492	−	13.8315i	−0.488030	−	0.671716i
$425$		0			0
$426$	0.634003	+	0.0916996i	0.0307176	+	0.00444286i
$427$	15.5691	+	11.3116i	0.753440	+	0.547407i
$428$	4.76399			0.230276
$429$	−20.2493	−	13.5846i	−0.977646	−	0.655871i
$430$		0			0
$431$	14.8290	+	10.7739i	0.714287	+	0.518960i	0.884554	−	0.466438i	$-0.154463\pi$
$431$	14.8290	+	10.7739i	0.714287	+	0.518960i	−0.170267	+	0.985398i	$0.554463\pi$
$432$	−1.30190	−	6.50939i	−0.0626378	−	0.313183i
$433$	2.02005	+	6.21706i	0.0970772	+	0.298773i	0.987789	−	0.155795i	$-0.0497938\pi$
$433$	2.02005	+	6.21706i	0.0970772	+	0.298773i	−0.890712	+	0.454568i	$0.849794\pi$
$434$	5.33610	+	7.34451i	0.256141	+	0.352548i
$435$		0			0
$436$	5.15967	−	1.67648i	0.247103	−	0.0802887i
$437$	0.360464	−	1.10939i	0.0172433	−	0.0530695i
$438$	−5.54606	+	11.2562i	−0.265001	+	0.537843i
$439$			6.71248i			0.320369i	0.987087	+	0.160185i	$0.0512090\pi$
$439$			6.71248i			0.320369i	−0.987087	+	0.160185i	$0.948791\pi$
$440$		0			0
$441$	8.57902	−	3.04475i	0.408525	−	0.144988i
$442$	−7.50078	+	10.3239i	−0.356776	+	0.491059i
$443$	14.6754	+	4.76834i	0.697252	+	0.226551i	0.636133	−	0.771580i	$-0.280533\pi$
$443$	14.6754	+	4.76834i	0.697252	+	0.226551i	0.0611190	+	0.998130i	$0.480533\pi$
$444$	7.24151	+	13.7522i	0.343667	+	0.652649i
$445$		0			0
$446$	8.98775	−	6.52999i	0.425582	−	0.309204i
$447$	7.04501	+	13.3790i	0.333217	+	0.632805i
$448$	−2.92341	−	0.949872i	−0.138118	−	0.0448772i
$449$	4.40619	−	6.06460i	0.207941	−	0.286206i	−0.692289	−	0.721620i	$-0.743398\pi$
$449$	4.40619	−	6.06460i	0.207941	−	0.286206i	0.900231	+	0.435414i	$0.143398\pi$
$450$		0			0
$451$	−4.20349	+	31.3932i	−0.197935	+	1.47825i
$452$			11.5756i			0.544471i
$453$	−14.4830	+	29.3946i	−0.680473	+	1.38108i
$454$	0.303422	−	0.933836i	0.0142403	−	0.0438271i
$455$		0			0
$456$	−0.828294	−	0.806324i	−0.0387884	−	0.0377596i
$457$	21.4314	+	29.4978i	1.00252	+	1.37985i	0.923767	+	0.382954i	$0.125093\pi$
$457$	21.4314	+	29.4978i	1.00252	+	1.37985i	0.0787515	+	0.996894i	$0.474907\pi$
$458$	2.28882	+	7.04425i	0.106949	+	0.329156i
$459$	−4.35674	−	21.7833i	−0.203355	−	1.01676i
$460$		0			0
$461$	9.37436			0.436607			0.218304	−	0.975881i	$-0.429948\pi$
$461$	9.37436			0.436607			0.218304	+	0.975881i	$0.429948\pi$
$462$	2.19794	−	7.73827i	0.102257	−	0.360017i
$463$	−0.0632711			−0.00294046			−0.00147023	−	0.999999i	$-0.500468\pi$
$463$	−0.0632711			−0.00294046			−0.00147023	+	0.999999i	$0.500468\pi$
$464$	7.57456	+	5.50324i	0.351640	+	0.255481i
$465$		0			0
$466$	−3.40141	−	10.4685i	−0.157567	−	0.484943i
$467$	−16.3955	−	22.5665i	−0.758694	−	1.04425i	−0.997322	−	0.0731419i	$-0.976697\pi$
$467$	−16.3955	−	22.5665i	−0.758694	−	1.04425i	0.238627	−	0.971111i	$-0.423303\pi$
$468$	−15.8071	−	10.8476i	−0.730683	−	0.501432i
$469$	−1.70774	+	0.554877i	−0.0788560	+	0.0256219i
$470$		0			0
$471$	22.2062	+	10.9413i	1.02321	+	0.504146i
$472$		−	26.0127i		−	1.19733i
$473$	1.00898	+	5.51181i	0.0463929	+	0.253433i
$474$	−0.0466177	−	0.270732i	−0.00214122	−	0.0124351i
$475$		0			0
$476$	12.1899	+	3.96073i	0.558722	+	0.181540i
$477$	16.4981	−	12.6778i	0.755395	−	0.580475i
$478$	−10.4508	+	7.59295i	−0.478009	+	0.347294i
$479$	−7.89453	+	5.73571i	−0.360710	+	0.262071i	−0.753348	−	0.657622i	$-0.771563\pi$
$479$	−7.89453	+	5.73571i	−0.360710	+	0.262071i	0.392638	+	0.919693i	$0.371563\pi$
$480$		0			0
$481$	24.0616	+	7.81809i	1.09712	+	0.356474i
$482$	0.724999	−	0.997876i	0.0330228	−	0.0454520i
$483$	14.6454	−	2.52181i	0.666388	−	0.114746i
$484$	−10.3650	−	12.9158i	−0.471135	−	0.587083i
$485$		0			0
$486$	−10.6873	+	2.43796i	−0.484788	+	0.110588i
$487$	−3.85975	+	11.8791i	−0.174902	+	0.538293i	−0.999629	−	0.0272380i	$-0.991329\pi$
$487$	−3.85975	+	11.8791i	−0.174902	+	0.538293i	0.824727	+	0.565531i	$0.191329\pi$
$488$	−22.6564	+	7.36152i	−1.02561	+	0.333240i
$489$	27.2477	−	27.9901i	1.23218	−	1.26576i
$490$		0			0
$491$	−6.27879	−	19.3241i	−0.283358	−	0.872086i	−0.986886	−	0.161419i	$-0.948393\pi$
$491$	−6.27879	−	19.3241i	−0.283358	−	0.872086i	0.703528	−	0.710667i	$-0.251607\pi$
$492$	−3.56468	+	24.6459i	−0.160708	+	1.11112i
$493$	25.3478	+	18.4163i	1.14161	+	0.829427i
$494$	−0.808121			−0.0363591
$495$		0			0
$496$	8.28220			0.371882
$497$	−0.847335	−	0.615625i	−0.0380082	−	0.0276145i
$498$	−0.350604	+	2.42405i	−0.0157109	+	0.108624i
$499$	−12.5106	−	38.5036i	−0.560050	−	1.72366i	−0.682220	−	0.731147i	$-0.738985\pi$
$499$	−12.5106	−	38.5036i	−0.560050	−	1.72366i	0.122170	−	0.992509i	$-0.461015\pi$
$500$		0			0
$501$	−6.47990	+	6.65646i	−0.289500	+	0.297389i
$502$	−7.49258	+	2.43449i	−0.334410	+	0.108656i
$503$	6.15652	−	18.9478i	0.274505	−	0.844841i	−0.714844	−	0.699284i	$-0.753502\pi$
$503$	6.15652	−	18.9478i	0.274505	−	0.844841i	0.989350	−	0.145557i	$-0.0464975\pi$
$504$	4.17273	−	14.1232i	0.185868	−	0.629097i
$505$		0			0
$506$	−4.34609	+	9.06026i	−0.193207	+	0.402777i
$507$	−8.56446	+	1.47473i	−0.380361	+	0.0654950i
$508$	−8.90326	+	12.2543i	−0.395018	+	0.543696i
$509$	24.3487	+	7.91139i	1.07924	+	0.350666i	0.794079	−	0.607814i	$-0.207953\pi$
$509$	24.3487	+	7.91139i	1.07924	+	0.350666i	0.285160	+	0.958480i	$0.407953\pi$
$510$		0			0
$511$	16.5980	−	12.0591i	0.734251	−	0.533464i
$512$	−11.1197	+	8.07895i	−0.491427	+	0.357042i
$513$	0.953846	−	1.03404i	0.0421133	−	0.0456540i
$514$	4.15760	+	1.35088i	0.183384	+	0.0595850i
$515$		0			0
$516$	0.747592	+	4.34163i	0.0329109	+	0.191130i
$517$	0.769543	+	0.103040i	0.0338445	+	0.00453171i
$518$			8.34654i			0.366726i
$519$	−25.3319	−	12.4813i	−1.11195	−	0.547867i
$520$		0			0
$521$	−2.77739	+	0.902428i	−0.121680	+	0.0395361i	−0.369224	−	0.929341i	$-0.620376\pi$
$521$	−2.77739	+	0.902428i	−0.121680	+	0.0395361i	0.247544	+	0.968877i	$0.420376\pi$
$522$	8.74809	−	12.7477i	0.382893	−	0.557950i
$523$	−13.1509	−	18.1007i	−0.575050	−	0.791488i	0.418092	−	0.908405i	$-0.362699\pi$
$523$	−13.1509	−	18.1007i	−0.575050	−	0.791488i	−0.993142	+	0.116917i	$0.962699\pi$
$524$	7.37313	+	22.6922i	0.322097	+	0.991312i
$525$		0			0
$526$	13.6937	+	9.94902i	0.597072	+	0.433798i
$527$	27.7159			1.20732
$528$	−4.53277	−	5.77180i	−0.197264	−	0.251186i
$529$	4.43631			0.192883
$530$		0			0
$531$	31.6459	−	0.850840i	1.37332	−	0.0369233i
$532$	0.250821	+	0.771948i	0.0108745	+	0.0334682i
$533$	23.8267	+	32.7946i	1.03205	+	1.42049i
$534$	13.8385	+	13.4714i	0.598850	+	0.582965i
$535$		0			0
$536$	0.686874	−	2.11398i	0.0296684	−	0.0913100i
$537$	−0.205318	+	0.416712i	−0.00886014	+	0.0179824i
$538$		−	17.7560i		−	0.765517i
$539$	6.94374	−	7.28492i	0.299088	−	0.313784i
$540$		0			0
$541$	−11.8895	+	16.3644i	−0.511168	+	0.703562i	−0.984116	−	0.177528i	$-0.943190\pi$
$541$	−11.8895	+	16.3644i	−0.511168	+	0.703562i	0.472948	+	0.881090i	$0.343190\pi$
$542$	−15.0304	−	4.88368i	−0.645612	−	0.209772i
$543$	0.172554	+	0.327692i	0.00740499	+	0.0140626i
$544$	−20.1594	+	14.6466i	−0.864325	+	0.627969i
$545$		0			0
$546$	−4.79686	−	9.10960i	−0.205287	−	0.389855i
$547$	−19.6221	−	6.37562i	−0.838982	−	0.272602i	−0.142158	−	0.989844i	$-0.545404\pi$
$547$	−19.6221	−	6.37562i	−0.838982	−	0.272602i	−0.696824	+	0.717242i	$0.745404\pi$
$548$	−11.2190	+	15.4416i	−0.479251	+	0.659633i
$549$	−9.69675	−	27.3220i	−0.413847	−	1.16607i
$550$		0			0
$551$			1.98414i			0.0845271i
$552$	−8.13060	+	16.5018i	−0.346061	+	0.702363i
$553$	−0.138796	+	0.427169i	−0.00590220	+	0.0181651i
$554$	6.54199	−	2.12562i	0.277943	−	0.0903090i
$555$		0			0
$556$	−13.4913	−	18.5692i	−0.572159	−	0.787510i
$557$	3.23830	+	9.96646i	0.137211	+	0.422292i	0.995927	−	0.0901589i	$-0.0287375\pi$
$557$	3.23830	+	9.96646i	0.137211	+	0.422292i	−0.858716	+	0.512451i	$0.828737\pi$
$558$	−0.367576	−	13.6715i	−0.0155607	−	0.578762i
$559$	5.80176	+	4.21523i	0.245388	+	0.178285i
$560$		0			0
$561$	−15.1687	−	19.3150i	−0.640421	−	0.815481i
$562$	−9.63230			−0.406314
$563$	−29.2694	−	21.2655i	−1.23356	−	0.896232i	−0.236406	−	0.971654i	$-0.575969\pi$
$563$	−29.2694	−	21.2655i	−1.23356	−	0.896232i	−0.997152	+	0.0754225i	$0.975969\pi$
$564$	0.604145	+	0.0873811i	0.0254391	+	0.00367941i
$565$		0			0
$566$	12.3393	+	16.9836i	0.518659	+	0.713873i
$567$	17.3181	+	4.61441i	0.727294	+	0.193787i
$568$	1.23306	−	0.400645i	0.0517379	−	0.0168107i
$569$	0.102235	−	0.314646i	0.00428590	−	0.0131907i	−0.948891	−	0.315605i	$-0.897793\pi$
$569$	0.102235	−	0.314646i	0.00428590	−	0.0131907i	0.953177	+	0.302414i	$0.0977926\pi$
$570$		0			0
$571$			23.8700i			0.998927i	0.866335	+	0.499463i	$0.166469\pi$
$571$			23.8700i			0.998927i	−0.866335	+	0.499463i	$0.833531\pi$
$572$	−21.0071	−	2.81281i	−0.878351	−	0.117610i
$573$	−1.17120	−	6.80172i	−0.0489275	−	0.284146i
$574$	−7.86052	+	10.8191i	−0.328092	+	0.451580i
$575$		0			0
$576$	2.82159	+	3.67185i	0.117566	+	0.152994i
$577$	14.0496	−	10.2076i	0.584893	−	0.424950i	−0.255592	−	0.966785i	$-0.582270\pi$
$577$	14.0496	−	10.2076i	0.584893	−	0.424950i	0.840485	+	0.541835i	$0.182270\pi$
$578$	−0.726785	+	0.528040i	−0.0302303	+	0.0219636i
$579$	−24.8213	+	13.0702i	−1.03154	+	0.543179i
$580$		0			0
$581$	2.35378	−	3.23970i	0.0976511	−	0.134405i
$582$	−3.96339	+	0.682464i	−0.164288	+	0.0282890i
$583$	9.94862	−	20.7398i	0.412030	−	0.858955i
$584$			25.3967i			1.05092i
$585$		0			0
$586$	5.30201	−	16.3179i	0.219024	−	0.674086i
$587$	−13.2288	+	4.29831i	−0.546012	+	0.177410i	−0.569018	−	0.822325i	$-0.692676\pi$
$587$	−13.2288	+	4.29831i	−0.546012	+	0.177410i	0.0230056	+	0.999735i	$0.492676\pi$
$588$	5.51936	−	5.66975i	0.227614	−	0.233816i
$589$	1.03166	+	1.41996i	0.0425088	+	0.0585084i
$590$		0			0
$591$	1.41218	−	9.76368i	0.0580892	−	0.401624i
$592$	6.16034	+	4.47575i	0.253188	+	0.183952i
$593$	21.9317			0.900628			0.450314	−	0.892870i	$-0.351312\pi$
$593$	21.9317			0.900628			0.450314	+	0.892870i	$0.351312\pi$
$594$	−9.32642	+	7.73846i	−0.382667	+	0.317513i
$595$		0			0
$596$	10.6327	+	7.72513i	0.435534	+	0.316434i
$597$	−3.03379	+	20.9754i	−0.124165	+	0.858465i
$598$	3.97414	+	12.2312i	0.162515	+	0.500169i
$599$	−9.26009	−	12.7454i	−0.378357	−	0.520764i	0.576791	−	0.816892i	$-0.304305\pi$
$599$	−9.26009	−	12.7454i	−0.378357	−	0.520764i	−0.955148	+	0.296128i	$0.904305\pi$
$600$		0			0
$601$	−32.7170	+	10.6304i	−1.33455	+	0.433623i	−0.887469	−	0.460868i	$-0.847538\pi$
$601$	−32.7170	+	10.6304i	−1.33455	+	0.433623i	−0.447086	+	0.894491i	$0.647538\pi$
$602$	−0.731093	+	2.25007i	−0.0297971	+	0.0917061i
$603$	2.59424	+	0.766475i	0.105646	+	0.0312133i
$604$			28.4828i			1.15895i
$605$		0			0
$606$	2.05179	−	0.353301i	0.0833482	−	0.0143519i
$607$	7.78585	−	10.7163i	0.316018	−	0.434962i	−0.621228	−	0.783630i	$-0.713366\pi$
$607$	7.78585	−	10.7163i	0.316018	−	0.434962i	0.937246	+	0.348668i	$0.113366\pi$
$608$	−1.50077	−	0.487630i	−0.0608643	−	0.0197760i
$609$	−22.3663	+	11.7775i	−0.906330	+	0.477248i
$610$		0			0
$611$	0.803895	−	0.584064i	0.0325221	−	0.0236287i
$612$	−11.7653	−	15.3107i	−0.475585	−	0.618898i
$613$	−3.50996	−	1.14046i	−0.141766	−	0.0460626i	0.237275	−	0.971443i	$-0.423746\pi$
$613$	−3.50996	−	1.14046i	−0.141766	−	0.0460626i	−0.379041	+	0.925380i	$0.623746\pi$
$614$	−3.01007	+	4.14301i	−0.121477	+	0.167198i
$615$		0			0
$616$	−2.93165	−	16.0149i	−0.118119	−	0.645258i
$617$		−	4.13390i		−	0.166425i	−0.996532	−	0.0832123i	$-0.973482\pi$
$617$		−	4.13390i		−	0.166425i	0.996532	−	0.0832123i	$-0.0265180\pi$
$618$	6.47828	+	3.19191i	0.260595	+	0.128398i
$619$	9.56349	−	29.4334i	0.384389	−	1.18303i	−0.552533	−	0.833491i	$-0.686339\pi$
$619$	9.56349	−	29.4334i	0.384389	−	1.18303i	0.936922	−	0.349537i	$-0.113661\pi$
$620$		0			0
$621$	−20.3413	−	9.35158i	−0.816267	−	0.375266i
$622$	0.979527	+	1.34820i	0.0392755	+	0.0540580i
$623$	−9.75746	−	30.0304i	−0.390924	−	1.20314i
$624$	−9.29580	−	1.34451i	−0.372130	−	0.0538233i
$625$		0			0
$626$	10.2751			0.410677
$627$	0.424941	−	1.49609i	0.0169705	−	0.0597480i
$628$	21.5174			0.858639
$629$	20.6152	+	14.9778i	0.821983	+	0.597205i
$630$		0			0
$631$	−6.88264	−	21.1826i	−0.273993	−	0.843265i	−0.989484	−	0.144643i	$-0.953797\pi$
$631$	−6.88264	−	21.1826i	−0.273993	−	0.843265i	0.715491	−	0.698622i	$-0.246203\pi$
$632$	−0.326808	−	0.449812i	−0.0129997	−	0.0178926i
$633$	4.56054	+	4.43958i	0.181265	+	0.176457i
$634$	16.5776	−	5.38640i	0.658382	−	0.213921i
$635$		0			0
$636$	7.99315	−	16.2228i	0.316949	−	0.643277i
$637$		−	12.8803i		−	0.510334i
$638$	2.26839	−	16.9412i	0.0898066	−	0.670708i
$639$	0.527738	+	1.48698i	0.0208770	+	0.0588240i
$640$		0			0
$641$	24.8632	+	8.07855i	0.982038	+	0.319083i	0.755666	−	0.654957i	$-0.227313\pi$
$641$	24.8632	+	8.07855i	0.982038	+	0.319083i	0.226372	+	0.974041i	$0.427313\pi$
$642$	−1.79576	−	3.41027i	−0.0708728	−	0.134593i
$643$	−16.6265	+	12.0799i	−0.655687	+	0.476385i	−0.865204	−	0.501421i	$-0.832811\pi$
$643$	−16.6265	+	12.0799i	−0.655687	+	0.476385i	0.209517	+	0.977805i	$0.432811\pi$
$644$	10.4502	−	7.59250i	0.411795	−	0.299187i
$645$		0			0
$646$	−0.774096	−	0.251519i	−0.0304564	−	0.00989588i
$647$	12.8452	−	17.6799i	0.504998	−	0.695070i	−0.478068	−	0.878323i	$-0.658663\pi$
$647$	12.8452	−	17.6799i	0.504998	−	0.695070i	0.983066	+	0.183253i	$0.0586628\pi$
$648$	−17.2220	+	13.9861i	−0.676546	+	0.549425i
$649$	30.7941	−	16.6319i	1.20877	−	0.652861i
$650$		0			0
$651$	−9.88283	+	20.0581i	−0.387339	+	0.786138i
$652$	10.4921	−	32.2915i	0.410904	−	1.26463i
$653$	2.45106	−	0.796398i	0.0959174	−	0.0311654i	−0.260665	−	0.965429i	$-0.583942\pi$
$653$	2.45106	−	0.796398i	0.0959174	−	0.0311654i	0.356583	+	0.934264i	$0.383942\pi$
$654$	−3.14500	−	3.06158i	−0.122979	−	0.119717i
$655$		0			0
$656$	3.77012	+	11.6032i	0.147199	+	0.453031i
$657$	−30.8965	+	0.830689i	−1.20539	+	0.0324083i
$658$	0.265209	+	0.192685i	0.0103389	+	0.00751166i
$659$	35.4001			1.37899			0.689496	−	0.724290i	$-0.257832\pi$
$659$	35.4001			1.37899			0.689496	+	0.724290i	$0.257832\pi$
$660$		0			0
$661$	−15.6254			−0.607759			−0.303879	−	0.952710i	$-0.598282\pi$
$661$	−15.6254			−0.607759			−0.303879	+	0.952710i	$0.598282\pi$
$662$	−5.84258	−	4.24489i	−0.227078	−	0.164982i
$663$	−31.1079	−	4.49931i	−1.20813	−	0.174739i
$664$	1.53182	+	4.71447i	0.0594463	+	0.182957i
$665$		0			0
$666$	7.11477	−	10.3676i	0.275692	−	0.401736i
$667$	30.0305	−	9.75751i	1.16279	−	0.377812i
$668$	−2.49518	+	7.67938i	−0.0965415	+	0.297124i
$669$	24.5458	+	12.0940i	0.948997	+	0.467581i
$670$		0			0
$671$	−23.2006	−	22.1141i	−0.895650	−	0.853704i
$672$	−3.41147	−	19.8120i	−0.131600	−	0.764266i
$673$	−7.96638	+	10.9648i	−0.307081	+	0.422661i	−0.934468	−	0.356047i	$-0.884124\pi$
$673$	−7.96638	+	10.9648i	−0.307081	+	0.422661i	0.627387	+	0.778708i	$0.284124\pi$
$674$	−5.86425	−	1.90541i	−0.225883	−	0.0733937i
$675$		0			0
$676$	−6.11116	+	4.44001i	−0.235044	+	0.170770i
$677$	33.6218	−	24.4276i	1.29219	−	0.938830i	0.292342	−	0.956314i	$-0.405565\pi$
$677$	33.6218	−	24.4276i	1.29219	−	0.938830i	0.999847	+	0.0174834i	$0.00556543\pi$
$678$	8.28634	−	4.36336i	0.318235	−	0.167574i
$679$	6.25358	+	2.03191i	0.239990	+	0.0779775i
$680$		0			0
$681$	2.38341	−	0.410403i	0.0913323	−	0.0157267i
$682$	−7.18525	−	13.3035i	−0.275138	−	0.509418i
$683$		−	9.96643i		−	0.381355i	−0.981653	−	0.190677i	$-0.938932\pi$
$683$		−	9.96643i		−	0.381355i	0.981653	−	0.190677i	$-0.0610684\pi$
$684$	0.346469	−	1.17267i	0.0132476	−	0.0448383i
$685$		0			0
$686$	13.3639	−	4.34220i	0.510237	−	0.165786i
$687$	−12.7255	+	13.0723i	−0.485509	+	0.498738i
$688$	1.26867	+	1.74618i	0.0483676	+	0.0665724i
$689$	−9.09720	−	27.9983i	−0.346576	−	1.06665i
$690$		0			0
$691$	17.8614	+	12.9771i	0.679480	+	0.493671i	0.873185	−	0.487389i	$-0.162051\pi$
$691$	17.8614	+	12.9771i	0.679480	+	0.493671i	−0.193705	+	0.981060i	$0.562051\pi$
$692$	−24.5461			−0.933102
$693$	19.3871	−	4.09033i	0.736456	−	0.155379i
$694$	11.0002			0.417561
$695$		0			0
$696$	4.47917	−	30.9686i	0.169783	−	1.17386i
$697$	12.6165	+	38.8296i	0.477884	+	1.47078i
$698$	−12.5922	−	17.3316i	−0.476621	−	0.656013i
$699$	18.9114	−	19.4267i	0.715296	−	0.734786i
$700$		0			0
$701$	−0.379885	+	1.16917i	−0.0143481	+	0.0441588i	−0.957974	−	0.286854i	$-0.907390\pi$
$701$	−0.379885	+	1.16917i	−0.0143481	+	0.0441588i	0.943626	+	0.331013i	$0.107390\pi$
$702$	−1.80683	+	15.4044i	−0.0681945	+	0.581400i
$703$			1.61369i			0.0608614i
$704$	4.61590	+	2.21419i	0.173968	+	0.0834503i
$705$		0			0
$706$	7.62366	−	10.4931i	0.286920	−	0.394912i
$707$	−3.23738	−	1.05189i	−0.121754	−	0.0395603i
$708$	24.3474	−	12.8207i	0.915032	−	0.481830i
$709$	−35.8795	+	26.0680i	−1.34748	+	0.979003i	−0.348349	+	0.937365i	$0.613258\pi$
$709$	−35.8795	+	26.0680i	−1.34748	+	0.979003i	−0.999133	+	0.0416377i	$0.986742\pi$
$710$		0			0
$711$	0.536532	−	0.412292i	0.0201215	−	0.0154622i
$712$	37.1741	+	12.0786i	1.39316	+	0.452664i
$713$	16.4180	−	22.5975i	0.614860	−	0.846283i
$714$	−1.75963	−	10.2190i	−0.0658525	−	0.382437i
$715$		0			0
$716$			0.403786i			0.0150902i
$717$	−28.5415	−	14.0627i	−1.06590	−	0.525180i
$718$	3.75825	−	11.5667i	0.140257	−	0.431665i
$719$	−21.3753	+	6.94525i	−0.797164	+	0.259014i	−0.679152	−	0.733998i	$-0.737652\pi$
$719$	−21.3753	+	6.94525i	−0.797164	+	0.259014i	−0.118012	+	0.993012i	$0.537652\pi$
$720$		0			0
$721$	−6.94037	−	9.55259i	−0.258473	−	0.355757i
$722$	4.11282	+	12.6580i	0.153063	+	0.471080i
$723$	3.00678	+	0.434888i	0.111823	+	0.0161737i
$724$	0.260428	+	0.189212i	0.00967872	+	0.00703200i
$725$		0			0
$726$	−5.33870	+	12.2882i	−0.198138	+	0.456059i
$727$	11.9207			0.442113			0.221057	−	0.975261i	$-0.429049\pi$
$727$	11.9207			0.442113			0.221057	+	0.975261i	$0.429049\pi$
$728$	−16.8574	−	12.2476i	−0.624775	−	0.453926i
$729$	−17.5782	−	20.4941i	−0.651043	−	0.759041i
$730$		0			0
$731$	4.24554	+	5.84348i	0.157027	+	0.216129i
$732$	−18.0567	−	17.5778i	−0.667395	−	0.649693i
$733$	33.1199	−	10.7613i	1.22331	−	0.397478i	0.375025	−	0.927015i	$-0.377634\pi$
$733$	33.1199	−	10.7613i	1.22331	−	0.397478i	0.848287	+	0.529537i	$0.177634\pi$
$734$	−0.495018	+	1.52351i	−0.0182714	+	0.0562337i
$735$		0			0
$736$			25.1127i			0.925665i
$737$	2.94172	−	0.538503i	0.108360	−	0.0198360i
$738$	18.9863	−	6.73836i	0.698895	−	0.248042i
$739$	−2.07357	+	2.85403i	−0.0762775	+	0.104987i	−0.845451	−	0.534053i	$-0.820668\pi$
$739$	−2.07357	+	2.85403i	−0.0762775	+	0.104987i	0.769173	+	0.639040i	$0.220668\pi$
$740$		0			0
$741$	−0.927407	−	1.76121i	−0.0340691	−	0.0646998i
$742$	7.85726	−	5.70863i	0.288449	−	0.209570i
$743$	40.3625	−	29.3251i	1.48076	−	1.07583i	0.503447	−	0.864026i	$-0.332065\pi$
$743$	40.3625	−	29.3251i	1.48076	−	1.07583i	0.977311	−	0.211807i	$-0.0679349\pi$
$744$	−12.8967	−	24.4918i	−0.472816	−	0.897913i
$745$		0			0
$746$	−12.2869	+	16.9115i	−0.449856	+	0.619174i
$747$	−5.68531	+	2.01775i	−0.208015	+	0.0738257i
$748$	−19.2471	−	9.23261i	−0.703745	−	0.337577i
$749$			6.30147i			0.230251i
$750$		0			0
$751$	5.26337	−	16.1990i	0.192063	−	0.591109i	−0.807935	−	0.589271i	$-0.799415\pi$
$751$	5.26337	−	16.1990i	0.192063	−	0.591109i	0.999998	−	0.00183792i	$-0.000585028\pi$
$752$	0.284431	−	0.0924172i	0.0103721	−	0.00337011i
$753$	−13.9042	−	13.5354i	−0.506699	−	0.493259i
$754$	−12.8580	−	17.6975i	−0.468259	−	0.644503i
$755$		0			0
$756$	15.2756	−	3.05518i	0.555569	−	0.111116i
$757$	−7.65784	−	5.56375i	−0.278329	−	0.202218i	0.439859	−	0.898067i	$-0.355028\pi$
$757$	−7.65784	−	5.56375i	−0.278329	−	0.202218i	−0.718188	+	0.695849i	$0.755028\pi$
$758$	14.6767			0.533081
$759$	−24.7335	+	0.925788i	−0.897768	+	0.0336040i
$760$		0			0
$761$	−39.8694	−	28.9668i	−1.44526	−	1.05005i	−0.986909	−	0.161276i	$-0.948439\pi$
$761$	−39.8694	−	28.9668i	−1.44526	−	1.05005i	−0.458354	−	0.888770i	$-0.651561\pi$
$762$	12.1282	+	1.75417i	0.439358	+	0.0635469i
$763$	2.21753	+	6.82484i	0.0802798	+	0.247076i
$764$	−3.52617	−	4.85335i	−0.127572	−	0.175588i
$765$		0			0
$766$	5.66085	−	1.83932i	0.204535	−	0.0664574i
$767$	13.8415	−	42.5997i	0.499787	−	1.53819i
$768$	16.3468	+	8.05422i	0.589863	+	0.290632i
$769$			14.5213i			0.523650i	0.965115	+	0.261825i	$0.0843244\pi$
$769$			14.5213i			0.523650i	−0.965115	+	0.261825i	$0.915676\pi$
$770$		0			0
$771$	1.82718	+	10.6113i	0.0658043	+	0.382158i
$772$	−14.3320	+	19.7263i	−0.515820	+	0.709965i
$773$	14.6962	+	4.77507i	0.528584	+	0.171747i	0.561138	−	0.827723i	$-0.310364\pi$
$773$	14.6962	+	4.77507i	0.528584	+	0.171747i	−0.0325533	+	0.999470i	$0.510364\pi$
$774$	2.82613	−	2.17171i	0.101583	−	0.0780605i
$775$		0			0
$776$	−6.58505	+	4.78432i	−0.236390	+	0.171747i
$777$	−18.1904	+	9.57856i	−0.652577	+	0.343629i
$778$	−17.6289	−	5.72799i	−0.632028	−	0.205358i
$779$	−1.51972	+	2.09172i	−0.0544497	+	0.0749436i
$780$		0			0
$781$	1.26268	+	1.20354i	0.0451821	+	0.0430661i
$782$			12.9531i			0.463201i
$783$	37.8215	+	4.43622i	1.35163	+	0.158538i
$784$	1.19794	−	3.68688i	0.0427836	−	0.131674i
$785$		0			0
$786$	13.4648	−	13.8317i	0.480273	−	0.493360i
$787$	−13.2291	−	18.2083i	−0.471568	−	0.649057i	0.505290	−	0.862950i	$-0.331386\pi$
$787$	−13.2291	−	18.2083i	−0.471568	−	0.649057i	−0.976857	+	0.213893i	$0.931386\pi$
$788$	−2.64980	−	8.15523i	−0.0943950	−	0.290518i
$789$	−5.96788	+	41.2614i	−0.212462	+	1.46895i
$790$		0			0
$791$	−15.3114			−0.544411
$792$	−10.0099	+	22.3918i	−0.355687	+	0.795656i
$793$	−41.0204			−1.45668
$794$	11.2295	+	8.15871i	0.398520	+	0.289542i
$795$		0			0
$796$	5.69257	+	17.5199i	0.201768	+	0.620978i
$797$	12.9924	+	17.8825i	0.460213	+	0.633429i	0.974553	−	0.224157i	$-0.0719629\pi$
$797$	12.9924	+	17.8825i	0.460213	+	0.633429i	−0.514340	+	0.857587i	$0.671963\pi$
$798$	0.458049	−	0.470530i	0.0162148	−	0.0166566i
$799$	0.951831	−	0.309269i	0.0336734	−	0.0109411i
$800$		0			0
$801$	−13.4784	+	45.6194i	−0.476235	+	1.61188i
$802$			24.8530i			0.877590i
$803$	−30.0648	+	16.2381i	−1.06096	+	0.573028i
$804$	2.31718	−	0.398999i	0.0817205	−	0.0140716i
$805$		0			0
$806$	−18.4037	−	5.97973i	−0.648243	−	0.210627i
$807$	38.6974	−	20.3770i	1.36221	−	0.717303i
$808$	3.40898	−	2.47677i	0.119928	−	0.0871324i
$809$	6.51749	−	4.73523i	0.229143	−	0.166482i	−0.467290	−	0.884104i	$-0.654770\pi$
$809$	6.51749	−	4.73523i	0.229143	−	0.166482i	0.696433	+	0.717622i	$0.254770\pi$
$810$		0			0
$811$	26.9185	+	8.74635i	0.945236	+	0.307126i	0.740778	−	0.671749i	$-0.234457\pi$
$811$	26.9185	+	8.74635i	0.945236	+	0.307126i	0.204458	+	0.978875i	$0.434457\pi$
$812$	−12.9145	+	17.7753i	−0.453210	+	0.623790i
$813$	−6.60558	−	38.3618i	−0.231668	−	1.34541i
$814$	1.84487	−	13.7782i	0.0646627	−	0.482925i
$815$		0			0
$816$	−8.48594	−	4.18111i	−0.297067	−	0.146368i
$817$	−0.141347	+	0.435020i	−0.00494509	+	0.0152194i
$818$	4.39614	−	1.42839i	0.153708	−	0.0499426i
$819$	14.3485	−	20.9085i	0.501377	−	0.730603i
$820$		0			0
$821$	14.6736	+	45.1606i	0.512111	+	1.57611i	0.788479	+	0.615062i	$0.210869\pi$
$821$	14.6736	+	45.1606i	0.512111	+	1.57611i	−0.276368	+	0.961052i	$0.589131\pi$
$822$	15.2827	+	2.21043i	0.533046	+	0.0770976i
$823$	5.89927	+	4.28607i	0.205636	+	0.149403i	0.685837	−	0.727755i	$-0.259436\pi$
$823$	5.89927	+	4.28607i	0.205636	+	0.149403i	−0.480201	+	0.877158i	$0.659436\pi$
$824$	14.6165			0.509190
$825$		0			0
$826$	14.7771			0.514160
$827$	39.9121	+	28.9978i	1.38788	+	1.00835i	0.996094	+	0.0882956i	$0.0281420\pi$
$827$	39.9121	+	28.9978i	1.38788	+	1.00835i	0.391784	+	0.920057i	$0.371858\pi$
$828$	−19.4526	+	0.523007i	−0.676025	+	0.0181758i
$829$	−8.50821	−	26.1856i	−0.295502	−	0.909463i	−0.983052	−	0.183326i	$-0.941314\pi$
$829$	−8.50821	−	26.1856i	−0.295502	−	0.909463i	0.687550	−	0.726137i	$-0.258686\pi$
$830$		0			0
$831$	12.1402	+	11.8182i	0.421139	+	0.409969i
$832$	6.23136	−	2.02469i	0.216034	−	0.0701936i
$833$	4.00884	−	12.3379i	0.138898	−	0.427484i
$834$	−8.20719	+	16.6572i	−0.284192	+	0.576793i
$835$		0			0
$836$	−0.243420	−	1.32974i	−0.00841884	−	0.0459902i
$837$	29.3738	−	16.4906i	1.01531	−	0.570000i
$838$	−0.701897	+	0.966079i	−0.0242466	+	0.0333726i
$839$	−11.3888	−	3.70044i	−0.393185	−	0.127753i	0.105751	−	0.994393i	$-0.466275\pi$
$839$	−11.3888	−	3.70044i	−0.393185	−	0.127753i	−0.498935	+	0.866639i	$0.666275\pi$
$840$		0			0
$841$	−19.9902	+	14.5237i	−0.689316	+	0.500817i
$842$	−10.9982	+	7.99069i	−0.379025	+	0.275377i
$843$	−11.0541	−	20.9926i	−0.380724	−	0.723023i
$844$	5.26138	+	1.70953i	0.181104	+	0.0588443i
$845$		0			0
$846$	−0.165178	−	0.465412i	−0.00567892	−	0.0160012i
$847$	17.0841	−	13.7101i	0.587018	−	0.471083i
$848$		−	8.86041i		−	0.304268i
$849$	−22.8532	+	46.3827i	−0.784321	+	1.59185i
$850$		0			0
$851$	24.4236	−	7.93572i	0.837231	−	0.272033i
$852$	0.982722	+	0.956656i	0.0336675	+	0.0327745i
$853$	17.6684	+	24.3184i	0.604954	+	0.832647i	0.996150	−	0.0876596i	$-0.0279388\pi$
$853$	17.6684	+	24.3184i	0.604954	+	0.832647i	−0.391197	+	0.920307i	$0.627939\pi$
$854$	−4.18186	−	12.8704i	−0.143100	−	0.440418i
$855$		0			0
$856$	−6.31073	−	4.58501i	−0.215696	−	0.156712i
$857$	23.3578			0.797886			0.398943	−	0.916976i	$-0.369377\pi$
$857$	23.3578			0.797886			0.398943	+	0.916976i	$0.369377\pi$
$858$	5.90496	+	16.0981i	0.201592	+	0.549579i
$859$	−0.342372			−0.0116816			−0.00584079	−	0.999983i	$-0.501859\pi$
$859$	−0.342372			−0.0116816			−0.00584079	+	0.999983i	$0.501859\pi$
$860$		0			0
$861$	−32.5998	−	4.71511i	−1.11100	−	0.160690i
$862$	−3.98307	−	12.2586i	−0.135664	−	0.417531i
$863$	−21.5350	−	29.6404i	−0.733060	−	1.00897i	−0.998988	−	0.0449774i	$-0.985678\pi$
$863$	−21.5350	−	29.6404i	−0.733060	−	1.00897i	0.265928	−	0.963993i	$-0.414322\pi$
$864$	−12.6507	+	27.5173i	−0.430384	+	0.936159i
$865$		0			0
$866$	1.42051	−	4.37187i	0.0482708	−	0.148562i
$867$	−1.98487	−	0.977967i	−0.0674098	−	0.0332135i
$868$			19.4359i			0.659697i
$869$	0.323538	−	0.674477i	0.0109753	−	0.0228801i
$870$		0			0
$871$	2.24972	−	3.09647i	0.0762287	−	0.104920i
$872$	−8.44836	−	2.74504i	−0.286098	−	0.0929587i
$873$	−6.03578	−	7.85460i	−0.204280	−	0.265838i
$874$	−0.663620	+	0.482148i	−0.0224473	+	0.0163089i
$875$		0			0
$876$	−23.7708	+	12.5170i	−0.803141	+	0.422912i
$877$	−25.0883	−	8.15170i	−0.847173	−	0.275263i	−0.146912	−	0.989150i	$-0.546933\pi$
$877$	−25.0883	−	8.15170i	−0.847173	−	0.275263i	−0.700262	+	0.713886i	$0.746933\pi$
$878$	2.77449	−	3.81876i	0.0936347	−	0.128877i
$879$	41.6478	−	7.17140i	1.40474	−	0.241885i
$880$		0			0
$881$			21.4753i			0.723520i	0.932271	+	0.361760i	$0.117824\pi$
$881$			21.4753i			0.723520i	−0.932271	+	0.361760i	$0.882176\pi$
$882$	−6.13914	−	1.81382i	−0.206716	−	0.0610747i
$883$	−14.0988	+	43.3915i	−0.474461	+	1.46024i	0.372223	+	0.928143i	$0.378596\pi$
$883$	−14.0988	+	43.3915i	−0.474461	+	1.46024i	−0.846684	+	0.532097i	$0.821404\pi$
$884$	−25.9832	+	8.44246i	−0.873911	+	0.283951i
$885$		0			0
$886$	−6.37802	−	8.77859i	−0.214274	−	0.294923i
$887$	−15.8520	−	48.7875i	−0.532259	−	1.63812i	−0.749498	−	0.662006i	$-0.769705\pi$
$887$	−15.8520	−	48.7875i	−0.532259	−	1.63812i	0.217239	−	0.976118i	$-0.430295\pi$
$888$	3.64288	−	25.1866i	0.122247	−	0.845206i
$889$	−16.2091	−	11.7766i	−0.543636	−	0.394975i
$890$		0			0
$891$	−27.5682	−	11.4452i	−0.923570	−	0.383429i
$892$	23.7844			0.796362
$893$	0.0512744	+	0.0372530i	0.00171583	+	0.00124662i
$894$	1.52205	−	10.5233i	0.0509049	−	0.351952i
$895$		0			0
$896$	−12.3741	−	17.0315i	−0.413390	−	0.568982i
$897$	−22.0957	+	22.6978i	−0.737755	+	0.757857i
$898$	−5.01341	+	1.62896i	−0.167300	+	0.0543590i
$899$	−14.6817	+	45.1857i	−0.489663	+	1.50703i
$900$		0			0
$901$		−	29.6508i		−	0.987813i
$902$	15.3673	−	16.1223i	0.511674	−	0.536814i
$903$	−5.74280	+	0.988863i	−0.191108	+	0.0329073i
$904$	11.1407	−	15.3339i	0.370535	−	0.509998i
$905$		0			0
$906$	20.3893	−	10.7364i	0.677388	−	0.356694i
$907$	−29.7713	+	21.6301i	−0.988541	+	0.718217i	−0.959601	−	0.281364i	$-0.909213\pi$
$907$	−29.7713	+	21.6301i	−0.988541	+	0.718217i	−0.0289397	+	0.999581i	$0.509213\pi$
$908$	1.70067	−	1.23561i	0.0564389	−	0.0410052i
$909$	3.12463	+	4.06620i	0.103637	+	0.134867i
$910$		0			0
$911$	28.7607	−	39.5856i	0.952883	−	1.31153i	0.00264805	−	0.999996i	$-0.499157\pi$
$911$	28.7607	−	39.5856i	0.952883	−	1.31153i	0.950235	−	0.311534i	$-0.100843\pi$
$912$	−0.101660	−	0.590389i	−0.00336630	−	0.0195497i
$913$	−4.60161	+	4.82771i	−0.152291	+	0.159774i
$914$		−	25.6398i		−	0.848088i
$915$		0			0
$916$	−4.90016	+	15.0811i	−0.161906	+	0.498295i
$917$	−30.0156	+	9.75266i	−0.991203	+	0.322061i
$918$	−6.52520	+	14.1934i	−0.215364	+	0.468452i
$919$	3.24014	+	4.45967i	0.106882	+	0.147111i	0.859107	−	0.511795i	$-0.171019\pi$
$919$	3.24014	+	4.45967i	0.106882	+	0.147111i	−0.752225	+	0.658906i	$0.771019\pi$
$920$		0			0
$921$	−12.4836	−	1.80558i	−0.411349	−	0.0594959i
$922$	−5.33312	−	3.87474i	−0.175637	−	0.127608i
$923$	2.23250			0.0734836
$924$	13.5447	−	10.6371i	0.445589	−	0.349935i
$925$		0			0
$926$	0.0359953	+	0.0261521i	0.00118288	+	0.000859411i
$927$	0.478085	+	17.7818i	0.0157024	+	0.584030i
$928$	−13.1998	−	40.6248i	−0.433305	−	1.33357i
$929$	−10.1583	−	13.9817i	−0.333282	−	0.458723i	0.609182	−	0.793030i	$-0.291498\pi$
$929$	−10.1583	−	13.9817i	−0.333282	−	0.458723i	−0.942464	+	0.334307i	$0.891498\pi$
$930$		0			0
$931$	0.781324	−	0.253868i	0.0256069	−	0.00832018i
$932$	7.28214	−	22.4121i	0.238534	−	0.734133i
$933$	−1.81415	+	3.68199i	−0.0593927	+	0.120543i
$934$			19.6150i			0.641823i
$935$		0			0
$936$	10.4991	+	29.5828i	0.343175	+	0.966944i
$937$	14.6552	−	20.1712i	0.478766	−	0.658964i	−0.499501	−	0.866313i	$-0.666483\pi$
$937$	14.6552	−	20.1712i	0.478766	−	0.658964i	0.978267	+	0.207349i	$0.0664834\pi$
$938$	1.20089	+	0.390193i	0.0392104	+	0.0127402i
$939$	11.7918	+	22.3935i	0.384811	+	0.730786i
$940$		0			0
$941$	0.979392	−	0.711570i	0.0319273	−	0.0231965i	−0.571707	−	0.820458i	$-0.693719\pi$
$941$	0.979392	−	0.711570i	0.0319273	−	0.0231965i	0.603634	+	0.797261i	$0.293719\pi$
$942$	−8.11086	−	15.4031i	−0.264266	−	0.501861i
$943$	39.1324	+	12.7149i	1.27433	+	0.414054i
$944$	7.92405	−	10.9065i	0.257906	−	0.354977i
$945$		0			0
$946$	1.70420	−	3.55274i	0.0554085	−	0.115510i
$947$			48.8953i			1.58888i	0.607340	+	0.794442i	$0.292237\pi$
$947$			48.8953i			1.58888i	−0.607340	+	0.794442i	$0.707763\pi$
$948$	0.259945	−	0.527581i	0.00844261	−	0.0171350i
$949$	−13.5137	+	41.5908i	−0.438673	+	1.35010i
$950$		0			0
$951$	30.7637	+	29.9477i	0.997581	+	0.971121i
$952$	−12.3357	−	16.9786i	−0.399801	−	0.550279i
$953$	6.45124	+	19.8549i	0.208976	+	0.643162i	0.999527	+	0.0307656i	$0.00979453\pi$
$953$	6.45124	+	19.8549i	0.208976	+	0.643162i	−0.790550	+	0.612397i	$0.790205\pi$
$954$	−14.6260	+	0.393238i	−0.473534	+	0.0127315i
$955$		0			0
$956$	−27.6561			−0.894463
$957$	39.5248	−	14.4981i	1.27765	−	0.468658i
$958$	6.86200			0.221701
$959$	−20.4251	−	14.8397i	−0.659561	−	0.479199i
$960$		0			0
$961$	3.40790	+	10.4884i	0.109932	+	0.338337i
$962$	−10.4573	−	14.3932i	−0.337157	−	0.464056i
$963$	5.37150	−	7.82732i	0.173094	−	0.252232i
$964$	2.51145	−	0.816020i	0.0808884	−	0.0262822i
$965$		0			0
$966$	−9.37418	−	4.61876i	−0.301609	−	0.148606i
$967$			35.6672i			1.14698i	0.819213	+	0.573490i	$0.194411\pi$
$967$			35.6672i			1.14698i	−0.819213	+	0.573490i	$0.805589\pi$
$968$	1.29962	+	27.0848i	0.0417712	+	0.870539i
$969$	−0.340200	−	1.97570i	−0.0109288	−	0.0634688i
$970$		0			0
$971$	4.98955	+	1.62120i	0.160122	+	0.0520269i	0.387981	−	0.921667i	$-0.373173\pi$
$971$	4.98955	+	1.62120i	0.160122	+	0.0520269i	−0.227859	+	0.973694i	$0.573173\pi$
$972$	−21.5788	−	9.22629i	−0.692140	−	0.295933i
$973$	24.5620	−	17.8454i	0.787423	−	0.572096i
$974$	7.10586	−	5.16271i	0.227687	−	0.165424i
$975$		0			0
$976$	−11.7418	−	3.81514i	−0.375845	−	0.122120i
$977$	12.0648	−	16.6058i	0.385987	−	0.531265i	−0.571171	−	0.820831i	$-0.693511\pi$
$977$	12.0648	−	16.6058i	0.385987	−	0.531265i	0.957158	+	0.289565i	$0.0935108\pi$
$978$	−27.0706	+	4.66133i	−0.865623	+	0.149053i
$979$	9.46952	+	51.7298i	0.302647	+	1.65329i
$980$		0			0
$981$	3.06316	−	10.3677i	0.0977991	−	0.331015i
$982$	−4.41528	+	13.5888i	−0.140897	+	0.433637i
$983$	21.9023	−	7.11648i	0.698574	−	0.226981i	0.0618651	−	0.998085i	$-0.480295\pi$
$983$	21.9023	−	7.11648i	0.698574	−	0.226981i	0.636709	+	0.771104i	$0.280295\pi$
$984$	28.4420	−	29.2170i	0.906698	−	0.931403i
$985$		0			0
$986$	−6.80844	−	20.9542i	−0.216825	−	0.667318i
$987$	−0.115582	+	0.799121i	−0.00367900	+	0.0254363i
$988$	−1.39970	−	1.01694i	−0.0445302	−	0.0323531i
$989$	7.27926			0.231467
$990$		0			0
$991$	−3.54759			−0.112693			−0.0563465	−	0.998411i	$-0.517945\pi$
$991$	−3.54759			−0.112693			−0.0563465	+	0.998411i	$0.517945\pi$
$992$	−30.5695	−	22.2101i	−0.970583	−	0.705170i
$993$	2.54628	−	17.6048i	0.0808037	−	0.558670i
$994$	0.227595	+	0.700464i	0.00721886	+	0.0222174i
$995$		0			0
$996$	−3.65767	+	3.75734i	−0.115898	+	0.119056i
$997$	4.65329	−	1.51195i	0.147371	−	0.0478838i	−0.234403	−	0.972140i	$-0.575313\pi$
$997$	4.65329	−	1.51195i	0.147371	−	0.0478838i	0.381774	+	0.924256i	$0.375313\pi$
$998$	−8.79750	+	27.0759i	−0.278480	+	0.857073i
$999$	30.7600	+	3.60795i	0.973204	+	0.114150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bi.h.326.8		80
3.2	odd	2	inner	825.2.bi.h.326.14		80
5.2	odd	4		165.2.r.a.29.13	yes	80
5.3	odd	4		165.2.r.a.29.8	yes	80
5.4	even	2	inner	825.2.bi.h.326.13		80
11.8	odd	10	inner	825.2.bi.h.701.14		80
15.2	even	4		165.2.r.a.29.7	✓	80
15.8	even	4		165.2.r.a.29.14	yes	80
15.14	odd	2	inner	825.2.bi.h.326.7		80
33.8	even	10	inner	825.2.bi.h.701.8		80
55.8	even	20		165.2.r.a.74.7	yes	80
55.19	odd	10	inner	825.2.bi.h.701.7		80
55.52	even	20		165.2.r.a.74.14	yes	80
165.8	odd	20		165.2.r.a.74.13	yes	80
165.74	even	10	inner	825.2.bi.h.701.13		80
165.107	odd	20		165.2.r.a.74.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.r.a.29.7	✓	80	15.2	even	4
165.2.r.a.29.8	yes	80	5.3	odd	4
165.2.r.a.29.13	yes	80	5.2	odd	4
165.2.r.a.29.14	yes	80	15.8	even	4
165.2.r.a.74.7	yes	80	55.8	even	20
165.2.r.a.74.8	yes	80	165.107	odd	20
165.2.r.a.74.13	yes	80	165.8	odd	20
165.2.r.a.74.14	yes	80	55.52	even	20
825.2.bi.h.326.7		80	15.14	odd	2	inner
825.2.bi.h.326.8		80	1.1	even	1	trivial
825.2.bi.h.326.13		80	5.4	even	2	inner
825.2.bi.h.326.14		80	3.2	odd	2	inner
825.2.bi.h.701.7		80	55.19	odd	10	inner
825.2.bi.h.701.8		80	33.8	even	10	inner
825.2.bi.h.701.13		80	165.74	even	10	inner
825.2.bi.h.701.14		80	11.8	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.568905 - 0.413334i) q^{2} +(0.247937 - 1.71421i) q^{3} +(-0.465226 - 1.43182i) q^{4} +(-0.849595 + 0.872744i) q^{6} +(1.89391 - 0.615368i) q^{7} +(-0.761754 + 2.34444i) q^{8} +(-2.87705 - 0.850033i) q^{9} +O(q^{10})\)	\(q+(-0.568905 - 0.413334i) q^{2} +(0.247937 - 1.71421i) q^{3} +(-0.465226 - 1.43182i) q^{4} +(-0.849595 + 0.872744i) q^{6} +(1.89391 - 0.615368i) q^{7} +(-0.761754 + 2.34444i) q^{8} +(-2.87705 - 0.850033i) q^{9} +(-3.26241 + 0.597209i) q^{11} +(-2.56979 + 0.442496i) q^{12} +(-2.49497 + 3.43403i) q^{13} +(-1.33181 - 0.432730i) q^{14} +(-1.03355 + 0.750920i) q^{16} +(-3.45873 + 2.51291i) q^{17} +(1.28542 + 1.67277i) q^{18} +(-0.257486 - 0.0836623i) q^{19} +(-0.585303 - 3.39914i) q^{21} +(2.10285 + 1.00871i) q^{22} +4.30856i q^{23} +(3.83000 + 1.88708i) q^{24} +(2.83880 - 0.922383i) q^{26} +(-2.17047 + 4.72113i) q^{27} +(-1.76219 - 2.42545i) q^{28} +(-2.26468 - 6.96997i) q^{29} +(-5.24479 - 3.81056i) q^{31} +5.82855 q^{32} +(0.214872 + 5.74054i) q^{33} +3.00636 q^{34} +(0.121388 + 4.51488i) q^{36} +(-1.84185 - 5.66863i) q^{37} +(0.111905 + 0.154024i) q^{38} +(5.26807 + 5.12834i) q^{39} +(2.95108 - 9.08248i) q^{41} +(-1.07200 + 2.17571i) q^{42} -1.68949i q^{43} +(2.37285 + 4.39334i) q^{44} +(1.78087 - 2.45116i) q^{46} +(-0.222639 - 0.0723398i) q^{47} +(1.03098 + 1.95791i) q^{48} +(-2.45491 + 1.78359i) q^{49} +(3.45012 + 6.55204i) q^{51} +(6.07763 + 1.97474i) q^{52} +(-4.07659 + 5.61095i) q^{53} +(3.18619 - 1.78875i) q^{54} +4.90891i q^{56} +(-0.207255 + 0.420643i) q^{57} +(-1.59253 + 4.90132i) q^{58} +(-10.0360 + 3.26089i) q^{59} +(5.68030 + 7.81826i) q^{61} +(1.40875 + 4.33570i) q^{62} +(-5.97196 + 0.160564i) q^{63} +(-1.24878 - 0.907295i) q^{64} +(2.25052 - 3.35464i) q^{66} -0.901700 q^{67} +(5.20712 + 3.78319i) q^{68} +(7.38579 + 1.06825i) q^{69} +(-0.309146 - 0.425503i) q^{71} +(4.18446 - 6.09756i) q^{72} +(9.79830 - 3.18366i) q^{73} +(-1.29520 + 3.98621i) q^{74} +0.407595i q^{76} +(-5.81121 + 3.13864i) q^{77} +(-0.877318 - 5.09501i) q^{78} +(-0.132574 + 0.182473i) q^{79} +(7.55489 + 4.89118i) q^{81} +(-5.43298 + 3.94729i) q^{82} +(1.62687 - 1.18199i) q^{83} +(-4.59464 + 2.41941i) q^{84} +(-0.698323 + 0.961159i) q^{86} +(-12.5095 + 2.15403i) q^{87} +(1.08504 - 8.10345i) q^{88} -15.8563i q^{89} +(-2.61205 + 8.03907i) q^{91} +(6.16907 - 2.00445i) q^{92} +(-7.83249 + 8.04591i) q^{93} +(0.0967600 + 0.133179i) q^{94} +(1.44511 - 9.99138i) q^{96} +(2.67133 + 1.94083i) q^{97} +2.13383 q^{98} +(9.89379 + 1.05496i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9	\( 80 q - 4 q^{4} - 10 q^{6} + 10 q^{9} - 60 q^{16} + 20 q^{19} + 30 q^{24} - 20 q^{31} + 56 q^{34} + 2 q^{36} + 50 q^{39} - 40 q^{46} - 72 q^{49} + 30 q^{51} - 96 q^{64} - 42 q^{66} - 30 q^{69} - 66 q^{81} - 140 q^{84} + 48 q^{91} - 60 q^{94} - 70 q^{96} - 60 q^{99}+O(q^{100}) \) 80 * q - 4 * q^4 - 10 * q^6 + 10 * q^9 - 60 * q^16 + 20 * q^19 + 30 * q^24 - 20 * q^31 + 56 * q^34 + 2 * q^36 + 50 * q^39 - 40 * q^46 - 72 * q^49 + 30 * q^51 - 96 * q^64 - 42 * q^66 - 30 * q^69 - 66 * q^81 - 140 * q^84 + 48 * q^91 - 60 * q^94 - 70 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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