LMFDB - Embedded newform 735.2.y.j.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(128,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("735.128");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.1
Character	$\chi$	$=$	735.263
Dual form			735.2.y.j.422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.658710 + 2.45834i) q^{2} +(0.405074 - 1.68402i) q^{3} +(-3.87749 - 2.23867i) q^{4} +(0.108509 - 2.23343i) q^{5} +(3.87306 + 2.10509i) q^{6} +(4.45829 - 4.45829i) q^{8} +(-2.67183 - 1.36430i) q^{9} +(5.41906 + 1.73794i) q^{10} +(-1.35854 - 0.784351i) q^{11} +(-5.34063 + 5.62293i) q^{12} +(2.21881 + 2.21881i) q^{13} +(-3.71719 - 1.08744i) q^{15} +(3.54593 + 6.14174i) q^{16} +(-4.92759 + 1.32034i) q^{17} +(5.11388 - 5.66959i) q^{18} +(1.45527 - 0.840200i) q^{19} +(-5.42066 + 8.41719i) q^{20} +(2.82308 - 2.82308i) q^{22} +(-1.36036 - 0.364506i) q^{23} +(-5.70190 - 9.31377i) q^{24} +(-4.97645 - 0.484694i) q^{25} +(-6.91613 + 3.99303i) q^{26} +(-3.37980 + 3.94676i) q^{27} -8.91955 q^{29} +(5.12184 - 8.42181i) q^{30} +(-1.37417 + 2.38013i) q^{31} +(-5.25396 + 1.40779i) q^{32} +(-1.87117 + 1.97008i) q^{33} -12.9834i q^{34} +(7.30576 + 11.2714i) q^{36} +(-0.601543 - 0.161183i) q^{37} +(1.10690 + 4.13100i) q^{38} +(4.63529 - 2.83773i) q^{39} +(-9.47353 - 10.4411i) q^{40} -6.44292i q^{41} +(-5.47734 - 5.47734i) q^{43} +(3.51180 + 6.08262i) q^{44} +(-3.33700 + 5.81932i) q^{45} +(1.79216 - 3.10412i) q^{46} +(1.35194 - 5.04552i) q^{47} +(11.7792 - 3.48356i) q^{48} +(4.46958 - 11.9145i) q^{50} +(0.227443 + 8.83299i) q^{51} +(-3.63622 - 13.5706i) q^{52} +(1.03716 + 3.87074i) q^{53} +(-7.47618 - 10.9085i) q^{54} +(-1.89921 + 2.94909i) q^{55} +(-0.825420 - 2.79104i) q^{57} +(5.87540 - 21.9273i) q^{58} +(-2.77436 + 4.80533i) q^{59} +(11.9789 + 12.5381i) q^{60} +(-3.70333 - 6.41435i) q^{61} +(-4.94599 - 4.94599i) q^{62} +0.340400i q^{64} +(5.19632 - 4.71480i) q^{65} +(-3.61056 - 5.89768i) q^{66} +(-1.37347 - 5.12587i) q^{67} +(22.0625 + 5.91162i) q^{68} +(-1.16488 + 2.14321i) q^{69} +3.61943i q^{71} +(-17.9943 + 5.82933i) q^{72} +(8.05596 - 2.15859i) q^{73} +(0.792485 - 1.37262i) q^{74} +(-2.83207 + 8.18409i) q^{75} -7.52372 q^{76} +(3.92279 + 13.2644i) q^{78} +(-14.7720 + 8.52862i) q^{79} +(14.1019 - 7.25318i) q^{80} +(5.27735 + 7.29037i) q^{81} +(15.8389 + 4.24402i) q^{82} +(3.21312 - 3.21312i) q^{83} +(2.41421 + 11.1487i) q^{85} +(17.0731 - 9.85718i) q^{86} +(-3.61308 + 15.0207i) q^{87} +(-9.55360 + 2.55988i) q^{88} +(4.70137 + 8.14301i) q^{89} +(-12.1077 - 12.0367i) q^{90} +(4.45876 + 4.45876i) q^{92} +(3.45154 + 3.27825i) q^{93} +(11.5131 + 6.64707i) q^{94} +(-1.71862 - 3.34142i) q^{95} +(0.242507 + 9.41801i) q^{96} +(4.39640 - 4.39640i) q^{97} +(2.55968 + 3.94911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{3} + 16 q^{10} - 16 q^{12} - 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} - 32 q^{27} - 20 q^{30} - 28 q^{33} + 32 q^{36} + 16 q^{37} - 64 q^{40} - 80 q^{43} - 20 q^{45}+ \cdots + 48 q^{97}+O(q^{100}) $ 48 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 - 16 * q^13 - 32 * q^15 + 16 * q^16 + 20 * q^18 + 16 * q^22 + 16 * q^25 - 32 * q^27 - 20 * q^30 - 28 * q^33 + 32 * q^36 + 16 * q^37 - 64 * q^40 - 80 * q^43 - 20 * q^45 + 64 * q^46 + 32 * q^48 + 20 * q^51 + 80 * q^55 + 8 * q^57 - 40 * q^58 - 32 * q^60 - 32 * q^61 + 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 60 * q^75 + 64 * q^76 + 120 * q^78 - 52 * q^81 + 80 * q^82 + 48 * q^85 - 4 * q^87 - 96 * q^88 - 48 * q^90 + 76 * q^93 + 96 * q^96 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.658710	+	2.45834i	−0.465779	+	1.73831i	0.188517	+	0.982070i	$0.439632\pi$
$2$	−0.658710	+	2.45834i	−0.465779	+	1.73831i	−0.654295	+	0.756239i	$0.727035\pi$
$3$	0.405074	−	1.68402i	0.233870	−	0.972268i
$3$	0.405074	−	1.68402i	0.233870	−	0.972268i
$4$	−3.87749	−	2.23867i	−1.93874	−	1.11933i
$5$	0.108509	−	2.23343i	0.0485266	−	0.998822i
$5$	0.108509	−	2.23343i	0.0485266	−	0.998822i
$6$	3.87306	+	2.10509i	1.58117	+	0.859399i
$7$		0			0
$7$		0			0
$8$	4.45829	−	4.45829i	1.57624	−	1.57624i
$9$	−2.67183	−	1.36430i	−0.890610	−	0.454768i
$10$	5.41906	+	1.73794i	1.71366	+	0.549584i
$11$	−1.35854	−	0.784351i	−0.409614	−	0.236491i	0.281010	−	0.959705i	$-0.409331\pi$
$11$	−1.35854	−	0.784351i	−0.409614	−	0.236491i	−0.690624	+	0.723214i	$0.742664\pi$
$12$	−5.34063	+	5.62293i	−1.54171	+	1.62320i
$13$	2.21881	+	2.21881i	0.615386	+	0.615386i	0.944345	−	0.328958i	$-0.106697\pi$
$13$	2.21881	+	2.21881i	0.615386	+	0.615386i	−0.328958	+	0.944345i	$0.606697\pi$
$14$		0			0
$15$	−3.71719	−	1.08744i	−0.959774	−	0.280775i
$16$	3.54593	+	6.14174i	0.886484	+	1.53543i
$17$	−4.92759	+	1.32034i	−1.19512	+	0.320230i	−0.800906	−	0.598790i	$-0.795648\pi$
$17$	−4.92759	+	1.32034i	−1.19512	+	0.320230i	−0.394210	+	0.919020i	$0.628982\pi$
$18$	5.11388	−	5.66959i	1.20535	−	1.33633i
$19$	1.45527	−	0.840200i	0.333862	−	0.192755i	−0.323693	−	0.946162i	$-0.604924\pi$
$19$	1.45527	−	0.840200i	0.333862	−	0.192755i	0.657554	+	0.753407i	$0.271591\pi$
$20$	−5.42066	+	8.41719i	−1.21210	+	1.88214i
$21$		0			0
$22$	2.82308	−	2.82308i	0.601883	−	0.601883i
$23$	−1.36036	−	0.364506i	−0.283654	−	0.0760049i	0.114187	−	0.993459i	$-0.463574\pi$
$23$	−1.36036	−	0.364506i	−0.283654	−	0.0760049i	−0.397841	+	0.917454i	$0.630240\pi$
$24$	−5.70190	−	9.31377i	−1.16390	−	1.90117i
$25$	−4.97645	−	0.484694i	−0.995290	−	0.0969389i
$26$	−6.91613	+	3.99303i	−1.35637	+	0.783098i
$27$	−3.37980	+	3.94676i	−0.650443	+	0.759555i
$28$		0			0
$29$	−8.91955			−1.65632			−0.828159	−	0.560493i	$-0.810612\pi$
$29$	−8.91955			−1.65632			−0.828159	+	0.560493i	$0.810612\pi$
$30$	5.12184	−	8.42181i	0.935116	−	1.53760i
$31$	−1.37417	+	2.38013i	−0.246808	+	0.427484i	−0.962638	−	0.270790i	$-0.912715\pi$
$31$	−1.37417	+	2.38013i	−0.246808	+	0.427484i	0.715830	+	0.698274i	$0.246048\pi$
$32$	−5.25396	+	1.40779i	−0.928777	+	0.248865i
$33$	−1.87117	+	1.97008i	−0.325728	+	0.342946i
$34$		−	12.9834i		−	2.22664i
$35$		0			0
$36$	7.30576	+	11.2714i	1.21763	+	1.87857i
$37$	−0.601543	−	0.161183i	−0.0988930	−	0.0264983i	0.209033	−	0.977909i	$-0.432968\pi$
$37$	−0.601543	−	0.161183i	−0.0988930	−	0.0264983i	−0.307926	+	0.951410i	$0.599635\pi$
$38$	1.10690	+	4.13100i	0.179562	+	0.670136i
$39$	4.63529	−	2.83773i	0.742241	−	0.454400i
$40$	−9.47353	−	10.4411i	−1.49790	−	1.65088i
$41$		−	6.44292i		−	1.00622i	−0.864224	−	0.503108i	$-0.832190\pi$
$41$		−	6.44292i		−	1.00622i	0.864224	−	0.503108i	$-0.167810\pi$
$42$		0			0
$43$	−5.47734	−	5.47734i	−0.835286	−	0.835286i	0.152948	−	0.988234i	$-0.451123\pi$
$43$	−5.47734	−	5.47734i	−0.835286	−	0.835286i	−0.988234	+	0.152948i	$0.951123\pi$
$44$	3.51180	+	6.08262i	0.529424	+	0.916989i
$45$	−3.33700	+	5.81932i	−0.497450	+	0.867492i
$46$	1.79216	−	3.10412i	0.264240	−	0.457677i
$47$	1.35194	−	5.04552i	0.197201	−	0.735965i	−0.794485	−	0.607284i	$-0.792259\pi$
$47$	1.35194	−	5.04552i	0.197201	−	0.735965i	0.991686	−	0.128681i	$-0.0410743\pi$
$48$	11.7792	−	3.48356i	1.70018	−	0.502808i
$49$		0			0
$50$	4.46958	−	11.9145i	0.632095	−	1.68497i
$51$	0.227443	+	8.83299i	0.0318484	+	1.23687i
$52$	−3.63622	−	13.5706i	−0.504253	−	1.88190i
$53$	1.03716	+	3.87074i	0.142465	+	0.531687i	0.999855	+	0.0170196i	$0.00541776\pi$
$53$	1.03716	+	3.87074i	0.142465	+	0.531687i	−0.857390	+	0.514667i	$0.827916\pi$
$54$	−7.47618	−	10.9085i	−1.01738	−	1.48446i
$55$	−1.89921	+	2.94909i	−0.256089	+	0.397655i
$56$		0			0
$57$	−0.825420	−	2.79104i	−0.109330	−	0.369683i
$58$	5.87540	−	21.9273i	0.771478	−	2.87919i
$59$	−2.77436	+	4.80533i	−0.361191	+	0.625600i	−0.988157	−	0.153446i	$-0.950963\pi$
$59$	−2.77436	+	4.80533i	−0.361191	+	0.625600i	0.626967	+	0.779046i	$0.284296\pi$
$60$	11.9789	+	12.5381i	1.54647	+	1.61866i
$61$	−3.70333	−	6.41435i	−0.474162	−	0.821273i	0.525400	−	0.850855i	$-0.323916\pi$
$61$	−3.70333	−	6.41435i	−0.474162	−	0.821273i	−0.999562	+	0.0295820i	$0.990582\pi$
$62$	−4.94599	−	4.94599i	−0.628141	−	0.628141i
$63$		0			0
$64$			0.340400i			0.0425500i
$65$	5.19632	−	4.71480i	0.644524	−	0.584799i
$66$	−3.61056	−	5.89768i	−0.444429	−	0.725954i
$67$	−1.37347	−	5.12587i	−0.167797	−	0.626225i	−0.997667	−	0.0682690i	$-0.978252\pi$
$67$	−1.37347	−	5.12587i	−0.167797	−	0.626225i	0.829870	−	0.557956i	$-0.188414\pi$
$68$	22.0625	+	5.91162i	2.67547	+	0.716890i
$69$	−1.16488	+	2.14321i	−0.140235	+	0.258012i
$70$		0			0
$71$			3.61943i			0.429548i	0.976664	+	0.214774i	$0.0689015\pi$
$71$			3.61943i			0.429548i	−0.976664	+	0.214774i	$0.931099\pi$
$72$	−17.9943	+	5.82933i	−2.12064	+	0.686993i
$73$	8.05596	−	2.15859i	0.942878	−	0.252644i	0.245541	−	0.969386i	$-0.421034\pi$
$73$	8.05596	−	2.15859i	0.942878	−	0.252644i	0.697338	+	0.716743i	$0.254368\pi$
$74$	0.792485	−	1.37262i	0.0921245	−	0.159564i
$75$	−2.83207	+	8.18409i	−0.327019	+	0.945018i
$76$	−7.52372			−0.863030
$77$		0			0
$78$	3.92279	+	13.2644i	0.444168	+	1.50189i
$79$	−14.7720	+	8.52862i	−1.66198	+	0.959544i	−0.690211	+	0.723608i	$0.742482\pi$
$79$	−14.7720	+	8.52862i	−1.66198	+	0.959544i	−0.971769	+	0.235936i	$0.924184\pi$
$80$	14.1019	−	7.25318i	1.57664	−	0.810930i
$81$	5.27735	+	7.29037i	0.586372	+	0.810042i
$82$	15.8389	+	4.24402i	1.74911	+	0.468674i
$83$	3.21312	−	3.21312i	0.352686	−	0.352686i	−0.508422	−	0.861108i	$-0.669771\pi$
$83$	3.21312	−	3.21312i	0.352686	−	0.352686i	0.861108	+	0.508422i	$0.169771\pi$
$84$		0			0
$85$	2.41421	+	11.1487i	0.261858	+	1.20925i
$86$	17.0731	−	9.85718i	1.84104	−	1.06293i
$87$	−3.61308	+	15.0207i	−0.387363	+	1.61039i
$88$	−9.55360	+	2.55988i	−1.01842	+	0.272884i
$89$	4.70137	+	8.14301i	0.498344	+	0.863157i	0.999998	−	0.00191126i	$-0.000608372\pi$
$89$	4.70137	+	8.14301i	0.498344	+	0.863157i	−0.501654	+	0.865068i	$0.667275\pi$
$90$	−12.1077	−	12.0367i	−1.27627	−	1.26878i
$91$		0			0
$92$	4.45876	+	4.45876i	0.464858	+	0.464858i
$93$	3.45154	+	3.27825i	0.357908	+	0.339939i
$94$	11.5131	+	6.64707i	1.18748	+	0.685593i
$95$	−1.71862	−	3.34142i	−0.176327	−	0.342822i
$96$	0.242507	+	9.41801i	0.0247508	+	0.961222i
$97$	4.39640	−	4.39640i	0.446386	−	0.446386i	−0.447765	−	0.894151i	$-0.647780\pi$
$97$	4.39640	−	4.39640i	0.446386	−	0.446386i	0.894151	+	0.447765i	$0.147780\pi$
$98$		0			0
$99$	2.55968	+	3.94911i	0.257258	+	0.396900i
$100$	18.2111	+	13.0200i	1.82111	+	1.30200i
$101$	0.875832	+	0.505662i	0.0871485	+	0.0503152i	0.542941	−	0.839771i	$-0.317311\pi$
$101$	0.875832	+	0.505662i	0.0871485	+	0.0503152i	−0.455792	+	0.890086i	$0.650644\pi$
$102$	−21.8643	−	5.25925i	−2.16489	−	0.520743i
$103$	−1.47530	+	5.50588i	−0.145365	+	0.542511i	0.854374	+	0.519659i	$0.173941\pi$
$103$	−1.47530	+	5.50588i	−0.145365	+	0.542511i	−0.999739	+	0.0228513i	$0.992726\pi$
$104$	19.7842			1.94000
$105$		0			0
$106$	−10.1988			−0.990593
$107$	1.03131	−	3.84892i	0.0997009	−	0.372089i	−0.897989	−	0.440017i	$-0.854972\pi$
$107$	1.03131	−	3.84892i	0.0997009	−	0.372089i	0.997690	+	0.0679285i	$0.0216390\pi$
$108$	21.9406	−	7.73728i	2.11124	−	0.744520i
$109$	−5.56202	−	3.21123i	−0.532744	−	0.307580i	0.209389	−	0.977832i	$-0.432853\pi$
$109$	−5.56202	−	3.21123i	−0.532744	−	0.307580i	−0.742133	+	0.670252i	$0.766186\pi$
$110$	−5.99884	−	6.61150i	−0.571967	−	0.630381i
$111$	−0.515104	+	0.947718i	−0.0488915	+	0.0899534i
$112$		0			0
$113$	3.29246	−	3.29246i	0.309729	−	0.309729i	−0.535075	−	0.844804i	$-0.679717\pi$
$113$	3.29246	−	3.29246i	0.309729	−	0.309729i	0.844804	+	0.535075i	$0.179717\pi$
$114$	7.40505	−	0.190675i	0.693546	−	0.0178583i
$115$	−0.961712	+	2.99871i	−0.0896801	+	0.279632i
$116$	34.5854	+	19.9679i	3.21118	+	1.85397i
$117$	−2.90115	−	8.95540i	−0.268211	−	0.827927i
$118$	−9.98563	−	9.98563i	−0.919252	−	0.919252i
$119$		0			0
$120$	−21.4204	+	11.7242i	−1.95541	+	1.07027i
$121$	−4.26959	−	7.39514i	−0.388144	−	0.672286i
$122$	18.2081	−	4.87884i	1.64848	−	0.441709i
$123$	−10.8500	−	2.60986i	−0.978311	−	0.235323i
$124$	10.6566	−	6.15262i	0.956995	−	0.552521i
$125$	−1.62252	+	11.0620i	−0.145123	+	0.989414i
$126$		0			0
$127$	14.2818	−	14.2818i	1.26730	−	1.26730i	0.319826	−	0.947476i	$-0.396376\pi$
$127$	14.2818	−	14.2818i	1.26730	−	1.26730i	0.947476	−	0.319826i	$-0.103624\pi$
$128$	−11.3447	−	3.03981i	−1.00274	−	0.268684i
$129$	−11.4427	+	7.00520i	−1.00747	+	0.616774i
$130$	8.16771	+	15.8800i	0.716356	+	1.39277i
$131$	4.24118	−	2.44864i	0.370553	−	0.213939i	−0.303147	−	0.952944i	$-0.598037\pi$
$131$	4.24118	−	2.44864i	0.370553	−	0.213939i	0.673700	+	0.739005i	$0.264704\pi$
$132$	11.6658	−	3.45002i	1.01538	−	0.300286i
$133$		0			0
$134$	13.5059			1.16673
$135$	8.44810	+	7.97682i	0.727097	+	0.686535i
$136$	−16.0821	+	27.8551i	−1.37903	+	2.38856i
$137$	6.22744	−	1.66864i	0.532046	−	0.142561i	0.0172133	−	0.999852i	$-0.494521\pi$
$137$	6.22744	−	1.66864i	0.532046	−	0.142561i	0.514833	+	0.857290i	$0.327854\pi$
$138$	−4.50143	−	4.27543i	−0.383187	−	0.363949i
$139$			10.2045i			0.865536i	0.901505	+	0.432768i	$0.142463\pi$
$139$			10.2045i			0.865536i	−0.901505	+	0.432768i	$0.857537\pi$
$140$		0			0
$141$	−7.94911	−	4.32050i	−0.669435	−	0.363852i
$142$	−8.89780	−	2.38416i	−0.746687	−	0.200074i
$143$	−1.27400	−	4.75465i	−0.106538	−	0.397604i
$144$	−1.09494	−	21.2474i	−0.0912449	−	1.77062i
$145$	−0.967850	+	19.9212i	−0.0803755	+	1.65437i
$146$			21.2262i			1.75669i
$147$		0			0
$148$	1.97164	+	1.97164i	0.162068	+	0.162068i
$149$	0.461562	+	0.799449i	0.0378126	+	0.0654934i	0.884312	−	0.466896i	$-0.154628\pi$
$149$	0.461562	+	0.799449i	0.0378126	+	0.0654934i	−0.846500	+	0.532389i	$0.821294\pi$
$150$	−18.2538	−	12.3531i	−1.49041	−	1.00863i
$151$	6.86549	−	11.8914i	0.558705	−	0.967706i	−0.438900	−	0.898536i	$-0.644632\pi$
$151$	6.86549	−	11.8914i	0.558705	−	0.967706i	0.997605	−	0.0691699i	$-0.0220350\pi$
$152$	2.74216	−	10.2339i	0.222418	−	0.830077i
$153$	14.9670	+	3.19499i	1.21001	+	0.258300i
$154$		0			0
$155$	5.16675	+	3.32738i	0.415004	+	0.267262i
$156$	−24.3260	+	0.626378i	−1.94764	+	0.0501504i
$157$	−5.02228	−	18.7434i	−0.400822	−	1.49589i	−0.811634	−	0.584166i	$-0.801422\pi$
$157$	−5.02228	−	18.7434i	−0.400822	−	1.49589i	0.410812	−	0.911720i	$-0.365245\pi$
$158$	−11.2358	−	41.9325i	−0.893870	−	3.33597i
$159$	6.93851	−	0.178662i	0.550260	−	0.0141688i
$160$	2.57411	+	11.8871i	0.203501	+	0.939759i
$161$		0			0
$162$	−21.3985	+	8.17128i	−1.68122	+	0.641997i
$163$	2.41784	−	9.02349i	0.189380	−	0.706775i	−0.804271	−	0.594263i	$-0.797444\pi$
$163$	2.41784	−	9.02349i	0.189380	−	0.706775i	0.993650	−	0.112512i	$-0.0358895\pi$
$164$	−14.4236	+	24.9823i	−1.12629	+	1.95079i
$165$	4.19700	+	4.39290i	0.326736	+	0.341987i
$166$	5.78243	+	10.0155i	0.448804	+	0.777350i
$167$	−3.11442	−	3.11442i	−0.241001	−	0.241001i	0.576263	−	0.817264i	$-0.304510\pi$
$167$	−3.11442	−	3.11442i	−0.241001	−	0.241001i	−0.817264	+	0.576263i	$0.804510\pi$
$168$		0			0
$169$		−	3.15379i		−	0.242599i
$170$	−28.9976	−	1.40882i	−2.22401	−	0.108051i
$171$	−5.03452	+	0.259443i	−0.385000	+	0.0198401i
$172$	8.97636	+	33.5002i	0.684441	+	2.55437i
$173$	−11.1040	−	2.97531i	−0.844222	−	0.226209i	−0.189313	−	0.981917i	$-0.560626\pi$
$173$	−11.1040	−	2.97531i	−0.844222	−	0.226209i	−0.654909	+	0.755708i	$0.727293\pi$
$174$	−34.5460	−	18.7764i	−2.61892	−	1.42344i
$175$		0			0
$176$		−	11.1250i		−	0.838580i
$177$	6.96844	+	6.61858i	0.523780	+	0.497483i
$178$	−23.1151	+	6.19368i	−1.73255	+	0.464236i
$179$	−8.29901	+	14.3743i	−0.620297	+	1.07439i	0.369133	+	0.929377i	$0.379655\pi$
$179$	−8.29901	+	14.3743i	−0.620297	+	1.07439i	−0.989430	+	0.145010i	$0.953679\pi$
$180$	25.9667	−	15.0939i	1.93544	−	1.12503i
$181$	11.6532			0.866174			0.433087	−	0.901352i	$-0.357424\pi$
$181$	11.6532			0.866174			0.433087	+	0.901352i	$0.357424\pi$
$182$		0			0
$183$	−12.3020	+	3.63818i	−0.909390	+	0.268942i
$184$	−7.68994	+	4.43979i	−0.566910	+	0.327306i
$185$	−0.425264	+	1.32602i	−0.0312660	+	0.0974907i
$186$	−10.3326	+	6.32564i	−0.757625	+	0.463819i
$187$	7.72992	+	2.07123i	0.565268	+	0.151463i
$188$	−16.5374	+	16.5374i	−1.20611	+	1.20611i
$189$		0			0
$190$	9.34642	−	2.02393i	0.678060	−	0.146831i
$191$	−11.1322	+	6.42717i	−0.805497	+	0.465054i	−0.845390	−	0.534150i	$-0.820632\pi$
$191$	−11.1322	+	6.42717i	−0.805497	+	0.465054i	0.0398927	+	0.999204i	$0.487298\pi$
$192$	0.573240	+	0.137887i	0.0413700	+	0.00995116i
$193$	11.0123	−	2.95074i	0.792684	−	0.212399i	0.160315	−	0.987066i	$-0.448749\pi$
$193$	11.0123	−	2.95074i	0.792684	−	0.212399i	0.632370	+	0.774667i	$0.282082\pi$
$194$	7.91189	+	13.7038i	0.568040	+	0.983875i
$195$	−5.83491	−	10.6605i	−0.417847	−	0.763417i
$196$		0			0
$197$	−18.7512	−	18.7512i	−1.33597	−	1.33597i	−0.899929	−	0.436036i	$-0.856382\pi$
$197$	−18.7512	−	18.7512i	−1.33597	−	1.33597i	−0.436036	−	0.899929i	$-0.643618\pi$
$198$	−11.3943	+	3.69125i	−0.809760	+	0.262326i
$199$	−3.64362	−	2.10364i	−0.258289	−	0.149123i	0.365265	−	0.930904i	$-0.380978\pi$
$199$	−3.64362	−	2.10364i	−0.258289	−	0.149123i	−0.623554	+	0.781780i	$0.714312\pi$
$200$	−24.3474	+	20.0256i	−1.72162	+	1.41602i
$201$	−9.18842	+	0.236595i	−0.648101	+	0.0166882i
$202$	−1.82001	+	1.82001i	−0.128055	+	0.128055i
$203$		0			0
$204$	18.8922	−	34.7590i	1.32272	−	2.43361i
$205$	−14.3898	−	0.699114i	−1.00503	−	0.0488282i
$206$	−12.5635	−	7.25356i	−0.875343	−	0.505380i
$207$	3.13734	+	2.82984i	0.218061	+	0.196687i
$208$	−5.75959	+	21.4951i	−0.399356	+	1.49042i
$209$	−2.63605			−0.182339
$210$		0			0
$211$	−21.5211			−1.48158			−0.740788	−	0.671739i	$-0.765548\pi$
$211$	−21.5211			−1.48158			−0.740788	+	0.671739i	$0.765548\pi$
$212$	4.64372	−	17.3306i	0.318932	−	1.19027i
$213$	6.09519	+	1.46614i	0.417636	+	0.100458i
$214$	8.78261	+	5.07064i	0.600367	+	0.346622i
$215$	−12.8276	+	11.6389i	−0.874836	+	0.793768i
$216$	2.52769	+	32.6639i	0.171988	+	2.22250i
$217$		0			0
$218$	11.5581	−	11.5581i	0.782810	−	0.782810i
$219$	−0.371840	−	14.4408i	−0.0251266	−	0.975816i
$220$	13.9662	−	7.18336i	0.941600	−	0.484302i
$221$	−13.8630	−	8.00378i	−0.932524	−	0.538393i
$222$	−1.99051	−	1.89057i	−0.133594	−	0.126887i
$223$	12.4001	+	12.4001i	0.830375	+	0.830375i	0.987568	−	0.157193i	$-0.0502445\pi$
$223$	12.4001	+	12.4001i	0.830375	+	0.830375i	−0.157193	+	0.987568i	$0.550244\pi$
$224$		0			0
$225$	12.6350	+	8.08441i	0.842331	+	0.538961i
$226$	5.92522	+	10.2628i	0.394139	+	0.682670i
$227$	11.8920	−	3.18646i	0.789301	−	0.211493i	0.158420	−	0.987372i	$-0.449360\pi$
$227$	11.8920	−	3.18646i	0.789301	−	0.211493i	0.630881	+	0.775879i	$0.282693\pi$
$228$	−3.04766	+	12.6701i	−0.201836	+	0.839096i
$229$	3.86544	−	2.23171i	0.255435	−	0.147476i	−0.366815	−	0.930294i	$-0.619552\pi$
$229$	3.86544	−	2.23171i	0.255435	−	0.147476i	0.622251	+	0.782818i	$0.286219\pi$
$230$	−6.73837	−	4.33950i	−0.444315	−	0.286138i
$231$		0			0
$232$	−39.7659	+	39.7659i	−2.61076	+	2.61076i
$233$	7.70659	+	2.06497i	0.504875	+	0.135281i	0.502262	−	0.864716i	$-0.332501\pi$
$233$	7.70659	+	2.06497i	0.504875	+	0.135281i	0.00261362	+	0.999997i	$0.499168\pi$
$234$	23.9264	−	1.23300i	1.56412	−	0.0806035i
$235$	−11.1221	−	3.56696i	−0.725528	−	0.232683i
$236$	21.5151	−	12.4217i	1.40051	−	0.808586i
$237$	8.37859	+	28.3310i	0.544248	+	1.84030i
$238$		0			0
$239$	11.8594			0.767124			0.383562	−	0.923515i	$-0.374697\pi$
$239$	11.8594			0.767124			0.383562	+	0.923515i	$0.374697\pi$
$240$	−6.50215	−	26.6860i	−0.419712	−	1.72257i
$241$	9.03617	−	15.6511i	0.582071	−	1.00818i	−0.413163	−	0.910657i	$-0.635576\pi$
$241$	9.03617	−	15.6511i	0.582071	−	1.00818i	0.995234	−	0.0975190i	$-0.0310907\pi$
$242$	20.9922	−	5.62484i	1.34943	−	0.361579i
$243$	14.4148	−	5.93401i	0.924712	−	0.380667i
$244$			33.1621i			2.12298i
$245$		0			0
$246$	13.5629	−	24.9538i	0.864741	−	1.59100i
$247$	5.09321	+	1.36472i	0.324073	+	0.0868351i
$248$	4.48487	+	16.7378i	0.284789	+	1.06285i
$249$	−4.10940	−	6.71250i	−0.260423	−	0.425388i
$250$	−26.1253	−	11.2754i	−1.65231	−	0.713116i
$251$			3.19253i			0.201511i	0.994911	+	0.100755i	$0.0321259\pi$
$251$			3.19253i			0.201511i	−0.994911	+	0.100755i	$0.967874\pi$
$252$		0			0
$253$	1.56219	+	1.56219i	0.0982141	+	0.0982141i
$254$	25.7019	+	44.5170i	1.61268	+	2.79324i
$255$	19.7526	+	0.450477i	1.23695	+	0.0282100i
$256$	14.6054	−	25.2973i	0.912836	−	1.58108i
$257$	4.32342	−	16.1352i	0.269687	−	1.00649i	−0.689631	−	0.724161i	$-0.742227\pi$
$257$	4.32342	−	16.1352i	0.269687	−	1.00649i	0.959319	−	0.282326i	$-0.0911059\pi$
$258$	−9.68378	−	32.7443i	−0.602886	−	2.03857i
$259$		0			0
$260$	−30.7035	+	6.64874i	−1.90415	+	0.412337i
$261$	23.8315	+	12.1690i	1.47513	+	0.753240i
$262$	3.22589	+	12.0392i	0.199296	+	0.743784i
$263$	4.81330	+	17.9635i	0.296801	+	1.10768i	0.939777	+	0.341789i	$0.111033\pi$
$263$	4.81330	+	17.9635i	0.296801	+	1.10768i	−0.642976	+	0.765886i	$0.722301\pi$
$264$	0.440967	+	17.1254i	0.0271396	+	1.05399i
$265$	8.75757	−	1.89642i	0.537974	−	0.116496i
$266$		0			0
$267$	15.6174	−	4.61866i	0.955767	−	0.282658i
$268$	−6.14950	+	22.9503i	−0.375641	+	1.40191i
$269$	14.6703	−	25.4096i	0.894461	−	1.54925i	0.0599909	−	0.998199i	$-0.480893\pi$
$269$	14.6703	−	25.4096i	0.894461	−	1.54925i	0.834470	−	0.551053i	$-0.185774\pi$
$270$	−25.1746	+	15.5139i	−1.53208	+	0.944145i
$271$	−1.59183	−	2.75713i	−0.0966968	−	0.167484i	0.813619	−	0.581399i	$-0.197494\pi$
$271$	−1.59183	−	2.75713i	−0.0966968	−	0.167484i	−0.910316	+	0.413915i	$0.864161\pi$
$272$	−25.5821	−	25.5821i	−1.55114	−	1.55114i
$273$		0			0
$274$			16.4083i			0.991263i
$275$	6.38051	+	4.56176i	0.384759	+	0.275084i
$276$	9.31475	−	5.70250i	0.560682	−	0.343250i
$277$	6.17251	+	23.0361i	0.370870	+	1.38411i	0.859286	+	0.511495i	$0.170908\pi$
$277$	6.17251	+	23.0361i	0.370870	+	1.38411i	−0.488416	+	0.872611i	$0.662425\pi$
$278$	−25.0862	−	6.72182i	−1.50457	−	0.403148i
$279$	6.91877	−	4.48452i	0.414216	−	0.268481i
$280$		0			0
$281$			24.8052i			1.47975i	0.672742	+	0.739877i	$0.265116\pi$
$281$			24.8052i			1.47975i	−0.672742	+	0.739877i	$0.734884\pi$
$282$	15.8574	−	16.6956i	0.944296	−	0.994211i
$283$	−7.40274	+	1.98356i	−0.440047	+	0.117910i	−0.472039	−	0.881578i	$-0.656482\pi$
$283$	−7.40274	+	1.98356i	−0.440047	+	0.117910i	0.0319914	+	0.999488i	$0.489815\pi$
$284$	8.10271	−	14.0343i	0.480807	−	0.832783i
$285$	−6.32318	+	1.54067i	−0.374553	+	0.0912613i
$286$	12.5277			0.740781
$287$		0			0
$288$	15.9583	+	3.40661i	0.940354	+	0.200736i
$289$	7.81541	−	4.51223i	0.459730	−	0.265425i
$290$	−48.3356	−	15.5016i	−2.83836	−	0.910286i
$291$	−5.62274	−	9.18447i	−0.329611	−	0.538403i
$292$	−36.0692	−	9.66472i	−2.11079	−	0.565585i
$293$	8.60739	−	8.60739i	0.502849	−	0.502849i	−0.409473	−	0.912322i	$-0.634288\pi$
$293$	8.60739	−	8.60739i	0.502849	−	0.502849i	0.912322	+	0.409473i	$0.134288\pi$
$294$		0			0
$295$	10.4313	+	6.71776i	0.607336	+	0.391123i
$296$	−3.40045	+	1.96325i	−0.197647	+	0.114112i
$297$	7.68722	−	2.71087i	0.446058	−	0.157301i
$298$	−2.26935	+	0.608072i	−0.131460	+	0.0352246i
$299$	−2.20960	−	3.82714i	−0.127784	−	0.221329i
$300$	29.3028	−	25.3937i	1.69180	−	1.46610i
$301$		0			0
$302$	24.7107	+	24.7107i	1.42194	+	1.42194i
$303$	1.20632	−	1.27009i	0.0693013	−	0.0729645i
$304$	10.3206	+	5.95859i	0.591926	+	0.341749i
$305$	−14.7279	+	7.57512i	−0.843315	+	0.433750i
$306$	−17.7133	+	34.6895i	−1.01260	+	1.98307i
$307$	−11.8525	+	11.8525i	−0.676457	+	0.676457i	−0.959197	−	0.282740i	$-0.908757\pi$
$307$	−11.8525	+	11.8525i	−0.676457	+	0.676457i	0.282740	+	0.959197i	$0.408757\pi$
$308$		0			0
$309$	8.67440	+	4.71471i	0.493469	+	0.268211i
$310$	−11.5832	+	10.5099i	−0.657883	+	0.596920i
$311$	25.3572	+	14.6400i	1.43788	+	0.830158i	0.997702	−	0.0677541i	$-0.0215833\pi$
$311$	25.3572	+	14.6400i	1.43788	+	0.830158i	0.440174	+	0.897912i	$0.354917\pi$
$312$	8.01405	−	33.3169i	0.453706	−	1.88620i
$313$	0.448664	−	1.67444i	0.0253600	−	0.0946448i	−0.952086	−	0.305831i	$-0.901066\pi$
$313$	0.448664	−	1.67444i	0.0253600	−	0.0946448i	0.977446	+	0.211186i	$0.0677325\pi$
$314$	49.3859			2.78701
$315$		0			0
$316$	76.3710			4.29620
$317$	−1.57449	+	5.87608i	−0.0884322	+	0.330034i	−0.995942	−	0.0899974i	$-0.971314\pi$
$317$	−1.57449	+	5.87608i	−0.0884322	+	0.330034i	0.907510	+	0.420031i	$0.137981\pi$
$318$	−4.13126	+	17.1749i	−0.231670	+	0.963122i
$319$	12.1175	+	6.99605i	0.678451	+	0.391704i
$320$	0.760261	+	0.0369364i	0.0424999	+	0.00206481i
$321$	−6.06388	−	3.29585i	−0.338453	−	0.183956i
$322$		0			0
$323$	−6.06162	+	6.06162i	−0.337278	+	0.337278i
$324$	−4.14213	−	40.0826i	−0.230119	−	2.22681i
$325$	−9.96634	−	12.1172i	−0.552833	−	0.672143i
$326$	20.5902	+	11.8877i	1.14038	+	0.658401i
$327$	−7.66080	+	8.06575i	−0.423643	+	0.446037i
$328$	−28.7244	−	28.7244i	−1.58604	−	1.58604i
$329$		0			0
$330$	−13.5638	+	7.42400i	−0.746665	+	0.408678i
$331$	−16.6301	−	28.8042i	−0.914074	−	1.58322i	−0.808252	−	0.588837i	$-0.799586\pi$
$331$	−16.6301	−	28.8042i	−0.914074	−	1.58322i	−0.105822	−	0.994385i	$-0.533747\pi$
$332$	−19.6519	+	5.26572i	−1.07854	+	0.288994i
$333$	1.38732	+	1.25134i	0.0760245	+	0.0685730i
$334$	9.70781	−	5.60481i	0.531188	−	0.306681i
$335$	−11.5973	+	2.51136i	−0.633630	+	0.137210i
$336$		0			0
$337$	10.3056	−	10.3056i	0.561383	−	0.561383i	−0.368317	−	0.929700i	$-0.620066\pi$
$337$	10.3056	−	10.3056i	0.561383	−	0.561383i	0.929700	+	0.368317i	$0.120066\pi$
$338$	7.75309	+	2.07743i	0.421712	+	0.112997i
$339$	−4.21087	−	6.87826i	−0.228703	−	0.373576i
$340$	15.5972	−	48.6336i	0.845877	−	2.63753i
$341$	3.73371	−	2.15566i	0.202192	−	0.116736i
$342$	2.67849	−	12.5475i	0.144836	−	0.678489i
$343$		0			0
$344$	−48.8391			−2.63323
$345$	4.66032	+	2.83424i	0.250903	+	0.152590i
$346$	14.6286	−	25.3376i	0.786441	−	1.36216i
$347$	−26.2606	+	7.03650i	−1.40974	+	0.377739i	−0.881833	−	0.471562i	$-0.843691\pi$
$347$	−26.2606	+	7.03650i	−1.40974	+	0.377739i	−0.527909	+	0.849301i	$0.677024\pi$
$348$	47.6360	−	50.1540i	2.55356	−	2.68854i
$349$		−	30.1301i		−	1.61283i	−0.591353	−	0.806413i	$-0.701406\pi$
$349$		−	30.1301i		−	1.61283i	0.591353	−	0.806413i	$-0.298594\pi$
$350$		0			0
$351$	−16.2562	+	1.25799i	−0.867694	+	0.0671463i
$352$	8.24189	+	2.20841i	0.439294	+	0.117708i
$353$	−6.23486	−	23.2688i	−0.331848	−	1.23847i	−0.907246	−	0.420600i	$-0.861820\pi$
$353$	−6.23486	−	23.2688i	−0.331848	−	1.23847i	0.575398	−	0.817873i	$-0.304847\pi$
$354$	−20.8609	+	12.7711i	−1.10874	+	0.678774i
$355$	8.08377	+	0.392740i	0.429042	+	0.0208445i
$356$		−	42.0992i		−	2.23125i
$357$		0			0
$358$	−29.8703	−	29.8703i	−1.57869	−	1.57869i
$359$	−0.368991	−	0.639111i	−0.0194746	−	0.0337310i	0.856124	−	0.516771i	$-0.172866\pi$
$359$	−0.368991	−	0.639111i	−0.0194746	−	0.0337310i	−0.875598	+	0.483040i	$0.839533\pi$
$360$	11.0669	+	40.8215i	0.583276	+	2.15148i
$361$	−8.08813	+	14.0090i	−0.425691	+	0.737318i
$362$	−7.67607	+	28.6475i	−0.403445	+	1.50568i
$363$	−14.1831	+	4.19448i	−0.744417	+	0.220153i
$364$		0			0
$365$	−3.94692	−	18.2267i	−0.206591	−	0.954028i
$366$	−0.840432	−	32.6390i	−0.0439301	−	1.70607i
$367$	8.52557	+	31.8179i	0.445031	+	1.66088i	0.715854	+	0.698250i	$0.246038\pi$
$367$	8.52557	+	31.8179i	0.445031	+	1.66088i	−0.270822	+	0.962629i	$0.587296\pi$
$368$	−2.58503	−	9.64747i	−0.134754	−	0.502909i
$369$	−8.79010	+	17.2144i	−0.457594	+	0.896146i
$370$	−2.97967	−	1.91890i	−0.154906	−	0.0997591i
$371$		0			0
$372$	−6.04438	−	20.4382i	−0.313387	−	1.05967i
$373$	−1.93302	+	7.21411i	−0.100088	+	0.373533i	−0.997742	−	0.0671685i	$-0.978603\pi$
$373$	−1.93302	+	7.21411i	−0.100088	+	0.373533i	0.897654	+	0.440701i	$0.145270\pi$
$374$	−10.1836	+	17.6384i	−0.526579	+	0.912062i
$375$	17.9713	+	7.21328i	0.928035	+	0.372492i
$376$	−16.4670	−	28.5217i	−0.849222	−	1.47090i
$377$	−19.7908	−	19.7908i	−1.01928	−	1.01928i
$378$		0			0
$379$		−	3.38353i		−	0.173800i	−0.996217	−	0.0869000i	$-0.972304\pi$
$379$		−	3.38353i		−	0.173800i	0.996217	−	0.0869000i	$-0.0276961\pi$
$380$	−0.816390	+	16.8037i	−0.0418799	+	0.862013i
$381$	−18.2656	−	29.8359i	−0.935774	−	1.52854i
$382$	−8.46729	−	31.6004i	−0.433224	−	1.61681i
$383$	−3.91696	−	1.04955i	−0.200147	−	0.0536293i	0.157353	−	0.987542i	$-0.449704\pi$
$383$	−3.91696	−	1.04955i	−0.200147	−	0.0536293i	−0.357500	+	0.933913i	$0.616371\pi$
$384$	−9.71455	+	17.8734i	−0.495744	+	0.912097i
$385$		0			0
$386$			29.0157i			1.47686i
$387$	7.16176	+	22.1073i	0.364053	+	1.12378i
$388$	−26.8890	+	7.20490i	−1.36508	+	0.365773i
$389$	5.10508	−	8.84225i	0.258838	−	0.448320i	−0.707093	−	0.707120i	$-0.749994\pi$
$389$	5.10508	−	8.84225i	0.258838	−	0.448320i	0.965931	+	0.258800i	$0.0833272\pi$
$390$	30.0507	−	7.32199i	1.52168	−	0.370763i
$391$	7.18455			0.363339
$392$		0			0
$393$	−2.40557	−	8.13410i	−0.121345	−	0.410311i
$394$	58.4483	−	33.7452i	2.94458	−	1.70006i
$395$	17.4452	+	33.9177i	0.877764	+	1.70658i
$396$	−1.08440	−	21.0429i	−0.0544931	−	1.05744i
$397$	32.8576	+	8.80417i	1.64908	+	0.441869i	0.959354	−	0.282205i	$-0.0910658\pi$
$397$	32.8576	+	8.80417i	1.64908	+	0.441869i	0.689723	+	0.724074i	$0.257732\pi$
$398$	7.57156	−	7.57156i	0.379528	−	0.379528i
$399$		0			0
$400$	−14.6693	−	32.2828i	−0.733465	−	1.61414i
$401$	−17.3995	+	10.0456i	−0.868891	+	0.501654i	−0.866980	−	0.498344i	$-0.833942\pi$
$401$	−17.3995	+	10.0456i	−0.868891	+	0.501654i	−0.00191140	+	0.999998i	$0.500608\pi$
$402$	5.47087	−	22.7441i	0.272862	−	1.13437i
$403$	−8.33007	+	2.23203i	−0.414950	+	0.111186i
$404$	−2.26402	−	3.92139i	−0.112639	−	0.195097i
$405$	16.8552	−	10.9955i	0.837542	−	0.546373i
$406$		0			0
$407$	0.690793	+	0.690793i	0.0342413	+	0.0342413i
$408$	40.3940	+	38.3660i	1.99980	+	1.89940i
$409$	−29.0207	−	16.7551i	−1.43498	−	0.828487i	−0.437487	−	0.899225i	$-0.644131\pi$
$409$	−29.0207	−	16.7551i	−1.43498	−	0.828487i	−0.997495	+	0.0707377i	$0.977465\pi$
$410$	11.1974	−	34.9146i	0.553000	−	1.72431i
$411$	−0.287441	−	11.1630i	−0.0141784	−	0.550632i
$412$	18.0463	−	18.0463i	0.889077	−	0.889077i
$413$		0			0
$414$	−9.02331	+	5.84862i	−0.443471	+	0.287444i
$415$	−6.82764	−	7.52494i	−0.335156	−	0.369385i
$416$	−14.7811	−	8.53389i	−0.724705	−	0.418408i
$417$	17.1846	+	4.13359i	0.841533	+	0.202423i
$418$	1.73639	−	6.48030i	0.0849297	−	0.316962i
$419$	25.8773			1.26419			0.632093	−	0.774892i	$-0.282196\pi$
$419$	25.8773			1.26419			0.632093	+	0.774892i	$0.282196\pi$
$420$		0			0
$421$	10.4030			0.507013			0.253507	−	0.967334i	$-0.418416\pi$
$421$	10.4030			0.507013			0.253507	+	0.967334i	$0.418416\pi$
$422$	14.1762	−	52.9063i	0.690086	−	2.57544i
$423$	−10.4958	+	11.6363i	−0.510322	+	0.565777i
$424$	21.8808	+	12.6329i	1.06263	+	0.613508i
$425$	25.1619	−	4.18225i	1.22053	−	0.202869i
$426$	−7.61923	+	14.0183i	−0.369153	+	0.679188i
$427$		0			0
$428$	−12.6154	+	12.6154i	−0.609786	+	0.609786i
$429$	−8.52298	+	0.219461i	−0.411493	+	0.0105957i
$430$	−20.1628	−	39.2013i	−0.972335	−	1.89045i
$431$	−0.388850	−	0.224503i	−0.0187303	−	0.0108139i	0.490606	−	0.871382i	$-0.336776\pi$
$431$	−0.388850	−	0.224503i	−0.0187303	−	0.0108139i	−0.509336	+	0.860568i	$0.670109\pi$
$432$	−36.2245	−	6.76288i	−1.74285	−	0.325379i
$433$	−17.7813	−	17.7813i	−0.854517	−	0.854517i	0.136169	−	0.990686i	$-0.456521\pi$
$433$	−17.7813	−	17.7813i	−0.854517	−	0.854517i	−0.990686	+	0.136169i	$0.956521\pi$
$434$		0			0
$435$	33.1556	+	9.69944i	1.58969	+	0.465053i
$436$	14.3778	+	24.9030i	0.688570	+	1.19264i
$437$	−2.28594	+	0.612517i	−0.109352	+	0.0293007i
$438$	35.7452	+	8.59817i	1.70797	+	0.410836i
$439$	−25.5732	+	14.7647i	−1.22054	+	0.704679i	−0.965033	−	0.262128i	$-0.915576\pi$
$439$	−25.5732	+	14.7647i	−1.22054	+	0.704679i	−0.255507	+	0.966807i	$0.582243\pi$
$440$	4.68067	+	21.6151i	0.223142	+	1.03046i
$441$		0			0
$442$	28.8077	−	28.8077i	1.37024	−	1.37024i
$443$	21.2613	+	5.69694i	1.01015	+	0.270670i	0.725693	−	0.688018i	$-0.241519\pi$
$443$	21.2613	+	5.69694i	1.01015	+	0.270670i	0.284460	+	0.958688i	$0.408186\pi$
$444$	4.11894	−	2.52162i	0.195476	−	0.119671i
$445$	18.6970	−	9.61660i	0.886323	−	0.455871i
$446$	−38.6519	+	22.3157i	−1.83022	+	1.05668i
$447$	1.53325	−	0.453443i	0.0725204	−	0.0214471i
$448$		0			0
$449$	16.3214			0.770252			0.385126	−	0.922864i	$-0.374158\pi$
$449$	16.3214			0.770252			0.385126	+	0.922864i	$0.374158\pi$
$450$	−28.1970	+	25.7358i	−1.32922	+	1.21320i
$451$	−5.05351	+	8.75294i	−0.237961	+	0.412160i
$452$	−20.1372	+	5.39575i	−0.947175	+	0.253795i
$453$	−17.2442	−	16.3785i	−0.810205	−	0.769528i
$454$			31.3336i			1.47056i
$455$		0			0
$456$	−16.1232	−	8.76332i	−0.755040	−	0.410380i
$457$	28.1810	+	7.55108i	1.31825	+	0.353225i	0.848323	−	0.529479i	$-0.177613\pi$
$457$	28.1810	+	7.55108i	1.31825	+	0.353225i	0.469929	+	0.882704i	$0.344279\pi$
$458$	2.94010	+	10.9726i	0.137382	+	0.512717i
$459$	11.4432	−	23.9105i	0.534122	−	1.11605i
$460$	10.4422	−	9.47452i	0.486868	−	0.441752i
$461$		−	15.2893i		−	0.712094i	−0.934468	−	0.356047i	$-0.884124\pi$
$461$		−	15.2893i		−	0.712094i	0.934468	−	0.356047i	$-0.115876\pi$
$462$		0			0
$463$	0.492195	+	0.492195i	0.0228743	+	0.0228743i	0.718451	−	0.695577i	$-0.244851\pi$
$463$	0.492195	+	0.492195i	0.0228743	+	0.0228743i	−0.695577	+	0.718451i	$0.744851\pi$
$464$	−31.6281	−	54.7815i	−1.46830	−	2.54317i
$465$	7.69628	−	7.35307i	0.356907	−	0.340990i
$466$	−10.1528	+	17.5852i	−0.470320	+	0.814619i
$467$	−3.29439	+	12.2948i	−0.152446	+	0.568937i	0.846864	+	0.531809i	$0.178488\pi$
$467$	−3.29439	+	12.2948i	−0.152446	+	0.568937i	−0.999311	+	0.0371280i	$0.988179\pi$
$468$	−8.79901	+	41.2192i	−0.406734	+	1.90536i
$469$		0			0
$470$	16.0951	−	24.9924i	0.742410	−	1.15281i
$471$	−33.5986	+	0.865141i	−1.54814	+	0.0398636i
$472$	9.05465	+	33.7924i	0.416774	+	1.55542i
$473$	3.14500	+	11.7373i	0.144607	+	0.539682i
$474$	−75.1664	+	1.93548i	−3.45251	+	0.0888996i
$475$	−7.64932	+	3.47586i	−0.350975	+	0.159483i
$476$		0			0
$477$	2.50974	−	11.7570i	0.114913	−	0.538314i
$478$	−7.81194	+	29.1546i	−0.357310	+	1.33350i
$479$	11.3786	−	19.7083i	0.519901	−	0.900496i	−0.479831	−	0.877361i	$-0.659302\pi$
$479$	11.3786	−	19.7083i	0.519901	−	0.900496i	0.999732	−	0.0231347i	$-0.00736465\pi$
$480$	21.0608	+	0.480313i	0.961291	+	0.0219232i
$481$	−0.977074	−	1.69234i	−0.0445507	−	0.0771641i
$482$	32.5235	+	32.5235i	1.48141	+	1.48141i
$483$		0			0
$484$			38.2328i			1.73785i
$485$	−9.34201	−	10.2961i	−0.424199	−	0.467522i
$486$	5.09262	+	39.3454i	0.231006	+	1.78474i
$487$	−4.20631	−	15.6982i	−0.190606	−	0.711352i	−0.993361	−	0.115042i	$-0.963300\pi$
$487$	−4.20631	−	15.6982i	−0.190606	−	0.711352i	0.802754	−	0.596310i	$-0.203367\pi$
$488$	−45.1075	−	12.0865i	−2.04192	−	0.547131i
$489$	−14.2163	−	7.72687i	−0.642884	−	0.349421i
$490$		0			0
$491$		−	0.301729i		−	0.0136168i	−0.999977	−	0.00680841i	$-0.997833\pi$
$491$		−	0.301729i		−	0.0136168i	0.999977	−	0.00680841i	$-0.00216720\pi$
$492$	36.2281	+	34.4092i	1.63329	+	1.55129i
$493$	43.9519	−	11.7769i	1.97949	−	0.530404i
$494$	−6.70989	+	11.6219i	−0.301892	+	0.522893i
$495$	9.09781	−	5.28837i	0.408916	−	0.237694i
$496$	−19.4909			−0.875165
$497$		0			0
$498$	19.2085	−	5.68071i	0.860754	−	0.254559i
$499$	−17.5116	+	10.1103i	−0.783928	+	0.452601i	−0.837821	−	0.545946i	$-0.816170\pi$
$499$	−17.5116	+	10.1103i	−0.783928	+	0.452601i	0.0538926	+	0.998547i	$0.482837\pi$
$500$	31.0554	−	39.2604i	1.38884	−	1.75578i
$501$	−6.50631	+	3.98317i	−0.290681	+	0.177955i
$502$	−7.84832	−	2.10295i	−0.350288	−	0.0938593i
$503$	−23.8859	+	23.8859i	−1.06502	+	1.06502i	−0.0672882	+	0.997734i	$0.521435\pi$
$503$	−23.8859	+	23.8859i	−1.06502	+	1.06502i	−0.997734	+	0.0672882i	$0.978565\pi$
$504$		0			0
$505$	1.22440	−	1.90124i	0.0544850	−	0.0846042i
$506$	−4.86943	+	2.81137i	−0.216473	+	0.124980i
$507$	−5.31104	−	1.27752i	−0.235871	−	0.0567366i
$508$	−87.3495	+	23.4052i	−3.87551	+	1.03844i
$509$	5.88603	+	10.1949i	0.260894	+	0.451881i	0.966480	−	0.256743i	$-0.0826494\pi$
$509$	5.88603	+	10.1949i	0.260894	+	0.451881i	−0.705586	+	0.708624i	$0.749316\pi$
$510$	−14.1186	+	48.2618i	−0.625184	+	2.13707i
$511$		0			0
$512$	35.9587	+	35.9587i	1.58917	+	1.58917i
$513$	−1.60245	+	8.58332i	−0.0707498	+	0.378963i
$514$	36.8179	+	21.2569i	1.62397	+	0.937600i
$515$	12.1369	+	3.89241i	0.534817	+	0.171520i
$516$	60.0511	−	1.54627i	2.64360	−	0.0680709i
$517$	−5.79412	+	5.79412i	−0.254825	+	0.254825i
$518$		0			0
$519$	−9.50842	+	17.4941i	−0.417373	+	0.767907i
$520$	2.14676	−	44.1866i	0.0941415	−	1.93771i
$521$	−25.7965	−	14.8936i	−1.13016	−	0.652500i	−0.186187	−	0.982514i	$-0.559613\pi$
$521$	−25.7965	−	14.8936i	−1.13016	−	0.652500i	−0.943976	+	0.330014i	$0.892947\pi$
$522$	−45.6135	+	50.5702i	−1.99645	+	2.21340i
$523$	6.39348	−	23.8608i	0.279567	−	1.04336i	−0.673151	−	0.739505i	$-0.735060\pi$
$523$	6.39348	−	23.8608i	0.279567	−	1.04336i	0.952719	−	0.303854i	$-0.0982736\pi$
$524$	−21.9268			−0.957877
$525$		0			0
$526$	−47.3309			−2.06373
$527$	3.62875	−	13.5427i	0.158071	−	0.589929i
$528$	−18.7347	−	4.50646i	−0.815325	−	0.196118i
$529$	−18.2009	−	10.5083i	−0.791343	−	0.456882i
$530$	−1.10666	+	22.7783i	−0.0480701	+	0.989426i
$531$	13.9685	−	9.05395i	0.606183	−	0.392908i
$532$		0			0
$533$	14.2956	−	14.2956i	0.619211	−	0.619211i
$534$	1.06693	+	41.4352i	0.0461704	+	1.79307i
$535$	−8.48439	−	2.72101i	−0.366812	−	0.117640i
$536$	−28.9760	−	16.7293i	−1.25157	−	0.722595i
$537$	20.8449	+	19.7983i	0.899523	+	0.854361i
$538$	52.8021	+	52.8021i	2.27646	+	2.27646i
$539$		0			0
$540$	−14.8999	−	49.8425i	−0.641192	−	2.14488i
$541$	11.5559	+	20.0153i	0.496825	+	0.860526i	0.999993	−	0.00366246i	$-0.00116580\pi$
$541$	11.5559	+	20.0153i	0.496825	+	0.860526i	−0.503168	+	0.864188i	$0.667832\pi$
$542$	7.82652	−	2.09711i	0.336178	−	0.0900786i
$543$	4.72040	−	19.6242i	0.202572	−	0.842153i
$544$	24.0306	−	13.8741i	1.03030	−	0.594845i
$545$	−7.77560	+	12.0739i	−0.333070	+	0.517191i
$546$		0			0
$547$	−25.6689	+	25.6689i	−1.09752	+	1.09752i	−0.102823	+	0.994700i	$0.532787\pi$
$547$	−25.6689	+	25.6689i	−1.09752	+	1.09752i	−0.994700	+	0.102823i	$0.967213\pi$
$548$	−27.8824	−	7.47105i	−1.19108	−	0.319148i
$549$	1.14354	+	22.1905i	0.0488051	+	0.947068i
$550$	−15.4173	+	12.6806i	−0.657394	+	0.540703i
$551$	−12.9804	+	7.49421i	−0.552982	+	0.319264i
$552$	4.36169	+	14.7484i	0.185646	+	0.627735i
$553$		0			0
$554$	−60.6965			−2.57875
$555$	2.06077	+	1.25329i	0.0874749	+	0.0531991i
$556$	22.8445	−	39.5679i	0.968824	−	1.67805i
$557$	14.4497	−	3.87177i	0.612252	−	0.164052i	0.0606487	−	0.998159i	$-0.480683\pi$
$557$	14.4497	−	3.87177i	0.612252	−	0.164052i	0.551603	+	0.834107i	$0.314016\pi$
$558$	6.46701	+	19.9627i	0.273771	+	0.845088i
$559$		−	24.3063i		−	1.02805i
$560$		0			0
$561$	6.61917	−	12.1783i	0.279462	−	0.514169i
$562$	−60.9796	−	16.3394i	−2.57227	−	0.689238i
$563$	−3.99759	−	14.9192i	−0.168478	−	0.628769i	−0.997571	−	0.0696580i	$-0.977809\pi$
$563$	−3.99759	−	14.9192i	−0.168478	−	0.628769i	0.829093	−	0.559111i	$-0.188857\pi$
$564$	21.1504	+	34.5481i	0.890592	+	1.45474i
$565$	−6.99624	−	7.71076i	−0.294334	−	0.324394i
$566$		−	19.5050i		−	0.819858i
$567$		0			0
$568$	16.1365	+	16.1365i	0.677072	+	0.677072i
$569$	−21.0355	−	36.4346i	−0.881854	−	1.52742i	−0.849277	−	0.527947i	$-0.822962\pi$
$569$	−21.0355	−	36.4346i	−0.881854	−	1.52742i	−0.0325765	−	0.999469i	$-0.510371\pi$
$570$	0.377653	−	16.5594i	0.0158182	−	0.693596i
$571$	−5.41712	+	9.38272i	−0.226699	+	0.392655i	−0.956828	−	0.290655i	$-0.906127\pi$
$571$	−5.41712	+	9.38272i	−0.226699	+	0.392655i	0.730129	+	0.683310i	$0.239460\pi$
$572$	−5.70415	+	21.2882i	−0.238502	+	0.890103i
$573$	6.31411	+	21.3503i	0.263776	+	0.891921i
$574$		0			0
$575$	6.59308	+	2.47331i	0.274950	+	0.103144i
$576$	0.464409	−	0.909492i	0.0193504	−	0.0378955i
$577$	5.37966	+	20.0772i	0.223958	+	0.835823i	0.982819	+	0.184571i	$0.0590895\pi$
$577$	5.37966	+	20.0772i	0.223958	+	0.835823i	−0.758861	+	0.651253i	$0.774244\pi$
$578$	5.94450	+	22.1852i	0.247259	+	0.922782i
$579$	−0.508297	−	19.7402i	−0.0211241	−	0.820375i
$580$	48.3498	−	75.0776i	2.00762	−	3.11743i
$581$		0			0
$582$	26.2823	−	7.77271i	1.08944	−	0.322189i
$583$	1.62700	−	6.07203i	0.0673833	−	0.251478i
$584$	26.2922	−	45.5394i	1.08798	−	1.88443i
$585$	−20.3161	+	5.50778i	−0.839967	+	0.227719i
$586$	15.4901	+	26.8297i	0.639891	+	1.10832i
$587$	4.89737	+	4.89737i	0.202136	+	0.202136i	0.800915	−	0.598779i	$-0.204347\pi$
$587$	4.89737	+	4.89737i	0.202136	+	0.202136i	−0.598779	+	0.800915i	$0.704347\pi$
$588$		0			0
$589$			4.61831i			0.190294i
$590$	−23.3858	+	21.2187i	−0.962777	+	0.873561i
$591$	−39.1729	+	23.9817i	−1.61136	+	0.986475i
$592$	−1.14309	−	4.26606i	−0.0469806	−	0.175334i
$593$	30.8223	+	8.25882i	1.26572	+	0.339149i	0.828390	−	0.560151i	$-0.189257\pi$
$593$	30.8223	+	8.25882i	1.26572	+	0.339149i	0.437331	+	0.899300i	$0.355924\pi$
$594$	1.60059	+	20.6835i	0.0656729	+	0.848654i
$595$		0			0
$596$		−	4.13314i		−	0.169300i
$597$	−5.01850	+	5.28378i	−0.205394	+	0.216251i
$598$	10.8639	−	2.91097i	0.444258	−	0.119039i
$599$	−3.40986	+	5.90604i	−0.139323	+	0.241314i	−0.927241	−	0.374466i	$-0.877826\pi$
$599$	−3.40986	+	5.90604i	−0.139323	+	0.241314i	0.787918	+	0.615781i	$0.211159\pi$
$600$	23.8609	+	49.1132i	0.974117	+	2.00504i
$601$	−8.46733			−0.345390			−0.172695	−	0.984975i	$-0.555247\pi$
$601$	−8.46733			−0.345390			−0.172695	+	0.984975i	$0.555247\pi$
$602$		0			0
$603$	−3.32356	+	15.5693i	−0.135346	+	0.634031i
$604$	−53.2417	+	30.7391i	−2.16637	+	1.25076i
$605$	−16.9799	+	8.73340i	−0.690329	+	0.355063i
$606$	2.32769	+	3.80216i	0.0945558	+	0.154452i
$607$	−8.60998	−	2.30704i	−0.349468	−	0.0936398i	0.0798148	−	0.996810i	$-0.474567\pi$
$607$	−8.60998	−	2.30704i	−0.349468	−	0.0936398i	−0.429283	+	0.903170i	$0.641234\pi$
$608$	−6.46309	+	6.46309i	−0.262113	+	0.262113i
$609$		0			0
$610$	−8.92083	−	41.1959i	−0.361194	−	1.66797i
$611$	14.1947	−	8.19533i	0.574258	−	0.331548i
$612$	−50.8820	−	45.8948i	−2.05678	−	1.85519i
$613$	7.16791	−	1.92064i	0.289509	−	0.0775738i	−0.111142	−	0.993805i	$-0.535451\pi$
$613$	7.16791	−	1.92064i	0.289509	−	0.0775738i	0.400651	+	0.916231i	$0.368784\pi$
$614$	−21.3301	−	36.9448i	−0.860812	−	1.49097i
$615$	−7.00627	+	23.9496i	−0.282520	+	0.965739i
$616$		0			0
$617$	−2.10719	−	2.10719i	−0.0848323	−	0.0848323i	0.663417	−	0.748250i	$-0.269105\pi$
$617$	−2.10719	−	2.10719i	−0.0848323	−	0.0848323i	−0.748250	+	0.663417i	$0.769105\pi$
$618$	−17.3043	+	18.2190i	−0.696080	+	0.732875i
$619$	18.2501	+	10.5367i	0.733534	+	0.423506i	0.819714	−	0.572773i	$-0.194133\pi$
$619$	18.2501	+	10.5367i	0.733534	+	0.423506i	−0.0861795	+	0.996280i	$0.527466\pi$
$620$	−12.5851	−	24.4685i	−0.505431	−	0.982679i
$621$	6.03636	−	4.13705i	0.242231	−	0.166014i
$622$	−52.6932	+	52.6932i	−2.11280	+	2.11280i
$623$		0			0
$624$	33.8650	+	18.4063i	1.35569	+	0.736844i
$625$	24.5301	+	4.82412i	0.981206	+	0.192965i
$626$	3.82080	+	2.20594i	0.152710	+	0.0881670i
$627$	−1.06779	+	4.43915i	−0.0426436	+	0.177283i
$628$	−22.4864	+	83.9205i	−0.897306	+	3.34879i
$629$	3.17697			0.126674
$630$		0			0
$631$	−11.6376			−0.463287			−0.231643	−	0.972801i	$-0.574410\pi$
$631$	−11.6376			−0.463287			−0.231643	+	0.972801i	$0.574410\pi$
$632$	−27.8348	+	103.881i	−1.10721	+	4.13216i
$633$	−8.71765	+	36.2420i	−0.346496	+	1.44049i
$634$	−13.4083	−	7.74127i	−0.532511	−	0.307445i
$635$	−30.3477	−	33.4471i	−1.20431	−	1.32731i
$636$	−27.3040	−	14.8403i	−1.08267	−	0.588455i
$637$		0			0
$638$	−25.1806	+	25.1806i	−0.996910	+	0.996910i
$639$	4.93801	−	9.67051i	0.195345	−	0.382560i
$640$	−8.02022	+	25.0079i	−0.317027	+	0.988522i
$641$	−31.2666	−	18.0518i	−1.23496	−	0.713003i	−0.266898	−	0.963725i	$-0.585999\pi$
$641$	−31.2666	−	18.0518i	−1.23496	−	0.713003i	−0.968059	+	0.250722i	$0.919332\pi$
$642$	12.0967	−	12.7361i	0.477417	−	0.502653i
$643$	−21.0115	−	21.0115i	−0.828614	−	0.828614i	0.158711	−	0.987325i	$-0.449266\pi$
$643$	−21.0115	−	21.0115i	−0.828614	−	0.828614i	−0.987325	+	0.158711i	$0.949266\pi$
$644$		0			0
$645$	14.4040	+	26.3165i	0.567158	+	1.03621i
$646$	−10.9087	−	18.8944i	−0.429196	−	0.743389i
$647$	−25.8213	+	6.91879i	−1.01514	+	0.272006i	−0.727775	−	0.685816i	$-0.759446\pi$
$647$	−25.8213	+	6.91879i	−1.01514	+	0.272006i	−0.287364	+	0.957821i	$0.592779\pi$
$648$	56.0306	+	8.97464i	2.20109	+	0.352557i
$649$	7.53812	−	4.35214i	0.295897	−	0.170836i
$650$	36.3532	−	16.5189i	1.42589	−	0.647925i
$651$		0			0
$652$	−29.5757	+	29.5757i	−1.15828	+	1.15828i
$653$	−16.7835	−	4.49712i	−0.656788	−	0.175986i	−0.0849922	−	0.996382i	$-0.527087\pi$
$653$	−16.7835	−	4.49712i	−0.656788	−	0.175986i	−0.571796	+	0.820396i	$0.693753\pi$
$654$	−14.7821	−	24.1458i	−0.578026	−	0.944177i
$655$	−5.00868	−	9.73809i	−0.195705	−	0.380499i
$656$	39.5707	−	22.8462i	1.54498	−	0.891994i
$657$	−24.4691	−	5.22339i	−0.954631	−	0.203784i
$658$		0			0
$659$	0.708622			0.0276040			0.0138020	−	0.999905i	$-0.495607\pi$
$659$	0.708622			0.0276040			0.0138020	+	0.999905i	$0.495607\pi$
$660$	−6.43956	−	26.4291i	−0.250660	−	1.02875i
$661$	−8.71029	+	15.0867i	−0.338791	+	0.586803i	−0.984206	−	0.177029i	$-0.943351\pi$
$661$	−8.71029	+	15.0867i	−0.338791	+	0.586803i	0.645414	+	0.763833i	$0.276685\pi$
$662$	81.7650	−	21.9089i	3.17789	−	0.851512i
$663$	−19.0940	+	20.1033i	−0.741551	+	0.780749i
$664$		−	28.6500i		−	1.11184i
$665$		0			0
$666$	−3.99006	+	2.58623i	−0.154612	+	0.100214i
$667$	12.1338	+	3.25123i	0.469821	+	0.125888i
$668$	5.10397	+	19.0483i	0.197479	+	0.737000i
$669$	25.9050	−	15.8591i	1.00155	−	0.613147i
$670$	1.46551	−	30.1644i	0.0566174	−	1.16535i
$671$			11.6188i			0.448540i
$672$		0			0
$673$	−8.20389	−	8.20389i	−0.316237	−	0.316237i	0.531083	−	0.847320i	$-0.321785\pi$
$673$	−8.20389	−	8.20389i	−0.316237	−	0.316237i	−0.847320	+	0.531083i	$0.821785\pi$
$674$	18.5463	+	32.1231i	0.714377	+	1.23734i
$675$	18.7324	−	18.0027i	0.721010	−	0.692925i
$676$	−7.06029	+	12.2288i	−0.271550	+	0.470338i
$677$	12.0278	−	44.8882i	0.462264	−	1.72519i	−0.203539	−	0.979067i	$-0.565244\pi$
$677$	12.0278	−	44.8882i	0.462264	−	1.72519i	0.665803	−	0.746128i	$-0.268089\pi$
$678$	19.6828	−	5.82098i	0.755915	−	0.223554i
$679$		0			0
$680$	60.4675	+	38.9409i	2.31882	+	1.49332i
$681$	−0.548901	−	21.3171i	−0.0210339	−	0.816874i
$682$	2.83991	+	10.5987i	0.108746	+	0.405845i
$683$	−10.4309	−	38.9287i	−0.399128	−	1.48957i	−0.814634	−	0.579975i	$-0.803062\pi$
$683$	−10.4309	−	38.9287i	−0.399128	−	1.48957i	0.415506	−	0.909590i	$-0.363604\pi$
$684$	20.1021	+	10.2646i	0.768623	+	0.392478i
$685$	−3.05106	−	14.0896i	−0.116575	−	0.538338i
$686$		0			0
$687$	−2.19245	−	7.41347i	−0.0836473	−	0.282842i
$688$	14.2181	−	53.0626i	0.542060	−	2.02299i
$689$	−6.28716	+	10.8897i	−0.239522	+	0.414864i
$690$	−10.0373	+	9.58972i	−0.382115	+	0.365074i
$691$	−2.89969	−	5.02242i	−0.110310	−	0.191062i	0.805586	−	0.592480i	$-0.201851\pi$
$691$	−2.89969	−	5.02242i	−0.110310	−	0.191062i	−0.915895	+	0.401418i	$0.868518\pi$
$692$	36.3949	+	36.3949i	1.38353	+	1.38353i
$693$		0			0
$694$		−	69.1925i		−	2.62651i
$695$	22.7911	+	1.10728i	0.864516	+	0.0420015i
$696$	50.8584	+	83.0747i	1.92778	+	3.14894i
$697$	8.50687	+	31.7481i	0.322221	+	1.20254i
$698$	74.0699	+	19.8470i	2.80359	+	0.751219i
$699$	6.59919	−	12.1416i	0.249604	−	0.459236i
$700$		0			0
$701$		−	4.92775i		−	0.186118i	−0.995661	−	0.0930592i	$-0.970335\pi$
$701$		−	4.92775i		−	0.186118i	0.995661	−	0.0930592i	$-0.0296646\pi$
$702$	7.61559	−	40.7920i	0.287432	−	1.53960i
$703$	−1.01083	+	0.270852i	−0.0381243	+	0.0102154i
$704$	0.266993	−	0.462446i	0.0100627	−	0.0174291i
$705$	−10.5121	+	17.2850i	−0.395909	+	0.650990i
$706$	61.3096			2.30742
$707$		0			0
$708$	−12.2032	−	41.2635i	−0.458625	−	1.55078i
$709$	14.8889	−	8.59609i	0.559163	−	0.322833i	−0.193647	−	0.981071i	$-0.562032\pi$
$709$	14.8889	−	8.59609i	0.559163	−	0.322833i	0.752809	+	0.658239i	$0.228698\pi$
$710$	−6.29035	+	19.6139i	−0.236073	+	0.736098i
$711$	51.1039	−	2.63353i	1.91655	−	0.0987649i
$712$	57.2639	+	15.3438i	2.14606	+	0.575034i
$713$	2.73693	−	2.73693i	0.102499	−	0.102499i
$714$		0			0
$715$	−10.7574	+	2.32948i	−0.402305	+	0.0871177i
$716$	64.3586	−	37.1575i	2.40519	−	1.38864i
$717$	4.80395	−	19.9715i	0.179407	−	0.745850i
$718$	1.81421	−	0.486116i	0.0677057	−	0.0181417i
$719$	−6.12782	−	10.6137i	−0.228529	−	0.395824i	0.728843	−	0.684681i	$-0.240058\pi$
$719$	−6.12782	−	10.6137i	−0.228529	−	0.395824i	−0.957372	+	0.288856i	$0.906725\pi$
$720$	−47.5735	+	0.139941i	−1.77296	+	0.00521528i
$721$		0			0
$722$	−29.1113	−	29.1113i	−1.08341	−	1.08341i
$723$	−22.6964	−	21.5569i	−0.844089	−	0.801711i
$724$	−45.1850	−	26.0876i	−1.67929	−	0.969538i
$725$	44.3877	+	4.32326i	1.64852	+	0.160562i
$726$	−0.968939	−	37.6297i	−0.0359607	−	1.39657i
$727$	5.83842	−	5.83842i	0.216535	−	0.216535i	−0.590501	−	0.807037i	$-0.701070\pi$
$727$	5.83842	−	5.83842i	0.216535	−	0.216535i	0.807037	+	0.590501i	$0.201070\pi$
$728$		0			0
$729$	−4.15390	−	26.6786i	−0.153848	−	0.988094i
$730$	47.4072	+	2.30323i	1.75462	+	0.0852462i
$731$	34.2220	+	19.7581i	1.26575	+	0.730780i
$732$	55.8455	+	13.4331i	2.06411	+	0.496502i
$733$	4.97574	−	18.5697i	0.183783	−	0.685888i	−0.811105	−	0.584901i	$-0.801133\pi$
$733$	4.97574	−	18.5697i	0.183783	−	0.685888i	0.994888	−	0.100987i	$-0.0321999\pi$
$734$	−83.8351			−3.09441
$735$		0			0
$736$	7.66040			0.282366
$737$	−2.15457	+	8.04096i	−0.0793646	+	0.296193i
$738$	−36.5287	−	32.9484i	−1.34464	−	1.21285i
$739$	−13.1464	−	7.59007i	−0.483598	−	0.279205i	0.238317	−	0.971187i	$-0.423404\pi$
$739$	−13.1464	−	7.59007i	−0.483598	−	0.279205i	−0.721915	+	0.691982i	$0.756738\pi$
$740$	4.61747	−	4.18959i	0.169741	−	0.154012i
$741$	4.36134	−	8.02424i	0.160218	−	0.294778i
$742$		0			0
$743$	−34.4215	+	34.4215i	−1.26280	+	1.26280i	−0.313073	+	0.949729i	$0.601358\pi$
$743$	−34.4215	+	34.4215i	−1.26280	+	1.26280i	−0.949729	+	0.313073i	$0.898642\pi$
$744$	30.0034	−	0.772566i	1.09998	−	0.0283236i
$745$	1.83560	−	0.944121i	0.0672512	−	0.0345899i
$746$	−16.4614	−	9.50402i	−0.602696	−	0.347967i
$747$	−12.9686	+	4.20124i	−0.474496	+	0.153715i
$748$	−25.3359	−	25.3359i	−0.926371	−	0.926371i
$749$		0			0
$750$	−29.5706	+	39.4282i	−1.07977	+	1.43971i
$751$	11.1258	+	19.2704i	0.405985	+	0.703186i	0.994436	−	0.105347i	$-0.0335952\pi$
$751$	11.1258	+	19.2704i	0.405985	+	0.703186i	−0.588451	+	0.808533i	$0.700262\pi$
$752$	35.7822	−	9.58780i	1.30484	−	0.349631i
$753$	5.37628	+	1.29321i	0.195922	+	0.0471272i
$754$	61.6888	−	35.6160i	2.24657	−	1.29706i
$755$	−25.8136	−	16.6239i	−0.939454	−	0.605007i
$756$		0			0
$757$	−1.88407	+	1.88407i	−0.0684777	+	0.0684777i	−0.740516	−	0.672038i	$-0.765419\pi$
$757$	−1.88407	+	1.88407i	−0.0684777	+	0.0684777i	0.672038	+	0.740516i	$0.265419\pi$
$758$	8.31786	+	2.22876i	0.302118	+	0.0809523i
$759$	3.26356	−	1.99795i	0.118460	−	0.0725212i
$760$	−22.5591	−	7.23489i	−0.818305	−	0.262437i
$761$	−30.8889	+	17.8337i	−1.11972	+	0.646472i	−0.941330	−	0.337488i	$-0.890423\pi$
$761$	−30.8889	+	17.8337i	−1.11972	+	0.646472i	−0.178392	+	0.983960i	$0.557089\pi$
$762$	85.3786	−	25.2498i	3.09294	−	0.914703i
$763$		0			0
$764$	57.5532			2.08220
$765$	8.75986	−	33.0812i	0.316714	−	1.19605i
$766$	5.16028	−	8.93787i	0.186449	−	0.322938i
$767$	−16.8179	+	4.50633i	−0.607258	+	0.162714i
$768$	−36.6848	−	34.8430i	−1.32375	−	1.25729i
$769$			31.7331i			1.14432i	0.820141	+	0.572162i	$0.193895\pi$
$769$			31.7331i			1.14432i	−0.820141	+	0.572162i	$0.806105\pi$
$770$		0			0
$771$	−25.4207	−	13.8167i	−0.915503	−	0.497595i
$772$	−49.3059	−	13.2115i	−1.77456	−	0.475491i
$773$	1.82223	+	6.80067i	0.0655412	+	0.244603i	0.990922	−	0.134434i	$-0.0429218\pi$
$773$	1.82223	+	6.80067i	0.0655412	+	0.244603i	−0.925381	+	0.379038i	$0.876255\pi$
$774$	−59.0647	+	3.04377i	−2.12304	+	0.109406i
$775$	7.99212	−	11.1786i	0.287085	−	0.401545i
$776$		−	39.2008i		−	1.40723i
$777$		0			0
$778$	18.3745	+	18.3745i	0.658758	+	0.658758i
$779$	−5.41335	−	9.37619i	−0.193953	−	0.335937i
$780$	−1.24061	+	54.3985i	−0.0444211	+	1.94778i
$781$	2.83891	−	4.91713i	0.101584	−	0.175949i
$782$	−4.73254	+	17.6621i	−0.169235	+	0.631595i
$783$	30.1463	−	35.2034i	1.07734	−	1.25807i
$784$		0			0
$785$	−42.4071	+	9.18310i	−1.51357	+	0.327759i
$786$	21.5810	−	0.555695i	0.769767	−	0.0198210i
$787$	6.86494	+	25.6203i	0.244709	+	0.913266i	0.973530	+	0.228561i	$0.0734021\pi$
$787$	6.86494	+	25.6203i	0.244709	+	0.913266i	−0.728821	+	0.684705i	$0.759931\pi$
$788$	30.7298	+	114.685i	1.09470	+	4.08549i
$789$	32.2005	−	0.829142i	1.14637	−	0.0295182i
$790$	−94.8726	+	20.5443i	−3.37542	+	0.730934i
$791$		0			0
$792$	29.0181	+	6.19445i	1.03111	+	0.220110i
$793$	6.01524	−	22.4492i	0.213607	−	0.797194i
$794$	−43.2873	+	74.9758i	−1.53621	+	2.66079i
$795$	0.353860	−	15.5161i	0.0125501	−	0.550299i
$796$	9.41871	+	16.3137i	0.333837	+	0.578223i
$797$	−7.92792	−	7.92792i	−0.280821	−	0.280821i	0.552615	−	0.833437i	$-0.313630\pi$
$797$	−7.92792	−	7.92792i	−0.280821	−	0.280821i	−0.833437	+	0.552615i	$0.813630\pi$
$798$		0			0
$799$			26.6473i			0.942713i
$800$	26.8284	−	4.45925i	0.948527	−	0.157658i
$801$	−1.45172	−	28.1708i	−0.0512940	−	0.995367i
$802$	−13.2343	−	49.3911i	−0.467320	−	1.74406i
$803$	−12.6374	−	3.38618i	−0.445964	−	0.119496i
$804$	36.1576	+	19.6524i	1.27518	+	0.693088i
$805$		0			0
$806$		−	21.9484i		−	0.773099i
$807$	−36.8477	−	34.9977i	−1.29710	−	1.23198i
$808$	6.15910	−	1.65032i	0.216676	−	0.0580582i
$809$	−16.6141	+	28.7764i	−0.584119	+	1.01172i	0.410865	+	0.911696i	$0.365227\pi$
$809$	−16.6141	+	28.7764i	−0.584119	+	1.01172i	−0.994985	+	0.100028i	$0.968107\pi$
$810$	15.9281	+	48.6787i	0.559656	+	1.71040i
$811$	−49.8680			−1.75110			−0.875550	−	0.483127i	$-0.839501\pi$
$811$	−49.8680			−1.75110			−0.875550	+	0.483127i	$0.839501\pi$
$812$		0			0
$813$	−5.28787	+	1.56383i	−0.185454	+	0.0548458i
$814$	−2.15324	+	1.24317i	−0.0754709	+	0.0435732i
$815$	−19.8910	−	6.37921i	−0.696752	−	0.223454i
$816$	−53.4434	+	32.7181i	−1.87089	+	1.14536i
$817$	−12.5731	−	3.36894i	−0.439876	−	0.117864i
$818$	60.3060	−	60.3060i	2.10855	−	2.10855i
$819$		0			0
$820$	54.2313	+	34.9249i	1.89384	+	1.21963i
$821$	−28.0956	+	16.2210i	−0.980542	+	0.566116i	−0.902434	−	0.430829i	$-0.858221\pi$
$821$	−28.0956	+	16.2210i	−0.980542	+	0.566116i	−0.0781084	+	0.996945i	$0.524888\pi$
$822$	27.6319	+	6.64659i	0.963773	+	0.231826i
$823$	44.7011	−	11.9776i	1.55818	−	0.417514i	0.626095	−	0.779747i	$-0.284652\pi$
$823$	44.7011	−	11.9776i	1.55818	−	0.417514i	0.932088	+	0.362233i	$0.117985\pi$
$824$	17.9695	+	31.1241i	0.625998	+	1.08426i
$825$	10.2667	−	8.89705i	0.357439	−	0.309755i
$826$		0			0
$827$	−36.7198	−	36.7198i	−1.27687	−	1.27687i	−0.942408	−	0.334465i	$-0.891444\pi$
$827$	−36.7198	−	36.7198i	−1.27687	−	1.27687i	−0.334465	−	0.942408i	$-0.608556\pi$
$828$	−5.82994	−	17.9961i	−0.202605	−	0.625409i
$829$	12.3817	+	7.14860i	0.430036	+	0.248281i	0.699362	−	0.714768i	$-0.253468\pi$
$829$	12.3817	+	7.14860i	0.430036	+	0.248281i	−0.269326	+	0.963049i	$0.586801\pi$
$830$	22.9963	−	11.8279i	0.798214	−	0.410553i
$831$	41.2935	−	1.06328i	1.43246	−	0.0368848i
$832$	−0.755282	+	0.755282i	−0.0261847	+	0.0261847i
$833$		0			0
$834$	−21.4814	+	39.5227i	−0.743841	+	1.36856i
$835$	−7.29380	+	6.61791i	−0.252412	+	0.229022i
$836$	10.2212	+	5.90123i	0.353509	+	0.204098i
$837$	−4.74940	−	13.4679i	−0.164163	−	0.465518i
$838$	−17.0456	+	63.6151i	−0.588831	+	2.19755i
$839$	−33.6309			−1.16107			−0.580534	−	0.814236i	$-0.697156\pi$
$839$	−33.6309			−1.16107			−0.580534	+	0.814236i	$0.697156\pi$
$840$		0			0
$841$	50.5583			1.74339
$842$	−6.85259	+	25.5742i	−0.236156	+	0.881346i
$843$	41.7724	+	10.0479i	1.43872	+	0.346069i
$844$	83.4479	+	48.1787i	2.87240	+	1.65838i
$845$	−7.04378	−	0.342214i	−0.242313	−	0.0117725i
$846$	−21.6923	−	33.4672i	−0.745798	−	1.15062i
$847$		0			0
$848$	−20.0953	+	20.0953i	−0.690077	+	0.690077i
$849$	0.341689	+	13.2698i	0.0117267	+	0.455420i
$850$	−6.29299	+	64.6114i	−0.215848	+	2.21615i
$851$	0.759561	+	0.438533i	0.0260374	+	0.0150327i
$852$	−20.3518	−	19.3300i	−0.697242	−	0.662236i
$853$	26.5544	+	26.5544i	0.909206	+	0.909206i	0.996208	−	0.0870025i	$-0.0277288\pi$
$853$	26.5544	+	26.5544i	0.909206	+	0.909206i	−0.0870025	+	0.996208i	$0.527729\pi$
$854$		0			0
$855$	0.0331586	+	11.2724i	0.00113400	+	0.385509i
$856$	−12.5617	−	21.7575i	−0.429350	−	0.743655i
$857$	−31.5157	+	8.44459i	−1.07655	+	0.288462i	−0.753184	−	0.657810i	$-0.771483\pi$
$857$	−31.5157	+	8.44459i	−1.07655	+	0.288462i	−0.323371	+	0.946272i	$0.604816\pi$
$858$	5.07467	−	21.0969i	0.173246	−	0.720238i
$859$	−15.0032	+	8.66212i	−0.511903	+	0.295548i	−0.733616	−	0.679565i	$-0.762169\pi$
$859$	−15.0032	+	8.66212i	−0.511903	+	0.295548i	0.221712	+	0.975112i	$0.428835\pi$
$860$	75.7946	−	16.4130i	2.58457	−	0.559680i
$861$		0			0
$862$	0.808044	−	0.808044i	0.0275221	−	0.0275221i
$863$	12.3656	+	3.31336i	0.420931	+	0.112788i	0.463066	−	0.886324i	$-0.346749\pi$
$863$	12.3656	+	3.31336i	0.420931	+	0.112788i	−0.0421348	+	0.999112i	$0.513416\pi$
$864$	12.2011	−	25.4942i	0.415090	−	0.867330i
$865$	−7.85004	+	24.4772i	−0.266909	+	0.832250i
$866$	55.4253	−	31.9998i	1.88343	−	1.08740i
$867$	−4.43285	−	14.9891i	−0.150548	−	0.509056i
$868$		0			0
$869$	26.7577			0.907693
$870$	−45.6845	+	75.1187i	−1.54885	+	2.54676i
$871$	8.32585	−	14.4208i	0.282111	−	0.488630i
$872$	−39.1137	+	10.4805i	−1.32456	+	0.354914i
$873$	−17.7444	+	5.74840i	−0.600558	+	0.194554i
$874$		−	6.02310i		−	0.203734i
$875$		0			0
$876$	−30.8863	+	56.8263i	−1.04355	+	1.91998i
$877$	−21.1228	−	5.65985i	−0.713267	−	0.191119i	−0.116102	−	0.993237i	$-0.537040\pi$
$877$	−21.1228	−	5.65985i	−0.713267	−	0.191119i	−0.597166	+	0.802118i	$0.703707\pi$
$878$	−19.4513	−	72.5932i	−0.656449	−	2.44990i
$879$	−11.0084	−	17.9816i	−0.371303	−	0.606505i
$880$	−24.8470	−	1.20716i	−0.837592	−	0.0406935i
$881$			3.93409i			0.132543i	0.997802	+	0.0662714i	$0.0211103\pi$
$881$			3.93409i			0.132543i	−0.997802	+	0.0662714i	$0.978890\pi$
$882$		0			0
$883$	13.5688	+	13.5688i	0.456625	+	0.456625i	0.897546	−	0.440921i	$-0.145348\pi$
$883$	13.5688	+	13.5688i	0.456625	+	0.456625i	−0.440921	+	0.897546i	$0.645348\pi$
$884$	35.8356	+	62.0691i	1.20528	+	2.08761i
$885$	15.5383	−	14.8454i	0.522314	−	0.499021i
$886$	−28.0100	+	48.5148i	−0.941015	+	1.62989i
$887$	1.80264	−	6.72756i	0.0605269	−	0.225889i	−0.929036	−	0.369988i	$-0.879362\pi$
$887$	1.80264	−	6.72756i	0.0605269	−	0.225889i	0.989563	+	0.144099i	$0.0460284\pi$
$888$	1.92872	+	6.52168i	0.0647235	+	0.218853i
$889$		0			0
$890$	11.3250	+	52.2982i	0.379614	+	1.75304i
$891$	−1.45126	−	14.0435i	−0.0486190	−	0.470476i
$892$	−20.3216	−	75.8412i	−0.680417	−	2.53935i
$893$	−2.27181	−	8.47850i	−0.0760231	−	0.283722i
$894$	0.104747	+	4.06795i	0.00350326	+	0.136052i
$895$	31.2035	+	20.0950i	1.04302	+	0.671703i
$896$		0			0
$897$	−7.34002	+	2.17073i	−0.245076	+	0.0724786i
$898$	−10.7510	+	40.1234i	−0.358767	+	1.33894i
$899$	12.2570	−	21.2297i	0.408793	−	0.708050i
$900$	−30.8936	−	59.6327i	−1.02979	−	1.98776i
$901$	−10.2214	−	17.7040i	−0.340524	−	0.589806i
$902$	−18.1889	−	18.1889i	−0.605624	−	0.605624i
$903$		0			0
$904$		−	29.3575i		−	0.976416i
$905$	1.26447	−	26.0266i	0.0420325	−	0.865153i
$906$	51.6228	−	31.6035i	1.71505	−	1.04996i
$907$	−6.96610	−	25.9978i	−0.231305	−	0.863244i	−0.979780	−	0.200080i	$-0.935880\pi$
$907$	−6.96610	−	25.9978i	−0.231305	−	0.863244i	0.748474	−	0.663164i	$-0.230787\pi$
$908$	−53.2446	−	14.2668i	−1.76698	−	0.473462i
$909$	−1.65020	−	2.54594i	−0.0547336	−	0.0844436i
$910$		0			0
$911$		−	17.7669i		−	0.588644i	−0.955706	−	0.294322i	$-0.904906\pi$
$911$		−	17.7669i		−	0.588644i	0.955706	−	0.294322i	$-0.0950938\pi$
$912$	14.2150	−	14.9664i	0.470705	−	0.495586i
$913$	−6.88535	+	1.84492i	−0.227872	+	0.0610581i
$914$	−37.1263	+	64.3046i	−1.22803	+	2.12701i
$915$	6.79076	+	27.8705i	0.224496	+	0.921370i
$916$	−19.9842			−0.660298
$917$		0			0
$918$	51.2425	+	43.8814i	1.69125	+	1.44830i
$919$	−7.36529	+	4.25235i	−0.242958	+	0.140272i	−0.616536	−	0.787327i	$-0.711464\pi$
$919$	−7.36529	+	4.25235i	−0.242958	+	0.140272i	0.373577	+	0.927599i	$0.378131\pi$
$920$	9.08155	+	17.6567i	0.299410	+	0.582125i
$921$	15.1586	+	24.7609i	0.499494	+	0.815900i
$922$	37.5863	+	10.0712i	1.23784	+	0.331678i
$923$	−8.03083	+	8.03083i	−0.264338	+	0.264338i
$924$		0			0
$925$	2.91542	+	1.09368i	0.0958586	+	0.0359601i
$926$	−1.53420	+	0.885769i	−0.0504169	+	0.0291082i
$927$	11.4534	−	12.6980i	0.376180	−	0.417058i
$928$	46.8629	−	12.5569i	1.53835	−	0.412200i
$929$	7.07945	+	12.2620i	0.232269	+	0.402302i	0.958476	−	0.285175i	$-0.0920517\pi$
$929$	7.07945	+	12.2620i	0.232269	+	0.402302i	−0.726206	+	0.687477i	$0.758718\pi$
$930$	13.0067	+	23.7636i	0.426507	+	0.779240i
$931$		0			0
$932$	−25.2594	−	25.2594i	−0.827399	−	0.827399i
$933$	34.9256	−	36.7717i	1.14341	−	1.20385i
$934$	−28.0548	−	16.1975i	−0.917982	−	0.529997i
$935$	5.46471	−	17.0395i	0.178715	−	0.557252i
$936$	−52.8599	−	26.9916i	−1.72778	−	0.882248i
$937$	28.7165	−	28.7165i	0.938127	−	0.938127i	−0.0600678	−	0.998194i	$-0.519132\pi$
$937$	28.7165	−	28.7165i	0.938127	−	0.938127i	0.998194	+	0.0600678i	$0.0191317\pi$
$938$		0			0
$939$	−2.63804	−	1.43383i	−0.0860891	−	0.0467912i
$940$	35.1407	+	38.7296i	1.14616	+	1.26322i
$941$	−15.0690	−	8.70007i	−0.491234	−	0.283614i	0.233852	−	0.972272i	$-0.424867\pi$
$941$	−15.0690	−	8.70007i	−0.491234	−	0.283614i	−0.725086	+	0.688658i	$0.758200\pi$
$942$	20.0049	−	83.1667i	0.651796	−	2.70972i
$943$	−2.34849	+	8.76467i	−0.0764773	+	0.285417i
$944$	−39.3508			−1.28076
$945$		0			0
$946$	−30.9259			−1.00549
$947$	−2.98564	+	11.1426i	−0.0970204	+	0.362085i	−0.997318	−	0.0731898i	$-0.976682\pi$
$947$	−2.98564	+	11.1426i	−0.0970204	+	0.362085i	0.900298	+	0.435275i	$0.143349\pi$
$948$	30.9359	−	128.610i	1.00475	−	4.17706i
$949$	22.6641	+	13.0851i	0.735708	+	0.424761i
$950$	−3.50615	−	21.0942i	−0.113755	−	0.684387i
$951$	9.25764	+	5.03172i	0.300199	+	0.163165i
$952$		0			0
$953$	38.6159	−	38.6159i	1.25089	−	1.25089i	0.295569	−	0.955321i	$-0.404491\pi$
$953$	38.6159	−	38.6159i	1.25089	−	1.25089i	0.955321	−	0.295569i	$-0.0955091\pi$
$954$	27.2494	+	13.9142i	0.882232	+	0.450490i
$955$	13.1467	+	25.5604i	0.425418	+	0.827115i
$956$	−45.9848	−	26.5494i	−1.48726	−	0.858668i
$957$	16.6900	−	17.5722i	0.539510	−	0.568028i
$958$	40.9545	+	40.9545i	1.32318	+	1.32318i
$959$		0			0
$960$	0.370164	−	1.26533i	0.0119470	−	0.0408384i
$961$	11.7233	+	20.3054i	0.378172	+	0.655012i
$962$	4.80396	−	1.28722i	0.154886	−	0.0415015i
$963$	−8.00659	+	8.87663i	−0.258009	+	0.286045i
$964$	−70.0753	+	40.4580i	−2.25697	+	1.30306i
$965$	−5.39535	−	24.9155i	−0.173683	−	0.802058i
$966$		0			0
$967$	−18.6836	+	18.6836i	−0.600824	+	0.600824i	−0.940531	−	0.339707i	$-0.889672\pi$
$967$	−18.6836	+	18.6836i	−0.600824	+	0.600824i	0.339707	+	0.940531i	$0.389672\pi$
$968$	−52.0047	−	13.9346i	−1.67150	−	0.447876i
$969$	7.75247	+	12.6633i	0.249045	+	0.406803i
$970$	31.4650	−	16.1837i	1.01028	−	0.519627i
$971$	49.7947	−	28.7490i	1.59799	−	0.922599i	0.606114	−	0.795378i	$-0.292728\pi$
$971$	49.7947	−	28.7490i	1.59799	−	0.922599i	0.991874	−	0.127221i	$-0.0406057\pi$
$972$	−69.1776	−	9.26098i	−2.21887	−	0.297046i
$973$		0			0
$974$	41.3622			1.32533
$975$	−24.4427	+	11.8751i	−0.782794	+	0.380308i
$976$	26.2635	−	45.4897i	0.840674	−	1.45609i
$977$	2.84837	−	0.763219i	0.0911275	−	0.0244175i	−0.212967	−	0.977059i	$-0.568313\pi$
$977$	2.84837	−	0.763219i	0.0911275	−	0.0244175i	0.304095	+	0.952642i	$0.401646\pi$
$978$	28.3597	−	29.8588i	0.906843	−	0.954779i
$979$		−	14.7501i		−	0.471415i
$980$		0			0
$981$	10.4797	+	16.1681i	0.334590	+	0.516209i
$982$	0.741751	+	0.198752i	0.0236702	+	0.00634242i
$983$	4.24741	+	15.8515i	0.135471	+	0.505585i	0.999996	+	0.00299438i	$0.000953143\pi$
$983$	4.24741	+	15.8515i	0.135471	+	0.505585i	−0.864524	+	0.502591i	$0.832380\pi$
$984$	−60.0079	+	36.7369i	−1.91298	+	1.17113i
$985$	−43.9142	+	39.8448i	−1.39922	+	1.26956i
$986$			115.806i			3.68802i
$987$		0			0
$988$	−16.6937	−	16.6937i	−0.531097	−	0.531097i
$989$	5.45461	+	9.44766i	0.173446	+	0.300418i
$990$	7.00779	+	25.8490i	0.222722	+	0.821536i
$991$	3.17062	−	5.49168i	0.100718	−	0.174449i	−0.811263	−	0.584682i	$-0.801219\pi$
$991$	3.17062	−	5.49168i	0.100718	−	0.174449i	0.911981	+	0.410233i	$0.134553\pi$
$992$	3.86909	−	14.4396i	0.122844	−	0.458459i
$993$	−55.2432	+	16.3376i	−1.75309	+	0.518457i
$994$		0			0
$995$	−5.09371	+	7.90951i	−0.161481	+	0.250748i
$996$	0.907077	+	35.2272i	0.0287418	+	1.11622i
$997$	0.694156	+	2.59062i	0.0219841	+	0.0820459i	0.976046	−	0.217563i	$-0.0698106\pi$
$997$	0.694156	+	2.59062i	0.0219841	+	0.0820459i	−0.954062	+	0.299608i	$0.903144\pi$
$998$	−13.3196	−	49.7093i	−0.421624	−	1.57352i
$999$	2.66925	−	1.82938i	0.0844512	−	0.0578791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.j.263.1		48
3.2	odd	2	inner	735.2.y.j.263.12		48
5.2	odd	4	inner	735.2.y.j.557.1		48
7.2	even	3	inner	735.2.y.j.128.12		48
7.3	odd	6		735.2.j.h.638.1		24
7.4	even	3		105.2.j.a.8.1	✓	24
7.5	odd	6		735.2.y.g.128.12		48
7.6	odd	2		735.2.y.g.263.1		48
15.2	even	4	inner	735.2.y.j.557.12		48
21.2	odd	6	inner	735.2.y.j.128.1		48
21.5	even	6		735.2.y.g.128.1		48
21.11	odd	6		105.2.j.a.8.12	yes	24
21.17	even	6		735.2.j.h.638.12		24
21.20	even	2		735.2.y.g.263.12		48
35.2	odd	12	inner	735.2.y.j.422.12		48
35.4	even	6		525.2.j.b.218.12		24
35.12	even	12		735.2.y.g.422.12		48
35.17	even	12		735.2.j.h.197.12		24
35.18	odd	12		525.2.j.b.407.1		24
35.27	even	4		735.2.y.g.557.1		48
35.32	odd	12		105.2.j.a.92.12	yes	24
105.2	even	12	inner	735.2.y.j.422.1		48
105.17	odd	12		735.2.j.h.197.1		24
105.32	even	12		105.2.j.a.92.1	yes	24
105.47	odd	12		735.2.y.g.422.1		48
105.53	even	12		525.2.j.b.407.12		24
105.62	odd	4		735.2.y.g.557.12		48
105.74	odd	6		525.2.j.b.218.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.1	✓	24	7.4	even	3
105.2.j.a.8.12	yes	24	21.11	odd	6
105.2.j.a.92.1	yes	24	105.32	even	12
105.2.j.a.92.12	yes	24	35.32	odd	12
525.2.j.b.218.1		24	105.74	odd	6
525.2.j.b.218.12		24	35.4	even	6
525.2.j.b.407.1		24	35.18	odd	12
525.2.j.b.407.12		24	105.53	even	12
735.2.j.h.197.1		24	105.17	odd	12
735.2.j.h.197.12		24	35.17	even	12
735.2.j.h.638.1		24	7.3	odd	6
735.2.j.h.638.12		24	21.17	even	6
735.2.y.g.128.1		48	21.5	even	6
735.2.y.g.128.12		48	7.5	odd	6
735.2.y.g.263.1		48	7.6	odd	2
735.2.y.g.263.12		48	21.20	even	2
735.2.y.g.422.1		48	105.47	odd	12
735.2.y.g.422.12		48	35.12	even	12
735.2.y.g.557.1		48	35.27	even	4
735.2.y.g.557.12		48	105.62	odd	4
735.2.y.j.128.1		48	21.2	odd	6	inner
735.2.y.j.128.12		48	7.2	even	3	inner
735.2.y.j.263.1		48	1.1	even	1	trivial
735.2.y.j.263.12		48	3.2	odd	2	inner
735.2.y.j.422.1		48	105.2	even	12	inner
735.2.y.j.422.12		48	35.2	odd	12	inner
735.2.y.j.557.1		48	5.2	odd	4	inner
735.2.y.j.557.12		48	15.2	even	4	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.658710 + 2.45834i) q^{2} +(0.405074 - 1.68402i) q^{3} +(-3.87749 - 2.23867i) q^{4} +(0.108509 - 2.23343i) q^{5} +(3.87306 + 2.10509i) q^{6} +(4.45829 - 4.45829i) q^{8} +(-2.67183 - 1.36430i) q^{9} +(5.41906 + 1.73794i) q^{10} +(-1.35854 - 0.784351i) q^{11} +(-5.34063 + 5.62293i) q^{12} +(2.21881 + 2.21881i) q^{13} +(-3.71719 - 1.08744i) q^{15} +(3.54593 + 6.14174i) q^{16} +(-4.92759 + 1.32034i) q^{17} +(5.11388 - 5.66959i) q^{18} +(1.45527 - 0.840200i) q^{19} +(-5.42066 + 8.41719i) q^{20} +(2.82308 - 2.82308i) q^{22} +(-1.36036 - 0.364506i) q^{23} +(-5.70190 - 9.31377i) q^{24} +(-4.97645 - 0.484694i) q^{25} +(-6.91613 + 3.99303i) q^{26} +(-3.37980 + 3.94676i) q^{27} -8.91955 q^{29} +(5.12184 - 8.42181i) q^{30} +(-1.37417 + 2.38013i) q^{31} +(-5.25396 + 1.40779i) q^{32} +(-1.87117 + 1.97008i) q^{33} -12.9834i q^{34} +(7.30576 + 11.2714i) q^{36} +(-0.601543 - 0.161183i) q^{37} +(1.10690 + 4.13100i) q^{38} +(4.63529 - 2.83773i) q^{39} +(-9.47353 - 10.4411i) q^{40} -6.44292i q^{41} +(-5.47734 - 5.47734i) q^{43} +(3.51180 + 6.08262i) q^{44} +(-3.33700 + 5.81932i) q^{45} +(1.79216 - 3.10412i) q^{46} +(1.35194 - 5.04552i) q^{47} +(11.7792 - 3.48356i) q^{48} +(4.46958 - 11.9145i) q^{50} +(0.227443 + 8.83299i) q^{51} +(-3.63622 - 13.5706i) q^{52} +(1.03716 + 3.87074i) q^{53} +(-7.47618 - 10.9085i) q^{54} +(-1.89921 + 2.94909i) q^{55} +(-0.825420 - 2.79104i) q^{57} +(5.87540 - 21.9273i) q^{58} +(-2.77436 + 4.80533i) q^{59} +(11.9789 + 12.5381i) q^{60} +(-3.70333 - 6.41435i) q^{61} +(-4.94599 - 4.94599i) q^{62} +0.340400i q^{64} +(5.19632 - 4.71480i) q^{65} +(-3.61056 - 5.89768i) q^{66} +(-1.37347 - 5.12587i) q^{67} +(22.0625 + 5.91162i) q^{68} +(-1.16488 + 2.14321i) q^{69} +3.61943i q^{71} +(-17.9943 + 5.82933i) q^{72} +(8.05596 - 2.15859i) q^{73} +(0.792485 - 1.37262i) q^{74} +(-2.83207 + 8.18409i) q^{75} -7.52372 q^{76} +(3.92279 + 13.2644i) q^{78} +(-14.7720 + 8.52862i) q^{79} +(14.1019 - 7.25318i) q^{80} +(5.27735 + 7.29037i) q^{81} +(15.8389 + 4.24402i) q^{82} +(3.21312 - 3.21312i) q^{83} +(2.41421 + 11.1487i) q^{85} +(17.0731 - 9.85718i) q^{86} +(-3.61308 + 15.0207i) q^{87} +(-9.55360 + 2.55988i) q^{88} +(4.70137 + 8.14301i) q^{89} +(-12.1077 - 12.0367i) q^{90} +(4.45876 + 4.45876i) q^{92} +(3.45154 + 3.27825i) q^{93} +(11.5131 + 6.64707i) q^{94} +(-1.71862 - 3.34142i) q^{95} +(0.242507 + 9.41801i) q^{96} +(4.39640 - 4.39640i) q^{97} +(2.55968 + 3.94911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{3} + 16 q^{10} - 16 q^{12} - 16 q^{13} - 32 q^{15} + 16 q^{16} + 20 q^{18} + 16 q^{22} + 16 q^{25} - 32 q^{27} - 20 q^{30} - 28 q^{33} + 32 q^{36} + 16 q^{37} - 64 q^{40} - 80 q^{43} - 20 q^{45}+ \cdots + 48 q^{97}+O(q^{100}) \) 48 * q + 4 * q^3 + 16 * q^10 - 16 * q^12 - 16 * q^13 - 32 * q^15 + 16 * q^16 + 20 * q^18 + 16 * q^22 + 16 * q^25 - 32 * q^27 - 20 * q^30 - 28 * q^33 + 32 * q^36 + 16 * q^37 - 64 * q^40 - 80 * q^43 - 20 * q^45 + 64 * q^46 + 32 * q^48 + 20 * q^51 + 80 * q^55 + 8 * q^57 - 40 * q^58 - 32 * q^60 - 32 * q^61 + 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 60 * q^75 + 64 * q^76 + 120 * q^78 - 52 * q^81 + 80 * q^82 + 48 * q^85 - 4 * q^87 - 96 * q^88 - 48 * q^90 + 76 * q^93 + 96 * q^96 + 48 * q^97

Introduction

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