LMFDB - Embedded newform 841.2.d.e.574.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(190,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.190"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,5,2,5,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			574.1
Root			$0.222521 + 0.974928i$ of defining polynomial
Character	$\chi$	$=$	841.574
Dual form			841.2.d.e.778.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.777479 - 0.974928i) q^{2} +(-0.400969 + 1.75676i) q^{3} +(0.0990311 + 0.433884i) q^{4} +(-2.52446 + 3.16557i) q^{5} +(1.40097 + 1.75676i) q^{6} +(-0.153989 + 0.674671i) q^{7} +(2.74698 + 1.32288i) q^{8} +(-0.222521 - 0.107160i) q^{9} +(1.12349 + 4.92233i) q^{10} +(2.56853 - 1.23694i) q^{11} -0.801938 q^{12} +(-1.32155 + 0.636426i) q^{13} +(0.538032 + 0.674671i) q^{14} +(-4.54892 - 5.70416i) q^{15} +(2.62349 - 1.26341i) q^{16} -1.60388 q^{17} +(-0.277479 + 0.133627i) q^{18} +(0.599031 + 2.62453i) q^{19} +(-1.62349 - 0.781831i) q^{20} +(-1.12349 - 0.541044i) q^{21} +(0.791053 - 3.46583i) q^{22} +(-3.21648 - 4.03334i) q^{23} +(-3.42543 + 4.29535i) q^{24} +(-2.53534 - 11.1081i) q^{25} +(-0.407010 + 1.78323i) q^{26} +(-3.09299 + 3.87849i) q^{27} -0.307979 q^{28} -9.09783 q^{30} +(-1.21648 + 1.52542i) q^{31} +(-0.548917 + 2.40496i) q^{32} +(1.14310 + 5.00827i) q^{33} +(-1.24698 + 1.56366i) q^{34} +(-1.74698 - 2.19064i) q^{35} +(0.0244587 - 0.107160i) q^{36} +(-2.56853 - 1.23694i) q^{37} +(3.02446 + 1.45650i) q^{38} +(-0.588146 - 2.57684i) q^{39} +(-11.1223 + 5.35621i) q^{40} +6.49396 q^{41} +(-1.40097 + 0.674671i) q^{42} +(0.414542 + 0.519820i) q^{43} +(0.791053 + 0.991949i) q^{44} +(0.900969 - 0.433884i) q^{45} -6.43296 q^{46} +(4.28232 - 2.06226i) q^{47} +(1.16756 + 5.11543i) q^{48} +(5.87531 + 2.82940i) q^{49} +(-12.8007 - 6.16451i) q^{50} +(0.643104 - 2.81762i) q^{51} +(-0.407010 - 0.510374i) q^{52} +(0.0304995 - 0.0382451i) q^{53} +(1.37651 + 6.03089i) q^{54} +(-2.56853 + 11.2535i) q^{55} +(-1.31551 + 1.64960i) q^{56} -4.85086 q^{57} -6.39612 q^{59} +(2.02446 - 2.53859i) q^{60} +(0.291053 - 1.27518i) q^{61} +(0.541385 + 2.37196i) q^{62} +(0.106564 - 0.133627i) q^{63} +(5.54892 + 6.95812i) q^{64} +(1.32155 - 5.79010i) q^{65} +(5.77144 + 2.77938i) q^{66} +(-13.4683 - 6.48599i) q^{67} +(-0.158834 - 0.695895i) q^{68} +(8.37531 - 4.03334i) q^{69} -3.49396 q^{70} +(2.03534 - 0.980170i) q^{71} +(-0.469501 - 0.588735i) q^{72} +(5.18933 + 6.50722i) q^{73} +(-3.20291 + 1.54244i) q^{74} +20.5308 q^{75} +(-1.07942 + 0.519820i) q^{76} +(0.439001 + 1.92339i) q^{77} +(-2.96950 - 1.43004i) q^{78} +(8.77628 + 4.22643i) q^{79} +(-2.62349 + 11.4943i) q^{80} +(-6.03534 - 7.56808i) q^{81} +(5.04892 - 6.33114i) q^{82} +(0.894928 + 3.92094i) q^{83} +(0.123490 - 0.541044i) q^{84} +(4.04892 - 5.07718i) q^{85} +0.829085 q^{86} +8.69202 q^{88} +(7.01842 - 8.80082i) q^{89} +(0.277479 - 1.21572i) q^{90} +(-0.225873 - 0.989616i) q^{91} +(1.43147 - 1.79500i) q^{92} +(-2.19202 - 2.74871i) q^{93} +(1.31886 - 5.77832i) q^{94} +(-9.82036 - 4.72923i) q^{95} +(-4.00484 - 1.92863i) q^{96} +(1.01693 + 4.45544i) q^{97} +(7.32640 - 3.52821i) q^{98} -0.704103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 6 q^{5} + 4 q^{6} - 6 q^{7} + 7 q^{8} - q^{9} + 2 q^{10} + 10 q^{11} + 4 q^{12} - 12 q^{13} - 12 q^{14} - 9 q^{15} + 11 q^{16} + 8 q^{17} - 2 q^{18} + 8 q^{19} - 5 q^{20}+ \cdots - 32 q^{99}+O(q^{100}) $ 6 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 6 * q^5 + 4 * q^6 - 6 * q^7 + 7 * q^8 - q^9 + 2 * q^10 + 10 * q^11 + 4 * q^12 - 12 * q^13 - 12 * q^14 - 9 * q^15 + 11 * q^16 + 8 * q^17 - 2 * q^18 + 8 * q^19 - 5 * q^20 - 2 * q^21 - q^22 - 7 * q^24 - 3 * q^25 - 17 * q^26 - 4 * q^27 - 12 * q^28 - 18 * q^30 + 12 * q^31 + 15 * q^32 + 15 * q^33 + 2 * q^34 - q^35 - 9 * q^36 - 10 * q^37 + 9 * q^38 - 11 * q^39 - 21 * q^40 + 20 * q^41 - 4 * q^42 - 8 * q^43 - q^44 + q^45 + 4 * q^47 + 6 * q^48 - q^49 - 27 * q^50 + 12 * q^51 - 17 * q^52 + 10 * q^53 + 13 * q^54 - 10 * q^55 + 7 * q^56 - 2 * q^57 - 56 * q^59 + 3 * q^60 - 4 * q^61 + 10 * q^62 - 20 * q^63 + 15 * q^64 + 12 * q^65 + 16 * q^66 - 30 * q^67 + 16 * q^68 + 14 * q^69 - 2 * q^70 + 7 * q^72 + 24 * q^73 - 6 * q^74 + 48 * q^75 + 2 * q^76 - 17 * q^77 - 8 * q^78 + 12 * q^79 - 11 * q^80 - 24 * q^81 + 12 * q^82 - 18 * q^83 - 4 * q^84 + 6 * q^85 - 16 * q^86 + 42 * q^88 + 14 * q^89 + 2 * q^90 - 23 * q^91 + 14 * q^92 - 3 * q^93 + 15 * q^94 - 22 * q^95 - 2 * q^96 + 22 * q^97 + 26 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

Coefficient data

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

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

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

$2$	0.777479	−	0.974928i	0.549761	−	0.689378i	−0.426867	−	0.904314i	$-0.640383\pi$
$2$	0.777479	−	0.974928i	0.549761	−	0.689378i	0.976628	+	0.214936i	$0.0689543\pi$
$3$	−0.400969	+	1.75676i	−0.231499	+	1.01427i	0.716897	+	0.697179i	$0.245562\pi$
$3$	−0.400969	+	1.75676i	−0.231499	+	1.01427i	−0.948397	+	0.317087i	$0.897295\pi$
$4$	0.0990311	+	0.433884i	0.0495156	+	0.216942i
$5$	−2.52446	+	3.16557i	−1.12897	+	1.41569i	−0.232494	+	0.972598i	$0.574689\pi$
$5$	−2.52446	+	3.16557i	−1.12897	+	1.41569i	−0.896478	+	0.443089i	$0.853883\pi$
$6$	1.40097	+	1.75676i	0.571943	+	0.717194i
$7$	−0.153989	+	0.674671i	−0.0582025	+	0.255002i	−0.995656	−	0.0931090i	$-0.970320\pi$
$7$	−0.153989	+	0.674671i	−0.0582025	+	0.255002i	0.937453	+	0.348111i	$0.113177\pi$
$8$	2.74698	+	1.32288i	0.971204	+	0.467707i
$9$	−0.222521	−	0.107160i	−0.0741736	−	0.0357201i
$10$	1.12349	+	4.92233i	0.355279	+	1.55658i
$11$	2.56853	−	1.23694i	0.774441	−	0.372951i	−0.00454697	−	0.999990i	$-0.501447\pi$
$11$	2.56853	−	1.23694i	0.774441	−	0.372951i	0.778988	+	0.627038i	$0.215733\pi$
$12$	−0.801938			−0.231499
$13$	−1.32155	+	0.636426i	−0.366533	+	0.176513i	−0.608079	−	0.793876i	$-0.708060\pi$
$13$	−1.32155	+	0.636426i	−0.366533	+	0.176513i	0.241546	+	0.970389i	$0.422345\pi$
$14$	0.538032	+	0.674671i	0.143795	+	0.180313i
$15$	−4.54892	−	5.70416i	−1.17453	−	1.47281i
$16$	2.62349	−	1.26341i	0.655872	−	0.315852i
$17$	−1.60388			−0.388997			−0.194498	−	0.980903i	$-0.562308\pi$
$17$	−1.60388			−0.388997			−0.194498	+	0.980903i	$0.562308\pi$
$18$	−0.277479	+	0.133627i	−0.0654024	+	0.0314962i
$19$	0.599031	+	2.62453i	0.137427	+	0.602108i	0.995995	+	0.0894079i	$0.0284975\pi$
$19$	0.599031	+	2.62453i	0.137427	+	0.602108i	−0.858568	+	0.512700i	$0.828645\pi$
$20$	−1.62349	−	0.781831i	−0.363023	−	0.174823i
$21$	−1.12349	−	0.541044i	−0.245166	−	0.118066i
$22$	0.791053	−	3.46583i	0.168653	−	0.738917i
$23$	−3.21648	−	4.03334i	−0.670682	−	0.841009i	0.323777	−	0.946134i	$-0.395047\pi$
$23$	−3.21648	−	4.03334i	−0.670682	−	0.841009i	−0.994459	+	0.105124i	$0.966476\pi$
$24$	−3.42543	+	4.29535i	−0.699212	+	0.876785i
$25$	−2.53534	−	11.1081i	−0.507069	−	2.22161i
$26$	−0.407010	+	1.78323i	−0.0798212	+	0.349719i
$27$	−3.09299	+	3.87849i	−0.595246	+	0.746415i
$28$	−0.307979			−0.0582025
$29$		0			0
$29$		0			0
$30$	−9.09783			−1.66103
$31$	−1.21648	+	1.52542i	−0.218486	+	0.273973i	−0.878980	−	0.476858i	$-0.841775\pi$
$31$	−1.21648	+	1.52542i	−0.218486	+	0.273973i	0.660494	+	0.750831i	$0.270347\pi$
$32$	−0.548917	+	2.40496i	−0.0970358	+	0.425142i
$33$	1.14310	+	5.00827i	0.198989	+	0.871827i
$34$	−1.24698	+	1.56366i	−0.213855	+	0.268166i
$35$	−1.74698	−	2.19064i	−0.295293	−	0.370286i
$36$	0.0244587	−	0.107160i	0.00407644	−	0.0178601i
$37$	−2.56853	−	1.23694i	−0.422264	−	0.203352i	0.210670	−	0.977557i	$-0.432435\pi$
$37$	−2.56853	−	1.23694i	−0.422264	−	0.203352i	−0.632934	+	0.774206i	$0.718150\pi$
$38$	3.02446	+	1.45650i	0.490632	+	0.236276i
$39$	−0.588146	−	2.57684i	−0.0941787	−	0.412624i
$40$	−11.1223	+	5.35621i	−1.75859	+	0.846892i
$41$	6.49396			1.01419			0.507093	−	0.861891i	$-0.330720\pi$
$41$	6.49396			1.01419			0.507093	+	0.861891i	$0.330720\pi$
$42$	−1.40097	+	0.674671i	−0.216174	+	0.104104i
$43$	0.414542	+	0.519820i	0.0632171	+	0.0792718i	0.812435	−	0.583052i	$-0.198142\pi$
$43$	0.414542	+	0.519820i	0.0632171	+	0.0792718i	−0.749218	+	0.662324i	$0.769570\pi$
$44$	0.791053	+	0.991949i	0.119256	+	0.149542i
$45$	0.900969	−	0.433884i	0.134309	−	0.0646796i
$46$	−6.43296			−0.948488
$47$	4.28232	−	2.06226i	0.624641	−	0.300811i	−0.0946601	−	0.995510i	$-0.530176\pi$
$47$	4.28232	−	2.06226i	0.624641	−	0.300811i	0.719301	+	0.694698i	$0.244462\pi$
$48$	1.16756	+	5.11543i	0.168523	+	0.738348i
$49$	5.87531	+	2.82940i	0.839331	+	0.404200i
$50$	−12.8007	−	6.16451i	−1.81030	−	0.871794i
$51$	0.643104	−	2.81762i	0.0900526	−	0.394546i
$52$	−0.407010	−	0.510374i	−0.0564421	−	0.0707761i
$53$	0.0304995	−	0.0382451i	0.00418942	−	0.00525337i	−0.779732	−	0.626113i	$-0.784645\pi$
$53$	0.0304995	−	0.0382451i	0.00418942	−	0.00525337i	0.783922	+	0.620860i	$0.213216\pi$
$54$	1.37651	+	6.03089i	0.187319	+	0.820700i
$55$	−2.56853	+	11.2535i	−0.346341	+	1.51742i
$56$	−1.31551	+	1.64960i	−0.175793	+	0.220437i
$57$	−4.85086			−0.642511
$58$		0			0
$59$	−6.39612			−0.832704			−0.416352	−	0.909203i	$-0.636692\pi$
$59$	−6.39612			−0.832704			−0.416352	+	0.909203i	$0.636692\pi$
$60$	2.02446	−	2.53859i	0.261356	−	0.327731i
$61$	0.291053	−	1.27518i	0.0372655	−	0.163271i	−0.952871	−	0.303375i	$-0.901887\pi$
$61$	0.291053	−	1.27518i	0.0372655	−	0.163271i	0.990137	+	0.140104i	$0.0447437\pi$
$62$	0.541385	+	2.37196i	0.0687559	+	0.301239i
$63$	0.106564	−	0.133627i	0.0134258	−	0.0168354i
$64$	5.54892	+	6.95812i	0.693615	+	0.869765i
$65$	1.32155	−	5.79010i	0.163918	−	0.718173i
$66$	5.77144	+	2.77938i	0.710415	+	0.342118i
$67$	−13.4683	−	6.48599i	−1.64542	−	0.792390i	−0.999582	−	0.0289117i	$-0.990796\pi$
$67$	−13.4683	−	6.48599i	−1.64542	−	0.792390i	−0.645833	−	0.763478i	$-0.723490\pi$
$68$	−0.158834	−	0.695895i	−0.0192614	−	0.0843897i
$69$	8.37531	−	4.03334i	1.00827	−	0.485557i
$70$	−3.49396			−0.417608
$71$	2.03534	−	0.980170i	0.241551	−	0.116325i	−0.309192	−	0.951000i	$-0.600059\pi$
$71$	2.03534	−	0.980170i	0.241551	−	0.116325i	0.550743	+	0.834675i	$0.314344\pi$
$72$	−0.469501	−	0.588735i	−0.0553312	−	0.0693831i
$73$	5.18933	+	6.50722i	0.607365	+	0.761612i	0.986506	−	0.163727i	$-0.0523516\pi$
$73$	5.18933	+	6.50722i	0.607365	+	0.761612i	−0.379140	+	0.925339i	$0.623780\pi$
$74$	−3.20291	+	1.54244i	−0.372330	+	0.179305i
$75$	20.5308			2.37069
$76$	−1.07942	+	0.519820i	−0.123818	+	0.0596274i
$77$	0.439001	+	1.92339i	0.0500288	+	0.219191i
$78$	−2.96950	−	1.43004i	−0.336230	−	0.161920i
$79$	8.77628	+	4.22643i	0.987409	+	0.475511i	0.856647	−	0.515903i	$-0.172543\pi$
$79$	8.77628	+	4.22643i	0.987409	+	0.475511i	0.130762	+	0.991414i	$0.458258\pi$
$80$	−2.62349	+	11.4943i	−0.293315	+	1.28510i
$81$	−6.03534	−	7.56808i	−0.670594	−	0.840898i
$82$	5.04892	−	6.33114i	0.557560	−	0.699158i
$83$	0.894928	+	3.92094i	0.0982311	+	0.430379i	0.999998	−	0.00184346i	$-0.000586791\pi$
$83$	0.894928	+	3.92094i	0.0982311	+	0.430379i	−0.901767	+	0.432222i	$0.857730\pi$
$84$	0.123490	−	0.541044i	0.0134738	−	0.0590328i
$85$	4.04892	−	5.07718i	0.439167	−	0.550698i
$86$	0.829085			0.0894025
$87$		0			0
$88$	8.69202			0.926573
$89$	7.01842	−	8.80082i	0.743951	−	0.932885i	−0.255473	−	0.966816i	$-0.582231\pi$
$89$	7.01842	−	8.80082i	0.743951	−	0.932885i	0.999424	+	0.0339313i	$0.0108027\pi$
$90$	0.277479	−	1.21572i	0.0292489	−	0.128148i
$91$	−0.225873	−	0.989616i	−0.0236780	−	0.103740i
$92$	1.43147	−	1.79500i	0.149241	−	0.187142i
$93$	−2.19202	−	2.74871i	−0.227302	−	0.285028i
$94$	1.31886	−	5.77832i	0.136030	−	0.595988i
$95$	−9.82036	−	4.72923i	−1.00755	−	0.485209i
$96$	−4.00484	−	1.92863i	−0.408743	−	0.196840i
$97$	1.01693	+	4.45544i	0.103253	+	0.452382i	0.999953	+	0.00974167i	$0.00310092\pi$
$97$	1.01693	+	4.45544i	0.103253	+	0.452382i	−0.896699	+	0.442640i	$0.854042\pi$
$98$	7.32640	−	3.52821i	0.740078	−	0.356403i
$99$	−0.704103			−0.0707650
$100$	4.56853	−	2.20009i	0.456853	−	0.220009i
$101$	2.00335	+	2.51212i	0.199341	+	0.249966i	0.871448	−	0.490489i	$-0.163182\pi$
$101$	2.00335	+	2.51212i	0.199341	+	0.249966i	−0.672107	+	0.740454i	$0.734610\pi$
$102$	−2.24698	−	2.81762i	−0.222484	−	0.278986i
$103$	5.88620	−	2.83464i	0.579984	−	0.279306i	−0.120802	−	0.992677i	$-0.538547\pi$
$103$	5.88620	−	2.83464i	0.579984	−	0.279306i	0.700787	+	0.713371i	$0.252832\pi$
$104$	−4.47219			−0.438534
$105$	4.54892	−	2.19064i	0.443929	−	0.213785i
$106$	−0.0135735	−	0.0594696i	−0.00131838	−	0.00577619i
$107$	5.21164	+	2.50979i	0.503828	+	0.242631i	0.668492	−	0.743719i	$-0.266940\pi$
$107$	5.21164	+	2.50979i	0.503828	+	0.242631i	−0.164665	+	0.986350i	$0.552654\pi$
$108$	−1.98911	−	0.957907i	−0.191403	−	0.0921747i
$109$	−2.04407	+	8.95567i	−0.195787	+	0.857798i	0.777624	+	0.628730i	$0.216425\pi$
$109$	−2.04407	+	8.95567i	−0.195787	+	0.857798i	−0.973410	+	0.229068i	$0.926432\pi$
$110$	8.97434	+	11.2535i	0.855670	+	1.07298i
$111$	3.20291	−	4.01632i	0.304006	−	0.381212i
$112$	0.448394	+	1.96454i	0.0423693	+	0.185632i
$113$	1.99516	−	8.74135i	0.187688	−	0.822317i	−0.790143	−	0.612923i	$-0.789994\pi$
$113$	1.99516	−	8.74135i	0.187688	−	0.822317i	0.977831	−	0.209394i	$-0.0671492\pi$
$114$	−3.77144	+	4.72923i	−0.353228	+	0.442933i
$115$	20.8877			1.94779
$116$		0			0
$117$	0.362273			0.0334921
$118$	−4.97285	+	6.23576i	−0.457788	+	0.574048i
$119$	0.246980	−	1.08209i	0.0226406	−	0.0991949i
$120$	−4.94989	−	21.6869i	−0.451861	−	1.97973i
$121$	−1.79105	+	2.24591i	−0.162823	+	0.204174i
$122$	−1.01693	−	1.27518i	−0.0920681	−	0.115450i
$123$	−2.60388	+	11.4083i	−0.234784	+	1.02865i
$124$	−0.782323	−	0.376747i	−0.0702547	−	0.0338329i
$125$	23.3240	+	11.2322i	2.08616	+	1.00464i
$126$	−0.0474254	−	0.207784i	−0.00422499	−	0.0185109i
$127$	−14.0233	+	6.75325i	−1.24436	+	0.599254i	−0.935995	−	0.352013i	$-0.885497\pi$
$127$	−14.0233	+	6.75325i	−1.24436	+	0.599254i	−0.308368	+	0.951267i	$0.599783\pi$
$128$	6.16421			0.544844
$129$	−1.07942	+	0.519820i	−0.0950374	+	0.0457676i
$130$	−4.61745	−	5.79010i	−0.404977	−	0.507825i
$131$	8.37531	+	10.5023i	0.731755	+	0.917591i	0.998939	−	0.0460542i	$-0.0146647\pi$
$131$	8.37531	+	10.5023i	0.731755	+	0.917591i	−0.267184	+	0.963645i	$0.586093\pi$
$132$	−2.05980	+	0.991949i	−0.179283	+	0.0863380i
$133$	−1.86294			−0.161537
$134$	−16.7947	+	8.08790i	−1.45084	+	0.698688i
$135$	−4.46950	−	19.5822i	−0.384673	−	1.68536i
$136$	−4.40581	−	2.12173i	−0.377795	−	0.181937i
$137$	15.3095	+	7.37265i	1.30798	+	0.629888i	0.952426	−	0.304769i	$-0.0985793\pi$
$137$	15.3095	+	7.37265i	1.30798	+	0.629888i	0.355550	+	0.934657i	$0.384294\pi$
$138$	2.57942	−	11.3012i	0.219575	−	0.962019i
$139$	7.77144	+	9.74508i	0.659165	+	0.826567i	0.993252	−	0.115976i	$-0.0369995\pi$
$139$	7.77144	+	9.74508i	0.659165	+	0.826567i	−0.334087	+	0.942542i	$0.608428\pi$
$140$	0.777479	−	0.974928i	0.0657090	−	0.0823964i
$141$	1.90581	+	8.34991i	0.160498	+	0.703190i
$142$	0.626842	−	2.74638i	0.0526034	−	0.230471i
$143$	−2.60723	+	3.26936i	−0.218027	+	0.273398i
$144$	−0.719169			−0.0599307
$145$		0			0
$146$	10.3787			0.858945
$147$	−7.32640	+	9.18701i	−0.604271	+	0.757732i
$148$	0.282323	−	1.23694i	0.0232068	−	0.101676i
$149$	4.07553	+	17.8561i	0.333881	+	1.46283i	0.811548	+	0.584286i	$0.198625\pi$
$149$	4.07553	+	17.8561i	0.333881	+	1.46283i	−0.477667	+	0.878541i	$0.658518\pi$
$150$	15.9623	−	20.0160i	1.30331	−	1.63430i
$151$	−11.8693	−	14.8836i	−0.965908	−	1.21121i	−0.977426	−	0.211276i	$-0.932238\pi$
$151$	−11.8693	−	14.8836i	−0.965908	−	1.21121i	0.0115186	−	0.999934i	$-0.496333\pi$
$152$	−1.82640	+	8.00197i	−0.148140	+	0.649045i
$153$	0.356896	+	0.171872i	0.0288533	+	0.0138950i
$154$	2.21648	+	1.06740i	0.178609	+	0.0860136i
$155$	−1.75786	−	7.70171i	−0.141195	−	0.618616i
$156$	1.05980	−	0.510374i	0.0848521	−	0.0408626i
$157$	−11.4383			−0.912879			−0.456439	−	0.889755i	$-0.650875\pi$
$157$	−11.4383			−0.912879			−0.456439	+	0.889755i	$0.650875\pi$
$158$	10.9438	−	5.27028i	0.870646	−	0.419281i
$159$	0.0549581	+	0.0689153i	0.00435846	+	0.00546534i
$160$	−6.22737	−	7.80887i	−0.492316	−	0.617345i
$161$	3.21648	−	1.54898i	0.253494	−	0.122076i
$162$	−12.0707			−0.948363
$163$	6.01357	−	2.89598i	0.471019	−	0.226831i	−0.183289	−	0.983059i	$-0.558674\pi$
$163$	6.01357	−	2.89598i	0.471019	−	0.226831i	0.654308	+	0.756228i	$0.272960\pi$
$164$	0.643104	+	2.81762i	0.0502180	+	0.220019i
$165$	−18.7397	−	9.02458i	−1.45889	−	0.702563i
$166$	4.51842	+	2.17596i	0.350697	+	0.168887i
$167$	3.26391	−	14.3001i	0.252569	−	1.10658i	−0.676434	−	0.736503i	$-0.736476\pi$
$167$	3.26391	−	14.3001i	0.252569	−	1.10658i	0.929003	−	0.370072i	$-0.120667\pi$
$168$	−2.37047	−	2.97247i	−0.182886	−	0.229331i
$169$	−6.76391	+	8.48167i	−0.520300	+	0.652436i
$170$	−1.80194	−	7.89481i	−0.138202	−	0.605504i
$171$	0.147948	−	0.648205i	0.0113139	−	0.0495694i
$172$	−0.184489	+	0.231342i	−0.0140671	+	0.0176396i
$173$	−23.3599			−1.77602			−0.888009	−	0.459825i	$-0.847912\pi$
$173$	−23.3599			−1.77602			−0.888009	+	0.459825i	$0.847912\pi$
$174$		0			0
$175$	7.88471			0.596028
$176$	5.17576	−	6.49020i	0.390138	−	0.489217i
$177$	2.56465	−	11.2365i	0.192771	−	0.844583i
$178$	−3.12349	−	13.6849i	−0.234115	−	1.02573i
$179$	−0.414542	+	0.519820i	−0.0309844	+	0.0388532i	−0.797082	−	0.603871i	$-0.793624\pi$
$179$	−0.414542	+	0.519820i	−0.0309844	+	0.0388532i	0.766098	+	0.642724i	$0.222196\pi$
$180$	0.277479	+	0.347948i	0.0206821	+	0.0259345i
$181$	−2.44020	+	10.6912i	−0.181378	+	0.794671i	0.799597	+	0.600537i	$0.205047\pi$
$181$	−2.44020	+	10.6912i	−0.181378	+	0.794671i	−0.980975	+	0.194134i	$0.937810\pi$
$182$	−1.14042	−	0.549195i	−0.0845332	−	0.0407091i
$183$	2.12349	+	1.02262i	0.156973	+	0.0755942i
$184$	−3.50000	−	15.3345i	−0.258023	−	1.13047i
$185$	10.3998	−	5.00827i	0.764606	−	0.368215i
$186$	−4.38404			−0.321454
$187$	−4.11960	+	1.98390i	−0.301255	+	0.145077i
$188$	1.31886	+	1.65380i	0.0961880	+	0.120616i
$189$	−2.14042	−	2.68400i	−0.155692	−	0.195232i
$190$	−12.2458	+	5.89726i	−0.888402	+	0.427832i
$191$	−0.518122			−0.0374900			−0.0187450	−	0.999824i	$-0.505967\pi$
$191$	−0.518122			−0.0374900			−0.0187450	+	0.999824i	$0.505967\pi$
$192$	−14.4487	+	6.95812i	−1.04274	+	0.502159i
$193$	−0.308511	−	1.35168i	−0.0222071	−	0.0972957i	0.962610	−	0.270892i	$-0.0873185\pi$
$193$	−0.308511	−	1.35168i	−0.0222071	−	0.0972957i	−0.984817	+	0.173596i	$0.944461\pi$
$194$	5.13437	+	2.47258i	0.368627	+	0.177521i
$195$	9.64191	+	4.64330i	0.690471	+	0.332513i
$196$	−0.645793	+	2.82940i	−0.0461280	+	0.202100i
$197$	8.07942	+	10.1313i	0.575635	+	0.721823i	0.981361	−	0.192171i	$-0.0615530\pi$
$197$	8.07942	+	10.1313i	0.575635	+	0.721823i	−0.405727	+	0.913994i	$0.632982\pi$
$198$	−0.547425	+	0.686450i	−0.0389038	+	0.0487839i
$199$	4.33997	+	19.0147i	0.307652	+	1.34791i	0.858288	+	0.513167i	$0.171528\pi$
$199$	4.33997	+	19.0147i	0.307652	+	1.34791i	−0.550636	+	0.834745i	$0.685615\pi$
$200$	7.73005	−	33.8676i	0.546597	−	2.39480i
$201$	16.7947	−	21.0599i	1.18461	−	1.48545i
$202$	4.00670			0.281911
$203$		0			0
$204$	1.28621			0.0900526
$205$	−16.3937	+	20.5571i	−1.14499	+	1.43577i
$206$	1.81282	−	7.94250i	0.126305	−	0.553380i
$207$	0.283520	+	1.24218i	0.0197060	+	0.0863376i
$208$	−2.66301	+	3.33931i	−0.184647	+	0.231540i
$209$	4.78501	+	6.00022i	0.330986	+	0.415044i
$210$	1.40097	−	6.13805i	0.0966760	−	0.423565i
$211$	18.5879	+	8.95147i	1.27964	+	0.616244i	0.945299	−	0.326206i	$-0.105770\pi$
$211$	18.5879	+	8.95147i	1.27964	+	0.616244i	0.334346	+	0.942450i	$0.391485\pi$
$212$	0.0196143	+	0.00944576i	0.00134712	+	0.000648738i
$213$	0.905813	+	3.96863i	0.0620653	+	0.271926i
$214$	6.49880	−	3.12966i	0.444249	−	0.213939i
$215$	−2.69202			−0.183594
$216$	−13.6271	+	6.56248i	−0.927209	+	0.446520i
$217$	−0.841830	−	1.05562i	−0.0571472	−	0.0716603i
$218$	7.14191	+	8.95567i	0.483711	+	0.606554i
$219$	−13.5124	+	6.50722i	−0.913082	+	0.439717i
$220$	−5.13706			−0.346341
$221$	2.11960	−	1.02075i	0.142580	−	0.0686629i
$222$	−1.42543	−	6.24521i	−0.0956684	−	0.419151i
$223$	19.0112	+	9.15530i	1.27308	+	0.613084i	0.943603	−	0.331078i	$-0.107412\pi$
$223$	19.0112	+	9.15530i	1.27308	+	0.613084i	0.329480	+	0.944163i	$0.393127\pi$
$224$	−1.53803	−	0.740677i	−0.102764	−	0.0494886i
$225$	−0.626178	+	2.74347i	−0.0417452	+	0.182898i
$226$	−6.97099	−	8.74135i	−0.463704	−	0.581466i
$227$	4.44839	−	5.57811i	0.295250	−	0.370232i	−0.611975	−	0.790877i	$-0.709625\pi$
$227$	4.44839	−	5.57811i	0.295250	−	0.370232i	0.907225	+	0.420645i	$0.138196\pi$
$228$	−0.480386	−	2.10471i	−0.0318143	−	0.139388i
$229$	0.501196	−	2.19589i	0.0331200	−	0.145108i	−0.955664	−	0.294458i	$-0.904861\pi$
$229$	0.501196	−	2.19589i	0.0331200	−	0.145108i	0.988784	+	0.149350i	$0.0477180\pi$
$230$	16.2397	−	20.3640i	1.07082	−	1.34276i
$231$	−3.55496			−0.233899
$232$		0			0
$233$	18.9095			1.23880			0.619400	−	0.785076i	$-0.287376\pi$
$233$	18.9095			1.23880			0.619400	+	0.785076i	$0.287376\pi$
$234$	0.281659	−	0.353190i	0.0184127	−	0.0230887i
$235$	−4.28232	+	18.7621i	−0.279348	+	1.22390i
$236$	−0.633415	−	2.77517i	−0.0412318	−	0.180648i
$237$	−10.9438	+	13.7231i	−0.710879	+	0.891414i
$238$	−0.862937	−	1.08209i	−0.0559359	−	0.0701414i
$239$	4.55549	−	19.9589i	0.294670	−	1.29103i	−0.583276	−	0.812274i	$-0.698229\pi$
$239$	4.55549	−	19.9589i	0.294670	−	1.29103i	0.877946	−	0.478760i	$-0.158914\pi$
$240$	−19.1407	−	9.21768i	−1.23553	−	0.594999i
$241$	−6.63922	−	3.19728i	−0.427670	−	0.205955i	0.207651	−	0.978203i	$-0.433418\pi$
$241$	−6.63922	−	3.19728i	−0.427670	−	0.205955i	−0.635321	+	0.772248i	$0.719132\pi$
$242$	0.797093	+	3.49229i	0.0512391	+	0.224493i
$243$	2.30678	−	1.11089i	0.147980	−	0.0712635i
$244$	0.582105			0.0372655
$245$	−23.7887	+	11.4560i	−1.51980	+	0.731898i
$246$	9.09783	+	11.4083i	0.580057	+	0.727368i
$247$	−2.46197	−	3.08721i	−0.156651	−	0.196434i
$248$	−5.35958	+	2.58104i	−0.340334	+	0.163896i
$249$	−7.24698			−0.459259
$250$	29.0846	−	14.0064i	1.83947	−	0.885842i
$251$	−2.88285	−	12.6306i	−0.181964	−	0.797235i	−0.980694	−	0.195546i	$-0.937352\pi$
$251$	−2.88285	−	12.6306i	−0.181964	−	0.797235i	0.798731	−	0.601689i	$-0.205505\pi$
$252$	0.0685317	+	0.0330031i	0.00431709	+	0.00207900i
$253$	−13.2506	−	6.38117i	−0.833060	−	0.401180i
$254$	−4.31886	+	18.9222i	−0.270990	+	1.18728i
$255$	7.29590	+	9.14877i	0.456887	+	0.572918i
$256$	−6.30529	+	7.90658i	−0.394081	+	0.494161i
$257$	−3.71432	−	16.2735i	−0.231693	−	1.01511i	−0.948235	−	0.317570i	$-0.897133\pi$
$257$	−3.71432	−	16.2735i	−0.231693	−	1.01511i	0.716542	−	0.697544i	$-0.245724\pi$
$258$	−0.332437	+	1.45650i	−0.0206966	+	0.0906779i
$259$	1.23005	−	1.54244i	0.0764318	−	0.0958425i
$260$	2.64310			0.163918
$261$		0			0
$262$	16.7506			1.03486
$263$	10.9792	−	13.7675i	0.677006	−	0.848938i	−0.318069	−	0.948068i	$-0.603034\pi$
$263$	10.9792	−	13.7675i	0.677006	−	0.848938i	0.995075	+	0.0991292i	$0.0316057\pi$
$264$	−3.48523	+	15.2698i	−0.214501	+	0.939791i
$265$	0.0440730	+	0.193096i	0.00270738	+	0.0118618i
$266$	−1.44839	+	1.81623i	−0.0888067	+	0.111360i
$267$	12.6468	+	15.8585i	0.773969	+	0.970526i
$268$	1.48039	−	6.48599i	0.0904289	−	0.396195i
$269$	−6.04503	−	2.91113i	−0.368572	−	0.177495i	0.240424	−	0.970668i	$-0.422713\pi$
$269$	−6.04503	−	2.91113i	−0.368572	−	0.177495i	−0.608997	+	0.793173i	$0.708428\pi$
$270$	−22.5661	−	10.8673i	−1.37333	−	0.661362i
$271$	−2.81886	−	12.3502i	−0.171234	−	0.750224i	−0.985492	−	0.169721i	$-0.945713\pi$
$271$	−2.81886	−	12.3502i	−0.171234	−	0.750224i	0.814258	−	0.580503i	$-0.197144\pi$
$272$	−4.20775	+	2.02635i	−0.255132	+	0.122865i
$273$	1.82908			0.110701
$274$	19.0906	−	9.19355i	1.15331	−	0.555402i
$275$	−20.2521	−	25.3954i	−1.22125	−	1.53140i
$276$	2.57942	+	3.23449i	0.155263	+	0.194693i
$277$	−14.1821	+	6.82974i	−0.852120	+	0.410359i	−0.808364	−	0.588683i	$-0.799647\pi$
$277$	−14.1821	+	6.82974i	−0.852120	+	0.410359i	−0.0437557	+	0.999042i	$0.513932\pi$
$278$	15.5429			0.932200
$279$	0.434157	−	0.209079i	0.0259923	−	0.0125172i
$280$	−1.90097	−	8.32869i	−0.113605	−	0.497734i
$281$	−10.6446	−	5.12617i	−0.635003	−	0.305802i	0.0885481	−	0.996072i	$-0.471777\pi$
$281$	−10.6446	−	5.12617i	−0.635003	−	0.305802i	−0.723552	+	0.690270i	$0.757492\pi$
$282$	9.62229	+	4.63385i	0.572999	+	0.275942i
$283$	0.489115	−	2.14295i	0.0290749	−	0.127385i	−0.958308	−	0.285738i	$-0.907761\pi$
$283$	0.489115	−	2.14295i	0.0290749	−	0.127385i	0.987383	+	0.158353i	$0.0506184\pi$
$284$	0.626842	+	0.786035i	0.0371962	+	0.0466426i
$285$	12.2458	−	15.3557i	0.725378	−	0.909595i
$286$	1.16033	+	5.08372i	0.0686115	+	0.300607i
$287$	−1.00000	+	4.38129i	−0.0590281	+	0.258619i
$288$	0.379863	−	0.476333i	0.0223836	−	0.0280682i
$289$	−14.4276			−0.848681
$290$		0			0
$291$	−8.23490			−0.482738
$292$	−2.30947	+	2.89598i	−0.135152	+	0.169475i
$293$	4.59365	−	20.1261i	0.268364	−	1.17578i	−0.643552	−	0.765403i	$-0.722540\pi$
$293$	4.59365	−	20.1261i	0.268364	−	1.17578i	0.911916	−	0.410377i	$-0.134603\pi$
$294$	3.26055	+	14.2854i	0.190159	+	0.833142i
$295$	16.1468	−	20.2474i	0.940100	−	1.17885i
$296$	−5.41939	−	6.79570i	−0.314995	−	0.394992i
$297$	−3.14699	+	13.7879i	−0.182607	+	0.800053i
$298$	20.5770	+	9.90937i	1.19199	+	0.574035i
$299$	6.81767	+	3.28322i	0.394276	+	0.189873i
$300$	2.03319	+	8.90798i	0.117386	+	0.514302i
$301$	−0.414542	+	0.199633i	−0.0238938	+	0.0115067i
$302$	−23.7385			−1.36600
$303$	−5.21648	+	2.51212i	−0.299679	+	0.144318i
$304$	4.88740	+	6.12860i	0.280311	+	0.351499i
$305$	3.30194	+	4.14050i	0.189068	+	0.237084i
$306$	0.445042	−	0.214321i	0.0254414	−	0.0122519i
$307$	22.8116			1.30193			0.650964	−	0.759108i	$-0.274365\pi$
$307$	22.8116			1.30193			0.650964	+	0.759108i	$0.274365\pi$
$308$	−0.791053	+	0.380951i	−0.0450744	+	0.0217067i
$309$	2.61960	+	11.4772i	0.149024	+	0.652917i
$310$	−8.87531	−	4.27413i	−0.504084	−	0.242754i
$311$	−28.0112	−	13.4895i	−1.58837	−	0.764918i	−0.589293	−	0.807919i	$-0.700594\pi$
$311$	−28.0112	−	13.4895i	−1.58837	−	0.764918i	−0.999075	+	0.0430013i	$0.986308\pi$
$312$	1.79321	−	7.85656i	0.101520	−	0.444790i
$313$	−7.00335	−	8.78193i	−0.395853	−	0.496384i	0.543465	−	0.839432i	$-0.317112\pi$
$313$	−7.00335	−	8.78193i	−0.395853	−	0.496384i	−0.939318	+	0.343048i	$0.888541\pi$
$314$	−8.89307	+	11.1516i	−0.501865	+	0.629319i
$315$	0.153989	+	0.674671i	0.00867631	+	0.0380134i
$316$	−0.964656	+	4.22643i	−0.0542662	+	0.237756i
$317$	−3.69537	+	4.63385i	−0.207553	+	0.260263i	−0.874702	−	0.484661i	$-0.838943\pi$
$317$	−3.69537	+	4.63385i	−0.207553	+	0.260263i	0.667149	+	0.744924i	$0.267514\pi$
$318$	0.109916			0.00616380
$319$		0			0
$320$	−36.0344			−2.01439
$321$	−6.49880	+	8.14924i	−0.362728	+	0.454846i
$322$	0.990607	−	4.34013i	0.0552044	−	0.241866i
$323$	−0.960771	−	4.20941i	−0.0534587	−	0.234218i
$324$	2.68598	−	3.36811i	0.149221	−	0.187117i
$325$	10.4201	+	13.0663i	0.578000	+	0.724790i
$326$	1.85205	−	8.11437i	0.102576	−	0.449413i
$327$	−14.9133	−	7.18189i	−0.824710	−	0.397159i
$328$	17.8388	+	8.59070i	0.984981	+	0.474342i
$329$	0.731914	+	3.20673i	0.0403517	+	0.176792i
$330$	−23.3681	+	11.2535i	−1.28637	+	0.619483i
$331$	30.9095			1.69894			0.849469	−	0.527639i	$-0.176923\pi$
$331$	30.9095			1.69894			0.849469	+	0.527639i	$0.176923\pi$
$332$	−1.61260	+	0.776589i	−0.0885032	+	0.0426209i
$333$	0.439001	+	0.550490i	0.0240571	+	0.0301667i
$334$	−11.4040	−	14.3001i	−0.623997	−	0.782467i
$335$	54.5320	−	26.2613i	2.97940	−	1.43481i
$336$	−3.63102			−0.198089
$337$	−7.22132	+	3.47761i	−0.393371	+	0.189437i	−0.620104	−	0.784520i	$-0.712910\pi$
$337$	−7.22132	+	3.47761i	−0.393371	+	0.189437i	0.226733	+	0.973957i	$0.427195\pi$
$338$	3.01022	+	13.1886i	0.163734	+	0.717367i
$339$	14.5565	+	7.01002i	0.790598	+	0.380732i
$340$	2.60388	+	1.25396i	0.141215	+	0.0680055i
$341$	−1.23772	+	5.42280i	−0.0670262	+	0.293661i
$342$	−0.516926	−	0.648205i	−0.0279522	−	0.0350509i
$343$	−5.83393	+	7.31552i	−0.315003	+	0.395001i
$344$	0.451083	+	1.97632i	0.0243207	+	0.106556i
$345$	−8.37531	+	36.6946i	−0.450912	+	1.97557i
$346$	−18.1618	+	22.7742i	−0.976385	+	1.22435i
$347$	−2.26337			−0.121504			−0.0607521	−	0.998153i	$-0.519350\pi$
$347$	−2.26337			−0.121504			−0.0607521	+	0.998153i	$0.519350\pi$
$348$		0			0
$349$	−23.5690			−1.26162			−0.630809	−	0.775938i	$-0.717277\pi$
$349$	−23.5690			−1.26162			−0.630809	+	0.775938i	$0.717277\pi$
$350$	6.13019	−	7.68702i	0.327673	−	0.410889i
$351$	1.61918	−	7.09408i	0.0864253	−	0.378654i
$352$	1.56488	+	6.85620i	0.0834086	+	0.365437i
$353$	−0.612605	+	0.768182i	−0.0326057	+	0.0408862i	−0.797867	−	0.602834i	$-0.794038\pi$
$353$	−0.612605	+	0.768182i	−0.0326057	+	0.0408862i	0.765261	+	0.643720i	$0.222610\pi$
$354$	−8.96077	−	11.2365i	−0.476260	−	0.597211i
$355$	−2.03534	+	8.91742i	−0.108025	+	0.473288i
$356$	4.51357	+	2.17362i	0.239219	+	0.115202i
$357$	1.80194	+	0.867767i	0.0953687	+	0.0459271i
$358$	0.184489	+	0.808298i	0.00975053	+	0.0427199i
$359$	7.10172	−	3.42001i	0.374814	−	0.180501i	−0.236986	−	0.971513i	$-0.576160\pi$
$359$	7.10172	−	3.42001i	0.374814	−	0.180501i	0.611801	+	0.791012i	$0.290445\pi$
$360$	3.04892			0.160692
$361$	10.5891	−	5.09944i	0.557321	−	0.268392i
$362$	8.52595	+	10.6912i	0.448114	+	0.561917i
$363$	−3.22737	−	4.04699i	−0.169393	−	0.212412i
$364$	0.407010	−	0.196006i	0.0213331	−	0.0102735i
$365$	−33.6993			−1.76390
$366$	2.64795	−	1.27518i	0.138410	−	0.0666550i
$367$	6.52164	+	28.5732i	0.340427	+	1.49151i	0.798175	+	0.602425i	$0.205799\pi$
$367$	6.52164	+	28.5732i	0.340427	+	1.49151i	−0.457748	+	0.889082i	$0.651344\pi$
$368$	−13.5341	−	6.51770i	−0.705516	−	0.339759i
$369$	−1.44504	−	0.695895i	−0.0752259	−	0.0362269i
$370$	3.20291	−	14.0329i	0.166511	−	0.729533i
$371$	0.0211063	+	0.0264664i	0.00109578	+	0.00137407i
$372$	0.975541	−	1.22329i	0.0505795	−	0.0634246i
$373$	0.848404	+	3.71710i	0.0439287	+	0.192464i	0.992131	−	0.125202i	$-0.0399580\pi$
$373$	0.848404	+	3.71710i	0.0439287	+	0.192464i	−0.948203	+	0.317666i	$0.897101\pi$
$374$	−1.26875	+	5.55876i	−0.0656055	+	0.287436i
$375$	−29.0846	+	36.4709i	−1.50192	+	1.88335i
$376$	14.4916			0.747345
$377$		0			0
$378$	−4.28083			−0.220182
$379$	5.62767	−	7.05688i	0.289074	−	0.362487i	−0.615996	−	0.787749i	$-0.711246\pi$
$379$	5.62767	−	7.05688i	0.289074	−	0.362487i	0.905070	+	0.425262i	$0.139818\pi$
$380$	1.07942	−	4.72923i	0.0553729	−	0.242605i
$381$	−6.24094	−	27.3433i	−0.319733	−	1.40084i
$382$	−0.402829	+	0.505132i	−0.0206105	+	0.0258448i
$383$	−20.6930	−	25.9482i	−1.05736	−	1.32589i	−0.943126	−	0.332436i	$-0.892129\pi$
$383$	−20.6930	−	25.9482i	−1.05736	−	1.32589i	−0.114236	−	0.993454i	$-0.536442\pi$
$384$	−2.47166	+	10.8290i	−0.126131	+	0.552617i
$385$	−7.19687	−	3.46583i	−0.366786	−	0.176635i
$386$	−1.55765	−	0.750123i	−0.0792821	−	0.0381803i
$387$	−0.0365403	−	0.160093i	−0.00185745	−	0.00813800i
$388$	−1.83244	+	0.882455i	−0.0930279	+	0.0447999i
$389$	27.5362			1.39614			0.698070	−	0.716030i	$-0.254043\pi$
$389$	27.5362			1.39614			0.698070	+	0.716030i	$0.254043\pi$
$390$	12.0233	−	5.79010i	0.608822	−	0.293193i
$391$	5.15883	+	6.46897i	0.260893	+	0.327150i
$392$	12.3964	+	15.5446i	0.626114	+	0.785122i
$393$	−21.8083	+	10.5023i	−1.10008	+	0.529772i
$394$	16.1588			0.814070
$395$	−35.5344	+	17.1125i	−1.78793	+	0.861023i
$396$	−0.0697281	−	0.305499i	−0.00350397	−	0.0153519i
$397$	17.3192	+	8.34047i	0.869224	+	0.418596i	0.814677	−	0.579915i	$-0.196914\pi$
$397$	17.3192	+	8.34047i	0.869224	+	0.418596i	0.0545468	+	0.998511i	$0.482629\pi$
$398$	21.9121	+	10.5523i	1.09836	+	0.528941i
$399$	0.746980	−	3.27273i	0.0373958	−	0.163842i
$400$	−20.6854	−	25.9387i	−1.03427	−	1.29694i
$401$	6.87465	−	8.62054i	0.343304	−	0.430489i	−0.579967	−	0.814640i	$-0.696934\pi$
$401$	6.87465	−	8.62054i	0.343304	−	0.430489i	0.923270	+	0.384151i	$0.125506\pi$
$402$	−7.47434	−	32.7472i	−0.372786	−	1.63328i
$403$	0.636826	−	2.79012i	0.0317226	−	0.138986i
$404$	−0.891576	+	1.11800i	−0.0443575	+	0.0556226i
$405$	39.1933			1.94753
$406$		0			0
$407$	−8.12737			−0.402859
$408$	5.49396	−	6.88921i	0.271992	−	0.341067i
$409$	−7.52595	+	32.9733i	−0.372134	+	1.63043i	0.348640	+	0.937257i	$0.386644\pi$
$409$	−7.52595	+	32.9733i	−0.372134	+	1.63043i	−0.720774	+	0.693170i	$0.756213\pi$
$410$	7.29590	+	31.9654i	0.360319	+	1.57866i
$411$	−19.0906	+	23.9389i	−0.941670	+	1.18082i
$412$	1.81282	+	2.27321i	0.0893114	+	0.111993i
$413$	0.984935	−	4.31528i	0.0484655	−	0.212341i
$414$	1.43147	+	0.689359i	0.0703528	+	0.0338801i
$415$	−14.6712	−	7.06528i	−0.720181	−	0.346821i
$416$	−0.805159	−	3.52763i	−0.0394761	−	0.172956i
$417$	−20.2359	+	9.74508i	−0.990954	+	0.477218i
$418$	9.57002			0.468085
$419$	32.0916	−	15.4545i	1.56778	−	0.755001i	0.569998	−	0.821646i	$-0.306944\pi$
$419$	32.0916	−	15.4545i	1.56778	−	0.755001i	0.997777	+	0.0666451i	$0.0212295\pi$
$420$	1.40097	+	1.75676i	0.0683603	+	0.0857211i
$421$	−5.89642	−	7.39388i	−0.287374	−	0.360356i	0.617100	−	0.786885i	$-0.288307\pi$
$421$	−5.89642	−	7.39388i	−0.287374	−	0.360356i	−0.904474	+	0.426529i	$0.859736\pi$
$422$	23.1787	−	11.1623i	1.12832	−	0.543372i
$423$	−1.17390			−0.0570769
$424$	0.134375	−	0.0647116i	0.00652582	−	0.00314267i
$425$	4.06638	+	17.8160i	0.197248	+	0.864201i
$426$	4.57338	+	2.20242i	0.221581	+	0.106708i
$427$	0.815511	+	0.392730i	0.0394654	+	0.0190055i
$428$	−0.572844	+	2.50979i	−0.0276894	+	0.121315i
$429$	−4.69806	−	5.89118i	−0.226825	−	0.284429i
$430$	−2.09299	+	2.62453i	−0.100933	+	0.126566i
$431$	−0.219300	−	0.960816i	−0.0105633	−	0.0462809i	0.969372	−	0.245599i	$-0.0789845\pi$
$431$	−0.219300	−	0.960816i	−0.0105633	−	0.0462809i	−0.979935	+	0.199318i	$0.936127\pi$
$432$	−3.21432	+	14.0829i	−0.154649	+	0.677563i
$433$	−17.8843	+	22.4263i	−0.859466	+	1.07774i	0.136731	+	0.990608i	$0.456341\pi$
$433$	−17.8843	+	22.4263i	−0.859466	+	1.07774i	−0.996197	+	0.0871286i	$0.972231\pi$
$434$	−1.68366			−0.0808183
$435$		0			0
$436$	−4.08815			−0.195787
$437$	8.65883	−	10.8578i	0.414208	−	0.519401i
$438$	−4.16152	+	18.2328i	−0.198845	+	0.871198i
$439$	1.46734	+	6.42886i	0.0700325	+	0.306833i	0.997798	−	0.0663323i	$-0.0211297\pi$
$439$	1.46734	+	6.42886i	0.0700325	+	0.306833i	−0.927765	+	0.373165i	$0.878273\pi$
$440$	−21.9426	+	27.5152i	−1.04607	+	1.31174i
$441$	−1.00418	−	1.25920i	−0.0478181	−	0.0599620i
$442$	0.652793	−	2.86007i	0.0310502	−	0.136040i
$443$	19.2702	+	9.28006i	0.915557	+	0.440909i	0.831483	−	0.555551i	$-0.187492\pi$
$443$	19.2702	+	9.28006i	0.915557	+	0.440909i	0.0840741	+	0.996460i	$0.473207\pi$
$444$	2.05980	+	0.991949i	0.0977539	+	0.0470758i
$445$	10.1419	+	44.4346i	0.480773	+	2.10640i
$446$	23.7066	−	11.4165i	1.12254	−	0.540586i
$447$	−33.0030			−1.56099
$448$	−5.54892	+	2.67222i	−0.262162	+	0.126250i
$449$	18.2412	+	22.8738i	0.860857	+	1.07948i	0.996062	+	0.0886629i	$0.0282594\pi$
$449$	18.2412	+	22.8738i	0.860857	+	1.07948i	−0.135205	+	0.990818i	$0.543169\pi$
$450$	2.18784	+	2.74347i	0.103136	+	0.129328i
$451$	16.6799	−	8.03264i	0.785428	−	0.378242i
$452$	3.99031			0.187688
$453$	30.9061	−	14.8836i	1.45210	−	0.699292i
$454$	−1.97972	−	8.67373i	−0.0929129	−	0.407078i
$455$	3.70291	+	1.78323i	0.173595	+	0.0835989i
$456$	−13.3252	−	6.41708i	−0.624010	−	0.300507i
$457$	0.0537617	−	0.235545i	0.00251487	−	0.0110183i	−0.973655	−	0.228027i	$-0.926773\pi$
$457$	0.0537617	−	0.235545i	0.00251487	−	0.0110183i	0.976170	+	0.217008i	$0.0696298\pi$
$458$	−1.75116	−	2.19589i	−0.0818263	−	0.102607i
$459$	4.96077	−	6.22061i	0.231549	−	0.290353i
$460$	2.06853	+	9.06283i	0.0964458	+	0.422557i
$461$	−3.85809	+	16.9034i	−0.179689	+	0.787270i	0.802084	+	0.597212i	$0.203725\pi$
$461$	−3.85809	+	16.9034i	−0.179689	+	0.787270i	−0.981773	+	0.190058i	$0.939132\pi$
$462$	−2.76391	+	3.46583i	−0.128589	+	0.161245i
$463$	4.24996			0.197513			0.0987563	−	0.995112i	$-0.468514\pi$
$463$	4.24996			0.197513			0.0987563	+	0.995112i	$0.468514\pi$
$464$		0			0
$465$	14.2349			0.660128
$466$	14.7017	−	18.4354i	0.681044	−	0.854002i
$467$	6.41603	−	28.1105i	0.296899	−	1.30080i	−0.577819	−	0.816165i	$-0.696096\pi$
$467$	6.41603	−	28.1105i	0.296899	−	1.30080i	0.874718	−	0.484633i	$-0.161047\pi$
$468$	0.0358763	+	0.157184i	0.00165838	+	0.00726584i
$469$	6.44989	−	8.08790i	0.297828	−	0.373465i
$470$	14.9623	+	18.7621i	0.690158	+	0.865430i
$471$	4.58642	−	20.0944i	0.211331	−	0.925901i
$472$	−17.5700	−	8.46128i	−0.808726	−	0.389462i
$473$	1.70775	+	0.822410i	0.0785225	+	0.0378144i
$474$	4.87047	+	21.3389i	0.223708	+	0.980129i
$475$	27.6347	−	13.3082i	1.26797	−	0.610620i
$476$	0.493959			0.0226406
$477$	−0.0108851	+	0.00524200i	−0.000498396	+	0.000240015i
$478$	−15.9167	−	19.9589i	−0.728013	−	0.912899i
$479$	−15.0740	−	18.9022i	−0.688750	−	0.863666i	0.307377	−	0.951588i	$-0.400549\pi$
$479$	−15.0740	−	18.9022i	−0.688750	−	0.863666i	−0.996127	+	0.0879221i	$0.971977\pi$
$480$	16.2153	−	7.80887i	0.740123	−	0.356424i
$481$	4.18167			0.190668
$482$	−8.27897	+	3.98694i	−0.377097	+	0.181600i
$483$	1.43147	+	6.27167i	0.0651341	+	0.285371i
$484$	−1.15183	−	0.554694i	−0.0523561	−	0.0252133i
$485$	−16.6712	−	8.02843i	−0.757001	−	0.364552i
$486$	0.710439	−	3.11264i	0.0322262	−	0.141192i
$487$	12.0402	+	15.0979i	0.545593	+	0.684152i	0.975822	−	0.218568i	$-0.0701385\pi$
$487$	12.0402	+	15.0979i	0.545593	+	0.684152i	−0.430229	+	0.902720i	$0.641567\pi$
$488$	2.48643	−	3.11788i	0.112555	−	0.141140i
$489$	2.67629	+	11.7256i	0.121026	+	0.530250i
$490$	−7.32640	+	32.0990i	−0.330973	+	1.45009i
$491$	23.0010	−	28.8423i	1.03802	−	1.30163i	0.0857687	−	0.996315i	$-0.472665\pi$
$491$	23.0010	−	28.8423i	1.03802	−	1.30163i	0.952250	−	0.305319i	$-0.0987632\pi$
$492$	−5.20775			−0.234784
$493$		0			0
$494$	−4.92394			−0.221538
$495$	1.77748	−	2.22889i	0.0798917	−	0.100181i
$496$	−1.26420	+	5.53883i	−0.0567643	+	0.248701i
$497$	0.347871	+	1.52412i	0.0156042	+	0.0683663i
$498$	−5.63437	+	7.06528i	−0.252482	+	0.316603i
$499$	23.5154	+	29.4873i	1.05269	+	1.32003i	0.945438	+	0.325803i	$0.105634\pi$
$499$	23.5154	+	29.4873i	1.05269	+	1.32003i	0.107254	+	0.994232i	$0.465794\pi$
$500$	−2.56369	+	11.2322i	−0.114652	+	0.502321i
$501$	23.8131	+	11.4678i	1.06389	+	0.512343i
$502$	−14.5553	−	7.00944i	−0.649633	−	0.312847i
$503$	1.55980	+	6.83394i	0.0695482	+	0.304710i	0.997724	−	0.0674318i	$-0.0214805\pi$
$503$	1.55980	+	6.83394i	0.0695482	+	0.304710i	−0.928176	+	0.372142i	$0.878623\pi$
$504$	0.469501	−	0.226100i	0.0209132	−	0.0100713i
$505$	−13.0097			−0.578924
$506$	−16.5233	+	7.95718i	−0.734549	+	0.353740i
$507$	−12.1881	−	15.2834i	−0.541294	−	0.678761i
$508$	−4.31886	−	5.41568i	−0.191619	−	0.240282i
$509$	−16.5661	+	7.97783i	−0.734281	+	0.353611i	−0.763366	−	0.645966i	$-0.776455\pi$
$509$	−16.5661	+	7.97783i	−0.734281	+	0.353611i	0.0290852	+	0.999577i	$0.490741\pi$
$510$	14.5918			0.646135
$511$	−5.18933	+	2.49905i	−0.229563	+	0.110552i
$512$	5.54945	+	24.3137i	0.245253	+	1.07453i
$513$	−12.0320	−	5.79430i	−0.531225	−	0.255825i
$514$	−18.7533	−	9.03112i	−0.827173	−	0.398346i
$515$	−5.88620	+	25.7891i	−0.259377	+	1.13640i
$516$	−0.332437	−	0.416863i	−0.0146347	−	0.0183514i
$517$	8.44839	−	10.5940i	0.371560	−	0.465921i
$518$	−0.547425	−	2.39843i	−0.0240525	−	0.105381i
$519$	9.36658	−	41.0377i	0.411147	−	1.80135i
$520$	11.2899	−	14.1570i	0.495093	−	0.620827i
$521$	3.94571			0.172865			0.0864323	−	0.996258i	$-0.472453\pi$
$521$	3.94571			0.172865			0.0864323	+	0.996258i	$0.472453\pi$
$522$		0			0
$523$	−33.9952			−1.48651			−0.743253	−	0.669010i	$-0.766718\pi$
$523$	−33.9952			−1.48651			−0.743253	+	0.669010i	$0.766718\pi$
$524$	−3.72737	+	4.67397i	−0.162831	+	0.204183i
$525$	−3.16152	+	13.8515i	−0.137980	+	0.604530i
$526$	−4.88620	−	21.4078i	−0.213048	−	0.933426i
$527$	1.95108	−	2.44658i	0.0849905	−	0.106575i
$528$	9.32640	+	11.6949i	0.405879	+	0.508957i
$529$	−0.804094	+	3.52296i	−0.0349606	+	0.153172i
$530$	0.222521	+	0.107160i	0.00966569	+	0.00465475i
$531$	1.42327	+	0.685411i	0.0617647	+	0.0297443i
$532$	−0.184489	−	0.808298i	−0.00799860	−	0.0350442i
$533$	−8.58211	+	4.13292i	−0.371732	+	0.179017i
$534$	25.2935			1.09456
$535$	−21.1015	+	10.1619i	−0.912297	+	0.439339i
$536$	−28.4170	−	35.6338i	−1.22743	−	1.53915i
$537$	−0.746980	−	0.936683i	−0.0322345	−	0.0404208i
$538$	−7.53803	+	3.63012i	−0.324988	+	0.156506i
$539$	18.5907			0.800759
$540$	8.05376	−	3.87849i	0.346579	−	0.166904i
$541$	−5.21499	−	22.8484i	−0.224210	−	0.982328i	−0.954270	−	0.298945i	$-0.903365\pi$
$541$	−5.21499	−	22.8484i	−0.224210	−	0.982328i	0.730060	−	0.683383i	$-0.239492\pi$
$542$	−14.2322	−	6.85387i	−0.611326	−	0.294399i
$543$	−17.8034	−	8.57368i	−0.764018	−	0.367932i
$544$	0.880395	−	3.85726i	0.0377466	−	0.165379i
$545$	−23.1896	−	29.0789i	−0.993335	−	1.24560i
$546$	1.42208	−	1.78323i	0.0608592	−	0.0763150i
$547$	−7.18651	−	31.4862i	−0.307273	−	1.34625i	−0.858893	−	0.512156i	$-0.828847\pi$
$547$	−7.18651	−	31.4862i	−0.307273	−	1.34625i	0.551620	−	0.834096i	$-0.314010\pi$
$548$	−1.68276	+	7.37265i	−0.0718839	+	0.314944i
$549$	−0.201415	+	0.252566i	−0.00859617	+	0.0107793i
$550$	−40.5042			−1.72711
$551$		0			0
$552$	28.3424			1.20633
$553$	−4.20291	+	5.27028i	−0.178726	+	0.224115i
$554$	−4.36778	+	19.1365i	−0.185569	+	0.813032i
$555$	4.62833	+	20.2781i	0.196462	+	0.860756i
$556$	−3.45862	+	4.33697i	−0.146678	+	0.183928i
$557$	10.1163	+	12.6854i	0.428639	+	0.537497i	0.948510	−	0.316748i	$-0.102591\pi$
$557$	10.1163	+	12.6854i	0.428639	+	0.537497i	−0.519870	+	0.854245i	$0.674020\pi$
$558$	0.133711	−	0.585826i	0.00566044	−	0.0248000i
$559$	−0.878666	−	0.423143i	−0.0371636	−	0.0178971i
$560$	−7.35086	−	3.53999i	−0.310630	−	0.149592i
$561$	−1.83340	−	8.03264i	−0.0774061	−	0.339138i
$562$	−13.2736	+	6.39223i	−0.559913	+	0.269640i
$563$	−21.9168			−0.923681			−0.461841	−	0.886963i	$-0.652811\pi$
$563$	−21.9168			−0.923681			−0.461841	+	0.886963i	$0.652811\pi$
$564$	−3.43416	+	1.65380i	−0.144604	+	0.0696377i
$565$	22.6347	+	28.3830i	0.952248	+	1.19408i
$566$	−1.70895	−	2.14295i	−0.0718324	−	0.0900750i
$567$	6.03534	−	2.90647i	0.253461	−	0.122060i
$568$	6.88769			0.289001
$569$	33.7836	−	16.2693i	1.41628	−	0.682045i	0.439889	−	0.898052i	$-0.355018\pi$
$569$	33.7836	−	16.2693i	1.41628	−	0.682045i	0.976392	+	0.216007i	$0.0693033\pi$
$570$	−5.44989	−	23.8775i	−0.228271	−	1.00012i
$571$	−24.8838	−	11.9834i	−1.04135	−	0.501490i	−0.166584	−	0.986027i	$-0.553274\pi$
$571$	−24.8838	−	11.9834i	−1.04135	−	0.501490i	−0.874771	+	0.484537i	$0.838988\pi$
$572$	−1.67672	−	0.807465i	−0.0701071	−	0.0337618i
$573$	0.207751	−	0.910216i	0.00867892	−	0.0380248i
$574$	3.49396	+	4.38129i	0.145835	+	0.182871i
$575$	−36.6477	+	45.9548i	−1.52832	+	1.91645i
$576$	−0.489115	−	2.14295i	−0.0203798	−	0.0892897i
$577$	1.40874	−	6.17209i	0.0586466	−	0.256947i	−0.937103	−	0.349054i	$-0.886503\pi$
$577$	1.40874	−	6.17209i	0.0586466	−	0.256947i	0.995749	+	0.0921067i	$0.0293601\pi$
$578$	−11.2171	+	14.0659i	−0.466572	+	0.585062i
$579$	2.49827			0.103825
$580$		0			0
$581$	−2.78315			−0.115465
$582$	−6.40246	+	8.02843i	−0.265391	+	0.332789i
$583$	0.0310319	−	0.135960i	0.00128521	−	0.00563088i
$584$	5.64675	+	24.7400i	0.233664	+	1.02375i
$585$	−0.914542	+	1.14680i	−0.0378117	+	0.0474143i
$586$	−16.0500	−	20.1261i	−0.663021	−	0.831402i
$587$	4.34535	−	19.0382i	0.179352	−	0.785791i	−0.802578	−	0.596547i	$-0.796539\pi$
$587$	4.34535	−	19.0382i	0.179352	−	0.785791i	0.981930	−	0.189244i	$-0.0606038\pi$
$588$	−4.71164	−	2.26900i	−0.194305	−	0.0935722i
$589$	−4.73221	−	2.27891i	−0.194987	−	0.0939009i
$590$	−7.18598	−	31.4838i	−0.295842	−	1.29617i
$591$	−21.0378	+	10.1313i	−0.865379	+	0.416745i
$592$	−8.30127			−0.341180
$593$	2.22132	−	1.06973i	0.0912189	−	0.0439287i	−0.387718	−	0.921778i	$-0.626737\pi$
$593$	2.22132	−	1.06973i	0.0912189	−	0.0439287i	0.478937	+	0.877849i	$0.341022\pi$
$594$	10.9955	+	13.7879i	0.451149	+	0.565723i
$595$	2.80194	+	3.51352i	0.114868	+	0.144040i
$596$	−7.34385	+	3.53661i	−0.300816	+	0.144865i
$597$	−35.1444			−1.43836
$598$	8.50149	−	4.09410i	0.347652	−	0.167420i
$599$	1.14861	+	5.03240i	0.0469310	+	0.205618i	0.992958	−	0.118471i	$-0.0377993\pi$
$599$	1.14861	+	5.03240i	0.0469310	+	0.205618i	−0.946026	+	0.324089i	$0.894942\pi$
$600$	56.3977	+	27.1597i	2.30243	+	1.10879i
$601$	26.5487	+	12.7852i	1.08294	+	0.521518i	0.888257	−	0.459348i	$-0.151917\pi$
$601$	26.5487	+	12.7852i	1.08294	+	0.521518i	0.194687	+	0.980865i	$0.437631\pi$
$602$	−0.127670	+	0.559360i	−0.00520345	+	0.0227978i
$603$	2.30194	+	2.88654i	0.0937422	+	0.117549i
$604$	5.28232	−	6.62382i	0.214935	−	0.269520i
$605$	−2.58815	−	11.3394i	−0.105223	−	0.461013i
$606$	−1.60656	+	7.03882i	−0.0652622	+	0.285932i
$607$	21.6048	−	27.0916i	0.876913	−	1.09961i	−0.117396	−	0.993085i	$-0.537455\pi$
$607$	21.6048	−	27.0916i	0.876913	−	1.09961i	0.994310	−	0.106529i	$-0.0339738\pi$
$608$	−6.64071			−0.269316
$609$		0			0
$610$	6.60388			0.267383
$611$	−4.34684	+	5.45076i	−0.175854	+	0.220514i
$612$	−0.0392287	+	0.171872i	−0.00158572	+	0.00694751i
$613$	−6.11045	−	26.7716i	−0.246799	−	1.08130i	−0.934685	−	0.355477i	$-0.884318\pi$
$613$	−6.11045	−	26.7716i	−0.246799	−	1.08130i	0.687886	−	0.725819i	$-0.258539\pi$
$614$	17.7356	−	22.2397i	0.715749	−	0.897521i
$615$	−29.5405	−	37.0426i	−1.19119	−	1.49370i
$616$	−1.33848	+	5.86426i	−0.0539288	+	0.236278i
$617$	−30.8838	−	14.8729i	−1.24334	−	0.598759i	−0.307618	−	0.951510i	$-0.599532\pi$
$617$	−30.8838	−	14.8729i	−1.24334	−	0.598759i	−0.935717	+	0.352751i	$0.885246\pi$
$618$	13.2262	+	6.36939i	0.532035	+	0.256214i
$619$	−5.71134	−	25.0230i	−0.229558	−	1.00576i	−0.950001	−	0.312246i	$-0.898919\pi$
$619$	−5.71134	−	25.0230i	−0.229558	−	1.00576i	0.720443	−	0.693514i	$-0.243938\pi$
$620$	3.16756	−	1.52542i	0.127212	−	0.0612623i
$621$	25.5918			1.02696
$622$	−34.9294	+	16.8211i	−1.40054	+	0.674465i
$623$	4.85690	+	6.09035i	0.194587	+	0.244005i
$624$	−4.79859	−	6.01724i	−0.192097	−	0.240882i
$625$	−43.1100	+	20.7607i	−1.72440	+	0.830427i
$626$	−14.0067			−0.559821
$627$	−12.4596	+	6.00022i	−0.497587	+	0.239626i
$628$	−1.13275	−	4.96291i	−0.0452017	−	0.198042i
$629$	4.11960	+	1.98390i	0.164259	+	0.0791032i
$630$	0.777479	+	0.374414i	0.0309755	+	0.0149170i
$631$	6.54234	−	28.6639i	0.260447	−	1.14109i	−0.660322	−	0.750982i	$-0.729580\pi$
$631$	6.54234	−	28.6639i	0.260447	−	1.14109i	0.920769	−	0.390109i	$-0.127563\pi$
$632$	18.5172	+	23.2199i	0.736576	+	0.923636i
$633$	−23.1787	+	29.0652i	−0.921272	+	1.15524i
$634$	1.64460	+	7.20545i	0.0653153	+	0.286165i
$635$	14.0233	−	61.4399i	0.556496	−	2.43817i
$636$	−0.0244587	+	0.0306702i	−0.000969849	+	0.00121615i
$637$	−9.56524			−0.378989
$638$		0			0
$639$	−0.557942			−0.0220718
$640$	−15.5613	+	19.5132i	−0.615114	+	0.771329i
$641$	2.32922	−	10.2050i	0.0919985	−	0.403072i	−0.907871	−	0.419250i	$-0.862293\pi$
$641$	2.32922	−	10.2050i	0.0919985	−	0.403072i	0.999869	+	0.0161787i	$0.00515005\pi$
$642$	2.89224	+	12.6717i	0.114148	+	0.500113i
$643$	1.90180	−	2.38478i	0.0749995	−	0.0940465i	−0.742916	−	0.669384i	$-0.766558\pi$
$643$	1.90180	−	2.38478i	0.0749995	−	0.0940465i	0.817916	+	0.575338i	$0.195129\pi$
$644$	0.990607	+	1.24218i	0.0390354	+	0.0489488i
$645$	1.07942	−	4.72923i	0.0425020	−	0.186213i
$646$	−4.85086	−	2.33605i	−0.190854	−	0.0919106i
$647$	26.8523	+	12.9314i	1.05567	+	0.508386i	0.879464	−	0.475966i	$-0.157902\pi$
$647$	26.8523	+	12.9314i	1.05567	+	0.508386i	0.176211	+	0.984352i	$0.443616\pi$
$648$	−6.56734	−	28.7734i	−0.257989	−	1.13032i
$649$	−16.4286	+	7.91162i	−0.644881	+	0.310558i
$650$	20.8401			0.817416
$651$	2.19202	−	1.05562i	0.0859121	−	0.0413731i
$652$	1.85205	+	2.32240i	0.0725319	+	0.0909522i
$653$	7.10119	+	8.90461i	0.277891	+	0.348464i	0.901116	−	0.433578i	$-0.142749\pi$
$653$	7.10119	+	8.90461i	0.277891	+	0.348464i	−0.623225	+	0.782043i	$0.714178\pi$
$654$	−18.5966	+	8.95567i	−0.727186	+	0.350194i
$655$	−54.3889			−2.12515
$656$	17.0368	−	8.20451i	0.665177	−	0.320332i
$657$	−0.457419	−	2.00408i	−0.0178456	−	0.0781867i
$658$	3.69537	+	1.77960i	0.144061	+	0.0693760i
$659$	4.13318	+	1.99043i	0.161006	+	0.0775363i	0.512651	−	0.858597i	$-0.328663\pi$
$659$	4.13318	+	1.99043i	0.161006	+	0.0775363i	−0.351645	+	0.936133i	$0.614378\pi$
$660$	2.05980	−	9.02458i	0.0801777	−	0.351281i
$661$	−8.03348	−	10.0737i	−0.312466	−	0.391820i	0.600655	−	0.799508i	$-0.294907\pi$
$661$	−8.03348	−	10.0737i	−0.312466	−	0.391820i	−0.913121	+	0.407688i	$0.866335\pi$
$662$	24.0315	−	30.1345i	0.934009	−	1.17121i
$663$	0.943313	+	4.13292i	0.0366352	+	0.160509i
$664$	−2.72856	+	11.9546i	−0.105889	+	0.463929i
$665$	4.70291	−	5.89726i	0.182371	−	0.228686i
$666$	0.878002			0.0340219
$667$		0			0
$668$	6.52781			0.252569
$669$	−23.7066	+	29.7271i	−0.916548	+	1.14932i
$670$	16.7947	−	73.5824i	0.648836	−	2.84274i
$671$	−0.829749	−	3.63537i	−0.0320321	−	0.140342i
$672$	1.91789	−	2.40496i	0.0739844	−	0.0927735i
$673$	2.98457	+	3.74253i	0.115047	+	0.144264i	0.836020	−	0.548699i	$-0.184877\pi$
$673$	2.98457	+	3.74253i	0.115047	+	0.144264i	−0.720974	+	0.692962i	$0.756305\pi$
$674$	−2.22401	+	9.74404i	−0.0856658	+	0.375326i
$675$	50.9243	+	24.5238i	1.96008	+	0.943923i
$676$	−4.34990	−	2.09480i	−0.167304	−	0.0805692i
$677$	6.79278	+	29.7611i	0.261068	+	1.14381i	0.920095	+	0.391694i	$0.128111\pi$
$677$	6.79278	+	29.7611i	0.261068	+	1.14381i	−0.659028	+	0.752119i	$0.729032\pi$
$678$	18.1516	−	8.74135i	0.697108	−	0.335709i
$679$	−3.16255			−0.121368
$680$	17.8388	−	8.59070i	0.684086	−	0.329438i
$681$	8.01573	+	10.0514i	0.307163	+	0.385171i
$682$	4.32454	+	5.42280i	0.165595	+	0.207650i
$683$	−8.59999	+	4.14154i	−0.329069	+	0.158472i	−0.591122	−	0.806582i	$-0.701315\pi$
$683$	−8.59999	+	4.14154i	−0.329069	+	0.158472i	0.262053	+	0.965054i	$0.415601\pi$
$684$	0.295897			0.0113139
$685$	−61.9868	+	29.8513i	−2.36839	+	1.14056i
$686$	2.59634	+	11.3753i	0.0991288	+	0.434312i
$687$	3.65668	+	1.76096i	0.139511	+	0.0671849i
$688$	1.74429	+	0.840006i	0.0665005	+	0.0320249i
$689$	−0.0159664	+	0.0699536i	−0.000608273	+	0.00266502i
$690$	29.2630	+	36.6946i	1.11402	+	1.39694i
$691$	−10.2775	+	12.8876i	−0.390974	+	0.490266i	−0.937895	−	0.346918i	$-0.887228\pi$
$691$	−10.2775	+	12.8876i	−0.390974	+	0.490266i	0.546922	+	0.837184i	$0.315800\pi$
$692$	−2.31336	−	10.1355i	−0.0879406	−	0.385293i
$693$	0.108424	−	0.475038i	0.00411870	−	0.0180452i
$694$	−1.75973	+	2.20663i	−0.0667983	+	0.0837624i
$695$	−50.4674			−1.91434
$696$		0			0
$697$	−10.4155			−0.394515
$698$	−18.3244	+	22.9780i	−0.693588	+	0.869731i
$699$	−7.58211	+	33.2194i	−0.286782	+	1.25647i
$700$	0.780831	+	3.42105i	0.0295127	+	0.129303i
$701$	29.2208	−	36.6417i	1.10365	−	1.38394i	0.187905	−	0.982187i	$-0.439830\pi$
$701$	29.2208	−	36.6417i	1.10365	−	1.38394i	0.915749	−	0.401751i	$-0.131598\pi$
$702$	−5.65734	−	7.09408i	−0.213523	−	0.267749i
$703$	1.70775	−	7.48215i	0.0644090	−	0.282194i
$704$	22.8593	+	11.0085i	0.861544	+	0.414898i
$705$	−31.2434	−	15.0460i	−1.17669	−	0.566666i
$706$	0.272635	+	1.19449i	0.0102607	+	0.0449553i
$707$	−2.00335	+	0.964764i	−0.0753438	+	0.0362837i
$708$	5.12929			0.192771
$709$	−9.55107	+	4.59955i	−0.358698	+	0.172740i	−0.604549	−	0.796568i	$-0.706647\pi$
$709$	−9.55107	+	4.59955i	−0.358698	+	0.172740i	0.245851	+	0.969308i	$0.420933\pi$
$710$	7.11141	+	8.91742i	0.266886	+	0.334665i
$711$	−1.50000	−	1.88094i	−0.0562544	−	0.0705408i
$712$	30.9218	−	14.8912i	1.15884	−	0.558070i
$713$	10.0653			0.376949
$714$	2.24698	−	1.08209i	0.0840911	−	0.0404961i
$715$	−3.76755	−	16.5067i	−0.140899	−	0.617317i
$716$	−0.266594	−	0.128385i	−0.00996308	−	0.00479797i
$717$	33.2364	+	16.0058i	1.24124	+	0.597748i
$718$	2.18718	−	9.58265i	0.0816247	−	0.357621i
$719$	−8.29553	−	10.4023i	−0.309371	−	0.387939i	0.602702	−	0.797966i	$-0.294091\pi$
$719$	−8.29553	−	10.4023i	−0.309371	−	0.387939i	−0.912073	+	0.410027i	$0.865519\pi$
$720$	1.81551	−	2.27658i	0.0676601	−	0.0848431i
$721$	1.00604	+	4.40775i	0.0374669	+	0.164153i
$722$	3.26122	−	14.2883i	0.121370	−	0.531756i
$723$	8.27897	−	10.3815i	0.307898	−	0.386092i
$724$	−4.88040			−0.181378
$725$		0			0
$726$	−6.45473			−0.239558
$727$	20.5860	−	25.8141i	0.763494	−	0.957392i	−0.236404	−	0.971655i	$-0.575969\pi$
$727$	20.5860	−	25.8141i	0.763494	−	0.957392i	0.999898	+	0.0142633i	$0.00454031\pi$
$728$	0.688669	−	3.01726i	0.0255238	−	0.111827i
$729$	−5.43535	−	23.8138i	−0.201309	−	0.881994i
$730$	−26.2005	+	32.8544i	−0.969725	+	1.21600i
$731$	−0.664874	−	0.833726i	−0.0245913	−	0.0308365i
$732$	−0.233406	+	1.02262i	−0.00862694	+	0.0377971i
$733$	−28.6465	−	13.7954i	−1.05808	−	0.509546i	−0.177835	−	0.984060i	$-0.556909\pi$
$733$	−28.6465	−	13.7954i	−1.05808	−	0.509546i	−0.880248	+	0.474514i	$0.842624\pi$
$734$	32.9272	+	15.8569i	1.21537	+	0.585289i
$735$	−10.5869	−	46.3845i	−0.390506	−	1.71092i
$736$	11.4656	−	5.52155i	0.422628	−	0.203527i
$737$	−42.6165			−1.56980
$738$	−1.80194	+	0.867767i	−0.0663302	+	0.0319430i
$739$	−14.9236	−	18.7136i	−0.548972	−	0.688389i	0.427504	−	0.904013i	$-0.359393\pi$
$739$	−14.9236	−	18.7136i	−0.548972	−	0.688389i	−0.976476	+	0.215624i	$0.930821\pi$
$740$	3.20291	+	4.01632i	0.117741	+	0.147643i
$741$	6.41066	−	3.08721i	0.235501	−	0.113411i
$742$	0.0422126			0.00154967
$743$	6.67845	−	3.21617i	0.245008	−	0.117990i	−0.307350	−	0.951597i	$-0.599442\pi$
$743$	6.67845	−	3.21617i	0.245008	−	0.117990i	0.552359	+	0.833607i	$0.313728\pi$
$744$	−2.38524	−	10.4504i	−0.0874471	−	0.383131i
$745$	−66.8132	−	32.1755i	−2.44785	−	1.17882i
$746$	4.28352	+	2.06283i	0.156831	+	0.0755257i
$747$	0.221029	−	0.968391i	0.00808703	−	0.0354316i
$748$	−1.26875	−	1.59096i	−0.0463901	−	0.0581713i
$749$	−2.49582	+	3.12966i	−0.0911953	+	0.114355i
$750$	12.9438	+	56.7107i	0.472642	+	2.07078i
$751$	4.30851	−	18.8768i	0.157220	−	0.688825i	−0.833456	−	0.552586i	$-0.813641\pi$
$751$	4.30851	−	18.8768i	0.157220	−	0.688825i	0.990676	−	0.136239i	$-0.0435016\pi$
$752$	8.62916	−	10.8206i	0.314673	−	0.394588i
$753$	23.3448			0.850732
$754$		0			0
$755$	77.0786			2.80518
$756$	0.952575	−	1.19449i	0.0346448	−	0.0434432i
$757$	7.61841	−	33.3784i	0.276896	−	1.21316i	−0.624799	−	0.780786i	$-0.714819\pi$
$757$	7.61841	−	33.3784i	0.276896	−	1.21316i	0.901694	−	0.432374i	$-0.142324\pi$
$758$	−2.50455	−	10.9731i	−0.0909693	−	0.398563i
$759$	16.5233	−	20.7195i	0.599756	−	0.752071i
$760$	−20.7201	−	25.9822i	−0.751598	−	0.942474i
$761$	−3.23974	+	14.1942i	−0.117441	+	0.514541i	0.881650	+	0.471904i	$0.156433\pi$
$761$	−3.23974	+	14.1942i	−0.117441	+	0.514541i	−0.999091	+	0.0426370i	$0.986424\pi$
$762$	−31.5100	−	15.1744i	−1.14149	−	0.549711i
$763$	−5.72737	−	2.75815i	−0.207345	−	0.0998519i
$764$	−0.0513102	−	0.224805i	−0.00185634	−	0.00813315i
$765$	−1.44504	+	0.695895i	−0.0522456	+	0.0251602i
$766$	−41.3860			−1.49534
$767$	8.45281	−	4.07066i	0.305213	−	0.146983i
$768$	−11.3617	−	14.2472i	−0.409981	−	0.514101i
$769$	7.20978	+	9.04077i	0.259991	+	0.326019i	0.894645	−	0.446778i	$-0.147429\pi$
$769$	7.20978	+	9.04077i	0.259991	+	0.326019i	−0.634654	+	0.772797i	$0.718857\pi$
$770$	−8.97434	+	4.32182i	−0.323413	+	0.155747i
$771$	30.0780			1.08323
$772$	0.555918	−	0.267716i	0.0200079	−	0.00963530i
$773$	−1.86347	−	8.16439i	−0.0670243	−	0.293653i	0.930296	−	0.366809i	$-0.119550\pi$
$773$	−1.86347	−	8.16439i	−0.0670243	−	0.293653i	−0.997320	+	0.0731566i	$0.976693\pi$
$774$	−0.184489	−	0.0888451i	−0.00663131	−	0.00319347i
$775$	20.0286	+	9.64528i	0.719450	+	0.346469i
$776$	−3.10052	+	13.5843i	−0.111302	+	0.487647i
$777$	2.21648	+	2.77938i	0.0795158	+	0.0997096i
$778$	21.4088	−	26.8458i	0.767543	−	0.962468i
$779$	3.89008	+	17.0436i	0.139377	+	0.610649i
$780$	−1.05980	+	4.64330i	−0.0379470	+	0.166257i
$781$	4.01543	−	5.03519i	0.143684	−	0.180173i
$782$	10.3177			0.368959
$783$		0			0
$784$	18.9885			0.678161
$785$	28.8756	−	36.2089i	1.03061	−	1.29235i
$786$	−6.71648	+	29.4268i	−0.239569	+	1.04962i
$787$	2.16368	+	9.47969i	0.0771268	+	0.337915i	0.998739	−	0.0501966i	$-0.0159848\pi$
$787$	2.16368	+	9.47969i	0.0771268	+	0.337915i	−0.921613	+	0.388111i	$0.873128\pi$
$788$	−3.59568	+	4.50884i	−0.128091	+	0.160621i
$789$	19.7838	+	24.8081i	0.704322	+	0.883192i
$790$	−10.9438	+	47.9481i	−0.389365	+	1.70592i
$791$	5.59030	+	2.69215i	0.198768	+	0.0957217i
$792$	−1.93416	−	0.931441i	−0.0687273	−	0.0330973i
$793$	0.426919	+	1.87046i	0.0151604	+	0.0664219i
$794$	21.5966	−	10.4004i	0.766436	−	0.369096i
$795$	−0.356896			−0.0126578
$796$	−7.82036	+	3.76608i	−0.277185	+	0.133485i
$797$	−16.4664	−	20.6483i	−0.583271	−	0.731399i	0.399396	−	0.916779i	$-0.369220\pi$
$797$	−16.4664	−	20.6483i	−0.583271	−	0.731399i	−0.982667	+	0.185380i	$0.940649\pi$
$798$	−2.60992	−	3.27273i	−0.0923900	−	0.115853i
$799$	−6.86831	+	3.30761i	−0.242983	+	0.117015i
$800$	28.1062			0.993704
$801$	−2.50484	+	1.20627i	−0.0885043	+	0.0426214i
$802$	−3.05951	−	13.4046i	−0.108035	−	0.473332i
$803$	21.3780	+	10.2951i	0.754413	+	0.363306i
$804$	10.8007	+	5.20136i	0.380913	+	0.183438i
$805$	−3.21648	+	14.0923i	−0.113366	+	0.496689i
$806$	−2.22505	−	2.79012i	−0.0783739	−	0.0982777i
$807$	7.53803	−	9.45239i	0.265351	−	0.332740i
$808$	2.17994	+	9.55094i	0.0766900	+	0.336001i
$809$	−4.18114	+	18.3188i	−0.147001	+	0.644053i	0.846708	+	0.532058i	$0.178581\pi$
$809$	−4.18114	+	18.3188i	−0.147001	+	0.644053i	−0.993709	+	0.111995i	$0.964276\pi$
$810$	30.4720	−	38.2106i	1.07068	−	1.34258i
$811$	48.6983			1.71003			0.855013	−	0.518606i	$-0.173549\pi$
$811$	48.6983			1.71003			0.855013	+	0.518606i	$0.173549\pi$
$812$		0			0
$813$	22.8267			0.800567
$814$	−6.31886	+	7.92360i	−0.221476	+	0.277722i
$815$	−6.01357	+	26.3472i	−0.210646	+	0.922902i
$816$	−1.87263	−	8.20451i	−0.0655550	−	0.287215i
$817$	−1.11596	+	1.39937i	−0.0390424	+	0.0489576i
$818$	26.2954	+	32.9733i	0.919396	+	1.15289i
$819$	−0.0557861	+	0.244415i	−0.00194932	+	0.00854055i
$820$	−10.5429	−	5.07718i	−0.368173	−	0.177303i
$821$	−5.63922	−	2.71570i	−0.196810	−	0.0947788i	0.332883	−	0.942968i	$-0.391979\pi$
$821$	−5.63922	−	2.71570i	−0.196810	−	0.0947788i	−0.529693	+	0.848189i	$0.677693\pi$
$822$	8.49612	+	37.2239i	0.296336	+	1.29833i
$823$	13.5293	−	6.51537i	0.471602	−	0.227111i	−0.182959	−	0.983120i	$-0.558568\pi$
$823$	13.5293	−	6.51537i	0.471602	−	0.227111i	0.654561	+	0.756009i	$0.272853\pi$
$824$	19.9191			0.693916
$825$	52.7340	−	25.3954i	1.83596	−	0.884153i
$826$	−3.44132	−	4.31528i	−0.119739	−	0.150148i
$827$	7.45510	+	9.34840i	0.259239	+	0.325076i	0.894369	−	0.447330i	$-0.147625\pi$
$827$	7.45510	+	9.34840i	0.259239	+	0.325076i	−0.635130	+	0.772405i	$0.719053\pi$
$828$	−0.510885	+	0.246029i	−0.0177545	+	0.00855011i
$829$	28.6305			0.994380			0.497190	−	0.867642i	$-0.334365\pi$
$829$	28.6305			0.994380			0.497190	+	0.867642i	$0.334365\pi$
$830$	−18.2947	+	8.81026i	−0.635018	+	0.305809i
$831$	−6.31163	−	27.6530i	−0.218948	−	0.959273i
$832$	−11.7615	−	5.66405i	−0.407757	−	0.196365i
$833$	−9.42327	−	4.53801i	−0.326497	−	0.157233i
$834$	−6.23221	+	27.3051i	−0.215804	+	0.945498i
$835$	37.0284	+	46.4321i	1.28142	+	1.60685i
$836$	−2.12953	+	2.67035i	−0.0736514	+	0.0923559i
$837$	−2.15375	−	9.43621i	−0.0744446	−	0.326163i
$838$	9.88351	−	43.3025i	0.341420	−	1.49586i
$839$	−30.1289	+	37.7805i	−1.04017	+	1.30433i	−0.0888716	+	0.996043i	$0.528326\pi$
$839$	−30.1289	+	37.7805i	−1.04017	+	1.30433i	−0.951294	+	0.308284i	$0.900245\pi$
$840$	15.3937			0.531134
$841$		0			0
$842$	−11.7928			−0.406408
$843$	13.2736	−	16.6446i	0.457167	−	0.573269i
$844$	−2.04311	+	8.95147i	−0.0703269	+	0.308122i
$845$	−9.77413	−	42.8232i	−0.336240	−	1.47316i
$846$	−0.912682	+	1.14447i	−0.0313787	+	0.0393476i
$847$	−1.23945	−	1.55422i	−0.0425879	−	0.0534035i
$848$	0.0316959	−	0.138869i	0.00108844	−	0.00476878i
$849$	3.56853	+	1.71851i	0.122472	+	0.0589793i
$850$	20.5308	+	9.88711i	0.704200	+	0.339125i
$851$	3.27263	+	14.3383i	0.112184	+	0.491512i
$852$	−1.63222	+	0.786035i	−0.0559189	+	0.0269291i
$853$	−6.40688			−0.219367			−0.109684	−	0.993967i	$-0.534984\pi$
$853$	−6.40688			−0.219367			−0.109684	+	0.993967i	$0.534984\pi$
$854$	1.01693	−	0.489726i	0.0347985	−	0.0167581i
$855$	1.67845	+	2.10471i	0.0574017	+	0.0719795i
$856$	10.9961	+	13.7887i	0.375839	+	0.471288i
$857$	0.646989	−	0.311573i	0.0221007	−	0.0106431i	−0.422801	−	0.906223i	$-0.638953\pi$
$857$	0.646989	−	0.311573i	0.0221007	−	0.0106431i	0.444901	+	0.895580i	$0.353239\pi$
$858$	−9.39612			−0.320778
$859$	14.0528	−	6.76747i	0.479475	−	0.230903i	−0.178504	−	0.983939i	$-0.557126\pi$
$859$	14.0528	−	6.76747i	0.479475	−	0.230903i	0.657979	+	0.753036i	$0.271411\pi$
$860$	−0.266594	−	1.16802i	−0.00909078	−	0.0398293i
$861$	−7.29590	−	3.51352i	−0.248644	−	0.119740i
$862$	−1.10723	−	0.533213i	−0.0377123	−	0.0181613i
$863$	−3.00293	+	13.1567i	−0.102221	+	0.447858i	0.897752	+	0.440501i	$0.145199\pi$
$863$	−3.00293	+	13.1567i	−0.102221	+	0.447858i	−0.999973	+	0.00735754i	$0.997658\pi$
$864$	−7.62983	−	9.56750i	−0.259572	−	0.325493i
$865$	58.9711	−	73.9474i	2.00508	−	2.51429i
$866$	7.95928	+	34.8719i	0.270467	+	1.18499i
$867$	5.78501	−	25.3458i	0.196469	−	0.860788i
$868$	0.374650	−	0.469796i	0.0127164	−	0.0159459i
$869$	27.7700			0.942033
$870$		0			0
$871$	21.9269			0.742965
$872$	−17.4623	+	21.8970i	−0.591347	+	0.741525i
$873$	0.251160	−	1.10040i	0.00850048	−	0.0372430i
$874$	−3.85354	−	16.8835i	−0.130348	−	0.571092i
$875$	−11.1697	+	14.0064i	−0.377605	+	0.473502i
$876$	−4.16152	−	5.21838i	−0.140605	−	0.176313i
$877$	3.49343	−	15.3057i	0.117965	−	0.516837i	−0.881073	−	0.472980i	$-0.843178\pi$
$877$	3.49343	−	15.3057i	0.117965	−	0.516837i	0.999038	−	0.0438569i	$-0.0139646\pi$
$878$	7.40850	+	3.56775i	0.250025	+	0.120406i
$879$	33.5148	+	16.1399i	1.13043	+	0.544385i
$880$	7.47919	+	32.7685i	0.252123	+	1.10462i
$881$	9.75882	−	4.69960i	0.328783	−	0.158334i	−0.262209	−	0.965011i	$-0.584451\pi$
$881$	9.75882	−	4.69960i	0.328783	−	0.158334i	0.590992	+	0.806678i	$0.298737\pi$
$882$	−2.00836			−0.0676250
$883$	14.8470	−	7.14992i	0.499640	−	0.240614i	−0.167051	−	0.985948i	$-0.553424\pi$
$883$	14.8470	−	7.14992i	0.499640	−	0.240614i	0.666691	+	0.745334i	$0.267710\pi$
$884$	0.652793	+	0.818576i	0.0219558	+	0.0275317i
$885$	29.0954	+	36.4845i	0.978033	+	1.22641i
$886$	24.0296	−	11.5720i	0.807290	−	0.388770i
$887$	−28.5763			−0.959497			−0.479748	−	0.877406i	$-0.659272\pi$
$887$	−28.5763			−0.959497			−0.479748	+	0.877406i	$0.659272\pi$
$888$	14.1114	−	6.79570i	0.473548	−	0.228049i
$889$	−2.39679	−	10.5010i	−0.0803857	−	0.352193i
$890$	51.2057	+	24.6593i	1.71642	+	0.826583i
$891$	−24.8632	−	11.9735i	−0.832950	−	0.401127i
$892$	−2.08964	+	9.15530i	−0.0699663	+	0.306542i
$893$	7.97770	+	10.0037i	0.266963	+	0.334762i
$894$	−25.6591	+	32.1755i	−0.858170	+	1.07611i
$895$	−0.599031	−	2.62453i	−0.0200234	−	0.0877283i
$896$	−0.949222	+	4.15881i	−0.0317113	+	0.138936i
$897$	−8.50149	+	10.6605i	−0.283857	+	0.355945i
$898$	36.4825			1.21744
$899$		0			0
$900$	−1.25236			−0.0417452
$901$	−0.0489173	+	0.0613404i	−0.00162967	+	0.00204355i
$902$	5.13706	−	22.5069i	0.171045	−	0.749399i
$903$	−0.184489	−	0.808298i	−0.00613940	−	0.0268985i
$904$	17.0444	−	21.3730i	0.566887	−	0.710854i
$905$	−27.6836	−	34.7141i	−0.920234	−	1.15394i
$906$	9.51842	−	41.7029i	0.316228	−	1.38549i
$907$	−29.6054	−	14.2572i	−0.983030	−	0.473402i	−0.127884	−	0.991789i	$-0.540818\pi$
$907$	−29.6054	−	14.2572i	−0.983030	−	0.473402i	−0.855146	+	0.518387i	$0.826533\pi$
$908$	2.86078	+	1.37768i	0.0949383	+	0.0457199i
$909$	−0.176587	−	0.773680i	−0.00585704	−	0.0256614i
$910$	4.61745	−	2.22365i	0.153067	−	0.0737132i
$911$	10.9638			0.363245			0.181623	−	0.983368i	$-0.441865\pi$
$911$	10.9638			0.363245			0.181623	+	0.983368i	$0.441865\pi$
$912$	−12.7262	+	6.12860i	−0.421406	+	0.202938i
$913$	7.14861	+	8.96408i	0.236585	+	0.296668i
$914$	−0.187841	−	0.235545i	−0.00621323	−	0.00779115i
$915$	−8.59783	+	4.14050i	−0.284236	+	0.136881i
$916$	1.00239			0.0331200
$917$	−8.37531	+	4.03334i	−0.276577	+	0.133193i
$918$	−2.20775	−	9.67279i	−0.0728666	−	0.319250i
$919$	−6.90366	−	3.32463i	−0.227731	−	0.109669i	0.316539	−	0.948579i	$-0.397479\pi$
$919$	−6.90366	−	3.32463i	−0.227731	−	0.109669i	−0.544270	+	0.838910i	$0.683193\pi$
$920$	57.3781	+	27.6318i	1.89170	+	0.910994i
$921$	−9.14675	+	40.0745i	−0.301396	+	1.32050i
$922$	13.4800	+	16.9034i	0.443941	+	0.556684i
$923$	−2.06601	+	2.59069i	−0.0680035	+	0.0852736i
$924$	−0.352052	−	1.54244i	−0.0115816	−	0.0507425i
$925$	−7.22790	+	31.6675i	−0.237652	+	1.04122i
$926$	3.30426	−	4.14341i	0.108585	−	0.136161i
$927$	−1.61356			−0.0529964
$928$		0			0
$929$	9.35988			0.307088			0.153544	−	0.988142i	$-0.450931\pi$
$929$	9.35988			0.307088			0.153544	+	0.988142i	$0.450931\pi$
$930$	11.0673	−	13.8780i	0.362912	−	0.455078i
$931$	−3.90635	+	17.1148i	−0.128025	+	0.560916i
$932$	1.87263	+	8.20451i	0.0613399	+	0.268748i
$933$	34.9294	−	43.8000i	1.14354	−	1.43395i
$934$	−22.4174	−	28.1105i	−0.733519	−	0.919803i
$935$	4.11960	−	18.0492i	0.134725	−	0.590271i
$936$	0.995156	+	0.479242i	0.0325277	+	0.0156645i
$937$	−7.03103	−	3.38597i	−0.229694	−	0.110615i	0.315497	−	0.948926i	$-0.397829\pi$
$937$	−7.03103	−	3.38597i	−0.229694	−	0.110615i	−0.545191	+	0.838312i	$0.683543\pi$
$938$	−2.87047	−	12.5763i	−0.0937241	−	0.410632i
$939$	18.2359	−	8.78193i	0.595105	−	0.286587i
$940$	−8.56465			−0.279348
$941$	25.9013	−	12.4734i	0.844357	−	0.406621i	0.0388772	−	0.999244i	$-0.487622\pi$
$941$	25.9013	−	12.4734i	0.844357	−	0.406621i	0.805480	+	0.592623i	$0.201908\pi$
$942$	−16.0248	−	20.0944i	−0.522115	−	0.654711i
$943$	−20.8877	−	26.1923i	−0.680197	−	0.852940i
$944$	−16.7802	+	8.08090i	−0.546148	+	0.263011i
$945$	13.8998			0.452160
$946$	2.12953	−	1.02553i	0.0692370	−	0.0333428i
$947$	0.513869	+	2.25141i	0.0166985	+	0.0731609i	0.982591	−	0.185784i	$-0.0594824\pi$
$947$	0.513869	+	2.25141i	0.0166985	+	0.0731609i	−0.965892	+	0.258945i	$0.916625\pi$
$948$	−7.03803	−	3.38934i	−0.228585	−	0.110081i
$949$	−10.9993	−	5.29700i	−0.357054	−	0.171948i
$950$	8.51089	−	37.2886i	0.276130	−	1.20980i
$951$	−6.65883	−	8.34991i	−0.215927	−	0.270764i
$952$	2.10992	−	2.64575i	0.0683828	−	0.0857493i
$953$	7.68372	+	33.6646i	0.248900	+	1.09050i	0.932649	+	0.360785i	$0.117491\pi$
$953$	7.68372	+	33.6646i	0.248900	+	1.09050i	−0.683749	+	0.729717i	$0.739652\pi$
$954$	−0.00335239	+	0.0146878i	−0.000108538	+	0.000475534i
$955$	1.30798	−	1.64015i	0.0423252	−	0.0530741i
$956$	9.11098			0.294670
$957$		0			0
$958$	−30.1481			−0.974040
$959$	−7.33161	+	9.19355i	−0.236750	+	0.296875i
$960$	14.4487	−	63.3038i	0.466329	−	2.04312i
$961$	6.05107	+	26.5115i	0.195196	+	0.855209i
$962$	3.25116	−	4.07683i	0.104822	−	0.131442i
$963$	−0.890748	−	1.11696i	−0.0287039	−	0.0359936i
$964$	0.729758	−	3.19728i	0.0235039	−	0.102977i
$965$	5.05765	+	2.43563i	0.162811	+	0.0784058i
$966$	7.22737	+	3.48052i	0.232537	+	0.111984i
$967$	−11.4639	−	50.2266i	−0.368654	−	1.61518i	−0.730481	−	0.682933i	$-0.760704\pi$
$967$	−11.4639	−	50.2266i	−0.368654	−	1.61518i	0.361828	−	0.932245i	$-0.382153\pi$
$968$	−7.89104	+	3.80013i	−0.253628	+	0.122141i
$969$	7.78017			0.249935
$970$	−20.7887	+	10.0113i	−0.667484	+	0.321443i
$971$	4.94773	+	6.20426i	0.158780	+	0.199104i	0.854858	−	0.518863i	$-0.173644\pi$
$971$	4.94773	+	6.20426i	0.158780	+	0.199104i	−0.696077	+	0.717967i	$0.745073\pi$
$972$	0.710439	+	0.890863i	0.0227874	+	0.0285744i
$973$	−7.77144	+	3.74253i	−0.249141	+	0.119980i
$974$	24.0804			0.771585
$975$	−27.1325	+	13.0663i	−0.868936	+	0.418457i
$976$	−0.847503	−	3.71315i	−0.0271279	−	0.118855i
$977$	−24.8663	−	11.9750i	−0.795545	−	0.383114i	−0.00846415	−	0.999964i	$-0.502694\pi$
$977$	−24.8663	−	11.9750i	−0.795545	−	0.383114i	−0.787081	+	0.616850i	$0.788409\pi$
$978$	13.5124	+	6.50722i	0.432078	+	0.208078i
$979$	7.14095	−	31.2865i	0.228226	−	0.999922i
$980$	−7.32640	−	9.18701i	−0.234033	−	0.293468i
$981$	1.41454	−	1.77378i	0.0451629	−	0.0566324i
$982$	−10.2364	−	44.8486i	−0.326656	−	1.43117i
$983$	−7.86108	+	34.4416i	−0.250729	+	1.09852i	0.680116	+	0.733104i	$0.261929\pi$
$983$	−7.86108	+	34.4416i	−0.250729	+	1.09852i	−0.930846	+	0.365413i	$0.880928\pi$
$984$	−22.2446	+	27.8938i	−0.709132	+	0.889223i
$985$	−52.4674			−1.67175
$986$		0			0
$987$	−5.92692			−0.188656
$988$	1.09568	−	1.37394i	0.0348582	−	0.0437108i
$989$	0.763242	−	3.34398i	0.0242697	−	0.106332i
$990$	−0.791053	−	3.46583i	−0.0251413	−	0.110151i
$991$	−0.345183	+	0.432845i	−0.0109651	+	0.0137498i	−0.787284	−	0.616591i	$-0.788513\pi$
$991$	−0.345183	+	0.432845i	−0.0109651	+	0.0137498i	0.776319	+	0.630341i	$0.217085\pi$
$992$	−3.00083	−	3.76292i	−0.0952764	−	0.119473i
$993$	−12.3937	+	54.3005i	−0.393303	+	1.72317i
$994$	1.75637	+	0.845825i	0.0557088	+	0.0268279i
$995$	−71.1483	−	34.2632i	−2.25555	−	1.08622i
$996$	−0.717677	−	3.14435i	−0.0227405	−	0.0996324i
$997$	−20.0426	+	9.65203i	−0.634757	+	0.305683i	−0.723451	−	0.690376i	$-0.757445\pi$
$997$	−20.0426	+	9.65203i	−0.634757	+	0.305683i	0.0886938	+	0.996059i	$0.471731\pi$
$998$	47.0307			1.48873
$999$	12.7419	−	6.13617i	0.403136	−	0.194140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.e.574.1		6
29.2	odd	28		841.2.e.b.63.2		12
29.3	odd	28		841.2.e.d.236.2		12
29.4	even	14		841.2.d.c.571.1		6
29.5	even	14		841.2.d.a.778.1		6
29.6	even	14		841.2.d.c.190.1		6
29.7	even	7		29.2.d.a.25.1	yes	6
29.8	odd	28		841.2.e.d.196.2		12
29.9	even	14		841.2.d.d.645.1		6
29.10	odd	28		841.2.e.c.270.1		12
29.11	odd	28		841.2.b.c.840.2		6
29.12	odd	4		841.2.e.b.267.2		12
29.13	even	14		841.2.a.f.1.1		3
29.14	odd	28		841.2.e.c.651.1		12
29.15	odd	28		841.2.e.c.651.2		12
29.16	even	7		841.2.a.e.1.3		3
29.17	odd	4		841.2.e.b.267.1		12
29.18	odd	28		841.2.b.c.840.5		6
29.19	odd	28		841.2.e.c.270.2		12
29.20	even	7		29.2.d.a.7.1	✓	6
29.21	odd	28		841.2.e.d.196.1		12
29.22	even	14		841.2.d.d.605.1		6
29.23	even	7		841.2.d.b.190.1		6
29.24	even	7	inner	841.2.d.e.778.1		6
29.25	even	7		841.2.d.b.571.1		6
29.26	odd	28		841.2.e.d.236.1		12
29.27	odd	28		841.2.e.b.63.1		12
29.28	even	2		841.2.d.a.574.1		6
87.20	odd	14		261.2.k.a.181.1		6
87.65	odd	14		261.2.k.a.199.1		6
87.71	odd	14		7569.2.a.p.1.3		3
87.74	odd	14		7569.2.a.r.1.1		3
116.7	odd	14		464.2.u.f.257.1		6
116.107	odd	14		464.2.u.f.65.1		6
145.7	odd	28		725.2.r.b.199.1		12
145.49	even	14		725.2.l.b.326.1		6
145.78	odd	28		725.2.r.b.674.1		12
145.94	even	14		725.2.l.b.576.1		6
145.107	odd	28		725.2.r.b.674.2		12
145.123	odd	28		725.2.r.b.199.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.7.1	✓	6	29.20	even	7
29.2.d.a.25.1	yes	6	29.7	even	7
261.2.k.a.181.1		6	87.20	odd	14
261.2.k.a.199.1		6	87.65	odd	14
464.2.u.f.65.1		6	116.107	odd	14
464.2.u.f.257.1		6	116.7	odd	14
725.2.l.b.326.1		6	145.49	even	14
725.2.l.b.576.1		6	145.94	even	14
725.2.r.b.199.1		12	145.7	odd	28
725.2.r.b.199.2		12	145.123	odd	28
725.2.r.b.674.1		12	145.78	odd	28
725.2.r.b.674.2		12	145.107	odd	28
841.2.a.e.1.3		3	29.16	even	7
841.2.a.f.1.1		3	29.13	even	14
841.2.b.c.840.2		6	29.11	odd	28
841.2.b.c.840.5		6	29.18	odd	28
841.2.d.a.574.1		6	29.28	even	2
841.2.d.a.778.1		6	29.5	even	14
841.2.d.b.190.1		6	29.23	even	7
841.2.d.b.571.1		6	29.25	even	7
841.2.d.c.190.1		6	29.6	even	14
841.2.d.c.571.1		6	29.4	even	14
841.2.d.d.605.1		6	29.22	even	14
841.2.d.d.645.1		6	29.9	even	14
841.2.d.e.574.1		6	1.1	even	1	trivial
841.2.d.e.778.1		6	29.24	even	7	inner
841.2.e.b.63.1		12	29.27	odd	28
841.2.e.b.63.2		12	29.2	odd	28
841.2.e.b.267.1		12	29.17	odd	4
841.2.e.b.267.2		12	29.12	odd	4
841.2.e.c.270.1		12	29.10	odd	28
841.2.e.c.270.2		12	29.19	odd	28
841.2.e.c.651.1		12	29.14	odd	28
841.2.e.c.651.2		12	29.15	odd	28
841.2.e.d.196.1		12	29.21	odd	28
841.2.e.d.196.2		12	29.8	odd	28
841.2.e.d.236.1		12	29.26	odd	28
841.2.e.d.236.2		12	29.3	odd	28
7569.2.a.p.1.3		3	87.71	odd	14
7569.2.a.r.1.1		3	87.74	odd	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.777479 - 0.974928i) q^{2} +(-0.400969 + 1.75676i) q^{3} +(0.0990311 + 0.433884i) q^{4} +(-2.52446 + 3.16557i) q^{5} +(1.40097 + 1.75676i) q^{6} +(-0.153989 + 0.674671i) q^{7} +(2.74698 + 1.32288i) q^{8} +(-0.222521 - 0.107160i) q^{9} +(1.12349 + 4.92233i) q^{10} +(2.56853 - 1.23694i) q^{11} -0.801938 q^{12} +(-1.32155 + 0.636426i) q^{13} +(0.538032 + 0.674671i) q^{14} +(-4.54892 - 5.70416i) q^{15} +(2.62349 - 1.26341i) q^{16} -1.60388 q^{17} +(-0.277479 + 0.133627i) q^{18} +(0.599031 + 2.62453i) q^{19} +(-1.62349 - 0.781831i) q^{20} +(-1.12349 - 0.541044i) q^{21} +(0.791053 - 3.46583i) q^{22} +(-3.21648 - 4.03334i) q^{23} +(-3.42543 + 4.29535i) q^{24} +(-2.53534 - 11.1081i) q^{25} +(-0.407010 + 1.78323i) q^{26} +(-3.09299 + 3.87849i) q^{27} -0.307979 q^{28} -9.09783 q^{30} +(-1.21648 + 1.52542i) q^{31} +(-0.548917 + 2.40496i) q^{32} +(1.14310 + 5.00827i) q^{33} +(-1.24698 + 1.56366i) q^{34} +(-1.74698 - 2.19064i) q^{35} +(0.0244587 - 0.107160i) q^{36} +(-2.56853 - 1.23694i) q^{37} +(3.02446 + 1.45650i) q^{38} +(-0.588146 - 2.57684i) q^{39} +(-11.1223 + 5.35621i) q^{40} +6.49396 q^{41} +(-1.40097 + 0.674671i) q^{42} +(0.414542 + 0.519820i) q^{43} +(0.791053 + 0.991949i) q^{44} +(0.900969 - 0.433884i) q^{45} -6.43296 q^{46} +(4.28232 - 2.06226i) q^{47} +(1.16756 + 5.11543i) q^{48} +(5.87531 + 2.82940i) q^{49} +(-12.8007 - 6.16451i) q^{50} +(0.643104 - 2.81762i) q^{51} +(-0.407010 - 0.510374i) q^{52} +(0.0304995 - 0.0382451i) q^{53} +(1.37651 + 6.03089i) q^{54} +(-2.56853 + 11.2535i) q^{55} +(-1.31551 + 1.64960i) q^{56} -4.85086 q^{57} -6.39612 q^{59} +(2.02446 - 2.53859i) q^{60} +(0.291053 - 1.27518i) q^{61} +(0.541385 + 2.37196i) q^{62} +(0.106564 - 0.133627i) q^{63} +(5.54892 + 6.95812i) q^{64} +(1.32155 - 5.79010i) q^{65} +(5.77144 + 2.77938i) q^{66} +(-13.4683 - 6.48599i) q^{67} +(-0.158834 - 0.695895i) q^{68} +(8.37531 - 4.03334i) q^{69} -3.49396 q^{70} +(2.03534 - 0.980170i) q^{71} +(-0.469501 - 0.588735i) q^{72} +(5.18933 + 6.50722i) q^{73} +(-3.20291 + 1.54244i) q^{74} +20.5308 q^{75} +(-1.07942 + 0.519820i) q^{76} +(0.439001 + 1.92339i) q^{77} +(-2.96950 - 1.43004i) q^{78} +(8.77628 + 4.22643i) q^{79} +(-2.62349 + 11.4943i) q^{80} +(-6.03534 - 7.56808i) q^{81} +(5.04892 - 6.33114i) q^{82} +(0.894928 + 3.92094i) q^{83} +(0.123490 - 0.541044i) q^{84} +(4.04892 - 5.07718i) q^{85} +0.829085 q^{86} +8.69202 q^{88} +(7.01842 - 8.80082i) q^{89} +(0.277479 - 1.21572i) q^{90} +(-0.225873 - 0.989616i) q^{91} +(1.43147 - 1.79500i) q^{92} +(-2.19202 - 2.74871i) q^{93} +(1.31886 - 5.77832i) q^{94} +(-9.82036 - 4.72923i) q^{95} +(-4.00484 - 1.92863i) q^{96} +(1.01693 + 4.45544i) q^{97} +(7.32640 - 3.52821i) q^{98} -0.704103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 6 q^{5} + 4 q^{6} - 6 q^{7} + 7 q^{8} - q^{9} + 2 q^{10} + 10 q^{11} + 4 q^{12} - 12 q^{13} - 12 q^{14} - 9 q^{15} + 11 q^{16} + 8 q^{17} - 2 q^{18} + 8 q^{19} - 5 q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) 6 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 6 * q^5 + 4 * q^6 - 6 * q^7 + 7 * q^8 - q^9 + 2 * q^10 + 10 * q^11 + 4 * q^12 - 12 * q^13 - 12 * q^14 - 9 * q^15 + 11 * q^16 + 8 * q^17 - 2 * q^18 + 8 * q^19 - 5 * q^20 - 2 * q^21 - q^22 - 7 * q^24 - 3 * q^25 - 17 * q^26 - 4 * q^27 - 12 * q^28 - 18 * q^30 + 12 * q^31 + 15 * q^32 + 15 * q^33 + 2 * q^34 - q^35 - 9 * q^36 - 10 * q^37 + 9 * q^38 - 11 * q^39 - 21 * q^40 + 20 * q^41 - 4 * q^42 - 8 * q^43 - q^44 + q^45 + 4 * q^47 + 6 * q^48 - q^49 - 27 * q^50 + 12 * q^51 - 17 * q^52 + 10 * q^53 + 13 * q^54 - 10 * q^55 + 7 * q^56 - 2 * q^57 - 56 * q^59 + 3 * q^60 - 4 * q^61 + 10 * q^62 - 20 * q^63 + 15 * q^64 + 12 * q^65 + 16 * q^66 - 30 * q^67 + 16 * q^68 + 14 * q^69 - 2 * q^70 + 7 * q^72 + 24 * q^73 - 6 * q^74 + 48 * q^75 + 2 * q^76 - 17 * q^77 - 8 * q^78 + 12 * q^79 - 11 * q^80 - 24 * q^81 + 12 * q^82 - 18 * q^83 - 4 * q^84 + 6 * q^85 - 16 * q^86 + 42 * q^88 + 14 * q^89 + 2 * q^90 - 23 * q^91 + 14 * q^92 - 3 * q^93 + 15 * q^94 - 22 * q^95 - 2 * q^96 + 22 * q^97 + 26 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more