LMFDB - Embedded newform 925.2.bb.e.326.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			326.8
Character	$\chi$	$=$	925.326
Dual form			925.2.bb.e.576.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0583632 - 0.160351i) q^{2} +(-0.674605 - 0.245536i) q^{3} +(1.50978 - 1.26686i) q^{4} +0.122504i q^{6} +(0.618951 + 3.51024i) q^{7} +(-0.586820 - 0.338800i) q^{8} +(-1.90333 - 1.59708i) q^{9} +(-2.79800 + 4.84627i) q^{11} +(-1.32957 + 0.483922i) q^{12} +(1.17531 + 1.40068i) q^{13} +(0.526749 - 0.304118i) q^{14} +(0.664401 - 3.76801i) q^{16} +(-4.07242 + 4.85332i) q^{17} +(-0.145010 + 0.398412i) q^{18} +(-0.400455 + 1.10024i) q^{19} +(0.444344 - 2.52000i) q^{21} +(0.940407 + 0.165819i) q^{22} +(-7.19469 + 4.15386i) q^{23} +(0.312684 + 0.372642i) q^{24} +(0.156006 - 0.270210i) q^{26} +(1.96870 + 3.40989i) q^{27} +(5.38146 + 4.51558i) q^{28} +(-2.90414 - 1.67670i) q^{29} -2.55670i q^{31} +(-1.97760 + 0.348703i) q^{32} +(3.07748 - 2.58231i) q^{33} +(1.01592 + 0.369763i) q^{34} -4.89689 q^{36} +(3.27409 - 5.12643i) q^{37} +0.199797 q^{38} +(-0.448951 - 1.23348i) q^{39} +(-0.879400 + 0.737904i) q^{41} +(-0.430019 + 0.0758240i) q^{42} +1.23182i q^{43} +(1.91517 + 10.8615i) q^{44} +(1.08598 + 0.911247i) q^{46} +(2.78479 + 4.82340i) q^{47} +(-1.37339 + 2.37878i) q^{48} +(-5.36086 + 1.95119i) q^{49} +(3.93894 - 2.27415i) q^{51} +(3.54892 + 0.625770i) q^{52} +(1.58638 - 8.99680i) q^{53} +(0.431882 - 0.514697i) q^{54} +(0.826060 - 2.26958i) q^{56} +(0.540298 - 0.643902i) q^{57} +(-0.0993673 + 0.563540i) q^{58} +(9.96639 + 1.75734i) q^{59} +(2.36411 + 2.81744i) q^{61} +(-0.409970 + 0.149217i) q^{62} +(4.42808 - 7.66966i) q^{63} +(-3.65480 - 6.33030i) q^{64} +(-0.593689 - 0.342766i) q^{66} +(1.84077 + 10.4395i) q^{67} +12.4866i q^{68} +(5.87350 - 1.03566i) q^{69} +(6.13971 + 2.23467i) q^{71} +(0.575819 + 1.58205i) q^{72} -6.54940 q^{73} +(-1.01312 - 0.225811i) q^{74} +(0.789250 + 2.16845i) q^{76} +(-18.7434 - 6.82205i) q^{77} +(-0.171589 + 0.143980i) q^{78} +(-14.1537 + 2.49567i) q^{79} +(0.803505 + 4.55690i) q^{81} +(0.169649 + 0.0979466i) q^{82} +(-0.277634 - 0.232963i) q^{83} +(-2.52162 - 4.36758i) q^{84} +(0.197524 - 0.0718927i) q^{86} +(1.54745 + 1.84418i) q^{87} +(3.28384 - 1.89593i) q^{88} +(11.2979 + 1.99213i) q^{89} +(-4.18926 + 4.99256i) q^{91} +(-5.60007 + 15.3861i) q^{92} +(-0.627761 + 1.72476i) q^{93} +(0.610910 - 0.728054i) q^{94} +(1.41971 + 0.250334i) q^{96} +(2.90491 - 1.67715i) q^{97} +(0.625753 + 0.745743i) q^{98} +(13.0654 - 4.75542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

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 $

$2$	−0.0583632	−	0.160351i	−0.0412690	−	0.113386i	0.917346	−	0.398090i	$-0.130327\pi$
$2$	−0.0583632	−	0.160351i	−0.0412690	−	0.113386i	−0.958615	+	0.284704i	$0.908105\pi$
$3$	−0.674605	−	0.245536i	−0.389483	−	0.141760i	0.139853	−	0.990172i	$-0.455337\pi$
$3$	−0.674605	−	0.245536i	−0.389483	−	0.141760i	−0.529337	+	0.848412i	$0.677559\pi$
$4$	1.50978	−	1.26686i	0.754891	−	0.633429i
$5$		0			0
$5$		0			0
$6$			0.122504i			0.0500121i
$7$	0.618951	+	3.51024i	0.233941	+	1.32675i	0.844832	+	0.535032i	$0.179700\pi$
$7$	0.618951	+	3.51024i	0.233941	+	1.32675i	−0.610891	+	0.791715i	$0.709188\pi$
$8$	−0.586820	−	0.338800i	−0.207472	−	0.119784i
$9$	−1.90333	−	1.59708i	−0.634443	−	0.532361i
$10$		0			0
$11$	−2.79800	+	4.84627i	−0.843628	+	1.46121i	0.0431797	+	0.999067i	$0.486251\pi$
$11$	−2.79800	+	4.84627i	−0.843628	+	1.46121i	−0.886808	+	0.462139i	$0.847082\pi$
$12$	−1.32957	+	0.483922i	−0.383813	+	0.139696i
$13$	1.17531	+	1.40068i	0.325972	+	0.388478i	0.903995	−	0.427542i	$-0.140620\pi$
$13$	1.17531	+	1.40068i	0.325972	+	0.388478i	−0.578024	+	0.816020i	$0.696176\pi$
$14$	0.526749	−	0.304118i	0.140779	−	0.0812791i
$15$		0			0
$16$	0.664401	−	3.76801i	0.166100	−	0.942002i
$17$	−4.07242	+	4.85332i	−0.987706	+	1.17710i	−0.00351439	+	0.999994i	$0.501119\pi$
$17$	−4.07242	+	4.85332i	−0.987706	+	1.17710i	−0.984191	+	0.177108i	$0.943326\pi$
$18$	−0.145010	+	0.398412i	−0.0341792	+	0.0939067i
$19$	−0.400455	+	1.10024i	−0.0918708	+	0.252413i	−0.977114	−	0.212715i	$-0.931769\pi$
$19$	−0.400455	+	1.10024i	−0.0918708	+	0.252413i	0.885244	+	0.465128i	$0.153992\pi$
$20$		0			0
$21$	0.444344	−	2.52000i	0.0969639	−	0.549909i
$22$	0.940407	+	0.165819i	0.200495	+	0.0353528i
$23$	−7.19469	+	4.15386i	−1.50020	+	0.866139i	−0.500198	+	0.865911i	$0.666739\pi$
$23$	−7.19469	+	4.15386i	−1.50020	+	0.866139i	−1.00000		0.000228074i	$0.999927\pi$
$24$	0.312684	+	0.372642i	0.0638263	+	0.0760652i
$25$		0			0
$26$	0.156006	−	0.270210i	0.0305953	−	0.0529926i
$27$	1.96870	+	3.40989i	0.378877	+	0.656234i
$28$	5.38146	+	4.51558i	1.01700	+	0.853365i
$29$	−2.90414	−	1.67670i	−0.539285	−	0.311356i	0.205504	−	0.978656i	$-0.434117\pi$
$29$	−2.90414	−	1.67670i	−0.539285	−	0.311356i	−0.744789	+	0.667300i	$0.767450\pi$
$30$		0			0
$31$		−	2.55670i		−	0.459196i	−0.973286	−	0.229598i	$-0.926259\pi$
$31$		−	2.55670i		−	0.459196i	0.973286	−	0.229598i	$-0.0737411\pi$
$32$	−1.97760	+	0.348703i	−0.349593	+	0.0616426i
$33$	3.07748	−	2.58231i	0.535720	−	0.449523i
$34$	1.01592	+	0.369763i	0.174228	+	0.0634138i
$35$		0			0
$36$	−4.89689			−0.816149
$37$	3.27409	−	5.12643i	0.538257	−	0.842780i
$37$	3.27409	−	5.12643i	0.538257	−	0.842780i
$38$	0.199797			0.0324114
$39$	−0.448951	−	1.23348i	−0.0718898	−	0.197515i
$40$		0			0
$41$	−0.879400	+	0.737904i	−0.137339	+	0.115241i	−0.708869	−	0.705340i	$-0.750794\pi$
$41$	−0.879400	+	0.737904i	−0.137339	+	0.115241i	0.571530	+	0.820581i	$0.306350\pi$
$42$	−0.430019	+	0.0758240i	−0.0663534	+	0.0116999i
$43$			1.23182i			0.187850i	0.995579	+	0.0939251i	$0.0299414\pi$
$43$			1.23182i			0.187850i	−0.995579	+	0.0939251i	$0.970059\pi$
$44$	1.91517	+	10.8615i	0.288723	+	1.63743i
$45$		0			0
$46$	1.08598	+	0.911247i	0.160119	+	0.134356i
$47$	2.78479	+	4.82340i	0.406204	+	0.703565i	0.994461	−	0.105109i	$-0.0335190\pi$
$47$	2.78479	+	4.82340i	0.406204	+	0.703565i	−0.588257	+	0.808674i	$0.700186\pi$
$48$	−1.37339	+	2.37878i	−0.198232	+	0.343348i
$49$	−5.36086	+	1.95119i	−0.765837	+	0.278742i
$50$		0			0
$51$	3.93894	−	2.27415i	0.551561	−	0.318444i
$52$	3.54892	+	0.625770i	0.492146	+	0.0867787i
$53$	1.58638	−	8.99680i	0.217906	−	1.23581i	−0.657887	−	0.753117i	$-0.728549\pi$
$53$	1.58638	−	8.99680i	0.217906	−	1.23581i	0.875792	−	0.482688i	$-0.160340\pi$
$54$	0.431882	−	0.514697i	0.0587717	−	0.0700413i
$55$		0			0
$56$	0.826060	−	2.26958i	0.110387	−	0.303285i
$57$	0.540298	−	0.643902i	0.0715643	−	0.0852870i
$58$	−0.0993673	+	0.563540i	−0.0130476	+	0.0739965i
$59$	9.96639	+	1.75734i	1.29751	+	0.228787i	0.779401	−	0.626526i	$-0.215524\pi$
$59$	9.96639	+	1.75734i	1.29751	+	0.228787i	0.518113	+	0.855312i	$0.326635\pi$
$60$		0			0
$61$	2.36411	+	2.81744i	0.302693	+	0.360736i	0.895854	−	0.444348i	$-0.146565\pi$
$61$	2.36411	+	2.81744i	0.302693	+	0.360736i	−0.593161	+	0.805084i	$0.702120\pi$
$62$	−0.409970	+	0.149217i	−0.0520662	+	0.0189506i
$63$	4.42808	−	7.66966i	0.557886	−	0.966287i
$64$	−3.65480	−	6.33030i	−0.456850	−	0.791288i
$65$		0			0
$66$	−0.593689	−	0.342766i	−0.0730780	−	0.0421916i
$67$	1.84077	+	10.4395i	0.224886	+	1.27539i	0.862902	+	0.505370i	$0.168644\pi$
$67$	1.84077	+	10.4395i	0.224886	+	1.27539i	−0.638016	+	0.770023i	$0.720245\pi$
$68$			12.4866i			1.51423i
$69$	5.87350	−	1.03566i	0.707086	−	0.124678i
$70$		0			0
$71$	6.13971	+	2.23467i	0.728650	+	0.265207i	0.679593	−	0.733589i	$-0.262156\pi$
$71$	6.13971	+	2.23467i	0.728650	+	0.265207i	0.0490566	+	0.998796i	$0.484379\pi$
$72$	0.575819	+	1.58205i	0.0678609	+	0.186446i
$73$	−6.54940			−0.766549			−0.383275	−	0.923634i	$-0.625204\pi$
$73$	−6.54940			−0.766549			−0.383275	+	0.923634i	$0.625204\pi$
$74$	−1.01312	−	0.225811i	−0.117773	−	0.0262499i
$75$		0			0
$76$	0.789250	+	2.16845i	0.0905332	+	0.248738i
$77$	−18.7434	−	6.82205i	−2.13601	−	0.777444i
$78$	−0.171589	+	0.143980i	−0.0194286	+	0.0163025i
$79$	−14.1537	+	2.49567i	−1.59241	+	0.280785i	−0.898400	−	0.439179i	$-0.855269\pi$
$79$	−14.1537	+	2.49567i	−1.59241	+	0.280785i	−0.694012	+	0.719964i	$0.744158\pi$
$80$		0			0
$81$	0.803505	+	4.55690i	0.0892783	+	0.506322i
$82$	0.169649	+	0.0979466i	0.0187345	+	0.0108164i
$83$	−0.277634	−	0.232963i	−0.0304743	−	0.0255710i	0.627423	−	0.778678i	$-0.284110\pi$
$83$	−0.277634	−	0.232963i	−0.0304743	−	0.0255710i	−0.657898	+	0.753107i	$0.728554\pi$
$84$	−2.52162	−	4.36758i	−0.275131	−	0.476542i
$85$		0			0
$86$	0.197524	−	0.0718927i	0.0212995	−	0.00775239i
$87$	1.54745	+	1.84418i	0.165904	+	0.197717i
$88$	3.28384	−	1.89593i	0.350058	−	0.202106i
$89$	11.2979	+	1.99213i	1.19758	+	0.211165i	0.736650	−	0.676274i	$-0.236406\pi$
$89$	11.2979	+	1.99213i	1.19758	+	0.211165i	0.460926	+	0.887439i	$0.347517\pi$
$90$		0			0
$91$	−4.18926	+	4.99256i	−0.439154	+	0.523363i
$92$	−5.60007	+	15.3861i	−0.583848	+	1.60411i
$93$	−0.627761	+	1.72476i	−0.0650958	+	0.178849i
$94$	0.610910	−	0.728054i	0.0630106	−	0.0750931i
$95$		0			0
$96$	1.41971	+	0.250334i	0.144899	+	0.0255496i
$97$	2.90491	−	1.67715i	0.294949	−	0.170289i	−0.345223	−	0.938521i	$-0.612197\pi$
$97$	2.90491	−	1.67715i	0.294949	−	0.170289i	0.640171	+	0.768232i	$0.278863\pi$
$98$	0.625753	+	0.745743i	0.0632106	+	0.0753315i
$99$	13.0654	−	4.75542i	1.31312	−	0.477938i
$100$		0			0
$101$	2.77691	+	4.80974i	0.276313	+	0.478587i	0.970465	−	0.241240i	$-0.0775542\pi$
$101$	2.77691	+	4.80974i	0.276313	+	0.478587i	−0.694153	+	0.719828i	$0.744221\pi$
$102$	−0.594551	−	0.498888i	−0.0588693	−	0.0493972i
$103$	−6.93072	−	4.00145i	−0.682904	−	0.394275i	0.118044	−	0.993008i	$-0.462338\pi$
$103$	−6.93072	−	4.00145i	−0.682904	−	0.394275i	−0.800948	+	0.598733i	$0.795671\pi$
$104$	−0.215143	−	1.22014i	−0.0210966	−	0.119644i
$105$		0			0
$106$	−1.53524	+	0.270703i	−0.149115	+	0.0262930i
$107$	−2.14007	+	1.79573i	−0.206889	+	0.173600i	−0.740344	−	0.672228i	$-0.765338\pi$
$107$	−2.14007	+	1.79573i	−0.206889	+	0.173600i	0.533456	+	0.845828i	$0.320893\pi$
$108$	7.29217	+	2.65413i	0.701689	+	0.255394i
$109$	4.17259	+	11.4641i	0.399661	+	1.09806i	0.962450	+	0.271459i	$0.0875063\pi$
$109$	4.17259	+	11.4641i	0.399661	+	1.09806i	−0.562789	+	0.826601i	$0.690272\pi$
$110$		0			0
$111$	−3.46744	+	2.65441i	−0.329115	+	0.251945i
$112$	13.6379			1.28866
$113$	0.645004	+	1.77213i	0.0606769	+	0.166708i	0.966327	−	0.257318i	$-0.0828387\pi$
$113$	0.645004	+	1.77213i	0.0606769	+	0.166708i	−0.905650	+	0.424026i	$0.860616\pi$
$114$	−0.134784	−	0.0490574i	−0.0126237	−	0.00459465i
$115$		0			0
$116$	−6.50876	+	1.14767i	−0.604323	+	0.106558i
$117$		−	4.54301i		−	0.420002i
$118$	−0.299877	−	1.70069i	−0.0276059	−	0.156561i
$119$	−19.5569	−	11.2912i	−1.79278	−	1.03506i
$120$		0			0
$121$	−10.1576	−	17.5934i	−0.923416	−	1.59940i
$122$	0.313803	−	0.543523i	0.0284104	−	0.0492082i
$123$	0.774429	−	0.281869i	0.0698280	−	0.0254153i
$124$	−3.23897	−	3.86005i	−0.290868	−	0.346643i
$125$		0			0
$126$	−1.48828	−	0.262424i	−0.132586	−	0.0233786i
$127$	1.49309	−	8.46771i	0.132490	−	0.751388i	−0.844085	−	0.536210i	$-0.819856\pi$
$127$	1.49309	−	8.46771i	0.132490	−	0.751388i	0.976575	−	0.215178i	$-0.0690332\pi$
$128$	−3.38333	+	4.03210i	−0.299047	+	0.356391i
$129$	0.302455	−	0.830989i	0.0266297	−	0.0731645i
$130$		0			0
$131$	−2.93728	+	3.50052i	−0.256631	+	0.305841i	−0.878942	−	0.476929i	$-0.841750\pi$
$131$	−2.93728	+	3.50052i	−0.256631	+	0.305841i	0.622310	+	0.782771i	$0.286194\pi$
$132$	1.37490	−	7.79745i	0.119670	−	0.678681i
$133$	−4.10998	−	0.724700i	−0.356380	−	0.0628395i
$134$	1.56656	−	0.904455i	0.135330	−	0.0781331i
$135$		0			0
$136$	4.03408	−	1.46828i	0.345919	−	0.125904i
$137$	3.41597	−	5.91663i	0.291846	−	0.505492i	−0.682400	−	0.730979i	$-0.739064\pi$
$137$	3.41597	−	5.91663i	0.291846	−	0.505492i	0.974246	+	0.225487i	$0.0723973\pi$
$138$	−0.508865	−	0.881380i	−0.0433175	−	0.0750280i
$139$	−2.54684	−	2.13705i	−0.216020	−	0.181263i	0.528356	−	0.849023i	$-0.322809\pi$
$139$	−2.54684	−	2.13705i	−0.216020	−	0.181263i	−0.744376	+	0.667760i	$0.767253\pi$
$140$		0			0
$141$	−0.694315	−	3.93766i	−0.0584719	−	0.331611i
$142$		−	1.11493i		−	0.0935632i
$143$	−10.0766	+	1.77677i	−0.842645	+	0.148581i
$144$	−7.28240	+	6.11066i	−0.606866	+	0.509221i
$145$		0			0
$146$	0.382244	+	1.05021i	0.0316347	+	0.0869157i
$147$	4.09555			0.337795
$148$	−1.55130	−	11.8876i	−0.127516	−	0.977155i
$149$	11.9540			0.979313			0.489656	−	0.871916i	$-0.337122\pi$
$149$	11.9540			0.979313			0.489656	+	0.871916i	$0.337122\pi$
$150$		0			0
$151$	20.4486	+	7.44269i	1.66408	+	0.605677i	0.990997	−	0.133885i	$-0.0427453\pi$
$151$	20.4486	+	7.44269i	1.66408	+	0.605677i	0.673088	+	0.739562i	$0.264968\pi$
$152$	0.607758	−	0.509969i	0.0492956	−	0.0413640i
$153$	15.5023	−	2.73347i	1.25329	−	0.220988i
$154$			3.40369i			0.274277i
$155$		0			0
$156$	−2.24047	−	1.29353i	−0.179381	−	0.103566i
$157$	−11.8833	−	9.97130i	−0.948393	−	0.795796i	0.0306333	−	0.999531i	$-0.490248\pi$
$157$	−11.8833	−	9.97130i	−0.948393	−	0.795796i	−0.979026	+	0.203735i	$0.934692\pi$
$158$	1.22624	+	2.12390i	0.0975542	+	0.168969i
$159$	−3.27922	+	5.67977i	−0.260059	+	0.450435i
$160$		0			0
$161$	−19.0342	−	22.6841i	−1.50011	−	1.78776i
$162$	0.683811	−	0.394798i	0.0537252	−	0.0310183i
$163$	−8.68536	−	1.53146i	−0.680290	−	0.119954i	−0.177184	−	0.984178i	$-0.556699\pi$
$163$	−8.68536	−	1.53146i	−0.680290	−	0.119954i	−0.503107	+	0.864224i	$0.667810\pi$
$164$	−0.392883	+	2.22815i	−0.0306790	+	0.173989i
$165$		0			0
$166$	−0.0211523	+	0.0581155i	−0.00164174	+	0.00451064i
$167$	3.51894	−	9.66821i	0.272304	−	0.748149i	−0.725875	−	0.687826i	$-0.758565\pi$
$167$	3.51894	−	9.66821i	0.272304	−	0.748149i	0.998179	−	0.0603221i	$-0.0192128\pi$
$168$	−1.11453	+	1.32824i	−0.0859877	+	0.102476i
$169$	1.67688	−	9.51005i	0.128991	−	0.731542i
$170$		0			0
$171$	2.51938	−	1.45456i	0.192662	−	0.111233i
$172$	1.56054	+	1.85977i	0.118990	+	0.141807i
$173$	−14.0346	+	5.10817i	−1.06703	+	0.388367i	−0.815065	−	0.579369i	$-0.803299\pi$
$173$	−14.0346	+	5.10817i	−1.06703	+	0.388367i	−0.251965	+	0.967736i	$0.581077\pi$
$174$	0.205403	−	0.355769i	0.0155716	−	0.0269708i
$175$		0			0
$176$	16.4018	+	13.7627i	1.23633	+	1.03741i
$177$	−6.29188	−	3.63262i	−0.472927	−	0.273044i
$178$	−0.339941	−	1.92790i	−0.0254797	−	0.144502i
$179$			4.15086i			0.310250i	0.987895	+	0.155125i	$0.0495780\pi$
$179$			4.15086i			0.310250i	−0.987895	+	0.155125i	$0.950422\pi$
$180$		0			0
$181$	10.5148	−	8.82295i	0.781558	−	0.655805i	−0.162083	−	0.986777i	$-0.551821\pi$
$181$	10.5148	−	8.82295i	0.781558	−	0.655805i	0.943640	+	0.330972i	$0.107377\pi$
$182$	1.04506	+	0.380372i	0.0774652	+	0.0281950i
$183$	−0.903057	−	2.48113i	−0.0667559	−	0.183410i
$184$	5.62932			0.414999
$185$		0			0
$186$	0.313206			0.0229654
$187$	−12.1259	−	33.3156i	−0.886733	−	2.43628i
$188$	10.3150	+	3.75435i	0.752298	+	0.273814i
$189$	−10.7510	+	9.02118i	−0.782022	+	0.656194i
$190$		0			0
$191$			1.78215i			0.128952i	0.997919	+	0.0644759i	$0.0205376\pi$
$191$			1.78215i			0.128952i	−0.997919	+	0.0644759i	$0.979462\pi$
$192$	0.911229	+	5.16784i	0.0657623	+	0.372957i
$193$	12.8826	+	7.43780i	0.927313	+	0.535384i	0.885961	−	0.463760i	$-0.153500\pi$
$193$	12.8826	+	7.43780i	0.927313	+	0.535384i	0.0413522	+	0.999145i	$0.486833\pi$
$194$	−0.438473	−	0.367922i	−0.0314805	−	0.0264153i
$195$		0			0
$196$	−5.62184	+	9.73732i	−0.401560	+	0.695523i
$197$	−12.3903	+	4.50971i	−0.882775	+	0.321304i	−0.743329	−	0.668926i	$-0.766754\pi$
$197$	−12.3903	+	4.50971i	−0.882775	+	0.321304i	−0.139446	+	0.990230i	$0.544532\pi$
$198$	−1.52508	−	1.81752i	−0.108383	−	0.129165i
$199$	6.44509	−	3.72107i	0.456880	−	0.263780i	−0.253851	−	0.967243i	$-0.581697\pi$
$199$	6.44509	−	3.72107i	0.456880	−	0.263780i	0.710731	+	0.703463i	$0.248364\pi$
$200$		0			0
$201$	1.32149	−	7.49454i	0.0932108	−	0.528624i
$202$	0.609180	−	0.725993i	0.0428618	−	0.0510807i
$203$	4.08812	−	11.2320i	0.286930	−	0.788333i
$204$	3.06592	−	8.42354i	0.214657	−	0.589766i
$205$		0			0
$206$	−0.237140	+	1.34489i	−0.0165223	+	0.0937028i
$207$	20.3279	+	3.58436i	1.41289	+	0.249130i
$208$	6.05864	−	3.49796i	0.420091	−	0.242540i
$209$	−4.21160	−	5.01919i	−0.291323	−	0.347185i
$210$		0			0
$211$	0.649216	−	1.12448i	0.0446939	−	0.0774121i	−0.842813	−	0.538206i	$-0.819102\pi$
$211$	0.649216	−	1.12448i	0.0446939	−	0.0774121i	0.887507	+	0.460794i	$0.152435\pi$
$212$	−9.00258	−	15.5929i	−0.618300	−	1.07093i
$213$	−3.59319	−	3.01504i	−0.246201	−	0.206587i
$214$	0.412850	+	0.238359i	0.0282218	+	0.0162939i
$215$		0			0
$216$		−	2.66799i		−	0.181534i
$217$	8.97462	−	1.58247i	0.609237	−	0.107425i
$218$	1.59476	−	1.33816i	0.108011	−	0.0906317i
$219$	4.41826	+	1.60811i	0.298558	+	0.108666i
$220$		0			0
$221$	−11.5843			−0.779242
$222$	0.628009	+	0.401090i	0.0421492	+	0.0269194i
$223$	13.6327			0.912914			0.456457	−	0.889746i	$-0.349118\pi$
$223$	13.6327			0.912914			0.456457	+	0.889746i	$0.349118\pi$
$224$	−2.44807	−	6.72601i	−0.163568	−	0.449400i
$225$		0			0
$226$	0.246520	−	0.206855i	0.0163983	−	0.0137598i
$227$	29.3267	−	5.17109i	1.94648	−	0.343217i	0.946706	−	0.322099i	$-0.104389\pi$
$227$	29.3267	−	5.17109i	1.94648	−	0.343217i	0.999777	−	0.0211181i	$-0.00672260\pi$
$228$		−	1.65663i		−	0.109713i
$229$	2.55052	+	14.4647i	0.168543	+	0.955856i	0.945336	+	0.326099i	$0.105734\pi$
$229$	2.55052	+	14.4647i	0.168543	+	0.955856i	−0.776792	+	0.629757i	$0.783155\pi$
$230$		0			0
$231$	10.9693	+	9.20437i	0.721730	+	0.605603i
$232$	1.13614	+	1.96785i	0.0745910	+	0.129195i
$233$	−7.00728	+	12.1370i	−0.459062	+	0.795119i	−0.998912	−	0.0466428i	$-0.985148\pi$
$233$	−7.00728	+	12.1370i	−0.459062	+	0.795119i	0.539850	+	0.841761i	$0.318481\pi$
$234$	−0.728479	+	0.265145i	−0.0476221	+	0.0173330i
$235$		0			0
$236$	17.2734	−	9.97279i	1.12440	−	0.649174i
$237$	10.1609	+	1.79164i	0.660022	+	0.116380i
$238$	−0.669156	+	3.79497i	−0.0433750	+	0.245992i
$239$	−10.2597	+	12.2270i	−0.663643	+	0.790899i	−0.987904	−	0.155068i	$-0.950440\pi$
$239$	−10.2597	+	12.2270i	−0.663643	+	0.790899i	0.324260	+	0.945968i	$0.394885\pi$
$240$		0			0
$241$	−7.57694	+	20.8175i	−0.488074	+	1.34097i	0.414349	+	0.910118i	$0.364009\pi$
$241$	−7.57694	+	20.8175i	−0.488074	+	1.34097i	−0.902422	+	0.430853i	$0.858213\pi$
$242$	−2.22830	+	2.65559i	−0.143241	+	0.170708i
$243$	2.62801	−	14.9042i	0.168587	−	0.956102i
$244$	7.13858	+	1.25872i	0.457001	+	0.0805816i
$245$		0			0
$246$	−0.0903963	−	0.107730i	−0.00576346	−	0.00686862i
$247$	−2.01174	+	0.732214i	−0.128004	+	0.0465897i
$248$	−0.866210	+	1.50032i	−0.0550044	+	0.0952703i
$249$	0.130093	+	0.225327i	0.00824428	+	0.0142795i
$250$		0			0
$251$	−15.0176	−	8.67039i	−0.947900	−	0.547270i	−0.0554721	−	0.998460i	$-0.517666\pi$
$251$	−15.0176	−	8.67039i	−0.947900	−	0.547270i	−0.892428	+	0.451190i	$0.851000\pi$
$252$	−3.03093	−	17.1893i	−0.190931	−	1.08282i
$253$		−	46.4899i		−	2.92280i
$254$	−1.44495	+	0.254784i	−0.0906643	+	0.0159866i
$255$		0			0
$256$	−12.8935	−	4.69287i	−0.805846	−	0.293304i
$257$	−4.04907	−	11.1247i	−0.252574	−	0.693942i	−0.999576	−	0.0291200i	$-0.990730\pi$
$257$	−4.04907	−	11.1247i	−0.252574	−	0.693942i	0.747002	−	0.664822i	$-0.231493\pi$
$258$	−0.150903			−0.00939479
$259$	20.0215	+	8.31985i	1.24408	+	0.516970i
$260$		0			0
$261$	2.84969	+	7.82947i	0.176392	+	0.484632i
$262$	0.732742	+	0.266696i	0.0452689	+	0.0164765i
$263$	4.40775	−	3.69854i	0.271793	−	0.228062i	−0.496696	−	0.867925i	$-0.665453\pi$
$263$	4.40775	−	3.69854i	0.271793	−	0.228062i	0.768489	+	0.639863i	$0.221009\pi$
$264$	−2.68081	+	0.472699i	−0.164993	+	0.0290926i
$265$		0			0
$266$	0.123665	+	0.701337i	0.00758236	+	0.0430017i
$267$	−7.13249	−	4.11794i	−0.436501	−	0.252014i
$268$	16.0046	+	13.4294i	0.977636	+	0.820334i
$269$	−14.2604	−	24.6997i	−0.869471	−	1.50597i	−0.862538	−	0.505993i	$-0.831126\pi$
$269$	−14.2604	−	24.6997i	−0.869471	−	1.50597i	−0.00693373	−	0.999976i	$-0.502207\pi$
$270$		0			0
$271$	−12.0165	+	4.37366i	−0.729953	+	0.265681i	−0.680145	−	0.733078i	$-0.738083\pi$
$271$	−12.0165	+	4.37366i	−0.729953	+	0.265681i	−0.0498079	+	0.998759i	$0.515861\pi$
$272$	15.5816	+	18.5694i	0.944774	+	1.12594i
$273$	4.05195	−	2.33939i	0.245235	−	0.141587i
$274$	−1.14811	−	0.202442i	−0.0693597	−	0.0122300i
$275$		0			0
$276$	7.55568	−	9.00450i	0.454798	−	0.542007i
$277$	−4.75363	+	13.0605i	−0.285618	+	0.784729i	0.711048	+	0.703143i	$0.248221\pi$
$277$	−4.75363	+	13.0605i	−0.285618	+	0.784729i	−0.996666	+	0.0815860i	$0.974001\pi$
$278$	−0.194038	+	0.533115i	−0.0116376	+	0.0319741i
$279$	−4.08325	+	4.86623i	−0.244458	+	0.291334i
$280$		0			0
$281$	6.16133	+	1.08641i	0.367554	+	0.0648097i	0.354375	−	0.935103i	$-0.384694\pi$
$281$	6.16133	+	1.08641i	0.367554	+	0.0648097i	0.0131793	+	0.999913i	$0.495805\pi$
$282$	−0.590887	+	0.341148i	−0.0351868	+	0.0203151i
$283$	7.33500	+	8.74151i	0.436021	+	0.519629i	0.938649	−	0.344873i	$-0.112078\pi$
$283$	7.33500	+	8.74151i	0.436021	+	0.519629i	−0.502629	+	0.864502i	$0.667634\pi$
$284$	12.1006	−	4.40427i	0.718041	−	0.261346i
$285$		0			0
$286$	0.873008	+	1.51209i	0.0516221	+	0.0894120i
$287$	−3.13453	−	2.63018i	−0.185025	−	0.155255i
$288$	4.32092	+	2.49469i	0.254613	+	0.147001i
$289$	−4.01809	−	22.7877i	−0.236358	−	1.34045i
$290$		0			0
$291$	−2.37146	+	0.418153i	−0.139018	+	0.0245126i
$292$	−9.88817	+	8.29716i	−0.578661	+	0.485555i
$293$	−20.4058	−	7.42711i	−1.19212	−	0.433896i	−0.331653	−	0.943401i	$-0.607606\pi$
$293$	−20.4058	−	7.42711i	−1.19212	−	0.433896i	−0.860468	+	0.509505i	$0.829829\pi$
$294$	−0.239029	−	0.656727i	−0.0139405	−	0.0383011i
$295$		0			0
$296$	−3.65814	+	1.89903i	−0.212625	+	0.110379i
$297$	−22.0337			−1.27853
$298$	−0.697675	−	1.91685i	−0.0404152	−	0.111040i
$299$	−14.2742	−	5.19538i	−0.825498	−	0.300457i
$300$		0			0
$301$	−4.32397	+	0.762433i	−0.249230	+	0.0439459i
$302$		−	3.71334i		−	0.213679i
$303$	−0.692349	−	3.92651i	−0.0397744	−	0.225572i
$304$	3.87966	+	2.23992i	0.222514	+	0.128468i
$305$		0			0
$306$	−1.34308	−	2.32628i	−0.0767787	−	0.132985i
$307$	−3.51879	+	6.09472i	−0.200828	+	0.347844i	−0.948795	−	0.315891i	$-0.897697\pi$
$307$	−3.51879	+	6.09472i	−0.200828	+	0.347844i	0.747968	+	0.663735i	$0.231030\pi$
$308$	−36.9410	+	13.4454i	−2.10491	+	0.766125i
$309$	3.69300	+	4.40114i	0.210087	+	0.250372i
$310$		0			0
$311$	−13.3911	−	2.36122i	−0.759342	−	0.133892i	−0.219446	−	0.975625i	$-0.570425\pi$
$311$	−13.3911	−	2.36122i	−0.759342	−	0.133892i	−0.539895	+	0.841732i	$0.681536\pi$
$312$	−0.154451	+	0.875937i	−0.00874409	+	0.0495902i
$313$	−0.0729772	+	0.0869709i	−0.00412492	+	0.00491588i	−0.768103	−	0.640326i	$-0.778799\pi$
$313$	−0.0729772	+	0.0869709i	−0.00412492	+	0.00491588i	0.763978	+	0.645242i	$0.223244\pi$
$314$	−0.905363	+	2.48747i	−0.0510926	+	0.140376i
$315$		0			0
$316$	−18.2073	+	21.6986i	−1.02424	+	1.22064i
$317$	−0.480414	+	2.72456i	−0.0269828	+	0.153027i	−0.995322	−	0.0966099i	$-0.969200\pi$
$317$	−0.480414	+	2.72456i	−0.0269828	+	0.153027i	0.968340	+	0.249637i	$0.0803112\pi$
$318$	1.10214	+	0.194338i	0.0618052	+	0.0108979i
$319$	16.2515	−	9.38283i	0.909911	−	0.525337i
$320$		0			0
$321$	1.88462	−	0.685946i	0.105189	−	0.0382858i
$322$	−2.52653	+	4.37608i	−0.140798	+	0.243869i
$323$	−3.70900	−	6.42418i	−0.206374	−	0.357451i
$324$	6.98606	+	5.86200i	0.388115	+	0.325667i
$325$		0			0
$326$	0.261333	+	1.48209i	0.0144739	+	0.0820855i
$327$		−	8.75825i		−	0.484332i
$328$	0.766051	−	0.135075i	0.0422981	−	0.00745830i
$329$	−15.2077	+	12.7607i	−0.838425	+	0.703522i
$330$		0			0
$331$	−1.86733	−	5.13046i	−0.102638	−	0.281996i	0.877735	−	0.479146i	$-0.159054\pi$
$331$	−1.86733	−	5.13046i	−0.102638	−	0.281996i	−0.980373	+	0.197150i	$0.936831\pi$
$332$	−0.714298			−0.0392022
$333$	−14.4190	+	4.52829i	−0.790157	+	0.248149i
$334$	−1.75569			−0.0960670
$335$		0			0
$336$	−9.20016	−	3.34859i	−0.501910	−	0.182680i
$337$	−7.77558	+	6.52449i	−0.423563	+	0.355411i	−0.829517	−	0.558482i	$-0.811384\pi$
$337$	−7.77558	+	6.52449i	−0.423563	+	0.355411i	0.405954	+	0.913894i	$0.366939\pi$
$338$	−1.62282	+	0.286147i	−0.0882697	+	0.0155643i
$339$		−	1.35386i		−	0.0735317i
$340$		0			0
$341$	12.3904	+	7.15363i	0.670980	+	0.387391i
$342$	−0.380280	−	0.319093i	−0.0205632	−	0.0172546i
$343$	2.30812	+	3.99777i	0.124627	+	0.215860i
$344$	0.417340	−	0.722854i	0.0225015	−	0.0389737i
$345$		0			0
$346$	1.63821	+	1.95234i	0.0880705	+	0.104958i
$347$	−19.6945	+	11.3707i	−1.05726	+	0.610409i	−0.924673	−	0.380763i	$-0.875661\pi$
$347$	−19.6945	+	11.3707i	−1.05726	+	0.610409i	−0.132586	+	0.991171i	$0.542328\pi$
$348$	4.67264	+	0.823912i	0.250480	+	0.0441663i
$349$	−4.05073	+	22.9728i	−0.216830	+	1.22971i	0.660871	+	0.750499i	$0.270187\pi$
$349$	−4.05073	+	22.9728i	−0.216830	+	1.22971i	−0.877702	+	0.479207i	$0.840924\pi$
$350$		0			0
$351$	−2.46233	+	6.76519i	−0.131429	+	0.361099i
$352$	3.84339	−	10.5596i	0.204854	−	0.562831i
$353$	−12.9672	+	15.4537i	−0.690176	+	0.822520i	−0.991377	−	0.131041i	$-0.958168\pi$
$353$	−12.9672	+	15.4537i	−0.690176	+	0.822520i	0.301201	+	0.953561i	$0.402613\pi$
$354$	−0.215282	+	1.22092i	−0.0114421	+	0.0648914i
$355$		0			0
$356$	19.5811	−	11.3052i	1.03780	−	0.599173i
$357$	10.4208	+	12.4190i	0.551528	+	0.657285i
$358$	0.665596	−	0.242257i	0.0351778	−	0.0128037i
$359$	−1.39032	+	2.40811i	−0.0733784	+	0.127095i	−0.900380	−	0.435105i	$-0.856711\pi$
$359$	−1.39032	+	2.40811i	−0.0733784	+	0.127095i	0.827002	+	0.562200i	$0.190045\pi$
$360$		0			0
$361$	13.5047	+	11.3318i	0.710772	+	0.596409i
$362$	−2.02845	−	1.17113i	−0.106613	−	0.0615530i
$363$	2.53253	+	14.3627i	0.132923	+	0.753845i
$364$			12.8449i			0.673255i
$365$		0			0
$366$	−0.345148	+	0.289613i	−0.0180411	+	0.0151383i
$367$	30.7438	+	11.1898i	1.60481	+	0.584104i	0.980404	−	0.196995i	$-0.0631184\pi$
$367$	30.7438	+	11.1898i	1.60481	+	0.584104i	0.624407	+	0.781099i	$0.285341\pi$
$368$	10.8716	+	29.8695i	0.566722	+	1.55705i
$369$	2.85228			0.148484
$370$		0			0
$371$	32.5628			1.69058
$372$	1.23724	+	3.39930i	0.0641480	+	0.176245i
$373$	9.95135	+	3.62199i	0.515261	+	0.187540i	0.586546	−	0.809916i	$-0.300488\pi$
$373$	9.95135	+	3.62199i	0.515261	+	0.187540i	−0.0712842	+	0.997456i	$0.522710\pi$
$374$	−4.63450	+	3.88881i	−0.239644	+	0.201085i
$375$		0			0
$376$		−	3.77395i		−	0.194627i
$377$	−1.06473	−	6.03840i	−0.0548365	−	0.310993i
$378$	2.07402	+	1.19744i	0.106676	+	0.0615896i
$379$	−4.77502	−	4.00671i	−0.245276	−	0.205811i	0.511859	−	0.859070i	$-0.328957\pi$
$379$	−4.77502	−	4.00671i	−0.245276	−	0.205811i	−0.757135	+	0.653258i	$0.773402\pi$
$380$		0			0
$381$	−3.08637	+	5.34575i	−0.158120	+	0.273871i
$382$	0.285770	−	0.104012i	0.0146213	−	0.00532171i
$383$	−4.56694	−	5.44267i	−0.233360	−	0.278108i	0.636638	−	0.771163i	$-0.280325\pi$
$383$	−4.56694	−	5.44267i	−0.233360	−	0.278108i	−0.869998	+	0.493055i	$0.835880\pi$
$384$	3.27244	−	1.88934i	0.166996	−	0.0964152i
$385$		0			0
$386$	0.440790	−	2.49984i	0.0224356	−	0.127239i
$387$	1.96731	−	2.34455i	0.100004	−	0.119180i
$388$	2.26107	−	6.21223i	0.114788	−	0.315378i
$389$	−2.81925	+	7.74584i	−0.142942	+	0.392730i	−0.990418	−	0.138104i	$-0.955899\pi$
$389$	−2.81925	+	7.74584i	−0.142942	+	0.392730i	0.847476	+	0.530834i	$0.178121\pi$
$390$		0			0
$391$	9.13980	−	51.8344i	0.462219	−	2.62138i
$392$	3.80692	+	0.671263i	0.192279	+	0.0339039i
$393$	2.84101	−	1.64026i	0.143310	−	0.0827400i
$394$	1.44628	+	1.72361i	0.0728624	+	0.0868340i
$395$		0			0
$396$	13.7015	−	23.7317i	0.688526	−	1.19256i
$397$	−4.07183	−	7.05262i	−0.204360	−	0.353961i	0.745569	−	0.666428i	$-0.232178\pi$
$397$	−4.07183	−	7.05262i	−0.204360	−	0.353961i	−0.949928	+	0.312467i	$0.898844\pi$
$398$	−0.972835	−	0.816305i	−0.0487638	−	0.0409177i
$399$	2.59467	+	1.49803i	0.129896	+	0.0749955i
$400$		0			0
$401$		−	0.784302i		−	0.0391662i	−0.999808	−	0.0195831i	$-0.993766\pi$
$401$		−	0.784302i		−	0.0391662i	0.999808	−	0.0195831i	$-0.00623389\pi$
$402$	−1.27889	+	0.225502i	−0.0637851	+	0.0112470i
$403$	3.58110	−	3.00490i	0.178387	−	0.149685i
$404$	10.2858	+	3.74372i	0.511737	+	0.186257i
$405$		0			0
$406$	−2.03967			−0.101227
$407$	15.6832	+	30.2109i	0.777387	+	1.49750i
$408$	−3.08193			−0.152578
$409$	−11.6764	−	32.0806i	−0.577359	−	1.58628i	−0.792614	−	0.609724i	$-0.791280\pi$
$409$	−11.6764	−	32.0806i	−0.577359	−	1.58628i	0.215254	−	0.976558i	$-0.430942\pi$
$410$		0			0
$411$	−3.75717	+	3.15264i	−0.185328	+	0.155508i
$412$	−15.5332	+	2.73891i	−0.765264	+	0.134937i
$413$			36.0722i			1.77499i
$414$	−0.611644	−	3.46881i	−0.0300607	−	0.170483i
$415$		0			0
$416$	−2.81270	−	2.36014i	−0.137904	−	0.115715i
$417$	1.19339	+	2.06701i	0.0584405	+	0.101222i
$418$	−0.559032	+	0.968272i	−0.0273432	+	0.0473597i
$419$	20.4064	−	7.42733i	0.996920	−	0.362849i	0.208524	−	0.978017i	$-0.433134\pi$
$419$	20.4064	−	7.42733i	0.996920	−	0.362849i	0.788396	+	0.615168i	$0.210912\pi$
$420$		0			0
$421$	−23.9644	+	13.8359i	−1.16795	+	0.674318i	−0.953197	−	0.302350i	$-0.902229\pi$
$421$	−23.9644	+	13.8359i	−1.16795	+	0.674318i	−0.214756	+	0.976668i	$0.568896\pi$
$422$	−0.218202	−	0.0384748i	−0.0106219	−	0.00187293i
$423$	2.40300	−	13.6281i	0.116838	−	0.662619i
$424$	−3.97904	+	4.74203i	−0.193239	+	0.230293i
$425$		0			0
$426$	−0.273757	+	0.752140i	−0.0132636	+	0.0364413i
$427$	−8.42662	+	10.0424i	−0.407793	+	0.485988i
$428$	−0.956104	+	5.42233i	−0.0462150	+	0.262098i
$429$	7.23396	+	1.27554i	0.349259	+	0.0615838i
$430$		0			0
$431$	2.12509	+	2.53258i	0.102362	+	0.121990i	0.814793	−	0.579752i	$-0.196850\pi$
$431$	2.12509	+	2.53258i	0.102362	+	0.121990i	−0.712431	+	0.701742i	$0.752406\pi$
$432$	14.1565	−	5.15255i	0.681106	−	0.247902i
$433$	−8.03371	+	13.9148i	−0.386076	+	0.668702i	−0.991918	−	0.126882i	$-0.959503\pi$
$433$	−8.03371	+	13.9148i	−0.386076	+	0.668702i	0.605842	+	0.795585i	$0.292836\pi$
$434$	−0.777538	−	1.34674i	−0.0373230	−	0.0646454i
$435$		0			0
$436$	20.8231	+	12.0222i	0.997244	+	0.575759i
$437$	−1.68910	−	9.57934i	−0.0808004	−	0.458242i
$438$		−	0.802329i		−	0.0383368i
$439$	23.5611	−	4.15446i	1.12451	−	0.198282i	0.419690	−	0.907667i	$-0.362139\pi$
$439$	23.5611	−	4.15446i	1.12451	−	0.198282i	0.704820	+	0.709386i	$0.251028\pi$
$440$		0			0
$441$	13.3197	+	4.84797i	0.634271	+	0.230856i
$442$	0.676094	+	1.85755i	0.0321585	+	0.0883548i
$443$	1.64369			0.0780942			0.0390471	−	0.999237i	$-0.487568\pi$
$443$	1.64369			0.0780942			0.0390471	+	0.999237i	$0.487568\pi$
$444$	−1.87233	+	8.40034i	−0.0888566	+	0.398662i
$445$		0			0
$446$	−0.795648	−	2.18602i	−0.0376750	−	0.103511i
$447$	−8.06425	−	2.93515i	−0.381426	−	0.138828i
$448$	19.9588	−	16.7474i	0.942962	−	0.791239i
$449$	19.6132	−	3.45834i	0.925606	−	0.163209i	0.309524	−	0.950892i	$-0.399830\pi$
$449$	19.6132	−	3.45834i	0.925606	−	0.163209i	0.616082	+	0.787682i	$0.288719\pi$
$450$		0			0
$451$	−1.11553	−	6.32646i	−0.0525281	−	0.297902i
$452$	3.21886	+	1.85841i	0.151402	+	0.0874122i
$453$	−11.9673	−	10.0417i	−0.562272	−	0.471802i
$454$	−2.54079	−	4.40078i	−0.119245	−	0.206539i
$455$		0			0
$456$	−0.535212	+	0.194801i	−0.0250636	+	0.00912240i
$457$	8.23792	+	9.81757i	0.385354	+	0.459247i	0.923496	−	0.383607i	$-0.125318\pi$
$457$	8.23792	+	9.81757i	0.385354	+	0.459247i	−0.538143	+	0.842854i	$0.680874\pi$
$458$	2.17058	−	1.25319i	0.101425	−	0.0585576i
$459$	−24.5667	−	4.33177i	−1.14667	−	0.202190i
$460$		0			0
$461$	−14.6976	+	17.5159i	−0.684535	+	0.815797i	−0.990683	−	0.136187i	$-0.956515\pi$
$461$	−14.6976	+	17.5159i	−0.684535	+	0.815797i	0.306148	+	0.951984i	$0.400960\pi$
$462$	0.835729	−	2.29615i	0.0388816	−	0.106826i
$463$	−3.90392	+	10.7259i	−0.181430	+	0.498476i	−0.996752	−	0.0805325i	$-0.974338\pi$
$463$	−3.90392	+	10.7259i	−0.181430	+	0.498476i	0.815322	+	0.579008i	$0.196560\pi$
$464$	−8.24735	+	9.82880i	−0.382873	+	0.456291i
$465$		0			0
$466$	2.35515	+	0.415276i	0.109100	+	0.0192373i
$467$	12.3972	−	7.15751i	0.573673	−	0.331210i	−0.184942	−	0.982749i	$-0.559210\pi$
$467$	12.3972	−	7.15751i	0.573673	−	0.331210i	0.758615	+	0.651539i	$0.225876\pi$
$468$	−5.75535	−	6.85896i	−0.266041	−	0.317056i
$469$	−35.5060	+	12.9231i	−1.63951	+	0.596734i
$470$		0			0
$471$	5.56824	+	9.64447i	0.256571	+	0.444394i
$472$	−5.25308	−	4.40786i	−0.241793	−	0.202888i
$473$	−5.96972	−	3.44662i	−0.274488	−	0.158476i
$474$	−0.305730	−	1.73388i	−0.0140427	−	0.0796398i
$475$		0			0
$476$	−43.8311	+	7.72860i	−2.00899	+	0.354240i
$477$	−17.3880	+	14.5903i	−0.796143	+	0.668044i
$478$	2.55941	+	0.931548i	0.117064	+	0.0426080i
$479$	1.55534	+	4.27327i	0.0710654	+	0.195251i	0.970140	−	0.242544i	$-0.0779819\pi$
$479$	1.55534	+	4.27327i	0.0710654	+	0.195251i	−0.899075	+	0.437795i	$0.855760\pi$
$480$		0			0
$481$	11.0285	−	1.43919i	0.502858	−	0.0656214i
$482$	3.78033			0.172189
$483$	7.27081	+	19.9764i	0.330833	+	0.908957i
$484$	−37.6241	−	13.6941i	−1.71019	−	0.622457i
$485$		0			0
$486$	−2.54328	+	0.448449i	−0.115366	+	0.0203421i
$487$			21.4485i			0.971926i	0.873979	+	0.485963i	$0.161531\pi$
$487$			21.4485i			0.971926i	−0.873979	+	0.485963i	$0.838469\pi$
$488$	−0.432757	−	2.45429i	−0.0195900	−	0.111100i
$489$	5.48316	+	3.16570i	0.247957	+	0.143158i
$490$		0			0
$491$	−0.812860	−	1.40792i	−0.0366839	−	0.0635383i	0.847101	−	0.531433i	$-0.178346\pi$
$491$	−0.812860	−	1.40792i	−0.0366839	−	0.0635383i	−0.883784	+	0.467894i	$0.845013\pi$
$492$	0.812132	−	1.40665i	0.0366137	−	0.0634168i
$493$	19.9644	−	7.26646i	0.899152	−	0.327265i
$494$	0.234823	+	0.279851i	0.0105652	+	0.0125911i
$495$		0			0
$496$	−9.63365	−	1.69867i	−0.432564	−	0.0762726i
$497$	−4.04407	+	22.9350i	−0.181401	+	1.02878i
$498$	0.0285389	−	0.0340113i	0.00127886	−	0.00152408i
$499$	−0.220549	+	0.605952i	−0.00987311	+	0.0271262i	−0.944531	−	0.328421i	$-0.893483\pi$
$499$	−0.220549	+	0.605952i	−0.00987311	+	0.0271262i	0.934658	+	0.355548i	$0.115706\pi$
$500$		0			0
$501$	−4.74779	+	5.65820i	−0.212116	+	0.252790i
$502$	−0.513838	+	2.91412i	−0.0229337	+	0.130063i
$503$	5.97480	+	1.05352i	0.266403	+	0.0469741i	0.305254	−	0.952271i	$-0.401259\pi$
$503$	5.97480	+	1.05352i	0.266403	+	0.0469741i	−0.0388508	+	0.999245i	$0.512370\pi$
$504$	−5.19697	+	3.00047i	−0.231491	+	0.133652i
$505$		0			0
$506$	−7.45473	+	2.71330i	−0.331403	+	0.120621i
$507$	−3.46629	+	6.00379i	−0.153943	+	0.266638i
$508$	−8.47315	−	14.6759i	−0.375935	−	0.651139i
$509$	20.6005	+	17.2859i	0.913100	+	0.766182i	0.972706	−	0.232040i	$-0.0745399\pi$
$509$	20.6005	+	17.2859i	0.913100	+	0.766182i	−0.0596059	+	0.998222i	$0.518984\pi$
$510$		0			0
$511$	−4.05376	−	22.9900i	−0.179328	−	1.01702i
$512$			12.8685i			0.568711i
$513$	−4.54009	+	0.800540i	−0.200450	+	0.0353447i
$514$	−1.54755	+	1.29855i	−0.0682596	+	0.0572766i
$515$		0			0
$516$	−0.596104	−	1.63778i	−0.0262420	−	0.0720993i
$517$	−31.1674			−1.37074
$518$	0.165580	−	3.69605i	0.00727519	−	0.162395i
$519$	10.7220			0.470646
$520$		0			0
$521$	12.4894	+	4.54577i	0.547171	+	0.199154i	0.600789	−	0.799408i	$-0.294853\pi$
$521$	12.4894	+	4.54577i	0.547171	+	0.199154i	−0.0536184	+	0.998562i	$0.517075\pi$
$522$	1.08915	−	0.913905i	0.0476708	−	0.0400005i
$523$	20.0195	−	3.52997i	0.875391	−	0.154355i	0.282140	−	0.959373i	$-0.408956\pi$
$523$	20.0195	−	3.52997i	0.875391	−	0.154355i	0.593250	+	0.805018i	$0.297845\pi$
$524$			9.00614i			0.393435i
$525$		0			0
$526$	−0.850316	−	0.490930i	−0.0370755	−	0.0214056i
$527$	12.4084	+	10.4119i	0.540521	+	0.453551i
$528$	−7.68548	−	13.3116i	−0.334468	−	0.579315i
$529$	23.0091	−	39.8529i	1.00039	−	1.73273i
$530$		0			0
$531$	−16.1627	−	19.2620i	−0.701401	−	0.835898i
$532$	−7.12327	+	4.11262i	−0.308833	+	0.178305i
$533$	−2.06713	−	0.364491i	−0.0895373	−	0.0157878i
$534$	−0.244044	+	1.38404i	−0.0105608	+	0.0598933i
$535$		0			0
$536$	2.45672	−	6.74978i	0.106114	−	0.291546i
$537$	1.01919	−	2.80019i	0.0439811	−	0.120837i
$538$	−3.12835	+	3.72823i	−0.134873	+	0.160735i
$539$	5.54365	−	31.4396i	0.238782	−	1.35420i
$540$		0			0
$541$	−1.25114	+	0.722345i	−0.0537906	+	0.0310560i	−0.526654	−	0.850080i	$-0.676554\pi$
$541$	−1.25114	+	0.722345i	−0.0537906	+	0.0310560i	0.472864	+	0.881136i	$0.343220\pi$
$542$	1.40265	+	1.67161i	0.0602488	+	0.0718017i
$543$	−9.25968	+	3.37025i	−0.397371	+	0.144631i
$544$	6.36122	−	11.0180i	0.272735	−	0.472391i
$545$		0			0
$546$	−0.611610	−	0.513201i	−0.0261745	−	0.0219630i
$547$	24.1863	+	13.9639i	1.03413	+	0.597055i	0.918165	−	0.396198i	$-0.129671\pi$
$547$	24.1863	+	13.9639i	1.03413	+	0.597055i	0.115965	+	0.993253i	$0.463004\pi$
$548$	−2.33816	−	13.2604i	−0.0998813	−	0.566455i
$549$		−	9.13819i		−	0.390008i
$550$		0			0
$551$	3.00776	−	2.52381i	0.128135	−	0.107518i
$552$	−3.79756	−	1.38220i	−0.161635	−	0.0588304i
$553$	−17.5208	−	48.1381i	−0.745061	−	2.04704i
$554$	2.37171			0.100764
$555$		0			0
$556$	−6.55252			−0.277889
$557$	6.41452	+	17.6238i	0.271792	+	0.746742i	0.998228	+	0.0595080i	$0.0189532\pi$
$557$	6.41452	+	17.6238i	0.271792	+	0.746742i	−0.726436	+	0.687234i	$0.758825\pi$
$558$	1.01862	+	0.370747i	0.0431216	+	0.0156950i
$559$	−1.72538	+	1.44776i	−0.0729757	+	0.0612338i
$560$		0			0
$561$			25.4522i			1.07459i
$562$	−0.185388	−	1.05138i	−0.00782010	−	0.0443500i
$563$	23.2239	+	13.4083i	0.978771	+	0.565094i	0.901899	−	0.431947i	$-0.142173\pi$
$563$	23.2239	+	13.4083i	0.978771	+	0.565094i	0.0768721	+	0.997041i	$0.475507\pi$
$564$	−6.03672	−	5.06541i	−0.254192	−	0.213292i
$565$		0			0
$566$	0.973621	−	1.68636i	0.0409243	−	0.0708830i
$567$	−15.4985	+	5.64099i	−0.650876	+	0.236899i
$568$	−2.84580	−	3.39149i	−0.119407	−	0.142304i
$569$	−10.2253	+	5.90356i	−0.428665	+	0.247490i	−0.698778	−	0.715339i	$-0.746272\pi$
$569$	−10.2253	+	5.90356i	−0.428665	+	0.247490i	0.270113	+	0.962829i	$0.412939\pi$
$570$		0			0
$571$	−1.37023	+	7.77099i	−0.0573425	+	0.325206i	−0.999962	−	0.00866199i	$-0.997243\pi$
$571$	−1.37023	+	7.77099i	−0.0573425	+	0.325206i	0.942620	+	0.333868i	$0.108354\pi$
$572$	−12.9625	+	15.4481i	−0.541990	+	0.645918i
$573$	0.437582	−	1.20225i	0.0182803	−	0.0502246i
$574$	−0.238812	+	0.656132i	−0.00996784	+	0.0273864i
$575$		0			0
$576$	−3.15373	+	17.8857i	−0.131405	+	0.745236i
$577$	−8.57004	−	1.51113i	−0.356776	−	0.0629092i	−0.00761221	−	0.999971i	$-0.502423\pi$
$577$	−8.57004	−	1.51113i	−0.356776	−	0.0629092i	−0.349163	+	0.937062i	$0.613534\pi$
$578$	−3.41953	+	1.97427i	−0.142234	+	0.0821187i
$579$	−6.86445	−	8.18073i	−0.285277	−	0.339980i
$580$		0			0
$581$	0.645914	−	1.11876i	0.0267970	−	0.0464138i
$582$	0.205458	+	0.355863i	0.00851649	+	0.0147510i
$583$	39.1623	+	32.8610i	1.62193	+	1.36096i
$584$	3.84332	+	2.21894i	0.159038	+	0.0918204i
$585$		0			0
$586$			3.70557i			0.153076i
$587$	−7.74442	+	1.36555i	−0.319647	+	0.0563623i	−0.331169	−	0.943571i	$-0.607443\pi$
$587$	−7.74442	+	1.36555i	−0.319647	+	0.0563623i	0.0115229	+	0.999934i	$0.496332\pi$
$588$	6.18339	−	5.18848i	0.254999	−	0.213969i
$589$	2.81298	+	1.02384i	0.115907	+	0.0421867i
$590$		0			0
$591$	9.46588			0.389374
$592$	−17.1411	−	15.7428i	−0.704496	−	0.647026i
$593$	−5.03777			−0.206877			−0.103438	−	0.994636i	$-0.532984\pi$
$593$	−5.03777			−0.206877			−0.103438	+	0.994636i	$0.532984\pi$
$594$	1.28596	+	3.53314i	0.0527634	+	0.144966i
$595$		0			0
$596$	18.0480	−	15.1441i	0.739275	−	0.620325i
$597$	−5.26154	+	0.927752i	−0.215341	+	0.0379704i
$598$			2.59211i			0.105999i
$599$	−3.33298	−	18.9023i	−0.136182	−	0.772326i	−0.974029	−	0.226421i	$-0.927297\pi$
$599$	−3.33298	−	18.9023i	−0.136182	−	0.772326i	0.837848	−	0.545904i	$-0.183814\pi$
$600$		0			0
$601$	18.8863	+	15.8475i	0.770389	+	0.646433i	0.940808	−	0.338939i	$-0.110068\pi$
$601$	18.8863	+	15.8475i	0.770389	+	0.646433i	−0.170420	+	0.985372i	$0.554512\pi$
$602$	0.374618	+	0.648858i	0.0152683	+	0.0264455i
$603$	13.1692	−	22.8098i	0.536292	−	0.928885i
$604$	40.3018	−	14.6687i	1.63986	−	0.596859i
$605$		0			0
$606$	−0.589213	+	0.340183i	−0.0239352	+	0.0138190i
$607$	25.7234	+	4.53572i	1.04408	+	0.184099i	0.669283	−	0.743008i	$-0.266602\pi$
$607$	25.7234	+	4.53572i	1.04408	+	0.184099i	0.374796	+	0.927107i	$0.377713\pi$
$608$	0.408280	−	2.31547i	0.0165580	−	0.0939049i
$609$	−5.51573	+	6.57340i	−0.223509	+	0.266367i
$610$		0			0
$611$	−3.48304	+	9.56957i	−0.140909	+	0.387143i
$612$	19.9422	−	23.7662i	0.806115	−	0.960690i
$613$	−6.16036	+	34.9372i	−0.248815	+	1.41110i	0.562649	+	0.826696i	$0.309782\pi$
$613$	−6.16036	+	34.9372i	−0.248815	+	1.41110i	−0.811464	+	0.584403i	$0.801329\pi$
$614$	1.18266	+	0.208536i	0.0477285	+	0.00841582i
$615$		0			0
$616$	8.68769	+	10.3536i	0.350037	+	0.417158i
$617$	2.06181	−	0.750439i	0.0830055	−	0.0302115i	−0.300184	−	0.953881i	$-0.597048\pi$
$617$	2.06181	−	0.750439i	0.0830055	−	0.0302115i	0.383189	+	0.923670i	$0.374826\pi$
$618$	0.490195	−	0.849042i	0.0197185	−	0.0341535i
$619$	19.0489	+	32.9936i	0.765639	+	1.32613i	0.939908	+	0.341427i	$0.110910\pi$
$619$	19.0489	+	32.9936i	0.765639	+	1.32613i	−0.174269	+	0.984698i	$0.555756\pi$
$620$		0			0
$621$	−28.3284	−	16.3554i	−1.13678	−	0.656321i
$622$	0.402924	+	2.28510i	0.0161558	+	0.0916240i
$623$			40.8914i			1.63828i
$624$	−4.94606	+	0.872124i	−0.198001	+	0.0349129i
$625$		0			0
$626$	0.0182051	+	0.00662611i	0.000727622	+	0.000264833i
$627$	1.60877	+	4.42007i	0.0642482	+	0.176521i
$628$	−30.5735			−1.22001
$629$	11.5467	+	36.7672i	0.460399	+	1.46600i
$630$		0			0
$631$	−1.31640	−	3.61678i	−0.0524050	−	0.143982i	0.910728	−	0.413006i	$-0.135521\pi$
$631$	−1.31640	−	3.61678i	−0.0524050	−	0.143982i	−0.963133	+	0.269024i	$0.913299\pi$
$632$	9.15118	+	3.33076i	0.364014	+	0.132490i
$633$	−0.714064	+	0.599171i	−0.0283815	+	0.0238149i
$634$	0.464926	−	0.0819791i	0.0184646	−	0.00325580i
$635$		0			0
$636$	2.24456	+	12.7295i	0.0890025	+	0.504758i
$637$	−9.03364	−	5.21558i	−0.357926	−	0.206649i
$638$	−2.45304	−	2.05835i	−0.0971168	−	0.0814907i
$639$	−8.11694	−	14.0589i	−0.321101	−	0.556163i
$640$		0			0
$641$	41.2918	−	15.0290i	1.63093	−	0.593609i	0.645508	−	0.763753i	$-0.276646\pi$
$641$	41.2918	−	15.0290i	1.63093	−	0.593609i	0.985419	+	0.170144i	$0.0544234\pi$
$642$	−0.219985	−	0.262168i	−0.00868211	−	0.0103469i
$643$	−26.6233	+	15.3709i	−1.04992	+	0.606171i	−0.922627	−	0.385694i	$-0.873962\pi$
$643$	−26.6233	+	15.3709i	−1.04992	+	0.606171i	−0.127292	+	0.991865i	$0.540629\pi$
$644$	−57.4750	−	10.1344i	−2.26483	−	0.399351i
$645$		0			0
$646$	−0.813657	+	0.969679i	−0.0320129	+	0.0381515i
$647$	8.89918	−	24.4503i	0.349863	−	0.961241i	−0.632550	−	0.774519i	$-0.717992\pi$
$647$	8.89918	−	24.4503i	0.349863	−	0.961241i	0.982413	−	0.186721i	$-0.0597860\pi$
$648$	1.07237	−	2.94631i	0.0421266	−	0.115742i
$649$	−36.4025	+	43.3828i	−1.42892	+	1.70292i
$650$		0			0
$651$	−6.44288	−	1.13605i	−0.252516	−	0.0445254i
$652$	−15.0532	+	8.69094i	−0.589527	+	0.340364i
$653$	−11.0171	−	13.1297i	−0.431134	−	0.513806i	0.506115	−	0.862466i	$-0.331081\pi$
$653$	−11.0171	−	13.1297i	−0.431134	−	0.513806i	−0.937249	+	0.348660i	$0.886637\pi$
$654$	−1.40440	+	0.511159i	−0.0549163	+	0.0199879i
$655$		0			0
$656$	2.19615	+	3.80385i	0.0857454	+	0.148515i
$657$	12.4657	+	10.4599i	0.486332	+	0.408081i
$658$	2.93377	+	1.69381i	0.114370	+	0.0660317i
$659$	1.96874	+	11.1653i	0.0766911	+	0.434937i	0.998842	+	0.0481068i	$0.0153188\pi$
$659$	1.96874	+	11.1653i	0.0766911	+	0.434937i	−0.922151	+	0.386830i	$0.873570\pi$
$660$		0			0
$661$	20.2994	−	3.57933i	0.789556	−	0.139220i	0.235693	−	0.971828i	$-0.424264\pi$
$661$	20.2994	−	3.57933i	0.789556	−	0.139220i	0.553863	+	0.832608i	$0.313153\pi$
$662$	−0.713693	+	0.598860i	−0.0277385	+	0.0232753i
$663$	7.81480	+	2.84436i	0.303502	+	0.110466i
$664$	0.0839933	+	0.230770i	0.00325957	+	0.00895560i
$665$		0			0
$666$	1.56766	+	2.04782i	0.0607455	+	0.0793516i
$667$	27.8592			1.07871
$668$	−6.93541	−	19.0549i	−0.268339	−	0.737256i
$669$	−9.19669	−	3.34732i	−0.355565	−	0.129415i
$670$		0			0
$671$	−20.2688	+	3.57394i	−0.782470	+	0.137970i
$672$			5.13849i			0.198221i
$673$	−0.774129	−	4.39031i	−0.0298405	−	0.169234i	0.966246	−	0.257623i	$-0.0829392\pi$
$673$	−0.774129	−	4.39031i	−0.0298405	−	0.169234i	−0.996086	+	0.0883891i	$0.971828\pi$
$674$	1.50002	+	0.866036i	0.0577786	+	0.0333585i
$675$		0			0
$676$	−9.51616	−	16.4825i	−0.366006	−	0.633941i
$677$	25.2799	−	43.7861i	0.971587	−	1.68284i	0.280821	−	0.959760i	$-0.409393\pi$
$677$	25.2799	−	43.7861i	0.971587	−	1.68284i	0.690766	−	0.723078i	$-0.257273\pi$
$678$	−0.217094	+	0.0790157i	−0.00833744	+	0.00303458i
$679$	7.68519	+	9.15885i	0.294931	+	0.351485i
$680$		0			0
$681$	−21.0536	−	3.71232i	−0.806777	−	0.142257i
$682$	0.423949	−	2.40433i	0.0162338	−	0.0920667i
$683$	−16.8426	+	20.0722i	−0.644465	+	0.768043i	−0.985068	−	0.172164i	$-0.944924\pi$
$683$	−16.8426	+	20.0722i	−0.644465	+	0.768043i	0.340604	+	0.940207i	$0.389369\pi$
$684$	1.96099	−	5.38777i	0.0749802	−	0.206006i
$685$		0			0
$686$	0.506340	−	0.603432i	0.0193321	−	0.0230392i
$687$	1.83102	−	10.3842i	0.0698577	−	0.396183i
$688$	4.64149	+	0.818420i	0.176955	+	0.0312020i
$689$	14.4661	−	8.35200i	0.551114	−	0.318186i
$690$		0			0
$691$	−19.0751	+	6.94277i	−0.725651	+	0.264115i	−0.678323	−	0.734764i	$-0.737293\pi$
$691$	−19.0751	+	6.94277i	−0.725651	+	0.264115i	−0.0473282	+	0.998879i	$0.515071\pi$
$692$	−14.7179	+	25.4921i	−0.559489	+	0.969063i
$693$	24.7795	+	42.9194i	0.941296	+	1.63037i
$694$	2.97274	+	2.49442i	0.112844	+	0.0946870i
$695$		0			0
$696$	−0.283266	−	1.60648i	−0.0107372	−	0.0608935i
$697$		−	7.27306i		−	0.275487i
$698$	3.92014	−	0.691226i	0.148379	−	0.0261633i
$699$	7.70721	−	6.46711i	0.291513	−	0.244609i
$700$		0			0
$701$	−0.514224	−	1.41282i	−0.0194220	−	0.0533614i	0.929603	−	0.368563i	$-0.120150\pi$
$701$	−0.514224	−	1.41282i	−0.0194220	−	0.0533614i	−0.949025	+	0.315202i	$0.897928\pi$
$702$	1.22852			0.0463674
$703$	4.32919	+	5.65520i	0.163278	+	0.213290i
$704$	40.9045			1.54165
$705$		0			0
$706$	3.23484	+	1.17739i	0.121745	+	0.0443115i
$707$	−15.1646	+	12.7246i	−0.570323	+	0.478558i
$708$	−14.1014	+	2.48646i	−0.529963	+	0.0934467i
$709$			20.3464i			0.764124i	0.924137	+	0.382062i	$0.124786\pi$
$709$			20.3464i			0.764124i	−0.924137	+	0.382062i	$0.875214\pi$
$710$		0			0
$711$	30.9249	+	17.8545i	1.15977	+	0.669595i
$712$	−5.95490	−	4.99676i	−0.223169	−	0.187261i
$713$	10.6202	+	18.3946i	0.397728	+	0.688885i
$714$	1.38322	−	2.39581i	0.0517657	−	0.0896608i
$715$		0			0
$716$	5.25855	+	6.26689i	0.196521	+	0.234205i
$717$	9.92340	−	5.72928i	0.370596	−	0.213964i
$718$	0.467287	+	0.0823953i	0.0174390	+	0.00307497i
$719$	−6.97428	+	39.5531i	−0.260097	+	1.47508i	0.522547	+	0.852611i	$0.324982\pi$
$719$	−6.97428	+	39.5531i	−0.260097	+	1.47508i	−0.782643	+	0.622470i	$0.786129\pi$
$720$		0			0
$721$	9.75630	−	26.8052i	0.363344	−	0.998278i
$722$	1.02889	−	2.82685i	0.0382913	−	0.105205i
$723$	10.2229	−	12.1832i	0.380193	−	0.453096i
$724$	4.69761	−	26.6415i	0.174585	−	0.990123i
$725$		0			0
$726$	2.15527	−	1.24434i	0.0799895	−	0.0461820i
$727$	−26.1199	−	31.1285i	−0.968734	−	1.15449i	−0.987965	−	0.154677i	$-0.950566\pi$
$727$	−26.1199	−	31.1285i	−0.968734	−	1.15449i	0.0192316	−	0.999815i	$-0.493878\pi$
$728$	4.14982	−	1.51041i	0.153803	−	0.0559796i
$729$	1.50842	−	2.61266i	0.0558675	−	0.0967653i
$730$		0			0
$731$	−5.97839	−	5.01647i	−0.221119	−	0.185541i
$732$	−4.50666	−	2.60192i	−0.166571	−	0.0961698i
$733$	−8.04113	−	45.6035i	−0.297006	−	1.68440i	−0.658936	−	0.752199i	$-0.728993\pi$
$733$	−8.04113	−	45.6035i	−0.297006	−	1.68440i	0.361930	−	0.932205i	$-0.382118\pi$
$734$		−	5.58288i		−	0.206068i
$735$		0			0
$736$	12.7797	−	10.7235i	0.471067	−	0.395272i
$737$	−55.7434	−	20.2889i	−2.05333	−	0.747352i
$738$	−0.166468	−	0.457367i	−0.00612778	−	0.0168359i
$739$	37.7948			1.39030			0.695152	−	0.718863i	$-0.255337\pi$
$739$	37.7948			1.39030			0.695152	+	0.718863i	$0.255337\pi$
$740$		0			0
$741$	1.53692			0.0564600
$742$	−1.90047	−	5.22150i	−0.0697684	−	0.191687i
$743$	−3.29307	−	1.19858i	−0.120811	−	0.0439716i	0.280907	−	0.959735i	$-0.409365\pi$
$743$	−3.29307	−	1.19858i	−0.120811	−	0.0439716i	−0.401718	+	0.915763i	$0.631587\pi$
$744$	0.952732	−	0.799437i	0.0349288	−	0.0293088i
$745$		0			0
$746$		−	1.80710i		−	0.0661628i
$747$	0.156368	+	0.886810i	0.00572122	+	0.0324467i
$748$	−60.5136	−	34.9375i	−2.21260	−	1.27744i
$749$	−7.62806	−	6.40070i	−0.278723	−	0.233877i
$750$		0			0
$751$	11.9496	−	20.6973i	0.436047	−	0.755255i	−0.561334	−	0.827590i	$-0.689712\pi$
$751$	11.9496	−	20.6973i	0.436047	−	0.755255i	0.997380	+	0.0723345i	$0.0230449\pi$
$752$	20.0248	−	7.28844i	0.730230	−	0.265782i
$753$	8.00203	+	9.53644i	0.291610	+	0.347527i
$754$	−0.906125	+	0.523151i	−0.0329991	+	0.0190521i
$755$		0			0
$756$	−4.80316	+	27.2400i	−0.174689	+	0.990711i
$757$	1.81240	−	2.15994i	0.0658729	−	0.0785042i	−0.732102	−	0.681195i	$-0.761460\pi$
$757$	1.81240	−	2.15994i	0.0658729	−	0.0785042i	0.797975	+	0.602691i	$0.205905\pi$
$758$	−0.363797	+	0.999525i	−0.0132137	+	0.0363044i
$759$	−11.4150	+	31.3623i	−0.414337	+	1.13838i
$760$		0			0
$761$	5.05316	−	28.6579i	0.183177	−	1.03885i	−0.745098	−	0.666955i	$-0.767597\pi$
$761$	5.05316	−	28.6579i	0.183177	−	1.03885i	0.928275	−	0.371894i	$-0.121291\pi$
$762$	1.03733	+	0.182909i	0.0375785	+	0.00662610i
$763$	−37.6591	+	21.7425i	−1.36335	+	0.787131i
$764$	2.25773	+	2.69066i	0.0816819	+	0.0973446i
$765$		0			0
$766$	−0.606199	+	1.04997i	−0.0219029	+	0.0379369i
$767$	9.25210	+	16.0251i	0.334074	+	0.578633i
$768$	7.54578	+	6.33166i	0.272285	+	0.228474i
$769$	−23.6197	−	13.6368i	−0.851747	−	0.491756i	0.00949305	−	0.999955i	$-0.496978\pi$
$769$	−23.6197	−	13.6368i	−0.851747	−	0.491756i	−0.861240	+	0.508199i	$0.830312\pi$
$770$		0			0
$771$			8.49900i			0.306084i
$772$	28.8726	−	5.09102i	1.03915	−	0.183230i
$773$	5.33809	−	4.47919i	0.191998	−	0.161105i	−0.541721	−	0.840558i	$-0.682227\pi$
$773$	5.33809	−	4.47919i	0.191998	−	0.161105i	0.733719	+	0.679453i	$0.237783\pi$
$774$	−0.490771	−	0.178626i	−0.0176404	−	0.00642058i
$775$		0			0
$776$	−2.27287			−0.0815914
$777$	−11.4638	−	10.5286i	−0.411261	−	0.377712i
$778$	1.40660			0.0504289
$779$	−0.459713	−	1.26305i	−0.0164709	−	0.0452535i
$780$		0			0
$781$	−28.0087	+	23.5021i	−1.00223	+	0.840972i
$782$	−8.84514	+	1.55964i	−0.316302	+	0.0557725i
$783$		−	13.2037i		−	0.471863i
$784$	3.79035	+	21.4961i	0.135369	+	0.767719i
$785$		0			0
$786$	−0.428828	−	0.359829i	−0.0152958	−	0.0128347i
$787$	−9.03840	−	15.6550i	−0.322184	−	0.558040i	0.658754	−	0.752358i	$-0.271084\pi$
$787$	−9.03840	−	15.6550i	−0.322184	−	0.558040i	−0.980938	+	0.194319i	$0.937750\pi$
$788$	−12.9935	+	22.5055i	−0.462876	+	0.801724i
$789$	−3.88161	+	1.41279i	−0.138189	+	0.0502967i
$790$		0			0
$791$	−5.82140	+	3.36099i	−0.206985	+	0.119503i
$792$	−9.27818	−	1.63599i	−0.329686	−	0.0581325i
$793$	−1.16776	+	6.62271i	−0.0414684	+	0.235179i
$794$	−0.893253	+	1.06454i	−0.0317004	+	0.0377790i
$795$		0			0
$796$	5.01661	−	13.7830i	0.177809	−	0.488526i
$797$	4.62819	−	5.51566i	0.163939	−	0.195375i	−0.677821	−	0.735227i	$-0.737076\pi$
$797$	4.62819	−	5.51566i	0.163939	−	0.195375i	0.841760	+	0.539852i	$0.181520\pi$
$798$	0.0887788	−	0.503489i	0.00314273	−	0.0178233i
$799$	−34.7503	−	6.12742i	−1.22938	−	0.216772i
$800$		0			0
$801$	−18.3221	−	21.8354i	−0.647378	−	0.771515i
$802$	−0.125764	+	0.0457743i	−0.00444088	+	0.00161635i
$803$	18.3252	−	31.7402i	0.646682	−	1.12009i
$804$	−7.49936	−	12.9893i	−0.264482	−	0.458096i
$805$		0			0
$806$	−0.690845	−	0.398860i	−0.0243340	−	0.0140492i
$807$	3.55546	+	20.1640i	0.125158	+	0.709806i
$808$		−	3.76327i		−	0.132391i
$809$	−21.2731	+	3.75102i	−0.747923	+	0.131879i	−0.534603	−	0.845103i	$-0.679539\pi$
$809$	−21.2731	+	3.75102i	−0.747923	+	0.131879i	−0.213320	+	0.976982i	$0.568428\pi$
$810$		0			0
$811$	−23.9554	−	8.71906i	−0.841189	−	0.306168i	−0.114746	−	0.993395i	$-0.536606\pi$
$811$	−23.9554	−	8.71906i	−0.841189	−	0.306168i	−0.726443	+	0.687227i	$0.758828\pi$
$812$	−8.05720	−	22.1370i	−0.282752	−	0.776856i
$813$	9.18031			0.321967
$814$	3.92904	−	4.27803i	0.137713	−	0.149945i
$815$		0			0
$816$	−5.95196	−	16.3529i	−0.208360	−	0.572465i
$817$	−1.35530	−	0.493287i	−0.0474158	−	0.0172579i
$818$	−4.46270	+	3.74465i	−0.156035	+	0.130928i
$819$	15.9471	−	2.81190i	0.557236	−	0.0982557i
$820$		0			0
$821$	−0.959028	−	5.43892i	−0.0334703	−	0.189820i	0.963489	−	0.267750i	$-0.0862800\pi$
$821$	−0.959028	−	5.43892i	−0.0334703	−	0.189820i	−0.996959	+	0.0779301i	$0.975169\pi$
$822$	0.724812	+	0.418470i	0.0252807	+	0.0145958i
$823$	14.9064	+	12.5080i	0.519605	+	0.436001i	0.864494	−	0.502643i	$-0.167639\pi$
$823$	14.9064	+	12.5080i	0.519605	+	0.436001i	−0.344889	+	0.938644i	$0.612083\pi$
$824$	2.71139	+	4.69626i	0.0944557	+	0.163602i
$825$		0			0
$826$	5.78422	−	2.10528i	0.201259	−	0.0732522i
$827$	−13.3476	−	15.9070i	−0.464140	−	0.553141i	0.482306	−	0.876003i	$-0.339799\pi$
$827$	−13.3476	−	15.9070i	−0.464140	−	0.553141i	−0.946446	+	0.322862i	$0.895355\pi$
$828$	35.2316	−	20.3410i	1.22438	−	0.706898i
$829$	−19.7559	−	3.48349i	−0.686149	−	0.120987i	−0.180304	−	0.983611i	$-0.557708\pi$
$829$	−19.7559	−	3.48349i	−0.686149	−	0.120987i	−0.505845	+	0.862624i	$0.668819\pi$
$830$		0			0
$831$	6.41365	−	7.64349i	0.222487	−	0.265150i
$832$	4.57119	−	12.5592i	0.158478	−	0.435413i
$833$	12.3619	−	33.9640i	0.428314	−	1.17678i
$834$	0.261798	−	0.311999i	0.00906532	−	0.0108036i
$835$		0			0
$836$	−12.7172	−	2.24239i	−0.439834	−	0.0775545i
$837$	8.71806	−	5.03337i	0.301340	−	0.173979i
$838$	−2.38197	−	2.83872i	−0.0822837	−	0.0980619i
$839$	1.95773	−	0.712555i	0.0675883	−	0.0246001i	−0.308005	−	0.951385i	$-0.599661\pi$
$839$	1.95773	−	0.712555i	0.0675883	−	0.0246001i	0.375593	+	0.926785i	$0.377439\pi$
$840$		0			0
$841$	−8.87733	−	15.3760i	−0.306115	−	0.530206i
$842$	3.61724	+	3.03522i	0.124658	+	0.104601i
$843$	−3.88971	−	2.24573i	−0.133969	−	0.0773469i
$844$	−0.444376	−	2.52018i	−0.0152960	−	0.0867481i
$845$		0			0
$846$	−2.32553	+	0.410053i	−0.0799532	+	0.0140979i
$847$	55.4702	−	46.5450i	1.90598	−	1.59931i
$848$	−32.8460	−	11.9550i	−1.12794	−	0.410535i
$849$	−2.80187	−	7.69808i	−0.0961599	−	0.264197i
$850$		0			0
$851$	−2.26161	+	50.4832i	−0.0775271	+	1.73054i
$852$	−9.24456			−0.316713
$853$	6.80260	+	18.6900i	0.232917	+	0.639933i	0.999999	−	0.00161596i	$-0.000514375\pi$
$853$	6.80260	+	18.6900i	0.232917	+	0.639933i	−0.767082	+	0.641549i	$0.778292\pi$
$854$	2.10213	+	0.765111i	0.0719332	+	0.0261816i
$855$		0			0
$856$	1.86423	−	0.328714i	0.0637181	−	0.0112352i
$857$		−	26.3623i		−	0.900519i	−0.892898	−	0.450259i	$-0.851332\pi$
$857$		−	26.3623i		−	0.900519i	0.892898	−	0.450259i	$-0.148668\pi$
$858$	−0.217662	−	1.23442i	−0.00743085	−	0.0421424i
$859$	−41.7109	−	24.0818i	−1.42316	−	0.821660i	−0.426589	−	0.904445i	$-0.640285\pi$
$859$	−41.7109	−	24.0818i	−1.42316	−	0.821660i	−0.996567	+	0.0827856i	$0.973618\pi$
$860$		0			0
$861$	1.46876	+	2.54397i	0.0500553	+	0.0866983i
$862$	0.282076	−	0.488570i	0.00960756	−	0.0166408i
$863$	39.5328	−	14.3888i	1.34571	−	0.489799i	0.434105	−	0.900862i	$-0.357065\pi$
$863$	39.5328	−	14.3888i	1.34571	−	0.489799i	0.911607	+	0.411064i	$0.134843\pi$
$864$	−5.08234	−	6.05690i	−0.172905	−	0.206060i
$865$		0			0
$866$	2.70013	+	0.476106i	0.0917542	+	0.0161787i
$867$	−2.88458	+	16.3593i	−0.0979656	+	0.555590i
$868$	11.5450	−	13.7588i	0.391862	−	0.467003i
$869$	27.5072	−	75.5754i	0.933118	−	2.56372i
$870$		0			0
$871$	−12.4590	+	14.8480i	−0.422156	+	0.503105i
$872$	1.43548	−	8.14102i	0.0486116	−	0.275690i
$873$	−8.20754	−	1.44721i	−0.277783	−	0.0489807i
$874$	−1.43748	+	0.829930i	−0.0486235	+	0.0280728i
$875$		0			0
$876$	8.70786	−	3.16940i	0.294211	−	0.107084i
$877$	24.9439	−	43.2041i	0.842296	−	1.45890i	−0.0456525	−	0.998957i	$-0.514537\pi$
$877$	24.9439	−	43.2041i	0.842296	−	1.45890i	0.887949	−	0.459942i	$-0.152130\pi$
$878$	−2.04127	−	3.53559i	−0.0688897	−	0.119320i
$879$	11.9422	+	10.0207i	0.402802	+	0.337991i
$880$		0			0
$881$	2.81023	+	15.9376i	0.0946791	+	0.536952i	0.994845	+	0.101405i	$0.0323338\pi$
$881$	2.81023	+	15.9376i	0.0946791	+	0.536952i	−0.900166	+	0.435547i	$0.856555\pi$
$882$		−	2.41877i		−	0.0814444i
$883$	31.1610	−	5.49453i	1.04865	−	0.184906i	0.377335	−	0.926077i	$-0.376840\pi$
$883$	31.1610	−	5.49453i	1.04865	−	0.184906i	0.671316	+	0.741171i	$0.265729\pi$
$884$	−17.4897	+	14.6756i	−0.588243	+	0.493595i
$885$		0			0
$886$	−0.0959311	−	0.263568i	−0.00322287	−	0.00885475i
$887$	29.3969			0.987051			0.493526	−	0.869731i	$-0.335708\pi$
$887$	29.3969			0.987051			0.493526	+	0.869731i	$0.335708\pi$
$888$	2.93408	−	0.382888i	0.0984612	−	0.0128489i
$889$	30.6479			1.02790
$890$		0			0
$891$	−24.3322	−	8.85619i	−0.815159	−	0.296694i
$892$	20.5824	−	17.2707i	0.689150	−	0.578266i
$893$	−6.42209	+	1.13239i	−0.214907	+	0.0378939i
$894$			1.46442i			0.0489775i
$895$		0			0
$896$	−16.2478	−	9.38065i	−0.542800	−	0.313386i
$897$	8.35379	+	7.00966i	0.278925	+	0.234046i
$898$	−1.69924	−	2.94317i	−0.0567044	−	0.0982149i
$899$	−4.28682	+	7.42499i	−0.142973	+	0.247637i
$900$		0			0
$901$	37.2039	+	44.3379i	1.23944	+	1.47711i
$902$	−0.949352	+	0.548109i	−0.0316100	+	0.0182500i
$903$	3.10418	+	0.547351i	0.103301	+	0.0182147i
$904$	0.221899	−	1.25845i	0.00738025	−	0.0418555i
$905$		0			0
$906$	−0.911760	+	2.50504i	−0.0302912	+	0.0832244i
$907$	−19.7519	+	54.2679i	−0.655851	+	1.80194i	−0.0609459	+	0.998141i	$0.519412\pi$
$907$	−19.7519	+	54.2679i	−0.655851	+	1.80194i	−0.594905	+	0.803796i	$0.702810\pi$
$908$	37.7259	−	44.9600i	1.25198	−	1.49205i
$909$	2.39619	−	13.5895i	0.0794766	−	0.450734i
$910$		0			0
$911$	−8.80962	+	5.08623i	−0.291876	+	0.168514i	−0.638787	−	0.769383i	$-0.720564\pi$
$911$	−8.80962	+	5.08623i	−0.291876	+	0.168514i	0.346912	+	0.937898i	$0.387230\pi$
$912$	−2.06725	−	2.46366i	−0.0684536	−	0.0815799i
$913$	1.90582	−	0.693662i	0.0630735	−	0.0229569i
$914$	1.09347	−	1.89395i	0.0361688	−	0.0626462i
$915$		0			0
$916$	22.1755	+	18.6074i	0.732699	+	0.614807i
$917$	−14.1057	−	8.14392i	−0.465811	−	0.268936i
$918$	0.739183	+	4.19212i	0.0243967	+	0.138360i
$919$		−	0.219914i		−	0.00725429i	−0.999993	−	0.00362715i	$-0.998845\pi$
$919$		−	0.219914i		−	0.00725429i	0.999993	−	0.00362715i	$-0.00115456\pi$
$920$		0			0
$921$	3.87027	−	3.24754i	0.127530	−	0.107010i
$922$	3.66650	+	1.33450i	0.120750	+	0.0439493i
$923$	4.08600	+	11.2262i	0.134492	+	0.369514i
$924$	28.2220			0.928434
$925$		0			0
$926$	1.94776			0.0640074
$927$	6.80079	+	18.6850i	0.223367	+	0.613697i
$928$	6.32788	+	2.30316i	0.207723	+	0.0756049i
$929$	42.0310	−	35.2682i	1.37899	−	1.15711i	0.409409	−	0.912351i	$-0.365735\pi$
$929$	42.0310	−	35.2682i	1.37899	−	1.15711i	0.969583	−	0.244761i	$-0.0787096\pi$
$930$		0			0
$931$		−	6.67960i		−	0.218915i
$932$	4.79634	+	27.2014i	0.157109	+	0.891011i
$933$	8.45396	+	4.88090i	0.276770	+	0.159793i
$934$	−1.87126	−	1.57017i	−0.0612294	−	0.0513775i
$935$		0			0
$936$	−1.53917	+	2.66593i	−0.0503095	+	0.0871386i
$937$	41.4633	−	15.0914i	1.35455	−	0.493015i	0.440183	−	0.897908i	$-0.354914\pi$
$937$	41.4633	−	15.0914i	1.35455	−	0.493015i	0.914364	+	0.404893i	$0.132691\pi$
$938$	4.14448	+	4.93920i	0.135322	+	0.161271i
$939$	0.0705853	−	0.0407524i	0.00230346	−	0.00132991i
$940$		0			0
$941$	−3.08919	+	17.5197i	−0.100705	+	0.571125i	0.892144	+	0.451750i	$0.149200\pi$
$941$	−3.08919	+	17.5197i	−0.100705	+	0.571125i	−0.992849	+	0.119375i	$0.961911\pi$
$942$	1.22153	−	1.45576i	0.0397994	−	0.0474311i
$943$	3.26186	−	8.96190i	0.106221	−	0.291839i
$944$	13.2434	−	36.3858i	0.431035	−	1.18426i
$945$		0			0
$946$	−0.204259	+	1.15841i	−0.00664102	+	0.0376631i
$947$	−45.7348	−	8.06428i	−1.48618	−	0.262054i	−0.629136	−	0.777295i	$-0.716591\pi$
$947$	−45.7348	−	8.06428i	−1.48618	−	0.262054i	−0.857045	+	0.515242i	$0.827702\pi$
$948$	17.6105	−	10.1674i	0.571963	−	0.330223i
$949$	−7.69756	−	9.17359i	−0.249873	−	0.297787i
$950$		0			0
$951$	0.993069	−	1.72005i	0.0322025	−	0.0557763i
$952$	7.65093	+	13.2518i	0.247968	+	0.429493i
$953$	−42.6499	−	35.7875i	−1.38157	−	1.15927i	−0.968629	−	0.248513i	$-0.920058\pi$
$953$	−42.6499	−	35.7875i	−1.38157	−	1.15927i	−0.412938	−	0.910759i	$-0.635497\pi$
$954$	3.35440	+	1.93666i	0.108603	+	0.0627017i
$955$		0			0
$956$			31.4577i			1.01741i
$957$	−13.2672	+	2.33936i	−0.428867	+	0.0756209i
$958$	0.594450	−	0.498803i	0.0192058	−	0.0161156i
$959$	22.8831	+	8.32877i	0.738934	+	0.268950i
$960$		0			0
$961$	24.4633			0.789139
$962$	−0.874437	−	1.68445i	−0.0281930	−	0.0543087i
$963$	6.94120			0.223677
$964$	14.9332	+	41.0288i	0.480968	+	1.32145i
$965$		0			0
$966$	2.77890	−	2.33177i	0.0894095	−	0.0750235i
$967$	−5.57465	+	0.982962i	−0.179269	+	0.0316099i	−0.262562	−	0.964915i	$-0.584567\pi$
$967$	−5.57465	+	0.982962i	−0.179269	+	0.0316099i	0.0832930	+	0.996525i	$0.473456\pi$
$968$			13.7656i			0.442442i
$969$	0.924743	+	5.24448i	0.0297070	+	0.168477i
$970$		0			0
$971$	−8.95214	−	7.51173i	−0.287288	−	0.241063i	0.487742	−	0.872988i	$-0.337821\pi$
$971$	−8.95214	−	7.51173i	−0.287288	−	0.241063i	−0.775030	+	0.631925i	$0.782265\pi$
$972$	−14.9137	−	25.8314i	−0.478358	−	0.828541i
$973$	5.92521	−	10.2628i	0.189953	−	0.329009i
$974$	3.43930	−	1.25180i	0.110202	−	0.0401104i
$975$		0			0
$976$	12.1868	−	7.03607i	0.390091	−	0.225219i
$977$	−26.4056	−	4.65601i	−0.844788	−	0.148959i	−0.265530	−	0.964103i	$-0.585547\pi$
$977$	−26.4056	−	4.65601i	−0.844788	−	0.148959i	−0.579259	+	0.815144i	$0.696658\pi$
$978$	0.187611	−	1.06399i	0.00599913	−	0.0340227i
$979$	−41.2659	+	49.1788i	−1.31886	+	1.57176i
$980$		0			0
$981$	10.3673	−	28.4839i	0.331002	−	0.909421i
$982$	−0.178320	+	0.212514i	−0.00569043	+	0.00678159i
$983$	5.82176	−	33.0168i	0.185685	−	1.05307i	−0.739387	−	0.673281i	$-0.764884\pi$
$983$	5.82176	−	33.0168i	0.185685	−	1.05307i	0.925072	−	0.379792i	$-0.124004\pi$
$984$	−0.549948	−	0.0969706i	−0.0175317	−	0.00309131i
$985$		0			0
$986$	−2.33037	−	2.77723i	−0.0742142	−	0.0884451i
$987$	13.3924	−	4.87443i	0.426284	−	0.155155i
$988$	−2.10968	+	3.65408i	−0.0671179	+	0.116252i
$989$	−5.11679	−	8.86254i	−0.162704	−	0.281812i
$990$		0			0
$991$	6.47557	+	3.73867i	0.205703	+	0.118763i	0.599313	−	0.800515i	$-0.295441\pi$
$991$	6.47557	+	3.73867i	0.205703	+	0.118763i	−0.393610	+	0.919278i	$0.628774\pi$
$992$	0.891528	+	5.05611i	0.0283061	+	0.160532i
$993$			3.91953i			0.124383i
$994$	3.91369	−	0.690089i	0.124135	−	0.0218883i
$995$		0			0
$996$	0.481869	+	0.175386i	0.0152686	+	0.00555732i
$997$	10.5675	+	29.0340i	0.334676	+	0.919516i	0.986878	+	0.161470i	$0.0516235\pi$
$997$	10.5675	+	29.0340i	0.334676	+	0.919516i	−0.652201	+	0.758046i	$0.726154\pi$
$998$	0.110037			0.00348317
$999$	23.9263	+	1.07188i	0.756995	+	0.0339128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.326.8		96
5.2	odd	4		185.2.v.a.104.9	yes	96
5.3	odd	4		185.2.v.a.104.8	✓	96
5.4	even	2	inner	925.2.bb.e.326.9		96
37.21	even	18	inner	925.2.bb.e.576.8		96
185.58	odd	36		185.2.v.a.169.9	yes	96
185.132	odd	36		185.2.v.a.169.8	yes	96
185.169	even	18	inner	925.2.bb.e.576.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.8	✓	96	5.3	odd	4
185.2.v.a.104.9	yes	96	5.2	odd	4
185.2.v.a.169.8	yes	96	185.132	odd	36
185.2.v.a.169.9	yes	96	185.58	odd	36
925.2.bb.e.326.8		96	1.1	even	1	trivial
925.2.bb.e.326.9		96	5.4	even	2	inner
925.2.bb.e.576.8		96	37.21	even	18	inner
925.2.bb.e.576.9		96	185.169	even	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0583632 - 0.160351i) q^{2} +(-0.674605 - 0.245536i) q^{3} +(1.50978 - 1.26686i) q^{4} +0.122504i q^{6} +(0.618951 + 3.51024i) q^{7} +(-0.586820 - 0.338800i) q^{8} +(-1.90333 - 1.59708i) q^{9} +(-2.79800 + 4.84627i) q^{11} +(-1.32957 + 0.483922i) q^{12} +(1.17531 + 1.40068i) q^{13} +(0.526749 - 0.304118i) q^{14} +(0.664401 - 3.76801i) q^{16} +(-4.07242 + 4.85332i) q^{17} +(-0.145010 + 0.398412i) q^{18} +(-0.400455 + 1.10024i) q^{19} +(0.444344 - 2.52000i) q^{21} +(0.940407 + 0.165819i) q^{22} +(-7.19469 + 4.15386i) q^{23} +(0.312684 + 0.372642i) q^{24} +(0.156006 - 0.270210i) q^{26} +(1.96870 + 3.40989i) q^{27} +(5.38146 + 4.51558i) q^{28} +(-2.90414 - 1.67670i) q^{29} -2.55670i q^{31} +(-1.97760 + 0.348703i) q^{32} +(3.07748 - 2.58231i) q^{33} +(1.01592 + 0.369763i) q^{34} -4.89689 q^{36} +(3.27409 - 5.12643i) q^{37} +0.199797 q^{38} +(-0.448951 - 1.23348i) q^{39} +(-0.879400 + 0.737904i) q^{41} +(-0.430019 + 0.0758240i) q^{42} +1.23182i q^{43} +(1.91517 + 10.8615i) q^{44} +(1.08598 + 0.911247i) q^{46} +(2.78479 + 4.82340i) q^{47} +(-1.37339 + 2.37878i) q^{48} +(-5.36086 + 1.95119i) q^{49} +(3.93894 - 2.27415i) q^{51} +(3.54892 + 0.625770i) q^{52} +(1.58638 - 8.99680i) q^{53} +(0.431882 - 0.514697i) q^{54} +(0.826060 - 2.26958i) q^{56} +(0.540298 - 0.643902i) q^{57} +(-0.0993673 + 0.563540i) q^{58} +(9.96639 + 1.75734i) q^{59} +(2.36411 + 2.81744i) q^{61} +(-0.409970 + 0.149217i) q^{62} +(4.42808 - 7.66966i) q^{63} +(-3.65480 - 6.33030i) q^{64} +(-0.593689 - 0.342766i) q^{66} +(1.84077 + 10.4395i) q^{67} +12.4866i q^{68} +(5.87350 - 1.03566i) q^{69} +(6.13971 + 2.23467i) q^{71} +(0.575819 + 1.58205i) q^{72} -6.54940 q^{73} +(-1.01312 - 0.225811i) q^{74} +(0.789250 + 2.16845i) q^{76} +(-18.7434 - 6.82205i) q^{77} +(-0.171589 + 0.143980i) q^{78} +(-14.1537 + 2.49567i) q^{79} +(0.803505 + 4.55690i) q^{81} +(0.169649 + 0.0979466i) q^{82} +(-0.277634 - 0.232963i) q^{83} +(-2.52162 - 4.36758i) q^{84} +(0.197524 - 0.0718927i) q^{86} +(1.54745 + 1.84418i) q^{87} +(3.28384 - 1.89593i) q^{88} +(11.2979 + 1.99213i) q^{89} +(-4.18926 + 4.99256i) q^{91} +(-5.60007 + 15.3861i) q^{92} +(-0.627761 + 1.72476i) q^{93} +(0.610910 - 0.728054i) q^{94} +(1.41971 + 0.250334i) q^{96} +(2.90491 - 1.67715i) q^{97} +(0.625753 + 0.745743i) q^{98} +(13.0654 - 4.75542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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