LMFDB - Embedded newform 841.2.e.c.236.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 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:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			236.2
Root			$-0.974928 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	841.236
Dual form			841.2.e.c.196.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.75676 + 0.400969i) q^{2} +(-0.193096 - 0.400969i) 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} +(-1.06086 - 0.846011i) q^{8} +(1.74698 - 2.19064i) q^{9} +(0.279032 - 0.579417i) q^{10} +(-2.27658 + 1.81551i) q^{11} -0.554958i q^{12} +(-3.23341 - 4.05456i) q^{13} +(7.11297 - 1.62349i) q^{14} +(-0.154851 + 0.0353438i) q^{15} +(-3.07942 - 3.86147i) q^{16} +1.10992i q^{17} +(3.94740 - 3.14795i) q^{18} +(0.888992 - 1.84601i) q^{19} +(0.277479 - 0.347948i) q^{20} +(-1.40881 - 1.12349i) 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} +(-4.05456 - 8.41939i) q^{26} +(-2.51737 - 0.574572i) q^{27} +5.04892 q^{28} -0.286208 q^{30} +(6.19752 + 1.41454i) q^{31} +(-2.68400 - 5.57338i) 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} +(2.27658 + 1.81551i) q^{37} +(2.30194 - 2.88654i) q^{38} +(-1.00139 + 2.07942i) q^{39} +(-0.378618 + 0.301938i) q^{40} -0.396125i q^{41} +(-2.02446 - 2.53859i) q^{42} +(5.59700 - 1.27748i) q^{43} +(-3.53999 + 0.807979i) q^{44} +(-0.623490 - 0.781831i) q^{45} +7.45473i q^{46} +(-6.09980 + 4.86443i) q^{47} +(-0.953703 + 1.98039i) q^{48} +(5.85690 - 7.34432i) q^{49} +(6.86461 + 5.47434i) 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} +(0.450904 + 0.936313i) q^{55} +(-5.35621 - 1.22252i) q^{56} -0.911854 q^{57} -9.10992 q^{59} +(-0.193096 - 0.0440730i) q^{60} +(2.62453 + 5.44989i) 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} +(1.82567 + 1.45593i) q^{66} +(-0.233406 + 0.292682i) q^{67} +(-0.600514 + 1.24698i) q^{68} +(1.43948 - 1.14795i) q^{69} -2.60388i q^{70} +(7.11141 + 8.91742i) q^{71} +(-3.70662 + 0.846011i) q^{72} +(8.72433 - 1.99127i) q^{73} +(3.27144 + 4.10225i) q^{74} -2.16852i q^{75} +(1.99755 - 1.59299i) q^{76} +(-5.11543 + 10.6223i) q^{77} +(-2.59299 + 3.25151i) q^{78} +(-0.464554 - 0.370469i) 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} +(-0.974928 - 2.02446i) q^{84} +(0.386193 + 0.0881460i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(-1.38759 - 0.316708i) q^{89} +(-0.781831 - 1.62349i) 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} +(-0.571714 - 0.455927i) q^{95} +(-1.71648 + 2.15240i) q^{96} +(-6.83394 + 14.1908i) q^{97} +(13.2340 - 10.5538i) q^{98} +8.15883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 16 q^{5} + 6 q^{6} + 16 q^{7} + 2 q^{9} - 32 q^{13} - 20 q^{16} + 4 q^{20} - 12 q^{22} + 28 q^{23} + 14 q^{24} + 50 q^{25} + 24 q^{28} - 36 q^{30} + 12 q^{33} - 4 q^{34} - 12 q^{35} + 10 q^{36}+ \cdots + 18 q^{96}+O(q^{100}) $ 12 * q + 4 * q^4 - 16 * q^5 + 6 * q^6 + 16 * q^7 + 2 * q^9 - 32 * q^13 - 20 * q^16 + 4 * q^20 - 12 * q^22 + 28 * q^23 + 14 * q^24 + 50 * q^25 + 24 * q^28 - 36 * q^30 + 12 * q^33 - 4 * q^34 - 12 * q^35 + 10 * q^36 + 10 * q^38 - 6 * q^42 + 2 * q^45 + 54 * q^49 + 4 * q^51 + 22 * q^52 - 8 * q^53 - 30 * q^54 + 4 * q^57 - 112 * q^59 + 50 * q^62 + 12 * q^63 + 40 * q^64 - 18 * q^65 + 4 * q^67 + 2 * q^74 - 2 * q^78 - 34 * q^80 + 22 * q^81 - 32 * q^82 + 20 * q^83 + 32 * q^86 + 84 * q^88 - 80 * q^91 + 14 * q^92 - 36 * q^93 - 68 * q^94 + 18 * q^96

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

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 $

$2$	1.75676	+	0.400969i	1.24222	+	0.283528i	0.792627	−	0.609707i	$-0.208713\pi$
$2$	1.75676	+	0.400969i	1.24222	+	0.283528i	0.449590	+	0.893235i	$0.351570\pi$
$3$	−0.193096	−	0.400969i	−0.111484	−	0.231499i	0.837760	−	0.546038i	$-0.183865\pi$
$3$	−0.193096	−	0.400969i	−0.111484	−	0.231499i	−0.949245	+	0.314538i	$0.898150\pi$
$4$	1.12349	+	0.541044i	0.561745	+	0.270522i
$5$	0.0794168	−	0.347948i	0.0355163	−	0.155607i	−0.954060	−	0.299615i	$-0.903142\pi$
$5$	0.0794168	−	0.347948i	0.0355163	−	0.155607i	0.989577	+	0.144008i	$0.0459990\pi$
$6$	−0.178448	−	0.781831i	−0.0728511	−	0.319181i
$7$	3.64795	−	1.75676i	1.37879	−	0.663993i	0.410053	−	0.912062i	$-0.365510\pi$
$7$	3.64795	−	1.75676i	1.37879	−	0.663993i	0.968742	+	0.248069i	$0.0797960\pi$
$8$	−1.06086	−	0.846011i	−0.375072	−	0.299110i
$9$	1.74698	−	2.19064i	0.582327	−	0.730214i
$10$	0.279032	−	0.579417i	0.0882378	−	0.183228i
$11$	−2.27658	+	1.81551i	−0.686414	+	0.547397i	−0.903411	−	0.428775i	$-0.858945\pi$
$11$	−2.27658	+	1.81551i	−0.686414	+	0.547397i	0.216997	+	0.976172i	$0.430374\pi$
$12$		−	0.554958i		−	0.160203i
$13$	−3.23341	−	4.05456i	−0.896785	−	1.12453i	−0.991639	−	0.129042i	$-0.958810\pi$
$13$	−3.23341	−	4.05456i	−0.896785	−	1.12453i	0.0948536	−	0.995491i	$-0.469762\pi$
$14$	7.11297	−	1.62349i	1.90102	−	0.433896i
$15$	−0.154851	+	0.0353438i	−0.0399824	+	0.00912573i
$16$	−3.07942	−	3.86147i	−0.769854	−	0.965367i
$17$			1.10992i			0.269194i	0.990900	+	0.134597i	$0.0429740\pi$
$17$			1.10992i			0.269194i	−0.990900	+	0.134597i	$0.957026\pi$
$18$	3.94740	−	3.14795i	0.930412	−	0.741979i
$19$	0.888992	−	1.84601i	0.203949	−	0.423504i	−0.773757	−	0.633482i	$-0.781625\pi$
$19$	0.888992	−	1.84601i	0.203949	−	0.423504i	0.977706	+	0.209978i	$0.0673393\pi$
$20$	0.277479	−	0.347948i	0.0620462	−	0.0778035i
$21$	−1.40881	−	1.12349i	−0.307428	−	0.245166i
$22$	−4.72737	+	2.27658i	−1.00788	+	0.485368i
$23$	0.920583	+	4.03334i	0.191955	+	0.841009i	0.975557	+	0.219746i	$0.0705230\pi$
$23$	0.920583	+	4.03334i	0.191955	+	0.841009i	−0.783602	+	0.621263i	$0.786620\pi$
$24$	−0.134375	+	0.588735i	−0.0274292	+	0.120175i
$25$	4.39008	+	2.11415i	0.878017	+	0.422831i
$26$	−4.05456	−	8.41939i	−0.795165	−	1.65118i
$27$	−2.51737	−	0.574572i	−0.484467	−	0.110577i
$28$	5.04892			0.954156
$29$		0			0
$29$		0			0
$30$	−0.286208			−0.0522542
$31$	6.19752	+	1.41454i	1.11311	+	0.254059i	0.739253	−	0.673428i	$-0.235179\pi$
$31$	6.19752	+	1.41454i	1.11311	+	0.254059i	0.373854	+	0.927488i	$0.378036\pi$
$32$	−2.68400	−	5.57338i	−0.474468	−	0.985243i
$33$	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
$37$	2.27658	+	1.81551i	0.374267	+	0.298468i	0.792500	−	0.609872i	$-0.208779\pi$
$37$	2.27658	+	1.81551i	0.374267	+	0.298468i	−0.418233	+	0.908340i	$0.637350\pi$
$38$	2.30194	−	2.88654i	0.373424	−	0.468258i
$39$	−1.00139	+	2.07942i	−0.160351	+	0.332973i
$40$	−0.378618	+	0.301938i	−0.0598648	+	0.0477405i
$41$		−	0.396125i		−	0.0618643i	−0.999521	−	0.0309321i	$-0.990152\pi$
$41$		−	0.396125i		−	0.0618643i	0.999521	−	0.0309321i	$-0.00984757\pi$
$42$	−2.02446	−	2.53859i	−0.312381	−	0.391713i
$43$	5.59700	−	1.27748i	0.853535	−	0.194814i	0.226699	−	0.973965i	$-0.427207\pi$
$43$	5.59700	−	1.27748i	0.853535	−	0.194814i	0.626836	+	0.779151i	$0.284350\pi$
$44$	−3.53999	+	0.807979i	−0.533673	+	0.121807i
$45$	−0.623490	−	0.781831i	−0.0929444	−	0.116549i
$46$			7.45473i			1.09914i
$47$	−6.09980	+	4.86443i	−0.889747	+	0.709550i	−0.957586	−	0.288146i	$-0.906961\pi$
$47$	−6.09980	+	4.86443i	−0.889747	+	0.709550i	0.0678390	+	0.997696i	$0.478390\pi$
$48$	−0.953703	+	1.98039i	−0.137655	+	0.285844i
$49$	5.85690	−	7.34432i	0.836699	−	1.04919i
$50$	6.86461	+	5.47434i	0.970803	+	0.774189i
$51$	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	−0.863671	−	0.504055i	$-0.831841\pi$
$53$	0.969501	−	4.24766i	0.133171	−	0.583461i	0.996842	−	0.0794054i	$-0.0253022\pi$
$54$	−4.19202	−	2.01877i	−0.570462	−	0.274720i
$55$	0.450904	+	0.936313i	0.0607999	+	0.126252i
$56$	−5.35621	−	1.22252i	−0.715754	−	0.163366i
$57$	−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	$0.702059\pi$
$60$	−0.193096	−	0.0440730i	−0.0249286	−	0.00568980i
$61$	2.62453	+	5.44989i	0.336036	+	0.697786i	0.998692	−	0.0511381i	$-0.0162849\pi$
$61$	2.62453	+	5.44989i	0.336036	+	0.697786i	−0.662655	+	0.748924i	$0.730571\pi$
$62$	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
$66$	1.82567	+	1.45593i	0.224725	+	0.179212i
$67$	−0.233406	+	0.292682i	−0.0285151	+	0.0357568i	−0.795885	−	0.605448i	$-0.792994\pi$
$67$	−0.233406	+	0.292682i	−0.0285151	+	0.0357568i	0.767369	+	0.641205i	$0.221565\pi$
$68$	−0.600514	+	1.24698i	−0.0728230	+	0.151218i
$69$	1.43948	−	1.14795i	0.173293	−	0.138197i
$70$		−	2.60388i		−	0.311223i
$71$	7.11141	+	8.91742i	0.843969	+	1.05830i	0.997535	+	0.0701652i	$0.0223526\pi$
$71$	7.11141	+	8.91742i	0.843969	+	1.05830i	−0.153567	+	0.988138i	$0.549076\pi$
$72$	−3.70662	+	0.846011i	−0.436829	+	0.0997033i
$73$	8.72433	−	1.99127i	1.02111	−	0.233061i	0.320984	−	0.947085i	$-0.395986\pi$
$73$	8.72433	−	1.99127i	1.02111	−	0.233061i	0.700121	+	0.714024i	$0.253129\pi$
$74$	3.27144	+	4.10225i	0.380297	+	0.476877i
$75$		−	2.16852i		−	0.250399i
$76$	1.99755	−	1.59299i	0.229134	−	0.182729i
$77$	−5.11543	+	10.6223i	−0.582957	+	1.21052i
$78$	−2.59299	+	3.25151i	−0.293598	+	0.368161i
$79$	−0.464554	−	0.370469i	−0.0522664	−	0.0416811i	0.597008	−	0.802235i	$-0.296356\pi$
$79$	−0.464554	−	0.370469i	−0.0522664	−	0.0416811i	−0.649275	+	0.760554i	$0.724927\pi$
$80$	−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	0.837647	−	0.546212i	$-0.183931\pi$
$83$	8.49880	+	4.09281i	0.932865	+	0.449244i	0.0952182	+	0.995456i	$0.469645\pi$
$84$	−0.974928	−	2.02446i	−0.106373	−	0.220887i
$85$	0.386193	+	0.0881460i	0.0418885	+	0.00956078i
$86$	10.3448			1.11551
$87$		0			0
$88$	3.95108			0.421187
$89$	−1.38759	−	0.316708i	−0.147084	−	0.0335710i	0.148345	−	0.988936i	$-0.452605\pi$
$89$	−1.38759	−	0.316708i	−0.147084	−	0.0335710i	−0.295429	+	0.955365i	$0.595463\pi$
$90$	−0.781831	−	1.62349i	−0.0824123	−	0.171131i
$91$	−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
$95$	−0.571714	−	0.455927i	−0.0586567	−	0.0467771i
$96$	−1.71648	+	2.15240i	−0.175188	+	0.219678i
$97$	−6.83394	+	14.1908i	−0.693882	+	1.44086i	0.194100	+	0.980982i	$0.437821\pi$
$97$	−6.83394	+	14.1908i	−0.693882	+	1.44086i	−0.887982	+	0.459878i	$0.847893\pi$
$98$	13.2340	−	10.5538i	1.33684	−	1.06609i
$99$			8.15883i			0.819994i
$100$	3.78836	+	4.75046i	0.378836	+	0.475046i
$101$	−17.0053	+	3.88135i	−1.69209	+	0.386209i	−0.956619	−	0.291343i	$-0.905898\pi$
$101$	−17.0053	+	3.88135i	−1.69209	+	0.386209i	−0.735475	+	0.677552i	$0.763041\pi$
$102$	0.867767	−	0.198062i	0.0859218	−	0.0196111i
$103$	−1.75451	−	2.20009i	−0.172877	−	0.216781i	0.687843	−	0.725860i	$-0.258558\pi$
$103$	−1.75451	−	2.20009i	−0.172877	−	0.216781i	−0.860720	+	0.509078i	$0.829986\pi$
$104$			7.03684i			0.690019i
$105$	−0.502799	+	0.400969i	−0.0490682	+	0.0391306i
$106$	3.40636	−	7.07338i	0.330855	−	0.687027i
$107$	−4.65130	+	5.83255i	−0.449658	+	0.563854i	−0.954060	−	0.299615i	$-0.903142\pi$
$107$	−4.65130	+	5.83255i	−0.449658	+	0.563854i	0.504402	+	0.863469i	$0.331713\pi$
$108$	−2.51737	−	2.00753i	−0.242234	−	0.193175i
$109$	−1.48911	+	0.717120i	−0.142631	+	0.0686876i	−0.503838	−	0.863798i	$-0.668079\pi$
$109$	−1.48911	+	0.717120i	−0.142631	+	0.0686876i	0.361207	+	0.932486i	$0.382365\pi$
$110$	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
$113$	3.74906	+	7.78501i	0.352682	+	0.732352i	0.999542	−	0.0302566i	$-0.00963243\pi$
$113$	3.74906	+	7.78501i	0.352682	+	0.732352i	−0.646860	+	0.762609i	$0.723918\pi$
$114$	−1.60191	−	0.365625i	−0.150032	−	0.0342439i
$115$	1.47650			0.137684
$116$		0			0
$117$	−14.5308			−1.34337
$118$	−16.0039	−	3.65279i	−1.47328	−	0.336267i
$119$	1.94986	+	4.04892i	0.178743	+	0.371164i
$120$	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
$124$	6.19752	+	4.94235i	0.556553	+	0.443836i
$125$	2.19687	−	2.75478i	0.196494	−	0.246395i
$126$	8.86973	−	18.4182i	0.790179	−	1.64082i
$127$	−8.18749	+	6.52930i	−0.726522	+	0.579382i	−0.915365	−	0.402625i	$-0.868098\pi$
$127$	−8.18749	+	6.52930i	−0.726522	+	0.579382i	0.188843	+	0.982007i	$0.439526\pi$
$128$			10.0858i			0.891463i
$129$	−1.59299	−	1.99755i	−0.140255	−	0.175874i
$130$	−3.25151	+	0.742135i	−0.285176	+	0.0650896i
$131$	0.443330	−	0.101187i	0.0387339	−	0.00884076i	−0.203110	−	0.979156i	$-0.565105\pi$
$131$	0.443330	−	0.101187i	0.0387339	−	0.00884076i	0.241844	+	0.970315i	$0.422248\pi$
$132$	1.00753	+	1.26341i	0.0876945	+	0.109965i
$133$		−	8.29590i		−	0.719345i
$134$	−0.527395	+	0.420583i	−0.0455600	+	0.0363329i
$135$	−0.399842	+	0.830281i	−0.0344130	+	0.0714592i
$136$	0.939001	−	1.17747i	0.0805187	−	0.100967i
$137$	−10.3517	−	8.25518i	−0.884402	−	0.705287i	0.0719797	−	0.997406i	$-0.477068\pi$
$137$	−10.3517	−	8.25518i	−0.884402	−	0.705287i	−0.956382	+	0.292119i	$0.905640\pi$
$138$	2.98911	−	1.43948i	0.254450	−	0.122537i
$139$	0.622293	+	2.72645i	0.0527822	+	0.231254i	0.994438	−	0.105323i	$-0.0335878\pi$
$139$	0.622293	+	2.72645i	0.0527822	+	0.231254i	−0.941656	+	0.336577i	$0.890731\pi$
$140$	0.400969	−	1.75676i	0.0338881	−	0.148473i
$141$	3.12833	+	1.50653i	0.263453	+	0.126872i
$142$	8.91742	+	18.5172i	0.748334	+	1.55393i
$143$	14.7222	+	3.36025i	1.23113	+	0.280998i
$144$	−13.8388			−1.15323
$145$		0			0
$146$	16.1250			1.33451
$147$	−4.07579	−	0.930272i	−0.336165	−	0.0767275i
$148$	1.57544	+	3.27144i	0.129501	+	0.268911i
$149$	2.44020	+	1.17514i	0.199909	+	0.0962710i	0.531160	−	0.847272i	$-0.321756\pi$
$149$	2.44020	+	1.17514i	0.199909	+	0.0962710i	−0.331251	+	0.943543i	$0.607471\pi$
$150$	0.869510	−	3.80957i	0.0709952	−	0.311050i
$151$	−0.541917	−	2.37429i	−0.0441006	−	0.193217i	0.948079	−	0.318034i	$-0.103023\pi$
$151$	−0.541917	−	2.37429i	−0.0441006	−	0.193217i	−0.992180	+	0.124817i	$0.960166\pi$
$152$	−2.50484	+	1.20627i	−0.203170	+	0.0978414i
$153$	2.43143	+	1.93900i	0.196570	+	0.156759i
$154$	−13.2458	+	16.6097i	−1.06738	+	1.33845i
$155$	0.984374	−	2.04407i	0.0790668	−	0.164184i
$156$	−2.25011	+	1.79440i	−0.180153	+	0.143667i
$157$		−	17.6775i		−	1.41082i	−0.708799	−	0.705411i	$-0.750762\pi$
$157$		−	17.6775i		−	1.41082i	0.708799	−	0.705411i	$-0.249238\pi$
$158$	−0.667563	−	0.837097i	−0.0531084	−	0.0665959i
$159$	−1.89039	+	0.431468i	−0.149917	+	0.0342177i
$160$	−2.15240	+	0.491271i	−0.170162	+	0.0388384i
$161$	10.4438	+	13.0962i	0.823090	+	1.03212i
$162$		−	13.0761i		−	1.02735i
$163$	−3.88269	+	3.09634i	−0.304116	+	0.242524i	−0.763642	−	0.645640i	$-0.776591\pi$
$163$	−3.88269	+	3.09634i	−0.304116	+	0.242524i	0.459526	+	0.888164i	$0.348019\pi$
$164$	0.214321	−	0.445042i	0.0167356	−	0.0347519i
$165$	0.288364	−	0.361597i	0.0224491	−	0.0281503i
$166$	13.2893	+	10.5978i	1.03145	+	0.822551i
$167$	13.0320	−	6.27588i	1.00845	−	0.485642i	0.144649	−	0.989483i	$-0.453795\pi$
$167$	13.0320	−	6.27588i	1.00845	−	0.485642i	0.863796	+	0.503841i	$0.168080\pi$
$168$	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
$171$	−2.49090	−	5.17241i	−0.190484	−	0.395544i
$172$	6.97935	+	1.59299i	0.532170	+	0.121464i
$173$	−10.5133			−0.799314			−0.399657	−	0.916665i	$-0.630871\pi$
$173$	−10.5133			−0.799314			−0.399657	+	0.916665i	$0.630871\pi$
$174$		0			0
$175$	19.7289			1.49136
$176$	14.0211	+	3.20022i	1.05688	+	0.241226i
$177$	1.75909	+	3.65279i	0.132221	+	0.274561i
$178$	−2.31067	−	1.11276i	−0.173192	−	0.0834048i
$179$	−1.27748	+	5.59700i	−0.0954833	+	0.418340i	−0.999967	−	0.00816938i	$-0.997400\pi$
$179$	−1.27748	+	5.59700i	−0.0954833	+	0.418340i	0.904483	+	0.426509i	$0.140257\pi$
$180$	−0.277479	−	1.21572i	−0.0206821	−	0.0906141i
$181$	5.98307	−	2.88130i	0.444718	−	0.214165i	−0.198103	−	0.980181i	$-0.563478\pi$
$181$	5.98307	−	2.88130i	0.444718	−	0.214165i	0.642821	+	0.766016i	$0.277764\pi$
$182$	−29.5817	−	23.5906i	−2.19274	−	1.74865i
$183$	1.67845	−	2.10471i	0.124074	−	0.155584i
$184$	2.43563	−	5.05765i	0.179557	−	0.372855i
$185$	0.812502	−	0.647948i	0.0597363	−	0.0476381i
$186$		−	5.09783i		−	0.373791i
$187$	−2.01507	−	2.52681i	−0.147356	−	0.184779i
$188$	−9.48493	+	2.16487i	−0.691760	+	0.157890i
$189$	−10.1926	+	2.32640i	−0.741403	+	0.169220i
$190$	−0.821552	−	1.03019i	−0.0596017	−	0.0747381i
$191$		−	18.8116i		−	1.36116i	−0.732673	−	0.680581i	$-0.761728\pi$
$191$		−	18.8116i		−	1.36116i	0.732673	−	0.680581i	$-0.238272\pi$
$192$	−0.441459	+	0.352052i	−0.0318595	+	0.0254071i
$193$	4.72270	−	9.80678i	0.339947	−	0.705908i	−0.658983	−	0.752158i	$-0.729013\pi$
$193$	4.72270	−	9.80678i	0.339947	−	0.705908i	0.998930	+	0.0462505i	$0.0147272\pi$
$194$	−17.6957	+	22.1897i	−1.27048	+	1.59313i
$195$	0.644001	+	0.513574i	0.0461179	+	0.0367778i
$196$	10.5538	−	5.08242i	0.753840	−	0.363030i
$197$	1.86927	+	8.18982i	0.133180	+	0.583501i	0.996841	+	0.0794266i	$0.0253089\pi$
$197$	1.86927	+	8.18982i	0.133180	+	0.583501i	−0.863661	+	0.504074i	$0.831834\pi$
$198$	−3.27144	+	14.3331i	−0.232491	+	1.01861i
$199$	5.96562	+	2.87289i	0.422891	+	0.203654i	0.633211	−	0.773979i	$-0.281736\pi$
$199$	5.96562	+	2.87289i	0.422891	+	0.203654i	−0.210320	+	0.977633i	$0.567451\pi$
$200$	−2.86869	−	5.95689i	−0.202847	−	0.421215i
$201$	0.162426	+	0.0370727i	0.0114567	+	0.00261491i
$202$	−31.4306			−2.21145
$203$		0			0
$204$	0.615957			0.0431256
$205$	−0.137831	−	0.0314589i	−0.00962651	−	0.00219719i
$206$	−2.20009	−	4.56853i	−0.153287	−	0.318305i
$207$	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
$211$	6.33301	+	5.05041i	0.435983	+	0.347685i	0.816755	−	0.576984i	$-0.195771\pi$
$211$	6.33301	+	5.05041i	0.435983	+	0.347685i	−0.380773	+	0.924669i	$0.624342\pi$
$212$	3.38740	−	4.24766i	0.232647	−	0.291730i
$213$	2.20242	−	4.57338i	0.150907	−	0.313363i
$214$	−10.5099	+	8.38135i	−0.718441	+	0.572938i
$215$		−	2.04892i		−	0.139735i
$216$	2.18449	+	2.73926i	0.148636	+	0.186383i
$217$	25.0932	−	5.72737i	1.70344	−	0.388799i
$218$	−2.90356	+	0.662718i	−0.196654	+	0.0448850i
$219$	−2.48307	−	3.11368i	−0.167791	−	0.210403i
$220$			1.29590i			0.0873694i
$221$	4.50023	−	3.58881i	0.302718	−	0.241409i
$222$	1.01317	−	2.10388i	0.0679997	−	0.141203i
$223$	13.6664	−	17.1371i	0.915168	−	1.14758i	−0.0734749	−	0.997297i	$-0.523409\pi$
$223$	13.6664	−	17.1371i	0.915168	−	1.14758i	0.988642	−	0.150287i	$-0.0480197\pi$
$224$	−19.5822	−	15.6163i	−1.30839	−	1.04340i
$225$	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	−0.640102	−	0.768290i	$-0.721108\pi$
$227$	4.06734	−	17.8202i	0.269959	−	1.18277i	0.910060	−	0.414476i	$-0.136035\pi$
$228$	−1.02446	−	0.493353i	−0.0678464	−	0.0326731i
$229$	6.95288	+	14.4378i	0.459459	+	0.954077i	0.994046	+	0.108963i	$0.0347531\pi$
$229$	6.95288	+	14.4378i	0.459459	+	0.954077i	−0.534587	+	0.845114i	$0.679533\pi$
$230$	2.59386	+	0.592031i	0.171034	+	0.0390374i
$231$	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	$0.479587\pi$
$234$	−25.5271	−	5.82640i	−1.66876	−	0.380883i
$235$	1.20814	+	2.50873i	0.0788104	+	0.163651i
$236$	−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	−0.154071	−	0.988060i	$-0.549239\pi$
$239$	8.07553	−	3.88897i	0.522363	−	0.251557i	0.676434	+	0.736503i	$0.263524\pi$
$240$	0.613331	+	0.489115i	0.0395903	+	0.0315722i
$241$	−12.4073	+	15.5583i	−0.799225	+	1.00220i	0.200522	+	0.979689i	$0.435736\pi$
$241$	−12.4073	+	15.5583i	−0.799225	+	1.00220i	−0.999747	+	0.0225070i	$0.992835\pi$
$242$	−1.97108	+	4.09299i	−0.126706	+	0.263107i
$243$	−8.58125	+	6.84332i	−0.550488	+	0.438999i
$244$			7.54288i			0.482883i
$245$	−2.09030	−	2.62116i	−0.133544	−	0.167459i
$246$	−0.309703	+	0.0706876i	−0.0197459	+	0.00450688i
$247$	−10.3592	+	2.36443i	−0.659143	+	0.150445i
$248$	−5.37800	−	6.74380i	−0.341503	−	0.428232i
$249$		−	4.19806i		−	0.266041i
$250$	4.96395	−	3.95862i	0.313948	−	0.250365i
$251$	11.1963	−	23.2494i	0.706706	−	1.46749i	−0.169487	−	0.985532i	$-0.554211\pi$
$251$	11.1963	−	23.2494i	0.706706	−	1.46749i	0.876194	−	0.481959i	$-0.160074\pi$
$252$	8.82036	−	11.0604i	0.555630	−	0.696738i
$253$	−9.41835	−	7.51089i	−0.592127	−	0.472205i
$254$	−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	0.0667848	−	0.997767i	$-0.478726\pi$
$257$	−10.7676	−	5.18538i	−0.671662	−	0.323455i	−0.738446	+	0.674312i	$0.764440\pi$
$258$	−1.99755	−	4.14795i	−0.124362	−	0.258240i
$259$	11.4943	+	2.62349i	0.714219	+	0.163016i
$260$	−2.30798			−0.143135
$261$		0			0
$262$	0.819396			0.0506225
$263$	0.324390	+	0.0740400i	0.0200028	+	0.00456550i	0.232511	−	0.972594i	$-0.425306\pi$
$263$	0.324390	+	0.0740400i	0.0200028	+	0.00456550i	−0.212508	+	0.977159i	$0.568163\pi$
$264$	−0.762940	−	1.58426i	−0.0469557	−	0.0975045i
$265$	−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
$269$	0.831855	+	0.663382i	0.0507191	+	0.0404471i	0.648521	−	0.761197i	$-0.275388\pi$
$269$	0.831855	+	0.663382i	0.0507191	+	0.0404471i	−0.597802	+	0.801644i	$0.703959\pi$
$270$	−1.03534	+	1.29828i	−0.0630090	+	0.0790108i
$271$	7.14364	−	14.8339i	0.433945	−	0.901097i	−0.563252	−	0.826285i	$-0.690450\pi$
$271$	7.14364	−	14.8339i	0.433945	−	0.901097i	0.997198	−	0.0748120i	$-0.0238357\pi$
$272$	4.28590	−	3.41789i	0.259871	−	0.207240i
$273$			9.34481i			0.565574i
$274$	−14.8753	−	18.6531i	−0.898651	−	1.12687i
$275$	−13.8326	+	3.15721i	−0.834140	+	0.190387i
$276$	2.23833	−	0.510885i	0.134732	−	0.0307517i
$277$	4.11141	+	5.15554i	0.247031	+	0.309767i	0.889852	−	0.456250i	$-0.150808\pi$
$277$	4.11141	+	5.15554i	0.247031	+	0.309767i	−0.642821	+	0.766016i	$0.722236\pi$
$278$			5.03923i			0.302233i
$279$	13.9257	−	11.1054i	0.833709	−	0.664861i
$280$	−0.850747	+	1.76659i	−0.0508418	+	0.105574i
$281$	−19.0383	+	23.8733i	−1.13573	+	1.42416i	−0.245064	+	0.969507i	$0.578809\pi$
$281$	−19.0383	+	23.8733i	−1.13573	+	1.42416i	−0.890668	+	0.454655i	$0.849762\pi$
$282$	4.89166	+	3.90097i	0.291294	+	0.232299i
$283$	−3.20291	+	1.54244i	−0.190393	+	0.0916885i	−0.526652	−	0.850081i	$-0.676553\pi$
$283$	−3.20291	+	1.54244i	−0.190393	+	0.0916885i	0.336258	+	0.941770i	$0.390838\pi$
$284$	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
$287$	−0.695895	−	1.44504i	−0.0410774	−	0.0852981i
$288$	−16.8982	−	3.85690i	−0.995734	−	0.227270i
$289$	15.7681			0.927534
$290$		0			0
$291$	7.00969			0.410915
$292$	10.8791	+	2.48307i	0.636649	+	0.145311i
$293$	−14.2661	−	29.6238i	−0.833432	−	1.73064i	−0.667647	−	0.744478i	$-0.732698\pi$
$293$	−14.2661	−	29.6238i	−0.833432	−	1.73064i	−0.165786	−	0.986162i	$-0.553016\pi$
$294$	−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
$298$	3.81565	+	3.04288i	0.221034	+	0.176269i
$299$	13.3768	−	16.7740i	0.773601	−	0.970065i
$300$	1.17327	−	2.43631i	0.0677386	−	0.140661i
$301$	18.1733	−	14.4928i	1.04749	−	0.835349i
$302$		−	4.38835i		−	0.252521i
$303$	4.83997	+	6.06913i	0.278049	+	0.348662i
$304$	−9.86589	+	2.25182i	−0.565847	+	0.129151i
$305$	2.10471	−	0.480386i	0.120515	−	0.0275068i
$306$	3.49396	+	4.38129i	0.199736	+	0.250461i
$307$			14.6703i			0.837275i	0.908153	+	0.418638i	$0.137492\pi$
$307$			14.6703i			0.837275i	−0.908153	+	0.418638i	$0.862508\pi$
$308$	−11.4943	+	9.16637i	−0.654946	+	0.522302i
$309$	−0.543377	+	1.12833i	−0.0309116	+	0.0641887i
$310$	2.54892	−	3.19624i	0.144769	−	0.181534i
$311$	14.4846	+	11.5511i	0.821346	+	0.655001i	0.941222	−	0.337788i	$-0.109679\pi$
$311$	14.4846	+	11.5511i	0.821346	+	0.655001i	−0.119877	+	0.992789i	$0.538250\pi$
$312$	2.82155	−	1.35879i	0.159739	−	0.0769262i
$313$	−5.11625	−	22.4158i	−0.289188	−	1.26701i	−0.885643	−	0.464367i	$-0.846282\pi$
$313$	−5.11625	−	22.4158i	−0.289188	−	1.26701i	0.596455	−	0.802647i	$-0.296575\pi$
$314$	7.08815	−	31.0552i	0.400007	−	1.75255i
$315$	−3.64795	−	1.75676i	−0.205539	−	0.0989822i
$316$	−0.321481	−	0.667563i	−0.0180847	−	0.0375533i
$317$	13.7061	+	3.12833i	0.769813	+	0.175705i	0.589351	−	0.807877i	$-0.299384\pi$
$317$	13.7061	+	3.12833i	0.769813	+	0.175705i	0.180462	+	0.983582i	$0.442241\pi$
$318$	−3.49396			−0.195932
$319$		0			0
$320$	−0.452812			−0.0253129
$321$	3.23682	+	0.738783i	0.180662	+	0.0412348i
$322$	13.0962	+	27.1945i	0.729821	+	1.51549i
$323$	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
$327$	0.575086	+	0.458615i	0.0318023	+	0.0253615i
$328$	−0.335126	+	0.420234i	−0.0185042	+	0.0232036i
$329$	−13.7061	+	28.4611i	−0.755643	+	1.56911i
$330$	0.651576	−	0.519614i	0.0358681	−	0.0286038i
$331$		−	13.9565i		−	0.767116i	−0.923517	−	0.383558i	$-0.874699\pi$
$331$		−	13.9565i		−	0.767116i	0.923517	−	0.383558i	$-0.125301\pi$
$332$	7.33393	+	9.19646i	0.402502	+	0.504721i
$333$	7.95427	−	1.81551i	0.435892	−	0.0994894i
$334$	25.4105	−	5.79978i	1.39040	−	0.317350i
$335$	0.0833017	+	0.104457i	0.00455126	+	0.00570709i
$336$			8.89977i			0.485522i
$337$	−10.9438	+	8.72737i	−0.596145	+	0.475410i	−0.874472	−	0.485077i	$-0.838792\pi$
$337$	−10.9438	+	8.72737i	−0.596145	+	0.475410i	0.278327	+	0.960487i	$0.410220\pi$
$338$	−10.8631	+	22.5574i	−0.590873	+	1.22696i
$339$	2.39762	−	3.00652i	0.130221	−	0.163292i
$340$	0.386193	+	0.307979i	0.0209442	+	0.0167025i
$341$	−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
$345$	−0.285107	−	0.592031i	−0.0153496	−	0.0318739i
$346$	−18.4694	−	4.21552i	−0.992921	−	0.226628i
$347$	19.8538			1.06581			0.532905	−	0.846175i	$-0.321100\pi$
$347$	19.8538			1.06581			0.532905	+	0.846175i	$0.321100\pi$
$348$		0			0
$349$	−26.9202			−1.44101			−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202			−1.44101			−0.720503	+	0.693452i	$0.756089\pi$
$350$	34.6589	+	7.91066i	1.85259	+	0.422842i
$351$	5.81003	+	12.0646i	0.310116	+	0.643963i
$352$	16.2289	+	7.81541i	0.865001	+	0.416563i
$353$	−0.893436	+	3.91440i	−0.0475528	+	0.208342i	−0.993123	−	0.117076i	$-0.962648\pi$
$353$	−0.893436	+	3.91440i	−0.0475528	+	0.208342i	0.945570	+	0.325418i	$0.105505\pi$
$354$	1.62565	+	7.12242i	0.0864021	+	0.378552i
$355$	3.66756	−	1.76621i	0.194654	−	0.0937404i
$356$	−1.38759	−	1.10656i	−0.0735420	−	0.0586478i
$357$	1.24698	−	1.56366i	0.0659972	−	0.0827578i
$358$	−4.48845	+	9.32036i	−0.237222	+	0.492596i
$359$	0.583493	−	0.465320i	0.0307956	−	0.0245587i	−0.607971	−	0.793959i	$-0.708016\pi$
$359$	0.583493	−	0.465320i	0.0307956	−	0.0245587i	0.638767	+	0.769401i	$0.279445\pi$
$360$			1.35690i			0.0715147i
$361$	9.22886	+	11.5726i	0.485729	+	0.609085i
$362$	11.6661	−	2.66272i	0.613158	−	0.139949i
$363$	1.09387	−	0.249668i	0.0574131	−	0.0131042i
$364$	−16.3252	−	20.4712i	−0.855673	−	1.07298i
$365$		−	3.19375i		−	0.167169i
$366$	3.79255	−	3.02446i	0.198240	−	0.158091i
$367$	−14.7733	+	30.6770i	−0.771158	+	1.60133i	0.0275585	+	0.999620i	$0.491227\pi$
$367$	−14.7733	+	30.6770i	−0.771158	+	1.60133i	−0.798717	+	0.601707i	$0.794488\pi$
$368$	12.7397	−	15.9751i	0.664105	−	0.832761i
$369$	−0.867767	−	0.692021i	−0.0451742	−	0.0360252i
$370$	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	−0.354240	−	0.935154i	$-0.615261\pi$
$373$	−25.2277	−	12.1490i	−1.30624	−	0.629051i	−0.951998	+	0.306103i	$0.900975\pi$
$374$	−2.52681	−	5.24698i	−0.130658	−	0.271315i
$375$	−1.52879	−	0.348936i	−0.0789463	−	0.0180190i
$376$	10.5864			0.545953
$377$		0			0
$378$	−18.8388			−0.968962
$379$	−22.3073	−	5.09150i	−1.14585	−	0.261533i	−0.392881	−	0.919589i	$-0.628522\pi$
$379$	−22.3073	−	5.09150i	−1.14585	−	0.261533i	−0.752969	+	0.658057i	$0.771379\pi$
$380$	−0.395639	−	0.821552i	−0.0202958	−	0.0421447i
$381$	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	0.996524	+	0.0833027i	$0.0265468\pi$
$383$	2.63869	+	11.5608i	0.134831	+	0.590731i	−0.861694	+	0.507429i	$0.830596\pi$
$384$	4.04407	−	1.94752i	0.206373	−	0.0993841i
$385$	3.28975	+	2.62349i	0.167661	+	0.133705i
$386$	12.2289	−	15.3345i	0.622432	−	0.780506i
$387$	6.97935	−	14.4928i	0.354780	−	0.736709i
$388$	−15.3557	+	12.2458i	−0.779569	+	0.621685i
$389$			10.3913i			0.526862i	0.964678	+	0.263431i	$0.0848541\pi$
$389$			10.3913i			0.526862i	−0.964678	+	0.263431i	$0.915146\pi$
$390$	0.925428	+	1.16045i	0.0468608	+	0.0587616i
$391$	−4.47667	+	1.02177i	−0.226395	+	0.0516731i
$392$	−12.4267	+	2.83632i	−0.627645	+	0.143256i
$393$	−0.126178	−	0.158222i	−0.00636485	−	0.00798127i
$394$			15.1371i			0.762594i
$395$	−0.165797	+	0.132219i	−0.00834217	+	0.00665266i
$396$	−4.41429	+	9.16637i	−0.221826	+	0.460627i
$397$	5.12349	−	6.42465i	0.257141	−	0.322444i	−0.636458	−	0.771312i	$-0.719601\pi$
$397$	5.12349	−	6.42465i	0.257141	−	0.322444i	0.893598	+	0.448867i	$0.148172\pi$
$398$	9.32821	+	7.43900i	0.467581	+	0.372883i
$399$	−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	0.625726	+	0.780043i	$0.284803\pi$
$401$	−5.53654	+	24.2572i	−0.276482	+	1.21135i	−0.902208	+	0.431302i	$0.858054\pi$
$402$	0.270479	+	0.130256i	0.0134903	+	0.00649656i
$403$	−14.3037	−	29.7020i	−0.712520	−	1.47956i
$404$	−21.2053	−	4.83997i	−1.05500	−	0.240798i
$405$	−2.58987			−0.128692
$406$		0			0
$407$	−8.47889			−0.420283
$408$	−0.653447	−	0.149145i	−0.0323504	−	0.00738377i
$409$	−8.19843	−	17.0242i	−0.405386	−	0.841794i	−0.999305	−	0.0372686i	$-0.988134\pi$
$409$	−8.19843	−	17.0242i	−0.405386	−	0.841794i	0.593919	−	0.804525i	$-0.297580\pi$
$410$	−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
$414$	16.3307	+	13.0233i	0.802608	+	0.640058i
$415$	2.09903	−	2.63210i	0.103037	−	0.129205i
$416$	−13.9192	+	28.9034i	−0.682443	+	1.41711i
$417$	0.973057	−	0.775987i	0.0476508	−	0.0380003i
$418$			10.7506i			0.525830i
$419$	6.79135	+	8.51608i	0.331779	+	0.416038i	0.919540	−	0.392997i	$-0.128562\pi$
$419$	6.79135	+	8.51608i	0.331779	+	0.416038i	−0.587761	+	0.809035i	$0.699990\pi$
$420$	−0.781831	+	0.178448i	−0.0381495	+	0.00870737i
$421$	19.4603	−	4.44169i	0.948438	−	0.216475i	0.279796	−	0.960059i	$-0.409733\pi$
$421$	19.4603	−	4.44169i	0.948438	−	0.216475i	0.668642	+	0.743585i	$0.266876\pi$
$422$	9.10052	+	11.4117i	0.443007	+	0.555513i
$423$			21.8605i			1.06290i
$424$	−4.62207	+	3.68598i	−0.224468	+	0.179007i
$425$	−2.34653	+	4.87263i	−0.113824	+	0.236357i
$426$	5.70291	−	7.15122i	0.276307	−	0.346478i
$427$	19.1483	+	15.2702i	0.926650	+	0.738979i
$428$	−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	0.952973	−	0.303056i	$-0.0980070\pi$
$431$	27.2005	+	13.0991i	1.31020	+	0.630960i	0.357230	+	0.934016i	$0.383721\pi$
$432$	5.53333	+	11.4901i	0.266222	+	0.552816i
$433$	−19.6851	−	4.49300i	−0.946006	−	0.215920i	−0.278426	−	0.960458i	$-0.589813\pi$
$433$	−19.6851	−	4.49300i	−0.946006	−	0.215920i	−0.667580	+	0.744538i	$0.732670\pi$
$434$	46.3793			2.22628
$435$		0			0
$436$	−2.06100			−0.0987039
$437$	8.26398	+	1.88620i	0.395320	+	0.0902291i
$438$	−3.11368	−	6.46562i	−0.148777	−	0.308939i
$439$	−9.60872	−	4.62732i	−0.458599	−	0.220850i	0.190297	−	0.981727i	$-0.439055\pi$
$439$	−9.60872	−	4.62732i	−0.458599	−	0.220850i	−0.648896	+	0.760877i	$0.724769\pi$
$440$	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
$443$	15.9104	+	12.6881i	0.755927	+	0.602832i	0.923755	−	0.382985i	$-0.125104\pi$
$443$	15.9104	+	12.6881i	0.755927	+	0.602832i	−0.167828	+	0.985816i	$0.553675\pi$
$444$	1.00753	−	1.26341i	0.0478154	−	0.0599586i
$445$	−0.220395	+	0.457656i	−0.0104477	+	0.0216950i
$446$	30.8800	−	24.6259i	1.46221	−	1.16607i
$447$		−	1.20536i		−	0.0570115i
$448$	−3.20291	−	4.01632i	−0.151323	−	0.189753i
$449$	18.9363	−	4.32208i	0.893659	−	0.203972i	0.249056	−	0.968489i	$-0.419880\pi$
$449$	18.9363	−	4.32208i	0.893659	−	0.203972i	0.644603	+	0.764517i	$0.277023\pi$
$450$	23.9847	−	5.47434i	1.13065	−	0.258063i
$451$	0.719169	+	0.901809i	0.0338643	+	0.0424645i
$452$			10.7748i			0.506804i
$453$	−0.847376	+	0.675760i	−0.0398132	+	0.0317500i
$454$	14.2907	−	29.6749i	0.670694	−	1.39271i
$455$	−4.67241	+	5.85901i	−0.219046	+	0.274675i
$456$	0.967353	+	0.771438i	0.0453005	+	0.0361259i
$457$	−11.1908	+	5.38922i	−0.523485	+	0.252097i	−0.676913	−	0.736063i	$-0.736683\pi$
$457$	−11.1908	+	5.38922i	−0.523485	+	0.252097i	0.153429	+	0.988160i	$0.450969\pi$
$458$	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
$461$	−9.52214	−	19.7729i	−0.443490	−	0.920917i	−0.996163	−	0.0875187i	$-0.972106\pi$
$461$	−9.52214	−	19.7729i	−0.443490	−	0.920917i	0.552673	−	0.833399i	$-0.313608\pi$
$462$	9.21768	+	2.10388i	0.428845	+	0.0978811i
$463$	33.0073			1.53398			0.766990	−	0.641660i	$-0.221754\pi$
$463$	33.0073			1.53398			0.766990	+	0.641660i	$0.221754\pi$
$464$		0			0
$465$	−1.00969			−0.0468232
$466$	3.43703	+	0.784479i	0.159217	+	0.0363403i
$467$	11.3258	+	23.5182i	0.524094	+	1.08829i	0.980135	+	0.198333i	$0.0635527\pi$
$467$	11.3258	+	23.5182i	0.524094	+	1.08829i	−0.456041	+	0.889959i	$0.650733\pi$
$468$	−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
$472$	9.66438	+	7.70709i	0.444839	+	0.354747i
$473$	−10.4227	+	13.0697i	−0.479238	+	0.600946i
$474$	−0.206746	+	0.429312i	−0.00949616	+	0.0197190i
$475$	7.80550	−	6.22468i	0.358141	−	0.285608i
$476$			5.60388i			0.256853i
$477$	−7.61141	−	9.54440i	−0.348502	−	0.437008i
$478$	15.7461	−	3.59395i	0.720211	−	0.164383i
$479$	−32.2369	+	7.35786i	−1.47294	+	0.336189i	−0.882278	−	0.470730i	$-0.843991\pi$
$479$	−32.2369	+	7.35786i	−1.47294	+	0.336189i	−0.590663	+	0.806919i	$0.701134\pi$
$480$	0.612605	+	0.768182i	0.0279614	+	0.0350625i
$481$		−	15.1008i		−	0.688538i
$482$	−28.0350	+	22.3572i	−1.27696	+	1.01834i
$483$	3.23449	−	6.71648i	0.147174	−	0.305610i
$484$	−1.96011	+	2.45790i	−0.0890958	+	0.111723i
$485$	4.39494	+	3.50484i	0.199564	+	0.159147i
$486$	−17.8192	+	8.58125i	−0.808293	+	0.389254i
$487$	2.26002	+	9.90180i	0.102411	+	0.448693i	0.999970	+	0.00779746i	$0.00248203\pi$
$487$	2.26002	+	9.90180i	0.102411	+	0.448693i	−0.897558	+	0.440896i	$0.854661\pi$
$488$	1.82640	−	8.00197i	0.0826771	−	0.362232i
$489$	1.99127	+	0.958945i	0.0900484	+	0.0433650i
$490$	−2.62116	−	5.44289i	−0.118412	−	0.245885i
$491$	−19.1884	−	4.37963i	−0.865960	−	0.197650i	−0.233608	−	0.972331i	$-0.575053\pi$
$491$	−19.1884	−	4.37963i	−0.865960	−	0.197650i	−0.632352	+	0.774681i	$0.717910\pi$
$492$	−0.219833			−0.00991082
$493$		0			0
$494$	−19.1468			−0.861453
$495$	2.83885	+	0.647948i	0.127597	+	0.0291231i
$496$	−13.6225	−	28.2875i	−0.611669	−	1.27014i
$497$	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	0.901042	+	0.433732i	$0.142803\pi$
$499$	6.19710	+	27.1513i	0.277420	+	1.21546i	−0.623622	+	0.781726i	$0.714339\pi$
$500$	3.95862	−	1.90637i	0.177035	−	0.0852554i
$501$	−5.03286	−	4.01357i	−0.224852	−	0.179313i
$502$	28.9916	−	36.3543i	1.29396	−	1.62257i
$503$	0.0977147	−	0.202907i	0.00435688	−	0.00904716i	−0.898779	−	0.438402i	$-0.855545\pi$
$503$	0.0977147	−	0.202907i	0.00435688	−	0.00904716i	0.903136	+	0.429355i	$0.141259\pi$
$504$	−12.0353	+	9.59783i	−0.536095	+	0.427522i
$505$			6.22521i			0.277018i
$506$	−13.5341	−	16.9713i	−0.601666	−	0.754466i
$507$	6.02855	−	1.37598i	0.267737	−	0.0611093i
$508$	−12.7312	+	2.90581i	−0.564856	+	0.128925i
$509$	−15.7763	−	19.7828i	−0.699271	−	0.876859i	0.297697	−	0.954660i	$-0.403781\pi$
$509$	−15.7763	−	19.7828i	−0.699271	−	0.876859i	−0.996969	+	0.0778016i	$0.975210\pi$
$510$		−	0.317667i		−	0.0140665i
$511$	28.3277	−	22.5906i	1.25314	−	0.999349i
$512$	−7.44074	+	15.4508i	−0.328837	+	0.682837i
$513$	−3.29859	+	4.13630i	−0.145636	+	0.182622i
$514$	−16.8368	−	13.4269i	−0.742640	−	0.592236i
$515$	−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
$519$	2.03009	+	4.21552i	0.0891110	+	0.185041i
$520$	2.44845	+	0.558843i	0.107372	+	0.0245069i
$521$	−23.5797			−1.03305			−0.516523	−	0.856273i	$-0.672774\pi$
$521$	−23.5797			−1.03305			−0.516523	+	0.856273i	$0.672774\pi$
$522$		0			0
$523$	3.96508			0.173381			0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508			0.173381			0.0866905	+	0.996235i	$0.472371\pi$
$524$	0.552823	+	0.126178i	0.0241502	+	0.00551212i
$525$	−3.80957	−	7.91066i	−0.166263	−	0.345249i
$526$	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
$530$	−2.19064	−	1.74698i	−0.0951555	−	0.0758839i
$531$	−15.9148	+	19.9566i	−0.690645	+	0.866042i
$532$	4.48845	−	9.32036i	0.194599	−	0.404089i
$533$	−1.60611	+	1.28083i	−0.0695684	+	0.0554790i
$534$			1.14138i			0.0493921i
$535$	1.66003	+	2.08161i	0.0717694	+	0.0899959i
$536$	0.495224	−	0.113032i	0.0213904	−	0.00488222i
$537$	2.49090	−	0.568532i	0.107490	−	0.0245340i
$538$	1.19537	+	1.49895i	0.0515362	+	0.0646244i
$539$			27.3532i			1.17818i
$540$	−0.898438	+	0.716480i	−0.0386626	+	0.0308324i
$541$	−10.6996	+	22.2180i	−0.460012	+	0.955225i	0.533951	+	0.845515i	$0.320707\pi$
$541$	−10.6996	+	22.2180i	−0.460012	+	0.955225i	−0.993964	+	0.109710i	$0.965008\pi$
$542$	18.4976	−	23.1953i	0.794540	−	0.996322i
$543$	−2.31062	−	1.84266i	−0.0991582	−	0.0790760i
$544$	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	−0.110831	−	0.993839i	$-0.535351\pi$
$547$	−22.3811	−	10.7782i	−0.956947	−	0.460842i	−0.846117	+	0.532998i	$0.821065\pi$
$548$	−7.16357	−	14.8753i	−0.306013	−	0.635442i
$549$	16.5238	+	3.77144i	0.705216	+	0.160961i
$550$	−25.5666			−1.09016
$551$		0			0
$552$	−2.49827			−0.106333
$553$	−2.34549	−	0.535344i	−0.0997406	−	0.0227651i
$554$	5.15554	+	10.7056i	0.219038	+	0.454837i
$555$	−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	$-0.0188246\pi$
$557$	1.72790	+	7.57041i	0.0732134	+	0.320769i	−0.925038	+	0.379874i	$0.875967\pi$
$558$	28.9170	−	13.9257i	1.22415	−	0.589521i
$559$	−23.2770	−	18.5628i	−0.984512	−	0.785122i
$560$	−4.44989	+	5.57998i	−0.188042	+	0.235797i
$561$	−0.624071	+	1.29590i	−0.0263483	+	0.0547128i
$562$	−43.0182	+	34.3059i	−1.81461	+	1.44711i
$563$		−	20.8009i		−	0.876652i	−0.898816	−	0.438326i	$-0.855571\pi$
$563$		−	20.8009i		−	0.876652i	0.898816	−	0.438326i	$-0.144429\pi$
$564$	2.69955	+	3.38513i	0.113672	+	0.142540i
$565$	3.00652	−	0.686218i	0.126485	−	0.0288694i
$566$	−6.24521	+	1.42543i	−0.262506	+	0.0599152i
$567$	−18.3192	−	22.9715i	−0.769332	−	0.964712i
$568$		−	15.4765i		−	0.649380i
$569$	2.19635	−	1.75153i	0.0920757	−	0.0734279i	−0.576370	−	0.817189i	$-0.695531\pi$
$569$	2.19635	−	1.75153i	0.0920757	−	0.0734279i	0.668446	+	0.743761i	$0.266960\pi$
$570$	−0.254437	+	0.528344i	−0.0106572	+	0.0221299i
$571$	1.80343	−	2.26143i	0.0754712	−	0.0946379i	−0.742663	−	0.669666i	$-0.766437\pi$
$571$	1.80343	−	2.26143i	0.0754712	−	0.0946379i	0.818134	+	0.575028i	$0.195009\pi$
$572$	14.7222	+	11.7406i	0.615567	+	0.490898i
$573$	−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
$577$	3.11917	+	6.47703i	0.129853	+	0.269642i	0.955751	−	0.294177i	$-0.0950456\pi$
$577$	3.11917	+	6.47703i	0.129853	+	0.269642i	−0.825898	+	0.563820i	$0.809331\pi$
$578$	27.7007	+	6.32251i	1.15220	+	0.262982i
$579$	−4.84415			−0.201316
$580$		0			0
$581$	38.1933			1.58452
$582$	12.3143	+	2.81067i	0.510446	+	0.116506i
$583$	5.50453	+	11.4303i	0.227974	+	0.473393i
$584$	−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	0.243883	−	0.969805i	$-0.421579\pi$
$587$	27.9632	−	13.4664i	1.15417	−	0.555817i	0.910282	+	0.413988i	$0.135864\pi$
$588$	−4.07579	−	3.25033i	−0.168083	−	0.134041i
$589$	8.12080	−	10.1832i	0.334612	−	0.419590i
$590$	−2.54196	+	5.27844i	−0.104651	+	0.217310i
$591$	2.92291	−	2.33095i	0.120233	−	0.0958823i
$592$		−	14.3817i		−	0.591082i
$593$	−22.7371	−	28.5114i	−0.933699	−	1.17082i	−0.985072	−	0.172142i	$-0.944931\pi$
$593$	−22.7371	−	28.5114i	−0.933699	−	1.17082i	0.0513733	−	0.998680i	$-0.483640\pi$
$594$	13.2086	−	3.01477i	0.541954	−	0.123698i
$595$	1.56366	−	0.356896i	0.0641039	−	0.0146313i
$596$	2.10574	+	2.64051i	0.0862543	+	0.108159i
$597$		−	2.94677i		−	0.120603i
$598$	30.2257	−	24.1042i	1.23602	−	0.985693i
$599$	13.0461	−	27.0906i	0.533051	−	1.10689i	−0.444419	−	0.895819i	$-0.646590\pi$
$599$	13.0461	−	27.0906i	0.533051	−	1.10689i	0.977470	−	0.211073i	$-0.0676958\pi$
$600$	−1.83459	+	2.30051i	−0.0748970	+	0.0939178i
$601$	−25.9458	−	20.6911i	−1.05835	−	0.844008i	−0.0702081	−	0.997532i	$-0.522366\pi$
$601$	−25.9458	−	20.6911i	−1.05835	−	0.844008i	−0.988145	+	0.153524i	$0.950938\pi$
$602$	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
$606$	6.06913	+	12.6027i	0.246542	+	0.511949i
$607$	−14.7411	−	3.36456i	−0.598323	−	0.136563i	−0.0873757	−	0.996175i	$-0.527848\pi$
$607$	−14.7411	−	3.36456i	−0.598323	−	0.136563i	−0.510947	+	0.859612i	$0.670705\pi$
$608$	−12.6746			−0.514021
$609$		0			0
$610$	3.89008			0.157505
$611$	39.4463	+	9.00335i	1.59583	+	0.364237i
$612$	1.68260	+	3.49396i	0.0680152	+	0.141235i
$613$	3.38351	+	1.62941i	0.136659	+	0.0658114i	0.500964	−	0.865468i	$-0.332979\pi$
$613$	3.38351	+	1.62941i	0.136659	+	0.0658114i	−0.364305	+	0.931280i	$0.618693\pi$
$614$	−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
$617$	−23.3425	−	18.6151i	−0.939735	−	0.749414i	0.0284638	−	0.999595i	$-0.490938\pi$
$617$	−23.3425	−	18.6151i	−0.939735	−	0.749414i	−0.968199	+	0.250181i	$0.919510\pi$
$618$	−1.40701	+	1.76433i	−0.0565982	+	0.0709719i
$619$	20.0098	−	41.5507i	0.804260	−	1.67006i	0.0638010	−	0.997963i	$-0.479678\pi$
$619$	20.0098	−	41.5507i	0.804260	−	1.67006i	0.740459	−	0.672101i	$-0.234608\pi$
$620$	2.21187	−	1.76391i	0.0888307	−	0.0708402i
$621$		−	10.6823i		−	0.428667i
$622$	20.8143	+	26.1003i	0.834578	+	1.04653i
$623$	−5.61823	+	1.28232i	−0.225089	+	0.0513752i
$624$	11.1133	−	2.53654i	0.444888	−	0.101543i
$625$	14.4061	+	18.0647i	0.576244	+	0.722588i
$626$		−	41.4306i		−	1.65590i
$627$	2.07591	−	1.65548i	0.0829038	−	0.0661136i
$628$	9.56433	−	19.8605i	0.381658	−	0.792522i
$629$	−2.01507	+	2.52681i	−0.0803459	+	0.100751i
$630$	−5.70416	−	4.54892i	−0.227259	−	0.181233i
$631$	11.3792	−	5.47993i	0.452999	−	0.218153i	−0.193450	−	0.981110i	$-0.561968\pi$
$631$	11.3792	−	5.47993i	0.452999	−	0.218153i	0.646449	+	0.762957i	$0.276253\pi$
$632$	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
$635$	1.62163	+	3.36735i	0.0643525	+	0.133629i
$636$	−2.35727	−	0.538032i	−0.0934720	−	0.0213344i
$637$	−48.7157			−1.93019
$638$		0			0
$639$	31.9584			1.26425
$640$	3.50932	+	0.800978i	0.138718	+	0.0316614i
$641$	−16.9223	−	35.1395i	−0.668391	−	1.38793i	−0.908790	−	0.417253i	$-0.862993\pi$
$641$	−16.9223	−	35.1395i	−0.668391	−	1.38793i	0.240400	−	0.970674i	$-0.422722\pi$
$642$	5.39008	+	2.59573i	0.212730	+	0.102445i
$643$	9.18933	−	40.2611i	0.362392	−	1.58774i	−0.384713	−	0.923036i	$-0.625699\pi$
$643$	9.18933	−	40.2611i	0.362392	−	1.58774i	0.747105	−	0.664706i	$-0.231443\pi$
$644$	4.64795	+	20.3640i	0.183155	+	0.802454i
$645$	−0.821552	+	0.395639i	−0.0323486	+	0.0155783i
$646$	3.20382	+	2.55496i	0.126052	+	0.100523i
$647$	11.1670	−	14.0030i	0.439021	−	0.550515i	−0.512264	−	0.858828i	$-0.671193\pi$
$647$	11.1670	−	14.0030i	0.439021	−	0.550515i	0.951285	+	0.308313i	$0.0997644\pi$
$648$	−4.27225	+	8.87143i	−0.167830	+	0.348503i
$649$	20.7394	−	16.5392i	0.814094	−	0.649219i
$650$		−	45.5338i		−	1.78598i
$651$	−7.14191	−	8.95567i	−0.279913	−	0.351000i
$652$	−6.03742	+	1.37800i	−0.236444	+	0.0539667i
$653$	12.9867	−	2.96412i	0.508208	−	0.115995i	0.0392741	−	0.999228i	$-0.487495\pi$
$653$	12.9867	−	2.96412i	0.508208	−	0.115995i	0.468934	+	0.883233i	$0.344638\pi$
$654$	0.826396	+	1.03627i	0.0323147	+	0.0405213i
$655$		−	0.162291i		−	0.00634125i
$656$	−1.52962	+	1.21983i	−0.0597217	+	0.0476265i
$657$	10.8791	−	22.5906i	0.424432	−	0.881343i
$658$	−35.4904	+	44.5035i	−1.38356	+	1.73493i
$659$	14.6716	+	11.7002i	0.571525	+	0.455776i	0.866113	−	0.499849i	$-0.166611\pi$
$659$	14.6716	+	11.7002i	0.571525	+	0.455776i	−0.294588	+	0.955624i	$0.595182\pi$
$660$	0.519614	−	0.250233i	0.0202260	−	0.00974031i
$661$	5.50269	+	24.1089i	0.214030	+	0.937726i	0.961797	+	0.273764i	$0.0882689\pi$
$661$	5.50269	+	24.1089i	0.214030	+	0.937726i	−0.747767	+	0.663961i	$0.768874\pi$
$662$	5.59611	−	24.5181i	0.217499	−	0.952925i
$663$	−2.30798	−	1.11146i	−0.0896345	−	0.0431657i
$664$	−5.55351	−	11.5320i	−0.215518	−	0.447528i
$665$	−2.88654	−	0.658834i	−0.111935	−	0.0255485i
$666$	14.7017			0.569680
$667$		0			0
$668$	18.0368			0.697866
$669$	−9.51036	−	2.17068i	−0.367692	−	0.0839233i
$670$	0.104457	+	0.216907i	0.00403553	+	0.00837985i
$671$	−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	0.958781	+	0.284146i	$0.0917102\pi$
$673$	5.66152	+	24.8047i	0.218236	+	0.956153i	−0.740545	+	0.672006i	$0.765433\pi$
$674$	−22.7250	+	10.9438i	−0.875333	+	0.421538i
$675$	−9.83672	−	7.84452i	−0.378615	−	0.301936i
$676$	−10.8026	+	13.5460i	−0.415485	+	0.521001i
$677$	−0.267510	+	0.555491i	−0.0102813	+	0.0213492i	−0.906046	−	0.423179i	$-0.860914\pi$
$677$	−0.267510	+	0.555491i	−0.0102813	+	0.0213492i	0.895765	+	0.444528i	$0.146629\pi$
$678$	5.41755	−	4.32036i	0.208060	−	0.165922i
$679$			63.7730i			2.44738i
$680$	−0.335126	−	0.420234i	−0.0128515	−	0.0161152i
$681$	−7.93072	+	1.81013i	−0.303906	+	0.0693645i
$682$	−32.5182	+	7.42208i	−1.24519	+	0.284206i
$683$	11.2364	+	14.0900i	0.429949	+	0.539138i	0.948863	−	0.315688i	$-0.102235\pi$
$683$	11.2364	+	14.0900i	0.429949	+	0.539138i	−0.518915	+	0.854826i	$0.673664\pi$
$684$		−	7.15883i		−	0.273725i
$685$	−3.69447	+	2.94624i	−0.141158	+	0.112570i
$686$	7.57753	−	15.7349i	0.289311	−	0.600761i
$687$	4.44653	−	5.57578i	0.169646	−	0.212729i
$688$	−22.1684	−	17.6787i	−0.845164	−	0.673996i
$689$	−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	0.895409	+	0.445245i	$0.146883\pi$
$691$	−2.74728	+	12.0366i	−0.104511	+	0.457894i	−0.999920	+	0.0126487i	$0.995974\pi$
$692$	−11.8116	−	5.68818i	−0.449011	−	0.216232i
$693$	14.3331	+	29.7630i	0.544470	+	1.13060i
$694$	34.8784	+	7.96077i	1.32397	+	0.302187i
$695$	0.998081			0.0378594
$696$		0			0
$697$	0.439665			0.0166535
$698$	−47.2923	−	10.7942i	−1.79004	−	0.408565i
$699$	−0.377785	−	0.784479i	−0.0142892	−	0.0296717i
$700$	22.1652	+	10.6742i	0.837765	+	0.403446i
$701$	−7.58738	+	33.2425i	−0.286571	+	1.25555i	0.602625	+	0.798025i	$0.294122\pi$
$701$	−7.58738	+	33.2425i	−0.286571	+	1.25555i	−0.889196	+	0.457526i	$0.848736\pi$
$702$	5.36927	+	23.5243i	0.202650	+	0.887868i
$703$	5.37531	−	2.58861i	0.202734	−	0.0976315i
$704$	2.88841	+	2.30343i	0.108861	+	0.0868138i
$705$	0.772635	−	0.968853i	0.0290991	−	0.0364891i
$706$	−3.13910	+	6.51842i	−0.118142	+	0.245324i
$707$	−55.2159	+	44.0332i	−2.07661	+	1.65604i
$708$			5.05562i			0.190002i
$709$	−26.2461	−	32.9115i	−0.985692	−	1.23602i	−0.971725	−	0.236116i	$-0.924125\pi$
$709$	−26.2461	−	32.9115i	−0.985692	−	1.23602i	−0.0139674	−	0.999902i	$-0.504446\pi$
$710$	7.15122	−	1.63222i	0.268380	−	0.0612561i
$711$	−1.62313	+	0.370469i	−0.0608722	+	0.0138937i
$712$	1.20410	+	1.50990i	0.0451257	+	0.0565858i
$713$			26.2989i			0.984901i
$714$	2.81762	−	2.24698i	0.105447	−	0.0840911i
$715$	2.33838	−	4.85570i	0.0874505	−	0.181593i
$716$	−4.46346	+	5.59700i	−0.166807	+	0.209170i
$717$	−3.11871	−	2.48709i	−0.116470	−	0.0928821i
$718$	1.21164	−	0.583493i	0.0452178	−	0.0217758i
$719$	11.6277	+	50.9442i	0.433639	+	1.89990i	0.436098	+	0.899899i	$0.356360\pi$
$719$	11.6277	+	50.9442i	0.433639	+	1.89990i	−0.00245885	+	0.999997i	$0.500783\pi$
$720$	−1.09903	+	4.81517i	−0.0409585	+	0.179451i
$721$	−10.2654	−	4.94355i	−0.382303	−	0.184108i
$722$	11.5726	+	24.0308i	0.430688	+	0.894334i
$723$	8.63419	+	1.97070i	0.321109	+	0.0732910i
$724$	8.28083			0.307755
$725$		0			0
$726$	2.02177			0.0750349
$727$	−29.2331	−	6.67228i	−1.08420	−	0.247461i	−0.357149	−	0.934047i	$-0.616251\pi$
$727$	−29.2331	−	6.67228i	−1.08420	−	0.247461i	−0.727048	+	0.686586i	$0.759108\pi$
$728$	12.3620	+	25.6700i	0.458167	+	0.951394i
$729$	−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
$733$	−2.35681	−	1.87949i	−0.0870508	−	0.0694207i	0.578997	−	0.815329i	$-0.303444\pi$
$733$	−2.35681	−	1.87949i	−0.0870508	−	0.0694207i	−0.666048	+	0.745909i	$0.732016\pi$
$734$	−38.2536	+	47.9685i	−1.41197	+	1.77055i
$735$	−0.647372	+	1.34428i	−0.0238787	+	0.0495846i
$736$	20.0085	−	15.9562i	0.737522	−	0.588154i
$737$		−	1.09006i		−	0.0401531i
$738$	−1.24698	−	1.56366i	−0.0459020	−	0.0575592i
$739$	−20.3150	+	4.63677i	−0.747300	+	0.170566i	−0.579179	−	0.815200i	$-0.696627\pi$
$739$	−20.3150	+	4.63677i	−0.747300	+	0.170566i	−0.168120	+	0.985766i	$0.553770\pi$
$740$	1.26341	−	0.288364i	0.0464437	−	0.0106005i
$741$	2.94839	+	3.69717i	0.108312	+	0.135819i
$742$		−	31.7875i		−	1.16695i
$743$	−24.0536	+	19.1821i	−0.882441	+	0.703723i	−0.955937	−	0.293573i	$-0.905156\pi$
$743$	−24.0536	+	19.1821i	−0.882441	+	0.703723i	0.0734962	+	0.997295i	$0.476584\pi$
$744$	−1.66558	+	3.45862i	−0.0610632	+	0.126799i
$745$	0.602679	−	0.755736i	0.0220805	−	0.0276880i
$746$	−39.4476	−	31.4584i	−1.44428	−	1.15177i
$747$	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
$751$	−1.93912	−	4.02661i	−0.0707593	−	0.146933i	0.862589	−	0.505905i	$-0.168842\pi$
$751$	−1.93912	−	4.02661i	−0.0707593	−	0.146933i	−0.933348	+	0.358972i	$0.883127\pi$
$752$	37.5677	+	8.57457i	1.36995	+	0.312682i
$753$	−11.4843			−0.418510
$754$		0			0
$755$	−0.869167			−0.0316322
$756$	−12.7100	−	2.90097i	−0.462257	−	0.105507i
$757$	3.66883	+	7.61841i	0.133346	+	0.276896i	0.956941	−	0.290283i	$-0.0937493\pi$
$757$	3.66883	+	7.61841i	0.133346	+	0.276896i	−0.823595	+	0.567178i	$0.808035\pi$
$758$	−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	−0.791265	−	0.611474i	$-0.790577\pi$
$761$	−22.2494	+	10.7148i	−0.806541	+	0.388410i	−0.0152763	+	0.999883i	$0.504863\pi$
$762$	6.56585	+	5.23609i	0.237856	+	0.189684i
$763$	−4.17241	+	5.23203i	−0.151051	+	0.189412i
$764$	10.1779	−	21.1347i	0.368224	−	0.764626i
$765$	0.867767	−	0.692021i	0.0313742	−	0.0250201i
$766$			21.3676i			0.772045i
$767$	29.4561	+	36.9367i	1.06360	+	1.33371i
$768$	8.98634	−	2.05107i	0.324267	−	0.0740117i
$769$	−29.3873	+	6.70746i	−1.05973	+	0.241877i	−0.716653	−	0.697429i	$-0.754327\pi$
$769$	−29.3873	+	6.70746i	−1.05973	+	0.241877i	−0.343079	+	0.939307i	$0.611470\pi$
$770$	4.72737	+	5.92793i	0.170362	+	0.213628i
$771$			5.31873i			0.191549i
$772$	10.6118	−	8.46263i	0.381927	−	0.304577i
$773$	2.46314	−	5.11476i	0.0885929	−	0.183965i	−0.851965	−	0.523599i	$-0.824589\pi$
$773$	2.46314	−	5.11476i	0.0885929	−	0.183965i	0.940558	+	0.339634i	$0.110303\pi$
$774$	18.0722	−	22.6618i	0.649591	−	0.814561i
$775$	24.2171	+	19.3125i	0.869902	+	0.693724i
$776$	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
$780$	0.445662	+	0.925428i	0.0159573	+	0.0331356i
$781$	−32.3794	−	7.39038i	−1.15862	−	0.264449i
$782$	−8.27413			−0.295882
$783$		0			0
$784$	−46.3957			−1.65699
$785$	−6.15086	−	1.40389i	−0.219534	−	0.0501071i
$786$	−0.158222	−	0.328552i	−0.00564361	−	0.0117191i
$787$	−3.25182	−	1.56600i	−0.115915	−	0.0558217i	0.375028	−	0.927014i	$-0.377633\pi$
$787$	−3.25182	−	1.56600i	−0.115915	−	0.0558217i	−0.490943	+	0.871192i	$0.663348\pi$
$788$	−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
$791$	27.3528	+	21.8131i	0.972553	+	0.775585i
$792$	6.90246	−	8.65541i	0.245268	−	0.307557i
$793$	13.6107	−	28.2630i	0.483332	−	1.00365i
$794$	11.5768	−	9.23221i	0.410846	−	0.327639i
$795$			0.692021i			0.0245435i
$796$	5.14795	+	6.45532i	0.182464	+	0.228803i
$797$	−30.0114	+	6.84990i	−1.06306	+	0.242636i	−0.718069	−	0.695972i	$-0.754974\pi$
$797$	−30.0114	+	6.84990i	−1.06306	+	0.242636i	−0.344987	+	0.938607i	$0.612117\pi$
$798$	−6.48599	+	1.48039i	−0.229602	+	0.0524051i
$799$	−5.39911	−	6.77027i	−0.191007	−	0.239515i
$800$		−	30.1420i		−	1.06568i
$801$	−3.11788	+	2.48643i	−0.110165	+	0.0878536i
$802$	−19.4527	+	40.3940i	−0.686900	+	1.42636i
$803$	−16.2464	+	20.3724i	−0.573325	+	0.718926i
$804$	0.162426	+	0.129531i	0.00572833	+	0.00456819i
$805$	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
$809$	2.27238	+	4.71864i	0.0798925	+	0.165898i	0.937089	−	0.349092i	$-0.113510\pi$
$809$	2.27238	+	4.71864i	0.0798925	+	0.165898i	−0.857196	+	0.514990i	$0.827796\pi$
$810$	−4.54979	−	1.03846i	−0.159863	−	0.0364877i
$811$	−41.8646			−1.47006			−0.735032	−	0.678032i	$-0.762833\pi$
$811$	−41.8646			−1.47006			−0.735032	+	0.678032i	$0.762833\pi$
$812$		0			0
$813$	−7.32736			−0.256982
$814$	−14.8954	−	3.39977i	−0.522083	−	0.119162i
$815$	0.769015	+	1.59688i	0.0269374	+	0.0559361i
$816$	−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
$820$	−0.137831	−	0.109916i	−0.00481325	−	0.00383844i
$821$	−9.60537	+	12.0447i	−0.335230	+	0.420365i	−0.920665	−	0.390355i	$-0.872352\pi$
$821$	−9.60537	+	12.0447i	−0.335230	+	0.420365i	0.585435	+	0.810719i	$0.300924\pi$
$822$	−4.60692	+	9.56638i	−0.160685	+	0.333666i
$823$	27.8768	−	22.2310i	0.971724	−	0.774924i	−0.00261763	−	0.999997i	$-0.500833\pi$
$823$	27.8768	−	22.2310i	0.971724	−	0.774924i	0.974342	+	0.225072i	$0.0722618\pi$
$824$			3.81833i			0.133018i
$825$	3.93698	+	4.93681i	0.137068	+	0.171878i
$826$	−64.7986	+	14.7899i	−2.25463	+	0.514605i
$827$	50.7487	−	11.5831i	1.76471	−	0.402783i	0.787711	−	0.616045i	$-0.211266\pi$
$827$	50.7487	−	11.5831i	1.76471	−	0.402783i	0.976995	+	0.213262i	$0.0684089\pi$
$828$	9.01238	+	11.3012i	0.313202	+	0.392743i
$829$		−	13.4168i		−	0.465986i	−0.972478	−	0.232993i	$-0.925148\pi$
$829$		−	13.4168i		−	0.465986i	0.972478	−	0.232993i	$-0.0748519\pi$
$830$	4.74288	−	3.78232i	0.164628	−	0.131286i
$831$	1.27331	−	2.64406i	0.0441708	−	0.0917216i
$832$	−4.10238	+	5.14423i	−0.142225	+	0.178344i
$833$	8.15157	+	6.50066i	0.282435	+	0.225235i
$834$	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
$838$	8.51608	+	17.6838i	0.294183	+	0.610878i
$839$	−30.2728	−	6.90957i	−1.04513	−	0.238545i	−0.334711	−	0.942321i	$-0.608639\pi$
$839$	−30.2728	−	6.90957i	−1.04513	−	0.238545i	−0.710422	+	0.703776i	$0.751496\pi$
$840$	0.872625			0.0301084
$841$		0			0
$842$	35.9681			1.23954
$843$	13.2487	+	3.02393i	0.456309	+	0.104150i
$844$	4.38258	+	9.10052i	0.150855	+	0.313253i
$845$	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
$849$	1.23694	+	0.986426i	0.0424517	+	0.0338541i
$850$	−6.07606	+	7.61914i	−0.208407	+	0.261334i
$851$	−5.22679	+	10.8535i	−0.179172	+	0.372055i
$852$	4.94880	−	3.94653i	0.169543	−	0.135206i
$853$		−	21.3357i		−	0.730521i	−0.930905	−	0.365261i	$-0.880980\pi$
$853$		−	21.3357i		−	0.730521i	0.930905	−	0.365261i	$-0.119020\pi$
$854$	27.5160	+	34.5040i	0.941579	+	1.18070i
$855$	−1.99755	+	0.455927i	−0.0683147	+	0.0155924i
$856$	9.86879	−	2.25249i	0.337308	−	0.0769885i
$857$	−6.13019	−	7.68702i	−0.209403	−	0.262584i	0.666027	−	0.745928i	$-0.267994\pi$
$857$	−6.13019	−	7.68702i	−0.209403	−	0.262584i	−0.875431	+	0.483344i	$0.839422\pi$
$858$		−	12.1099i		−	0.413426i
$859$	−40.4862	+	32.2866i	−1.38137	+	1.10161i	−0.398528	+	0.917156i	$0.630479\pi$
$859$	−40.4862	+	32.2866i	−1.38137	+	1.10161i	−0.982842	+	0.184450i	$0.940950\pi$
$860$	1.10855	−	2.30194i	0.0378014	−	0.0784954i
$861$	−0.445042	+	0.558065i	−0.0151670	+	0.0190188i
$862$	42.5324	+	33.9185i	1.44866	+	1.15527i
$863$	−14.6630	+	7.06134i	−0.499135	+	0.240371i	−0.666473	−	0.745529i	$-0.732197\pi$
$863$	−14.6630	+	7.06134i	−0.499135	+	0.240371i	0.167339	+	0.985899i	$0.446483\pi$
$864$	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
$867$	−3.04476	−	6.32251i	−0.103406	−	0.214724i
$868$	31.2907	+	7.14191i	1.06208	+	0.242412i
$869$	1.73019			0.0586925
$870$		0			0
$871$	1.94139			0.0657816
$872$	2.18644	+	0.499041i	0.0740422	+	0.0168996i
$873$	19.1483	+	39.7618i	0.648071	+	1.34573i
$874$	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	−0.645337	−	0.763898i	$-0.723283\pi$
$877$	−13.3400	+	6.42419i	−0.450459	+	0.216930i	0.194878	+	0.980827i	$0.437569\pi$
$878$	−15.0248	−	11.9819i	−0.507062	−	0.404369i
$879$	−9.12349	+	11.4405i	−0.307728	+	0.385878i
$880$	2.22702	−	4.62445i	0.0750727	−	0.155890i
$881$	14.5716	−	11.6204i	0.490928	−	0.391502i	−0.346499	−	0.938050i	$-0.612630\pi$
$881$	14.5716	−	11.6204i	0.490928	−	0.391502i	0.837428	+	0.546548i	$0.184058\pi$
$882$		−	47.4282i		−	1.59699i
$883$	20.1972	+	25.3264i	0.679689	+	0.852303i	0.995325	−	0.0965775i	$-0.0307896\pi$
$883$	20.1972	+	25.3264i	0.679689	+	0.852303i	−0.315637	+	0.948880i	$0.602218\pi$
$884$	6.99766	−	1.59717i	0.235357	−	0.0537187i
$885$	1.41068	−	0.321979i	0.0474196	−	0.0108232i
$886$	22.8632	+	28.6696i	0.768105	+	0.963174i
$887$		−	6.16288i		−	0.206929i	−0.994633	−	0.103465i	$-0.967007\pi$
$887$		−	6.16288i		−	0.206929i	0.994633	−	0.103465i	$-0.0329929\pi$
$888$	−1.37477	+	1.09634i	−0.0461343	+	0.0367909i
$889$	−18.3971	+	38.2020i	−0.617019	+	1.28125i
$890$	−0.570688	+	0.715620i	−0.0191295	+	0.0239876i
$891$	16.5204	+	13.1746i	0.553454	+	0.441364i
$892$	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
$896$	17.7182	+	36.7923i	0.591925	+	1.22914i
$897$	−9.30886	−	2.12469i	−0.310814	−	0.0709412i
$898$	34.9995			1.16795
$899$		0			0
$900$	17.0248			0.567492
$901$	4.71455	+	1.07606i	0.157064	+	0.0358489i
$902$	0.901809	+	1.87263i	0.0300269	+	0.0623516i
$903$	−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
$907$	−34.3882	−	27.4237i	−1.14184	−	0.910589i	−0.144956	−	0.989438i	$-0.546304\pi$
$907$	−34.3882	−	27.4237i	−1.14184	−	0.910589i	−0.996887	+	0.0788492i	$0.974875\pi$
$908$	14.2111	−	17.8202i	0.471612	−	0.591383i
$909$	−21.2053	+	44.0332i	−0.703335	+	1.46049i
$910$	−10.5576	+	8.41939i	−0.349980	+	0.279100i
$911$			25.6233i			0.848936i	0.905443	+	0.424468i	$0.139539\pi$
$911$			25.6233i			0.848936i	−0.905443	+	0.424468i	$0.860461\pi$
$912$	2.80798	+	3.52109i	0.0929815	+	0.116595i
$913$	−26.7787	+	6.11207i	−0.886247	+	0.202280i
$914$	−21.8205	+	4.98039i	−0.721758	+	0.164737i
$915$	−0.599031	−	0.751161i	−0.0198034	−	0.0248326i
$916$			19.9825i			0.660242i
$917$	1.43948	−	1.14795i	0.0475359	−	0.0379086i
$918$	2.24067	−	4.65279i	0.0739530	−	0.153565i
$919$	−3.89158	+	4.87988i	−0.128371	+	0.160972i	−0.841863	−	0.539691i	$-0.818541\pi$
$919$	−3.89158	+	4.87988i	−0.128371	+	0.160972i	0.713492	+	0.700663i	$0.247113\pi$
$920$	−1.56637	−	1.24914i	−0.0516416	−	0.0411828i
$921$	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
$925$	6.15610	+	12.7833i	0.202411	+	0.420312i
$926$	57.9859	+	13.2349i	1.90553	+	0.434926i
$927$	−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	$0.631729\pi$
$930$	−1.77378	−	0.404854i	−0.0581645	−	0.0132757i
$931$	−8.35095	−	17.3409i	−0.273691	−	0.568326i
$932$	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
$936$	15.4152	+	12.2932i	0.503861	+	0.401816i
$937$	2.54975	−	3.19728i	0.0832965	−	0.104451i	−0.738437	−	0.674323i	$-0.764436\pi$
$937$	2.54975	−	3.19728i	0.0832965	−	0.104451i	0.821734	+	0.569872i	$0.193007\pi$
$938$	−1.18505	+	2.46077i	−0.0386931	+	0.0803470i
$939$	−8.00009	+	6.37986i	−0.261073	+	0.208199i
$940$			3.47219i			0.113250i
$941$	−3.84266	−	4.81854i	−0.125267	−	0.157080i	0.715243	−	0.698876i	$-0.246316\pi$
$941$	−3.84266	−	4.81854i	−0.125267	−	0.157080i	−0.840510	+	0.541796i	$0.817745\pi$
$942$	−13.8209	+	3.15452i	−0.450308	+	0.102780i
$943$	1.59770	−	0.364666i	0.0520284	−	0.0118751i
$944$	28.0532	+	35.1776i	0.913055	+	1.14493i
$945$			3.73125i			0.121378i
$946$	−23.5508	+	18.7811i	−0.765702	+	0.610627i
$947$	−21.5650	+	44.7802i	−0.700769	+	1.45516i	0.181001	+	0.983483i	$0.442066\pi$
$947$	−21.5650	+	44.7802i	−0.700769	+	1.45516i	−0.881770	+	0.471679i	$0.843648\pi$
$948$	−0.205595	+	0.257808i	−0.00667742	+	0.00837321i
$949$	−36.2830	−	28.9347i	−1.17780	−	0.939262i
$950$	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	0.157623	−	0.987499i	$-0.449617\pi$
$953$	−15.9342	−	7.67349i	−0.516158	−	0.248569i	−0.673781	+	0.738931i	$0.735331\pi$
$954$	−9.54440	−	19.8192i	−0.309011	−	0.641669i
$955$	−6.54546	−	1.49396i	−0.211806	−	0.0483434i
$956$	11.1769			0.361486
$957$		0			0
$958$	−59.5827			−1.92503
$959$	−52.2647	−	11.9291i	−1.68772	−	0.385210i
$960$	0.0874363	+	0.181563i	0.00282199	+	0.00585993i
$961$	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
$965$	−3.03719	−	2.42208i	−0.0977705	−	0.0779694i
$966$	8.37531	−	10.5023i	0.269471	−	0.337906i
$967$	5.59421	−	11.6165i	0.179898	−	0.373561i	−0.791447	−	0.611238i	$-0.790672\pi$
$967$	5.59421	−	11.6165i	0.179898	−	0.373561i	0.971344	+	0.237677i	$0.0763860\pi$
$968$	2.67455	−	2.13288i	0.0859633	−	0.0685535i
$969$		−	1.01208i		−	0.0325127i
$970$	6.31551	+	7.91940i	0.202779	+	0.254277i
$971$	4.71616	−	1.07643i	0.151349	−	0.0345444i	−0.146175	−	0.989259i	$-0.546696\pi$
$971$	4.71616	−	1.07643i	0.151349	−	0.0345444i	0.297524	+	0.954714i	$0.403839\pi$
$972$	−13.3435	+	3.04556i	−0.427993	+	0.0976865i
$973$	7.05980	+	8.85271i	0.226327	+	0.283805i
$974$			18.3013i			0.586411i
$975$	−8.79241	+	7.01171i	−0.281582	+	0.224555i
$976$	12.9625	−	26.9170i	0.414921	−	0.861592i
$977$	10.2515	−	12.8549i	0.327973	−	0.411265i	−0.590318	−	0.807171i	$-0.700998\pi$
$977$	10.2515	−	12.8549i	0.327973	−	0.411265i	0.918291	+	0.395905i	$0.129569\pi$
$978$	3.11368	+	2.48307i	0.0995644	+	0.0794000i
$979$	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
$983$	11.4976	+	23.8751i	0.366717	+	0.761497i	0.999922	−	0.0124878i	$-0.00397510\pi$
$983$	11.4976	+	23.8751i	0.366717	+	0.761497i	−0.633205	+	0.773984i	$0.718261\pi$
$984$	0.233212	+	0.0532292i	0.00743454	+	0.00169689i
$985$	2.99808			0.0955268
$986$		0			0
$987$	14.0586			0.447490
$988$	−12.9178	−	2.94839i	−0.410969	−	0.0938009i
$989$	10.3050	+	21.3986i	0.327680	+	0.680435i
$990$	4.72737	+	2.27658i	0.150246	+	0.0723544i
$991$	8.99127	−	39.3933i	0.285617	−	1.25137i	−0.604856	−	0.796335i	$-0.706769\pi$
$991$	8.99127	−	39.3933i	0.285617	−	1.25137i	0.890473	−	0.455036i	$-0.150373\pi$
$992$	−8.75033	−	38.3377i	−0.277823	−	1.21722i
$993$	−5.59611	+	2.69494i	−0.177587	+	0.0855214i
$994$	65.0606	+	51.8841i	2.06360	+	1.64566i
$995$	1.47339	−	1.84757i	0.0467095	−	0.0585718i
$996$	2.27134	−	4.71648i	0.0719701	−	0.149447i
$997$	18.3381	−	14.6242i	0.580774	−	0.463152i	−0.288502	−	0.957479i	$-0.593157\pi$
$997$	18.3381	−	14.6242i	0.580774	−	0.463152i	0.869276	+	0.494328i	$0.164586\pi$
$998$			50.1831i			1.58852i
$999$	−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.e.c.236.2		12
29.2	odd	28		841.2.d.e.190.1		6
29.3	odd	28		841.2.d.b.645.1		6
29.4	even	14		841.2.e.d.267.2		12
29.5	even	14		841.2.e.b.651.2		12
29.6	even	14		841.2.b.c.840.6		6
29.7	even	7	inner	841.2.e.c.196.1		12
29.8	odd	28		841.2.d.d.778.1		6
29.9	even	14		841.2.e.d.63.1		12
29.10	odd	28		841.2.d.d.574.1		6
29.11	odd	28		841.2.d.e.571.1		6
29.12	odd	4		841.2.d.c.605.1		6
29.13	even	14		841.2.e.b.270.1		12
29.14	odd	28		841.2.a.e.1.1		3
29.15	odd	28		841.2.a.f.1.3		3
29.16	even	7		841.2.e.b.270.2		12
29.17	odd	4		841.2.d.b.605.1		6
29.18	odd	28		841.2.d.a.571.1		6
29.19	odd	28		29.2.d.a.23.1	✓	6
29.20	even	7		841.2.e.d.63.2		12
29.21	odd	28		29.2.d.a.24.1	yes	6
29.22	even	14	inner	841.2.e.c.196.2		12
29.23	even	7		841.2.b.c.840.1		6
29.24	even	7		841.2.e.b.651.1		12
29.25	even	7		841.2.e.d.267.1		12
29.26	odd	28		841.2.d.c.645.1		6
29.27	odd	28		841.2.d.a.190.1		6
29.28	even	2	inner	841.2.e.c.236.1		12
87.14	even	28		7569.2.a.r.1.3		3
87.44	even	28		7569.2.a.p.1.1		3
87.50	even	28		261.2.k.a.82.1		6
87.77	even	28		261.2.k.a.226.1		6
116.19	even	28		464.2.u.f.81.1		6
116.79	even	28		464.2.u.f.401.1		6
145.19	odd	28		725.2.l.b.226.1		6
145.48	even	28		725.2.r.b.574.2		12
145.77	even	28		725.2.r.b.574.1		12
145.79	odd	28		725.2.l.b.401.1		6
145.108	even	28		725.2.r.b.24.1		12
145.137	even	28		725.2.r.b.24.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.19	odd	28
29.2.d.a.24.1	yes	6	29.21	odd	28
261.2.k.a.82.1		6	87.50	even	28
261.2.k.a.226.1		6	87.77	even	28
464.2.u.f.81.1		6	116.19	even	28
464.2.u.f.401.1		6	116.79	even	28
725.2.l.b.226.1		6	145.19	odd	28
725.2.l.b.401.1		6	145.79	odd	28
725.2.r.b.24.1		12	145.108	even	28
725.2.r.b.24.2		12	145.137	even	28
725.2.r.b.574.1		12	145.77	even	28
725.2.r.b.574.2		12	145.48	even	28
841.2.a.e.1.1		3	29.14	odd	28
841.2.a.f.1.3		3	29.15	odd	28
841.2.b.c.840.1		6	29.23	even	7
841.2.b.c.840.6		6	29.6	even	14
841.2.d.a.190.1		6	29.27	odd	28
841.2.d.a.571.1		6	29.18	odd	28
841.2.d.b.605.1		6	29.17	odd	4
841.2.d.b.645.1		6	29.3	odd	28
841.2.d.c.605.1		6	29.12	odd	4
841.2.d.c.645.1		6	29.26	odd	28
841.2.d.d.574.1		6	29.10	odd	28
841.2.d.d.778.1		6	29.8	odd	28
841.2.d.e.190.1		6	29.2	odd	28
841.2.d.e.571.1		6	29.11	odd	28
841.2.e.b.270.1		12	29.13	even	14
841.2.e.b.270.2		12	29.16	even	7
841.2.e.b.651.1		12	29.24	even	7
841.2.e.b.651.2		12	29.5	even	14
841.2.e.c.196.1		12	29.7	even	7	inner
841.2.e.c.196.2		12	29.22	even	14	inner
841.2.e.c.236.1		12	29.28	even	2	inner
841.2.e.c.236.2		12	1.1	even	1	trivial
841.2.e.d.63.1		12	29.9	even	14
841.2.e.d.63.2		12	29.20	even	7
841.2.e.d.267.1		12	29.25	even	7
841.2.e.d.267.2		12	29.4	even	14
7569.2.a.p.1.1		3	87.44	even	28
7569.2.a.r.1.3		3	87.14	even	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.75676 + 0.400969i) q^{2} +(-0.193096 - 0.400969i) 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} +(-1.06086 - 0.846011i) q^{8} +(1.74698 - 2.19064i) q^{9} +(0.279032 - 0.579417i) q^{10} +(-2.27658 + 1.81551i) q^{11} -0.554958i q^{12} +(-3.23341 - 4.05456i) q^{13} +(7.11297 - 1.62349i) q^{14} +(-0.154851 + 0.0353438i) q^{15} +(-3.07942 - 3.86147i) q^{16} +1.10992i q^{17} +(3.94740 - 3.14795i) q^{18} +(0.888992 - 1.84601i) q^{19} +(0.277479 - 0.347948i) q^{20} +(-1.40881 - 1.12349i) 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} +(-4.05456 - 8.41939i) q^{26} +(-2.51737 - 0.574572i) q^{27} +5.04892 q^{28} -0.286208 q^{30} +(6.19752 + 1.41454i) q^{31} +(-2.68400 - 5.57338i) 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} +(2.27658 + 1.81551i) q^{37} +(2.30194 - 2.88654i) q^{38} +(-1.00139 + 2.07942i) q^{39} +(-0.378618 + 0.301938i) q^{40} -0.396125i q^{41} +(-2.02446 - 2.53859i) q^{42} +(5.59700 - 1.27748i) q^{43} +(-3.53999 + 0.807979i) q^{44} +(-0.623490 - 0.781831i) q^{45} +7.45473i q^{46} +(-6.09980 + 4.86443i) q^{47} +(-0.953703 + 1.98039i) q^{48} +(5.85690 - 7.34432i) q^{49} +(6.86461 + 5.47434i) 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} +(0.450904 + 0.936313i) q^{55} +(-5.35621 - 1.22252i) q^{56} -0.911854 q^{57} -9.10992 q^{59} +(-0.193096 - 0.0440730i) q^{60} +(2.62453 + 5.44989i) 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} +(1.82567 + 1.45593i) q^{66} +(-0.233406 + 0.292682i) q^{67} +(-0.600514 + 1.24698i) q^{68} +(1.43948 - 1.14795i) q^{69} -2.60388i q^{70} +(7.11141 + 8.91742i) q^{71} +(-3.70662 + 0.846011i) q^{72} +(8.72433 - 1.99127i) q^{73} +(3.27144 + 4.10225i) q^{74} -2.16852i q^{75} +(1.99755 - 1.59299i) q^{76} +(-5.11543 + 10.6223i) q^{77} +(-2.59299 + 3.25151i) q^{78} +(-0.464554 - 0.370469i) 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} +(-0.974928 - 2.02446i) q^{84} +(0.386193 + 0.0881460i) q^{85} +10.3448 q^{86} +3.95108 q^{88} +(-1.38759 - 0.316708i) q^{89} +(-0.781831 - 1.62349i) 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} +(-0.571714 - 0.455927i) q^{95} +(-1.71648 + 2.15240i) q^{96} +(-6.83394 + 14.1908i) q^{97} +(13.2340 - 10.5538i) q^{98} +8.15883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 16 q^{5} + 6 q^{6} + 16 q^{7} + 2 q^{9} - 32 q^{13} - 20 q^{16} + 4 q^{20} - 12 q^{22} + 28 q^{23} + 14 q^{24} + 50 q^{25} + 24 q^{28} - 36 q^{30} + 12 q^{33} - 4 q^{34} - 12 q^{35} + 10 q^{36}+ \cdots + 18 q^{96}+O(q^{100}) \) 12 * q + 4 * q^4 - 16 * q^5 + 6 * q^6 + 16 * q^7 + 2 * q^9 - 32 * q^13 - 20 * q^16 + 4 * q^20 - 12 * q^22 + 28 * q^23 + 14 * q^24 + 50 * q^25 + 24 * q^28 - 36 * q^30 + 12 * q^33 - 4 * q^34 - 12 * q^35 + 10 * q^36 + 10 * q^38 - 6 * q^42 + 2 * q^45 + 54 * q^49 + 4 * q^51 + 22 * q^52 - 8 * q^53 - 30 * q^54 + 4 * q^57 - 112 * q^59 + 50 * q^62 + 12 * q^63 + 40 * q^64 - 18 * q^65 + 4 * q^67 + 2 * q^74 - 2 * q^78 - 34 * q^80 + 22 * q^81 - 32 * q^82 + 20 * q^83 + 32 * q^86 + 84 * q^88 - 80 * q^91 + 14 * q^92 - 36 * q^93 - 68 * q^94 + 18 * q^96

Introduction

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