LMFDB - Embedded newform 841.2.e.c.270.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(63,841)] 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([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.63"); 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:traces = [12,0,0,4,-16,6,16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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			270.1
Root			$-0.433884 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	841.270
Dual form			841.2.e.c.651.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.541044 - 1.12349i) q^{2} +(-1.40881 + 1.12349i) q^{3} +(0.277479 - 0.347948i) q^{4} +(-3.64795 + 1.75676i) q^{5} +(2.02446 + 0.974928i) q^{6} +(0.431468 + 0.541044i) q^{7} +(-2.97247 - 0.678448i) q^{8} +(0.0549581 - 0.240787i) q^{9} +(3.94740 + 3.14795i) q^{10} +(-2.77938 + 0.634375i) q^{11} +0.801938i q^{12} +(0.326396 + 1.43004i) q^{13} +(0.374414 - 0.777479i) q^{14} +(3.16557 - 6.57338i) q^{15} +(0.647948 + 2.83885i) q^{16} -1.60388i q^{17} +(-0.300257 + 0.0685317i) q^{18} +(-2.10471 - 1.67845i) q^{19} +(-0.400969 + 1.75676i) q^{20} +(-1.21572 - 0.277479i) q^{21} +(2.21648 + 2.77938i) q^{22} +(4.64795 + 2.23833i) q^{23} +(4.94989 - 2.38374i) q^{24} +(7.10388 - 8.90798i) q^{25} +(1.43004 - 1.14042i) q^{26} +(-2.15240 - 4.46950i) q^{27} +0.307979 q^{28} -9.09783 q^{30} +(0.846543 + 1.75786i) q^{31} +(-1.92863 + 1.53803i) q^{32} +(3.20291 - 4.01632i) q^{33} +(-1.80194 + 0.867767i) q^{34} +(-2.52446 - 1.21572i) q^{35} +(-0.0685317 - 0.0859360i) q^{36} +(2.77938 + 0.634375i) q^{37} +(-0.746980 + 3.27273i) q^{38} +(-2.06646 - 1.64795i) q^{39} +(12.0353 - 2.74698i) q^{40} -6.49396i q^{41} +(0.346011 + 1.51597i) q^{42} +(0.288478 - 0.599031i) q^{43} +(-0.550490 + 1.14310i) q^{44} +(0.222521 + 0.974928i) q^{45} -6.43296i q^{46} +(4.63385 - 1.05765i) q^{47} +(-4.10225 - 3.27144i) q^{48} +(1.45108 - 6.35761i) q^{49} +(-13.8515 - 3.16152i) q^{50} +(1.80194 + 2.25956i) q^{51} +(0.588146 + 0.283236i) q^{52} +(-0.0440730 + 0.0212244i) q^{53} +(-3.85690 + 4.83639i) q^{54} +(9.02458 - 7.19687i) q^{55} +(-0.915458 - 1.90097i) q^{56} +4.85086 q^{57} -6.39612 q^{59} +(-1.40881 - 2.92543i) q^{60} +(1.02262 - 0.815511i) q^{61} +(1.51693 - 1.90216i) q^{62} +(0.153989 - 0.0741573i) q^{63} +(8.01842 + 3.86147i) q^{64} +(-3.70291 - 4.64330i) q^{65} +(-6.24521 - 1.42543i) q^{66} +(3.32640 - 14.5739i) q^{67} +(-0.558065 - 0.445042i) q^{68} +(-9.06283 + 2.06853i) q^{69} +3.49396i q^{70} +(-0.502688 - 2.20242i) q^{71} +(-0.326723 + 0.678448i) q^{72} +(-3.61123 + 7.49880i) q^{73} +(-0.791053 - 3.46583i) q^{74} +20.5308i q^{75} +(-1.16802 + 0.266594i) q^{76} +(-1.54244 - 1.23005i) q^{77} +(-0.733406 + 3.21326i) q^{78} +(9.49671 + 2.16756i) q^{79} +(-7.35086 - 9.21768i) q^{80} +(8.72132 + 4.19997i) q^{81} +(-7.29590 + 3.51352i) q^{82} +(-2.50753 + 3.14435i) q^{83} +(-0.433884 + 0.346011i) q^{84} +(2.81762 + 5.85086i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(-4.88409 - 10.1419i) q^{89} +(0.974928 - 0.777479i) q^{90} +(-0.632883 + 0.793610i) q^{91} +(2.06853 - 0.996152i) q^{92} +(-3.16756 - 1.52542i) q^{93} +(-3.69537 - 4.63385i) q^{94} +(10.6265 + 2.42543i) q^{95} +(0.989115 - 4.33360i) q^{96} +(3.57299 + 2.84936i) q^{97} +(-7.92781 + 1.80947i) q^{98} +0.704103i 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 $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

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 $

$2$	−0.541044	−	1.12349i	−0.382576	−	0.794427i	−0.999970	−	0.00777301i	$-0.997526\pi$
$2$	−0.541044	−	1.12349i	−0.382576	−	0.794427i	0.617394	−	0.786654i	$-0.288189\pi$
$3$	−1.40881	+	1.12349i	−0.813378	+	0.648647i	−0.939187	−	0.343407i	$-0.888419\pi$
$3$	−1.40881	+	1.12349i	−0.813378	+	0.648647i	0.125809	+	0.992055i	$0.459847\pi$
$4$	0.277479	−	0.347948i	0.138740	−	0.173974i
$5$	−3.64795	+	1.75676i	−1.63141	+	0.785647i	−0.631465	+	0.775405i	$0.717546\pi$
$5$	−3.64795	+	1.75676i	−1.63141	+	0.785647i	−0.999948	+	0.0102420i	$0.996740\pi$
$6$	2.02446	+	0.974928i	0.826482	+	0.398013i
$7$	0.431468	+	0.541044i	0.163080	+	0.204495i	0.856657	−	0.515887i	$-0.172538\pi$
$7$	0.431468	+	0.541044i	0.163080	+	0.204495i	−0.693577	+	0.720383i	$0.743966\pi$
$8$	−2.97247	−	0.678448i	−1.05093	−	0.239868i
$9$	0.0549581	−	0.240787i	0.0183194	−	0.0802624i
$10$	3.94740	+	3.14795i	1.24828	+	0.995469i
$11$	−2.77938	+	0.634375i	−0.838014	+	0.191271i	−0.619928	−	0.784658i	$-0.712838\pi$
$11$	−2.77938	+	0.634375i	−0.838014	+	0.191271i	−0.218086	+	0.975930i	$0.569981\pi$
$12$			0.801938i			0.231499i
$13$	0.326396	+	1.43004i	0.0905261	+	0.396621i	0.999809	−	0.0195585i	$-0.00622606\pi$
$13$	0.326396	+	1.43004i	0.0905261	+	0.396621i	−0.909283	+	0.416179i	$0.863369\pi$
$14$	0.374414	−	0.777479i	0.100066	−	0.207790i
$15$	3.16557	−	6.57338i	0.817347	−	1.69724i
$16$	0.647948	+	2.83885i	0.161987	+	0.709712i
$17$		−	1.60388i		−	0.388997i	−0.980903	−	0.194498i	$-0.937692\pi$
$17$		−	1.60388i		−	0.388997i	0.980903	−	0.194498i	$-0.0623079\pi$
$18$	−0.300257	+	0.0685317i	−0.0707712	+	0.0161531i
$19$	−2.10471	−	1.67845i	−0.482853	−	0.385062i	0.351592	−	0.936153i	$-0.385640\pi$
$19$	−2.10471	−	1.67845i	−0.482853	−	0.385062i	−0.834445	+	0.551091i	$0.814212\pi$
$20$	−0.400969	+	1.75676i	−0.0896594	+	0.392823i
$21$	−1.21572	−	0.277479i	−0.265291	−	0.0605509i
$22$	2.21648	+	2.77938i	0.472555	+	0.592565i
$23$	4.64795	+	2.23833i	0.969164	+	0.466725i	0.850365	−	0.526193i	$-0.176381\pi$
$23$	4.64795	+	2.23833i	0.969164	+	0.466725i	0.118799	+	0.992918i	$0.462095\pi$
$24$	4.94989	−	2.38374i	1.01039	−	0.486579i
$25$	7.10388	−	8.90798i	1.42078	−	1.78160i
$26$	1.43004	−	1.14042i	0.280453	−	0.223654i
$27$	−2.15240	−	4.46950i	−0.414229	−	0.860156i
$28$	0.307979			0.0582025
$29$		0			0
$29$		0			0
$30$	−9.09783			−1.66103
$31$	0.846543	+	1.75786i	0.152044	+	0.315722i	0.963053	−	0.269311i	$-0.0867959\pi$
$31$	0.846543	+	1.75786i	0.152044	+	0.315722i	−0.811010	+	0.585033i	$0.801082\pi$
$32$	−1.92863	+	1.53803i	−0.340937	+	0.271888i
$33$	3.20291	−	4.01632i	0.557554	−	0.699151i
$34$	−1.80194	+	0.867767i	−0.309030	+	0.148821i
$35$	−2.52446	−	1.21572i	−0.426711	−	0.205493i
$36$	−0.0685317	−	0.0859360i	−0.0114219	−	0.0143227i
$37$	2.77938	+	0.634375i	0.456927	+	0.104291i	0.444788	−	0.895636i	$-0.353279\pi$
$37$	2.77938	+	0.634375i	0.456927	+	0.104291i	0.0121386	+	0.999926i	$0.496136\pi$
$38$	−0.746980	+	3.27273i	−0.121176	+	0.530907i
$39$	−2.06646	−	1.64795i	−0.330899	−	0.263883i
$40$	12.0353	−	2.74698i	1.90295	−	0.434336i
$41$		−	6.49396i		−	1.01419i	−0.861891	−	0.507093i	$-0.830720\pi$
$41$		−	6.49396i		−	1.01419i	0.861891	−	0.507093i	$-0.169280\pi$
$42$	0.346011	+	1.51597i	0.0533906	+	0.233920i
$43$	0.288478	−	0.599031i	0.0439925	−	0.0913514i	−0.877814	−	0.479002i	$-0.840999\pi$
$43$	0.288478	−	0.599031i	0.0439925	−	0.0913514i	0.921807	+	0.387650i	$0.126713\pi$
$44$	−0.550490	+	1.14310i	−0.0829895	+	0.172329i
$45$	0.222521	+	0.974928i	0.0331715	+	0.145334i
$46$		−	6.43296i		−	0.948488i
$47$	4.63385	−	1.05765i	0.675917	−	0.154274i	0.129235	−	0.991614i	$-0.458748\pi$
$47$	4.63385	−	1.05765i	0.675917	−	0.154274i	0.546682	+	0.837340i	$0.315891\pi$
$48$	−4.10225	−	3.27144i	−0.592109	−	0.472191i
$49$	1.45108	−	6.35761i	0.207298	−	0.908230i
$50$	−13.8515	−	3.16152i	−1.95890	−	0.447107i
$51$	1.80194	+	2.25956i	0.252322	+	0.316401i
$52$	0.588146	+	0.283236i	0.0815612	+	0.0392778i
$53$	−0.0440730	+	0.0212244i	−0.00605389	+	0.00291540i	−0.436908	−	0.899506i	$-0.643927\pi$
$53$	−0.0440730	+	0.0212244i	−0.00605389	+	0.00291540i	0.430854	+	0.902421i	$0.358212\pi$
$54$	−3.85690	+	4.83639i	−0.524857	+	0.658150i
$55$	9.02458	−	7.19687i	1.21687	−	0.970425i
$56$	−0.915458	−	1.90097i	−0.122333	−	0.254028i
$57$	4.85086			0.642511
$58$		0			0
$59$	−6.39612			−0.832704			−0.416352	−	0.909203i	$-0.636692\pi$
$59$	−6.39612			−0.832704			−0.416352	+	0.909203i	$0.636692\pi$
$60$	−1.40881	−	2.92543i	−0.181877	−	0.377671i
$61$	1.02262	−	0.815511i	0.130933	−	0.104416i	−0.555834	−	0.831294i	$-0.687601\pi$
$61$	1.02262	−	0.815511i	0.130933	−	0.104416i	0.686767	+	0.726878i	$0.259029\pi$
$62$	1.51693	−	1.90216i	0.192650	−	0.241575i
$63$	0.153989	−	0.0741573i	0.0194008	−	0.00934294i
$64$	8.01842	+	3.86147i	1.00230	+	0.482683i
$65$	−3.70291	−	4.64330i	−0.459289	−	0.575930i
$66$	−6.24521	−	1.42543i	−0.768732	−	0.175458i
$67$	3.32640	−	14.5739i	0.406384	−	1.78048i	−0.194241	−	0.980954i	$-0.562224\pi$
$67$	3.32640	−	14.5739i	0.406384	−	1.78048i	0.600625	−	0.799531i	$-0.294918\pi$
$68$	−0.558065	−	0.445042i	−0.0676753	−	0.0539693i
$69$	−9.06283	+	2.06853i	−1.09104	+	0.249022i
$70$			3.49396i			0.417608i
$71$	−0.502688	−	2.20242i	−0.0596581	−	0.261379i	0.936300	−	0.351202i	$-0.114227\pi$
$71$	−0.502688	−	2.20242i	−0.0596581	−	0.261379i	−0.995958	+	0.0898229i	$0.971370\pi$
$72$	−0.326723	+	0.678448i	−0.0385047	+	0.0799559i
$73$	−3.61123	+	7.49880i	−0.422663	+	0.877669i	0.575542	+	0.817772i	$0.304791\pi$
$73$	−3.61123	+	7.49880i	−0.422663	+	0.877669i	−0.998205	+	0.0598961i	$0.980923\pi$
$74$	−0.791053	−	3.46583i	−0.0919580	−	0.402894i
$75$			20.5308i			2.37069i
$76$	−1.16802	+	0.266594i	−0.133982	+	0.0305804i
$77$	−1.54244	−	1.23005i	−0.175777	−	0.140178i
$78$	−0.733406	+	3.21326i	−0.0830419	+	0.363830i
$79$	9.49671	+	2.16756i	1.06846	+	0.243870i	0.720370	−	0.693590i	$-0.243972\pi$
$79$	9.49671	+	2.16756i	1.06846	+	0.243870i	0.348094	+	0.937460i	$0.386829\pi$
$80$	−7.35086	−	9.21768i	−0.821851	−	1.03057i
$81$	8.72132	+	4.19997i	0.969036	+	0.466663i
$82$	−7.29590	+	3.51352i	−0.805697	+	0.388003i
$83$	−2.50753	+	3.14435i	−0.275237	+	0.345137i	−0.900167	−	0.435544i	$-0.856556\pi$
$83$	−2.50753	+	3.14435i	−0.275237	+	0.345137i	0.624930	+	0.780681i	$0.285127\pi$
$84$	−0.433884	+	0.346011i	−0.0473406	+	0.0377529i
$85$	2.81762	+	5.85086i	0.305614	+	0.634614i
$86$	−0.829085			−0.0894025
$87$		0			0
$88$	8.69202			0.926573
$89$	−4.88409	−	10.1419i	−0.517712	−	1.07504i	−0.981917	−	0.189312i	$-0.939374\pi$
$89$	−4.88409	−	10.1419i	−0.517712	−	1.07504i	0.464205	−	0.885728i	$-0.346340\pi$
$90$	0.974928	−	0.777479i	0.102766	−	0.0819535i
$91$	−0.632883	+	0.793610i	−0.0663442	+	0.0831929i
$92$	2.06853	−	0.996152i	0.215659	−	0.103856i
$93$	−3.16756	−	1.52542i	−0.328461	−	0.158178i
$94$	−3.69537	−	4.63385i	−0.381149	−	0.477945i
$95$	10.6265	+	2.42543i	1.09026	+	0.248844i
$96$	0.989115	−	4.33360i	0.100951	−	0.442296i
$97$	3.57299	+	2.84936i	0.362782	+	0.289309i	0.787868	−	0.615844i	$-0.211185\pi$
$97$	3.57299	+	2.84936i	0.362782	+	0.289309i	−0.425086	+	0.905153i	$0.639756\pi$
$98$	−7.92781	+	1.80947i	−0.800830	+	0.182784i
$99$			0.704103i			0.0707650i
$100$	−1.12833	−	4.94355i	−0.112833	−	0.494355i
$101$	1.39412	−	2.89493i	0.138721	−	0.288056i	−0.820022	−	0.572332i	$-0.806039\pi$
$101$	1.39412	−	2.89493i	0.138721	−	0.288056i	0.958743	+	0.284276i	$0.0917532\pi$
$102$	1.56366	−	3.24698i	0.154826	−	0.321499i
$103$	1.45377	+	6.36939i	0.143244	+	0.627594i	0.994669	+	0.103118i	$0.0328818\pi$
$103$	1.45377	+	6.36939i	0.143244	+	0.627594i	−0.851425	+	0.524477i	$0.824261\pi$
$104$		−	4.47219i		−	0.438534i
$105$	4.92233	−	1.12349i	0.480370	−	0.109641i
$106$	0.0476909	+	0.0380322i	0.00463215	+	0.00369401i
$107$	1.28717	−	5.63945i	0.124435	−	0.545186i	−0.873826	−	0.486239i	$-0.838368\pi$
$107$	1.28717	−	5.63945i	0.124435	−	0.545186i	0.998261	−	0.0589473i	$-0.0187744\pi$
$108$	−2.15240	−	0.491271i	−0.207115	−	0.0472726i
$109$	−5.72737	−	7.18189i	−0.548582	−	0.687900i	0.427819	−	0.903864i	$-0.359282\pi$
$109$	−5.72737	−	7.18189i	−0.548582	−	0.687900i	−0.976401	+	0.215964i	$0.930711\pi$
$110$	−12.9683	−	6.24521i	−1.23648	−	0.595457i
$111$	−4.62833	+	2.22889i	−0.439302	+	0.211557i
$112$	−1.25637	+	1.57544i	−0.118716	+	0.148865i
$113$	−7.01002	+	5.59030i	−0.659447	+	0.525891i	−0.895054	−	0.445957i	$-0.852863\pi$
$113$	−7.01002	+	5.59030i	−0.659447	+	0.525891i	0.235608	+	0.971848i	$0.424292\pi$
$114$	−2.62453	−	5.44989i	−0.245809	−	0.510429i
$115$	−20.8877			−1.94779
$116$		0			0
$117$	0.362273			0.0334921
$118$	3.46059	+	7.18598i	0.318573	+	0.661523i
$119$	0.867767	−	0.692021i	0.0795481	−	0.0634375i
$120$	−13.8693	+	17.3915i	−1.26609	+	1.58762i
$121$	−2.58815	+	1.24639i	−0.235286	+	0.113308i
$122$	−1.46950	−	0.707674i	−0.133042	−	0.0640698i
$123$	7.29590	+	9.14877i	0.657849	+	0.824916i
$124$	0.846543	+	0.193218i	0.0760218	+	0.0173515i
$125$	−5.76055	+	25.2386i	−0.515240	+	2.25741i
$126$	−0.166630	−	0.132883i	−0.0148446	−	0.0118382i
$127$	15.1744	−	3.46346i	1.34651	−	0.307332i	0.512314	−	0.858798i	$-0.328789\pi$
$127$	15.1744	−	3.46346i	1.34651	−	0.307332i	0.834197	+	0.551466i	$0.185931\pi$
$128$		−	6.16421i		−	0.544844i
$129$	0.266594	+	1.16802i	0.0234723	+	0.102839i
$130$	−3.21326	+	6.67241i	−0.281822	+	0.585209i
$131$	−5.82834	+	12.1027i	−0.509225	+	1.05742i	0.474917	+	0.880031i	$0.342478\pi$
$131$	−5.82834	+	12.1027i	−0.509225	+	1.05742i	−0.984141	+	0.177385i	$0.943236\pi$
$132$	−0.508729	−	2.22889i	−0.0442792	−	0.194000i
$133$		−	1.86294i		−	0.161537i
$134$	−18.1733	+	4.14795i	−1.56994	+	0.358328i
$135$	15.7037	+	12.5233i	1.35156	+	1.07783i
$136$	−1.08815	+	4.76748i	−0.0933077	+	0.408808i
$137$	16.5662	+	3.78113i	1.41535	+	0.323043i	0.860729	−	0.509063i	$-0.170008\pi$
$137$	16.5662	+	3.78113i	1.41535	+	0.323043i	0.554616	+	0.832106i	$0.312865\pi$
$138$	7.22737	+	9.06283i	0.615234	+	0.771479i
$139$	−11.2301	−	5.40811i	−0.952521	−	0.458710i	−0.107951	−	0.994156i	$-0.534429\pi$
$139$	−11.2301	−	5.40811i	−0.952521	−	0.458710i	−0.844569	+	0.535446i	$0.820143\pi$
$140$	−1.12349	+	0.541044i	−0.0949522	+	0.0457266i
$141$	−5.33997	+	6.69611i	−0.449707	+	0.563914i
$142$	−2.20242	+	1.75637i	−0.184823	+	0.147392i
$143$	−1.81436	−	3.76755i	−0.151724	−	0.315059i
$144$	0.719169			0.0599307
$145$		0			0
$146$	10.3787			0.858945
$147$	5.09841	+	10.5869i	0.420509	+	0.873197i
$148$	0.991949	−	0.791053i	0.0815377	−	0.0650241i
$149$	11.4194	−	14.3195i	0.935513	−	1.17310i	−0.0491790	−	0.998790i	$-0.515660\pi$
$149$	11.4194	−	14.3195i	0.935513	−	1.17310i	0.984692	−	0.174306i	$-0.0557681\pi$
$150$	23.0661	−	11.1081i	1.88334	−	0.906970i
$151$	−17.1516	−	8.25977i	−1.39578	−	0.672171i	−0.423477	−	0.905907i	$-0.639191\pi$
$151$	−17.1516	−	8.25977i	−1.39578	−	0.672171i	−0.972300	+	0.233736i	$0.924905\pi$
$152$	5.11745	+	6.41708i	0.415080	+	0.520494i
$153$	−0.386193	−	0.0881460i	−0.0312218	−	0.00712618i
$154$	−0.547425	+	2.39843i	−0.0441128	+	0.193271i
$155$	−6.17629	−	4.92543i	−0.496092	−	0.395620i
$156$	−1.14680	+	0.261750i	−0.0918175	+	0.0209567i
$157$			11.4383i			0.912879i	0.889755	+	0.456439i	$0.150875\pi$
$157$			11.4383i			0.912879i	−0.889755	+	0.456439i	$0.849125\pi$
$158$	−2.70291	−	11.8422i	−0.215032	−	0.942115i
$159$	0.0382451	−	0.0794168i	0.00303303	−	0.00629816i
$160$	4.33360	−	8.99880i	0.342601	−	0.711418i
$161$	0.794405	+	3.48052i	0.0626079	+	0.274303i
$162$		−	12.0707i		−	0.948363i
$163$	6.50722	−	1.48523i	0.509685	−	0.116332i	0.0400581	−	0.999197i	$-0.487246\pi$
$163$	6.50722	−	1.48523i	0.509685	−	0.116332i	0.469627	+	0.882865i	$0.344389\pi$
$164$	−2.25956	−	1.80194i	−0.176442	−	0.140708i
$165$	−4.62833	+	20.2781i	−0.360315	+	1.57864i
$166$	4.88933	+	1.11596i	0.379485	+	0.0866151i
$167$	9.14526	+	11.4678i	0.707681	+	0.887404i	0.997571	−	0.0696556i	$-0.0221900\pi$
$167$	9.14526	+	11.4678i	0.707681	+	0.887404i	−0.289890	+	0.957060i	$0.593619\pi$
$168$	3.42543	+	1.64960i	0.264277	+	0.127269i
$169$	9.77413	−	4.70697i	0.751856	−	0.362075i
$170$	5.04892	−	6.33114i	0.387234	−	0.485576i
$171$	−0.519820	+	0.414542i	−0.0397516	+	0.0317009i
$172$	−0.128385	−	0.266594i	−0.00978925	−	0.0203276i
$173$	23.3599			1.77602			0.888009	−	0.459825i	$-0.152088\pi$
$173$	23.3599			1.77602			0.888009	+	0.459825i	$0.152088\pi$
$174$		0			0
$175$	7.88471			0.596028
$176$	−3.60179	−	7.47919i	−0.271495	−	0.563765i
$177$	9.01093	−	7.18598i	0.677303	−	0.540131i
$178$	−8.75182	+	10.9744i	−0.655977	+	0.822569i
$179$	−0.599031	+	0.288478i	−0.0447737	+	0.0215619i	−0.456137	−	0.889910i	$-0.650767\pi$
$179$	−0.599031	+	0.288478i	−0.0447737	+	0.0215619i	0.411363	+	0.911472i	$0.365053\pi$
$180$	0.400969	+	0.193096i	0.0298865	+	0.0143926i
$181$	6.83728	+	8.57368i	0.508211	+	0.637277i	0.968059	−	0.250721i	$-0.0806676\pi$
$181$	6.83728	+	8.57368i	0.508211	+	0.637277i	−0.459848	+	0.887997i	$0.652096\pi$
$182$	1.23403	+	0.281659i	0.0914724	+	0.0208780i
$183$	−0.524459	+	2.29780i	−0.0387691	+	0.169859i
$184$	−12.2973	−	9.80678i	−0.906570	−	0.722966i
$185$	−11.2535	+	2.56853i	−0.827372	+	0.188842i
$186$			4.38404i			0.321454i
$187$	1.01746	+	4.45778i	0.0744039	+	0.325985i
$188$	0.917791	−	1.90581i	0.0669368	−	0.138996i
$189$	1.48951	−	3.09299i	0.108346	−	0.224982i
$190$	−3.02446	−	13.2510i	−0.219417	−	0.961330i
$191$		−	0.518122i		−	0.0374900i	−0.999824	−	0.0187450i	$-0.994033\pi$
$191$		−	0.518122i		−	0.0374900i	0.999824	−	0.0187450i	$-0.00596707\pi$
$192$	−15.6348	+	3.56853i	−1.12834	+	0.257537i
$193$	1.08396	+	0.864429i	0.0780251	+	0.0622229i	0.661726	−	0.749746i	$-0.269824\pi$
$193$	1.08396	+	0.864429i	0.0780251	+	0.0622229i	−0.583701	+	0.811969i	$0.698396\pi$
$194$	1.26809	−	5.55585i	0.0910433	−	0.398887i
$195$	10.4334	+	2.38135i	0.747151	+	0.170532i
$196$	−1.80947	−	2.26900i	−0.129248	−	0.162072i
$197$	−11.6751	−	5.62243i	−0.831816	−	0.400582i	−0.0310201	−	0.999519i	$-0.509876\pi$
$197$	−11.6751	−	5.62243i	−0.831816	−	0.400582i	−0.800796	+	0.598937i	$0.795590\pi$
$198$	0.791053	−	0.380951i	0.0562177	−	0.0270730i
$199$	−12.1603	+	15.2486i	−0.862023	+	1.08094i	0.133924	+	0.990992i	$0.457242\pi$
$199$	−12.1603	+	15.2486i	−0.862023	+	1.08094i	−0.995946	+	0.0899505i	$0.971329\pi$
$200$	−27.1597	+	21.6591i	−1.92048	+	1.53153i
$201$	11.6874	+	24.2690i	0.824363	+	1.71181i
$202$	−4.00670			−0.281911
$203$		0			0
$204$	1.28621			0.0900526
$205$	11.4083	+	23.6896i	0.796792	+	1.65456i
$206$	6.36939	−	5.07942i	0.443776	−	0.353900i
$207$	0.794405	−	0.996152i	0.0552150	−	0.0692374i
$208$	−3.84817	+	1.85318i	−0.266822	+	0.128495i
$209$	6.91454	+	3.32987i	0.478289	+	0.230332i
$210$	−3.92543	−	4.92233i	−0.270880	−	0.339673i
$211$	−20.1138	−	4.59083i	−1.38469	−	0.316046i	−0.535678	−	0.844422i	$-0.679944\pi$
$211$	−20.1138	−	4.59083i	−1.38469	−	0.316046i	−0.849010	+	0.528376i	$0.822801\pi$
$212$	−0.00484434	+	0.0212244i	−0.000332711	+	0.00145770i
$213$	3.18259	+	2.53803i	0.218068	+	0.173903i
$214$	−7.03228	+	1.60507i	−0.480717	+	0.109720i
$215$			2.69202i			0.183594i
$216$	3.36563	+	14.7458i	0.229002	+	1.00332i
$217$	−0.585826	+	1.21648i	−0.0397685	+	0.0825801i
$218$	−4.97002	+	10.3204i	−0.336612	+	0.698983i
$219$	−3.33728	−	14.6216i	−0.225513	−	0.988035i
$220$		−	5.13706i		−	0.346341i
$221$	2.29360	−	0.523499i	0.154284	−	0.0352144i
$222$	5.00827	+	3.99396i	0.336133	+	0.268057i
$223$	4.69537	−	20.5718i	0.314425	−	1.37759i	−0.532749	−	0.846273i	$-0.678841\pi$
$223$	4.69537	−	20.5718i	0.314425	−	1.37759i	0.847174	−	0.531315i	$-0.178302\pi$
$224$	−1.66429	−	0.379863i	−0.111200	−	0.0253806i
$225$	−1.75451	−	2.20009i	−0.116967	−	0.146673i
$226$	10.0734	+	4.85108i	0.670071	+	0.322689i
$227$	−6.42812	+	3.09562i	−0.426649	+	0.205463i	−0.634871	−	0.772618i	$-0.718947\pi$
$227$	−6.42812	+	3.09562i	−0.426649	+	0.205463i	0.208222	+	0.978082i	$0.433232\pi$
$228$	1.34601	−	1.68784i	0.0891417	−	0.111780i
$229$	−1.76096	+	1.40432i	−0.116368	+	0.0928002i	−0.679945	−	0.733263i	$-0.737996\pi$
$229$	−1.76096	+	1.40432i	−0.116368	+	0.0928002i	0.563577	+	0.826064i	$0.309425\pi$
$230$	11.3012	+	23.4671i	0.745177	+	1.54738i
$231$	3.55496			0.233899
$232$		0			0
$233$	18.9095			1.23880			0.619400	−	0.785076i	$-0.287376\pi$
$233$	18.9095			1.23880			0.619400	+	0.785076i	$0.287376\pi$
$234$	−0.196006	−	0.407010i	−0.0128133	−	0.0266071i
$235$	−15.0460	+	11.9988i	−0.981494	+	0.782716i
$236$	−1.77479	+	2.22552i	−0.115529	+	0.144869i
$237$	−15.8143	+	7.61577i	−1.02725	+	0.494698i
$238$	−1.24698	−	0.600514i	−0.0808297	−	0.0389255i
$239$	−12.7642	−	16.0058i	−0.825648	−	1.03533i	−0.998728	−	0.0504216i	$-0.983944\pi$
$239$	−12.7642	−	16.0058i	−0.825648	−	1.03533i	0.173080	−	0.984908i	$-0.444628\pi$
$240$	20.7119	+	4.72737i	1.33695	+	0.305150i
$241$	1.63975	−	7.18422i	0.105626	−	0.462776i	−0.894258	−	0.447551i	$-0.852296\pi$
$241$	1.63975	−	7.18422i	0.105626	−	0.462776i	0.999884	−	0.0152254i	$-0.00484657\pi$
$242$	2.80060	+	2.23341i	0.180030	+	0.143569i
$243$	−2.49614	+	0.569728i	−0.160128	+	0.0365481i
$244$		−	0.582105i		−	0.0372655i
$245$	5.87531	+	25.7414i	0.375360	+	1.64456i
$246$	6.33114	−	13.1468i	0.403659	−	0.838206i
$247$	1.71327	−	3.55765i	0.109013	−	0.226368i
$248$	−1.32371	−	5.79954i	−0.0840555	−	0.368271i
$249$		−	7.24698i		−	0.459259i
$250$	31.4721	−	7.18329i	1.99047	−	0.454311i
$251$	10.1289	+	8.07756i	0.639333	+	0.509851i	0.888659	−	0.458569i	$-0.151638\pi$
$251$	10.1289	+	8.07756i	0.639333	+	0.509851i	−0.249326	+	0.968420i	$0.580209\pi$
$252$	0.0169259	−	0.0741573i	0.00106623	−	0.00467147i
$253$	−14.3383	−	3.27263i	−0.901444	−	0.205749i
$254$	−12.1012	−	15.1744i	−0.759296	−	0.952127i
$255$	−10.5429	−	5.07718i	−0.660221	−	0.317945i
$256$	9.11141	−	4.38782i	0.569463	−	0.274239i
$257$	10.4073	−	13.0503i	0.649190	−	0.814058i	−0.342929	−	0.939361i	$-0.611419\pi$
$257$	10.4073	−	13.0503i	0.649190	−	0.814058i	0.992119	+	0.125303i	$0.0399903\pi$
$258$	1.16802	−	0.931468i	0.0727180	−	0.0579907i
$259$	0.855989	+	1.77748i	0.0531886	+	0.110447i
$260$	−2.64310			−0.163918
$261$		0			0
$262$	16.7506			1.03486
$263$	−7.64037	−	15.8654i	−0.471125	−	0.978302i	−0.992184	−	0.124781i	$-0.960177\pi$
$263$	−7.64037	−	15.8654i	−0.471125	−	0.978302i	0.521059	−	0.853521i	$-0.325537\pi$
$264$	−12.2454	+	9.76540i	−0.753654	+	0.601019i
$265$	0.123490	−	0.154851i	0.00758592	−	0.00951244i
$266$	−2.09299	+	1.00793i	−0.128329	+	0.0618002i
$267$	18.2751	+	8.80082i	1.11842	+	0.538601i
$268$	−4.14795	−	5.20136i	−0.253376	−	0.317724i
$269$	6.54126	+	1.49300i	0.398828	+	0.0910298i	0.417230	−	0.908801i	$-0.363001\pi$
$269$	6.54126	+	1.49300i	0.398828	+	0.0910298i	−0.0184025	+	0.999831i	$0.505858\pi$
$270$	5.57338	−	24.4186i	0.339185	−	1.48607i
$271$	−9.90413	−	7.89828i	−0.601633	−	0.479786i	0.274675	−	0.961537i	$-0.411430\pi$
$271$	−9.90413	−	7.89828i	−0.601633	−	0.479786i	−0.876308	+	0.481751i	$0.840001\pi$
$272$	4.55316	−	1.03923i	0.276076	−	0.0630125i
$273$		−	1.82908i		−	0.110701i
$274$	−4.71499	−	20.6577i	−0.284843	−	1.24798i
$275$	−14.0934	+	29.2652i	−0.849861	+	1.76476i
$276$	−1.79500	+	3.72737i	−0.108047	+	0.224361i
$277$	−3.50269	−	15.3463i	−0.210456	−	0.922069i	−0.964258	−	0.264966i	$-0.914639\pi$
$277$	−3.50269	−	15.3463i	−0.210456	−	0.922069i	0.753801	−	0.657102i	$-0.228218\pi$
$278$			15.5429i			0.932200i
$279$	0.469796	−	0.107228i	0.0281259	−	0.00641956i
$280$	6.67909	+	5.32640i	0.399152	+	0.318313i
$281$	−2.62900	+	11.5184i	−0.156833	+	0.687130i	0.833969	+	0.551811i	$0.186063\pi$
$281$	−2.62900	+	11.5184i	−0.156833	+	0.687130i	−0.990802	+	0.135319i	$0.956794\pi$
$282$	10.4122	+	2.37651i	0.620036	+	0.141519i
$283$	1.37047	+	1.71851i	0.0814660	+	0.102155i	0.820894	−	0.571080i	$-0.193476\pi$
$283$	1.37047	+	1.71851i	0.0814660	+	0.102155i	−0.739428	+	0.673235i	$0.764904\pi$
$284$	−0.905813	−	0.436217i	−0.0537501	−	0.0258847i
$285$	−17.6957	+	8.52179i	−1.04820	+	0.504787i
$286$	−3.25116	+	4.07683i	−0.192245	+	0.241068i
$287$	3.51352	−	2.80194i	0.207396	−	0.165393i
$288$	0.264345	+	0.548917i	0.0155767	+	0.0323453i
$289$	14.4276			0.848681
$290$		0			0
$291$	−8.23490			−0.482738
$292$	1.60715	+	3.33728i	0.0940513	+	0.195300i
$293$	16.1399	−	12.8711i	0.942902	−	0.751940i	−0.0259281	−	0.999664i	$-0.508254\pi$
$293$	16.1399	−	12.8711i	0.942902	−	0.751940i	0.968831	+	0.247724i	$0.0796827\pi$
$294$	9.13587	−	11.4560i	0.532815	−	0.668128i
$295$	23.3327	−	11.2365i	1.35848	−	0.654212i
$296$	−7.83124	−	3.77133i	−0.455182	−	0.219204i
$297$	8.81767	+	11.0570i	0.511653	+	0.641593i
$298$	−22.2662	−	5.08211i	−1.28984	−	0.294398i
$299$	−1.68382	+	7.37732i	−0.0973781	+	0.426641i
$300$	7.14364	+	5.69687i	0.412438	+	0.328909i
$301$	0.448572	−	0.102384i	0.0258552	−	0.00590129i
$302$			23.7385i			1.36600i
$303$	1.28836	+	5.64469i	0.0740146	+	0.324279i
$304$	3.40112	−	7.06249i	0.195067	−	0.405062i
$305$	−2.29780	+	4.77144i	−0.131572	+	0.273212i
$306$	0.109916	+	0.481575i	0.00628349	+	0.0275298i
$307$			22.8116i			1.30193i	0.759108	+	0.650964i	$0.225635\pi$
$307$			22.8116i			1.30193i	−0.759108	+	0.650964i	$0.774365\pi$
$308$	−0.855989	+	0.195374i	−0.0487745	+	0.0111325i
$309$	−9.20403	−	7.33997i	−0.523599	−	0.417556i
$310$	−2.19202	+	9.60387i	−0.124498	+	0.545463i
$311$	−30.3106	−	6.91819i	−1.71875	−	0.392295i	−0.754297	−	0.656533i	$-0.772022\pi$
$311$	−30.3106	−	6.91819i	−1.71875	−	0.392295i	−0.964457	+	0.264238i	$0.914879\pi$
$312$	5.02446	+	6.30047i	0.284454	+	0.356694i
$313$	10.1201	+	4.87360i	0.572024	+	0.275472i	0.697453	−	0.716630i	$-0.254317\pi$
$313$	10.1201	+	4.87360i	0.572024	+	0.275472i	−0.125429	+	0.992103i	$0.540031\pi$
$314$	12.8509	−	6.18865i	0.725216	−	0.349245i
$315$	−0.431468	+	0.541044i	−0.0243105	+	0.0304844i
$316$	3.38934	−	2.70291i	0.190665	−	0.152050i
$317$	−2.57159	−	5.33997i	−0.144435	−	0.299923i	0.816184	−	0.577793i	$-0.196086\pi$
$317$	−2.57159	−	5.33997i	−0.144435	−	0.299923i	−0.960619	+	0.277870i	$0.910372\pi$
$318$	−0.109916			−0.00616380
$319$		0			0
$320$	−36.0344			−2.01439
$321$	4.52249	+	9.39104i	0.252421	+	0.524157i
$322$	3.48052	−	2.77562i	0.193962	−	0.154679i
$323$	−2.69202	+	3.37569i	−0.149788	+	0.187828i
$324$	3.88135	−	1.86916i	0.215631	−	0.103842i
$325$	15.0574	+	7.25127i	0.835235	+	0.402228i
$326$	−5.18933	−	6.50722i	−0.287411	−	0.360401i
$327$	16.1376	+	3.68329i	0.892409	+	0.203687i
$328$	−4.40581	+	19.3031i	−0.243270	+	1.06584i
$329$	2.57159	+	2.05078i	0.141777	+	0.113063i
$330$	25.2863	−	5.77144i	1.39197	−	0.317707i
$331$		−	30.9095i		−	1.69894i	−0.527639	−	0.849469i	$-0.676923\pi$
$331$		−	30.9095i		−	1.69894i	0.527639	−	0.849469i	$-0.323077\pi$
$332$	0.398280	+	1.74498i	0.0218585	+	0.0957683i
$333$	0.305499	−	0.634375i	0.0167412	−	0.0347635i
$334$	7.93596	−	16.4792i	0.434236	−	0.901701i
$335$	13.4683	+	59.0085i	0.735852	+	3.22398i
$336$		−	3.63102i		−	0.198089i
$337$	−7.81411	+	1.78352i	−0.425662	+	0.0971545i	−0.429985	−	0.902836i	$-0.641481\pi$
$337$	−7.81411	+	1.78352i	−0.425662	+	0.0971545i	0.00432302	+	0.999991i	$0.498624\pi$
$338$	−10.5765	−	8.43445i	−0.575284	−	0.458774i
$339$	3.59515	−	15.7514i	0.195262	−	0.855497i
$340$	2.81762	+	0.643104i	0.152807	+	0.0348772i
$341$	−3.46801	−	4.34875i	−0.187803	−	0.235498i
$342$	0.746980	+	0.359726i	0.0403920	+	0.0194518i
$343$	8.43027	−	4.05980i	0.455192	−	0.219209i
$344$	−1.26391	+	1.58489i	−0.0681452	+	0.0854514i
$345$	29.4268	−	23.4671i	1.58429	−	1.26343i
$346$	−12.6387	−	26.2446i	−0.679462	−	1.41092i
$347$	2.26337			0.121504			0.0607521	−	0.998153i	$-0.480650\pi$
$347$	2.26337			0.121504			0.0607521	+	0.998153i	$0.480650\pi$
$348$		0			0
$349$	−23.5690			−1.26162			−0.630809	−	0.775938i	$-0.717277\pi$
$349$	−23.5690			−1.26162			−0.630809	+	0.775938i	$0.717277\pi$
$350$	−4.26597	−	8.85839i	−0.228026	−	0.473501i
$351$	5.68901	−	4.53684i	0.303657	−	0.242158i
$352$	4.38471	−	5.49825i	0.233706	−	0.293058i
$353$	−0.885239	+	0.426309i	−0.0471165	+	0.0226901i	−0.457294	−	0.889316i	$-0.651181\pi$
$353$	−0.885239	+	0.426309i	−0.0471165	+	0.0226901i	0.410177	+	0.912006i	$0.365467\pi$
$354$	−12.9487	−	6.23576i	−0.688215	−	0.331427i
$355$	5.70291	+	7.15122i	0.302679	+	0.379547i
$356$	−4.88409	−	1.11476i	−0.258856	−	0.0590822i
$357$	−0.445042	+	1.94986i	−0.0235541	+	0.103197i
$358$	0.648205	+	0.516926i	0.0342587	+	0.0273204i
$359$	−7.68469	+	1.75398i	−0.405582	+	0.0925715i	−0.420445	−	0.907318i	$-0.638126\pi$
$359$	−7.68469	+	1.75398i	−0.405582	+	0.0925715i	0.0148627	+	0.999890i	$0.495269\pi$
$360$		−	3.04892i		−	0.160692i
$361$	−2.61529	−	11.4583i	−0.137647	−	0.603071i
$362$	5.93317	−	12.3204i	0.311841	−	0.647544i
$363$	2.24591	−	4.66368i	0.117880	−	0.244780i
$364$	0.100523	+	0.440420i	0.00526884	+	0.0230843i
$365$		−	33.6993i		−	1.76390i
$366$	2.86531	−	0.653989i	0.149772	−	0.0341846i
$367$	−22.9139	−	18.2732i	−1.19610	−	0.953855i	−0.196451	−	0.980514i	$-0.562942\pi$
$367$	−22.9139	−	18.2732i	−1.19610	−	0.953855i	−0.999645	+	0.0266590i	$0.991513\pi$
$368$	−3.34266	+	14.6451i	−0.174248	+	0.763431i
$369$	−1.56366	−	0.356896i	−0.0814010	−	0.0185793i
$370$	8.97434	+	11.2535i	0.466554	+	0.585040i
$371$	−0.0304995	−	0.0146878i	−0.00158345	−	0.000762551i
$372$	−1.40970	+	0.678875i	−0.0730894	+	0.0351980i
$373$	−2.37717	+	2.98088i	−0.123085	+	0.154344i	−0.839556	−	0.543273i	$-0.817185\pi$
$373$	−2.37717	+	2.98088i	−0.123085	+	0.154344i	0.716471	+	0.697617i	$0.245756\pi$
$374$	4.45778	−	3.55496i	0.230506	−	0.183823i
$375$	−20.2398	−	42.0284i	−1.04518	−	2.17034i
$376$	−14.4916			−0.747345
$377$		0			0
$378$	−4.28083			−0.220182
$379$	−3.91627	−	8.13222i	−0.201165	−	0.417724i	0.775843	−	0.630926i	$-0.217325\pi$
$379$	−3.91627	−	8.13222i	−0.201165	−	0.417724i	−0.977008	+	0.213202i	$0.931611\pi$
$380$	3.79255	−	3.02446i	0.194554	−	0.155151i
$381$	−17.4867	+	21.9277i	−0.895872	+	1.12339i
$382$	−0.582105	+	0.280327i	−0.0297831	+	0.0143428i
$383$	−29.9022	−	14.4002i	−1.52793	−	0.735813i	−0.533967	−	0.845506i	$-0.679299\pi$
$383$	−29.9022	−	14.4002i	−1.52793	−	0.735813i	−0.993966	+	0.109692i	$0.965014\pi$
$384$	6.92543	+	8.68421i	0.353412	+	0.443164i
$385$	7.78764	+	1.77748i	0.396895	+	0.0905887i
$386$	0.384707	−	1.68551i	0.0195811	−	0.0857903i
$387$	−0.128385	−	0.102384i	−0.00652617	−	0.00520445i
$388$	1.98286	−	0.452575i	0.100664	−	0.0229760i
$389$		−	27.5362i		−	1.39614i	−0.716030	−	0.698070i	$-0.754043\pi$
$389$		−	27.5362i		−	1.39614i	0.716030	−	0.698070i	$-0.245957\pi$
$390$	−2.96950	−	13.0102i	−0.150367	−	0.658799i
$391$	3.59001	−	7.45473i	0.181555	−	0.377002i
$392$	−8.62661	+	17.9133i	−0.435710	+	0.904761i
$393$	−5.38620	−	23.5985i	−0.271698	−	1.19039i
$394$			16.1588i			0.814070i
$395$	−38.4514	+	8.77628i	−1.93470	+	0.441583i
$396$	0.244991	+	0.195374i	0.0123113	+	0.00981791i
$397$	4.27748	−	18.7409i	0.214681	−	0.940577i	−0.746658	−	0.665208i	$-0.768343\pi$
$397$	4.27748	−	18.7409i	0.214681	−	0.940577i	0.961339	−	0.275369i	$-0.0888000\pi$
$398$	23.7109	+	5.41185i	1.18852	+	0.271272i
$399$	2.09299	+	2.62453i	0.104781	+	0.131391i
$400$	29.8913	+	14.3949i	1.49457	+	0.719746i
$401$	−9.93416	+	4.78404i	−0.496088	+	0.238903i	−0.665161	−	0.746700i	$-0.731637\pi$
$401$	−9.93416	+	4.78404i	−0.496088	+	0.238903i	0.169073	+	0.985604i	$0.445923\pi$
$402$	20.9426	−	26.2613i	1.04452	−	1.30979i
$403$	−2.23750	+	1.78435i	−0.111458	+	0.0888847i
$404$	−0.620443	−	1.28836i	−0.0308682	−	0.0640985i
$405$	−39.1933			−1.94753
$406$		0			0
$407$	−8.12737			−0.402859
$408$	−3.82322	−	7.93900i	−0.189278	−	0.393039i
$409$	−26.4426	+	21.0872i	−1.30750	+	1.04270i	−0.311793	+	0.950150i	$0.600929\pi$
$409$	−26.4426	+	21.0872i	−1.30750	+	1.04270i	−0.995708	+	0.0925470i	$0.970499\pi$
$410$	20.4426	−	25.6343i	1.00959	−	1.26599i
$411$	−27.5867	+	13.2851i	−1.36075	+	0.655304i
$412$	2.61960	+	1.26154i	0.129059	+	0.0621514i
$413$	−2.75973	−	3.46059i	−0.135797	−	0.170284i
$414$	−1.54898	−	0.353543i	−0.0761280	−	0.0173757i
$415$	3.62349	−	15.8755i	0.177870	−	0.779300i
$416$	−2.82894	−	2.25600i	−0.138700	−	0.110610i
$417$	21.8970	−	4.99784i	1.07230	−	0.244745i
$418$		−	9.57002i		−	0.468085i
$419$	−7.92596	−	34.7259i	−0.387208	−	1.69647i	−0.674209	−	0.738541i	$-0.735515\pi$
$419$	−7.92596	−	34.7259i	−0.387208	−	1.69647i	0.287000	−	0.957930i	$-0.407342\pi$
$420$	0.974928	−	2.02446i	0.0475716	−	0.0987835i
$421$	4.10329	−	8.52057i	0.199982	−	0.415267i	−0.776726	−	0.629838i	$-0.783121\pi$
$421$	4.10329	−	8.52057i	0.199982	−	0.415267i	0.976708	+	0.214571i	$0.0688354\pi$
$422$	5.72468	+	25.0814i	0.278673	+	1.22095i
$423$		−	1.17390i		−	0.0570769i
$424$	0.145406	−	0.0331879i	0.00706152	−	0.00161175i
$425$	−14.2873	−	11.3937i	−0.693035	−	0.552677i
$426$	1.12953	−	4.94880i	0.0547259	−	0.239770i
$427$	0.882455	+	0.201415i	0.0427050	+	0.00974714i
$428$	−1.60507	−	2.01270i	−0.0775841	−	0.0972874i
$429$	6.78890	+	3.26936i	0.327771	+	0.157846i
$430$	3.02446	−	1.45650i	0.145852	−	0.0702388i
$431$	0.614465	−	0.770515i	0.0295977	−	0.0371144i	−0.766812	−	0.641871i	$-0.778158\pi$
$431$	0.614465	−	0.770515i	0.0295977	−	0.0371144i	0.796410	+	0.604757i	$0.206730\pi$
$432$	11.2936	−	9.00634i	0.543363	−	0.433318i
$433$	−12.4456	−	25.8436i	−0.598099	−	1.24197i	−0.951832	−	0.306619i	$-0.900802\pi$
$433$	−12.4456	−	25.8436i	−0.598099	−	1.24197i	0.353734	−	0.935346i	$-0.384912\pi$
$434$	1.68366			0.0808183
$435$		0			0
$436$	−4.08815			−0.195787
$437$	−6.02564	−	12.5124i	−0.288246	−	0.598548i
$438$	−14.6216	+	11.6603i	−0.698646	+	0.557152i
$439$	4.11141	−	5.15554i	0.196227	−	0.246061i	−0.673977	−	0.738752i	$-0.735415\pi$
$439$	4.11141	−	5.15554i	0.196227	−	0.246061i	0.870204	+	0.492691i	$0.163987\pi$
$440$	−31.7080	+	15.2698i	−1.51162	+	0.727959i
$441$	−1.45108	−	0.698805i	−0.0690992	−	0.0332764i
$442$	−1.82908	−	2.29360i	−0.0870007	−	0.109095i
$443$	−20.8521	−	4.75936i	−0.990713	−	0.226124i	−0.303699	−	0.952768i	$-0.598222\pi$
$443$	−20.8521	−	4.75936i	−0.990713	−	0.226124i	−0.687014	+	0.726644i	$0.741079\pi$
$444$	−0.508729	+	2.22889i	−0.0241432	+	0.105778i
$445$	35.6338	+	28.4170i	1.68920	+	1.34709i
$446$	−25.6526	+	5.85504i	−1.21469	+	0.277244i
$447$			33.0030i			1.56099i
$448$	1.37047	+	6.00442i	0.0647486	+	0.283682i
$449$	12.6940	−	26.3593i	0.599067	−	1.24397i	−0.352292	−	0.935890i	$-0.614598\pi$
$449$	12.6940	−	26.3593i	0.599067	−	1.24397i	0.951359	−	0.308085i	$-0.0996880\pi$
$450$	−1.52251	+	3.16152i	−0.0717718	+	0.149036i
$451$	4.11960	+	18.0492i	0.193985	+	0.849902i
$452$			3.99031i			0.187688i
$453$	33.4431	−	7.63318i	1.57130	−	0.358638i
$454$	6.95579	+	5.54706i	0.326451	+	0.260336i
$455$	0.914542	−	4.00687i	0.0428744	−	0.187845i
$456$	−14.4190	−	3.29105i	−0.675234	−	0.154118i
$457$	0.150637	+	0.188893i	0.00704650	+	0.00883603i	0.785342	−	0.619062i	$-0.212487\pi$
$457$	0.150637	+	0.188893i	0.00704650	+	0.00883603i	−0.778296	+	0.627898i	$0.783916\pi$
$458$	2.53050	+	1.21862i	0.118242	+	0.0569426i
$459$	−7.16852	+	3.45218i	−0.334598	+	0.161134i
$460$	−5.79590	+	7.26782i	−0.270235	+	0.338864i
$461$	13.5555	−	10.8101i	0.631342	−	0.503478i	−0.254739	−	0.967010i	$-0.581989\pi$
$461$	13.5555	−	10.8101i	0.631342	−	0.503478i	0.886080	+	0.463532i	$0.153418\pi$
$462$	−1.92339	−	3.99396i	−0.0894842	−	0.185816i
$463$	−4.24996			−0.197513			−0.0987563	−	0.995112i	$-0.531486\pi$
$463$	−4.24996			−0.197513			−0.0987563	+	0.995112i	$0.531486\pi$
$464$		0			0
$465$	14.2349			0.660128
$466$	−10.2309	−	21.2446i	−0.473935	−	0.984136i
$467$	22.5429	−	17.9773i	1.04316	−	0.831892i	0.0571135	−	0.998368i	$-0.481810\pi$
$467$	22.5429	−	17.9773i	1.04316	−	0.831892i	0.986045	+	0.166476i	$0.0532389\pi$
$468$	0.100523	−	0.126052i	0.00464668	−	0.00582675i
$469$	9.32036	−	4.48845i	0.430374	−	0.207257i
$470$	21.6211	+	10.4122i	0.997307	+	0.480278i
$471$	−12.8509	−	16.1145i	−0.592136	−	0.742515i
$472$	19.0123	+	4.33944i	0.875113	+	0.199739i
$473$	−0.421780	+	1.84794i	−0.0193934	+	0.0849683i
$474$	17.1125	+	13.6468i	0.786003	+	0.626816i
$475$	−29.9032	+	6.82520i	−1.37205	+	0.313162i
$476$		−	0.493959i		−	0.0226406i
$477$	0.00268841	+	0.0117787i	0.000123094	+	0.000539308i
$478$	−11.0764	+	23.0003i	−0.506621	+	1.05201i
$479$	10.4900	−	21.7826i	0.479298	−	0.995273i	−0.511419	−	0.859332i	$-0.670880\pi$
$479$	10.4900	−	21.7826i	0.479298	−	0.995273i	0.990717	−	0.135941i	$-0.0434059\pi$
$480$	4.00484	+	17.5464i	0.182795	+	0.800879i
$481$			4.18167i			0.190668i
$482$	−8.95858	+	2.04474i	−0.408052	+	0.0931352i
$483$	−5.02949	−	4.01089i	−0.228850	−	0.182502i
$484$	−0.284479	+	1.24639i	−0.0129309	+	0.0566539i
$485$	−18.0397	−	4.11745i	−0.819142	−	0.186964i
$486$	1.99061	+	2.49614i	0.0902958	+	0.113227i
$487$	−17.3986	−	8.37871i	−0.788405	−	0.379676i	−0.00405280	−	0.999992i	$-0.501290\pi$
$487$	−17.3986	−	8.37871i	−0.788405	−	0.379676i	−0.784352	+	0.620316i	$0.787004\pi$
$488$	−3.59299	+	1.73029i	−0.162647	+	0.0783267i
$489$	−7.49880	+	9.40320i	−0.339108	+	0.425228i
$490$	25.7414	−	20.5281i	1.16288	−	0.927365i
$491$	16.0063	+	33.2373i	0.722353	+	1.49998i	0.860435	+	0.509560i	$0.170192\pi$
$491$	16.0063	+	33.2373i	0.722353	+	1.49998i	−0.138083	+	0.990421i	$0.544094\pi$
$492$	5.20775			0.234784
$493$		0			0
$494$	−4.92394			−0.221538
$495$	−1.23694	−	2.56853i	−0.0555963	−	0.115447i
$496$	−4.44179	+	3.54221i	−0.199442	+	0.159050i
$497$	0.974713	−	1.22225i	0.0437219	−	0.0548255i
$498$	−8.14191	+	3.92094i	−0.364848	+	0.175701i
$499$	33.9807	+	16.3642i	1.52118	+	0.732564i	0.993170	−	0.116672i	$-0.0372227\pi$
$499$	33.9807	+	16.3642i	1.52118	+	0.732564i	0.528014	+	0.849236i	$0.322937\pi$
$500$	7.18329	+	9.00756i	0.321247	+	0.402830i
$501$	−25.7679	−	5.88135i	−1.15122	−	0.262760i
$502$	3.59485	−	15.7501i	0.160446	−	0.702960i
$503$	5.48040	+	4.37047i	0.244359	+	0.194870i	0.738009	−	0.674791i	$-0.235766\pi$
$503$	5.48040	+	4.37047i	0.244359	+	0.194870i	−0.493650	+	0.869661i	$0.664338\pi$
$504$	−0.508041	+	0.115957i	−0.0226299	+	0.00516514i
$505$			13.0097i			0.578924i
$506$	4.08091	+	17.8796i	0.181419	+	0.794846i
$507$	−8.48167	+	17.6124i	−0.376684	+	0.782193i
$508$	3.00548	−	6.24094i	0.133347	−	0.276897i
$509$	−4.09150	−	17.9260i	−0.181352	−	0.794557i	−0.980988	−	0.194071i	$-0.937831\pi$
$509$	−4.09150	−	17.9260i	−0.181352	−	0.794557i	0.799635	−	0.600486i	$-0.205026\pi$
$510$			14.5918i			0.646135i
$511$	−5.61532	+	1.28166i	−0.248407	+	0.0566973i
$512$	−19.4981	−	15.5492i	−0.861702	−	0.687185i
$513$	−2.97166	+	13.0197i	−0.131202	+	0.574833i
$514$	−20.2927	−	4.63169i	−0.895075	−	0.204295i
$515$	−16.4928	−	20.6813i	−0.726758	−	0.911326i
$516$	0.480386	+	0.231342i	0.0211478	+	0.0101842i
$517$	−12.2083	+	5.87920i	−0.536920	+	0.258567i
$518$	1.53385	−	1.92339i	0.0673936	−	0.0845089i
$519$	−32.9097	+	26.2446i	−1.44457	+	1.15201i
$520$	7.85656	+	16.3143i	0.344533	+	0.715430i
$521$	−3.94571			−0.172865			−0.0864323	−	0.996258i	$-0.527547\pi$
$521$	−3.94571			−0.172865			−0.0864323	+	0.996258i	$0.527547\pi$
$522$		0			0
$523$	−33.9952			−1.48651			−0.743253	−	0.669010i	$-0.766718\pi$
$523$	−33.9952			−1.48651			−0.743253	+	0.669010i	$0.766718\pi$
$524$	2.59386	+	5.38620i	0.113313	+	0.235297i
$525$	−11.1081	+	8.85839i	−0.484796	+	0.386612i
$526$	−13.6908	+	17.1678i	−0.596948	+	0.748550i
$527$	2.81940	−	1.35775i	0.122815	−	0.0591445i
$528$	13.4770	+	6.49020i	0.586513	+	0.282450i
$529$	2.25302	+	2.82520i	0.0979574	+	0.122835i
$530$	−0.240787	−	0.0549581i	−0.0104591	−	0.00238723i
$531$	−0.351519	+	1.54011i	−0.0152546	+	0.0668349i
$532$	−0.648205	−	0.516926i	−0.0281032	−	0.0224116i
$533$	9.28660	−	2.11960i	0.402247	−	0.0918103i
$534$		−	25.2935i		−	1.09456i
$535$	5.21164	+	22.8337i	0.225319	+	0.987186i
$536$	−19.7753	+	41.0637i	−0.854161	+	1.77368i
$537$	0.519820	−	1.07942i	0.0224319	−	0.0465803i
$538$	−1.86174	−	8.15682i	−0.0802653	−	0.351665i
$539$			18.5907i			0.800759i
$540$	8.71488	−	1.98911i	0.375029	−	0.0855979i
$541$	18.3230	+	14.6121i	0.787766	+	0.628222i	0.932468	−	0.361253i	$-0.117651\pi$
$541$	18.3230	+	14.6121i	0.787766	+	0.628222i	−0.144702	+	0.989475i	$0.546222\pi$
$542$	−3.51507	+	15.4005i	−0.150985	+	0.661508i
$543$	−19.2649	−	4.39708i	−0.826735	−	0.188697i
$544$	2.46681	+	3.09328i	0.105764	+	0.132623i
$545$	33.5100	+	16.1376i	1.43541	+	0.691257i
$546$	−2.05496	+	0.989616i	−0.0879441	+	0.0423516i
$547$	20.1362	−	25.2499i	0.860960	−	1.07961i	−0.135091	−	0.990833i	$-0.543133\pi$
$547$	20.1362	−	25.2499i	0.860960	−	1.07961i	0.996052	−	0.0887767i	$-0.0282958\pi$
$548$	5.91241	−	4.71499i	0.252566	−	0.201414i
$549$	−0.140164	−	0.291053i	−0.00598203	−	0.0124218i
$550$	40.5042			1.72711
$551$		0			0
$552$	28.3424			1.20633
$553$	2.92478	+	6.07338i	0.124374	+	0.258266i
$554$	−15.3463	+	12.2383i	−0.652001	+	0.519953i
$555$	12.9683	−	16.2617i	0.550474	−	0.690272i
$556$	−4.99784	+	2.40683i	−0.211956	+	0.102073i
$557$	14.6184	+	7.03985i	0.619402	+	0.298288i	0.717146	−	0.696923i	$-0.245448\pi$
$557$	14.6184	+	7.03985i	0.619402	+	0.298288i	−0.0977437	+	0.995212i	$0.531163\pi$
$558$	−0.374650	−	0.469796i	−0.0158602	−	0.0198880i
$559$	0.950794	+	0.217013i	0.0402143	+	0.00917866i
$560$	1.81551	−	7.95427i	0.0767194	−	0.336129i
$561$	−6.44167	−	5.13706i	−0.271968	−	0.216887i
$562$	14.3632	−	3.27831i	0.605875	−	0.138287i
$563$			21.9168i			0.923681i	0.886963	+	0.461841i	$0.152811\pi$
$563$			21.9168i			0.923681i	−0.886963	+	0.461841i	$0.847189\pi$
$564$	0.848167	+	3.71606i	0.0357143	+	0.156474i
$565$	15.7514	−	32.7080i	0.662665	−	1.37604i
$566$	1.18925	−	2.46950i	0.0499879	−	0.103801i
$567$	1.49061	+	6.53078i	0.0625996	+	0.274267i
$568$			6.88769i			0.289001i
$569$	36.5568	−	8.34385i	1.53254	−	0.349793i	0.628696	−	0.777651i	$-0.283589\pi$
$569$	36.5568	−	8.34385i	1.53254	−	0.349793i	0.903846	+	0.427859i	$0.140732\pi$
$570$	19.1483	+	15.2702i	0.802033	+	0.639600i
$571$	−6.14579	+	26.9265i	−0.257193	+	1.12684i	0.667044	+	0.745019i	$0.267559\pi$
$571$	−6.14579	+	26.9265i	−0.257193	+	1.12684i	−0.924237	+	0.381819i	$0.875298\pi$
$572$	−1.81436	−	0.414115i	−0.0758621	−	0.0173150i
$573$	0.582105	+	0.729937i	0.0243178	+	0.0304935i
$574$	−5.04892	−	2.43143i	−0.210738	−	0.101486i
$575$	52.9575	−	25.5030i	2.20848	−	1.06355i
$576$	1.37047	−	1.71851i	0.0571029	−	0.0716048i
$577$	−4.94963	+	3.94720i	−0.206056	+	0.164324i	−0.721080	−	0.692851i	$-0.756354\pi$
$577$	−4.94963	+	3.94720i	−0.206056	+	0.164324i	0.515025	+	0.857175i	$0.327783\pi$
$578$	−7.80596	−	16.2092i	−0.324685	−	0.674216i
$579$	−2.49827			−0.103825
$580$		0			0
$581$	−2.78315			−0.115465
$582$	4.45544	+	9.25182i	0.184684	+	0.383500i
$583$	0.109031	−	0.0869495i	0.00451561	−	0.00360108i
$584$	15.8218	−	19.8400i	0.654713	−	0.820984i
$585$	−1.32155	+	0.636426i	−0.0546395	+	0.0263130i
$586$	−23.1930	−	11.1692i	−0.958093	−	0.461393i
$587$	−12.1754	−	15.2675i	−0.502532	−	0.630155i	0.464266	−	0.885696i	$-0.346318\pi$
$587$	−12.1754	−	15.2675i	−0.502532	−	0.630155i	−0.966798	+	0.255540i	$0.917747\pi$
$588$	5.09841	+	1.16368i	0.210255	+	0.0479893i
$589$	1.16876	−	5.12067i	0.0481579	−	0.210993i
$590$	−25.2481	−	20.1347i	−1.03945	−	0.828931i
$591$	22.7648	−	5.19591i	0.936417	−	0.213731i
$592$			8.30127i			0.341180i
$593$	−0.548622	−	2.40367i	−0.0225292	−	0.0987069i	0.962413	−	0.271589i	$-0.0875492\pi$
$593$	−0.548622	−	2.40367i	−0.0225292	−	0.0987069i	−0.984943	+	0.172882i	$0.944692\pi$
$594$	7.65168	−	15.8889i	0.313952	−	0.651929i
$595$	−1.94986	+	4.04892i	−0.0799363	+	0.165989i
$596$	−1.81378	−	7.94670i	−0.0742954	−	0.325510i
$597$		−	35.1444i		−	1.43836i
$598$	9.19937	−	2.09970i	0.376190	−	0.0858629i
$599$	−4.03567	−	3.21834i	−0.164893	−	0.131498i	0.537567	−	0.843221i	$-0.319344\pi$
$599$	−4.03567	−	3.21834i	−0.164893	−	0.131498i	−0.702460	+	0.711723i	$0.747915\pi$
$600$	13.9291	−	61.0273i	0.568652	−	2.49143i
$601$	28.7280	+	6.55698i	1.17184	+	0.267465i	0.763772	−	0.645486i	$-0.223345\pi$
$601$	28.7280	+	6.55698i	1.17184	+	0.267465i	0.408069	+	0.912951i	$0.366202\pi$
$602$	−0.357724	−	0.448572i	−0.0145797	−	0.0182824i
$603$	−3.32640	−	1.60191i	−0.135461	−	0.0652347i
$604$	−7.63318	+	3.67595i	−0.310590	+	0.149572i
$605$	7.25182	−	9.09350i	0.294829	−	0.369703i
$606$	5.64469	−	4.50149i	0.229300	−	0.182861i
$607$	15.0347	+	31.2199i	0.610240	+	1.26718i	0.945675	+	0.325113i	$0.105402\pi$
$607$	15.0347	+	31.2199i	0.610240	+	1.26718i	−0.335435	+	0.942063i	$0.608883\pi$
$608$	6.64071			0.269316
$609$		0			0
$610$	6.60388			0.267383
$611$	3.02495	+	6.28136i	0.122376	+	0.254117i
$612$	−0.137831	+	0.109916i	−0.00557147	+	0.00444310i
$613$	−17.1211	+	21.4692i	−0.691515	+	0.867132i	−0.996358	−	0.0852707i	$-0.972825\pi$
$613$	−17.1211	+	21.4692i	−0.691515	+	0.867132i	0.304843	+	0.952403i	$0.401396\pi$
$614$	25.6286	−	12.3421i	1.03429	−	0.498087i
$615$	−42.6872	−	20.5571i	−1.72132	−	0.828942i
$616$	3.75033	+	4.70277i	0.151105	+	0.189480i
$617$	33.4190	+	7.62767i	1.34540	+	0.307078i	0.833762	−	0.552124i	$-0.186182\pi$
$617$	33.4190	+	7.62767i	1.34540	+	0.307078i	0.511636	+	0.859202i	$0.329040\pi$
$618$	−3.26659	+	14.3119i	−0.131402	+	0.575708i
$619$	−20.0669	−	16.0028i	−0.806557	−	0.643208i	0.130866	−	0.991400i	$-0.458224\pi$
$619$	−20.0669	−	16.0028i	−0.806557	−	0.643208i	−0.937423	+	0.348192i	$0.886796\pi$
$620$	−3.42758	+	0.782323i	−0.137655	+	0.0314189i
$621$		−	25.5918i		−	1.02696i
$622$	8.62684	+	37.7967i	0.345905	+	1.51551i
$623$	3.37989	−	7.01842i	0.135413	−	0.281187i
$624$	3.33931	−	6.93416i	0.133680	−	0.277588i
$625$	−10.6473	−	46.6488i	−0.425891	−	1.86595i
$626$		−	14.0067i		−	0.559821i
$627$	−13.4824	+	3.07726i	−0.538434	+	0.122894i
$628$	3.97994	+	3.17390i	0.158817	+	0.126652i
$629$	1.01746	−	4.45778i	0.0405687	−	0.177743i
$630$	0.841301	+	0.192021i	0.0335182	+	0.00765032i
$631$	18.3312	+	22.9866i	0.729755	+	0.915084i	0.998846	−	0.0480308i	$-0.0152946\pi$
$631$	18.3312	+	22.9866i	0.729755	+	0.915084i	−0.269091	+	0.963115i	$0.586723\pi$
$632$	−26.7582	−	12.8861i	−1.06438	−	0.512580i
$633$	33.4943	−	16.1300i	1.33128	−	0.641109i
$634$	−4.60806	+	5.77832i	−0.183009	+	0.229486i
$635$	−49.2710	+	39.2923i	−1.95526	+	1.55927i
$636$	−0.0170207	−	0.0353438i	−0.000674914	−	0.00140147i
$637$	9.56524			0.378989
$638$		0			0
$639$	−0.557942			−0.0220718
$640$	10.8290	+	22.4867i	0.428055	+	0.888866i
$641$	8.18375	−	6.52632i	0.323239	−	0.257774i	−0.448403	−	0.893831i	$-0.648007\pi$
$641$	8.18375	−	6.52632i	0.323239	−	0.257774i	0.771642	+	0.636057i	$0.219436\pi$
$642$	8.10388	−	10.1619i	0.319834	−	0.401060i
$643$	2.74818	−	1.32345i	0.108377	−	0.0521918i	−0.378910	−	0.925434i	$-0.623701\pi$
$643$	2.74818	−	1.32345i	0.108377	−	0.0521918i	0.487287	+	0.873242i	$0.337987\pi$
$644$	1.43147	+	0.689359i	0.0564078	+	0.0271645i
$645$	−3.02446	−	3.79255i	−0.119088	−	0.149332i
$646$	5.24905	+	1.19806i	0.206521	+	0.0471371i
$647$	−6.63198	+	29.0566i	−0.260730	+	1.14233i	0.659732	+	0.751501i	$0.270670\pi$
$647$	−6.63198	+	29.0566i	−0.260730	+	1.14233i	−0.920462	+	0.390832i	$0.872187\pi$
$648$	−23.0745	−	18.4013i	−0.906450	−	0.722870i
$649$	17.7772	−	4.05754i	0.697818	−	0.159272i
$650$		−	20.8401i		−	0.817416i
$651$	−0.541385	−	2.37196i	−0.0212185	−	0.0929645i
$652$	1.28883	−	2.67629i	0.0504746	−	0.104812i
$653$	−4.94168	+	10.2615i	−0.193383	+	0.401564i	−0.975003	−	0.222191i	$-0.928679\pi$
$653$	−4.94168	+	10.2615i	−0.193383	+	0.401564i	0.781620	+	0.623755i	$0.214394\pi$
$654$	−4.59299	−	20.1232i	−0.179600	−	0.786880i
$655$		−	54.3889i		−	2.12515i
$656$	18.4354	−	4.20775i	0.719780	−	0.164285i
$657$	1.60715	+	1.28166i	0.0627009	+	0.0500023i
$658$	0.912682	−	3.99872i	0.0355800	−	0.155886i
$659$	4.47246	+	1.02081i	0.174222	+	0.0397651i	0.308742	−	0.951146i	$-0.400092\pi$
$659$	4.47246	+	1.02081i	0.174222	+	0.0397651i	−0.134520	+	0.990911i	$0.542949\pi$
$660$	5.77144	+	7.23715i	0.224653	+	0.281706i
$661$	11.6087	+	5.59046i	0.451527	+	0.217444i	0.645805	−	0.763503i	$-0.276522\pi$
$661$	11.6087	+	5.59046i	0.451527	+	0.217444i	−0.194278	+	0.980947i	$0.562236\pi$
$662$	−34.7265	+	16.7234i	−1.34968	+	0.649973i
$663$	−2.64310	+	3.31435i	−0.102650	+	0.128719i
$664$	9.58685	−	7.64526i	0.372042	−	0.296694i
$665$	3.27273	+	6.79590i	0.126911	+	0.263534i
$666$	−0.878002			−0.0340219
$667$		0			0
$668$	6.52781			0.252569
$669$	16.4973	+	34.2570i	0.637822	+	1.32445i
$670$	59.0085	−	47.0577i	2.27970	−	1.81800i
$671$	−2.32490	+	2.91534i	−0.0897519	+	0.112545i
$672$	2.77144	−	1.33465i	0.106911	−	0.0514854i
$673$	4.31282	+	2.07695i	0.166247	+	0.0800604i	0.515157	−	0.857096i	$-0.327734\pi$
$673$	4.31282	+	2.07695i	0.166247	+	0.0800604i	−0.348910	+	0.937156i	$0.613448\pi$
$674$	6.23155	+	7.81411i	0.240030	+	0.300988i
$675$	−55.1046	−	12.5773i	−2.12098	−	0.484099i
$676$	1.07434	−	4.70697i	0.0413206	−	0.181037i
$677$	23.8666	+	19.0330i	0.917267	+	0.731496i	0.963577	−	0.267431i	$-0.0861749\pi$
$677$	23.8666	+	19.0330i	0.917267	+	0.731496i	−0.0463103	+	0.998927i	$0.514746\pi$
$678$	−19.6416	+	4.48307i	−0.754332	+	0.172171i
$679$			3.16255i			0.121368i
$680$	−4.40581	−	19.3031i	−0.168955	−	0.740241i
$681$	5.57811	−	11.5831i	0.213754	−	0.443864i
$682$	−3.00943	+	6.24914i	−0.115237	+	0.239292i
$683$	−2.12402	−	9.30595i	−0.0812735	−	0.356082i	0.917896	−	0.396820i	$-0.129886\pi$
$683$	−2.12402	−	9.30595i	−0.0812735	−	0.356082i	−0.999170	+	0.0407378i	$0.987029\pi$
$684$			0.295897i			0.0113139i
$685$	−67.0752	+	15.3095i	−2.56281	+	0.584945i
$686$	−9.12230	−	7.27479i	−0.348291	−	0.277753i
$687$	0.903125	−	3.95685i	0.0344564	−	0.150963i
$688$	1.88748	+	0.430804i	0.0719594	+	0.0164243i
$689$	−0.0447370	−	0.0560984i	−0.00170434	−	0.00213718i
$690$	−42.2863	−	20.3640i	−1.60981	−	0.775244i
$691$	14.8514	−	7.15205i	0.564973	−	0.272077i	−0.129519	−	0.991577i	$-0.541343\pi$
$691$	14.8514	−	7.15205i	0.564973	−	0.272077i	0.694492	+	0.719500i	$0.255629\pi$
$692$	6.48188	−	8.12802i	0.246404	−	0.308981i
$693$	−0.380951	+	0.303798i	−0.0144711	+	0.0115403i
$694$	−1.22458	−	2.54288i	−0.0464846	−	0.0965263i
$695$	50.4674			1.91434
$696$		0			0
$697$	−10.4155			−0.394515
$698$	12.7518	+	26.4795i	0.482665	+	1.00226i
$699$	−26.6399	+	21.2446i	−1.00761	+	0.803544i
$700$	2.18784	−	2.74347i	0.0826926	−	0.103693i
$701$	42.2253	−	20.3346i	1.59483	−	0.768028i	0.595452	−	0.803391i	$-0.296973\pi$
$701$	42.2253	−	20.3346i	1.59483	−	0.768028i	0.999375	+	0.0353631i	$0.0112588\pi$
$702$	−8.17510	−	3.93692i	−0.308549	−	0.148589i
$703$	−4.78501	−	6.00022i	−0.180470	−	0.226302i
$704$	−24.7358	−	5.64579i	−0.932267	−	0.212784i
$705$	7.71648	−	33.8081i	0.290619	−	1.27329i
$706$	0.957907	+	0.763906i	0.0360513	+	0.0287500i
$707$	2.16780	−	0.494787i	0.0815287	−	0.0186084i
$708$		−	5.12929i		−	0.192771i
$709$	2.35892	+	10.3351i	0.0885911	+	0.388143i	0.999712	−	0.0239961i	$-0.00763892\pi$
$709$	2.35892	+	10.3351i	0.0885911	+	0.388143i	−0.911121	+	0.412139i	$0.864782\pi$
$710$	4.94880	−	10.2763i	0.185725	−	0.385662i
$711$	1.04384	−	2.16756i	0.0391472	−	0.0812900i
$712$	7.63706	+	33.4602i	0.286211	+	1.25397i
$713$			10.0653i			0.376949i
$714$	2.43143	−	0.554958i	0.0909940	−	0.0207688i
$715$	13.2374	+	10.5565i	0.495050	+	0.394789i
$716$	−0.0658433	+	0.288478i	−0.00246068	+	0.0107809i
$717$	35.9647	+	8.20871i	1.34313	+	0.306560i
$718$	6.12833	+	7.68469i	0.228707	+	0.286790i
$719$	11.9874	+	5.77282i	0.447054	+	0.215290i	0.643846	−	0.765155i	$-0.277338\pi$
$719$	11.9874	+	5.77282i	0.447054	+	0.215290i	−0.196791	+	0.980445i	$0.563052\pi$
$720$	−2.62349	+	1.26341i	−0.0977717	+	0.0470844i
$721$	−2.81886	+	3.53474i	−0.104980	+	0.131641i
$722$	−11.4583	+	9.13773i	−0.426436	+	0.340071i
$723$	5.76130	+	11.9635i	0.214265	+	0.444926i
$724$	4.88040			0.181378
$725$		0			0
$726$	−6.45473			−0.239558
$727$	−14.3257	−	29.7477i	−0.531312	−	1.10328i	−0.978003	−	0.208593i	$-0.933112\pi$
$727$	−14.3257	−	29.7477i	−0.531312	−	1.10328i	0.446690	−	0.894689i	$-0.352603\pi$
$728$	2.41965	−	1.92961i	0.0896783	−	0.0715160i
$729$	−15.2295	+	19.0972i	−0.564056	+	0.707304i
$730$	−37.8608	+	18.2328i	−1.40129	+	0.674827i
$731$	−0.960771	−	0.462683i	−0.0355354	−	0.0171130i
$732$	0.653989	+	0.820077i	0.0241721	+	0.0303109i
$733$	30.9981	+	7.07510i	1.14494	+	0.261325i	0.752589	−	0.658491i	$-0.228805\pi$
$733$	30.9981	+	7.07510i	1.14494	+	0.261325i	0.392351	+	0.919816i	$0.371662\pi$
$734$	−8.13235	+	35.6302i	−0.300171	+	1.31513i
$735$	−37.1974	−	29.6640i	−1.37205	−	1.09417i
$736$	−12.4068	+	2.83177i	−0.457321	+	0.104381i
$737$			42.6165i			1.56980i
$738$	0.445042	+	1.94986i	0.0163822	+	0.0717752i
$739$	−10.3852	+	21.5652i	−0.382027	+	0.793288i	0.617948	+	0.786219i	$0.287964\pi$
$739$	−10.3852	+	21.5652i	−0.382027	+	0.793288i	−0.999975	+	0.00706872i	$0.997750\pi$
$740$	−2.22889	+	4.62833i	−0.0819356	+	0.170141i
$741$	1.58330	+	6.93690i	0.0581640	+	0.254833i
$742$			0.0422126i			0.00154967i
$743$	7.22667	−	1.64944i	0.265121	−	0.0605121i	−0.0878940	−	0.996130i	$-0.528014\pi$
$743$	7.22667	−	1.64944i	0.265121	−	0.0605121i	0.353015	+	0.935618i	$0.385157\pi$
$744$	8.38058	+	6.68329i	0.307247	+	0.245021i
$745$	−16.5015	+	72.2978i	−0.604568	+	2.64878i
$746$	4.63515	+	1.05794i	0.169705	+	0.0387340i
$747$	0.619309	+	0.776589i	0.0226593	+	0.0284139i
$748$	1.83340	+	0.882917i	0.0670356	+	0.0322827i
$749$	3.60656	−	1.73683i	0.131781	−	0.0634624i
$750$	−36.2678	+	45.4784i	−1.32431	+	1.66064i
$751$	−15.1380	+	12.0722i	−0.552395	+	0.440520i	−0.859485	−	0.511160i	$-0.829216\pi$
$751$	−15.1380	+	12.0722i	−0.552395	+	0.440520i	0.307091	+	0.951680i	$0.400644\pi$
$752$	6.00499	+	12.4695i	0.218980	+	0.454716i
$753$	−23.3448			−0.850732
$754$		0			0
$755$	77.0786			2.80518
$756$	−0.662892	−	1.37651i	−0.0241092	−	0.0500632i
$757$	26.7674	−	21.3463i	0.972878	−	0.775845i	−0.00167528	−	0.999999i	$-0.500533\pi$
$757$	26.7674	−	21.3463i	0.972878	−	0.775845i	0.974554	+	0.224154i	$0.0719618\pi$
$758$	−7.01759	+	8.79978i	−0.254890	+	0.319622i
$759$	23.8768	−	11.4985i	0.866673	−	0.417368i
$760$	−29.9415	−	14.4190i	−1.08609	−	0.523034i
$761$	9.07756	+	11.3829i	0.329061	+	0.412630i	0.918649	−	0.395075i	$-0.129281\pi$
$761$	9.07756	+	11.3829i	0.329061	+	0.412630i	−0.589588	+	0.807704i	$0.700710\pi$
$762$	34.0966	+	7.78232i	1.23519	+	0.281924i
$763$	1.41454	−	6.19752i	0.0512099	−	0.224365i
$764$	−0.180280	−	0.143768i	−0.00652228	−	0.00520135i
$765$	1.56366	−	0.356896i	0.0565344	−	0.0129036i
$766$			41.3860i			1.49534i
$767$	−2.08767	−	9.14669i	−0.0753815	−	0.330268i
$768$	−7.90658	+	16.4182i	−0.285304	+	0.592440i
$769$	−5.01725	+	10.4184i	−0.180927	+	0.375698i	−0.971632	−	0.236499i	$-0.924000\pi$
$769$	−5.01725	+	10.4184i	−0.180927	+	0.375698i	0.790705	+	0.612197i	$0.209714\pi$
$770$	−2.21648	−	9.71103i	−0.0798764	−	0.349961i
$771$			30.0780i			1.08323i
$772$	0.601552	−	0.137300i	0.0216503	−	0.00494155i
$773$	6.54733	+	5.22132i	0.235491	+	0.187798i	0.734124	−	0.679015i	$-0.237593\pi$
$773$	6.54733	+	5.22132i	0.235491	+	0.187798i	−0.498633	+	0.866813i	$0.666164\pi$
$774$	−0.0455650	+	0.199633i	−0.00163780	+	0.00717566i
$775$	21.6728	+	4.94667i	0.778508	+	0.177689i
$776$	−8.68747	−	10.8937i	−0.311862	−	0.391063i
$777$	−3.20291	−	1.54244i	−0.114904	−	0.0553347i
$778$	−30.9366	+	14.8983i	−1.10913	+	0.534129i
$779$	−10.8998	+	13.6679i	−0.390525	+	0.489703i
$780$	3.72364	−	2.96950i	0.133328	−	0.106325i
$781$	2.79432	+	5.80247i	0.0999887	+	0.207629i
$782$	−10.3177			−0.368959
$783$		0			0
$784$	18.9885			0.678161
$785$	−20.0944	−	41.7265i	−0.717200	−	1.48928i
$786$	−23.5985	+	18.8192i	−0.841730	+	0.671257i
$787$	6.06249	−	7.60212i	0.216104	−	0.270986i	−0.661949	−	0.749549i	$-0.730271\pi$
$787$	6.06249	−	7.60212i	0.216104	−	0.270986i	0.878054	+	0.478562i	$0.158842\pi$
$788$	−5.19591	+	2.50222i	−0.185096	+	0.0891378i
$789$	28.5884	+	13.7675i	1.01778	+	0.490135i
$790$	30.6640	+	38.4514i	1.09098	+	1.36804i
$791$	−6.04920	−	1.38069i	−0.215085	−	0.0490917i
$792$	0.477697	−	2.09293i	0.0169742	−	0.0743690i
$793$	1.49999	+	1.19620i	0.0532662	+	0.0424784i
$794$	−23.3695	+	5.33393i	−0.829351	+	0.189294i
$795$			0.356896i			0.0126578i
$796$	1.93147	+	8.46232i	0.0684591	+	0.299939i
$797$	−11.4589	+	23.7947i	−0.405896	+	0.842852i	0.593384	+	0.804919i	$0.297791\pi$
$797$	−11.4589	+	23.7947i	−0.405896	+	0.842852i	−0.999280	+	0.0379323i	$0.987923\pi$
$798$	1.81623	−	3.77144i	0.0642938	−	0.133507i
$799$	−1.69633	−	7.43212i	−0.0600120	−	0.262930i
$800$			28.1062i			0.993704i
$801$	−2.71046	+	0.618645i	−0.0957695	+	0.0218588i
$802$	10.7496	+	8.57255i	0.379583	+	0.302707i
$803$	5.27993	−	23.1329i	0.186325	−	0.816342i
$804$	11.6874	+	2.66756i	0.412181	+	0.0940777i
$805$	−9.01238	−	11.3012i	−0.317645	−	0.398314i
$806$	3.21528	+	1.54840i	0.113254	+	0.0545400i
$807$	−10.8928	+	5.24568i	−0.383444	+	0.184657i
$808$	−6.10806	+	7.65926i	−0.214881	+	0.269452i
$809$	14.6905	−	11.7153i	0.516491	−	0.411887i	−0.330250	−	0.943893i	$-0.607133\pi$
$809$	14.6905	−	11.7153i	0.516491	−	0.411887i	0.846741	+	0.532006i	$0.178562\pi$
$810$	21.2053	+	44.0332i	0.745078	+	1.54717i
$811$	−48.6983			−1.71003			−0.855013	−	0.518606i	$-0.826451\pi$
$811$	−48.6983			−1.71003			−0.855013	+	0.518606i	$0.826451\pi$
$812$		0			0
$813$	22.8267			0.800567
$814$	4.39727	+	9.13102i	0.154124	+	0.320042i
$815$	−21.1288	+	16.8497i	−0.740110	+	0.590218i
$816$	−5.24698	+	6.57950i	−0.183681	+	0.230329i
$817$	−1.61260	+	0.776589i	−0.0564179	+	0.0271694i
$818$	37.9979	+	18.2988i	1.32857	+	0.639803i
$819$	0.156309	+	0.196006i	0.00546189	+	0.00684899i
$820$	11.4083	+	2.60388i	0.398396	+	0.0909313i
$821$	1.39277	−	6.10213i	0.0486081	−	0.212966i	−0.944791	−	0.327673i	$-0.893736\pi$
$821$	1.39277	−	6.10213i	0.0486081	−	0.212966i	0.993399	+	0.114707i	$0.0365928\pi$
$822$	29.8513	+	23.8056i	1.04118	+	0.830315i
$823$	−14.6399	+	3.34146i	−0.510315	+	0.116476i	−0.469922	−	0.882708i	$-0.655718\pi$
$823$	−14.6399	+	3.34146i	−0.510315	+	0.116476i	−0.0403927	+	0.999184i	$0.512861\pi$
$824$		−	19.9191i		−	0.693916i
$825$	−13.0242	−	57.0628i	−0.453445	−	1.98667i
$826$	−2.39480	+	4.97285i	−0.0833257	+	0.173028i
$827$	−5.18797	+	10.7729i	−0.180403	+	0.374611i	−0.971486	−	0.237098i	$-0.923804\pi$
$827$	−5.18797	+	10.7729i	−0.180403	+	0.374611i	0.791082	+	0.611710i	$0.209518\pi$
$828$	−0.126178	−	0.552823i	−0.00438500	−	0.0192119i
$829$			28.6305i			0.994380i	0.867642	+	0.497190i	$0.165635\pi$
$829$			28.6305i			0.994380i	−0.867642	+	0.497190i	$0.834365\pi$
$830$	−19.7965	+	4.51842i	−0.687146	+	0.156837i
$831$	22.1760	+	17.6848i	0.769278	+	0.613478i
$832$	−2.90485	+	12.7270i	−0.100708	+	0.441229i
$833$	−10.1968	−	2.32736i	−0.353299	−	0.0806381i
$834$	−17.4623	−	21.8970i	−0.604669	−	0.758231i
$835$	−53.5076	−	25.7679i	−1.85171	−	0.891735i
$836$	3.07726	−	1.48193i	0.106429	−	0.0512536i
$837$	6.03468	−	7.56725i	0.208589	−	0.261562i
$838$	−34.7259	+	27.6930i	−1.19959	+	0.956638i
$839$	−20.9666	−	43.5376i	−0.723847	−	1.50308i	−0.858844	−	0.512237i	$-0.828817\pi$
$839$	−20.9666	−	43.5376i	−0.723847	−	1.50308i	0.134997	−	0.990846i	$-0.456898\pi$
$840$	−15.3937			−0.531134
$841$		0			0
$842$	−11.7928			−0.406408
$843$	−9.23703	−	19.1809i	−0.318140	−	0.660625i
$844$	−7.17852	+	5.72468i	−0.247095	+	0.197052i
$845$	−27.3865	+	34.3416i	−0.942124	+	1.18139i
$846$	−1.31886	+	0.635131i	−0.0453435	+	0.0218363i
$847$	−1.79105	−	0.862525i	−0.0615413	−	0.0296367i
$848$	−0.0888100	−	0.111364i	−0.00304975	−	0.00382426i
$849$	−3.86147	−	0.881355i	−0.132525	−	0.0302480i
$850$	−5.07069	+	22.2161i	−0.173923	+	0.762007i
$851$	11.4985	+	9.16972i	0.394162	+	0.314334i
$852$	1.76621	−	0.403125i	0.0605092	−	0.0138108i
$853$			6.40688i			0.219367i	0.993967	+	0.109684i	$0.0349838\pi$
$853$			6.40688i			0.219367i	−0.993967	+	0.109684i	$0.965016\pi$
$854$	−0.251160	−	1.10040i	−0.00859452	−	0.0376550i
$855$	1.16802	−	2.42543i	0.0399456	−	0.0829479i
$856$	−7.65215	+	15.8898i	−0.261545	+	0.543104i
$857$	0.159793	+	0.700099i	0.00545843	+	0.0239149i	0.977584	−	0.210547i	$-0.0675244\pi$
$857$	0.159793	+	0.700099i	0.00545843	+	0.0239149i	−0.972125	+	0.234462i	$0.924667\pi$
$858$		−	9.39612i		−	0.320778i
$859$	15.2064	−	3.47076i	0.518835	−	0.118421i	0.0449187	−	0.998991i	$-0.485697\pi$
$859$	15.2064	−	3.47076i	0.518835	−	0.118421i	0.473916	+	0.880570i	$0.342840\pi$
$860$	0.936683	+	0.746980i	0.0319406	+	0.0254718i
$861$	−1.80194	+	7.89481i	−0.0614099	+	0.269054i
$862$	−1.19812	−	0.273463i	−0.0408081	−	0.00931418i
$863$	−8.41401	−	10.5508i	−0.286416	−	0.359155i	0.617721	−	0.786398i	$-0.288056\pi$
$863$	−8.41401	−	10.5508i	−0.286416	−	0.359155i	−0.904137	+	0.427243i	$0.859485\pi$
$864$	11.0254	+	5.30956i	0.375092	+	0.180635i
$865$	−85.2156	+	41.0377i	−2.89742	+	1.39532i
$866$	−22.3014	+	27.9651i	−0.757833	+	0.950292i
$867$	−20.3257	+	16.2092i	−0.690299	+	0.550495i
$868$	0.260717	+	0.541385i	0.00884931	+	0.0183758i
$869$	−27.7700			−0.942033
$870$		0			0
$871$	21.9269			0.742965
$872$	12.1519	+	25.2337i	0.411516	+	0.854521i
$873$	0.882455	−	0.703735i	0.0298666	−	0.0238178i
$874$	−10.7974	+	13.5395i	−0.365227	+	0.457980i
$875$	−16.1407	+	7.77296i	−0.545656	+	0.262774i
$876$	−6.01357	−	2.89598i	−0.203180	−	0.0978462i
$877$	−9.78836	−	12.2742i	−0.330530	−	0.414471i	0.588601	−	0.808424i	$-0.299679\pi$
$877$	−9.78836	−	12.2742i	−0.330530	−	0.414471i	−0.919131	+	0.393953i	$0.871107\pi$
$878$	−8.01665	−	1.82975i	−0.270549	−	0.0617510i
$879$	−8.27748	+	36.2660i	−0.279192	+	1.22322i
$880$	26.2783	+	20.9562i	0.885840	+	0.706434i
$881$	−10.5599	+	2.41023i	−0.355772	+	0.0812027i	−0.396672	−	0.917961i	$-0.629835\pi$
$881$	−10.5599	+	2.41023i	−0.355772	+	0.0812027i	0.0408993	+	0.999163i	$0.486978\pi$
$882$			2.00836i			0.0676250i
$883$	−3.66690	−	16.0657i	−0.123401	−	0.540655i	−0.998401	−	0.0565318i	$-0.981996\pi$
$883$	−3.66690	−	16.0657i	−0.123401	−	0.540655i	0.875000	−	0.484123i	$-0.160861\pi$
$884$	0.454276	−	0.943313i	0.0152789	−	0.0317270i
$885$	−20.2474	+	42.0441i	−0.680608	+	1.41330i
$886$	5.93482	+	26.0021i	0.199384	+	0.873559i
$887$		−	28.5763i		−	0.959497i	−0.877406	−	0.479748i	$-0.840728\pi$
$887$		−	28.5763i		−	0.959497i	0.877406	−	0.479748i	$-0.159272\pi$
$888$	15.2698	−	3.48523i	0.512421	−	0.116957i
$889$	8.42116	+	6.71565i	0.282437	+	0.225236i
$890$	12.6468	−	55.4090i	0.423920	−	1.85732i
$891$	−26.9042	−	6.14071i	−0.901325	−	0.205722i
$892$	−5.85504	−	7.34198i	−0.196041	−	0.245828i
$893$	−11.5281	−	5.55164i	−0.385773	−	0.185779i
$894$	37.0785	−	17.8561i	1.24009	−	0.597196i
$895$	1.67845	−	2.10471i	0.0561043	−	0.0703526i
$896$	3.33511	−	2.65966i	0.111418	−	0.0888531i
$897$	−5.91615	−	12.2850i	−0.197534	−	0.410185i
$898$	−36.4825			−1.21744
$899$		0			0
$900$	−1.25236			−0.0417452
$901$	0.0340414	+	0.0706876i	0.00113408	+	0.00235495i
$902$	18.0492	−	14.3937i	0.600972	−	0.479259i
$903$	−0.516926	+	0.648205i	−0.0172022	+	0.0215709i
$904$	24.6298	−	11.8611i	0.819176	−	0.394494i
$905$	−40.0039	−	19.2649i	−1.32978	−	0.640386i
$906$	−26.6700	−	33.4431i	−0.886052	−	1.11107i
$907$	32.0356	+	7.31192i	1.06373	+	0.242788i	0.718354	−	0.695678i	$-0.244896\pi$
$907$	32.0356	+	7.31192i	1.06373	+	0.242788i	0.345371	+	0.938466i	$0.387753\pi$
$908$	−0.706554	+	3.09562i	−0.0234478	+	0.102732i
$909$	−0.620443	−	0.494787i	−0.0205788	−	0.0164111i
$910$	−4.99649	+	1.14042i	−0.165632	+	0.0378044i
$911$		−	10.9638i		−	0.363245i	−0.983368	−	0.181623i	$-0.941865\pi$
$911$		−	10.9638i		−	0.363245i	0.983368	−	0.181623i	$-0.0581350\pi$
$912$	3.14310	+	13.7708i	0.104079	+	0.455998i
$913$	4.97469	−	10.3300i	0.164638	−	0.341875i
$914$	0.130718	−	0.271438i	0.00432376	−	0.00897838i
$915$	−2.12349	−	9.30362i	−0.0702004	−	0.307568i
$916$			1.00239i			0.0331200i
$917$	−9.06283	+	2.06853i	−0.299281	+	0.0683089i
$918$	7.75697	+	6.18598i	0.256018	+	0.204168i
$919$	−1.70506	+	7.47037i	−0.0562448	+	0.246425i	−0.995233	−	0.0975244i	$-0.968908\pi$
$919$	−1.70506	+	7.47037i	−0.0562448	+	0.246425i	0.938988	+	0.343949i	$0.111765\pi$
$920$	62.0881	+	14.1712i	2.04699	+	0.467211i
$921$	−25.6286	−	32.1373i	−0.844492	−	1.05896i
$922$	−19.4792	−	9.38068i	−0.641513	−	0.308936i
$923$	2.98547	−	1.43773i	0.0982678	−	0.0473233i
$924$	0.986426	−	1.23694i	0.0324510	−	0.0406923i
$925$	25.3954	−	20.2521i	0.834994	−	0.665886i
$926$	2.29942	+	4.77479i	0.0755636	+	0.156909i
$927$	1.61356			0.0529964
$928$		0			0
$929$	9.35988			0.307088			0.153544	−	0.988142i	$-0.450931\pi$
$929$	9.35988			0.307088			0.153544	+	0.988142i	$0.450931\pi$
$930$	−7.70171	−	15.9928i	−0.252549	−	0.524423i
$931$	−13.7250	+	10.9453i	−0.449819	+	0.358719i
$932$	5.24698	−	6.57950i	0.171871	−	0.215519i
$933$	50.4744	−	24.3072i	1.65246	−	0.795782i
$934$	−32.3940	−	15.6001i	−1.05996	−	0.510452i
$935$	−11.5429	−	14.4743i	−0.377492	−	0.473361i
$936$	−1.07685	−	0.245783i	−0.0351978	−	0.00803367i
$937$	1.73652	−	7.60820i	0.0567297	−	0.248549i	−0.938610	−	0.344980i	$-0.887886\pi$
$937$	1.73652	−	7.60820i	0.0567297	−	0.248549i	0.995340	+	0.0964312i	$0.0307428\pi$
$938$	−10.0854	−	8.04288i	−0.329302	−	0.262609i
$939$	−19.7328	+	4.50388i	−0.643956	+	0.146979i
$940$			8.56465i			0.279348i
$941$	−6.39708	−	28.0275i	−0.208539	−	0.913669i	−0.965540	−	0.260255i	$-0.916193\pi$
$941$	−6.39708	−	28.0275i	−0.208539	−	0.913669i	0.757001	−	0.653414i	$-0.226664\pi$
$942$	−11.1516	+	23.1564i	−0.363337	+	0.754478i
$943$	14.5356	−	30.1836i	0.473346	−	0.982913i
$944$	−4.14436	−	18.1576i	−0.134887	−	0.590980i
$945$			13.8998i			0.452160i
$946$	2.30434	−	0.525951i	0.0749206	−	0.0171001i
$947$	−1.80549	−	1.43983i	−0.0586705	−	0.0467882i	0.593716	−	0.804675i	$-0.297660\pi$
$947$	−1.80549	−	1.43983i	−0.0586705	−	0.0467882i	−0.652386	+	0.757887i	$0.726232\pi$
$948$	−1.73825	+	7.61577i	−0.0564557	+	0.247349i
$949$	−11.9023	−	2.71661i	−0.386363	−	0.0881849i
$950$	23.8470	+	29.9032i	0.773698	+	0.970186i
$951$	9.62229	+	4.63385i	0.312024	+	0.150263i
$952$	−3.04892	+	1.46828i	−0.0988160	+	0.0475873i
$953$	−21.5293	+	26.9969i	−0.697403	+	0.874515i	−0.996826	−	0.0796051i	$-0.974634\pi$
$953$	−21.5293	+	26.9969i	−0.697403	+	0.874515i	0.299424	+	0.954120i	$0.403206\pi$
$954$	0.0117787	−	0.00939318i	0.000381349	−	0.000304115i
$955$	0.910216	+	1.89008i	0.0294539	+	0.0611617i
$956$	−9.11098			−0.294670
$957$		0			0
$958$	−30.1481			−0.974040
$959$	5.10203	+	10.5945i	0.164753	+	0.342114i
$960$	50.7657	−	40.4843i	1.63846	−	1.30663i
$961$	16.9547	−	21.2606i	0.546927	−	0.685825i
$962$	4.69806	−	2.26247i	0.151472	−	0.0729449i
$963$	−1.28717	−	0.619867i	−0.0414784	−	0.0199749i
$964$	−2.04474	−	2.56402i	−0.0658565	−	0.0825815i
$965$	−5.47282	−	1.24914i	−0.176176	−	0.0402111i
$966$	−1.78501	+	7.82065i	−0.0574318	+	0.251625i
$967$	−40.2786	−	32.1211i	−1.29527	−	1.03294i	−0.996915	−	0.0784905i	$-0.974990\pi$
$967$	−40.2786	−	32.1211i	−1.29527	−	1.03294i	−0.298357	−	0.954454i	$-0.596439\pi$
$968$	8.53881	−	1.94893i	0.274448	−	0.0626409i
$969$		−	7.78017i		−	0.249935i
$970$	5.13437	+	22.4952i	0.164855	+	0.722276i
$971$	3.44310	−	7.14968i	0.110494	−	0.229444i	−0.838388	−	0.545074i	$-0.816502\pi$
$971$	3.44310	−	7.14968i	0.110494	−	0.229444i	0.948882	+	0.315630i	$0.102216\pi$
$972$	−0.494392	+	1.02661i	−0.0158576	+	0.0329287i
$973$	−1.91939	−	8.40938i	−0.0615327	−	0.269592i
$974$			24.0804i			0.771585i
$975$	−29.3598	+	6.70118i	−0.940265	+	0.214609i
$976$	2.97772	+	2.37465i	0.0953144	+	0.0760107i
$977$	−6.14148	+	26.9076i	−0.196483	+	0.860850i	0.776526	+	0.630085i	$0.216980\pi$
$977$	−6.14148	+	26.9076i	−0.196483	+	0.860850i	−0.973010	+	0.230765i	$0.925877\pi$
$978$	14.6216	+	3.33728i	0.467547	+	0.106714i
$979$	20.0085	+	25.0899i	0.639474	+	0.801875i
$980$	10.5869	+	5.09841i	0.338188	+	0.162863i
$981$	−2.04407	+	0.984374i	−0.0652622	+	0.0314286i
$982$	28.6817	−	35.9657i	0.915271	−	1.14771i
$983$	27.6200	−	22.0262i	0.880942	−	0.702528i	−0.0746531	−	0.997210i	$-0.523785\pi$
$983$	27.6200	−	22.0262i	0.880942	−	0.702528i	0.955596	+	0.294681i	$0.0952135\pi$
$984$	−15.4799	−	32.1444i	−0.493481	−	1.02472i
$985$	52.4674			1.67175
$986$		0			0
$987$	−5.92692			−0.188656
$988$	−0.762478	−	1.58330i	−0.0242577	−	0.0503715i
$989$	2.68166	−	2.13856i	0.0852719	−	0.0680021i
$990$	−2.21648	+	2.77938i	−0.0704444	+	0.0883344i
$991$	−0.498804	+	0.240211i	−0.0158450	+	0.00763056i	−0.441789	−	0.897119i	$-0.645656\pi$
$991$	−0.498804	+	0.240211i	−0.0158450	+	0.00763056i	0.425944	+	0.904749i	$0.359942\pi$
$992$	−4.33632	−	2.08826i	−0.137678	−	0.0663024i
$993$	34.7265	+	43.5456i	1.10201	+	1.38188i
$994$	−1.90055	−	0.433788i	−0.0602818	−	0.0137589i
$995$	17.5722	−	76.9887i	0.557076	−	2.44071i
$996$	−2.52157	−	2.01089i	−0.0798990	−	0.0637173i
$997$	21.6879	−	4.95012i	0.686863	−	0.156772i	0.135174	−	0.990822i	$-0.456841\pi$
$997$	21.6879	−	4.95012i	0.686863	−	0.156772i	0.551689	+	0.834050i	$0.313984\pi$
$998$		−	47.0307i		−	1.48873i
$999$	−3.14699	−	13.7879i	−0.0995663	−	0.436229i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.7.1	✓	6	29.2	odd	28
29.2.d.a.25.1	yes	6	29.21	odd	28
261.2.k.a.181.1		6	87.2	even	28
261.2.k.a.199.1		6	87.50	even	28
464.2.u.f.65.1		6	116.31	even	28
464.2.u.f.257.1		6	116.79	even	28
725.2.l.b.326.1		6	145.89	odd	28
725.2.l.b.576.1		6	145.79	odd	28
725.2.r.b.199.1		12	145.137	even	28
725.2.r.b.199.2		12	145.108	even	28
725.2.r.b.674.1		12	145.118	even	28
725.2.r.b.674.2		12	145.2	even	28
841.2.a.e.1.3		3	29.19	odd	28
841.2.a.f.1.1		3	29.10	odd	28
841.2.b.c.840.2		6	29.4	even	14
841.2.b.c.840.5		6	29.25	even	7
841.2.d.a.574.1		6	29.26	odd	28
841.2.d.a.778.1		6	29.15	odd	28
841.2.d.b.190.1		6	29.11	odd	28
841.2.d.b.571.1		6	29.17	odd	4
841.2.d.c.190.1		6	29.18	odd	28
841.2.d.c.571.1		6	29.12	odd	4
841.2.d.d.605.1		6	29.8	odd	28
841.2.d.d.645.1		6	29.27	odd	28
841.2.d.e.574.1		6	29.3	odd	28
841.2.d.e.778.1		6	29.14	odd	28
841.2.e.b.63.1		12	29.23	even	7
841.2.e.b.63.2		12	29.6	even	14
841.2.e.b.267.1		12	29.22	even	14
841.2.e.b.267.2		12	29.7	even	7
841.2.e.c.270.1		12	1.1	even	1	trivial
841.2.e.c.270.2		12	29.28	even	2	inner
841.2.e.c.651.1		12	29.13	even	14	inner
841.2.e.c.651.2		12	29.16	even	7	inner
841.2.e.d.196.1		12	29.5	even	14
841.2.e.d.196.2		12	29.24	even	7
841.2.e.d.236.1		12	29.20	even	7
841.2.e.d.236.2		12	29.9	even	14
7569.2.a.p.1.3		3	87.68	even	28
7569.2.a.r.1.1		3	87.77	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.541044 - 1.12349i) q^{2} +(-1.40881 + 1.12349i) q^{3} +(0.277479 - 0.347948i) q^{4} +(-3.64795 + 1.75676i) q^{5} +(2.02446 + 0.974928i) q^{6} +(0.431468 + 0.541044i) q^{7} +(-2.97247 - 0.678448i) q^{8} +(0.0549581 - 0.240787i) q^{9} +(3.94740 + 3.14795i) q^{10} +(-2.77938 + 0.634375i) q^{11} +0.801938i q^{12} +(0.326396 + 1.43004i) q^{13} +(0.374414 - 0.777479i) q^{14} +(3.16557 - 6.57338i) q^{15} +(0.647948 + 2.83885i) q^{16} -1.60388i q^{17} +(-0.300257 + 0.0685317i) q^{18} +(-2.10471 - 1.67845i) q^{19} +(-0.400969 + 1.75676i) q^{20} +(-1.21572 - 0.277479i) q^{21} +(2.21648 + 2.77938i) q^{22} +(4.64795 + 2.23833i) q^{23} +(4.94989 - 2.38374i) q^{24} +(7.10388 - 8.90798i) q^{25} +(1.43004 - 1.14042i) q^{26} +(-2.15240 - 4.46950i) q^{27} +0.307979 q^{28} -9.09783 q^{30} +(0.846543 + 1.75786i) q^{31} +(-1.92863 + 1.53803i) q^{32} +(3.20291 - 4.01632i) q^{33} +(-1.80194 + 0.867767i) q^{34} +(-2.52446 - 1.21572i) q^{35} +(-0.0685317 - 0.0859360i) q^{36} +(2.77938 + 0.634375i) q^{37} +(-0.746980 + 3.27273i) q^{38} +(-2.06646 - 1.64795i) q^{39} +(12.0353 - 2.74698i) q^{40} -6.49396i q^{41} +(0.346011 + 1.51597i) q^{42} +(0.288478 - 0.599031i) q^{43} +(-0.550490 + 1.14310i) q^{44} +(0.222521 + 0.974928i) q^{45} -6.43296i q^{46} +(4.63385 - 1.05765i) q^{47} +(-4.10225 - 3.27144i) q^{48} +(1.45108 - 6.35761i) q^{49} +(-13.8515 - 3.16152i) q^{50} +(1.80194 + 2.25956i) q^{51} +(0.588146 + 0.283236i) q^{52} +(-0.0440730 + 0.0212244i) q^{53} +(-3.85690 + 4.83639i) q^{54} +(9.02458 - 7.19687i) q^{55} +(-0.915458 - 1.90097i) q^{56} +4.85086 q^{57} -6.39612 q^{59} +(-1.40881 - 2.92543i) q^{60} +(1.02262 - 0.815511i) q^{61} +(1.51693 - 1.90216i) q^{62} +(0.153989 - 0.0741573i) q^{63} +(8.01842 + 3.86147i) q^{64} +(-3.70291 - 4.64330i) q^{65} +(-6.24521 - 1.42543i) q^{66} +(3.32640 - 14.5739i) q^{67} +(-0.558065 - 0.445042i) q^{68} +(-9.06283 + 2.06853i) q^{69} +3.49396i q^{70} +(-0.502688 - 2.20242i) q^{71} +(-0.326723 + 0.678448i) q^{72} +(-3.61123 + 7.49880i) q^{73} +(-0.791053 - 3.46583i) q^{74} +20.5308i q^{75} +(-1.16802 + 0.266594i) q^{76} +(-1.54244 - 1.23005i) q^{77} +(-0.733406 + 3.21326i) q^{78} +(9.49671 + 2.16756i) q^{79} +(-7.35086 - 9.21768i) q^{80} +(8.72132 + 4.19997i) q^{81} +(-7.29590 + 3.51352i) q^{82} +(-2.50753 + 3.14435i) q^{83} +(-0.433884 + 0.346011i) q^{84} +(2.81762 + 5.85086i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(-4.88409 - 10.1419i) q^{89} +(0.974928 - 0.777479i) q^{90} +(-0.632883 + 0.793610i) q^{91} +(2.06853 - 0.996152i) q^{92} +(-3.16756 - 1.52542i) q^{93} +(-3.69537 - 4.63385i) q^{94} +(10.6265 + 2.42543i) q^{95} +(0.989115 - 4.33360i) q^{96} +(3.57299 + 2.84936i) q^{97} +(-7.92781 + 1.80947i) q^{98} +0.704103i 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

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