LMFDB - Embedded newform 847.2.f.z.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.6
Character	$\chi$	$=$	847.323
Dual form			847.2.f.z.729.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18693 + 1.58890i) q^{2} +(-0.867470 + 2.66980i) q^{3} +(1.64004 + 5.04751i) q^{4} +(0.360071 - 0.261607i) q^{5} +(-6.13913 + 4.46034i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.76267 + 8.50263i) q^{8} +(-3.94826 - 2.86858i) q^{9} +O(q^{10})$	\(q+(2.18693 + 1.58890i) q^{2} +(-0.867470 + 2.66980i) q^{3} +(1.64004 + 5.04751i) q^{4} +(0.360071 - 0.261607i) q^{5} +(-6.13913 + 4.46034i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.76267 + 8.50263i) q^{8} +(-3.94826 - 2.86858i) q^{9} +1.20312 q^{10} -14.8985 q^{12} +(0.364813 + 0.265052i) q^{13} +(0.835334 - 2.57089i) q^{14} +(0.386087 + 1.18825i) q^{15} +(-10.9643 + 7.96600i) q^{16} +(3.90850 - 2.83969i) q^{17} +(-4.07669 - 12.5468i) q^{18} +(0.335728 - 1.03326i) q^{19} +(1.91099 + 1.38842i) q^{20} +2.80719 q^{21} +4.57222 q^{23} +(-20.3038 - 14.7516i) q^{24} +(-1.48387 + 4.56689i) q^{25} +(0.376680 + 1.15930i) q^{26} +(4.27033 - 3.10257i) q^{27} +(4.29367 - 3.11953i) q^{28} +(0.613187 + 1.88719i) q^{29} +(-1.04367 + 3.21208i) q^{30} +(-6.68135 - 4.85429i) q^{31} -18.7549 q^{32} +13.0596 q^{34} +(-0.360071 - 0.261607i) q^{35} +(8.00390 - 24.6335i) q^{36} +(2.26116 + 6.95912i) q^{37} +(2.37596 - 1.72624i) q^{38} +(-1.02410 + 0.744051i) q^{39} +(1.22959 + 3.78429i) q^{40} +(-0.547186 + 1.68407i) q^{41} +(6.13913 + 4.46034i) q^{42} +11.4084 q^{43} -2.17209 q^{45} +(9.99913 + 7.26479i) q^{46} +(0.315996 - 0.972536i) q^{47} +(-11.7564 - 36.1826i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-10.5015 + 7.62975i) q^{50} +(4.19090 + 12.8983i) q^{51} +(-0.739547 + 2.27609i) q^{52} +(2.88998 + 2.09970i) q^{53} +14.2686 q^{54} +8.94020 q^{56} +(2.46737 + 1.79265i) q^{57} +(-1.65756 + 5.10146i) q^{58} +(-4.44972 - 13.6948i) q^{59} +(-5.36452 + 3.89755i) q^{60} +(3.98817 - 2.89758i) q^{61} +(-6.89869 - 21.2320i) q^{62} +(-1.50810 + 4.64146i) q^{63} +(-19.0871 - 13.8676i) q^{64} +0.200698 q^{65} -6.18858 q^{67} +(20.7435 + 15.0710i) q^{68} +(-3.96626 + 12.2069i) q^{69} +(-0.371784 - 1.14423i) q^{70} +(4.79072 - 3.48066i) q^{71} +(35.2982 - 25.6457i) q^{72} +(0.512277 + 1.57663i) q^{73} +(-6.11235 + 18.8119i) q^{74} +(-10.9055 - 7.92327i) q^{75} +5.76602 q^{76} -3.42186 q^{78} +(-2.91920 - 2.12092i) q^{79} +(-1.86395 + 5.73665i) q^{80} +(0.0545593 + 0.167916i) q^{81} +(-3.87247 + 2.81351i) q^{82} +(-8.74129 + 6.35092i) q^{83} +(4.60389 + 14.1693i) q^{84} +(0.664455 - 2.04498i) q^{85} +(24.9494 + 18.1268i) q^{86} -5.57035 q^{87} -5.21170 q^{89} +(-4.75022 - 3.45124i) q^{90} +(0.139346 - 0.428863i) q^{91} +(7.49860 + 23.0783i) q^{92} +(18.7558 - 13.6269i) q^{93} +(2.23632 - 1.62478i) q^{94} +(-0.149423 - 0.459877i) q^{95} +(16.2693 - 50.0716i) q^{96} +(4.29576 + 3.12105i) q^{97} -2.70320 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9 + 32 * q^10 - 56 * q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 22 * q^17 + 24 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 20 * q^30 + 2 * q^31 - 32 * q^32 + 96 * q^34 - 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 + 20 * q^39 + 18 * q^40 + 26 * q^41 + 6 * q^42 + 16 * q^43 - 144 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 - 4 * q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 128 * q^54 + 48 * q^56 + 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 + 8 * q^63 - 26 * q^64 - 96 * q^65 + 24 * q^67 + 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 + 16 * q^72 + 14 * q^73 + 44 * q^74 + 20 * q^75 + 120 * q^76 + 128 * q^78 - 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 + 22 * q^83 - 14 * q^84 - 24 * q^85 + 30 * q^86 - 88 * q^87 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 - 38 * q^94 - 24 * q^95 - 62 * q^96 + 4 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	2.18693	+	1.58890i	1.54639	+	1.12352i	0.946161	+	0.323696i	$0.104925\pi$
$2$	2.18693	+	1.58890i	1.54639	+	1.12352i	0.600233	+	0.799825i	$0.295075\pi$
$3$	−0.867470	+	2.66980i	−0.500834	+	1.54141i	0.306830	+	0.951764i	$0.400732\pi$
$3$	−0.867470	+	2.66980i	−0.500834	+	1.54141i	−0.807664	+	0.589644i	$0.799268\pi$
$4$	1.64004	+	5.04751i	0.820018	+	2.52376i
$5$	0.360071	−	0.261607i	0.161029	−	0.116994i	−0.504353	−	0.863498i	$-0.668269\pi$
$5$	0.360071	−	0.261607i	0.161029	−	0.116994i	0.665381	+	0.746503i	$0.268269\pi$
$6$	−6.13913	+	4.46034i	−2.50629	+	1.82093i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−2.76267	+	8.50263i	−0.976752	+	3.00613i
$9$	−3.94826	−	2.86858i	−1.31609	−	0.956193i
$10$	1.20312			0.380459
$11$		0			0
$11$		0			0
$12$	−14.8985			−4.30083
$13$	0.364813	+	0.265052i	0.101181	+	0.0735122i	0.637225	−	0.770678i	$-0.280082\pi$
$13$	0.364813	+	0.265052i	0.101181	+	0.0735122i	−0.536044	+	0.844190i	$0.680082\pi$
$14$	0.835334	−	2.57089i	0.223252	−	0.687100i
$15$	0.386087	+	1.18825i	0.0996872	+	0.306806i
$16$	−10.9643	+	7.96600i	−2.74106	+	1.99150i
$17$	3.90850	−	2.83969i	0.947951	−	0.688727i	−0.00237042	−	0.999997i	$-0.500755\pi$
$17$	3.90850	−	2.83969i	0.947951	−	0.688727i	0.950321	+	0.311271i	$0.100755\pi$
$18$	−4.07669	−	12.5468i	−0.960886	−	2.95730i
$19$	0.335728	−	1.03326i	0.0770212	−	0.237047i	−0.905132	−	0.425131i	$-0.860228\pi$
$19$	0.335728	−	1.03326i	0.0770212	−	0.237047i	0.982153	+	0.188084i	$0.0602279\pi$
$20$	1.91099	+	1.38842i	0.427311	+	0.310460i
$21$	2.80719			0.612579
$22$		0			0
$23$	4.57222			0.953373			0.476687	−	0.879073i	$-0.341838\pi$
$23$	4.57222			0.953373			0.476687	+	0.879073i	$0.341838\pi$
$24$	−20.3038	−	14.7516i	−4.14449	−	3.01115i
$25$	−1.48387	+	4.56689i	−0.296774	+	0.913378i
$26$	0.376680	+	1.15930i	0.0738729	+	0.227358i
$27$	4.27033	−	3.10257i	0.821825	−	0.597091i
$28$	4.29367	−	3.11953i	0.811428	−	0.589537i
$29$	0.613187	+	1.88719i	0.113866	+	0.350443i	0.991709	−	0.128505i	$-0.0410180\pi$
$29$	0.613187	+	1.88719i	0.113866	+	0.350443i	−0.877843	+	0.478949i	$0.841018\pi$
$30$	−1.04367	+	3.21208i	−0.190547	+	0.586443i
$31$	−6.68135	−	4.85429i	−1.20001	−	0.871856i	−0.205721	−	0.978611i	$-0.565954\pi$
$31$	−6.68135	−	4.85429i	−1.20001	−	0.871856i	−0.994285	+	0.106755i	$0.965954\pi$
$32$	−18.7549			−3.31542
$33$		0			0
$34$	13.0596			2.23970
$35$	−0.360071	−	0.261607i	−0.0608631	−	0.0442196i
$36$	8.00390	−	24.6335i	1.33398	−	4.10558i
$37$	2.26116	+	6.95912i	0.371732	+	1.14407i	0.945657	+	0.325165i	$0.105420\pi$
$37$	2.26116	+	6.95912i	0.371732	+	1.14407i	−0.573926	+	0.818907i	$0.694580\pi$
$38$	2.37596	−	1.72624i	0.385432	−	0.280033i
$39$	−1.02410	+	0.744051i	−0.163987	+	0.119144i
$40$	1.22959	+	3.78429i	0.194415	+	0.598348i
$41$	−0.547186	+	1.68407i	−0.0854561	+	0.263007i	−0.984649	−	0.174545i	$-0.944154\pi$
$41$	−0.547186	+	1.68407i	−0.0854561	+	0.263007i	0.899193	+	0.437552i	$0.144154\pi$
$42$	6.13913	+	4.46034i	0.947289	+	0.688246i
$43$	11.4084			1.73977			0.869884	−	0.493257i	$-0.164194\pi$
$43$	11.4084			1.73977			0.869884	+	0.493257i	$0.164194\pi$
$44$		0			0
$45$	−2.17209			−0.323797
$46$	9.99913	+	7.26479i	1.47429	+	1.07113i
$47$	0.315996	−	0.972536i	0.0460928	−	0.141859i	−0.925361	−	0.379086i	$-0.876238\pi$
$47$	0.315996	−	0.972536i	0.0460928	−	0.141859i	0.971454	+	0.237227i	$0.0762385\pi$
$48$	−11.7564	−	36.1826i	−1.69690	−	5.22251i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−10.5015	+	7.62975i	−1.48513	+	1.07901i
$51$	4.19090	+	12.8983i	0.586843	+	1.80612i
$52$	−0.739547	+	2.27609i	−0.102557	+	0.315637i
$53$	2.88998	+	2.09970i	0.396970	+	0.288416i	0.768306	−	0.640083i	$-0.221100\pi$
$53$	2.88998	+	2.09970i	0.396970	+	0.288416i	−0.371336	+	0.928499i	$0.621100\pi$
$54$	14.2686			1.94171
$55$		0			0
$56$	8.94020			1.19468
$57$	2.46737	+	1.79265i	0.326811	+	0.237442i
$58$	−1.65756	+	5.10146i	−0.217649	+	0.669854i
$59$	−4.44972	−	13.6948i	−0.579304	−	1.78291i	−0.621033	−	0.783784i	$-0.713287\pi$
$59$	−4.44972	−	13.6948i	−0.579304	−	1.78291i	0.0417292	−	0.999129i	$-0.486713\pi$
$60$	−5.36452	+	3.89755i	−0.692557	+	0.503172i
$61$	3.98817	−	2.89758i	0.510633	−	0.370996i	−0.302431	−	0.953171i	$-0.597798\pi$
$61$	3.98817	−	2.89758i	0.510633	−	0.370996i	0.813064	+	0.582175i	$0.197798\pi$
$62$	−6.89869	−	21.2320i	−0.876135	−	2.69647i
$63$	−1.50810	+	4.64146i	−0.190003	+	0.584769i
$64$	−19.0871	−	13.8676i	−2.38588	−	1.73345i
$65$	0.200698			0.0248935
$66$		0			0
$67$	−6.18858			−0.756055			−0.378028	−	0.925794i	$-0.623398\pi$
$67$	−6.18858			−0.756055			−0.378028	+	0.925794i	$0.623398\pi$
$68$	20.7435	+	15.0710i	2.51552	+	1.82763i
$69$	−3.96626	+	12.2069i	−0.477482	+	1.46954i
$70$	−0.371784	−	1.14423i	−0.0444367	−	0.136762i
$71$	4.79072	−	3.48066i	0.568553	−	0.413078i	−0.266026	−	0.963966i	$-0.585711\pi$
$71$	4.79072	−	3.48066i	0.568553	−	0.413078i	0.834579	+	0.550888i	$0.185711\pi$
$72$	35.2982	−	25.6457i	4.15994	−	3.02237i
$73$	0.512277	+	1.57663i	0.0599575	+	0.184530i	0.976549	−	0.215294i	$-0.0690711\pi$
$73$	0.512277	+	1.57663i	0.0599575	+	0.184530i	−0.916592	+	0.399825i	$0.869071\pi$
$74$	−6.11235	+	18.8119i	−0.710546	+	2.18683i
$75$	−10.9055	−	7.92327i	−1.25925	−	0.914901i
$76$	5.76602			0.661407
$77$		0			0
$78$	−3.42186			−0.387449
$79$	−2.91920	−	2.12092i	−0.328436	−	0.238623i	0.411331	−	0.911486i	$-0.365064\pi$
$79$	−2.91920	−	2.12092i	−0.328436	−	0.238623i	−0.739767	+	0.672864i	$0.765064\pi$
$80$	−1.86395	+	5.73665i	−0.208396	+	0.641377i
$81$	0.0545593	+	0.167916i	0.00606215	+	0.0186574i
$82$	−3.87247	+	2.81351i	−0.427642	+	0.310700i
$83$	−8.74129	+	6.35092i	−0.959481	+	0.697104i	−0.953030	−	0.302875i	$-0.902053\pi$
$83$	−8.74129	+	6.35092i	−0.959481	+	0.697104i	−0.00645109	+	0.999979i	$0.502053\pi$
$84$	4.60389	+	14.1693i	0.502326	+	1.54600i
$85$	0.664455	−	2.04498i	0.0720703	−	0.221809i
$86$	24.9494	+	18.1268i	2.69037	+	1.95467i
$87$	−5.57035			−0.597204
$88$		0			0
$89$	−5.21170			−0.552439			−0.276220	−	0.961095i	$-0.589082\pi$
$89$	−5.21170			−0.552439			−0.276220	+	0.961095i	$0.589082\pi$
$90$	−4.75022	−	3.45124i	−0.500717	−	0.363793i
$91$	0.139346	−	0.428863i	0.0146074	−	0.0449571i
$92$	7.49860	+	23.0783i	0.781783	+	2.40608i
$93$	18.7558	−	13.6269i	1.94489	−	1.41304i
$94$	2.23632	−	1.62478i	0.230659	−	0.167584i
$95$	−0.149423	−	0.459877i	−0.0153305	−	0.0471824i
$96$	16.2693	−	50.0716i	1.66047	−	5.11042i
$97$	4.29576	+	3.12105i	0.436168	+	0.316895i	0.784110	−	0.620621i	$-0.213120\pi$
$97$	4.29576	+	3.12105i	0.436168	+	0.316895i	−0.347943	+	0.937516i	$0.613120\pi$
$98$	−2.70320			−0.273064
$99$		0			0
$100$	−25.4850			−2.54850
$101$	12.5886	+	9.14616i	1.25261	+	0.910077i	0.998371	−	0.0570629i	$-0.0181735\pi$
$101$	12.5886	+	9.14616i	1.25261	+	0.910077i	0.254243	+	0.967140i	$0.418174\pi$
$102$	−11.3288	+	34.8665i	−1.12172	+	3.45230i
$103$	−4.37918	−	13.4777i	−0.431494	−	1.32800i	−0.896637	−	0.442766i	$-0.853997\pi$
$103$	−4.37918	−	13.4777i	−0.431494	−	1.32800i	0.465143	−	0.885235i	$-0.346003\pi$
$104$	−3.26150	+	2.36962i	−0.319816	+	0.232360i
$105$	1.01079	−	0.734380i	0.0986428	−	0.0716682i
$106$	2.98399	+	9.18379i	0.289831	+	0.892008i
$107$	3.63253	−	11.1798i	0.351170	−	1.08079i	−0.607027	−	0.794681i	$-0.707638\pi$
$107$	3.63253	−	11.1798i	0.351170	−	1.08079i	0.958197	−	0.286109i	$-0.0923620\pi$
$108$	22.6638	+	16.4662i	2.18082	+	1.58446i
$109$	−15.7800			−1.51145			−0.755723	−	0.654891i	$-0.772714\pi$
$109$	−15.7800			−1.51145			−0.755723	+	0.654891i	$0.772714\pi$
$110$		0			0
$111$	−20.5409			−1.94966
$112$	10.9643	+	7.96600i	1.03602	+	0.752716i
$113$	−1.83045	+	5.63356i	−0.172195	+	0.529960i	−0.999494	−	0.0318004i	$-0.989876\pi$
$113$	−1.83045	+	5.63356i	−0.172195	+	0.529960i	0.827300	+	0.561761i	$0.189876\pi$
$114$	2.54763	+	7.84080i	0.238608	+	0.734358i
$115$	1.64632	−	1.19612i	0.153520	−	0.111539i
$116$	−8.51999	+	6.19014i	−0.791061	+	0.574740i
$117$	−0.680053	−	2.09299i	−0.0628709	−	0.193497i
$118$	12.0285	−	37.0198i	1.10731	−	3.40795i
$119$	−3.90850	−	2.83969i	−0.358292	−	0.260314i
$120$	−11.1699			−1.01967
$121$		0			0
$122$	13.3258			1.20646
$123$	−4.02144	−	2.92175i	−0.362601	−	0.263445i
$124$	13.5444	−	41.6854i	1.21632	−	3.74346i
$125$	1.34810	+	4.14904i	0.120578	+	0.371101i
$126$	−10.6729	+	7.75433i	−0.950820	+	0.690811i
$127$	8.19835	−	5.95645i	0.727486	−	0.528549i	−0.161281	−	0.986908i	$-0.551563\pi$
$127$	8.19835	−	5.95645i	0.727486	−	0.528549i	0.888767	+	0.458359i	$0.151563\pi$
$128$	−8.11681	−	24.9810i	−0.717432	−	2.20803i
$129$	−9.89646	+	30.4582i	−0.871334	+	2.68169i
$130$	0.438912	+	0.318889i	0.0384952	+	0.0279684i
$131$	6.83340			0.597037			0.298519	−	0.954404i	$-0.403508\pi$
$131$	6.83340			0.597037			0.298519	+	0.954404i	$0.403508\pi$
$132$		0			0
$133$	−1.08644			−0.0942061
$134$	−13.5340	−	9.83302i	−1.16916	−	0.849444i
$135$	0.725966	−	2.23429i	0.0624812	−	0.192297i
$136$	13.3470	+	41.0777i	1.14449	+	3.52238i
$137$	−11.7043	+	8.50366i	−0.999965	+	0.726517i	−0.962081	−	0.272765i	$-0.912062\pi$
$137$	−11.7043	+	8.50366i	−0.999965	+	0.726517i	−0.0378839	+	0.999282i	$0.512062\pi$
$138$	−28.0695	+	20.3937i	−2.38943	+	1.73602i
$139$	4.54121	+	13.9764i	0.385180	+	1.18546i	0.936349	+	0.351070i	$0.114182\pi$
$139$	4.54121	+	13.9764i	0.385180	+	1.18546i	−0.551169	+	0.834394i	$0.685818\pi$
$140$	0.729935	−	2.24651i	0.0616907	−	0.189865i
$141$	2.32236	+	1.68729i	0.195578	+	0.142096i
$142$	16.0074			1.34331
$143$		0			0
$144$	66.1409			5.51174
$145$	0.714494	+	0.519110i	0.0593355	+	0.0431098i
$146$	−1.38479	+	4.26193i	−0.114606	+	0.352720i
$147$	−0.867470	−	2.66980i	−0.0715477	−	0.220201i
$148$	−31.4179	+	22.8264i	−2.58253	+	1.87632i
$149$	0.810148	−	0.588607i	0.0663699	−	0.0482206i	−0.554106	−	0.832446i	$-0.686940\pi$
$149$	0.810148	−	0.588607i	0.0663699	−	0.0482206i	0.620476	+	0.784226i	$0.286940\pi$
$150$	−11.2602	−	34.6553i	−0.919391	−	2.82959i
$151$	−0.425018	+	1.30807i	−0.0345874	+	0.106449i	−0.966860	−	0.255308i	$-0.917823\pi$
$151$	−0.425018	+	1.30807i	−0.0345874	+	0.106449i	0.932272	+	0.361757i	$0.117823\pi$
$152$	7.85795	+	5.70914i	0.637364	+	0.463072i
$153$	−23.5777			−1.90614
$154$		0			0
$155$	−3.67568			−0.295237
$156$	−5.43517	−	3.94888i	−0.435162	−	0.316163i
$157$	1.66149	−	5.11353i	0.132601	−	0.408104i	−0.862608	−	0.505873i	$-0.831171\pi$
$157$	1.66149	−	5.11353i	0.132601	−	0.408104i	0.995209	+	0.0977686i	$0.0311705\pi$
$158$	−3.01416	−	9.27663i	−0.239794	−	0.738009i
$159$	−8.11274	+	5.89425i	−0.643382	+	0.467444i
$160$	−6.75308	+	4.90640i	−0.533878	+	0.387885i
$161$	−1.41289	−	4.34844i	−0.111352	−	0.342705i
$162$	−0.147485	+	0.453911i	−0.0115875	+	0.0356626i
$163$	7.62509	+	5.53995i	0.597243	+	0.433922i	0.844899	−	0.534926i	$-0.179660\pi$
$163$	7.62509	+	5.53995i	0.597243	+	0.433922i	−0.247656	+	0.968848i	$0.579660\pi$
$164$	−9.39775			−0.733841
$165$		0			0
$166$	−29.2076			−2.26695
$167$	16.1899	+	11.7627i	1.25281	+	0.910222i	0.998382	−	0.0568684i	$-0.0181116\pi$
$167$	16.1899	+	11.7627i	1.25281	+	0.910222i	0.254432	+	0.967091i	$0.418112\pi$
$168$	−7.75535	+	23.8685i	−0.598338	+	1.84150i
$169$	−3.95439	−	12.1703i	−0.304183	−	0.936180i
$170$	4.70239	−	3.41648i	0.360657	−	0.262032i
$171$	−4.28954	+	3.11653i	−0.328029	+	0.238327i
$172$	18.7102	+	57.5841i	1.42664	+	4.39075i
$173$	−3.35177	+	10.3157i	−0.254830	+	0.784286i	0.739033	+	0.673669i	$0.235283\pi$
$173$	−3.35177	+	10.3157i	−0.254830	+	0.784286i	−0.993863	+	0.110617i	$0.964717\pi$
$174$	−12.1820	−	8.85072i	−0.923513	−	0.670971i
$175$	4.80191			0.362990
$176$		0			0
$177$	40.4224			3.03833
$178$	−11.3976	−	8.28087i	−0.854289	−	0.620677i
$179$	5.20644	−	16.0238i	0.389148	−	1.19767i	−0.544279	−	0.838904i	$-0.683197\pi$
$179$	5.20644	−	16.0238i	0.389148	−	1.19767i	0.933426	−	0.358769i	$-0.116803\pi$
$180$	−3.56231	−	10.9637i	−0.265519	−	0.817184i
$181$	16.4264	−	11.9345i	1.22096	−	0.887082i	0.224784	−	0.974409i	$-0.427832\pi$
$181$	16.4264	−	11.9345i	1.22096	−	0.887082i	0.996180	+	0.0873266i	$0.0278324\pi$
$182$	0.986160	−	0.716487i	0.0730990	−	0.0531096i
$183$	4.27632	+	13.1612i	0.316115	+	0.972901i
$184$	−12.6315	+	38.8759i	−0.931210	+	2.86597i
$185$	2.63473	+	1.91424i	0.193709	+	0.140738i
$186$	62.6695			4.59515
$187$		0			0
$188$	5.42714			0.395815
$189$	−4.27033	−	3.10257i	−0.310621	−	0.225679i
$190$	0.403920	−	1.24314i	0.0293034	−	0.0901867i
$191$	0.786247	+	2.41982i	0.0568908	+	0.175092i	0.975464	−	0.220159i	$-0.0706576\pi$
$191$	0.786247	+	2.41982i	0.0568908	+	0.175092i	−0.918573	+	0.395251i	$0.870658\pi$
$192$	53.5810	−	38.9289i	3.86688	−	2.80945i
$193$	14.1648	−	10.2913i	1.01960	−	0.740784i	0.0534000	−	0.998573i	$-0.482994\pi$
$193$	14.1648	−	10.2913i	1.01960	−	0.740784i	0.966201	+	0.257790i	$0.0829942\pi$
$194$	4.43549	+	13.6510i	0.318450	+	0.980088i
$195$	−0.174099	+	0.535823i	−0.0124675	+	0.0383710i
$196$	−4.29367	−	3.11953i	−0.306691	−	0.222824i
$197$	2.16558			0.154291			0.0771457	−	0.997020i	$-0.475419\pi$
$197$	2.16558			0.154291			0.0771457	+	0.997020i	$0.475419\pi$
$198$		0			0
$199$	−14.5756			−1.03324			−0.516620	−	0.856215i	$-0.672810\pi$
$199$	−14.5756			−1.03324			−0.516620	+	0.856215i	$0.672810\pi$
$200$	−34.7311	−	25.2336i	−2.45586	−	1.78429i
$201$	5.36840	−	16.5222i	0.378658	−	1.16539i
$202$	12.9981	+	40.0041i	0.914544	+	2.81468i
$203$	1.60534	−	1.16635i	0.112673	−	0.0818617i
$204$	−58.2309	+	42.3072i	−4.07698	+	2.96210i
$205$	0.243537	+	0.749531i	0.0170094	+	0.0523495i
$206$	11.8378	−	36.4330i	0.824778	−	2.53841i
$207$	−18.0523	−	13.1158i	−1.25472	−	0.911609i
$208$	−6.11130			−0.423743
$209$		0			0
$210$	3.37738			0.233061
$211$	−2.93701	−	2.13386i	−0.202192	−	0.146901i	0.482082	−	0.876126i	$-0.339881\pi$
$211$	−2.93701	−	2.13386i	−0.202192	−	0.146901i	−0.684274	+	0.729225i	$0.739881\pi$
$212$	−5.85857	+	18.0308i	−0.402368	+	1.23836i
$213$	5.13685	+	15.8096i	0.351971	+	1.08326i
$214$	25.7076	−	18.6777i	1.75734	−	1.27678i
$215$	4.10784	−	2.98452i	0.280152	−	0.203543i
$216$	14.5825	+	44.8804i	0.992216	+	3.05373i
$217$	−2.55205	+	7.85440i	−0.173244	+	0.533192i
$218$	−34.5097	−	25.0728i	−2.33729	−	1.69814i
$219$	−4.65366			−0.314465
$220$		0			0
$221$	2.17854			0.146544
$222$	−44.9216	−	32.6374i	−3.01494	−	2.19048i
$223$	−1.49583	+	4.60370i	−0.100168	+	0.308287i	−0.988566	−	0.150788i	$-0.951819\pi$
$223$	−1.49583	+	4.60370i	−0.100168	+	0.308287i	0.888398	+	0.459075i	$0.151819\pi$
$224$	5.79557	+	17.8369i	0.387233	+	1.19178i
$225$	18.9592	−	13.7747i	1.26395	−	0.918311i
$226$	−12.9542	+	9.41180i	−0.861702	+	0.626063i
$227$	−7.02415	−	21.6181i	−0.466209	−	1.43484i	−0.857456	−	0.514558i	$-0.827956\pi$
$227$	−7.02415	−	21.6181i	−0.466209	−	1.43484i	0.391247	−	0.920286i	$-0.372044\pi$
$228$	−5.00184	+	15.3941i	−0.331255	+	1.01950i
$229$	18.3430	+	13.3269i	1.21214	+	0.880669i	0.995423	−	0.0955657i	$-0.0304660\pi$
$229$	18.3430	+	13.3269i	1.21214	+	0.880669i	0.216714	+	0.976235i	$0.430466\pi$
$230$	5.50092			0.362720
$231$		0			0
$232$	−17.7402			−1.16470
$233$	−0.475121	−	0.345196i	−0.0311262	−	0.0226145i	0.572113	−	0.820175i	$-0.306124\pi$
$233$	−0.475121	−	0.345196i	−0.0311262	−	0.0226145i	−0.603240	+	0.797560i	$0.706124\pi$
$234$	1.83832	−	5.65776i	0.120175	−	0.369859i
$235$	−0.140641	−	0.432849i	−0.00917442	−	0.0282360i
$236$	61.8271	−	44.9200i	4.02460	−	2.92404i
$237$	8.19475	−	5.95384i	0.532306	−	0.386743i
$238$	−4.03564	−	12.4204i	−0.261592	−	0.805097i
$239$	4.62664	−	14.2393i	0.299272	−	0.921065i	−0.682481	−	0.730904i	$-0.739099\pi$
$239$	4.62664	−	14.2393i	0.299272	−	0.921065i	0.981753	−	0.190162i	$-0.0609012\pi$
$240$	−13.6988	−	9.95274i	−0.884252	−	0.642447i
$241$	18.2746			1.17717			0.588586	−	0.808435i	$-0.299685\pi$
$241$	18.2746			1.17717			0.588586	+	0.808435i	$0.299685\pi$
$242$		0			0
$243$	15.3396			0.984037
$244$	21.1663	+	15.3782i	1.35503	+	0.984489i
$245$	−0.137535	+	0.423289i	−0.00878678	+	0.0270429i
$246$	−4.15226	−	12.7793i	−0.264738	−	0.814781i
$247$	0.396346	−	0.287962i	0.0252189	−	0.0183226i
$248$	59.7326	−	43.3983i	3.79302	−	2.75579i
$249$	−9.37286	−	28.8467i	−0.593981	−	1.82809i
$250$	−3.64419	+	11.2157i	−0.230479	+	0.709341i
$251$	−8.54717	−	6.20988i	−0.539493	−	0.391964i	0.284404	−	0.958705i	$-0.408204\pi$
$251$	−8.54717	−	6.20988i	−0.539493	−	0.391964i	−0.823897	+	0.566740i	$0.808204\pi$
$252$	−25.9012			−1.63162
$253$		0			0
$254$	27.3934			1.71882
$255$	4.88329	+	3.54792i	0.305804	+	0.222179i
$256$	7.36011	−	22.6521i	0.460007	−	1.41576i
$257$	−6.01593	−	18.5151i	−0.375264	−	1.15494i	−0.943301	−	0.331940i	$-0.892297\pi$
$257$	−6.01593	−	18.5151i	−0.375264	−	1.15494i	0.568037	−	0.823003i	$-0.307703\pi$
$258$	−70.0378	+	50.8855i	−4.36036	+	3.16799i
$259$	5.91978	−	4.30097i	0.367837	−	0.267249i
$260$	0.329152	+	1.01303i	0.0204131	+	0.0628251i
$261$	2.99255	−	9.21011i	0.185234	−	0.570092i
$262$	14.9442	+	10.8576i	0.923255	+	0.670784i
$263$	−21.1885			−1.30654			−0.653269	−	0.757126i	$-0.726603\pi$
$263$	−21.1885			−1.30654			−0.653269	+	0.757126i	$0.726603\pi$
$264$		0			0
$265$	1.58989			0.0976665
$266$	−2.37596	−	1.72624i	−0.145680	−	0.105843i
$267$	4.52099	−	13.9142i	0.276680	−	0.851534i
$268$	−10.1495	−	31.2369i	−0.619979	−	1.90810i
$269$	−18.7339	+	13.6110i	−1.14223	+	0.829877i	−0.987428	−	0.158069i	$-0.949473\pi$
$269$	−18.7339	+	13.6110i	−1.14223	+	0.829877i	−0.154799	+	0.987946i	$0.549473\pi$
$270$	5.13771	−	3.73276i	0.312671	−	0.227169i
$271$	−8.28882	−	25.5104i	−0.503510	−	1.54964i	−0.803261	−	0.595627i	$-0.796904\pi$
$271$	−8.28882	−	25.5104i	−0.503510	−	1.54964i	0.299751	−	0.954017i	$-0.403096\pi$
$272$	−20.2328	+	62.2702i	−1.22680	+	3.77569i
$273$	1.02410	+	0.744051i	0.0619813	+	0.0450320i
$274$	−39.1079			−2.36260
$275$		0			0
$276$	−68.1193			−4.10030
$277$	−11.3673	−	8.25884i	−0.682996	−	0.496226i	0.191354	−	0.981521i	$-0.438712\pi$
$277$	−11.3673	−	8.25884i	−0.682996	−	0.496226i	−0.874350	+	0.485295i	$0.838712\pi$
$278$	−12.2758	+	37.7810i	−0.736252	+	2.26595i
$279$	12.4548	+	38.3320i	0.745650	+	2.29488i
$280$	3.21911	−	2.33882i	0.192378	−	0.139771i
$281$	−1.41204	+	1.02591i	−0.0842352	+	0.0612004i	−0.629106	−	0.777320i	$-0.716579\pi$
$281$	−1.41204	+	1.02591i	−0.0842352	+	0.0612004i	0.544871	+	0.838520i	$0.316579\pi$
$282$	2.39790	+	7.37998i	0.142793	+	0.439472i
$283$	1.44166	−	4.43697i	0.0856977	−	0.263750i	−0.899020	−	0.437907i	$-0.855720\pi$
$283$	1.44166	−	4.43697i	0.0856977	−	0.263750i	0.984718	+	0.174157i	$0.0557199\pi$
$284$	25.4256	+	18.4728i	1.50873	+	1.09616i
$285$	1.35740			0.0804053
$286$		0			0
$287$	1.77073			0.104523
$288$	74.0491	+	53.7998i	4.36338	+	3.17018i
$289$	1.95924	−	6.02993i	0.115250	−	0.354702i
$290$	0.737736	+	2.27052i	0.0433213	+	0.133329i
$291$	−12.0590	+	8.76138i	−0.706911	+	0.513601i
$292$	−7.11789	+	5.17145i	−0.416543	+	0.302636i
$293$	−4.48359	−	13.7991i	−0.261934	−	0.806151i	−0.992384	−	0.123184i	$-0.960689\pi$
$293$	−4.48359	−	13.7991i	−0.261934	−	0.806151i	0.730450	−	0.682967i	$-0.239311\pi$
$294$	2.34494	−	7.21698i	0.136760	−	0.420903i
$295$	−5.18487	−	3.76703i	−0.301875	−	0.219325i
$296$	−65.4177			−3.80232
$297$		0			0
$298$	2.70698			0.156811
$299$	1.66800	+	1.21187i	0.0964631	+	0.0700845i
$300$	22.1075	−	68.0399i	1.27638	−	3.92828i
$301$	−3.52540	−	10.8501i	−0.203200	−	0.625387i
$302$	−3.00787	+	2.18535i	−0.173084	+	0.125753i
$303$	−35.3386	+	25.6750i	−2.03015	+	1.47499i
$304$	4.54997	+	14.0034i	0.260959	+	0.803149i
$305$	0.677999	−	2.08667i	0.0388221	−	0.119482i
$306$	−51.5628	−	37.4625i	−2.94765	−	2.14159i
$307$	−2.35679			−0.134509			−0.0672547	−	0.997736i	$-0.521424\pi$
$307$	−2.35679			−0.134509			−0.0672547	+	0.997736i	$0.521424\pi$
$308$		0			0
$309$	39.7816			2.26310
$310$	−8.03845	−	5.84028i	−0.456553	−	0.331706i
$311$	−6.18189	+	19.0259i	−0.350543	+	1.07886i	0.608007	+	0.793932i	$0.291969\pi$
$311$	−6.18189	+	19.0259i	−0.350543	+	1.07886i	−0.958549	+	0.284927i	$0.908031\pi$
$312$	−3.49714	−	10.7631i	−0.197987	−	0.609341i
$313$	−15.1715	+	11.0228i	−0.857545	+	0.623043i	−0.927216	−	0.374527i	$-0.877805\pi$
$313$	−15.1715	+	11.0228i	−0.857545	+	0.623043i	0.0696707	+	0.997570i	$0.477805\pi$
$314$	11.7584	−	8.54301i	0.663567	−	0.482110i
$315$	0.671214	+	2.06578i	0.0378186	+	0.116394i
$316$	5.91779	−	18.2131i	0.332902	−	1.02457i
$317$	−3.39951	−	2.46989i	−0.190936	−	0.138723i	0.488211	−	0.872726i	$-0.337650\pi$
$317$	−3.39951	−	2.46989i	−0.190936	−	0.138723i	−0.679146	+	0.734003i	$0.737650\pi$
$318$	−27.1074			−1.52011
$319$		0			0
$320$	−10.5005			−0.586999
$321$	26.6966	+	19.3962i	1.49006	+	1.08259i
$322$	3.81933	−	11.7547i	0.212843	−	0.655063i
$323$	−1.62196	−	4.99188i	−0.0902482	−	0.277755i
$324$	−0.758081	+	0.550778i	−0.0421156	+	0.0305988i
$325$	−1.75180	+	1.27276i	−0.0971722	+	0.0705998i
$326$	7.87313	+	24.2310i	0.436052	+	1.34203i
$327$	13.6886	−	42.1293i	0.756984	−	2.32976i
$328$	−12.8073	−	9.30504i	−0.707164	−	0.513785i
$329$	−1.02259			−0.0563770
$330$		0			0
$331$	−0.0682694			−0.00375242			−0.00187621	−	0.999998i	$-0.500597\pi$
$331$	−0.0682694			−0.00375242			−0.00187621	+	0.999998i	$0.500597\pi$
$332$	−46.3924	−	33.7060i	−2.54611	−	1.84986i
$333$	11.0352	−	33.9627i	0.604723	−	1.86115i
$334$	16.7166	+	51.4483i	0.914689	+	2.81512i
$335$	−2.22833	+	1.61897i	−0.121747	+	0.0884540i
$336$	−30.7788	+	22.3621i	−1.67912	+	1.21995i
$337$	−6.71992	−	20.6818i	−0.366058	−	1.12661i	−0.949316	−	0.314323i	$-0.898223\pi$
$337$	−6.71992	−	20.6818i	−0.366058	−	1.12661i	0.583259	−	0.812287i	$-0.301777\pi$
$338$	10.6895	−	32.8988i	0.581431	−	1.78946i
$339$	−13.4526	−	9.77388i	−0.730644	−	0.530844i
$340$	11.4118			0.618892
$341$		0			0
$342$	−14.3328			−0.775028
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−31.5177	+	97.0016i	−1.69932	+	5.22998i
$345$	1.76527	+	5.43295i	0.0950391	+	0.292500i
$346$	−23.7206	+	17.2341i	−1.27523	+	0.926509i
$347$	19.3639	−	14.0687i	1.03951	−	0.755248i	0.0693194	−	0.997595i	$-0.477917\pi$
$347$	19.3639	−	14.0687i	1.03951	−	0.755248i	0.970190	+	0.242347i	$0.0779172\pi$
$348$	−9.13557	−	28.1164i	−0.489718	−	1.50720i
$349$	8.16270	−	25.1222i	0.436939	−	1.34476i	−0.454147	−	0.890927i	$-0.650056\pi$
$349$	8.16270	−	25.1222i	0.436939	−	1.34476i	0.891086	−	0.453834i	$-0.149944\pi$
$350$	10.5015	+	7.62975i	0.561326	+	0.407827i
$351$	2.38021			0.127046
$352$		0			0
$353$	−4.44182			−0.236414			−0.118207	−	0.992989i	$-0.537715\pi$
$353$	−4.44182			−0.236414			−0.118207	+	0.992989i	$0.537715\pi$
$354$	88.4010	+	64.2271i	4.69846	+	3.41363i
$355$	0.814434	−	2.50657i	0.0432256	−	0.133035i
$356$	−8.54738	−	26.3061i	−0.453010	−	1.39422i
$357$	10.9719	−	7.97156i	0.580695	−	0.421900i
$358$	36.8463	−	26.7704i	1.94739	−	1.41486i
$359$	4.49080	+	13.8212i	0.237015	+	0.729458i	0.996848	+	0.0793387i	$0.0252809\pi$
$359$	4.49080	+	13.8212i	0.237015	+	0.729458i	−0.759833	+	0.650119i	$0.774719\pi$
$360$	6.00079	−	18.4685i	0.316269	−	0.973377i
$361$	14.4164	+	10.4741i	0.758758	+	0.551270i
$362$	54.8860			2.88475
$363$		0			0
$364$	2.39322			0.125439
$365$	0.596913	+	0.433682i	0.0312438	+	0.0227000i
$366$	−11.5597	+	35.5772i	−0.604237	+	1.85965i
$367$	1.53939	+	4.73777i	0.0803557	+	0.247309i	0.983161	−	0.182739i	$-0.0584964\pi$
$367$	1.53939	+	4.73777i	0.0803557	+	0.247309i	−0.902806	+	0.430049i	$0.858496\pi$
$368$	−50.1310	+	36.4223i	−2.61326	+	1.89864i
$369$	6.99131	−	5.07948i	0.363953	−	0.264427i
$370$	2.72044	+	8.37264i	0.141429	+	0.435273i
$371$	1.10388	−	3.39738i	0.0573104	−	0.176383i
$372$	99.5422	+	72.3217i	5.16103	+	3.74970i
$373$	13.6638			0.707485			0.353743	−	0.935343i	$-0.384909\pi$
$373$	13.6638			0.707485			0.353743	+	0.935343i	$0.384909\pi$
$374$		0			0
$375$	−12.2465			−0.632408
$376$	7.39613	+	5.37360i	0.381426	+	0.277122i
$377$	−0.276506	+	0.850999i	−0.0142408	+	0.0438287i
$378$	−4.40924	−	13.5702i	−0.226787	−	0.697978i
$379$	6.76526	−	4.91525i	0.347508	−	0.252479i	−0.400315	−	0.916378i	$-0.631099\pi$
$379$	6.76526	−	4.91525i	0.347508	−	0.252479i	0.747823	+	0.663898i	$0.231099\pi$
$380$	2.07618	−	1.50843i	0.106506	−	0.0773808i
$381$	8.79069	+	27.0550i	0.450361	+	1.38607i
$382$	−2.12538	+	6.54124i	−0.108744	+	0.334679i
$383$	1.60735	+	1.16781i	0.0821316	+	0.0596721i	0.628093	−	0.778138i	$-0.283836\pi$
$383$	1.60735	+	1.16781i	0.0821316	+	0.0596721i	−0.545962	+	0.837810i	$0.683836\pi$
$384$	73.7352			3.76278
$385$		0			0
$386$	47.3292			2.40899
$387$	−45.0434	−	32.7260i	−2.28969	−	1.66355i
$388$	−8.70834	+	26.8015i	−0.442099	+	1.36064i
$389$	4.58350	+	14.1066i	0.232393	+	0.715231i	0.997457	+	0.0712769i	$0.0227074\pi$
$389$	4.58350	+	14.1066i	0.232393	+	0.715231i	−0.765064	+	0.643955i	$0.777293\pi$
$390$	−1.23211	+	0.895181i	−0.0623904	+	0.0453293i
$391$	17.8705	−	12.9837i	0.903751	−	0.656614i
$392$	−2.76267	−	8.50263i	−0.139536	−	0.429448i
$393$	−5.92777	+	18.2438i	−0.299016	+	0.920278i
$394$	4.73598	+	3.44089i	0.238595	+	0.173350i
$395$	−1.60597			−0.0808050
$396$		0			0
$397$	11.4630			0.575314			0.287657	−	0.957734i	$-0.407124\pi$
$397$	11.4630			0.575314			0.287657	+	0.957734i	$0.407124\pi$
$398$	−31.8759	−	23.1592i	−1.59780	−	1.16087i
$399$	0.942452	−	2.90057i	0.0471816	−	0.145210i
$400$	−20.1103	−	61.8931i	−1.00551	−	3.09465i
$401$	−3.48710	+	2.53353i	−0.174138	+	0.126518i	−0.671440	−	0.741059i	$-0.734324\pi$
$401$	−3.48710	+	2.53353i	−0.174138	+	0.126518i	0.497302	+	0.867577i	$0.334324\pi$
$402$	37.9925	−	27.6032i	1.89489	−	1.37672i
$403$	−1.15080	−	3.54181i	−0.0573256	−	0.176430i
$404$	−25.5196	+	78.5412i	−1.26965	+	3.90757i
$405$	0.0635733	+	0.0461887i	0.00315898	+	0.00229514i
$406$	5.36399			0.266210
$407$		0			0
$408$	−121.247			−6.00263
$409$	−7.53358	−	5.47347i	−0.372512	−	0.270646i	0.385740	−	0.922608i	$-0.373946\pi$
$409$	−7.53358	−	5.47347i	−0.372512	−	0.270646i	−0.758252	+	0.651962i	$0.773946\pi$
$410$	−0.658329	+	2.02613i	−0.0325126	+	0.100063i
$411$	−12.5499	−	38.6247i	−0.619043	−	1.90522i
$412$	60.8471	−	44.2080i	2.99772	−	2.17797i
$413$	−11.6495	+	8.46386i	−0.573235	+	0.416479i
$414$	−18.6395	−	57.3666i	−0.916083	−	2.81941i
$415$	−1.48604	+	4.57356i	−0.0729469	+	0.224507i
$416$	−6.84201	−	4.97101i	−0.335457	−	0.243724i
$417$	−41.2535			−2.02019
$418$		0			0
$419$	−26.3424			−1.28691			−0.643454	−	0.765485i	$-0.722499\pi$
$419$	−26.3424			−1.28691			−0.643454	+	0.765485i	$0.722499\pi$
$420$	5.36452	+	3.89755i	0.261762	+	0.190181i
$421$	4.38162	−	13.4852i	0.213547	−	0.657230i	−0.785706	−	0.618600i	$-0.787700\pi$
$421$	4.38162	−	13.4852i	0.213547	−	0.657230i	0.999254	−	0.0386309i	$-0.0122997\pi$
$422$	−3.03254	−	9.33321i	−0.147622	−	0.454334i
$423$	−4.03743	+	2.93337i	−0.196307	+	0.142625i
$424$	−25.8370	+	18.7717i	−1.25476	+	0.911634i
$425$	7.16884	+	22.0634i	0.347740	+	1.07023i
$426$	−13.8859	+	42.7365i	−0.672775	+	2.07059i
$427$	−3.98817	−	2.89758i	−0.193001	−	0.140223i
$428$	62.3876			3.01562
$429$		0			0
$430$	13.7257			0.661911
$431$	6.14474	+	4.46441i	0.295981	+	0.215043i	0.725858	−	0.687845i	$-0.241443\pi$
$431$	6.14474	+	4.46441i	0.295981	+	0.215043i	−0.429877	+	0.902888i	$0.641443\pi$
$432$	−22.1059	+	68.0348i	−1.06357	+	3.27333i
$433$	6.92224	+	21.3045i	0.332662	+	1.02383i	0.967862	+	0.251480i	$0.0809174\pi$
$433$	6.92224	+	21.3045i	0.332662	+	1.02383i	−0.635201	+	0.772347i	$0.719083\pi$
$434$	−18.0610	+	13.1221i	−0.866956	+	0.629880i
$435$	−2.00572	+	1.45724i	−0.0961669	+	0.0698694i
$436$	−25.8797	−	79.6496i	−1.23941	−	3.81452i
$437$	1.53502	−	4.72431i	0.0734300	−	0.225994i
$438$	−10.1772	−	7.39419i	−0.486287	−	0.353308i
$439$	−15.4051			−0.735244			−0.367622	−	0.929975i	$-0.619828\pi$
$439$	−15.4051			−0.735244			−0.367622	+	0.929975i	$0.619828\pi$
$440$		0			0
$441$	4.88032			0.232396
$442$	4.76431	+	3.46147i	0.226615	+	0.164646i
$443$	6.55423	−	20.1718i	0.311401	−	0.958393i	−0.665810	−	0.746121i	$-0.731914\pi$
$443$	6.55423	−	20.1718i	0.311401	−	0.958393i	0.977211	−	0.212272i	$-0.0680861\pi$
$444$	−33.6879	−	103.681i	−1.59875	−	4.92046i
$445$	−1.87658	+	1.36342i	−0.0889586	+	0.0646322i
$446$	−10.5861	+	7.69125i	−0.501267	+	0.364191i
$447$	0.868682	+	2.67353i	0.0410873	+	0.126454i
$448$	−7.29061	+	22.4382i	−0.344449	+	1.06010i
$449$	9.41020	+	6.83691i	0.444095	+	0.322654i	0.787260	−	0.616621i	$-0.211499\pi$
$449$	9.41020	+	6.83691i	0.444095	+	0.322654i	−0.343165	+	0.939275i	$0.611499\pi$
$450$	63.3490			2.98630
$451$		0			0
$452$	−31.4375			−1.47869
$453$	−3.12359	−	2.26942i	−0.146759	−	0.106627i
$454$	18.9876	−	58.4380i	0.891134	−	2.74263i
$455$	−0.0620190	−	0.190875i	−0.00290750	−	0.00894836i
$456$	−22.0588	+	16.0266i	−1.03300	+	0.750516i
$457$	25.5630	−	18.5726i	1.19579	−	0.868790i	0.201923	−	0.979401i	$-0.435281\pi$
$457$	25.5630	−	18.5726i	1.19579	−	0.868790i	0.993864	+	0.110612i	$0.0352810\pi$
$458$	18.9396	+	58.2902i	0.884992	+	2.72372i
$459$	7.88022	−	24.2528i	0.367817	−	1.13203i
$460$	8.73748	+	6.34815i	0.407387	+	0.295984i
$461$	8.86324			0.412802			0.206401	−	0.978467i	$-0.433825\pi$
$461$	8.86324			0.412802			0.206401	+	0.978467i	$0.433825\pi$
$462$		0			0
$463$	−25.6132			−1.19035			−0.595173	−	0.803597i	$-0.702917\pi$
$463$	−25.6132			−1.19035			−0.595173	+	0.803597i	$0.702917\pi$
$464$	−21.7565	−	15.8070i	−1.01002	−	0.733823i
$465$	3.18854	−	9.81331i	0.147865	−	0.455081i
$466$	−0.490577	−	1.50984i	−0.0227255	−	0.0699420i
$467$	−16.6174	+	12.0732i	−0.768959	+	0.558682i	−0.901645	−	0.432476i	$-0.857640\pi$
$467$	−16.6174	+	12.0732i	−0.768959	+	0.558682i	0.132686	+	0.991158i	$0.457640\pi$
$468$	9.44907	−	6.86515i	0.436784	−	0.317342i
$469$	1.91238	+	5.88569i	0.0883053	+	0.271776i
$470$	0.380181	−	1.17008i	0.0175364	−	0.0539716i
$471$	12.2108	+	8.87167i	0.562644	+	0.408785i
$472$	128.735			5.92551
$473$		0			0
$474$	27.3814			1.25767
$475$	4.22062	+	3.06646i	0.193655	+	0.140699i
$476$	7.92330	−	24.3854i	0.363164	−	1.11770i
$477$	−5.38727	−	16.5803i	−0.246666	−	0.759160i
$478$	32.7430	−	23.7892i	1.49763	−	1.08809i
$479$	−22.2874	+	16.1927i	−1.01834	+	0.739866i	−0.965941	−	0.258761i	$-0.916686\pi$
$479$	−22.2874	+	16.1927i	−1.01834	+	0.739866i	−0.0523962	+	0.998626i	$0.516686\pi$
$480$	−7.24100	−	22.2855i	−0.330505	−	1.01719i
$481$	−1.01963	+	3.13810i	−0.0464911	+	0.143085i
$482$	39.9654	+	29.0365i	1.82037	+	1.32258i
$483$	12.8351			0.584017
$484$		0			0
$485$	2.36327			0.107310
$486$	33.5467	+	24.3731i	1.52171	+	1.10559i
$487$	−3.73952	+	11.5091i	−0.169454	+	0.521525i	−0.999337	−	0.0364123i	$-0.988407\pi$
$487$	−3.73952	+	11.5091i	−0.169454	+	0.521525i	0.829883	+	0.557937i	$0.188407\pi$
$488$	13.6190	+	41.9150i	0.616503	+	1.89740i
$489$	−21.4051	+	15.5517i	−0.967971	+	0.703272i
$490$	−0.973343	+	0.707175i	−0.0439711	+	0.0319469i
$491$	12.1712	+	37.4590i	0.549277	+	1.69050i	0.710597	+	0.703599i	$0.248425\pi$
$491$	12.1712	+	37.4590i	0.549277	+	1.69050i	−0.161320	+	0.986902i	$0.551575\pi$
$492$	8.15226	−	25.0901i	0.367532	−	1.13115i
$493$	7.75569	+	5.63484i	0.349299	+	0.253780i
$494$	1.32432			0.0595842
$495$		0			0
$496$	111.925			5.02560
$497$	−4.79072	−	3.48066i	−0.214893	−	0.156129i
$498$	25.3367	−	77.9783i	1.13536	−	3.49429i
$499$	−10.7486	−	33.0808i	−0.481173	−	1.48090i	−0.837447	−	0.546518i	$-0.815953\pi$
$499$	−10.7486	−	33.0808i	−0.481173	−	1.48090i	0.356274	−	0.934382i	$-0.384047\pi$
$500$	−18.7314	+	13.6092i	−0.837693	+	0.608620i
$501$	−45.4482	+	33.0200i	−2.03048	+	1.47523i
$502$	−8.82520	−	27.1612i	−0.393888	−	1.21226i
$503$	−0.998818	+	3.07404i	−0.0445351	+	0.137065i	−0.970852	−	0.239681i	$-0.922957\pi$
$503$	−0.998818	+	3.07404i	−0.0445351	+	0.137065i	0.926317	+	0.376746i	$0.122957\pi$
$504$	−35.2982	−	25.6457i	−1.57231	−	1.14235i
$505$	6.92550			0.308181
$506$		0			0
$507$	35.9227			1.59538
$508$	43.5109	+	31.6125i	1.93048	+	1.40258i
$509$	−4.08573	+	12.5746i	−0.181097	+	0.557359i	−0.999859	−	0.0167737i	$-0.994661\pi$
$509$	−4.08573	+	12.5746i	−0.181097	+	0.557359i	0.818763	+	0.574132i	$0.194661\pi$
$510$	5.04214	+	15.5181i	0.223270	+	0.687154i
$511$	1.34116	−	0.974409i	0.0593294	−	0.0431053i
$512$	9.58778	−	6.96593i	0.423724	−	0.307854i
$513$	−1.77211	−	5.45399i	−0.0782406	−	0.240800i
$514$	16.2622	−	50.0501i	0.717297	−	2.20761i
$515$	−5.10269	−	3.70732i	−0.224851	−	0.163364i
$516$	−169.969			−7.48245
$517$		0			0
$518$	19.7800			0.869082
$519$	−24.6332	−	17.8971i	−1.08128	−	0.785594i
$520$	−0.554463	+	1.70646i	−0.0243148	+	0.0748332i
$521$	2.25656	+	6.94499i	0.0988619	+	0.304266i	0.988241	−	0.152905i	$-0.0488629\pi$
$521$	2.25656	+	6.94499i	0.0988619	+	0.304266i	−0.889379	+	0.457171i	$0.848863\pi$
$522$	21.1784	−	15.3870i	0.926955	−	0.673472i
$523$	6.77962	−	4.92568i	0.296452	−	0.215385i	−0.429609	−	0.903015i	$-0.641349\pi$
$523$	6.77962	−	4.92568i	0.296452	−	0.215385i	0.726061	+	0.687630i	$0.241349\pi$
$524$	11.2070	+	34.4917i	0.489581	+	1.50678i
$525$	−4.16551	+	12.8201i	−0.181798	+	0.559516i
$526$	−46.3378	−	33.6664i	−2.02042	−	1.46792i
$527$	−39.8988			−1.73802
$528$		0			0
$529$	−2.09483			−0.0910794
$530$	3.47699	+	2.52618i	0.151031	+	0.109730i
$531$	−21.7160	+	66.8351i	−0.942396	+	2.90040i
$532$	−1.78180	−	5.48381i	−0.0772507	−	0.237753i
$533$	−0.645985	+	0.469336i	−0.0279807	+	0.0203292i
$534$	31.9953	−	23.2460i	1.38457	−	1.00595i
$535$	−1.61674	−	4.97581i	−0.0698977	−	0.215123i
$536$	17.0970	−	52.6192i	0.738479	−	2.27280i
$537$	38.2638	+	27.8003i	1.65120	+	1.19967i
$538$	−62.5963			−2.69872
$539$		0			0
$540$	12.4682			0.536548
$541$	−3.07239	−	2.23222i	−0.132092	−	0.0959706i	0.519777	−	0.854302i	$-0.326015\pi$
$541$	−3.07239	−	2.23222i	−0.132092	−	0.0959706i	−0.651869	+	0.758331i	$0.726015\pi$
$542$	22.4063	−	68.9595i	0.962433	−	2.96206i
$543$	17.6132	+	54.2079i	0.755855	+	2.32628i
$544$	−73.3034	+	53.2580i	−3.14286	+	2.28342i
$545$	−5.68191	+	4.12815i	−0.243386	+	0.176830i
$546$	1.05741	+	3.25438i	0.0452530	+	0.139275i
$547$	−2.80892	+	8.64496i	−0.120101	+	0.369632i	−0.992977	−	0.118310i	$-0.962252\pi$
$547$	−2.80892	+	8.64496i	−0.120101	+	0.369632i	0.872876	+	0.487942i	$0.162252\pi$
$548$	−62.1178	−	45.1312i	−2.65354	−	1.92791i
$549$	−24.0583			−1.02678
$550$		0			0
$551$	2.15583			0.0918416
$552$	−92.8332	−	67.4473i	−3.95125	−	2.87075i
$553$	−1.11504	+	3.43173i	−0.0474161	+	0.145932i
$554$	−11.7371	−	36.1230i	−0.498661	−	1.53472i
$555$	−7.39619	+	5.37365i	−0.313951	+	0.228099i
$556$	−63.0984	+	45.8436i	−2.67597	+	1.94420i
$557$	−5.63561	−	17.3446i	−0.238788	−	0.734915i	−0.996596	−	0.0824374i	$-0.973730\pi$
$557$	−5.63561	−	17.3446i	−0.238788	−	0.734915i	0.757808	−	0.652478i	$-0.226270\pi$
$558$	−33.6678	+	103.619i	−1.42527	+	4.38654i
$559$	4.16194	+	3.02382i	0.176031	+	0.127894i
$560$	6.03187			0.254893
$561$		0			0
$562$	−4.71809			−0.199021
$563$	−12.6000	−	9.15442i	−0.531026	−	0.385813i	0.289716	−	0.957113i	$-0.406439\pi$
$563$	−12.6000	−	9.15442i	−0.531026	−	0.385813i	−0.820741	+	0.571300i	$0.806439\pi$
$564$	−4.70787	+	14.4893i	−0.198237	+	0.610112i
$565$	0.814684	+	2.50734i	0.0342740	+	0.105485i
$566$	10.2027	−	7.41270i	0.428852	−	0.311579i
$567$	0.142838	−	0.103778i	0.00599864	−	0.00435827i
$568$	16.3596	+	50.3496i	0.686433	+	2.11262i
$569$	−7.54788	+	23.2300i	−0.316423	+	0.973851i	0.658741	+	0.752370i	$0.271089\pi$
$569$	−7.54788	+	23.2300i	−0.316423	+	0.973851i	−0.975165	+	0.221482i	$0.928911\pi$
$570$	2.96854	+	2.15677i	0.124338	+	0.0903371i
$571$	14.9541			0.625808			0.312904	−	0.949785i	$-0.398698\pi$
$571$	14.9541			0.625808			0.312904	+	0.949785i	$0.398698\pi$
$572$		0			0
$573$	−7.14247			−0.298381
$574$	3.87247	+	2.81351i	0.161634	+	0.117434i
$575$	−6.78459	+	20.8808i	−0.282937	+	0.870790i
$576$	35.5805	+	109.506i	1.48252	+	4.56273i
$577$	17.3682	−	12.6187i	0.723046	−	0.525324i	−0.164310	−	0.986409i	$-0.552540\pi$
$577$	17.3682	−	12.6187i	0.723046	−	0.525324i	0.887356	+	0.461085i	$0.152540\pi$
$578$	13.8657	−	10.0740i	0.576736	−	0.419023i
$579$	15.1882	+	46.7444i	0.631199	+	1.94263i
$580$	−1.44842	+	4.45778i	−0.0601423	+	0.185099i
$581$	8.74129	+	6.35092i	0.362650	+	0.263481i
$582$	−40.2932			−1.67021
$583$		0			0
$584$	−14.8207			−0.613286
$585$	−0.792408	−	0.575718i	−0.0327620	−	0.0238030i
$586$	12.1200	−	37.3016i	0.500674	−	1.54092i
$587$	−6.38924	−	19.6641i	−0.263712	−	0.811623i	−0.991987	−	0.126338i	$-0.959678\pi$
$587$	−6.38924	−	19.6641i	−0.263712	−	0.811623i	0.728275	−	0.685285i	$-0.240322\pi$
$588$	12.0532	−	8.75713i	0.497064	−	0.361138i
$589$	−7.25887	+	5.27388i	−0.299097	+	0.217306i
$590$	−5.35353	−	16.4765i	−0.220401	−	0.678326i
$591$	−1.87858	+	5.78167i	−0.0772744	+	0.237826i
$592$	−80.2282	−	58.2892i	−3.29736	−	2.39567i
$593$	−3.30237			−0.135612			−0.0678060	−	0.997699i	$-0.521600\pi$
$593$	−3.30237			−0.135612			−0.0678060	+	0.997699i	$0.521600\pi$
$594$		0			0
$595$	−2.15022			−0.0881505
$596$	4.29967	+	3.12390i	0.176121	+	0.127960i
$597$	12.6439	−	38.9140i	0.517481	−	1.59264i
$598$	1.72226	+	5.30057i	0.0704285	+	0.216757i
$599$	−31.4880	+	22.8773i	−1.28656	+	0.934743i	−0.999730	−	0.0232380i	$-0.992602\pi$
$599$	−31.4880	+	22.8773i	−1.28656	+	0.934743i	−0.286833	+	0.957981i	$0.592602\pi$
$600$	97.4969	−	70.8356i	3.98029	−	2.89185i
$601$	−13.7137	−	42.2063i	−0.559392	−	1.72163i	−0.684054	−	0.729431i	$-0.739785\pi$
$601$	−13.7137	−	42.2063i	−0.559392	−	1.72163i	0.124663	−	0.992199i	$-0.460215\pi$
$602$	9.52984	−	29.3298i	0.388407	−	1.19539i
$603$	24.4341	+	17.7524i	0.995034	+	0.722935i
$604$	−7.29954			−0.297014
$605$		0			0
$606$	−118.078			−4.79660
$607$	−15.2952	−	11.1126i	−0.620812	−	0.451046i	0.232393	−	0.972622i	$-0.425344\pi$
$607$	−15.2952	−	11.1126i	−0.620812	−	0.451046i	−0.853205	+	0.521576i	$0.825344\pi$
$608$	−6.29652	+	19.3787i	−0.255358	+	0.785910i
$609$	1.72133	+	5.29771i	0.0697519	+	0.214674i
$610$	4.79824	−	3.48612i	0.194275	−	0.141149i
$611$	0.373052	−	0.271038i	0.0150921	−	0.0109650i
$612$	−38.6682	−	119.009i	−1.56307	−	4.81064i
$613$	2.99164	−	9.20733i	0.120831	−	0.371881i	−0.872287	−	0.488994i	$-0.837364\pi$
$613$	2.99164	−	9.20733i	0.120831	−	0.371881i	0.993119	+	0.117113i	$0.0373641\pi$
$614$	−5.15415	−	3.74471i	−0.208004	−	0.151124i
$615$	−2.21236			−0.0892108
$616$		0			0
$617$	−26.2775			−1.05789			−0.528947	−	0.848655i	$-0.677413\pi$
$617$	−26.2775			−1.05789			−0.528947	+	0.848655i	$0.677413\pi$
$618$	86.9997	+	63.2090i	3.49964	+	2.54264i
$619$	−7.66219	+	23.5818i	−0.307970	+	0.947833i	0.670583	+	0.741835i	$0.266044\pi$
$619$	−7.66219	+	23.5818i	−0.307970	+	0.947833i	−0.978552	+	0.205998i	$0.933956\pi$
$620$	−6.02824	−	18.5530i	−0.242100	−	0.745107i
$621$	19.5249	−	14.1856i	0.783506	−	0.569250i
$622$	−43.7496	+	31.7859i	−1.75420	+	1.27450i
$623$	1.61050	+	4.95662i	0.0645235	+	0.198583i
$624$	5.30137	−	16.3159i	0.212225	−	0.653160i
$625$	−17.8533	−	12.9712i	−0.714132	−	0.518847i
$626$	−50.6931			−2.02611
$627$		0			0
$628$	28.5355			1.13869
$629$	28.5995	+	20.7787i	1.14034	+	0.828503i
$630$	−1.81442	+	5.58422i	−0.0722884	+	0.222481i
$631$	−3.64972	−	11.2327i	−0.145293	−	0.447166i	0.851755	−	0.523940i	$-0.175538\pi$
$631$	−3.64972	−	11.2327i	−0.145293	−	0.447166i	−0.997049	+	0.0767733i	$0.975538\pi$
$632$	26.0982	−	18.9615i	1.03813	−	0.754247i
$633$	8.24474	−	5.99015i	0.327699	−	0.238087i
$634$	−3.51010	−	10.8030i	−0.139404	−	0.429041i
$635$	1.39374	−	4.28949i	0.0553089	−	0.170223i
$636$	−43.0565	−	31.2824i	−1.70730	−	1.24043i
$637$	−0.450933			−0.0178666
$638$		0			0
$639$	−28.8995			−1.14325
$640$	−9.45783	−	6.87151i	−0.373853	−	0.271620i
$641$	−6.95851	+	21.4161i	−0.274845	+	0.845885i	0.714416	+	0.699722i	$0.246693\pi$
$641$	−6.95851	+	21.4161i	−0.274845	+	0.845885i	−0.989260	+	0.146164i	$0.953307\pi$
$642$	27.5651	+	84.8365i	1.08791	+	3.34823i
$643$	−11.2374	+	8.16442i	−0.443158	+	0.321973i	−0.786889	−	0.617095i	$-0.788309\pi$
$643$	−11.2374	+	8.16442i	−0.443158	+	0.321973i	0.343730	+	0.939068i	$0.388309\pi$
$644$	19.6316	−	14.2632i	0.773593	−	0.562048i
$645$	4.40464	+	13.5561i	0.173432	+	0.533770i
$646$	4.38447	−	13.4940i	0.172505	−	0.530915i
$647$	−41.1074	−	29.8663i	−1.61610	−	1.17417i	−0.836780	−	0.547539i	$-0.815565\pi$
$647$	−41.1074	−	29.8663i	−1.61610	−	1.17417i	−0.779320	−	0.626627i	$-0.784435\pi$
$648$	−1.57846			−0.0620078
$649$		0			0
$650$	−5.85334			−0.229587
$651$	−18.7558	−	13.6269i	−0.735099	−	0.534081i
$652$	−15.4576	+	47.5735i	−0.605364	+	1.86312i
$653$	−1.48764	−	4.57849i	−0.0582159	−	0.179170i	0.917720	−	0.397228i	$-0.130028\pi$
$653$	−1.48764	−	4.57849i	−0.0582159	−	0.179170i	−0.975936	+	0.218058i	$0.930028\pi$
$654$	96.8753	−	70.3840i	3.78812	−	2.75223i
$655$	2.46051	−	1.78766i	0.0961401	−	0.0698499i
$656$	−7.41577	−	22.8234i	−0.289537	−	0.891104i
$657$	2.50008	−	7.69444i	0.0975373	−	0.300189i
$658$	−2.23632	−	1.62478i	−0.0871810	−	0.0633407i
$659$	28.0409			1.09232			0.546159	−	0.837681i	$-0.316089\pi$
$659$	28.0409			1.09232			0.546159	+	0.837681i	$0.316089\pi$
$660$		0			0
$661$	−41.7390			−1.62346			−0.811730	−	0.584033i	$-0.801474\pi$
$661$	−41.7390			−1.62346			−0.811730	+	0.584033i	$0.801474\pi$
$662$	−0.149300	−	0.108473i	−0.00580273	−	0.00421593i
$663$	−1.88981	+	5.81625i	−0.0733943	+	0.225884i
$664$	−29.8502	−	91.8695i	−1.15841	−	3.56523i
$665$	−0.391195	+	0.284220i	−0.0151699	+	0.0110216i
$666$	78.0965	−	56.7404i	3.02618	−	2.19865i
$667$	2.80362	+	8.62866i	0.108557	+	0.334103i
$668$	−32.8201	+	101.010i	−1.26985	+	3.90819i
$669$	−10.9934	−	7.98714i	−0.425028	−	0.308801i
$670$	−7.44559			−0.287648
$671$		0			0
$672$	−52.6484			−2.03096
$673$	−23.2792	−	16.9133i	−0.897348	−	0.651962i	0.0404352	−	0.999182i	$-0.487126\pi$
$673$	−23.2792	−	16.9133i	−0.897348	−	0.651962i	−0.937784	+	0.347220i	$0.887126\pi$
$674$	18.1653	−	55.9070i	0.699700	−	2.15346i
$675$	7.83249	+	24.1059i	0.301473	+	0.927838i
$676$	54.9446	−	39.9196i	2.11326	−	1.53537i
$677$	−9.93971	+	7.22162i	−0.382014	+	0.277549i	−0.762175	−	0.647371i	$-0.775869\pi$
$677$	−9.93971	+	7.22162i	−0.382014	+	0.277549i	0.380161	+	0.924920i	$0.375869\pi$
$678$	−13.8902	−	42.7496i	−0.533450	−	1.64179i
$679$	1.64083	−	5.04996i	0.0629694	−	0.193800i
$680$	15.5521	+	11.2992i	0.596394	+	0.433306i
$681$	63.8092			2.44517
$682$		0			0
$683$	30.5940			1.17065			0.585323	−	0.810800i	$-0.300968\pi$
$683$	30.5940			1.17065			0.585323	+	0.810800i	$0.300968\pi$
$684$	−22.7657	−	16.5403i	−0.870470	−	0.632433i
$685$	−1.98976	+	6.12384i	−0.0760247	+	0.233980i
$686$	0.835334	+	2.57089i	0.0318932	+	0.0981571i
$687$	−51.4922	+	37.4113i	−1.96455	+	1.42733i
$688$	−125.085	+	90.8795i	−4.76881	+	3.46475i
$689$	0.497774	+	1.53199i	0.0189637	+	0.0583642i
$690$	−4.77188	+	14.6863i	−0.181662	+	0.559099i
$691$	13.8440	+	10.0583i	0.526651	+	0.382634i	0.819103	−	0.573646i	$-0.194471\pi$
$691$	13.8440	+	10.0583i	0.526651	+	0.382634i	−0.292453	+	0.956280i	$0.594471\pi$
$692$	−57.5655			−2.18831
$693$		0			0
$694$	64.7013			2.45603
$695$	5.29148	+	3.84449i	0.200717	+	0.145830i
$696$	15.3890	−	47.3626i	0.583320	−	1.79528i
$697$	2.64355	+	8.13601i	0.100132	+	0.308173i
$698$	57.7679	−	41.9709i	2.18655	−	1.58862i
$699$	1.33376	−	0.969031i	0.0504473	−	0.0366521i
$700$	7.87531	+	24.2377i	0.297659	+	0.916099i
$701$	−4.20065	+	12.9283i	−0.158657	+	0.488295i	−0.998513	−	0.0545140i	$-0.982639\pi$
$701$	−4.20065	+	12.9283i	−0.158657	+	0.488295i	0.839856	+	0.542809i	$0.182639\pi$
$702$	5.20536	+	3.78192i	0.196464	+	0.142739i
$703$	7.94974			0.299830
$704$		0			0
$705$	1.27762			0.0481180
$706$	−9.71395	−	7.05760i	−0.365589	−	0.265616i
$707$	4.80842	−	14.7988i	0.180839	−	0.556566i
$708$	66.2942	+	204.032i	2.49149	+	7.66801i
$709$	−23.9465	+	17.3982i	−0.899330	+	0.653401i	−0.938294	−	0.345839i	$-0.887594\pi$
$709$	−23.9465	+	17.3982i	−0.899330	+	0.653401i	0.0389641	+	0.999241i	$0.487594\pi$
$710$	5.76379	−	4.18764i	0.216311	−	0.157159i
$711$	5.44173	+	16.7479i	0.204081	+	0.628096i
$712$	14.3982	−	44.3132i	0.539596	−	1.66071i
$713$	−30.5486	−	22.1949i	−1.14405	−	0.831204i
$714$	36.6608			1.37200
$715$		0			0
$716$	89.4190			3.34174
$717$	34.0026	+	24.7044i	1.26985	+	0.922601i
$718$	−12.1395	+	37.3615i	−0.453042	+	1.39432i
$719$	14.0728	+	43.3118i	0.524828	+	1.61526i	0.764655	+	0.644440i	$0.222909\pi$
$719$	14.0728	+	43.3118i	0.524828	+	1.61526i	−0.239826	+	0.970816i	$0.577091\pi$
$720$	23.8154	−	17.3029i	0.887548	−	0.644841i
$721$	−11.4649	+	8.32970i	−0.426973	+	0.310214i
$722$	14.8854	+	45.8124i	0.553976	+	1.70496i
$723$	−15.8527	+	48.7895i	−0.589568	+	1.81450i
$724$	87.1793	+	63.3394i	3.23999	+	2.35399i
$725$	−9.52850			−0.353880
$726$		0			0
$727$	−43.8796			−1.62740			−0.813702	−	0.581283i	$-0.802551\pi$
$727$	−43.8796			−1.62740			−0.813702	+	0.581283i	$0.802551\pi$
$728$	3.26150	+	2.36962i	0.120879	+	0.0878238i
$729$	−13.4703	+	41.4574i	−0.498901	+	1.53546i
$730$	0.616330	+	1.89687i	0.0228114	+	0.0702062i
$731$	44.5898	−	32.3964i	1.64921	−	1.19822i
$732$	−59.4178	+	43.1696i	−2.19615	+	1.59559i
$733$	−4.35337	−	13.3983i	−0.160795	−	0.494877i	0.837907	−	0.545814i	$-0.183779\pi$
$733$	−4.35337	−	13.3983i	−0.160795	−	0.494877i	−0.998702	+	0.0509365i	$0.983779\pi$
$734$	−4.16128	+	12.8071i	−0.153596	+	0.472719i
$735$	−1.01079	−	0.734380i	−0.0372835	−	0.0270880i
$736$	−85.7513			−3.16083
$737$		0			0
$738$	23.3603			0.859904
$739$	−31.9542	−	23.2161i	−1.17545	−	0.854016i	−0.183801	−	0.982963i	$-0.558840\pi$
$739$	−31.9542	−	23.2161i	−1.17545	−	0.854016i	−0.991651	+	0.128947i	$0.958840\pi$
$740$	−5.34112	+	16.4383i	−0.196343	+	0.604283i
$741$	0.424983	+	1.30796i	0.0156121	+	0.0480492i
$742$	7.81220	−	5.67589i	0.286795	−	0.208369i
$743$	15.0608	−	10.9423i	0.552528	−	0.401435i	−0.276189	−	0.961103i	$-0.589072\pi$
$743$	15.0608	−	10.9423i	0.552528	−	0.401435i	0.828717	+	0.559668i	$0.189072\pi$
$744$	64.0484	+	197.121i	2.34813	+	7.22679i
$745$	0.137727	−	0.423881i	0.00504593	−	0.0155298i
$746$	29.8818	+	21.7104i	1.09405	+	0.794875i
$747$	52.7310			1.92933
$748$		0			0
$749$	−11.7551			−0.429523
$750$	−26.7823	−	19.4585i	−0.977952	−	0.710524i
$751$	−4.88432	+	15.0324i	−0.178231	+	0.548539i	−0.999766	−	0.0216187i	$-0.993118\pi$
$751$	−4.88432	+	15.0324i	−0.178231	+	0.548539i	0.821535	+	0.570158i	$0.193118\pi$
$752$	4.28256	+	13.1804i	0.156169	+	0.480638i
$753$	23.9935	−	17.4323i	0.874373	−	0.635269i
$754$	−1.95685	+	1.42174i	−0.0712643	+	0.0517765i
$755$	0.189164	+	0.582185i	0.00688437	+	0.0211879i
$756$	8.65679	−	26.6429i	0.314844	−	0.968992i
$757$	2.92145	+	2.12256i	0.106182	+	0.0771458i	0.639609	−	0.768700i	$-0.279096\pi$
$757$	2.92145	+	2.12256i	0.106182	+	0.0771458i	−0.533427	+	0.845846i	$0.679096\pi$
$758$	22.6050			0.821051
$759$		0			0
$760$	4.32297			0.156811
$761$	32.0224	+	23.2657i	1.16081	+	0.843380i	0.989881	−	0.141903i	$-0.0453221\pi$
$761$	32.0224	+	23.2657i	1.16081	+	0.843380i	0.170932	+	0.985283i	$0.445322\pi$
$762$	−23.7630	+	73.1349i	−0.860841	+	2.64940i
$763$	4.87628	+	15.0076i	0.176533	+	0.543313i
$764$	−10.9246	+	7.93718i	−0.395238	+	0.287157i
$765$	−8.48964	+	6.16808i	−0.306943	+	0.223007i
$766$	1.65963	+	5.10782i	0.0599649	+	0.184553i
$767$	2.00652	−	6.17545i	0.0724514	−	0.222982i
$768$	54.0918	+	39.3000i	1.95187	+	1.41812i
$769$	10.5472			0.380341			0.190171	−	0.981751i	$-0.439096\pi$
$769$	10.5472			0.380341			0.190171	+	0.981751i	$0.439096\pi$
$770$		0			0
$771$	54.6503			1.96818
$772$	75.1761	+	54.6187i	2.70565	+	1.96577i
$773$	12.8437	−	39.5289i	0.461957	−	1.42176i	−0.400813	−	0.916160i	$-0.631272\pi$
$773$	12.8437	−	39.5289i	0.461957	−	1.42176i	0.862770	−	0.505597i	$-0.168728\pi$
$774$	−46.5086	−	143.139i	−1.67172	−	5.14502i
$775$	32.0833	−	23.3099i	1.15246	−	0.837315i
$776$	−38.4049	+	27.9028i	−1.37866	+	1.00165i
$777$	6.34749	+	19.5356i	0.227715	+	0.700835i
$778$	−12.3901	+	38.1328i	−0.444207	+	1.36713i
$779$	1.55638	+	1.13077i	0.0557630	+	0.0405142i
$780$	−2.99010			−0.107063
$781$		0			0
$782$	59.7114			2.13527
$783$	8.47367	+	6.15648i	0.302824	+	0.220015i
$784$	4.18797	−	12.8893i	0.149570	−	0.460331i
$785$	−0.739482	−	2.27589i	−0.0263932	−	0.0812300i
$786$	−41.9512	+	30.4793i	−1.49635	+	1.08716i
$787$	9.34204	−	6.78739i	0.333008	−	0.241944i	−0.408698	−	0.912670i	$-0.634017\pi$
$787$	9.34204	−	6.78739i	0.333008	−	0.241944i	0.741706	+	0.670725i	$0.234017\pi$
$788$	3.55164	+	10.9308i	0.126522	+	0.389394i
$789$	18.3804	−	56.5690i	0.654359	−	2.01391i
$790$	−3.51214	−	2.55172i	−0.124956	−	0.0907862i
$791$	5.92347			0.210614
$792$		0			0
$793$	2.22294			0.0789390
$794$	25.0689	+	18.2136i	0.889662	+	0.646377i
$795$	−1.37919	+	4.24470i	−0.0489147	+	0.150544i
$796$	−23.9046	−	73.5707i	−0.847275	−	2.60765i
$797$	−34.2340	+	24.8724i	−1.21263	+	0.881027i	−0.995467	−	0.0951081i	$-0.969680\pi$
$797$	−34.2340	+	24.8724i	−1.21263	+	0.881027i	−0.217163	+	0.976135i	$0.569680\pi$
$798$	6.66979	−	4.84588i	0.236108	−	0.171542i
$799$	−1.52663	−	4.69849i	−0.0540084	−	0.166221i
$800$	27.8298	−	85.6513i	0.983932	−	3.02823i
$801$	20.5772	+	14.9502i	0.727058	+	0.528239i
$802$	−11.6516			−0.411431
$803$		0			0
$804$	92.2006			3.25167
$805$	−1.64632	−	1.19612i	−0.0580253	−	0.0421578i
$806$	3.11085	−	9.57421i	0.109575	−	0.337237i
$807$	−20.0875	−	61.8229i	−0.707113	−	2.17627i
$808$	−112.545	+	81.7685i	−3.95931	+	2.87661i
$809$	−14.5473	+	10.5692i	−0.511456	+	0.371594i	−0.813375	−	0.581739i	$-0.802372\pi$
$809$	−14.5473	+	10.5692i	−0.511456	+	0.371594i	0.301920	+	0.953333i	$0.402372\pi$
$810$	0.0656413	+	0.202023i	0.00230640	+	0.00709837i
$811$	−9.61662	+	29.5969i	−0.337685	+	1.03929i	0.627699	+	0.778456i	$0.283997\pi$
$811$	−9.61662	+	29.5969i	−0.337685	+	1.03929i	−0.965384	+	0.260832i	$0.916003\pi$
$812$	8.51999	+	6.19014i	0.298993	+	0.217231i
$813$	75.2978			2.64081
$814$		0			0
$815$	4.19486			0.146940
$816$	−148.698	−	108.035i	−5.20545	−	3.78198i
$817$	3.83012	−	11.7879i	0.133999	−	0.412407i
$818$	−7.77864	−	23.9402i	−0.271974	−	0.837050i
$819$	−1.78040	+	1.29354i	−0.0622123	+	0.0451999i
$820$	−3.38386	+	2.45852i	−0.118169	+	0.0858551i
$821$	−15.1009	−	46.4758i	−0.527025	−	1.62202i	−0.760277	−	0.649599i	$-0.774937\pi$
$821$	−15.1009	−	46.4758i	−0.527025	−	1.62202i	0.233253	−	0.972416i	$-0.425063\pi$
$822$	33.9249	−	104.410i	1.18327	−	3.64172i
$823$	−23.9325	−	17.3879i	−0.834233	−	0.606106i	0.0865208	−	0.996250i	$-0.472425\pi$
$823$	−23.9325	−	17.3879i	−0.834233	−	0.606106i	−0.920754	+	0.390144i	$0.872425\pi$
$824$	126.695			4.41361
$825$		0			0
$826$	−38.9249			−1.35437
$827$	20.5429	+	14.9253i	0.714346	+	0.519003i	0.884573	−	0.466402i	$-0.154450\pi$
$827$	20.5429	+	14.9253i	0.714346	+	0.519003i	−0.170227	+	0.985405i	$0.554450\pi$
$828$	36.5956	−	112.630i	1.27178	−	3.91415i
$829$	2.19272	+	6.74851i	0.0761565	+	0.234385i	0.981887	−	0.189469i	$-0.0606767\pi$
$829$	2.19272	+	6.74851i	0.0761565	+	0.234385i	−0.905730	+	0.423855i	$0.860677\pi$
$830$	−10.5168	+	7.64090i	−0.365043	+	0.265220i
$831$	31.9102	−	23.1841i	1.10695	−	0.804249i
$832$	−3.28758	−	10.1181i	−0.113976	−	0.350783i
$833$	−1.49291	+	4.59472i	−0.0517264	+	0.159198i
$834$	−90.2187	−	65.5477i	−3.12402	−	2.26973i
$835$	8.90671			0.308230
$836$		0			0
$837$	−43.5923			−1.50677
$838$	−57.6089	−	41.8553i	−1.99007	−	1.44587i
$839$	−7.33250	+	22.5671i	−0.253146	+	0.779103i	0.741043	+	0.671457i	$0.234331\pi$
$839$	−7.33250	+	22.5671i	−0.253146	+	0.779103i	−0.994189	+	0.107646i	$0.965669\pi$
$840$	3.45169	+	10.6232i	0.119095	+	0.366536i
$841$	20.2760	−	14.7314i	0.699172	−	0.507978i
$842$	31.0090	−	22.5293i	1.06864	−	0.776413i
$843$	−1.51406	−	4.65980i	−0.0521470	−	0.160492i
$844$	5.95389	−	18.3242i	0.204941	−	0.630744i
$845$	−4.60771	−	3.34769i	−0.158510	−	0.115164i
$846$	−13.4904			−0.463810
$847$		0			0
$848$	−48.4127			−1.66250
$849$	10.5952	+	7.69787i	0.363627	+	0.264190i
$850$	−19.3788	+	59.6418i	−0.664687	+	2.04570i
$851$	10.3385	+	31.8186i	0.354399	+	1.09073i
$852$	−71.3746	+	51.8566i	−2.44525	+	1.77658i
$853$	−31.2719	+	22.7204i	−1.07073	+	0.777931i	−0.976043	−	0.217576i	$-0.930185\pi$
$853$	−31.2719	+	22.7204i	−1.07073	+	0.777931i	−0.0946872	+	0.995507i	$0.530185\pi$
$854$	−4.11790	−	12.6736i	−0.140912	−	0.433682i
$855$	−0.729232	+	2.24435i	−0.0249392	+	0.0767550i
$856$	85.0221	+	61.7722i	2.90600	+	2.11133i
$857$	−34.0838			−1.16428			−0.582139	−	0.813089i	$-0.697784\pi$
$857$	−34.0838			−1.16428			−0.582139	+	0.813089i	$0.697784\pi$
$858$		0			0
$859$	56.7283			1.93555			0.967773	−	0.251825i	$-0.0810308\pi$
$859$	56.7283			1.93555			0.967773	+	0.251825i	$0.0810308\pi$
$860$	21.8014	+	15.8397i	0.743422	+	0.540128i
$861$	−1.53606	+	4.72749i	−0.0523486	+	0.161112i
$862$	6.34462	+	19.5267i	0.216099	+	0.665083i
$863$	−19.7343	+	14.3378i	−0.671764	+	0.488065i	−0.870615	−	0.491964i	$-0.836279\pi$
$863$	−19.7343	+	14.3378i	−0.671764	+	0.488065i	0.198851	+	0.980030i	$0.436279\pi$
$864$	−80.0893	+	58.1883i	−2.72469	+	1.97961i
$865$	1.49178	+	4.59122i	0.0507220	+	0.156106i
$866$	−18.7122	+	57.5902i	−0.635866	+	1.95699i
$867$	14.3991	+	10.4616i	0.489019	+	0.355293i
$868$	−43.8306			−1.48771
$869$		0			0
$870$	−6.70178			−0.227212
$871$	−2.25767	−	1.64029i	−0.0764983	−	0.0555792i
$872$	43.5949	−	134.171i	1.47631	−	4.54361i
$873$	−8.00779	−	24.6454i	−0.271023	−	0.834122i
$874$	10.8634	−	7.89274i	0.367461	−	0.266976i
$875$	3.52938	−	2.56425i	0.119315	−	0.0866874i
$876$	−7.63217	−	23.4894i	−0.257867	−	0.793633i
$877$	−9.42347	+	29.0025i	−0.318208	+	0.979344i	0.656206	+	0.754582i	$0.272160\pi$
$877$	−9.42347	+	29.0025i	−0.318208	+	0.979344i	−0.974414	+	0.224762i	$0.927840\pi$
$878$	−33.6898	−	24.4771i	−1.13698	−	0.826062i
$879$	40.7301			1.37379
$880$		0			0
$881$	2.10056			0.0707697			0.0353848	−	0.999374i	$-0.488734\pi$
$881$	2.10056			0.0707697			0.0353848	+	0.999374i	$0.488734\pi$
$882$	10.6729	+	7.75433i	0.359376	+	0.261102i
$883$	13.9662	−	42.9835i	0.469999	−	1.44651i	−0.382585	−	0.923920i	$-0.624966\pi$
$883$	13.9662	−	42.9835i	0.469999	−	1.44651i	0.852585	−	0.522589i	$-0.175034\pi$
$884$	3.57288	+	10.9962i	0.120169	+	0.369842i
$885$	14.5549	−	10.5748i	0.489259	−	0.355467i
$886$	46.3847	−	33.7004i	1.55832	−	1.13219i
$887$	−1.60305	−	4.93369i	−0.0538252	−	0.165657i	0.920530	−	0.390671i	$-0.127757\pi$
$887$	−1.60305	−	4.93369i	−0.0538252	−	0.165657i	−0.974355	+	0.225014i	$0.927757\pi$
$888$	56.7478	−	174.652i	1.90433	−	5.86093i
$889$	−8.19835	−	5.95645i	−0.274964	−	0.199773i
$890$	−6.27029			−0.210181
$891$		0			0
$892$	−25.6905			−0.860181
$893$	−0.898798	−	0.653015i	−0.0300771	−	0.0218523i
$894$	−2.34822	+	7.22707i	−0.0785362	+	0.241710i
$895$	−2.31724	−	7.13174i	−0.0774569	−	0.238388i
$896$	−21.2501	+	15.4391i	−0.709916	+	0.515784i
$897$	−4.68240	+	3.40196i	−0.156341	+	0.113588i
$898$	9.71630	+	29.9037i	0.324237	+	0.997899i
$899$	5.06407	−	15.5856i	0.168896	−	0.519809i
$900$	100.622	+	73.1058i	3.35405	+	2.43686i
$901$	17.2580			0.574947
$902$		0			0
$903$	32.0256			1.06575
$904$	−42.8431	−	31.1273i	−1.42494	−	1.03528i
$905$	2.79253	−	8.59451i	0.0928267	−	0.285691i
$906$	−3.22520	−	9.92614i	−0.107150	−	0.329774i
$907$	31.2663	−	22.7163i	1.03818	−	0.754283i	0.0682513	−	0.997668i	$-0.478258\pi$
$907$	31.2663	−	22.7163i	1.03818	−	0.754283i	0.969930	+	0.243386i	$0.0782580\pi$
$908$	97.5978	−	70.9089i	3.23890	−	2.35320i
$909$	−23.4666	−	72.2229i	−0.778339	−	2.39548i
$910$	0.167650	−	0.515973i	0.00555753	−	0.0171043i
$911$	14.8851	+	10.8146i	0.493165	+	0.358305i	0.806400	−	0.591370i	$-0.201413\pi$
$911$	14.8851	+	10.8146i	0.493165	+	0.358305i	−0.313235	+	0.949676i	$0.601413\pi$
$912$	−41.3331			−1.36868
$913$		0			0
$914$	85.4145			2.82526
$915$	4.98283	+	3.62024i	0.164727	+	0.119681i
$916$	−37.1848	+	114.443i	−1.22862	+	3.78130i
$917$	−2.11164	−	6.49895i	−0.0697324	−	0.214614i
$918$	55.7688	−	40.5184i	1.84064	−	1.33731i
$919$	14.2819	−	10.3764i	0.471115	−	0.342285i	−0.326761	−	0.945107i	$-0.605957\pi$
$919$	14.2819	−	10.3764i	0.471115	−	0.342285i	0.797876	+	0.602822i	$0.205957\pi$
$920$	5.62195	+	17.3026i	0.185350	+	0.570449i
$921$	2.04445	−	6.29216i	0.0673668	−	0.207334i
$922$	19.3833	+	14.0828i	0.638355	+	0.463792i
$923$	2.67027			0.0878930
$924$		0			0
$925$	−35.1368			−1.15529
$926$	−56.0143	−	40.6968i	−1.84075	−	1.33738i
$927$	−21.3718	+	65.7757i	−0.701942	+	2.16036i
$928$	−11.5002	−	35.3941i	−0.377513	−	1.16187i
$929$	10.8800	−	7.90475i	0.356960	−	0.259346i	−0.394823	−	0.918757i	$-0.629194\pi$
$929$	10.8800	−	7.90475i	0.356960	−	0.259346i	0.751783	+	0.659411i	$0.229194\pi$
$930$	22.5655	−	16.3948i	0.739951	−	0.537606i
$931$	0.335728	+	1.03326i	0.0110030	+	0.0338638i
$932$	0.963164	−	2.96432i	0.0315495	−	0.0970994i
$933$	−45.4327	−	33.0088i	−1.48740	−	1.08066i
$934$	−55.5241			−1.81680
$935$		0			0
$936$	19.6747			0.643087
$937$	−6.95415	−	5.05249i	−0.227182	−	0.165058i	0.468372	−	0.883532i	$-0.344841\pi$
$937$	−6.95415	−	5.05249i	−0.227182	−	0.165058i	−0.695554	+	0.718474i	$0.744841\pi$
$938$	−5.16953	+	15.9102i	−0.168791	+	0.519485i
$939$	−16.2677	−	50.0668i	−0.530876	−	1.63387i
$940$	1.95415	−	1.41978i	0.0637375	−	0.0463080i
$941$	−27.2619	+	19.8069i	−0.888712	+	0.645687i	−0.935542	−	0.353216i	$-0.885088\pi$
$941$	−27.2619	+	19.8069i	−0.888712	+	0.645687i	0.0468300	+	0.998903i	$0.485088\pi$
$942$	12.6080	+	38.8035i	0.410791	+	1.26428i
$943$	−2.50185	+	7.69991i	−0.0814715	+	0.250744i
$944$	157.881	+	114.707i	5.13858	+	3.73340i
$945$	−2.34928			−0.0764220
$946$		0			0
$947$	−15.3289			−0.498121			−0.249061	−	0.968488i	$-0.580122\pi$
$947$	−15.3289			−0.498121			−0.249061	+	0.968488i	$0.580122\pi$
$948$	43.4918	+	31.5986i	1.41255	+	1.02628i
$949$	−0.231003	+	0.710953i	−0.00749867	+	0.0230785i
$950$	4.35792	+	13.4123i	0.141389	+	0.435152i
$951$	9.54308	−	6.93345i	0.309456	−	0.224833i
$952$	34.9428	−	25.3874i	1.13250	−	0.822811i
$953$	−13.8865	−	42.7382i	−0.449827	−	1.38443i	−0.877102	−	0.480304i	$-0.840527\pi$
$953$	−13.8865	−	42.7382i	−0.449827	−	1.38443i	0.427275	−	0.904122i	$-0.359473\pi$
$954$	14.5628	−	44.8198i	0.471489	−	1.45109i
$955$	0.916146	+	0.665619i	0.0296458	+	0.0215389i
$956$	79.4610			2.56995
$957$		0			0
$958$	−74.4697			−2.40601
$959$	11.7043	+	8.50366i	0.377951	+	0.274598i
$960$	9.10891	−	28.0343i	0.293989	−	0.904804i
$961$	11.4968	+	35.3837i	0.370866	+	1.14141i
$962$	−7.21598	+	5.24272i	−0.232653	+	0.169032i
$963$	−46.4123	+	33.7205i	−1.49561	+	1.08663i
$964$	29.9710	+	92.2414i	0.965302	+	2.97090i
$965$	2.40804	−	7.41119i	0.0775176	−	0.238575i
$966$	28.0695	+	20.3937i	0.903120	+	0.656155i
$967$	−33.9453			−1.09161			−0.545804	−	0.837913i	$-0.683776\pi$
$967$	−33.9453			−1.09161			−0.545804	+	0.837913i	$0.683776\pi$
$968$		0			0
$969$	14.7343			0.473334
$970$	5.16830	+	3.75499i	0.165944	+	0.120565i
$971$	−17.1381	+	52.7456i	−0.549988	+	1.69269i	0.158839	+	0.987305i	$0.449225\pi$
$971$	−17.1381	+	52.7456i	−0.549988	+	1.69269i	−0.708826	+	0.705383i	$0.750775\pi$
$972$	25.1575	+	77.4269i	0.806928	+	2.48347i
$973$	11.8890	−	8.63790i	0.381145	−	0.276918i
$974$	−26.4648	+	19.2278i	−0.847986	+	0.616098i
$975$	−1.87837	−	5.78102i	−0.0601559	−	0.185141i
$976$	−20.6452	+	63.5395i	−0.660838	+	2.03385i
$977$	30.6835	+	22.2928i	0.981651	+	0.713211i	0.958077	−	0.286511i	$-0.0924954\pi$
$977$	30.6835	+	22.2928i	0.981651	+	0.713211i	0.0235741	+	0.999722i	$0.492495\pi$
$978$	−71.5215			−2.28701
$979$		0			0
$980$	−2.36212			−0.0754551
$981$	62.3034	+	45.2661i	1.98920	+	1.44523i
$982$	−32.9011	+	101.259i	−1.04992	+	3.23131i
$983$	9.74444	+	29.9903i	0.310799	+	0.956542i	0.977449	+	0.211171i	$0.0677277\pi$
$983$	9.74444	+	29.9903i	0.310799	+	0.956542i	−0.666650	+	0.745371i	$0.732272\pi$
$984$	35.9525	−	26.1210i	1.14612	−	0.832708i
$985$	0.779764	−	0.566532i	0.0248453	−	0.0180512i
$986$	8.00798	+	24.6460i	0.255026	+	0.784889i
$987$	0.887062	−	2.73010i	0.0282355	−	0.0868999i
$988$	2.10352	+	1.52829i	0.0669217	+	0.0486215i
$989$	52.1618			1.65865
$990$		0			0
$991$	39.8173			1.26484			0.632419	−	0.774627i	$-0.282062\pi$
$991$	39.8173			1.26484			0.632419	+	0.774627i	$0.282062\pi$
$992$	125.308	+	91.0414i	3.97853	+	2.89057i
$993$	0.0592216	−	0.182265i	0.00187934	−	0.00578402i
$994$	−4.94655	−	15.2239i	−0.156895	−	0.482874i
$995$	−5.24827	+	3.81309i	−0.166381	+	0.120883i
$996$	130.232	−	94.6193i	4.12657	−	2.99813i
$997$	5.78448	+	17.8028i	0.183196	+	0.563821i	0.999913	−	0.0132190i	$-0.00420785\pi$
$997$	5.78448	+	17.8028i	0.183196	+	0.563821i	−0.816716	+	0.577040i	$0.804208\pi$
$998$	29.0556	−	89.4239i	0.919738	−	2.83066i
$999$	31.2471	+	22.7023i	0.988613	+	0.718269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.z.323.6		24
11.2	odd	10		847.2.f.y.148.6		24
11.3	even	5	inner	847.2.f.z.729.6		24
11.4	even	5	inner	847.2.f.z.372.1		24
11.5	even	5		847.2.a.m.1.1	✓	6
11.6	odd	10		847.2.a.n.1.6	yes	6
11.7	odd	10		847.2.f.y.372.6		24
11.8	odd	10		847.2.f.y.729.1		24
11.9	even	5	inner	847.2.f.z.148.1		24
11.10	odd	2		847.2.f.y.323.1		24
33.5	odd	10		7623.2.a.cs.1.6		6
33.17	even	10		7623.2.a.cp.1.1		6
77.6	even	10		5929.2.a.bm.1.6		6
77.27	odd	10		5929.2.a.bj.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.1	✓	6	11.5	even	5
847.2.a.n.1.6	yes	6	11.6	odd	10
847.2.f.y.148.6		24	11.2	odd	10
847.2.f.y.323.1		24	11.10	odd	2
847.2.f.y.372.6		24	11.7	odd	10
847.2.f.y.729.1		24	11.8	odd	10
847.2.f.z.148.1		24	11.9	even	5	inner
847.2.f.z.323.6		24	1.1	even	1	trivial
847.2.f.z.372.1		24	11.4	even	5	inner
847.2.f.z.729.6		24	11.3	even	5	inner
5929.2.a.bj.1.1		6	77.27	odd	10
5929.2.a.bm.1.6		6	77.6	even	10
7623.2.a.cp.1.1		6	33.17	even	10
7623.2.a.cs.1.6		6	33.5	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18693 + 1.58890i) q^{2} +(-0.867470 + 2.66980i) q^{3} +(1.64004 + 5.04751i) q^{4} +(0.360071 - 0.261607i) q^{5} +(-6.13913 + 4.46034i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.76267 + 8.50263i) q^{8} +(-3.94826 - 2.86858i) q^{9} +O(q^{10})\)	\(q+(2.18693 + 1.58890i) q^{2} +(-0.867470 + 2.66980i) q^{3} +(1.64004 + 5.04751i) q^{4} +(0.360071 - 0.261607i) q^{5} +(-6.13913 + 4.46034i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.76267 + 8.50263i) q^{8} +(-3.94826 - 2.86858i) q^{9} +1.20312 q^{10} -14.8985 q^{12} +(0.364813 + 0.265052i) q^{13} +(0.835334 - 2.57089i) q^{14} +(0.386087 + 1.18825i) q^{15} +(-10.9643 + 7.96600i) q^{16} +(3.90850 - 2.83969i) q^{17} +(-4.07669 - 12.5468i) q^{18} +(0.335728 - 1.03326i) q^{19} +(1.91099 + 1.38842i) q^{20} +2.80719 q^{21} +4.57222 q^{23} +(-20.3038 - 14.7516i) q^{24} +(-1.48387 + 4.56689i) q^{25} +(0.376680 + 1.15930i) q^{26} +(4.27033 - 3.10257i) q^{27} +(4.29367 - 3.11953i) q^{28} +(0.613187 + 1.88719i) q^{29} +(-1.04367 + 3.21208i) q^{30} +(-6.68135 - 4.85429i) q^{31} -18.7549 q^{32} +13.0596 q^{34} +(-0.360071 - 0.261607i) q^{35} +(8.00390 - 24.6335i) q^{36} +(2.26116 + 6.95912i) q^{37} +(2.37596 - 1.72624i) q^{38} +(-1.02410 + 0.744051i) q^{39} +(1.22959 + 3.78429i) q^{40} +(-0.547186 + 1.68407i) q^{41} +(6.13913 + 4.46034i) q^{42} +11.4084 q^{43} -2.17209 q^{45} +(9.99913 + 7.26479i) q^{46} +(0.315996 - 0.972536i) q^{47} +(-11.7564 - 36.1826i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-10.5015 + 7.62975i) q^{50} +(4.19090 + 12.8983i) q^{51} +(-0.739547 + 2.27609i) q^{52} +(2.88998 + 2.09970i) q^{53} +14.2686 q^{54} +8.94020 q^{56} +(2.46737 + 1.79265i) q^{57} +(-1.65756 + 5.10146i) q^{58} +(-4.44972 - 13.6948i) q^{59} +(-5.36452 + 3.89755i) q^{60} +(3.98817 - 2.89758i) q^{61} +(-6.89869 - 21.2320i) q^{62} +(-1.50810 + 4.64146i) q^{63} +(-19.0871 - 13.8676i) q^{64} +0.200698 q^{65} -6.18858 q^{67} +(20.7435 + 15.0710i) q^{68} +(-3.96626 + 12.2069i) q^{69} +(-0.371784 - 1.14423i) q^{70} +(4.79072 - 3.48066i) q^{71} +(35.2982 - 25.6457i) q^{72} +(0.512277 + 1.57663i) q^{73} +(-6.11235 + 18.8119i) q^{74} +(-10.9055 - 7.92327i) q^{75} +5.76602 q^{76} -3.42186 q^{78} +(-2.91920 - 2.12092i) q^{79} +(-1.86395 + 5.73665i) q^{80} +(0.0545593 + 0.167916i) q^{81} +(-3.87247 + 2.81351i) q^{82} +(-8.74129 + 6.35092i) q^{83} +(4.60389 + 14.1693i) q^{84} +(0.664455 - 2.04498i) q^{85} +(24.9494 + 18.1268i) q^{86} -5.57035 q^{87} -5.21170 q^{89} +(-4.75022 - 3.45124i) q^{90} +(0.139346 - 0.428863i) q^{91} +(7.49860 + 23.0783i) q^{92} +(18.7558 - 13.6269i) q^{93} +(2.23632 - 1.62478i) q^{94} +(-0.149423 - 0.459877i) q^{95} +(16.2693 - 50.0716i) q^{96} +(4.29576 + 3.12105i) q^{97} -2.70320 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 8 q^{9} + 32 q^{10} - 56 q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 22 q^{17} + 24 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 20 q^{30} + 2 q^{31} - 32 q^{32} + 96 q^{34} - 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} + 20 q^{39} + 18 q^{40} + 26 q^{41} + 6 q^{42} + 16 q^{43} - 144 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} - 4 q^{50} - 4 q^{51} + 12 q^{52} - 4 q^{53} + 128 q^{54} + 48 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} - 8 q^{61} + 20 q^{62} + 8 q^{63} - 26 q^{64} - 96 q^{65} + 24 q^{67} + 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} + 16 q^{72} + 14 q^{73} + 44 q^{74} + 20 q^{75} + 120 q^{76} + 128 q^{78} - 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} + 22 q^{83} - 14 q^{84} - 24 q^{85} + 30 q^{86} - 88 q^{87} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} - 38 q^{94} - 24 q^{95} - 62 q^{96} + 4 q^{97} - 16 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 8 * q^9 + 32 * q^10 - 56 * q^12 + 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 22 * q^17 + 24 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 + 8 * q^23 - 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 20 * q^30 + 2 * q^31 - 32 * q^32 + 96 * q^34 - 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 + 20 * q^39 + 18 * q^40 + 26 * q^41 + 6 * q^42 + 16 * q^43 - 144 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 - 4 * q^50 - 4 * q^51 + 12 * q^52 - 4 * q^53 + 128 * q^54 + 48 * q^56 + 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 - 8 * q^61 + 20 * q^62 + 8 * q^63 - 26 * q^64 - 96 * q^65 + 24 * q^67 + 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 + 16 * q^72 + 14 * q^73 + 44 * q^74 + 20 * q^75 + 120 * q^76 + 128 * q^78 - 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 + 22 * q^83 - 14 * q^84 - 24 * q^85 + 30 * q^86 - 88 * q^87 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 - 38 * q^94 - 24 * q^95 - 62 * q^96 + 4 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more