LMFDB - Embedded newform 841.2.d.c.645.1

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 = [6,2,-2,-2,8] 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			645.1
Root			$0.900969 - 0.433884i$ of defining polynomial
Character	$\chi$	$=$	841.645
Dual form			841.2.d.c.605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.400969 - 1.75676i) q^{2} +(0.400969 + 0.193096i) q^{3} +(-1.12349 + 0.541044i) q^{4} +(-0.0794168 - 0.347948i) q^{5} +(0.178448 - 0.781831i) q^{6} +(3.64795 + 1.75676i) q^{7} +(-0.846011 - 1.06086i) q^{8} +(-1.74698 - 2.19064i) q^{9} +(-0.579417 + 0.279032i) q^{10} +(-1.81551 + 2.27658i) q^{11} -0.554958 q^{12} +(3.23341 - 4.05456i) q^{13} +(1.62349 - 7.11297i) q^{14} +(0.0353438 - 0.154851i) q^{15} +(-3.07942 + 3.86147i) q^{16} -1.10992 q^{17} +(-3.14795 + 3.94740i) q^{18} +(1.84601 - 0.888992i) q^{19} +(0.277479 + 0.347948i) q^{20} +(1.12349 + 1.40881i) q^{21} +(4.72737 + 2.27658i) q^{22} +(0.920583 - 4.03334i) q^{23} +(-0.134375 - 0.588735i) q^{24} +(4.39008 - 2.11415i) q^{25} +(-8.41939 - 4.05456i) q^{26} +(-0.574572 - 2.51737i) q^{27} -5.04892 q^{28} -0.286208 q^{30} +(-1.41454 - 6.19752i) q^{31} +(5.57338 + 2.68400i) q^{32} +(-1.16756 + 0.562269i) q^{33} +(0.445042 + 1.94986i) q^{34} +(0.321552 - 1.40881i) q^{35} +(3.14795 + 1.51597i) q^{36} +(1.81551 + 2.27658i) q^{37} +(-2.30194 - 2.88654i) q^{38} +(2.07942 - 1.00139i) q^{39} +(-0.301938 + 0.378618i) q^{40} -0.396125 q^{41} +(2.02446 - 2.53859i) q^{42} +(1.27748 - 5.59700i) q^{43} +(0.807979 - 3.53999i) q^{44} +(-0.623490 + 0.781831i) q^{45} -7.45473 q^{46} +(4.86443 - 6.09980i) q^{47} +(-1.98039 + 0.953703i) q^{48} +(5.85690 + 7.34432i) q^{49} +(-5.47434 - 6.86461i) q^{50} +(-0.445042 - 0.214321i) q^{51} +(-1.43900 + 6.30468i) q^{52} +(0.969501 + 4.24766i) q^{53} +(-4.19202 + 2.01877i) q^{54} +(0.936313 + 0.450904i) q^{55} +(-1.22252 - 5.35621i) q^{56} +0.911854 q^{57} -9.10992 q^{59} +(0.0440730 + 0.193096i) q^{60} +(-5.44989 - 2.62453i) q^{61} +(-10.3204 + 4.97002i) q^{62} +(-2.52446 - 11.0604i) q^{63} +(0.282323 - 1.23694i) q^{64} +(-1.66756 - 0.803056i) q^{65} +(1.45593 + 1.82567i) q^{66} +(0.233406 + 0.292682i) q^{67} +(1.24698 - 0.600514i) q^{68} +(1.14795 - 1.43948i) q^{69} -2.60388 q^{70} +(-7.11141 + 8.91742i) q^{71} +(-0.846011 + 3.70662i) q^{72} +(-1.99127 + 8.72433i) q^{73} +(3.27144 - 4.10225i) q^{74} +2.16852 q^{75} +(-1.59299 + 1.99755i) q^{76} +(-10.6223 + 5.11543i) q^{77} +(-2.59299 - 3.25151i) q^{78} +(0.370469 + 0.464554i) q^{79} +(1.58815 + 0.764811i) q^{80} +(-1.61476 + 7.07473i) q^{81} +(0.158834 + 0.695895i) q^{82} +(8.49880 - 4.09281i) q^{83} +(-2.02446 - 0.974928i) q^{84} +(0.0881460 + 0.386193i) q^{85} -10.3448 q^{86} +3.95108 q^{88} +(0.316708 + 1.38759i) q^{89} +(1.62349 + 0.781831i) q^{90} +(18.9182 - 9.11052i) q^{91} +(1.14795 + 5.02949i) q^{92} +(0.629531 - 2.75815i) q^{93} +(-12.6664 - 6.09980i) q^{94} +(-0.455927 - 0.571714i) q^{95} +(1.71648 + 2.15240i) q^{96} +(14.1908 - 6.83394i) q^{97} +(10.5538 - 13.2340i) q^{98} +8.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 3 q^{6} + 8 q^{7} - q^{9} + 5 q^{10} + 4 q^{11} - 4 q^{12} + 16 q^{13} + 5 q^{14} - 12 q^{15} - 10 q^{16} - 8 q^{17} - 5 q^{18} + 6 q^{19} + 2 q^{20} + 2 q^{21}+ \cdots + 32 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 3 * q^6 + 8 * q^7 - q^9 + 5 * q^10 + 4 * q^11 - 4 * q^12 + 16 * q^13 + 5 * q^14 - 12 * q^15 - 10 * q^16 - 8 * q^17 - 5 * q^18 + 6 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 + 14 * q^23 + 7 * q^24 + 25 * q^25 - 18 * q^26 - 17 * q^27 - 12 * q^28 - 18 * q^30 + 2 * q^31 + 6 * q^32 - 6 * q^33 + 2 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 - 5 * q^38 + 4 * q^39 + 7 * q^40 - 20 * q^41 + 3 * q^42 + 8 * q^43 + 15 * q^44 + q^45 - 4 * q^47 + q^48 + 27 * q^49 - q^50 - 2 * q^51 + 11 * q^52 - 4 * q^53 - 15 * q^54 - 11 * q^55 - 7 * q^56 - 2 * q^57 - 56 * q^59 + 4 * q^60 - 10 * q^61 - 25 * q^62 - 6 * q^63 - 20 * q^64 - 9 * q^65 + 5 * q^66 - 2 * q^67 - 2 * q^68 - 7 * q^69 + 2 * q^70 + 4 * q^73 + q^74 - 48 * q^75 + 5 * q^76 - 18 * q^77 - q^78 - 12 * q^79 + 17 * q^80 + 11 * q^81 - 16 * q^82 + 10 * q^83 - 3 * q^84 + 8 * q^85 - 16 * q^86 + 42 * q^88 + 28 * q^89 + 5 * q^90 + 40 * q^91 - 7 * q^92 + 18 * q^93 - 34 * q^94 + q^95 - 9 * q^96 + 34 * q^97 + 23 * q^98 + 32 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{7}\right)$

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 $

$2$	−0.400969	−	1.75676i	−0.283528	−	1.24222i	−0.893235	−	0.449590i	$-0.851570\pi$
$2$	−0.400969	−	1.75676i	−0.283528	−	1.24222i	0.609707	−	0.792627i	$-0.291287\pi$
$3$	0.400969	+	0.193096i	0.231499	+	0.111484i	0.546038	−	0.837760i	$-0.316135\pi$
$3$	0.400969	+	0.193096i	0.231499	+	0.111484i	−0.314538	+	0.949245i	$0.601850\pi$
$4$	−1.12349	+	0.541044i	−0.561745	+	0.270522i
$5$	−0.0794168	−	0.347948i	−0.0355163	−	0.155607i	0.954060	−	0.299615i	$-0.0968581\pi$
$5$	−0.0794168	−	0.347948i	−0.0355163	−	0.155607i	−0.989577	+	0.144008i	$0.954001\pi$
$6$	0.178448	−	0.781831i	0.0728511	−	0.319181i
$7$	3.64795	+	1.75676i	1.37879	+	0.663993i	0.968742	−	0.248069i	$-0.0797960\pi$
$7$	3.64795	+	1.75676i	1.37879	+	0.663993i	0.410053	+	0.912062i	$0.365510\pi$
$8$	−0.846011	−	1.06086i	−0.299110	−	0.375072i
$9$	−1.74698	−	2.19064i	−0.582327	−	0.730214i
$10$	−0.579417	+	0.279032i	−0.183228	+	0.0882378i
$11$	−1.81551	+	2.27658i	−0.547397	+	0.686414i	−0.976172	−	0.216997i	$-0.930374\pi$
$11$	−1.81551	+	2.27658i	−0.547397	+	0.686414i	0.428775	+	0.903411i	$0.358945\pi$
$12$	−0.554958			−0.160203
$13$	3.23341	−	4.05456i	0.896785	−	1.12453i	−0.0948536	−	0.995491i	$-0.530238\pi$
$13$	3.23341	−	4.05456i	0.896785	−	1.12453i	0.991639	−	0.129042i	$-0.0411903\pi$
$14$	1.62349	−	7.11297i	0.433896	−	1.90102i
$15$	0.0353438	−	0.154851i	0.00912573	−	0.0399824i
$16$	−3.07942	+	3.86147i	−0.769854	+	0.965367i
$17$	−1.10992			−0.269194			−0.134597	−	0.990900i	$-0.542974\pi$
$17$	−1.10992			−0.269194			−0.134597	+	0.990900i	$0.542974\pi$
$18$	−3.14795	+	3.94740i	−0.741979	+	0.930412i
$19$	1.84601	−	0.888992i	0.423504	−	0.203949i	−0.209978	−	0.977706i	$-0.567339\pi$
$19$	1.84601	−	0.888992i	0.423504	−	0.203949i	0.633482	+	0.773757i	$0.281625\pi$
$20$	0.277479	+	0.347948i	0.0620462	+	0.0778035i
$21$	1.12349	+	1.40881i	0.245166	+	0.307428i
$22$	4.72737	+	2.27658i	1.00788	+	0.485368i
$23$	0.920583	−	4.03334i	0.191955	−	0.841009i	−0.783602	−	0.621263i	$-0.786620\pi$
$23$	0.920583	−	4.03334i	0.191955	−	0.841009i	0.975557	−	0.219746i	$-0.0705230\pi$
$24$	−0.134375	−	0.588735i	−0.0274292	−	0.120175i
$25$	4.39008	−	2.11415i	0.878017	−	0.422831i
$26$	−8.41939	−	4.05456i	−1.65118	−	0.795165i
$27$	−0.574572	−	2.51737i	−0.110577	−	0.484467i
$28$	−5.04892			−0.954156
$29$		0			0
$29$		0			0
$30$	−0.286208			−0.0522542
$31$	−1.41454	−	6.19752i	−0.254059	−	1.11311i	−0.927488	−	0.373854i	$-0.878036\pi$
$31$	−1.41454	−	6.19752i	−0.254059	−	1.11311i	0.673428	−	0.739253i	$-0.264821\pi$
$32$	5.57338	+	2.68400i	0.985243	+	0.474468i
$33$	−1.16756	+	0.562269i	−0.203247	+	0.0978784i
$34$	0.445042	+	1.94986i	0.0763241	+	0.334398i
$35$	0.321552	−	1.40881i	0.0543522	−	0.238133i
$36$	3.14795	+	1.51597i	0.524658	+	0.252662i
$37$	1.81551	+	2.27658i	0.298468	+	0.374267i	0.908340	−	0.418233i	$-0.137350\pi$
$37$	1.81551	+	2.27658i	0.298468	+	0.374267i	−0.609872	+	0.792500i	$0.708779\pi$
$38$	−2.30194	−	2.88654i	−0.373424	−	0.468258i
$39$	2.07942	−	1.00139i	0.332973	−	0.160351i
$40$	−0.301938	+	0.378618i	−0.0477405	+	0.0598648i
$41$	−0.396125			−0.0618643			−0.0309321	−	0.999521i	$-0.509848\pi$
$41$	−0.396125			−0.0618643			−0.0309321	+	0.999521i	$0.509848\pi$
$42$	2.02446	−	2.53859i	0.312381	−	0.391713i
$43$	1.27748	−	5.59700i	0.194814	−	0.853535i	−0.779151	−	0.626836i	$-0.784350\pi$
$43$	1.27748	−	5.59700i	0.194814	−	0.853535i	0.973965	−	0.226699i	$-0.0727933\pi$
$44$	0.807979	−	3.53999i	0.121807	−	0.533673i
$45$	−0.623490	+	0.781831i	−0.0929444	+	0.116549i
$46$	−7.45473			−1.09914
$47$	4.86443	−	6.09980i	0.709550	−	0.889747i	−0.288146	−	0.957586i	$-0.593039\pi$
$47$	4.86443	−	6.09980i	0.709550	−	0.889747i	0.997696	+	0.0678390i	$0.0216104\pi$
$48$	−1.98039	+	0.953703i	−0.285844	+	0.137655i
$49$	5.85690	+	7.34432i	0.836699	+	1.04919i
$50$	−5.47434	−	6.86461i	−0.774189	−	0.970803i
$51$	−0.445042	−	0.214321i	−0.0623183	−	0.0300109i
$52$	−1.43900	+	6.30468i	−0.199554	+	0.874301i
$53$	0.969501	+	4.24766i	0.133171	+	0.583461i	0.996842	+	0.0794054i	$0.0253022\pi$
$53$	0.969501	+	4.24766i	0.133171	+	0.583461i	−0.863671	+	0.504055i	$0.831841\pi$
$54$	−4.19202	+	2.01877i	−0.570462	+	0.274720i
$55$	0.936313	+	0.450904i	0.126252	+	0.0607999i
$56$	−1.22252	−	5.35621i	−0.163366	−	0.715754i
$57$	0.911854			0.120778
$58$		0			0
$59$	−9.10992			−1.18601			−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992			−1.18601			−0.593005	+	0.805199i	$0.702059\pi$
$60$	0.0440730	+	0.193096i	0.00568980	+	0.0249286i
$61$	−5.44989	−	2.62453i	−0.697786	−	0.336036i	0.0511381	−	0.998692i	$-0.483715\pi$
$61$	−5.44989	−	2.62453i	−0.697786	−	0.336036i	−0.748924	+	0.662655i	$0.769429\pi$
$62$	−10.3204	+	4.97002i	−1.31069	+	0.631193i
$63$	−2.52446	−	11.0604i	−0.318052	−	1.39348i
$64$	0.282323	−	1.23694i	0.0352904	−	0.154617i
$65$	−1.66756	−	0.803056i	−0.206836	−	0.0996068i
$66$	1.45593	+	1.82567i	0.179212	+	0.224725i
$67$	0.233406	+	0.292682i	0.0285151	+	0.0357568i	0.795885	−	0.605448i	$-0.207006\pi$
$67$	0.233406	+	0.292682i	0.0285151	+	0.0357568i	−0.767369	+	0.641205i	$0.778435\pi$
$68$	1.24698	−	0.600514i	0.151218	−	0.0728230i
$69$	1.14795	−	1.43948i	0.138197	−	0.173293i
$70$	−2.60388			−0.311223
$71$	−7.11141	+	8.91742i	−0.843969	+	1.05830i	0.153567	+	0.988138i	$0.450924\pi$
$71$	−7.11141	+	8.91742i	−0.843969	+	1.05830i	−0.997535	+	0.0701652i	$0.977647\pi$
$72$	−0.846011	+	3.70662i	−0.0997033	+	0.436829i
$73$	−1.99127	+	8.72433i	−0.233061	+	1.02111i	0.714024	+	0.700121i	$0.246871\pi$
$73$	−1.99127	+	8.72433i	−0.233061	+	1.02111i	−0.947085	+	0.320984i	$0.895986\pi$
$74$	3.27144	−	4.10225i	0.380297	−	0.476877i
$75$	2.16852			0.250399
$76$	−1.59299	+	1.99755i	−0.182729	+	0.229134i
$77$	−10.6223	+	5.11543i	−1.21052	+	0.582957i
$78$	−2.59299	−	3.25151i	−0.293598	−	0.368161i
$79$	0.370469	+	0.464554i	0.0416811	+	0.0522664i	0.802235	−	0.597008i	$-0.203644\pi$
$79$	0.370469	+	0.464554i	0.0416811	+	0.0522664i	−0.760554	+	0.649275i	$0.775073\pi$
$80$	1.58815	+	0.764811i	0.177560	+	0.0855084i
$81$	−1.61476	+	7.07473i	−0.179418	+	0.786081i
$82$	0.158834	+	0.695895i	0.0175402	+	0.0768488i
$83$	8.49880	−	4.09281i	0.932865	−	0.449244i	0.0952182	−	0.995456i	$-0.469645\pi$
$83$	8.49880	−	4.09281i	0.932865	−	0.449244i	0.837647	+	0.546212i	$0.183931\pi$
$84$	−2.02446	−	0.974928i	−0.220887	−	0.106373i
$85$	0.0881460	+	0.386193i	0.00956078	+	0.0418885i
$86$	−10.3448			−1.11551
$87$		0			0
$88$	3.95108			0.421187
$89$	0.316708	+	1.38759i	0.0335710	+	0.147084i	0.988936	−	0.148345i	$-0.0473946\pi$
$89$	0.316708	+	1.38759i	0.0335710	+	0.147084i	−0.955365	+	0.295429i	$0.904537\pi$
$90$	1.62349	+	0.781831i	0.171131	+	0.0824123i
$91$	18.9182	−	9.11052i	1.98317	−	0.955042i
$92$	1.14795	+	5.02949i	0.119682	+	0.524361i
$93$	0.629531	−	2.75815i	0.0652793	−	0.286007i
$94$	−12.6664	−	6.09980i	−1.30644	−	0.629146i
$95$	−0.455927	−	0.571714i	−0.0467771	−	0.0586567i
$96$	1.71648	+	2.15240i	0.175188	+	0.219678i
$97$	14.1908	−	6.83394i	1.44086	−	0.693882i	0.459878	−	0.887982i	$-0.347893\pi$
$97$	14.1908	−	6.83394i	1.44086	−	0.693882i	0.980982	+	0.194100i	$0.0621787\pi$
$98$	10.5538	−	13.2340i	1.06609	−	1.33684i
$99$	8.15883			0.819994
$100$	−3.78836	+	4.75046i	−0.378836	+	0.475046i
$101$	−3.88135	+	17.0053i	−0.386209	+	1.69209i	0.291343	+	0.956619i	$0.405898\pi$
$101$	−3.88135	+	17.0053i	−0.386209	+	1.69209i	−0.677552	+	0.735475i	$0.736959\pi$
$102$	−0.198062	+	0.867767i	−0.0196111	+	0.0859218i
$103$	−1.75451	+	2.20009i	−0.172877	+	0.216781i	−0.860720	−	0.509078i	$-0.829986\pi$
$103$	−1.75451	+	2.20009i	−0.172877	+	0.216781i	0.687843	+	0.725860i	$0.258558\pi$
$104$	−7.03684			−0.690019
$105$	0.400969	−	0.502799i	0.0391306	−	0.0490682i
$106$	7.07338	−	3.40636i	0.687027	−	0.330855i
$107$	−4.65130	−	5.83255i	−0.449658	−	0.563854i	0.504402	−	0.863469i	$-0.331713\pi$
$107$	−4.65130	−	5.83255i	−0.449658	−	0.563854i	−0.954060	+	0.299615i	$0.903142\pi$
$108$	2.00753	+	2.51737i	0.193175	+	0.242234i
$109$	1.48911	+	0.717120i	0.142631	+	0.0686876i	0.503838	−	0.863798i	$-0.331921\pi$
$109$	1.48911	+	0.717120i	0.142631	+	0.0686876i	−0.361207	+	0.932486i	$0.617635\pi$
$110$	0.416698	−	1.82567i	0.0397306	−	0.174071i
$111$	0.288364	+	1.26341i	0.0273703	+	0.119917i
$112$	−18.0172	+	8.67664i	−1.70247	+	0.819865i
$113$	7.78501	+	3.74906i	0.732352	+	0.352682i	0.762609	−	0.646860i	$-0.223918\pi$
$113$	7.78501	+	3.74906i	0.732352	+	0.352682i	−0.0302566	+	0.999542i	$0.509632\pi$
$114$	−0.365625	−	1.60191i	−0.0342439	−	0.150032i
$115$	−1.47650			−0.137684
$116$		0			0
$117$	−14.5308			−1.34337
$118$	3.65279	+	16.0039i	0.336267	+	1.47328i
$119$	−4.04892	−	1.94986i	−0.371164	−	0.178743i
$120$	−0.194177	+	0.0935109i	−0.0177259	+	0.00853634i
$121$	0.560999	+	2.45790i	0.0509999	+	0.223445i
$122$	−2.42543	+	10.6265i	−0.219588	+	0.962077i
$123$	−0.158834	−	0.0764902i	−0.0143215	−	0.00689689i
$124$	4.94235	+	6.19752i	0.443836	+	0.556553i
$125$	−2.19687	−	2.75478i	−0.196494	−	0.246395i
$126$	−18.4182	+	8.86973i	−1.64082	+	0.790179i
$127$	−6.52930	+	8.18749i	−0.579382	+	0.726522i	−0.982007	−	0.188843i	$-0.939526\pi$
$127$	−6.52930	+	8.18749i	−0.579382	+	0.726522i	0.402625	+	0.915365i	$0.368098\pi$
$128$	10.0858			0.891463
$129$	1.59299	−	1.99755i	0.140255	−	0.175874i
$130$	−0.742135	+	3.25151i	−0.0650896	+	0.285176i
$131$	−0.101187	+	0.443330i	−0.00884076	+	0.0387339i	−0.979156	−	0.203110i	$-0.934895\pi$
$131$	−0.101187	+	0.443330i	−0.00884076	+	0.0387339i	0.970315	+	0.241844i	$0.0777522\pi$
$132$	1.00753	−	1.26341i	0.0876945	−	0.109965i
$133$	8.29590			0.719345
$134$	0.420583	−	0.527395i	0.0363329	−	0.0455600i
$135$	−0.830281	+	0.399842i	−0.0714592	+	0.0344130i
$136$	0.939001	+	1.17747i	0.0805187	+	0.100967i
$137$	8.25518	+	10.3517i	0.705287	+	0.884402i	0.997406	−	0.0719797i	$-0.0229317\pi$
$137$	8.25518	+	10.3517i	0.705287	+	0.884402i	−0.292119	+	0.956382i	$0.594360\pi$
$138$	−2.98911	−	1.43948i	−0.254450	−	0.122537i
$139$	0.622293	−	2.72645i	0.0527822	−	0.231254i	−0.941656	−	0.336577i	$-0.890731\pi$
$139$	0.622293	−	2.72645i	0.0527822	−	0.231254i	0.994438	+	0.105323i	$0.0335878\pi$
$140$	0.400969	+	1.75676i	0.0338881	+	0.148473i
$141$	3.12833	−	1.50653i	0.263453	−	0.126872i
$142$	18.5172	+	8.91742i	1.55393	+	0.748334i
$143$	3.36025	+	14.7222i	0.280998	+	1.23113i
$144$	13.8388			1.15323
$145$		0			0
$146$	16.1250			1.33451
$147$	0.930272	+	4.07579i	0.0767275	+	0.336165i
$148$	−3.27144	−	1.57544i	−0.268911	−	0.129501i
$149$	−2.44020	+	1.17514i	−0.199909	+	0.0962710i	−0.531160	−	0.847272i	$-0.678244\pi$
$149$	−2.44020	+	1.17514i	−0.199909	+	0.0962710i	0.331251	+	0.943543i	$0.392529\pi$
$150$	−0.869510	−	3.80957i	−0.0709952	−	0.311050i
$151$	0.541917	−	2.37429i	0.0441006	−	0.193217i	−0.948079	−	0.318034i	$-0.896977\pi$
$151$	0.541917	−	2.37429i	0.0441006	−	0.193217i	0.992180	+	0.124817i	$0.0398344\pi$
$152$	−2.50484	−	1.20627i	−0.203170	−	0.0978414i
$153$	1.93900	+	2.43143i	0.156759	+	0.196570i
$154$	13.2458	+	16.6097i	1.06738	+	1.33845i
$155$	−2.04407	+	0.984374i	−0.164184	+	0.0790668i
$156$	−1.79440	+	2.25011i	−0.143667	+	0.180153i
$157$	−17.6775			−1.41082			−0.705411	−	0.708799i	$-0.749238\pi$
$157$	−17.6775			−1.41082			−0.705411	+	0.708799i	$0.749238\pi$
$158$	0.667563	−	0.837097i	0.0531084	−	0.0665959i
$159$	−0.431468	+	1.89039i	−0.0342177	+	0.149917i
$160$	0.491271	−	2.15240i	0.0388384	−	0.170162i
$161$	10.4438	−	13.0962i	0.823090	−	1.03212i
$162$	13.0761			1.02735
$163$	3.09634	−	3.88269i	0.242524	−	0.304116i	−0.645640	−	0.763642i	$-0.723409\pi$
$163$	3.09634	−	3.88269i	0.242524	−	0.304116i	0.888164	+	0.459526i	$0.151981\pi$
$164$	0.445042	−	0.214321i	0.0347519	−	0.0167356i
$165$	0.288364	+	0.361597i	0.0224491	+	0.0281503i
$166$	−10.5978	−	13.2893i	−0.822551	−	1.03145i
$167$	−13.0320	−	6.27588i	−1.00845	−	0.485642i	−0.144649	−	0.989483i	$-0.546205\pi$
$167$	−13.0320	−	6.27588i	−1.00845	−	0.485642i	−0.863796	+	0.503841i	$0.831920\pi$
$168$	0.544073	−	2.38374i	0.0419761	−	0.183910i
$169$	−3.09179	−	13.5460i	−0.237830	−	1.04200i
$170$	0.643104	−	0.309703i	0.0493238	−	0.0237531i
$171$	−5.17241	−	2.49090i	−0.395544	−	0.190484i
$172$	1.59299	+	6.97935i	0.121464	+	0.532170i
$173$	10.5133			0.799314			0.399657	−	0.916665i	$-0.369129\pi$
$173$	10.5133			0.799314			0.399657	+	0.916665i	$0.369129\pi$
$174$		0			0
$175$	19.7289			1.49136
$176$	−3.20022	−	14.0211i	−0.241226	−	1.05688i
$177$	−3.65279	−	1.75909i	−0.274561	−	0.132221i
$178$	2.31067	−	1.11276i	0.173192	−	0.0834048i
$179$	1.27748	+	5.59700i	0.0954833	+	0.418340i	0.999967	−	0.00816938i	$-0.00260042\pi$
$179$	1.27748	+	5.59700i	0.0954833	+	0.418340i	−0.904483	+	0.426509i	$0.859743\pi$
$180$	0.277479	−	1.21572i	0.0206821	−	0.0906141i
$181$	5.98307	+	2.88130i	0.444718	+	0.214165i	0.642821	−	0.766016i	$-0.277764\pi$
$181$	5.98307	+	2.88130i	0.444718	+	0.214165i	−0.198103	+	0.980181i	$0.563478\pi$
$182$	−23.5906	−	29.5817i	−1.74865	−	2.19274i
$183$	−1.67845	−	2.10471i	−0.124074	−	0.155584i
$184$	−5.05765	+	2.43563i	−0.372855	+	0.179557i
$185$	0.647948	−	0.812502i	0.0476381	−	0.0597363i
$186$	−5.09783			−0.373791
$187$	2.01507	−	2.52681i	0.147356	−	0.184779i
$188$	−2.16487	+	9.48493i	−0.157890	+	0.691760i
$189$	2.32640	−	10.1926i	0.169220	−	0.741403i
$190$	−0.821552	+	1.03019i	−0.0596017	+	0.0747381i
$191$	18.8116			1.36116			0.680581	−	0.732673i	$-0.261728\pi$
$191$	18.8116			1.36116			0.680581	+	0.732673i	$0.261728\pi$
$192$	0.352052	−	0.441459i	0.0254071	−	0.0318595i
$193$	9.80678	−	4.72270i	0.705908	−	0.339947i	−0.0462505	−	0.998930i	$-0.514727\pi$
$193$	9.80678	−	4.72270i	0.705908	−	0.339947i	0.752158	+	0.658983i	$0.229013\pi$
$194$	−17.6957	−	22.1897i	−1.27048	−	1.59313i
$195$	−0.513574	−	0.644001i	−0.0367778	−	0.0461179i
$196$	−10.5538	−	5.08242i	−0.753840	−	0.363030i
$197$	1.86927	−	8.18982i	0.133180	−	0.583501i	−0.863661	−	0.504074i	$-0.831834\pi$
$197$	1.86927	−	8.18982i	0.133180	−	0.583501i	0.996841	−	0.0794266i	$-0.0253089\pi$
$198$	−3.27144	−	14.3331i	−0.232491	−	1.01861i
$199$	5.96562	−	2.87289i	0.422891	−	0.203654i	−0.210320	−	0.977633i	$-0.567451\pi$
$199$	5.96562	−	2.87289i	0.422891	−	0.203654i	0.633211	+	0.773979i	$0.281736\pi$
$200$	−5.95689	−	2.86869i	−0.421215	−	0.202847i
$201$	0.0370727	+	0.162426i	0.00261491	+	0.0114567i
$202$	31.4306			2.21145
$203$		0			0
$204$	0.615957			0.0431256
$205$	0.0314589	+	0.137831i	0.00219719	+	0.00962651i
$206$	4.56853	+	2.20009i	0.318305	+	0.153287i
$207$	−10.4438	+	5.02949i	−0.725897	+	0.349574i
$208$	5.69955	+	24.9714i	0.395193	+	1.73145i
$209$	−1.32759	+	5.81656i	−0.0918315	+	0.402340i
$210$	−1.04407	−	0.502799i	−0.0720479	−	0.0346964i
$211$	5.05041	+	6.33301i	0.347685	+	0.435983i	0.924669	−	0.380773i	$-0.124342\pi$
$211$	5.05041	+	6.33301i	0.347685	+	0.435983i	−0.576984	+	0.816755i	$0.695771\pi$
$212$	−3.38740	−	4.24766i	−0.232647	−	0.291730i
$213$	−4.57338	+	2.20242i	−0.313363	+	0.150907i
$214$	−8.38135	+	10.5099i	−0.572938	+	0.718441i
$215$	−2.04892			−0.139735
$216$	−2.18449	+	2.73926i	−0.148636	+	0.186383i
$217$	5.72737	−	25.0932i	0.388799	−	1.70344i
$218$	0.662718	−	2.90356i	0.0448850	−	0.196654i
$219$	−2.48307	+	3.11368i	−0.167791	+	0.210403i
$220$	−1.29590			−0.0873694
$221$	−3.58881	+	4.50023i	−0.241409	+	0.302718i
$222$	2.10388	−	1.01317i	0.141203	−	0.0679997i
$223$	13.6664	+	17.1371i	0.915168	+	1.14758i	0.988642	+	0.150287i	$0.0480197\pi$
$223$	13.6664	+	17.1371i	0.915168	+	1.14758i	−0.0734749	+	0.997297i	$0.523409\pi$
$224$	15.6163	+	19.5822i	1.04340	+	1.30839i
$225$	−12.3007	−	5.92372i	−0.820049	−	0.394915i
$226$	3.46466	−	15.1797i	0.230466	−	1.00974i
$227$	4.06734	+	17.8202i	0.269959	+	1.18277i	0.910060	+	0.414476i	$0.136035\pi$
$227$	4.06734	+	17.8202i	0.269959	+	1.18277i	−0.640102	+	0.768290i	$0.721108\pi$
$228$	−1.02446	+	0.493353i	−0.0678464	+	0.0326731i
$229$	14.4378	+	6.95288i	0.954077	+	0.459459i	0.845114	−	0.534587i	$-0.179533\pi$
$229$	14.4378	+	6.95288i	0.954077	+	0.459459i	0.108963	+	0.994046i	$0.465247\pi$
$230$	0.592031	+	2.59386i	0.0390374	+	0.171034i
$231$	−5.24698			−0.345226
$232$		0			0
$233$	1.95646			0.128172			0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646			0.128172			0.0640860	+	0.997944i	$0.479587\pi$
$234$	5.82640	+	25.5271i	0.380883	+	1.66876i
$235$	−2.50873	−	1.20814i	−0.163651	−	0.0788104i
$236$	10.2349	−	4.92887i	0.666235	−	0.320842i
$237$	0.0588430	+	0.257808i	0.00382226	+	0.0167464i
$238$	−1.80194	+	7.89481i	−0.116802	+	0.511744i
$239$	8.07553	+	3.88897i	0.522363	+	0.251557i	0.676434	−	0.736503i	$-0.263524\pi$
$239$	8.07553	+	3.88897i	0.522363	+	0.251557i	−0.154071	+	0.988060i	$0.549239\pi$
$240$	0.489115	+	0.613331i	0.0315722	+	0.0395903i
$241$	12.4073	+	15.5583i	0.799225	+	1.00220i	0.999747	+	0.0225070i	$0.00716479\pi$
$241$	12.4073	+	15.5583i	0.799225	+	1.00220i	−0.200522	+	0.979689i	$0.564264\pi$
$242$	4.09299	−	1.97108i	0.263107	−	0.126706i
$243$	−6.84332	+	8.58125i	−0.438999	+	0.550488i
$244$	7.54288			0.482883
$245$	2.09030	−	2.62116i	0.133544	−	0.167459i
$246$	−0.0706876	+	0.309703i	−0.00450688	+	0.0197459i
$247$	2.36443	−	10.3592i	0.150445	−	0.659143i
$248$	−5.37800	+	6.74380i	−0.341503	+	0.428232i
$249$	4.19806			0.266041
$250$	−3.95862	+	4.96395i	−0.250365	+	0.313948i
$251$	23.2494	−	11.1963i	1.46749	−	0.706706i	0.481959	−	0.876194i	$-0.339926\pi$
$251$	23.2494	−	11.1963i	1.46749	−	0.706706i	0.985532	+	0.169487i	$0.0542112\pi$
$252$	8.82036	+	11.0604i	0.555630	+	0.696738i
$253$	7.51089	+	9.41835i	0.472205	+	0.592127i
$254$	17.0015	+	8.18749i	1.06677	+	0.513729i
$255$	−0.0392287	+	0.171872i	−0.00245659	+	0.0107630i
$256$	−4.60872	−	20.1921i	−0.288045	−	1.26201i
$257$	−10.7676	+	5.18538i	−0.671662	+	0.323455i	−0.738446	−	0.674312i	$-0.764440\pi$
$257$	−10.7676	+	5.18538i	−0.671662	+	0.323455i	0.0667848	+	0.997767i	$0.478726\pi$
$258$	−4.14795	−	1.99755i	−0.258240	−	0.124362i
$259$	2.62349	+	11.4943i	0.163016	+	0.714219i
$260$	2.30798			0.143135
$261$		0			0
$262$	0.819396			0.0506225
$263$	−0.0740400	−	0.324390i	−0.00456550	−	0.0200028i	0.972594	−	0.232511i	$-0.0746940\pi$
$263$	−0.0740400	−	0.324390i	−0.00456550	−	0.0200028i	−0.977159	+	0.212508i	$0.931837\pi$
$264$	1.58426	+	0.762940i	0.0975045	+	0.0469557i
$265$	1.40097	−	0.674671i	0.0860608	−	0.0414447i
$266$	−3.32640	−	14.5739i	−0.203954	−	0.893583i
$267$	−0.140948	+	0.617534i	−0.00862589	+	0.0377925i
$268$	−0.420583	−	0.202542i	−0.0256912	−	0.0123722i
$269$	0.663382	+	0.831855i	0.0404471	+	0.0507191i	0.801644	−	0.597802i	$-0.203959\pi$
$269$	0.663382	+	0.831855i	0.0404471	+	0.0507191i	−0.761197	+	0.648521i	$0.775388\pi$
$270$	1.03534	+	1.29828i	0.0630090	+	0.0790108i
$271$	−14.8339	+	7.14364i	−0.901097	+	0.433945i	−0.826285	−	0.563252i	$-0.809550\pi$
$271$	−14.8339	+	7.14364i	−0.901097	+	0.433945i	−0.0748120	+	0.997198i	$0.523836\pi$
$272$	3.41789	−	4.28590i	0.207240	−	0.259871i
$273$	9.34481			0.565574
$274$	14.8753	−	18.6531i	0.898651	−	1.12687i
$275$	−3.15721	+	13.8326i	−0.190387	+	0.834140i
$276$	−0.510885	+	2.23833i	−0.0307517	+	0.134732i
$277$	4.11141	−	5.15554i	0.247031	−	0.309767i	−0.642821	−	0.766016i	$-0.722236\pi$
$277$	4.11141	−	5.15554i	0.247031	−	0.309767i	0.889852	+	0.456250i	$0.150808\pi$
$278$	−5.03923			−0.302233
$279$	−11.1054	+	13.9257i	−0.664861	+	0.833709i
$280$	−1.76659	+	0.850747i	−0.105574	+	0.0508418i
$281$	−19.0383	−	23.8733i	−1.13573	−	1.42416i	−0.890668	−	0.454655i	$-0.849762\pi$
$281$	−19.0383	−	23.8733i	−1.13573	−	1.42416i	−0.245064	−	0.969507i	$-0.578809\pi$
$282$	−3.90097	−	4.89166i	−0.232299	−	0.291294i
$283$	3.20291	+	1.54244i	0.190393	+	0.0916885i	0.526652	−	0.850081i	$-0.323447\pi$
$283$	3.20291	+	1.54244i	0.190393	+	0.0916885i	−0.336258	+	0.941770i	$0.609162\pi$
$284$	3.16487	−	13.8662i	0.187801	−	0.822809i
$285$	−0.0724165	−	0.317278i	−0.00428958	−	0.0187939i
$286$	24.5160	−	11.8063i	1.44966	−	0.698121i
$287$	−1.44504	−	0.695895i	−0.0852981	−	0.0410774i
$288$	−3.85690	−	16.8982i	−0.227270	−	0.995734i
$289$	−15.7681			−0.927534
$290$		0			0
$291$	7.00969			0.410915
$292$	−2.48307	−	10.8791i	−0.145311	−	0.636649i
$293$	29.6238	+	14.2661i	1.73064	+	0.833432i	0.986162	+	0.165786i	$0.0530159\pi$
$293$	29.6238	+	14.2661i	1.73064	+	0.833432i	0.744478	+	0.667647i	$0.232698\pi$
$294$	6.78717	−	3.26853i	0.395836	−	0.190624i
$295$	0.723480	+	3.16977i	0.0421227	+	0.184551i
$296$	0.879199	−	3.85202i	0.0511024	−	0.223894i
$297$	6.77413	+	3.26225i	0.393075	+	0.189295i
$298$	3.04288	+	3.81565i	0.176269	+	0.221034i
$299$	−13.3768	−	16.7740i	−0.773601	−	0.970065i
$300$	−2.43631	+	1.17327i	−0.140661	+	0.0677386i
$301$	14.4928	−	18.1733i	0.835349	−	1.04749i
$302$	−4.38835			−0.252521
$303$	−4.83997	+	6.06913i	−0.278049	+	0.348662i
$304$	−2.25182	+	9.86589i	−0.129151	+	0.565847i
$305$	−0.480386	+	2.10471i	−0.0275068	+	0.120515i
$306$	3.49396	−	4.38129i	0.199736	−	0.250461i
$307$	−14.6703			−0.837275			−0.418638	−	0.908153i	$-0.637492\pi$
$307$	−14.6703			−0.837275			−0.418638	+	0.908153i	$0.637492\pi$
$308$	9.16637	−	11.4943i	0.522302	−	0.654946i
$309$	−1.12833	+	0.543377i	−0.0641887	+	0.0309116i
$310$	2.54892	+	3.19624i	0.144769	+	0.181534i
$311$	−11.5511	−	14.4846i	−0.655001	−	0.821346i	0.337788	−	0.941222i	$-0.390321\pi$
$311$	−11.5511	−	14.4846i	−0.655001	−	0.821346i	−0.992789	+	0.119877i	$0.961750\pi$
$312$	−2.82155	−	1.35879i	−0.159739	−	0.0769262i
$313$	−5.11625	+	22.4158i	−0.289188	+	1.26701i	0.596455	+	0.802647i	$0.296575\pi$
$313$	−5.11625	+	22.4158i	−0.289188	+	1.26701i	−0.885643	+	0.464367i	$0.846282\pi$
$314$	7.08815	+	31.0552i	0.400007	+	1.75255i
$315$	−3.64795	+	1.75676i	−0.205539	+	0.0989822i
$316$	−0.667563	−	0.321481i	−0.0375533	−	0.0180847i
$317$	3.12833	+	13.7061i	0.175705	+	0.769813i	0.983582	+	0.180462i	$0.0577593\pi$
$317$	3.12833	+	13.7061i	0.175705	+	0.769813i	−0.807877	+	0.589351i	$0.799384\pi$
$318$	3.49396			0.195932
$319$		0			0
$320$	−0.452812			−0.0253129
$321$	−0.738783	−	3.23682i	−0.0412348	−	0.180662i
$322$	−27.1945	−	13.0962i	−1.51549	−	0.729821i
$323$	−2.04892	+	0.986707i	−0.114005	+	0.0549018i
$324$	−2.01357	−	8.82204i	−0.111865	−	0.490113i
$325$	5.62296	−	24.6358i	0.311906	−	1.36655i
$326$	−8.06249	−	3.88269i	−0.446540	−	0.215042i
$327$	0.458615	+	0.575086i	0.0253615	+	0.0318023i
$328$	0.335126	+	0.420234i	0.0185042	+	0.0232036i
$329$	28.4611	−	13.7061i	1.56911	−	0.755643i
$330$	0.519614	−	0.651576i	0.0286038	−	0.0358681i
$331$	−13.9565			−0.767116			−0.383558	−	0.923517i	$-0.625301\pi$
$331$	−13.9565			−0.767116			−0.383558	+	0.923517i	$0.625301\pi$
$332$	−7.33393	+	9.19646i	−0.402502	+	0.504721i
$333$	1.81551	−	7.95427i	0.0994894	−	0.435892i
$334$	−5.79978	+	25.4105i	−0.317350	+	1.39040i
$335$	0.0833017	−	0.104457i	0.00455126	−	0.00570709i
$336$	−8.89977			−0.485522
$337$	8.72737	−	10.9438i	0.475410	−	0.596145i	−0.485077	−	0.874472i	$-0.661208\pi$
$337$	8.72737	−	10.9438i	0.475410	−	0.596145i	0.960487	+	0.278327i	$0.0897797\pi$
$338$	−22.5574	+	10.8631i	−1.22696	+	0.590873i
$339$	2.39762	+	3.00652i	0.130221	+	0.163292i
$340$	−0.307979	−	0.386193i	−0.0167025	−	0.0209442i
$341$	16.6773	+	8.03134i	0.903124	+	0.434922i
$342$	−2.30194	+	10.0854i	−0.124475	+	0.545359i
$343$	2.15668	+	9.44902i	0.116450	+	0.510199i
$344$	−7.01842	+	3.37989i	−0.378408	+	0.182232i
$345$	−0.592031	−	0.285107i	−0.0318739	−	0.0153496i
$346$	−4.21552	−	18.4694i	−0.226628	−	0.992921i
$347$	−19.8538			−1.06581			−0.532905	−	0.846175i	$-0.678900\pi$
$347$	−19.8538			−1.06581			−0.532905	+	0.846175i	$0.678900\pi$
$348$		0			0
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$	−7.91066	−	34.6589i	−0.422842	−	1.85259i
$351$	−12.0646	−	5.81003i	−0.643963	−	0.310116i
$352$	−16.2289	+	7.81541i	−0.865001	+	0.416563i
$353$	0.893436	+	3.91440i	0.0475528	+	0.208342i	0.993123	−	0.117076i	$-0.0373520\pi$
$353$	0.893436	+	3.91440i	0.0475528	+	0.208342i	−0.945570	+	0.325418i	$0.894495\pi$
$354$	−1.62565	+	7.12242i	−0.0864021	+	0.378552i
$355$	3.66756	+	1.76621i	0.194654	+	0.0937404i
$356$	−1.10656	−	1.38759i	−0.0586478	−	0.0735420i
$357$	−1.24698	−	1.56366i	−0.0659972	−	0.0827578i
$358$	9.32036	−	4.48845i	0.492596	−	0.237222i
$359$	0.465320	−	0.583493i	0.0245587	−	0.0307956i	−0.769401	−	0.638767i	$-0.779445\pi$
$359$	0.465320	−	0.583493i	0.0245587	−	0.0307956i	0.793959	+	0.607971i	$0.208016\pi$
$360$	1.35690			0.0715147
$361$	−9.22886	+	11.5726i	−0.485729	+	0.609085i
$362$	2.66272	−	11.6661i	0.139949	−	0.613158i
$363$	−0.249668	+	1.09387i	−0.0131042	+	0.0574131i
$364$	−16.3252	+	20.4712i	−0.855673	+	1.07298i
$365$	3.19375			0.167169
$366$	−3.02446	+	3.79255i	−0.158091	+	0.198240i
$367$	−30.6770	+	14.7733i	−1.60133	+	0.771158i	−0.999620	−	0.0275585i	$-0.991227\pi$
$367$	−30.6770	+	14.7733i	−1.60133	+	0.771158i	−0.601707	+	0.798717i	$0.705512\pi$
$368$	12.7397	+	15.9751i	0.664105	+	0.832761i
$369$	0.692021	+	0.867767i	0.0360252	+	0.0451742i
$370$	−1.68718	−	0.812502i	−0.0877122	−	0.0422400i
$371$	−3.92543	+	17.1984i	−0.203798	+	0.892898i
$372$	0.785012	+	3.43936i	0.0407010	+	0.178323i
$373$	−25.2277	+	12.1490i	−1.30624	+	0.629051i	−0.951998	−	0.306103i	$-0.900975\pi$
$373$	−25.2277	+	12.1490i	−1.30624	+	0.629051i	−0.354240	+	0.935154i	$0.615261\pi$
$374$	−5.24698	−	2.52681i	−0.271315	−	0.130658i
$375$	−0.348936	−	1.52879i	−0.0180190	−	0.0789463i
$376$	−10.5864			−0.545953
$377$		0			0
$378$	−18.8388			−0.968962
$379$	5.09150	+	22.3073i	0.261533	+	1.14585i	0.919589	+	0.392881i	$0.128522\pi$
$379$	5.09150	+	22.3073i	0.261533	+	1.14585i	−0.658057	+	0.752969i	$0.728621\pi$
$380$	0.821552	+	0.395639i	0.0421447	+	0.0202958i
$381$	−4.19902	+	2.02214i	−0.215122	+	0.103597i
$382$	−7.54288	−	33.0475i	−0.385927	−	1.69086i
$383$	−2.63869	+	11.5608i	−0.134831	+	0.590731i	0.861694	+	0.507429i	$0.169404\pi$
$383$	−2.63869	+	11.5608i	−0.134831	+	0.590731i	−0.996524	+	0.0833027i	$0.973453\pi$
$384$	4.04407	+	1.94752i	0.206373	+	0.0993841i
$385$	2.62349	+	3.28975i	0.133705	+	0.167661i
$386$	−12.2289	−	15.3345i	−0.622432	−	0.780506i
$387$	−14.4928	+	6.97935i	−0.736709	+	0.354780i
$388$	−12.2458	+	15.3557i	−0.621685	+	0.779569i
$389$	10.3913			0.526862			0.263431	−	0.964678i	$-0.415146\pi$
$389$	10.3913			0.526862			0.263431	+	0.964678i	$0.415146\pi$
$390$	−0.925428	+	1.16045i	−0.0468608	+	0.0587616i
$391$	−1.02177	+	4.47667i	−0.0516731	+	0.226395i
$392$	2.83632	−	12.4267i	0.143256	−	0.627645i
$393$	−0.126178	+	0.158222i	−0.00636485	+	0.00798127i
$394$	−15.1371			−0.762594
$395$	0.132219	−	0.165797i	0.00665266	−	0.00834217i
$396$	−9.16637	+	4.41429i	−0.460627	+	0.221826i
$397$	5.12349	+	6.42465i	0.257141	+	0.322444i	0.893598	−	0.448867i	$-0.148172\pi$
$397$	5.12349	+	6.42465i	0.257141	+	0.322444i	−0.636458	+	0.771312i	$0.719601\pi$
$398$	−7.43900	−	9.32821i	−0.372883	−	0.467581i
$399$	3.32640	+	1.60191i	0.166528	+	0.0801957i
$400$	−5.35517	+	23.4625i	−0.267758	+	1.17313i
$401$	−5.53654	−	24.2572i	−0.276482	−	1.21135i	−0.902208	−	0.431302i	$-0.858054\pi$
$401$	−5.53654	−	24.2572i	−0.276482	−	1.21135i	0.625726	−	0.780043i	$-0.284803\pi$
$402$	0.270479	−	0.130256i	0.0134903	−	0.00649656i
$403$	−29.7020	−	14.3037i	−1.47956	−	0.712520i
$404$	−4.83997	−	21.2053i	−0.240798	−	1.05500i
$405$	2.58987			0.128692
$406$		0			0
$407$	−8.47889			−0.420283
$408$	0.149145	+	0.653447i	0.00738377	+	0.0323504i
$409$	17.0242	+	8.19843i	0.841794	+	0.405386i	0.804525	−	0.593919i	$-0.202420\pi$
$409$	17.0242	+	8.19843i	0.841794	+	0.405386i	0.0372686	+	0.999305i	$0.488134\pi$
$410$	0.229521	−	0.110532i	0.0113352	−	0.00545877i
$411$	1.31120	+	5.74474i	0.0646767	+	0.283367i
$412$	0.780831	−	3.42105i	0.0384688	−	0.168543i
$413$	−33.2325	−	16.0039i	−1.63526	−	0.787502i
$414$	13.0233	+	16.3307i	0.640058	+	0.802608i
$415$	−2.09903	−	2.63210i	−0.103037	−	0.129205i
$416$	28.9034	−	13.9192i	1.41711	−	0.682443i
$417$	0.775987	−	0.973057i	0.0380003	−	0.0476508i
$418$	10.7506			0.525830
$419$	−6.79135	+	8.51608i	−0.331779	+	0.416038i	−0.919540	−	0.392997i	$-0.871438\pi$
$419$	−6.79135	+	8.51608i	−0.331779	+	0.416038i	0.587761	+	0.809035i	$0.300010\pi$
$420$	−0.178448	+	0.781831i	−0.00870737	+	0.0381495i
$421$	−4.44169	+	19.4603i	−0.216475	+	0.948438i	0.743585	+	0.668642i	$0.233124\pi$
$421$	−4.44169	+	19.4603i	−0.216475	+	0.948438i	−0.960059	+	0.279796i	$0.909733\pi$
$422$	9.10052	−	11.4117i	0.443007	−	0.555513i
$423$	−21.8605			−1.06290
$424$	3.68598	−	4.62207i	0.179007	−	0.224468i
$425$	−4.87263	+	2.34653i	−0.236357	+	0.113824i
$426$	5.70291	+	7.15122i	0.276307	+	0.346478i
$427$	−15.2702	−	19.1483i	−0.738979	−	0.926650i
$428$	8.38135	+	4.03625i	0.405128	+	0.195099i
$429$	−1.49545	+	6.55200i	−0.0722011	+	0.316334i
$430$	0.821552	+	3.59945i	0.0396188	+	0.173581i
$431$	27.2005	−	13.0991i	1.31020	−	0.630960i	0.357230	−	0.934016i	$-0.383721\pi$
$431$	27.2005	−	13.0991i	1.31020	−	0.630960i	0.952973	+	0.303056i	$0.0980070\pi$
$432$	11.4901	+	5.53333i	0.552816	+	0.266222i
$433$	−4.49300	−	19.6851i	−0.215920	−	0.946006i	−0.960458	−	0.278426i	$-0.910187\pi$
$433$	−4.49300	−	19.6851i	−0.215920	−	0.946006i	0.744538	−	0.667580i	$-0.232670\pi$
$434$	−46.3793			−2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	−1.88620	−	8.26398i	−0.0902291	−	0.395320i
$438$	6.46562	+	3.11368i	0.308939	+	0.148777i
$439$	9.60872	−	4.62732i	0.458599	−	0.220850i	−0.190297	−	0.981727i	$-0.560945\pi$
$439$	9.60872	−	4.62732i	0.458599	−	0.220850i	0.648896	+	0.760877i	$0.275231\pi$
$440$	−0.313782	−	1.37477i	−0.0149590	−	0.0655396i
$441$	5.85690	−	25.6607i	0.278900	−	1.22194i
$442$	9.34481	+	4.50023i	0.444487	+	0.214054i
$443$	12.6881	+	15.9104i	0.602832	+	0.755927i	0.985816	−	0.167828i	$-0.0536753\pi$
$443$	12.6881	+	15.9104i	0.602832	+	0.755927i	−0.382985	+	0.923755i	$0.625104\pi$
$444$	−1.00753	−	1.26341i	−0.0478154	−	0.0599586i
$445$	0.457656	−	0.220395i	0.0216950	−	0.0104477i
$446$	24.6259	−	30.8800i	1.16607	−	1.46221i
$447$	−1.20536			−0.0570115
$448$	3.20291	−	4.01632i	0.151323	−	0.189753i
$449$	4.32208	−	18.9363i	0.203972	−	0.893659i	−0.764517	−	0.644603i	$-0.777023\pi$
$449$	4.32208	−	18.9363i	0.203972	−	0.893659i	0.968489	−	0.249056i	$-0.0801202\pi$
$450$	−5.47434	+	23.9847i	−0.258063	+	1.13065i
$451$	0.719169	−	0.901809i	0.0338643	−	0.0424645i
$452$	−10.7748			−0.506804
$453$	0.675760	−	0.847376i	0.0317500	−	0.0398132i
$454$	29.6749	−	14.2907i	1.39271	−	0.670694i
$455$	−4.67241	−	5.85901i	−0.219046	−	0.274675i
$456$	−0.771438	−	0.967353i	−0.0361259	−	0.0453005i
$457$	11.1908	+	5.38922i	0.523485	+	0.252097i	0.676913	−	0.736063i	$-0.263317\pi$
$457$	11.1908	+	5.38922i	0.523485	+	0.252097i	−0.153429	+	0.988160i	$0.549031\pi$
$458$	6.42543	−	28.1516i	0.300241	−	1.31544i
$459$	0.637727	+	2.79407i	0.0297666	+	0.130416i
$460$	1.65883	−	0.798852i	0.0773435	−	0.0372467i
$461$	−19.7729	−	9.52214i	−0.920917	−	0.443490i	−0.0875187	−	0.996163i	$-0.527894\pi$
$461$	−19.7729	−	9.52214i	−0.920917	−	0.443490i	−0.833399	+	0.552673i	$0.813608\pi$
$462$	2.10388	+	9.21768i	0.0978811	+	0.428845i
$463$	−33.0073			−1.53398			−0.766990	−	0.641660i	$-0.778246\pi$
$463$	−33.0073			−1.53398			−0.766990	+	0.641660i	$0.778246\pi$
$464$		0			0
$465$	−1.00969			−0.0468232
$466$	−0.784479	−	3.43703i	−0.0363403	−	0.159217i
$467$	−23.5182	−	11.3258i	−1.08829	−	0.524094i	−0.198333	−	0.980135i	$-0.563553\pi$
$467$	−23.5182	−	11.3258i	−1.08829	−	0.524094i	−0.889959	+	0.456041i	$0.849267\pi$
$468$	16.3252	−	7.86180i	0.754633	−	0.363412i
$469$	0.337282	+	1.47773i	0.0155742	+	0.0682351i
$470$	−1.11649	+	4.89166i	−0.0514998	+	0.225635i
$471$	−7.08815	−	3.41347i	−0.326605	−	0.157284i
$472$	7.70709	+	9.66438i	0.354747	+	0.444839i
$473$	10.4227	+	13.0697i	0.479238	+	0.600946i
$474$	0.429312	−	0.206746i	0.0197190	−	0.00949616i
$475$	6.22468	−	7.80550i	0.285608	−	0.358141i
$476$	5.60388			0.256853
$477$	7.61141	−	9.54440i	0.348502	−	0.437008i
$478$	3.59395	−	15.7461i	0.164383	−	0.720211i
$479$	7.35786	−	32.2369i	0.336189	−	1.47294i	−0.470730	−	0.882278i	$-0.656009\pi$
$479$	7.35786	−	32.2369i	0.336189	−	1.47294i	0.806919	−	0.590663i	$-0.201134\pi$
$480$	0.612605	−	0.768182i	0.0279614	−	0.0350625i
$481$	15.1008			0.688538
$482$	22.3572	−	28.0350i	1.01834	−	1.27696i
$483$	6.71648	−	3.23449i	0.305610	−	0.147174i
$484$	−1.96011	−	2.45790i	−0.0890958	−	0.111723i
$485$	−3.50484	−	4.39494i	−0.159147	−	0.199564i
$486$	17.8192	+	8.58125i	0.808293	+	0.389254i
$487$	2.26002	−	9.90180i	0.102411	−	0.448693i	−0.897558	−	0.440896i	$-0.854661\pi$
$487$	2.26002	−	9.90180i	0.102411	−	0.448693i	0.999970	−	0.00779746i	$-0.00248203\pi$
$488$	1.82640	+	8.00197i	0.0826771	+	0.362232i
$489$	1.99127	−	0.958945i	0.0900484	−	0.0433650i
$490$	−5.44289	−	2.62116i	−0.245885	−	0.118412i
$491$	−4.37963	−	19.1884i	−0.197650	−	0.865960i	−0.972331	−	0.233608i	$-0.924947\pi$
$491$	−4.37963	−	19.1884i	−0.197650	−	0.865960i	0.774681	−	0.632352i	$-0.217910\pi$
$492$	0.219833			0.00991082
$493$		0			0
$494$	−19.1468			−0.861453
$495$	−0.647948	−	2.83885i	−0.0291231	−	0.127597i
$496$	28.2875	+	13.6225i	1.27014	+	0.611669i
$497$	−41.6078	+	20.0373i	−1.86637	+	0.898794i
$498$	−1.68329	−	7.37499i	−0.0754301	−	0.330481i
$499$	−6.19710	+	27.1513i	−0.277420	+	1.21546i	0.623622	+	0.781726i	$0.285661\pi$
$499$	−6.19710	+	27.1513i	−0.277420	+	1.21546i	−0.901042	+	0.433732i	$0.857197\pi$
$500$	3.95862	+	1.90637i	0.177035	+	0.0852554i
$501$	−4.01357	−	5.03286i	−0.179313	−	0.224852i
$502$	−28.9916	−	36.3543i	−1.29396	−	1.62257i
$503$	−0.202907	+	0.0977147i	−0.00904716	+	0.00435688i	−0.438402	−	0.898779i	$-0.644455\pi$
$503$	−0.202907	+	0.0977147i	−0.00904716	+	0.00435688i	0.429355	+	0.903136i	$0.358741\pi$
$504$	−9.59783	+	12.0353i	−0.427522	+	0.536095i
$505$	6.22521			0.277018
$506$	13.5341	−	16.9713i	0.601666	−	0.754466i
$507$	1.37598	−	6.02855i	0.0611093	−	0.267737i
$508$	2.90581	−	12.7312i	0.128925	−	0.564856i
$509$	−15.7763	+	19.7828i	−0.699271	+	0.876859i	−0.996969	−	0.0778016i	$-0.975210\pi$
$509$	−15.7763	+	19.7828i	−0.699271	+	0.876859i	0.297697	+	0.954660i	$0.403781\pi$
$510$	0.317667			0.0140665
$511$	−22.5906	+	28.3277i	−0.999349	+	1.25314i
$512$	−15.4508	+	7.44074i	−0.682837	+	0.328837i
$513$	−3.29859	−	4.13630i	−0.145636	−	0.182622i
$514$	13.4269	+	16.8368i	0.592236	+	0.742640i
$515$	0.904854	+	0.435755i	0.0398726	+	0.0192016i
$516$	−0.708947	+	3.10610i	−0.0312097	+	0.136738i
$517$	5.05525	+	22.1485i	0.222330	+	0.974091i
$518$	19.1407	−	9.21768i	0.840995	−	0.405002i
$519$	4.21552	+	2.03009i	0.185041	+	0.0891110i
$520$	0.558843	+	2.44845i	0.0245069	+	0.107372i
$521$	23.5797			1.03305			0.516523	−	0.856273i	$-0.327226\pi$
$521$	23.5797			1.03305			0.516523	+	0.856273i	$0.327226\pi$
$522$		0			0
$523$	3.96508			0.173381			0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508			0.173381			0.0866905	+	0.996235i	$0.472371\pi$
$524$	−0.126178	−	0.552823i	−0.00551212	−	0.0241502i
$525$	7.91066	+	3.80957i	0.345249	+	0.166263i
$526$	−0.540188	+	0.260141i	−0.0235533	+	0.0113427i
$527$	1.57002	+	6.87872i	0.0683913	+	0.299642i
$528$	1.42423	−	6.23996i	0.0619817	−	0.271560i
$529$	5.30194	+	2.55328i	0.230519	+	0.111012i
$530$	−1.74698	−	2.19064i	−0.0758839	−	0.0951555i
$531$	15.9148	+	19.9566i	0.690645	+	0.866042i
$532$	−9.32036	+	4.48845i	−0.404089	+	0.194599i
$533$	−1.28083	+	1.60611i	−0.0554790	+	0.0695684i
$534$	1.14138			0.0493921
$535$	−1.66003	+	2.08161i	−0.0717694	+	0.0899959i
$536$	0.113032	−	0.495224i	0.00488222	−	0.0213904i
$537$	−0.568532	+	2.49090i	−0.0245340	+	0.107490i
$538$	1.19537	−	1.49895i	0.0515362	−	0.0646244i
$539$	−27.3532			−1.17818
$540$	0.716480	−	0.898438i	0.0308324	−	0.0386626i
$541$	−22.2180	+	10.6996i	−0.955225	+	0.460012i	−0.845515	−	0.533951i	$-0.820707\pi$
$541$	−22.2180	+	10.6996i	−0.955225	+	0.460012i	−0.109710	+	0.993964i	$0.534992\pi$
$542$	18.4976	+	23.1953i	0.794540	+	0.996322i
$543$	1.84266	+	2.31062i	0.0790760	+	0.0991582i
$544$	−6.18598	−	2.97901i	−0.265222	−	0.127724i
$545$	0.131260	−	0.575086i	0.00562254	−	0.0246340i
$546$	−3.74698	−	16.4166i	−0.160356	−	0.702565i
$547$	−22.3811	+	10.7782i	−0.956947	+	0.460842i	−0.846117	−	0.532998i	$-0.821065\pi$
$547$	−22.3811	+	10.7782i	−0.956947	+	0.460842i	−0.110831	+	0.993839i	$0.535351\pi$
$548$	−14.8753	−	7.16357i	−0.635442	−	0.306013i
$549$	3.77144	+	16.5238i	0.160961	+	0.705216i
$550$	25.5666			1.09016
$551$		0			0
$552$	−2.49827			−0.106333
$553$	0.535344	+	2.34549i	0.0227651	+	0.0997406i
$554$	−10.7056	−	5.15554i	−0.454837	−	0.219038i
$555$	0.416698	−	0.200671i	0.0176879	−	0.00851802i
$556$	0.775987	+	3.39982i	0.0329092	+	0.144185i
$557$	−1.72790	+	7.57041i	−0.0732134	+	0.320769i	−0.998252	−	0.0591048i	$-0.981175\pi$
$557$	−1.72790	+	7.57041i	−0.0732134	+	0.320769i	0.925038	+	0.379874i	$0.124033\pi$
$558$	28.9170	+	13.9257i	1.22415	+	0.589521i
$559$	−18.5628	−	23.2770i	−0.785122	−	0.984512i
$560$	4.44989	+	5.57998i	0.188042	+	0.235797i
$561$	1.29590	−	0.624071i	0.0547128	−	0.0263483i
$562$	−34.3059	+	43.0182i	−1.44711	+	1.81461i
$563$	−20.8009			−0.876652			−0.438326	−	0.898816i	$-0.644429\pi$
$563$	−20.8009			−0.876652			−0.438326	+	0.898816i	$0.644429\pi$
$564$	−2.69955	+	3.38513i	−0.113672	+	0.142540i
$565$	0.686218	−	3.00652i	0.0288694	−	0.126485i
$566$	1.42543	−	6.24521i	0.0599152	−	0.262506i
$567$	−18.3192	+	22.9715i	−0.769332	+	0.964712i
$568$	15.4765			0.649380
$569$	−1.75153	+	2.19635i	−0.0734279	+	0.0920757i	−0.817189	−	0.576370i	$-0.804469\pi$
$569$	−1.75153	+	2.19635i	−0.0734279	+	0.0920757i	0.743761	+	0.668446i	$0.233040\pi$
$570$	−0.528344	+	0.254437i	−0.0221299	+	0.0106572i
$571$	1.80343	+	2.26143i	0.0754712	+	0.0946379i	0.818134	−	0.575028i	$-0.195009\pi$
$571$	1.80343	+	2.26143i	0.0754712	+	0.0946379i	−0.742663	+	0.669666i	$0.766437\pi$
$572$	−11.7406	−	14.7222i	−0.490898	−	0.615567i
$573$	7.54288	+	3.63246i	0.315108	+	0.151748i
$574$	−0.643104	+	2.81762i	−0.0268426	+	0.117605i
$575$	−4.48566	−	19.6529i	−0.187065	−	0.819585i
$576$	−3.20291	+	1.54244i	−0.133454	+	0.0642683i
$577$	6.47703	+	3.11917i	0.269642	+	0.129853i	0.563820	−	0.825898i	$-0.309331\pi$
$577$	6.47703	+	3.11917i	0.269642	+	0.129853i	−0.294177	+	0.955751i	$0.595046\pi$
$578$	6.32251	+	27.7007i	0.262982	+	1.15220i
$579$	4.84415			0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$	−2.81067	−	12.3143i	−0.116506	−	0.510446i
$583$	−11.4303	−	5.50453i	−0.473393	−	0.227974i
$584$	10.9400	−	5.26841i	0.452699	−	0.218008i
$585$	1.15399	+	5.05596i	0.0477116	+	0.209038i
$586$	13.1838	−	57.7621i	0.544619	−	2.38613i
$587$	27.9632	+	13.4664i	1.15417	+	0.555817i	0.910282	−	0.413988i	$-0.135864\pi$
$587$	27.9632	+	13.4664i	1.15417	+	0.555817i	0.243883	+	0.969805i	$0.421579\pi$
$588$	−3.25033	−	4.07579i	−0.134041	−	0.168083i
$589$	−8.12080	−	10.1832i	−0.334612	−	0.419590i
$590$	5.27844	−	2.54196i	0.217310	−	0.104651i
$591$	2.33095	−	2.92291i	0.0958823	−	0.120233i
$592$	−14.3817			−0.591082
$593$	22.7371	−	28.5114i	0.933699	−	1.17082i	−0.0513733	−	0.998680i	$-0.516360\pi$
$593$	22.7371	−	28.5114i	0.933699	−	1.17082i	0.985072	−	0.172142i	$-0.0550687\pi$
$594$	3.01477	−	13.2086i	0.123698	−	0.541954i
$595$	−0.356896	+	1.56366i	−0.0146313	+	0.0641039i
$596$	2.10574	−	2.64051i	0.0862543	−	0.108159i
$597$	2.94677			0.120603
$598$	−24.1042	+	30.2257i	−0.985693	+	1.23602i
$599$	27.0906	−	13.0461i	1.10689	−	0.533051i	0.211073	−	0.977470i	$-0.432304\pi$
$599$	27.0906	−	13.0461i	1.10689	−	0.533051i	0.895819	+	0.444419i	$0.146590\pi$
$600$	−1.83459	−	2.30051i	−0.0748970	−	0.0939178i
$601$	20.6911	+	25.9458i	0.844008	+	1.05835i	0.997532	+	0.0702081i	$0.0223663\pi$
$601$	20.6911	+	25.9458i	0.844008	+	1.05835i	−0.153524	+	0.988145i	$0.549062\pi$
$602$	−37.7373	−	18.1733i	−1.53806	−	0.740690i
$603$	0.233406	−	1.02262i	0.00950503	−	0.0416443i
$604$	0.675760	+	2.96070i	0.0274963	+	0.120469i
$605$	0.810667	−	0.390397i	0.0329583	−	0.0158719i
$606$	12.6027	+	6.06913i	0.511949	+	0.246542i
$607$	−3.36456	−	14.7411i	−0.136563	−	0.598323i	−0.996175	−	0.0873757i	$-0.972152\pi$
$607$	−3.36456	−	14.7411i	−0.136563	−	0.598323i	0.859612	−	0.510947i	$-0.170705\pi$
$608$	12.6746			0.514021
$609$		0			0
$610$	3.89008			0.157505
$611$	−9.00335	−	39.4463i	−0.364237	−	1.59583i
$612$	−3.49396	−	1.68260i	−0.141235	−	0.0680152i
$613$	−3.38351	+	1.62941i	−0.136659	+	0.0658114i	−0.500964	−	0.865468i	$-0.667021\pi$
$613$	−3.38351	+	1.62941i	−0.136659	+	0.0658114i	0.364305	+	0.931280i	$0.381307\pi$
$614$	5.88231	+	25.7721i	0.237391	+	1.04008i
$615$	−0.0140005	+	0.0613404i	−0.000564557	+	0.00247348i
$616$	14.4133	+	6.94110i	0.580730	+	0.279665i
$617$	−18.6151	−	23.3425i	−0.749414	−	0.939735i	0.250181	−	0.968199i	$-0.419510\pi$
$617$	−18.6151	−	23.3425i	−0.749414	−	0.939735i	−0.999595	+	0.0284638i	$0.990938\pi$
$618$	1.40701	+	1.76433i	0.0565982	+	0.0709719i
$619$	−41.5507	+	20.0098i	−1.67006	+	0.804260i	−0.672101	+	0.740459i	$0.734608\pi$
$619$	−41.5507	+	20.0098i	−1.67006	+	0.804260i	−0.997963	+	0.0638010i	$0.979678\pi$
$620$	1.76391	−	2.21187i	0.0708402	−	0.0888307i
$621$	−10.6823			−0.428667
$622$	−20.8143	+	26.1003i	−0.834578	+	1.04653i
$623$	−1.28232	+	5.61823i	−0.0513752	+	0.225089i
$624$	−2.53654	+	11.1133i	−0.101543	+	0.444888i
$625$	14.4061	−	18.0647i	0.576244	−	0.722588i
$626$	41.4306			1.65590
$627$	−1.65548	+	2.07591i	−0.0661136	+	0.0829038i
$628$	19.8605	−	9.56433i	0.792522	−	0.381658i
$629$	−2.01507	−	2.52681i	−0.0803459	−	0.100751i
$630$	4.54892	+	5.70416i	0.181233	+	0.227259i
$631$	−11.3792	−	5.47993i	−0.452999	−	0.218153i	0.193450	−	0.981110i	$-0.438032\pi$
$631$	−11.3792	−	5.47993i	−0.452999	−	0.218153i	−0.646449	+	0.762957i	$0.723747\pi$
$632$	0.179407	−	0.786035i	0.00713644	−	0.0312668i
$633$	0.802175	+	3.51456i	0.0318836	+	0.139691i
$634$	22.8240	−	10.9915i	0.906457	−	0.436527i
$635$	3.36735	+	1.62163i	0.133629	+	0.0643525i
$636$	−0.538032	−	2.35727i	−0.0213344	−	0.0934720i
$637$	48.7157			1.93019
$638$		0			0
$639$	31.9584			1.26425
$640$	−0.800978	−	3.50932i	−0.0316614	−	0.138718i
$641$	35.1395	+	16.9223i	1.38793	+	0.668391i	0.970674	−	0.240400i	$-0.0772785\pi$
$641$	35.1395	+	16.9223i	1.38793	+	0.668391i	0.417253	+	0.908790i	$0.362993\pi$
$642$	−5.39008	+	2.59573i	−0.212730	+	0.102445i
$643$	−9.18933	−	40.2611i	−0.362392	−	1.58774i	−0.747105	−	0.664706i	$-0.768557\pi$
$643$	−9.18933	−	40.2611i	−0.362392	−	1.58774i	0.384713	−	0.923036i	$-0.374301\pi$
$644$	−4.64795	+	20.3640i	−0.183155	+	0.802454i
$645$	−0.821552	−	0.395639i	−0.0323486	−	0.0155783i
$646$	2.55496	+	3.20382i	0.100523	+	0.126052i
$647$	−11.1670	−	14.0030i	−0.439021	−	0.550515i	0.512264	−	0.858828i	$-0.328807\pi$
$647$	−11.1670	−	14.0030i	−0.439021	−	0.550515i	−0.951285	+	0.308313i	$0.900236\pi$
$648$	8.87143	−	4.27225i	0.348503	−	0.167830i
$649$	16.5392	−	20.7394i	0.649219	−	0.814094i
$650$	−45.5338			−1.78598
$651$	7.14191	−	8.95567i	0.279913	−	0.351000i
$652$	−1.37800	+	6.03742i	−0.0539667	+	0.236444i
$653$	−2.96412	+	12.9867i	−0.115995	+	0.508208i	0.883233	+	0.468934i	$0.155362\pi$
$653$	−2.96412	+	12.9867i	−0.115995	+	0.508208i	−0.999228	+	0.0392741i	$0.987495\pi$
$654$	0.826396	−	1.03627i	0.0323147	−	0.0405213i
$655$	0.162291			0.00634125
$656$	1.21983	−	1.52962i	0.0476265	−	0.0597217i
$657$	22.5906	−	10.8791i	0.881343	−	0.424432i
$658$	−35.4904	−	44.5035i	−1.38356	−	1.73493i
$659$	−11.7002	−	14.6716i	−0.455776	−	0.571525i	0.499849	−	0.866113i	$-0.333389\pi$
$659$	−11.7002	−	14.6716i	−0.455776	−	0.571525i	−0.955624	+	0.294588i	$0.904818\pi$
$660$	−0.519614	−	0.250233i	−0.0202260	−	0.00974031i
$661$	5.50269	−	24.1089i	0.214030	−	0.937726i	−0.747767	−	0.663961i	$-0.768874\pi$
$661$	5.50269	−	24.1089i	0.214030	−	0.937726i	0.961797	−	0.273764i	$-0.0882689\pi$
$662$	5.59611	+	24.5181i	0.217499	+	0.952925i
$663$	−2.30798	+	1.11146i	−0.0896345	+	0.0431657i
$664$	−11.5320	−	5.55351i	−0.447528	−	0.215518i
$665$	−0.658834	−	2.88654i	−0.0255485	−	0.111935i
$666$	−14.7017			−0.569680
$667$		0			0
$668$	18.0368			0.697866
$669$	2.17068	+	9.51036i	0.0839233	+	0.367692i
$670$	−0.216907	−	0.104457i	−0.00837985	−	0.00403553i
$671$	15.8693	−	7.64224i	0.612626	−	0.295025i
$672$	2.48039	+	10.8673i	0.0956830	+	0.419214i
$673$	−5.66152	+	24.8047i	−0.218236	+	0.956153i	0.740545	+	0.672006i	$0.234567\pi$
$673$	−5.66152	+	24.8047i	−0.218236	+	0.956153i	−0.958781	+	0.284146i	$0.908290\pi$
$674$	−22.7250	−	10.9438i	−0.875333	−	0.421538i
$675$	−7.84452	−	9.83672i	−0.301936	−	0.378615i
$676$	10.8026	+	13.5460i	0.415485	+	0.521001i
$677$	0.555491	−	0.267510i	0.0213492	−	0.0102813i	−0.423179	−	0.906046i	$-0.639086\pi$
$677$	0.555491	−	0.267510i	0.0213492	−	0.0102813i	0.444528	+	0.895765i	$0.353371\pi$
$678$	4.32036	−	5.41755i	0.165922	−	0.208060i
$679$	63.7730			2.44738
$680$	0.335126	−	0.420234i	0.0128515	−	0.0161152i
$681$	−1.81013	+	7.93072i	−0.0693645	+	0.303906i
$682$	7.42208	−	32.5182i	0.284206	−	1.24519i
$683$	11.2364	−	14.0900i	0.429949	−	0.539138i	−0.518915	−	0.854826i	$-0.673664\pi$
$683$	11.2364	−	14.0900i	0.429949	−	0.539138i	0.948863	+	0.315688i	$0.102235\pi$
$684$	7.15883			0.273725
$685$	2.94624	−	3.69447i	0.112570	−	0.141158i
$686$	15.7349	−	7.57753i	0.600761	−	0.289311i
$687$	4.44653	+	5.57578i	0.169646	+	0.212729i
$688$	17.6787	+	22.1684i	0.673996	+	0.845164i
$689$	20.3572	+	9.80351i	0.775547	+	0.373484i
$690$	−0.263479	+	1.15437i	−0.0100305	+	0.0439463i
$691$	−2.74728	−	12.0366i	−0.104511	−	0.457894i	−0.999920	−	0.0126487i	$-0.995974\pi$
$691$	−2.74728	−	12.0366i	−0.104511	−	0.457894i	0.895409	−	0.445245i	$-0.146883\pi$
$692$	−11.8116	+	5.68818i	−0.449011	+	0.216232i
$693$	29.7630	+	14.3331i	1.13060	+	0.544470i
$694$	7.96077	+	34.8784i	0.302187	+	1.32397i
$695$	−0.998081			−0.0378594
$696$		0			0
$697$	0.439665			0.0166535
$698$	10.7942	+	47.2923i	0.408565	+	1.79004i
$699$	0.784479	+	0.377785i	0.0296717	+	0.0142892i
$700$	−22.1652	+	10.6742i	−0.837765	+	0.403446i
$701$	7.58738	+	33.2425i	0.286571	+	1.25555i	0.889196	+	0.457526i	$0.151264\pi$
$701$	7.58738	+	33.2425i	0.286571	+	1.25555i	−0.602625	+	0.798025i	$0.705878\pi$
$702$	−5.36927	+	23.5243i	−0.202650	+	0.887868i
$703$	5.37531	+	2.58861i	0.202734	+	0.0976315i
$704$	2.30343	+	2.88841i	0.0868138	+	0.108861i
$705$	−0.772635	−	0.968853i	−0.0290991	−	0.0364891i
$706$	6.51842	−	3.13910i	0.245324	−	0.118142i
$707$	−44.0332	+	55.2159i	−1.65604	+	2.07661i
$708$	5.05562			0.190002
$709$	26.2461	−	32.9115i	0.985692	−	1.23602i	0.0139674	−	0.999902i	$-0.495554\pi$
$709$	26.2461	−	32.9115i	0.985692	−	1.23602i	0.971725	−	0.236116i	$-0.0758747\pi$
$710$	1.63222	−	7.15122i	0.0612561	−	0.268380i
$711$	0.370469	−	1.62313i	0.0138937	−	0.0608722i
$712$	1.20410	−	1.50990i	0.0451257	−	0.0565858i
$713$	−26.2989			−0.984901
$714$	−2.24698	+	2.81762i	−0.0840911	+	0.105447i
$715$	4.85570	−	2.33838i	0.181593	−	0.0874505i
$716$	−4.46346	−	5.59700i	−0.166807	−	0.209170i
$717$	2.48709	+	3.11871i	0.0928821	+	0.116470i
$718$	−1.21164	−	0.583493i	−0.0452178	−	0.0217758i
$719$	11.6277	−	50.9442i	0.433639	−	1.89990i	−0.00245885	−	0.999997i	$-0.500783\pi$
$719$	11.6277	−	50.9442i	0.433639	−	1.89990i	0.436098	−	0.899899i	$-0.356360\pi$
$720$	−1.09903	−	4.81517i	−0.0409585	−	0.179451i
$721$	−10.2654	+	4.94355i	−0.382303	+	0.184108i
$722$	24.0308	+	11.5726i	0.894334	+	0.430688i
$723$	1.97070	+	8.63419i	0.0732910	+	0.321109i
$724$	−8.28083			−0.307755
$725$		0			0
$726$	2.02177			0.0750349
$727$	6.67228	+	29.2331i	0.247461	+	1.08420i	0.934047	+	0.357149i	$0.116251\pi$
$727$	6.67228	+	29.2331i	0.247461	+	1.08420i	−0.686586	+	0.727048i	$0.740892\pi$
$728$	−25.6700	−	12.3620i	−0.951394	−	0.458167i
$729$	15.2131	−	7.32626i	0.563449	−	0.271343i
$730$	−1.28059	−	5.61065i	−0.0473969	−	0.207660i
$731$	−1.41789	+	6.21220i	−0.0524427	+	0.229767i
$732$	3.02446	+	1.45650i	0.111787	+	0.0538339i
$733$	−1.87949	−	2.35681i	−0.0694207	−	0.0870508i	0.745909	−	0.666048i	$-0.232016\pi$
$733$	−1.87949	−	2.35681i	−0.0694207	−	0.0870508i	−0.815329	+	0.578997i	$0.803444\pi$
$734$	38.2536	+	47.9685i	1.41197	+	1.77055i
$735$	1.34428	−	0.647372i	0.0495846	−	0.0238787i
$736$	15.9562	−	20.0085i	0.588154	−	0.737522i
$737$	−1.09006			−0.0401531
$738$	1.24698	−	1.56366i	0.0459020	−	0.0575592i
$739$	−4.63677	+	20.3150i	−0.170566	+	0.747300i	0.815200	+	0.579179i	$0.196627\pi$
$739$	−4.63677	+	20.3150i	−0.170566	+	0.747300i	−0.985766	+	0.168120i	$0.946230\pi$
$740$	−0.288364	+	1.26341i	−0.0106005	+	0.0464437i
$741$	2.94839	−	3.69717i	0.108312	−	0.135819i
$742$	31.7875			1.16695
$743$	19.1821	−	24.0536i	0.703723	−	0.882441i	−0.293573	−	0.955937i	$-0.594844\pi$
$743$	19.1821	−	24.0536i	0.703723	−	0.882441i	0.997295	+	0.0734962i	$0.0234157\pi$
$744$	−3.45862	+	1.66558i	−0.126799	+	0.0610632i
$745$	0.602679	+	0.755736i	0.0220805	+	0.0276880i
$746$	31.4584	+	39.4476i	1.15177	+	1.44428i
$747$	−23.8131	−	11.4678i	−0.871276	−	0.419585i
$748$	−0.896789	+	3.92909i	−0.0327898	+	0.143662i
$749$	−6.72132	−	29.4480i	−0.245592	−	1.07601i
$750$	−2.54580	+	1.22599i	−0.0929595	+	0.0447670i
$751$	−4.02661	−	1.93912i	−0.146933	−	0.0707593i	0.358972	−	0.933348i	$-0.383127\pi$
$751$	−4.02661	−	1.93912i	−0.146933	−	0.0707593i	−0.505905	+	0.862589i	$0.668842\pi$
$752$	8.57457	+	37.5677i	0.312682	+	1.36995i
$753$	11.4843			0.418510
$754$		0			0
$755$	−0.869167			−0.0316322
$756$	2.90097	+	12.7100i	0.105507	+	0.462257i
$757$	−7.61841	−	3.66883i	−0.276896	−	0.133346i	0.290283	−	0.956941i	$-0.406251\pi$
$757$	−7.61841	−	3.66883i	−0.276896	−	0.133346i	−0.567178	+	0.823595i	$0.691965\pi$
$758$	37.1470	−	17.8891i	1.34924	−	0.649760i
$759$	1.19298	+	5.22679i	0.0433025	+	0.189720i
$760$	−0.220792	+	0.967353i	−0.00800897	+	0.0350896i
$761$	−22.2494	−	10.7148i	−0.806541	−	0.388410i	−0.0152763	−	0.999883i	$-0.504863\pi$
$761$	−22.2494	−	10.7148i	−0.806541	−	0.388410i	−0.791265	+	0.611474i	$0.790577\pi$
$762$	5.23609	+	6.56585i	0.189684	+	0.237856i
$763$	4.17241	+	5.23203i	0.151051	+	0.189412i
$764$	−21.1347	+	10.1779i	−0.764626	+	0.368224i
$765$	0.692021	−	0.867767i	0.0250201	−	0.0313742i
$766$	21.3676			0.772045
$767$	−29.4561	+	36.9367i	−1.06360	+	1.33371i
$768$	2.05107	−	8.98634i	0.0740117	−	0.324267i
$769$	6.70746	−	29.3873i	0.241877	−	1.05973i	−0.697429	−	0.716653i	$-0.745673\pi$
$769$	6.70746	−	29.3873i	0.241877	−	1.05973i	0.939307	−	0.343079i	$-0.111470\pi$
$770$	4.72737	−	5.92793i	0.170362	−	0.213628i
$771$	−5.31873			−0.191549
$772$	−8.46263	+	10.6118i	−0.304577	+	0.381927i
$773$	5.11476	−	2.46314i	0.183965	−	0.0885929i	−0.339634	−	0.940558i	$-0.610303\pi$
$773$	5.11476	−	2.46314i	0.183965	−	0.0885929i	0.523599	+	0.851965i	$0.324589\pi$
$774$	18.0722	+	22.6618i	0.649591	+	0.814561i
$775$	−19.3125	−	24.2171i	−0.693724	−	0.869902i
$776$	−19.2555	−	9.27295i	−0.691231	−	0.332879i
$777$	−1.16756	+	5.11543i	−0.0418861	+	0.183515i
$778$	−4.16660	−	18.2551i	−0.149380	−	0.654476i
$779$	−0.731250	+	0.352152i	−0.0261998	+	0.0126171i
$780$	0.925428	+	0.445662i	0.0331356	+	0.0159573i
$781$	−7.39038	−	32.3794i	−0.264449	−	1.15862i
$782$	8.27413			0.295882
$783$		0			0
$784$	−46.3957			−1.65699
$785$	1.40389	+	6.15086i	0.0501071	+	0.219534i
$786$	0.328552	+	0.158222i	0.0117191	+	0.00564361i
$787$	3.25182	−	1.56600i	0.115915	−	0.0558217i	−0.375028	−	0.927014i	$-0.622367\pi$
$787$	3.25182	−	1.56600i	0.115915	−	0.0558217i	0.490943	+	0.871192i	$0.336652\pi$
$788$	2.33095	+	10.2125i	0.0830365	+	0.363807i
$789$	0.0329509	−	0.144367i	0.00117308	−	0.00513961i
$790$	−0.344282	−	0.165797i	−0.0122490	−	0.00589881i
$791$	21.8131	+	27.3528i	0.775585	+	0.972553i
$792$	−6.90246	−	8.65541i	−0.245268	−	0.307557i
$793$	−28.2630	+	13.6107i	−1.00365	+	0.483332i
$794$	9.23221	−	11.5768i	0.327639	−	0.410846i
$795$	0.692021			0.0245435
$796$	−5.14795	+	6.45532i	−0.182464	+	0.228803i
$797$	−6.84990	+	30.0114i	−0.242636	+	1.06306i	0.695972	+	0.718069i	$0.254974\pi$
$797$	−6.84990	+	30.0114i	−0.242636	+	1.06306i	−0.938607	+	0.344987i	$0.887883\pi$
$798$	1.48039	−	6.48599i	0.0524051	−	0.229602i
$799$	−5.39911	+	6.77027i	−0.191007	+	0.239515i
$800$	30.1420			1.06568
$801$	2.48643	−	3.11788i	0.0878536	−	0.110165i
$802$	−40.3940	+	19.4527i	−1.42636	+	0.686900i
$803$	−16.2464	−	20.3724i	−0.573325	−	0.718926i
$804$	−0.129531	−	0.162426i	−0.00456819	−	0.00572833i
$805$	−5.38620	−	2.59386i	−0.189839	−	0.0914214i
$806$	−13.2186	+	57.9146i	−0.465607	+	2.03996i
$807$	0.105367	+	0.461645i	0.00370911	+	0.0162507i
$808$	21.3240	−	10.2691i	0.750176	−	0.361266i
$809$	4.71864	+	2.27238i	0.165898	+	0.0798925i	0.514990	−	0.857196i	$-0.327796\pi$
$809$	4.71864	+	2.27238i	0.165898	+	0.0798925i	−0.349092	+	0.937089i	$0.613510\pi$
$810$	−1.03846	−	4.54979i	−0.0364877	−	0.159863i
$811$	41.8646			1.47006			0.735032	−	0.678032i	$-0.237167\pi$
$811$	41.8646			1.47006			0.735032	+	0.678032i	$0.237167\pi$
$812$		0			0
$813$	−7.32736			−0.256982
$814$	3.39977	+	14.8954i	0.119162	+	0.522083i
$815$	−1.59688	−	0.769015i	−0.0559361	−	0.0269374i
$816$	2.19806	−	1.05853i	0.0769476	−	0.0370560i
$817$	−2.61745	−	11.4678i	−0.0915729	−	0.401207i
$818$	7.57649	−	33.1948i	0.264906	−	1.16063i
$819$	−53.0076	−	25.5271i	−1.85224	−	0.891989i
$820$	−0.109916	−	0.137831i	−0.00383844	−	0.00481325i
$821$	9.60537	+	12.0447i	0.335230	+	0.420365i	0.920665	−	0.390355i	$-0.127648\pi$
$821$	9.60537	+	12.0447i	0.335230	+	0.420365i	−0.585435	+	0.810719i	$0.699076\pi$
$822$	9.56638	−	4.60692i	0.333666	−	0.160685i
$823$	22.2310	−	27.8768i	0.774924	−	0.971724i	−0.225072	−	0.974342i	$-0.572262\pi$
$823$	22.2310	−	27.8768i	0.774924	−	0.971724i	0.999997	+	0.00261763i	$0.000833218\pi$
$824$	3.81833			0.133018
$825$	−3.93698	+	4.93681i	−0.137068	+	0.171878i
$826$	−14.7899	+	64.7986i	−0.514605	+	2.25463i
$827$	−11.5831	+	50.7487i	−0.402783	+	1.76471i	0.213262	+	0.976995i	$0.431591\pi$
$827$	−11.5831	+	50.7487i	−0.402783	+	1.76471i	−0.616045	+	0.787711i	$0.711266\pi$
$828$	9.01238	−	11.3012i	0.313202	−	0.392743i
$829$	13.4168			0.465986			0.232993	−	0.972478i	$-0.425148\pi$
$829$	13.4168			0.465986			0.232993	+	0.972478i	$0.425148\pi$
$830$	−3.78232	+	4.74288i	−0.131286	+	0.164628i
$831$	2.64406	−	1.27331i	0.0917216	−	0.0441708i
$832$	−4.10238	−	5.14423i	−0.142225	−	0.178344i
$833$	−6.50066	−	8.15157i	−0.225235	−	0.282435i
$834$	−2.02057	−	0.973057i	−0.0699667	−	0.0336942i
$835$	−1.14872	+	5.03286i	−0.0397530	+	0.174169i
$836$	−1.65548	−	7.25314i	−0.0572560	−	0.250855i
$837$	−14.7887	+	7.12184i	−0.511171	+	0.246167i
$838$	17.6838	+	8.51608i	0.610878	+	0.294183i
$839$	−6.90957	−	30.2728i	−0.238545	−	1.04513i	−0.942321	−	0.334711i	$-0.891361\pi$
$839$	−6.90957	−	30.2728i	−0.238545	−	1.04513i	0.703776	−	0.710422i	$-0.251496\pi$
$840$	−0.872625			−0.0301084
$841$		0			0
$842$	35.9681			1.23954
$843$	−3.02393	−	13.2487i	−0.104150	−	0.456309i
$844$	−9.10052	−	4.38258i	−0.313253	−	0.150855i
$845$	−4.46777	+	2.15157i	−0.153696	+	0.0740161i
$846$	8.76540	+	38.4037i	0.301361	+	1.32035i
$847$	−2.27144	+	9.95182i	−0.0780475	+	0.341949i
$848$	−19.3877	−	9.33662i	−0.665776	−	0.320621i
$849$	0.986426	+	1.23694i	0.0338541	+	0.0424517i
$850$	6.07606	+	7.61914i	0.208407	+	0.261334i
$851$	10.8535	−	5.22679i	0.372055	−	0.179172i
$852$	3.94653	−	4.94880i	0.135206	−	0.169543i
$853$	−21.3357			−0.730521			−0.365261	−	0.930905i	$-0.619020\pi$
$853$	−21.3357			−0.730521			−0.365261	+	0.930905i	$0.619020\pi$
$854$	−27.5160	+	34.5040i	−0.941579	+	1.18070i
$855$	−0.455927	+	1.99755i	−0.0155924	+	0.0683147i
$856$	−2.25249	+	9.86879i	−0.0769885	+	0.337308i
$857$	−6.13019	+	7.68702i	−0.209403	+	0.262584i	−0.875431	−	0.483344i	$-0.839422\pi$
$857$	−6.13019	+	7.68702i	−0.209403	+	0.262584i	0.666027	+	0.745928i	$0.267994\pi$
$858$	12.1099			0.413426
$859$	32.2866	−	40.4862i	1.10161	−	1.38137i	0.184450	−	0.982842i	$-0.440950\pi$
$859$	32.2866	−	40.4862i	1.10161	−	1.38137i	0.917156	−	0.398528i	$-0.130479\pi$
$860$	2.30194	−	1.10855i	0.0784954	−	0.0378014i
$861$	−0.445042	−	0.558065i	−0.0151670	−	0.0190188i
$862$	−33.9185	−	42.5324i	−1.15527	−	1.44866i
$863$	14.6630	+	7.06134i	0.499135	+	0.240371i	0.666473	−	0.745529i	$-0.267803\pi$
$863$	14.6630	+	7.06134i	0.499135	+	0.240371i	−0.167339	+	0.985899i	$0.553517\pi$
$864$	3.55429	−	15.5724i	0.120920	−	0.529783i
$865$	−0.834936	−	3.65809i	−0.0283887	−	0.124379i
$866$	−32.7805	+	15.7862i	−1.11393	+	0.536438i
$867$	−6.32251	−	3.04476i	−0.214724	−	0.103406i
$868$	7.14191	+	31.2907i	0.242412	+	1.06208i
$869$	−1.73019			−0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	−0.499041	−	2.18644i	−0.0168996	−	0.0740422i
$873$	−39.7618	−	19.1483i	−1.34573	−	0.648071i
$874$	−13.7615	+	6.62720i	−0.465490	+	0.224168i
$875$	−3.17456	−	13.9087i	−0.107320	−	0.470199i
$876$	1.10507	−	4.84164i	0.0373369	−	0.163584i
$877$	−13.3400	−	6.42419i	−0.450459	−	0.216930i	0.194878	−	0.980827i	$-0.437569\pi$
$877$	−13.3400	−	6.42419i	−0.450459	−	0.216930i	−0.645337	+	0.763898i	$0.723283\pi$
$878$	−11.9819	−	15.0248i	−0.404369	−	0.507062i
$879$	9.12349	+	11.4405i	0.307728	+	0.385878i
$880$	−4.62445	+	2.22702i	−0.155890	+	0.0750727i
$881$	11.6204	−	14.5716i	0.391502	−	0.490928i	−0.546548	−	0.837428i	$-0.684058\pi$
$881$	11.6204	−	14.5716i	0.391502	−	0.490928i	0.938050	+	0.346499i	$0.112630\pi$
$882$	−47.4282			−1.59699
$883$	−20.1972	+	25.3264i	−0.679689	+	0.852303i	−0.995325	−	0.0965775i	$-0.969210\pi$
$883$	−20.1972	+	25.3264i	−0.679689	+	0.852303i	0.315637	+	0.948880i	$0.397782\pi$
$884$	1.59717	−	6.99766i	0.0537187	−	0.235357i
$885$	−0.321979	+	1.41068i	−0.0108232	+	0.0474196i
$886$	22.8632	−	28.6696i	0.768105	−	0.963174i
$887$	6.16288			0.206929			0.103465	−	0.994633i	$-0.467007\pi$
$887$	6.16288			0.206929			0.103465	+	0.994633i	$0.467007\pi$
$888$	1.09634	−	1.37477i	0.0367909	−	0.0461343i
$889$	−38.2020	+	18.3971i	−1.28125	+	0.617019i
$890$	−0.570688	−	0.715620i	−0.0191295	−	0.0239876i
$891$	−13.1746	−	16.5204i	−0.441364	−	0.553454i
$892$	−24.6259	−	11.8592i	−0.824537	−	0.397076i
$893$	3.55711	−	15.5847i	0.119034	−	0.521523i
$894$	0.483311	+	2.11752i	0.0161643	+	0.0708206i
$895$	1.84601	−	0.888992i	0.0617053	−	0.0297157i
$896$	36.7923	+	17.7182i	1.22914	+	0.591925i
$897$	−2.12469	−	9.30886i	−0.0709412	−	0.310814i
$898$	−34.9995			−1.16795
$899$		0			0
$900$	17.0248			0.567492
$901$	−1.07606	−	4.71455i	−0.0358489	−	0.157064i
$902$	−1.87263	−	0.901809i	−0.0623516	−	0.0300269i
$903$	9.32036	−	4.48845i	0.310162	−	0.149366i
$904$	−2.60896	−	11.4306i	−0.0867726	−	0.380176i
$905$	0.527384	−	2.31062i	0.0175308	−	0.0768076i
$906$	−1.75959	−	0.847376i	−0.0584586	−	0.0281522i
$907$	−27.4237	−	34.3882i	−0.910589	−	1.14184i	−0.989438	−	0.144956i	$-0.953696\pi$
$907$	−27.4237	−	34.3882i	−0.910589	−	1.14184i	0.0788492	−	0.996887i	$-0.474875\pi$
$908$	−14.2111	−	17.8202i	−0.471612	−	0.591383i
$909$	44.0332	−	21.2053i	1.46049	−	0.703335i
$910$	−8.41939	+	10.5576i	−0.279100	+	0.349980i
$911$	25.6233			0.848936			0.424468	−	0.905443i	$-0.360461\pi$
$911$	25.6233			0.848936			0.424468	+	0.905443i	$0.360461\pi$
$912$	−2.80798	+	3.52109i	−0.0929815	+	0.116595i
$913$	−6.11207	+	26.7787i	−0.202280	+	0.886247i
$914$	4.98039	−	21.8205i	0.164737	−	0.721758i
$915$	−0.599031	+	0.751161i	−0.0198034	+	0.0248326i
$916$	−19.9825			−0.660242
$917$	−1.14795	+	1.43948i	−0.0379086	+	0.0475359i
$918$	4.65279	−	2.24067i	0.153565	−	0.0739530i
$919$	−3.89158	−	4.87988i	−0.128371	−	0.160972i	0.713492	−	0.700663i	$-0.247113\pi$
$919$	−3.89158	−	4.87988i	−0.128371	−	0.160972i	−0.841863	+	0.539691i	$0.818541\pi$
$920$	1.24914	+	1.56637i	0.0411828	+	0.0516416i
$921$	−5.88231	−	2.83277i	−0.193829	−	0.0933430i
$922$	−8.79978	+	38.5544i	−0.289805	+	1.26972i
$923$	13.1622	+	57.6673i	0.433239	+	1.89814i
$924$	5.89493	−	2.83885i	0.193929	−	0.0933912i
$925$	12.7833	+	6.15610i	0.420312	+	0.202411i
$926$	13.2349	+	57.9859i	0.434926	+	1.90553i
$927$	7.88471			0.258968
$928$		0			0
$929$	−24.5133			−0.804256			−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133			−0.804256			−0.402128	+	0.915583i	$0.631729\pi$
$930$	0.404854	+	1.77378i	0.0132757	+	0.0581645i
$931$	17.3409	+	8.35095i	0.568326	+	0.273691i
$932$	−2.19806	+	1.05853i	−0.0719999	+	0.0346733i
$933$	−1.83470	−	8.03834i	−0.0600653	−	0.263163i
$934$	−10.4666	+	45.8571i	−0.342477	+	1.50049i
$935$	−1.03923	−	0.500466i	−0.0339864	−	0.0163670i
$936$	12.2932	+	15.4152i	0.401816	+	0.503861i
$937$	−2.54975	−	3.19728i	−0.0832965	−	0.104451i	0.738437	−	0.674323i	$-0.235564\pi$
$937$	−2.54975	−	3.19728i	−0.0832965	−	0.104451i	−0.821734	+	0.569872i	$0.806993\pi$
$938$	2.46077	−	1.18505i	0.0803470	−	0.0386931i
$939$	−6.37986	+	8.00009i	−0.208199	+	0.261073i
$940$	3.47219			0.113250
$941$	3.84266	−	4.81854i	0.125267	−	0.157080i	−0.715243	−	0.698876i	$-0.753684\pi$
$941$	3.84266	−	4.81854i	0.125267	−	0.157080i	0.840510	+	0.541796i	$0.182255\pi$
$942$	−3.15452	+	13.8209i	−0.102780	+	0.450308i
$943$	−0.364666	+	1.59770i	−0.0118751	+	0.0520284i
$944$	28.0532	−	35.1776i	0.913055	−	1.14493i
$945$	−3.73125			−0.121378
$946$	18.7811	−	23.5508i	0.610627	−	0.765702i
$947$	−44.7802	+	21.5650i	−1.45516	+	0.700769i	−0.983483	−	0.181001i	$-0.942066\pi$
$947$	−44.7802	+	21.5650i	−1.45516	+	0.700769i	−0.471679	+	0.881770i	$0.656352\pi$
$948$	−0.205595	−	0.257808i	−0.00667742	−	0.00837321i
$949$	28.9347	+	36.2830i	0.939262	+	1.17780i
$950$	−16.2083	−	7.80550i	−0.525866	−	0.253244i
$951$	−1.39224	+	6.09980i	−0.0451465	+	0.197800i
$952$	1.35690	+	5.94495i	0.0439772	+	0.192677i
$953$	−15.9342	+	7.67349i	−0.516158	+	0.248569i	−0.673781	−	0.738931i	$-0.735331\pi$
$953$	−15.9342	+	7.67349i	−0.516158	+	0.248569i	0.157623	+	0.987499i	$0.449617\pi$
$954$	−19.8192	−	9.54440i	−0.641669	−	0.309011i
$955$	−1.49396	−	6.54546i	−0.0483434	−	0.211806i
$956$	−11.1769			−0.361486
$957$		0			0
$958$	−59.5827			−1.92503
$959$	11.9291	+	52.2647i	0.385210	+	1.68772i
$960$	−0.181563	−	0.0874363i	−0.00585993	−	0.00282199i
$961$	−8.47823	+	4.08290i	−0.273491	+	0.131706i
$962$	−6.05496	−	26.5285i	−0.195220	−	0.855313i
$963$	−4.65130	+	20.3787i	−0.149886	+	0.656694i
$964$	−22.3572	−	10.7667i	−0.720077	−	0.346771i
$965$	−2.42208	−	3.03719i	−0.0779694	−	0.0977705i
$966$	−8.37531	−	10.5023i	−0.269471	−	0.337906i
$967$	−11.6165	+	5.59421i	−0.373561	+	0.179898i	−0.611238	−	0.791447i	$-0.709328\pi$
$967$	−11.6165	+	5.59421i	−0.373561	+	0.179898i	0.237677	+	0.971344i	$0.423614\pi$
$968$	2.13288	−	2.67455i	0.0685535	−	0.0859633i
$969$	−1.01208			−0.0325127
$970$	−6.31551	+	7.91940i	−0.202779	+	0.254277i
$971$	1.07643	−	4.71616i	0.0345444	−	0.151349i	−0.954714	−	0.297524i	$-0.903839\pi$
$971$	1.07643	−	4.71616i	0.0345444	−	0.151349i	0.989259	+	0.146175i	$0.0466963\pi$
$972$	3.04556	−	13.3435i	0.0976865	−	0.427993i
$973$	7.05980	−	8.85271i	0.226327	−	0.283805i
$974$	−18.3013			−0.586411
$975$	7.01171	−	8.79241i	0.224555	−	0.281582i
$976$	26.9170	−	12.9625i	0.861592	−	0.414921i
$977$	10.2515	+	12.8549i	0.327973	+	0.411265i	0.918291	−	0.395905i	$-0.129569\pi$
$977$	10.2515	+	12.8549i	0.327973	+	0.411265i	−0.590318	+	0.807171i	$0.700998\pi$
$978$	−2.48307	−	3.11368i	−0.0794000	−	0.0995644i
$979$	−3.73394	−	1.79817i	−0.119337	−	0.0574698i
$980$	−0.930272	+	4.07579i	−0.0297164	+	0.130196i
$981$	−1.03050	−	4.51491i	−0.0329013	−	0.144150i
$982$	−31.9533	+	15.3879i	−1.01967	+	0.491048i
$983$	23.8751	+	11.4976i	0.761497	+	0.366717i	0.773984	−	0.633205i	$-0.218261\pi$
$983$	23.8751	+	11.4976i	0.761497	+	0.366717i	−0.0124878	+	0.999922i	$0.503975\pi$
$984$	0.0532292	+	0.233212i	0.00169689	+	0.00743454i
$985$	−2.99808			−0.0955268
$986$		0			0
$987$	14.0586			0.447490
$988$	2.94839	+	12.9178i	0.0938009	+	0.410969i
$989$	−21.3986	−	10.3050i	−0.680435	−	0.327680i
$990$	−4.72737	+	2.27658i	−0.150246	+	0.0723544i
$991$	−8.99127	−	39.3933i	−0.285617	−	1.25137i	−0.890473	−	0.455036i	$-0.849627\pi$
$991$	−8.99127	−	39.3933i	−0.285617	−	1.25137i	0.604856	−	0.796335i	$-0.293231\pi$
$992$	8.75033	−	38.3377i	0.277823	−	1.21722i
$993$	−5.59611	−	2.69494i	−0.177587	−	0.0855214i
$994$	51.8841	+	65.0606i	1.64566	+	2.06360i
$995$	−1.47339	−	1.84757i	−0.0467095	−	0.0585718i
$996$	−4.71648	+	2.27134i	−0.149447	+	0.0719701i
$997$	14.6242	−	18.3381i	0.463152	−	0.580774i	−0.494328	−	0.869276i	$-0.664586\pi$
$997$	14.6242	−	18.3381i	0.463152	−	0.580774i	0.957479	+	0.288502i	$0.0931572\pi$
$998$	50.1831			1.58852
$999$	4.68784	−	5.87837i	0.148317	−	0.185983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.c.645.1		6
29.2	odd	28		841.2.b.c.840.1		6
29.3	odd	28		841.2.e.d.63.2		12
29.4	even	14		841.2.d.b.605.1		6
29.5	even	14		841.2.a.e.1.1		3
29.6	even	14		841.2.d.e.571.1		6
29.7	even	7		841.2.d.d.778.1		6
29.8	odd	28		841.2.e.b.651.2		12
29.9	even	14		841.2.d.e.190.1		6
29.10	odd	28		841.2.e.c.236.1		12
29.11	odd	28		841.2.e.d.267.1		12
29.12	odd	4		841.2.e.c.196.2		12
29.13	even	14		29.2.d.a.23.1	✓	6
29.14	odd	28		841.2.e.b.270.2		12
29.15	odd	28		841.2.e.b.270.1		12
29.16	even	7		841.2.d.d.574.1		6
29.17	odd	4		841.2.e.c.196.1		12
29.18	odd	28		841.2.e.d.267.2		12
29.19	odd	28		841.2.e.c.236.2		12
29.20	even	7		841.2.d.a.190.1		6
29.21	odd	28		841.2.e.b.651.1		12
29.22	even	14		29.2.d.a.24.1	yes	6
29.23	even	7		841.2.d.a.571.1		6
29.24	even	7		841.2.a.f.1.3		3
29.25	even	7	inner	841.2.d.c.605.1		6
29.26	odd	28		841.2.e.d.63.1		12
29.27	odd	28		841.2.b.c.840.6		6
29.28	even	2		841.2.d.b.645.1		6
87.5	odd	14		7569.2.a.r.1.3		3
87.53	odd	14		7569.2.a.p.1.1		3
87.71	odd	14		261.2.k.a.226.1		6
87.80	odd	14		261.2.k.a.82.1		6
116.51	odd	14		464.2.u.f.401.1		6
116.71	odd	14		464.2.u.f.81.1		6
145.13	odd	28		725.2.r.b.574.2		12
145.22	odd	28		725.2.r.b.24.2		12
145.42	odd	28		725.2.r.b.574.1		12
145.109	even	14		725.2.l.b.401.1		6
145.129	even	14		725.2.l.b.226.1		6
145.138	odd	28		725.2.r.b.24.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.13	even	14
29.2.d.a.24.1	yes	6	29.22	even	14
261.2.k.a.82.1		6	87.80	odd	14
261.2.k.a.226.1		6	87.71	odd	14
464.2.u.f.81.1		6	116.71	odd	14
464.2.u.f.401.1		6	116.51	odd	14
725.2.l.b.226.1		6	145.129	even	14
725.2.l.b.401.1		6	145.109	even	14
725.2.r.b.24.1		12	145.138	odd	28
725.2.r.b.24.2		12	145.22	odd	28
725.2.r.b.574.1		12	145.42	odd	28
725.2.r.b.574.2		12	145.13	odd	28
841.2.a.e.1.1		3	29.5	even	14
841.2.a.f.1.3		3	29.24	even	7
841.2.b.c.840.1		6	29.2	odd	28
841.2.b.c.840.6		6	29.27	odd	28
841.2.d.a.190.1		6	29.20	even	7
841.2.d.a.571.1		6	29.23	even	7
841.2.d.b.605.1		6	29.4	even	14
841.2.d.b.645.1		6	29.28	even	2
841.2.d.c.605.1		6	29.25	even	7	inner
841.2.d.c.645.1		6	1.1	even	1	trivial
841.2.d.d.574.1		6	29.16	even	7
841.2.d.d.778.1		6	29.7	even	7
841.2.d.e.190.1		6	29.9	even	14
841.2.d.e.571.1		6	29.6	even	14
841.2.e.b.270.1		12	29.15	odd	28
841.2.e.b.270.2		12	29.14	odd	28
841.2.e.b.651.1		12	29.21	odd	28
841.2.e.b.651.2		12	29.8	odd	28
841.2.e.c.196.1		12	29.17	odd	4
841.2.e.c.196.2		12	29.12	odd	4
841.2.e.c.236.1		12	29.10	odd	28
841.2.e.c.236.2		12	29.19	odd	28
841.2.e.d.63.1		12	29.26	odd	28
841.2.e.d.63.2		12	29.3	odd	28
841.2.e.d.267.1		12	29.11	odd	28
841.2.e.d.267.2		12	29.18	odd	28
7569.2.a.p.1.1		3	87.53	odd	14
7569.2.a.r.1.3		3	87.5	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+(-0.400969 - 1.75676i) q^{2} +(0.400969 + 0.193096i) q^{3} +(-1.12349 + 0.541044i) q^{4} +(-0.0794168 - 0.347948i) q^{5} +(0.178448 - 0.781831i) q^{6} +(3.64795 + 1.75676i) q^{7} +(-0.846011 - 1.06086i) q^{8} +(-1.74698 - 2.19064i) q^{9} +(-0.579417 + 0.279032i) q^{10} +(-1.81551 + 2.27658i) q^{11} -0.554958 q^{12} +(3.23341 - 4.05456i) q^{13} +(1.62349 - 7.11297i) q^{14} +(0.0353438 - 0.154851i) q^{15} +(-3.07942 + 3.86147i) q^{16} -1.10992 q^{17} +(-3.14795 + 3.94740i) q^{18} +(1.84601 - 0.888992i) q^{19} +(0.277479 + 0.347948i) q^{20} +(1.12349 + 1.40881i) q^{21} +(4.72737 + 2.27658i) q^{22} +(0.920583 - 4.03334i) q^{23} +(-0.134375 - 0.588735i) q^{24} +(4.39008 - 2.11415i) q^{25} +(-8.41939 - 4.05456i) q^{26} +(-0.574572 - 2.51737i) q^{27} -5.04892 q^{28} -0.286208 q^{30} +(-1.41454 - 6.19752i) q^{31} +(5.57338 + 2.68400i) q^{32} +(-1.16756 + 0.562269i) q^{33} +(0.445042 + 1.94986i) q^{34} +(0.321552 - 1.40881i) q^{35} +(3.14795 + 1.51597i) q^{36} +(1.81551 + 2.27658i) q^{37} +(-2.30194 - 2.88654i) q^{38} +(2.07942 - 1.00139i) q^{39} +(-0.301938 + 0.378618i) q^{40} -0.396125 q^{41} +(2.02446 - 2.53859i) q^{42} +(1.27748 - 5.59700i) q^{43} +(0.807979 - 3.53999i) q^{44} +(-0.623490 + 0.781831i) q^{45} -7.45473 q^{46} +(4.86443 - 6.09980i) q^{47} +(-1.98039 + 0.953703i) q^{48} +(5.85690 + 7.34432i) q^{49} +(-5.47434 - 6.86461i) q^{50} +(-0.445042 - 0.214321i) q^{51} +(-1.43900 + 6.30468i) q^{52} +(0.969501 + 4.24766i) q^{53} +(-4.19202 + 2.01877i) q^{54} +(0.936313 + 0.450904i) q^{55} +(-1.22252 - 5.35621i) q^{56} +0.911854 q^{57} -9.10992 q^{59} +(0.0440730 + 0.193096i) q^{60} +(-5.44989 - 2.62453i) q^{61} +(-10.3204 + 4.97002i) q^{62} +(-2.52446 - 11.0604i) q^{63} +(0.282323 - 1.23694i) q^{64} +(-1.66756 - 0.803056i) q^{65} +(1.45593 + 1.82567i) q^{66} +(0.233406 + 0.292682i) q^{67} +(1.24698 - 0.600514i) q^{68} +(1.14795 - 1.43948i) q^{69} -2.60388 q^{70} +(-7.11141 + 8.91742i) q^{71} +(-0.846011 + 3.70662i) q^{72} +(-1.99127 + 8.72433i) q^{73} +(3.27144 - 4.10225i) q^{74} +2.16852 q^{75} +(-1.59299 + 1.99755i) q^{76} +(-10.6223 + 5.11543i) q^{77} +(-2.59299 - 3.25151i) q^{78} +(0.370469 + 0.464554i) q^{79} +(1.58815 + 0.764811i) q^{80} +(-1.61476 + 7.07473i) q^{81} +(0.158834 + 0.695895i) q^{82} +(8.49880 - 4.09281i) q^{83} +(-2.02446 - 0.974928i) q^{84} +(0.0881460 + 0.386193i) q^{85} -10.3448 q^{86} +3.95108 q^{88} +(0.316708 + 1.38759i) q^{89} +(1.62349 + 0.781831i) q^{90} +(18.9182 - 9.11052i) q^{91} +(1.14795 + 5.02949i) q^{92} +(0.629531 - 2.75815i) q^{93} +(-12.6664 - 6.09980i) q^{94} +(-0.455927 - 0.571714i) q^{95} +(1.71648 + 2.15240i) q^{96} +(14.1908 - 6.83394i) q^{97} +(10.5538 - 13.2340i) q^{98} +8.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 3 q^{6} + 8 q^{7} - q^{9} + 5 q^{10} + 4 q^{11} - 4 q^{12} + 16 q^{13} + 5 q^{14} - 12 q^{15} - 10 q^{16} - 8 q^{17} - 5 q^{18} + 6 q^{19} + 2 q^{20} + 2 q^{21}+ \cdots + 32 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 8 * q^5 - 3 * q^6 + 8 * q^7 - q^9 + 5 * q^10 + 4 * q^11 - 4 * q^12 + 16 * q^13 + 5 * q^14 - 12 * q^15 - 10 * q^16 - 8 * q^17 - 5 * q^18 + 6 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 + 14 * q^23 + 7 * q^24 + 25 * q^25 - 18 * q^26 - 17 * q^27 - 12 * q^28 - 18 * q^30 + 2 * q^31 + 6 * q^32 - 6 * q^33 + 2 * q^34 + 6 * q^35 + 5 * q^36 - 4 * q^37 - 5 * q^38 + 4 * q^39 + 7 * q^40 - 20 * q^41 + 3 * q^42 + 8 * q^43 + 15 * q^44 + q^45 - 4 * q^47 + q^48 + 27 * q^49 - q^50 - 2 * q^51 + 11 * q^52 - 4 * q^53 - 15 * q^54 - 11 * q^55 - 7 * q^56 - 2 * q^57 - 56 * q^59 + 4 * q^60 - 10 * q^61 - 25 * q^62 - 6 * q^63 - 20 * q^64 - 9 * q^65 + 5 * q^66 - 2 * q^67 - 2 * q^68 - 7 * q^69 + 2 * q^70 + 4 * q^73 + q^74 - 48 * q^75 + 5 * q^76 - 18 * q^77 - q^78 - 12 * q^79 + 17 * q^80 + 11 * q^81 - 16 * q^82 + 10 * q^83 - 3 * q^84 + 8 * q^85 - 16 * q^86 + 42 * q^88 + 28 * q^89 + 5 * q^90 + 40 * q^91 - 7 * q^92 + 18 * q^93 - 34 * q^94 + q^95 - 9 * q^96 + 34 * q^97 + 23 * q^98 + 32 * q^99

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